Answer:
A.-0.5x+1.7
Step-by-step explanation:
-3.4x+4.7-3+2.9x
-0.5x+1.7
Answer:
-0.5x+1.7
Step-by-step explanation:
If f(x) = -x2 + 6x, what is f(-3)?
Answer:
-12
Step-by-step explanation:
f(-3)= -(-3)2 + 6(-3)
= -(-6) -18
= 6 - 18
= - 12
The value of the quadratic function f(x) = -x² + 6x at x = -3 will be negative 27.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
f(x) = -x² + 6x
The degree of the function is 2. So, the function is a quadratic function.
The value of the function at x = -3 will be calculated as,
f(-3) = -(-3)² + 6(-3)
Simplify the equation, then we have
f(-3) = -(-3)² + 6(-3)
f(-3) = - 9 - 18
f(-3) = - 27
The worth of the quadratic capability f(x) = - x² + 6x at x = - 3 will be negative 27.
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What is 91.80 divided by 4 ????
Answer:
22.95
Step-by-step explanation:
91.80÷4=22.95
Therefore, 99.80÷4 is 22.95
What are the solutions to the equation 3(x - 4)(x + 5) = 0?
O
O
O
x= 4 or x = 5
x= 3, x = 4, or x = -5
x= 3, x= -4, or x = 5
x = 4 or x = -5
Answer:
Step-by-step explanation:
3(x - 4)(x + 5) = 0
Dividing through by 3
(x - 4)(x + 5) = 0
(x - 4) = 0 or x + 5 = 0
x - 4 = 0 or x + 5 = 0
x = 4 or x = - 5
How many thousands are in 38,000
Answer: 38
Step-by-step explanation:
Divide 38000/1000
Answer:
Step-by-step explanation: How many 10,000 are in 200,000
Which of the following points is NOT a solution to the inequality: y ≥ 2x − 10?
(5,0)
(-1,1)
(4,2)
(6, -2)
25 multiplied by 3 algebraic expression
Answer:
25*3 or 25(3)
Step-by-step explanation:
Understanding arithmetic operations, like multiplication, and the order of operations, is essential in algebra. Parentheses dictate the order, as seen in '2 + (3 x 5)', resulting in 17. For algebraic manipulation, this understanding helps when working with variables and complex expressions like cubing exponentials or solving simultaneous equations.
Explanation:When faced with the phrase '25 multiplied by 3 algebraic expression', we might interpret this as the task of multiplying an algebraic expression by 25. Considering the examples provided, the manipulation of parentheses greatly influences the outcome of mathematical expressions.
The expression 2 + (3 x 5) includes parentheses, which indicate that multiplication should occur before addition, following the order of operations (PEMDAS/BODMAS). Here, the product of 3 and 5 is 15, and adding 2 results in 17.
However, if we were to apply the principle of algebraic multiplication to an unknown variable, say 'x', the expression would be 25x. If 'x' was the expression (2 + (3 x 5)), then 25x would be 25 times 17, or 425, after applying the order of operations within the parentheses.
Applying this method to simultaneous equations or Cubing of Exponentials, we can see the importance of understanding the principles of algebra and arithmetic operations.
When cubing exponentials, for example, you multiply the exponent by 3. This concept is crucial for solving more complex algebraic problems like those involving unknowns and linear equations.
I really need help with this math problem
Common difference = [tex]\frac{1}{5}[/tex]
Solution:
Given arithmetic sequence:
[tex]$-2,-1\frac{4}{5} ,-1\frac{3}{5} , -1\frac{2}{5} , ....[/tex]
Let us first convert the improper fraction into mixed fraction.
[tex]$-2,-\frac{9}{5} ,-\frac{8}{5} , -\frac{7}{5} , ....[/tex]
Difference between two numbers in an arithmetic sequence is the common difference.
