Answer:
X>-9
X is greater than -9
Step-by-step explanation:
4(X-3)+4<10+6X
By clearing up the bracket :
4X-12+4<10+6X
Collecting like terms:
4X-6X<10+12-4
-2X<18
Dividing both sides by -2:
-2X/-2>18/-2
Therefore, X>-9
The mission step is in combining like terms which is 4X-8<10+6X instead of 4X-6X<10+8.
The missing step in solving the given inequality 4(x – 3) + 4 < 10 + 6x is; x > -9
How to solve Inequalities?We are given the inequality as:
4(x – 3) + 4 < 10 + 6x
The steps are given as:
The distributive property: 4x – 12 + 4 < 10 + 6xCombine like terms: 4x – 8 < 10 + 6xThe addition property of inequality: 4x < 18 + 6xThe subtraction property of inequality: –2x < 18The next step in solving the inequality is to apply the division property of inequality by dividing both sides by -2.
This gives; x > -9
Thus, the missing step in the inequality is x > -9
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The following equation has denominators that contain variables. For this equation write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. Keeping the restrictions in mind, solve the equation.
2/x=4/5x+2
x=
Answer:
X = 3/5
Step-by-step explanation:
2/x=4/5x+2
Find the LCM of the denominator 5x and 1
2/x =4/5x + 2/1
2/x = (4 + 10x)/5x
Cross multiply the equation
2× 5x = (4+ 10x) × x
10x = 4x + 10x^2
Collect like term of the mixed number
10x - 4x = 10x^2
6x = 10x^2
Divide both side by 2x
6x/2x = {10x^2 } / 2x
3 = 5x
Divide both side by the coefficient of x
3/5 = 5x/5
X = 3/5
Let P(x) and Q(x) be predicates and suppose D is the domain of x. For the statement forms in each pair, determine whether (a) they have the same truth value for every choice of P(x), Q(x), and D, or (b) there is a choice of P(x), Q(x), and D for which they have opposite truth values.
∃x∈D,(P(x)∧Q(x))
(∃x∈D,P(x))∧(∃x∈D,Q(x))
Answer / Step-by-step explanation:
Given the statement:
∃x∈D,(P(x)∧Q(x)) and (∃x∈D,P(x))∧(∃x∈D,Q(x)) ,
Then,
(a), The variable used in a ∃ statement does not matter, thus, we can change the appearance of one of the variable used in the ∃ statement.
That is:
(∃x∈D,P(x))∧(∃x∈D,Q(x)) = (∃x∈D,P(x))∧(∃y∈D,Q(y))
Where
(∃x∈D,P(x))∧(∃x∈D,Q(x)) = (∃x∈D,P(x))∧(∃y∈D,Q(y)) implies that P(x) is true for some element x in D and Q(y) is true for some element y in D. However, x and y are not necessary the same element and thus, we cannot be sure that
P(x) ∧ Q(x) or P(y) ∧ Q(y) is true.
Moreover, if P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D, while x ≠ y,
Then, P(x) ∧ Q(x) is false and P(y) ∧ Q(y) is also false. Moreover, there is no other known element (z) such that P(z) ∧ Q(z) is true and thus the statement
∃x∈D,(P(x)∧Q(x)) is false while the statement (∃x∈D,P(x))∧(∃x∈D,Q(x)) is true.
(b)
If the statement P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D, while x ≠ y, then Then, P(x) ∧ Q(x) is false and P(y) ∧ Q(y) is also false. Moreover, there is no other known element (z) such that P(z) ∧ Q(z) is true and thus the statement
∃x∈D,(P(x)∧Q(x)) is false while the statement (∃x∈D,P(x))∧(∃x∈D,Q(x)) is true.
So in summary, we can say for:
(a) the statement does not contain the same truth value.
(b) The statement depicts there is such a choice in the first place.
In this exercise we have to use the knowledge of sets to identify which of the statements is true and false, thus we can state that:
A) the statement does not contain the same truth value.