[tex]$a_2-a_1=-\frac{9}{5}-(-2)=-\frac{9}{5}+2=\frac{1}{5}[/tex]
[tex]$a_3-a_2=-\frac{8}{5}-\left(-\frac{9}{5}\right)=-\frac{8}{5}+\frac{9}{5}=\frac{1}{5}[/tex]
[tex]$a_4-a_3=-\frac{7}{5}-\left(-\frac{8}{5}\right)=-\frac{7}{5}+\frac{8}{5}=\frac{1}{5}[/tex]
Common difference = [tex]\frac{1}{5}[/tex].
Hence the common difference of the arithmetic sequence is [tex]\frac{1}{5}[/tex].
Common difference of the given arithmetic sequence is equal to [tex]\frac{1}{5}[/tex]
Explanation:The given arithmetic sequence is in mixed numbers. Converting them into proper fractions, we get:
[tex]First\ term = t_1 = -2\\\\Second\ term = t_2 = -1\frac{4}{5} = -\frac{(5\times1)+4}{5} = -\frac{9}{5}\\\\Third\ term = t_3 = -1\frac{3}{5} = -\frac{(5\times1)+3}{5} = -\frac{8}{5}\\\\Fourth\ term=t_4 = -1\frac{2}{5} = -\frac{(5\times1)+2}{5} = -\frac{7}{5}[/tex]
The sequence can thus be rewritten as [tex]-2, -\frac{9}{5}, -\frac{8}{5}, -\frac{7}{5}[/tex]
To find the common difference of the given arithmetic sequence, subtract any two consecutive numbers of the sequence. The difference between two consecutive numbers is always a constant and is termed as the common difference.
Hence,
[tex]d_1= t_2-t_1=(-\frac{9}{5} -(-2)= \frac{-9+10}{5}= \frac{1}{5} \\\\d_2=t_3-t_2= (-\frac{8}{5} -(-\frac{9}{5} )= \frac{-8+9}{5} = \frac{1}{5}\\\\d_3=t_4-t_3= (-\frac{7}{5} -(-\frac{8}{5} )= \frac{-7+8}{5} = \frac{1}{5}[/tex]
[tex]d_1=d_2=d_3 = d[/tex]
Common difference [tex]d=\frac{1}{5}[/tex]
PLEASE ANSWER ASAP! WILL MARK BRAINLIEST!!!! What is the percent of increase from 22.9 to 75.2? Round your answer to the nearest tenth of a percent and include a percent sign (%). (P.S. I have to have two people answer, though)
The speed of a boat in still water is 50km/h. It takes the same time for the boat to
travel 10km upstream as it does to travel 20km downstream. Find the speed of the
current.
The speed of a boat in still water (b) is 50km/h. It takes the same time (t) for the boat to travel 10km (x) upstream as it does to travel 20km (y) downstream. Find the speed of the current.
upstream speed (u) = speed in still water (b) - stream speed (s) = b-s = 50-s
downstream speed (d) = speed in still water (b) + stream speed (s) = 50+s
time (t) = x/u = y/d
10/(50-s) = 20/(50+s)
10(50+s) = 20(50-s)
500 + 10s = 1000 - 20s
30s = 500
stream speed (s) = 500/30 = 16.6 km/h
What is the inverse of the given relation? y=3x+12 Show your work.
Yo sup??
y=3x+12
y-12=3x
x=y/3 - 4
f(y)=y/3 - 4
or
f(x)=x/3 - 4
where f(x) is the inverse of y.
Hope this helps
The inverse relation of [tex]\( y = 3x + 12 \)[/tex] is [tex]\( x = \frac{y - 12}{3} \)[/tex].
To find the inverse of the relation [tex]\( y = 3x + 12 \)[/tex], we start by expressing it in terms of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ y = 3x + 12 \][/tex]
Next, solve for [tex]\( x \)[/tex]:
[tex]\[ y - 12 = 3x \][/tex]
[tex]\[ x = \frac{y - 12}{3} \][/tex]
Thus, the inverse relation is:
[tex]\[ x = \frac{y - 12}{3} \][/tex]
To verify, substitute [tex]\( x \)[/tex] with [tex]\( \frac{y - 12}{3} \)[/tex] back into the original equation:
[tex]\[ y = 3 \left( \frac{y - 12}{3} \right) + 12 \][/tex]
[tex]\[ y = y - 12 + 12 \][/tex]
[tex]\[ y = y \][/tex]
Therefore, the answer is [tex]\( x = \frac{y - 12}{3} \)[/tex].
The weight (W) of an object is the product of its mass (m) in kilograms and g, the acceleration due to gravity in meters/second2. If the acceleration due to gravity is 9.8 meters/second2, find the corresponding weights for these masses.
mass in kilograms = {22.1, 33.5, 41.3, 59.2, 78}
The weights (in newtons) for the given masses are -
A. 2165.8, 3283.0, 4047.4, 5801.6, 7644.0 B. 216.58, 328.30, 404.74, 580.16, 764.4 C. 319, 433, 511, 690, 878 D. 31.9, 43.3, 51.1, 69, 87.8
Answer:
B
Step-by-step explanation:
[tex]22.8 \times 9.8 = 216.58 \\[/tex]
If a=2b^3 and b= -1/2c ^-2,express a in terms of c.
Answer:
Part 1) [tex]a=-\frac{1}{4c^6}[/tex]
Part 2) [tex]a=-\frac{1}{4c^{-6}}[/tex]
Step-by-step explanation:
Part 1) we have
[tex]a=2b^{3}[/tex] ----> equation A
[tex]b=-\frac{1}{2}c^{-2}[/tex] ----> equation B
substitute equation B in equation A
[tex]a=2(-\frac{1}{2}c^{-2})^{3}[/tex]
Applying property of exponents
[tex](x^{m})^{n}=x^{m*n}[/tex]
[tex]x^{-m} =\frac{1}{x^{m}}[/tex]
[tex]a=2(-\frac{1}{2}c^{-2})^{3}=2(-\frac{1}{2})^3(c^{-2})^{3}=2(-\frac{1}{8})(c^{-6})=-\frac{1}{4c^6}[/tex]
therefore
[tex]a=-\frac{1}{4c^6}[/tex]
Part 2) we have
[tex]a=2b^{3}[/tex] ----> equation A
[tex]b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2}[/tex] ----> equation B
substitute equation B in equation A
[tex]a=2(-\frac{c^{2}}{2})^{3}[/tex]
Applying property of exponents
[tex](x^{m})^{n}=x^{m*n}[/tex]
[tex]x^{-m} =\frac{1}{x^{m}}[/tex]
[tex]a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})[/tex]
simplify
[tex]a=-\frac{c^{6}}{4}[/tex]
therefore
[tex]a=-\frac{1}{4c^{-6}}[/tex]
Find the value of x.
80
42
60
30
Answer:
I am pretty sure its 60 i am sorry if its wrong
Step-by-step explanation:
what is 2x cubed plus 2x squared simplified too
Answer:
4x^4
Step-by-step explanation:
Cubed and squared are the same thing
BRAINLESS PLS
Jaclyn has decided to purchase an $11,000 car. She plans on putting $1000
down toward the purchase, and financing the rest at a 4.8% interest rate for 3
years. Find her monthly payment.
O
A. $298.81
B. $204.78
O
O
O
C. $226.54
D. $236.89
Based on the cost of the car and the interest rate as well as the period, Jaclyn's monthly payment would be A. $298.81.
What would Jaclyn's monthly payment be?First find the amount she financed:
= Cost of car - down payment
= 11,000 - 1,000
= $10,000
Then find the monthly interest and number of periods:
= 4.8%/12 = 3 years x 12
= 0.4% = 36 months
Monthly payment would be:
Amount financed = Amount x ( 1 - (1 + rate)^-number of periods) / rate
10,000 = A x ( 1 - (1 + 0.4%)⁻³⁶) / 0.4%
10,000 = A x 33.4658758899
Amount = 10,000 / 33.4658758899
= $298.81
In conclusion, option A is correct.
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What is the name of a polygon that has four congruent sides and these angle
measures: 80°, 100°, 80°, 100°?