B) The statement depicts there is such a choice in the first place.
Then, the first statement says that:
A)The variable used in a ∃ statement does not matter, thus, we can change the appearance of one of the variable used in the ∃ statement. That is:
[tex](\exists \ x \in D,P(x)) \wedge ( \exists \ x\in D,Q(x)) = (\exists \ x \in D,P(x)) \wedge (\exists \ y \in D,Q(y))[/tex]
Where the equation above implies that P(x) is true for some element x in D and Q(y) is true for some element y in D.
However, x and y are not necessary the same element and thus, we cannot be sure that is true.
If P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D. Then, [tex]P(x) \wedge Q(x)[/tex] is false and [tex]P(y) \wedge Q(y)[/tex] is also false.
B) If the statement P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D. Then, [tex]P(x) \wedge Q(x) \ or \ P(y) \wedge Q(y)[/tex] is also false.
Moreover, there is no other known element (z) such that is true and thus the statement.
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Tina and Joey share a 18-ounce box of cereal. By the end of the week, Tina has eaten 1 6 of the box, and Joey has eaten 2 3 of the box of cereal. How many ounces are left in the box?
Answer:The number of ounces of cereals left in the box is 3
Step-by-step explanation:
Tina and Joey share a 18-ounce box of cereal. By the end of the week, Tina has eaten 1/6 of the box. This means that the amount of cereal that Tina ate is
1/6 × 18 = 3 ounce
Also, by the end of the week, Joey has eaten 2/ 3 of the box of cereal. This that the amount of cereal that Joey ate is
2/3 × 18 = 12 ounce
The number of ounces of cereals left in the box would be
18 - (12 + 3) = 18 - 15
= 3
A rectangle initially has width 7 meters and length 10 meters and is expanding so that the area increases at a rate of 8 square meters per hour. If the width increases by 40 centimeters per hour how quickly does the length increase initially
Final answer:
The length of the rectangle increases at a rate of 4/7 meters per hour (approximately 0.57 m/h) initially when the area is increasing at 8 square meters per hour and the width at 0.4 meters per hour.
Explanation:
To find how quickly the length of the rectangle increases, given that the area increases at a rate of 8 square meters per hour and the width increases by 40 centimeters (0.4 meters) per hour, we can use the area formula for a rectangle (Area = length × width). The rate of change of the area with respect to time (ΔA/Δt) can be related to the rates of change of the length and width with respect to time (ΔL/Δt and ΔW/Δt respectively) by the product rule for differentiation if we consider length and width as functions of time.
Initially, the area A is 10m × 7m = 70m². When the area is increasing at 8m²/h and the width is increasing at 0.4m/h, we can write the relation as follows:
ΔA/Δt = ΔL/Δt × W + L × ΔW/Δt
Substituting the given values and solving for the rate of change of the length (ΔL/Δt):
8 = ΔL/Δt × 7 + 10 × 0.4
8 = 7ΔL/Δt + 4
7ΔL/Δt = 4
ΔL/Δt = 4/7 m/h
Therefore, the length increases at a rate of 4/7 meters per hour (approximately 0.57 m/h) initially.
Use two points on the like to find the equation of the line in standard form
Answer:
y=1/3x-1
Step-by-step explanation:
A(0,-1)=(x1,y1) x1=0,y1=-1
B(3,0)=(x2,y2) x2=3, y2=0
m=(y2-y1)/(x2-x1)
m=(0-(-1))/(3-0)
m=1/3
y-y1=m(x-x1)
y-(-1)=1/3(x-0)
y+1=1/3*x
y=1/3*x-1
Final total cost of making a triangular sale that has a base dimension of 12 feet and the height of 25 feet if the price for making the sale is $19.50 per square foot
Answer:
$2925
Step-by-step explanation:
To find the cost, we need to get the area of the triangular sale. This can be obtained by using the area of a triangle.
This is A = 1/2 * b * h
Where in this case, b = 12ft and h = 25ft
The area is thus 1/2 * 12 * 25 = 150sq.ft
Now we know that 1sq.ft is $19.50, 150 will be 150 * 19.5 = $2925
last question and im not sure how to solve it?? pls help
Height of the rock wall is 52.2 ft.
Step-by-step explanation:
These two triangles are similar, so using the similarity ratio, we can write as,
Δ HTV ~ Δ JSV
Now we can write the ratio as,
HT/TV = JS/SV
5.8/4 = x/36
Rearranging the equation to get x as,
x = 36 × 5.8 /4
= 52.2 ft
When Akiko measured a rose, its height was 5.8 in. After 10 weeks, the height was 1 1/3 times the original height. What was the height of the rose after 10 weeks?
The solution is in the attachment
The height of the rose after 10 weeks was approximately 7.714 inches. This is calculated by multiplying the original height of the rose (5.8 inches) by 1 1/3 (converted to a decimal as 1.33).
Explanation:The subject of this question is Mathematics, and it involves performing multiplication to find the height of the rose after 10 weeks. Given that the height of the rose was 5.8 inches originally, and after 10 weeks, the height was 1 1/3 times the original height, we can calculate the new height as follows:
Convert 1 1/3 to a decimal. 1 1/3 equals 1.33 when converted to a decimal.Multiply the original height of the rose (5.8 inches) by 1.33 to get the new height after 10 weeks.So, 5.8 inches * 1.33 = 7.714 inches.
Therefore, the height of the rose after 10 weeks was approximately 7.714 inches.
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Ray Bond sells handcrafted yard decorations at county fairs. The variable cost to make these is $20 each, and he sells them for $50. The cost to rent a booth at the fair is $150. How many of these must Ray sell to break even?
Ray Bond is trying to find a new supplier that will reduce his variable cost of production to $15 per unit. If he was able to succeed in reducing this cost, what would the break-even point be?
Answer:
break even units for both the cases will be 5
Step-by-step explanation:
Data provided in the question:
For the case 1
Variable cost = $20 each
Selling cost = $50
Rent for the booth fair = $150
Now,
Let break even units be x
At break even
Total cost = Total revenue
Thus,
$20x + $150 = $50x
or
$50x - $20x = $150
or
$30x = $150
or
x = 5
Case 2
Variable cost = $15 per unit
Thus,
At break even
Total cost = Total revenue
Thus,
$15x + $150 = $50x
or
$50x - $15x = $150
or
$35x = $150
or
x = 4.28 ≈ 5
The break even point will still remain the same.
The break-even point is calculated by setting total cost equal to total revenue and solving for the number of units produced and sold (denoted as 'units').
Given the current variable cost per unit ($20), the sale price per unit ($50), and the fixed cost (booth rent - $150), we can set up the equation as follows:
Total Cost = Fixed cost (booth rent) + variable cost per unit * units
Total Revenue = sale price per unit * units
Setting these two equal to each other, we get:
150 + 20*units = 50*units
By rearranging this equation, we find:
units = 150 / (50 - 20)
This calculates out to 5 units. Therefore, Ray needs to sell 5 units to break even with his current costs.
If Ray is able to reduce his variable cost to $15 per unit, we will repeat the same calculation with the new variable cost:
units = 150 / (50 - 15)
This calculates out to approximately 4.29 units. Since Ray cannot sell a fraction of a unit, he would have to sell 5 units to fully cover his costs, but he would begin to make a profit sooner than with his current variable cost. In fact, from the 5th unit sold, part of the revenue would go towards profit. Therefore, with the reduced variable cost, his break-even point would be closer to 4 units, but practically still 5 units.
In conclusion, with his current costs, Ray's break-even point is at 5 units. If he is able to reduce his variable cost to $15 per unit, his break-even point would theoretically be lower at approximately 4.29 units, but practically still would round up to 5 units.
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A small business averages $5,500 per month in online revenue, plus another $300 per salesperson per month. Which graph shows all solutions for the number of salespeople who need to be working for the business to generate at least $7,300 in monthly revenue?
Answer:
Step-by-step explanation:
7,300 = 5,500 + 300x
7,300 - 5,500 = 300x
1,800 = 300x
x = 6
Answer:
greater than or equal to 6
Step-by-step explanation:
i just took the plato test
Solve. x+ y = 3 y = x-7 Use the substitution method. The solution is (5, −2). There is no solution. The solution is (8, 1). There are an infinite number of solutions.
Answer:
The solution is (5, −2)
Step-by-step explanation :
x + y = 3 => y = 3 - x
y = x - 7 } =>
=> 3 - x = x - 7 => 3 + 7 = x + x => 2x = 10 => x = 5
x + y = 3
5 + y = 3
y = 3 - 5
y = - 2
The manufacturer of a CD player has found that the revenue R (in dollars) is Upper R (p )equals negative 5 p squared plus 1 comma 550 p comma when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar? A. $961 comma 000
Answer:
The maximum revenue is $1,20,125 that occurs when the unit price is $155.
Step-by-step explanation:
The revenue function is given as:
[tex]R(p) = -5p^2 + 1550p[/tex]
where p is unit price in dollars.
First, we differentiate R(p) with respect to p, to get,
[tex]\dfrac{d(R(p))}{dp} = \dfrac{d(-5p^2 + 1550p)}{dp} = -10p + 1550[/tex]
Equating the first derivative to zero, we get,
[tex]\dfrac{d(R(p))}{dp} = 0\\\\-10p + 1550 = 0\\\\p = \dfrac{-1550}{-10} = 155[/tex]
Again differentiation R(p), with respect to p, we get,
[tex]\dfrac{d^2(R(p))}{dp^2} = -10[/tex]
At p = 155
[tex]\dfrac{d^2(R(p))}{dp^2} < 0[/tex]
Thus by double derivative test, maxima occurs at p = 155 for R(p).
Thus, maximum revenue occurs when p = $155.
Maximum revenue
[tex]R(155) = -5(155)^2 + 1550(155) = 120125[/tex]
Thus, maximum revenue is $120125 that occurs when the unit price is $155.
A total of $114,000 will be evenly spent to build 12 Bungalows. If the first 5 bungalows have been completed and paid for, then __?__ is still available for the remaining bungalows.
Answer:
66500
Step-by-step explanation:
114000/12=9500 9500x7=66500114000:total budget
12:total bungalows
9500:budget for each bungalow
7: unfinished bungalows
66500: remaining budget for unfinished bungalows
hope this helped and good luck :D
The remaining budget for unfinished bungalows is $66500
What are arithmetical operations?The four basic arithmetic operations in Maths, for all real numbers, are: Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×') Division (Finding the quotient; '÷')
Given that, A total of $114,000 will be evenly spent to build 12 Bungalows, the first 5 bungalows have been completed and paid. We need to find the amount available for the remaining bungalows.
Amount used in each bungalow;
114000/12 = $9500
Therefore, each bungalow will need $9500
Amount used = $9500 × 5 = $47500
Amount remaining for remaining bungalows = $114,000 - $47500 = $66500
Hence, $66500 is remaining budget for unfinished bungalows.
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Antonio is having a pizza party for his birthday. He ordered 5 large pizzas, which have a total of 40 slices. He invited 8 people to his party. If he plans to divide the pizza up equally among him and his friends, how many slices will each person get
Answer: the number of slices that each person will get is 4 4/9
Step-by-step explanation:
Antonio ordered 5 large pizzas, which have a total of 40 slices.
He invited 8 people to his party. If he plans to divide the pizza up equally among him and his friends, it means that the pizza would be divided among 9 people(Antonio and 8 friends = 9 people).
The number of slices that each of them will get would be
40/9 = 4 4/9 slices
Tommy's heart aches and he needs a minor surgery to mend it. Before you sharpen your scalpel, you have to make sure that you operate on correct organ. Where is Tommy's hear
Answer:
The heart is located in the middle of the 2 lung's in the middle of the chest and slightly to the left side of the chest.
Step-by-step explanation:
The heart is a muscular organ of the size of a fist just behind and to the left of the breastbone. The cardiovascular system is the heart pumping blood across the artery and vein network.Behind your sternum and between your two lungs your heart is found. The heart lies closer to the front of the chest and in the front of the spine. Your diaphragm, stomach and liver are underneath your heart.
Hiros family lives 448 kilometers from the beach.Each of the 5 adults drove the family van an equal distance to get to and from the beach.How far did each adult drive?
Answer:
179.2km
Step-by-step explanation:
The distance from their house to the beach is 448km. Now they have to drive to and from the beach. The total distance traveled by the family is 448km + 448km.
This is equal to 896km. Now we have 5 adults who took their turns to drive and they drove the same distance. The total distance traveled by each adult will be 896/5 = 179.2km
Hence, each adult in the family drove a distance of 179.2km
Given 10 < x + 12 Choose the solution set.
{x| x∈R, x > 2}
{x| x∈R, x < -2}
{x| x∈R, x > -2}
{x| x∈R, x < 2}
{x| x∈R, x > -4}
Answer:
{x| x∈R, x > -2}
Step-by-step explanation:
You solve the inequality just like you would solve an equality.
Everything that has the x on the left side, everything without x on the right side.
Be careful that when you multiply by -1, the inequality signal changes(for example, lesser than becomes higher than
So
[tex]10 < x + 12[/tex]
[tex]-x < 12 - 10[/tex]
[tex]-x < 2[/tex]
Multiplying by -1
[tex]x > -2[/tex]
So the correct answer is:
{x| x∈R, x > -2}
{x| x∈R, x > -2}
Step-by-step explanation:
You solve the inequality just like you would solve an equality.
Everything that has the x on the left side, everything without x on the right side.
Be careful that when you multiply by -1, the inequality signal changes(for example, lesser than becomes higher than
So
Multiplying by -1
So the correct answer is:
{x| x∈R, x > -2}
You use math in day-to-day routines when grocery shopping, going to the bank or mall, and while cooking. How do you imagine you will use math in your healthcare career?
Answer:
Use math in healthcare career: In healthcare career one must translate medication orders into the right doses and number of pills to administer.
Step-by-step explanation:
Consider the provided information.
Math in healthcare career play significant role one should must know the units of the measurement for temperature, blood pressure, pulse rate, breathing rate etc.
In healthcare career one must translate medication orders into the right doses and number of pills to administer.
For example, If a doctor recommends a 100 gram of a drug every 6 hours and the hospital has 50 milligram pills, then you need to give two pills every 6 hours. Because 50 milligram times 2 is 100 milligram.
Math is vital in a healthcare career for tasks such as dosage calculations, interpreting vital signs, and handling medical billing. Proper math skills ensure accuracy and safety. Mastery in math will enhance your ability to provide effective patient care.
You asked how you will use math in your healthcare career. Math is essential in healthcare for various day-to-day operations. Here are some specific examples:
Dosage Calculations: Nurses and pharmacists use arithmetic to calculate the correct dosages of medication for patients based on their weight and age. For instance, if a patient requires a dosage of 5 mg per kg of body weight and they weigh 70 kg, the total dosage would be 350 mg.Vital Signs: Medical professionals regularly monitor a patient's vital signs, such as heart rate, blood pressure, and respiratory rate. Understanding how to interpret these numbers often requires basic math skills to identify any abnormal trends and take appropriate actions.Medical Billing: Healthcare administrators use basic math when handling billing and insurance claims. Ensuring that the proper amounts are billed and received involves addition, subtraction, and sometimes percentages.Statistical Analysis: Research in healthcare often involves statistical analysis to determine the effectiveness of treatments. This requires knowledge of algebra and sometimes calculus to analyze data correctly.In conclusion, math is a vital skill in the healthcare field. Its applications range from dosage calculations to interpreting vital signs, and even handling billing. Mastery of math in your healthcare career will enable you to provide safe and effective patient care.
sinusoidal wave in a string is described by the wave function y 5 0.150 sin (0.800x 2 50.0t) where x and y are in meters and t is in seconds. The mass per length of the string is 12.0 g/m. (a) Find the maximum transverse acceleration of an element of this string. (b) Determine the maximum transverse force on a 1.00-cm segment of the string . (c) State how the force found in part (b) compares with the tension in the string
Answer:
a) 375m/s2
b) F = 0.045N
c) F/T = 0.00096
d) Tension = 46.9N
Step-by-step explanation:
The step by step calculation is as shown in the attached file.
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Solve the system using substitution Verify the solution.
1. 3x-3=y
x+3y=11 2.
2. y=4-3x
5x+2y=5
3. -3x-1=y
-2x-y=-1
4. y=3x-2
-6x+3y=-4
Answer:
55 because if u take the 6 and 3 and multiply then subtract 4 and whatever you get that's your answer same with the others
Answer:
1. the answer is x=1/3y+1 y=3x−3
Step-by-step explanation:
What is the distance between (-3, 2) and (3, -8)?
The distance between (-3, 2) and (3, -8) is approximately 11.66.
Explanation:To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, (-3, 2) can be denoted as (x1, y1) and (3, -8) can be denoted as (x2, y2). Substituting these values in the formula:
d = sqrt((3 - (-3))^2 + (-8 - 2)^2)
d = sqrt(6^2 + (-10)^2)
d = sqrt(36 + 100) = sqrt(136)
The distance between (-3, 2) and (3, -8) is approximately 11.66.
Final answer:
To calculate the distance between (-3, 2) and (3, -8), one must find the differences in both the x and y coordinates, square these differences, sum them, and take the square root of this sum, which yields approximately 11.66.
Explanation:
To find the distance between the points (-3, 2) and (3, -8), we use the Pythagorean Theorem. The distance d is calculated as the square root of the sum of the squares of the difference in the x-coordinates and the y-coordinates.
First, find the differences:
Δx = [tex]x_2 - x_1[/tex] = 3 - (-3) = 6
Δy = [tex]y_2 - y_1[/tex] = -8 - 2 = -10
Then calculate the distance squared:
d² = (Δx)² + (Δy)²
d² = (6)² + (-10)²
d² = 36 + 100
d² = 136
Take the square root of the distance squared to find the distance:
d = [tex]\sqrt{136}[/tex]
d ≈ 11.66
Refer to Exercise 4. How many wooden signs can be painted with one gallon of paint? Between what two whole numbers does the answer lie?
Question refers to below content.
Three gallons of paint are used to paint 16 wooden signs. How many wooden signs can be painted with one gallon of paint?? Between what two whole numbers does the number lie?
Answer:
[tex]5 \frac{1}{3}[/tex] wooden sign can be painted from 1 gallon of paint.
The answer lies between number 5 and 6.
Step-by-step explanation:
Given:
Amount of paint = 3 gallons
Number of wooden signs = 16
We need to find the Number of wooden signs can be painted with 1 gallon of paint.
Solution:
Now we know that;
3 gallons of paint = 16 wooden signs painted
1 gallon of paint = Number of wooden signs can be painted with 1 gallon of paint.
By using Unitary method we get;
Number of wooden signs can be painted with 1 gallon of paint = [tex]\frac{16}{3} \ \ Or \ \ 5 \frac{1}{3}[/tex]
Hence [tex]5 \frac{1}{3}[/tex] wooden sign can be painted from 1 gallon of paint.
Now we can say that;
[tex]5 \frac{1}{3}[/tex] lies between 5 and 6.
Hence The answer lies between number 5 and 6.
Jeanine owes $1,200 on a credit card. The cars charges 16% interest, compounded continuously. Write a formula that describes how much you knew on her card after t years, assuming she makes no payments and does not incur any additional charges.
The letter e is used for continuous compound, it is raised by the interest rate times the amount of time.
The formula would be 1200e^0.16t
The answer is C
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠H.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠H = °
Answer:
[tex]m\angle H = 44.4\°[/tex].
Step-by-step explanation:
Given:
In Right Angle Triangle GIH
∠ I = 90°
GI = 7 ....Side opposite to angle H
GH = 10 .... Hypotenuse
To Find:
m∠H = ?
Solution:
In Right Angle Triangle ABC ,Sine Identity,
[tex]sin \ H = \frac{Oppsite\ side\ to\ \angle H}{Hypotenuse}[/tex]
Substituting the values we get;
[tex]sin\ H = \frac{7}{10} = 0.7[/tex]
Now taking [tex]sin^{-1}[/tex] we get;
[tex]\angle H = sin^{-1}\ 0.7 = 44.427[/tex]
rounding to nearest tenth we get.
[tex]m\angle H = 44.4\°[/tex].
Hence [tex]m\angle H = 44.4\°[/tex].
having trouble with this and 3 other problems
Answer:
a.) 10
b.) -2
c.) 6
d.) y = 6
e.) T = π
f.) y = -6cos(2t) + 4
Step-by-step explanation:
a.) Max value is the highest value in the y-axis. It peaks at y=10
b.) Min value is the lowest value in the y-axis. Peaks at y=-2
c.) Amplitude is how high the peak is from the midpoint. It could be found by taking the average of the peaks. (10 - (-2))/2 = 6
d.) y = 6
e.) T = π
f.) General equation for a sinusoidal wave is
y = Acos(ωt - Ф) + k
y = Acos((2π/T)t - Ф) + k
The graph started at it's min, so the amplitude must had been fliped upsidedown because it normally starts at the max. Therefore I must make my equation negative to flip it.
y = -Acos((2π/T)t - Ф) + k
A = amplitude = 6T = period = πФ = phaseshift = 0k = shift_in_y_direction = 4 , because shifting from -6 to -2 is shifting 4 units upy = -(6)cos((2π/(π))t - (0)) + (4)
y = -6cos(2t) + 4
Alex has a truck. 42% of the miles he drove last month were for work. If Alex drove 588 miles for work, how many miles did he drive last month all together? A) 1,200 B) 1,400 C) 1,600 D) 1,800
Answer:
He drive 1,400 miles last month all together.
So, option B) 1,400 is the correct answer.
Step-by-step explanation:
Given:
Alex has a truck. 42% of the miles he drove last month were for work.
If Alex drove 588 miles for work.
Now, to find miles he drive last month all together.
Let the miles he drive last month all together be [tex]x.[/tex]
42% of the miles he drove last month were for work.
Alex drove 588 miles for work.
Now, to get the miles he drive last month all together we put an equation:
[tex]42\%\ of\ x=588[/tex]
[tex]\frac{42}{100} \times x=588[/tex]
[tex]0.42\times x=588[/tex]
[tex]0.42x=588[/tex]
Dividing both sides by 588 we get:
[tex]x=1400\ miles.[/tex]
Therefore, he drive 1,400 miles last month all together.
So, option B) 1,400 is the correct answer.
Answer:
The answer is 1,400
Step-by-step explanation: If you do 1,400x42%=588 So the answer is 1400!!!!!
How do I solve this? Please show steps clearly so i can understand, thank you
Answer:
The value of [tex]x=8[/tex].
Step-by-step explanation:
Given:
[tex]\frac{x+3}{x}-\frac{x+1}{x+4}=\frac{5}{x}[/tex]
We need to solve this equation.
Solution:
First combining equation having same denominators we get;
[tex]\frac{x+3}{x}-\frac{5}{x}=\frac{x+1}{x+4}[/tex]
Now denominators are common so we will solve the numerators we get;
[tex]\frac{x+3-5}{x}=\frac{x+1}{x+4}\\\\\frac{x-2}{x}=\frac{x+1}{x+4}[/tex]
Now by cross multiplication we get;
[tex](x-2)(x+4)=x(x+1)[/tex]
Now Applying distributive property we get;
[tex]x^2+4x-2x-8=x^2+x\\\\x^2+2x-8=x^2+x[/tex]
Now Combining the like terms we get;
[tex]x^2+2x-x^2-x=8\\\\x=8[/tex]
Hence on solving we get the value of [tex]x=8[/tex].
When equal amounts are invested in each of three accounts paying 7%, 9%, and 12.5%, one years combined interest income is $1,225.5. How much is invested in each account?
Answer:
$4300.
Step-by-step explanation:
Let x represent amount of money invested in each account.
We have been given that equal amounts are invested in each of three accounts paying 7%, 9%, and 12.5%, one years combined interest income is $1,225.5.
We will use simple interest formula to solve our given problem.
[tex]I=Prt[/tex], where,
I = Amount of interest after t years,
P = Principal amount,
r = Annual interest rate.
Since principal for each amount is equal and time is equal to 1 year, so we can represent our given information in an equation as:
[tex]1225.5=x(0.07+0.09+0.125)(1)[/tex]
[tex]1225.5=x(0.285)[/tex]
[tex]x=\frac{1225.5}{0.285}[/tex]
[tex]x=4300[/tex]
Therefore, an amount of $4300 is invested in each account.
Final answer:
The amount invested in each of the three accounts with different interest rates, which together yield a total interest income of $1,225.5, is $4,300 in each account.
Explanation:
To solve for the amount invested in each account, we need to set up an equation that represents the total interest income from the accounts.
Letting x represent the amount invested in each account, we can say that the interest from the first account at 7% is 0.07x, the second account at 9% is 0.09x, and the third account at 12.5% is 0.125x. The total interest income is the sum of these individual interests, which equals $1,225.5. Hence, the equation to solve is:
0.07x + 0.09x + 0.125x = 1,225.5
Combining like terms gives:
0.285x = 1,225.5
Dividing both sides by 0.285 gives us:
x = 1,225.5 / 0.285
x = 4,300
Therefore, the amount invested in each account is $4,300.
PLEASE HELP PLEASE PLEASE DUE TONIGHT I HAVE NO IDEA HOW TO DO THIS
Answer:
I feel bad for you I really would like to help you but I haven't even learn that stuff yet
The cost of renting a car is $24.50 plus $11 per day. Sales tax is 7%. A car was rented for a total cost of $108.61. Which equation can be used to determine the number of days d the car was rented?
Answer:
Step-by-step explanation:
(24.50+11 d)*(107/100)=108.61
24.50×107+1177 d=10861
1177 d=10861-24.50×107
=10861-2621.50
=8239.50
d≈7 days
Final answer:
The equation that can be used to determine the number of days d the car was rented is: $108.61 = $24.50 + ($11 * Number of days). By solving this equation, we find that the car was rented for 7 days.
Explanation:
To determine the number of days the car was rented, we can use the equation:
Total cost = Cost of renting a car + (Cost per day * Number of days)
In this case, the cost of renting a car is $24.50 and the cost per day is $11. The sales tax is 7%.
The equation becomes:
$108.61 = $24.50 + ($11 * Number of days)
Now, we can solve for the number of days:
Subtract $24.50 from both sides of the equation: $108.61 - $24.50 = $11 * Number of days
Calculate the difference: $84.11 = $11 * Number of days
Divide both sides of the equation by $11: Number of days = $84.11 / $11
Round the result to the nearest whole number: Number of days = 7