A. Hexagon
B. Trapezoid
C. Rhombus
D. Square
The polygon is rhombus
What is Polygon?In geometry, the definition of a polygon is given as a closed two-dimensional figure with three or more straight lines. The Greek word "Polygon" consists of Poly meaning "many" and gon meaning "angle". We see many different polygons around us. For example, the shape of a honeycomb is a hexagon. Each polygon is different in structure, they are categorized based on the number of sides and their properties. Thus, all polygons are closed plane shapes.
Identification and Naming of PolygonsIt is a closed shape, that is, there is no end that is left open in the shape. It ends and begins at the same point.It is a plane shape, that is, the shape is made of line segments or straight lines.It is a two-dimensional figure, that is, it has only two dimensions length and width. There is no depth or height to it.The shape must have three or more sides.The angles in the polygon may or may not be the same.The length of the sides of a polygon may or may not be the same.Given:
angle measures: 80°, 100°, 80°, 100°
As, the sum of angles is 360
= 80+ 80 +100 +100
= 160 +200= 360
Also, pair opposite angles are equal.
Hence, the given polygon is rhombus.
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PLEASE HELP MEEEEEEEE!!!!!!
Chris Shopper received a $1,500.00 discount loan to purchase a washer and dryer. The loan was offered at 15% for 120 days. Find the interest in dollars and the proceeds for the following problem.
The interest is $_______?
The proceeds are $_______?
Thanks!!!!!! :)
120 says is 1/3 of a year.
Interest = 1500 x 0.15 x 1/3 = $75
Proceeds = 1500 - 75 = $1425
Answer: Interest = 1500 x 0.15 x 1/3 = $75
Proceeds = 1500 - 75 = $1425
Step-by-step explanation:
Hope this helps:)
what is 5/5/8 divided by 1/2/9 in simplest form
The division of 5/5/8 by 1/2/9 in simplest form is 405/88 after converting the mixed numbers to improper fractions, then multiplying by the reciprocal, and simplifying.
Explanation:To find the simplest form of the division of two mixed numbers, first, both mixed numbers must be converted to improper fractions. Dividing by a fraction is the same as multiplying by its reciprocal. So, when dividing 5/5/8 by 1/2/9, we first turn these into improper fractions.
5/5/8 becomes 45/8 (since 5*8+5=45) and 1/2/9 becomes 11/9 (since 1*9+2=11). Now the problem is 45/8 divided by 11/9. To divide these fractions, we multiply by the reciprocal: 45/8 * 9/11 = (45*9)/(8*11) = 405/88.
To simplify 405/88, we find the Greatest Common Divisor (GCD) of the numerator and the denominator, which is 1 in this case, so the fraction is already in its simplest form, which is 405/88.
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 1/2/9 is 9/2/1. So, the expression becomes 5/5/8 multiplied by 9/2/1. To multiply fractions, we multiply the numerators together and the denominators together. So, (5 x 9) / (5 x 2) x 8 / 1 = 45/10 x 8/1 = 360/10 = 36.
How many nickels are in one roll of $10
Answer:
40 Nickels
Step-by-step explanation:
If you had 12 pieces of licorice to share equally among 5 people, how much licorice would each person get? Be sure to show your thinking clearly.
Answer:
Each person will be getting [tex]2\frac{2}{5}[/tex] pieces of licorice
Step-by-step explanation:
If we have 12 pieces of licorice
To divide it equally among 5 people following formula will be used
Pieces to be given to each person = [tex]\frac{total\, pieces}{total\,people}[/tex]
= [tex]=\frac{12}{5} \\2.4\\[/tex]
So
Each person will be getting [tex]2\frac{2}{5}[/tex] pieces of licorice
Keywords: Algebra
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How to solve 3 1/6 - 3/4 + 5/6
Answer: 3 1/2
Step-by-step explanation:
Plz help me with this the last person who did this for me got it wrong for me so i beg of u someone plz help me out with this i beg due today
a. The perimeter of the figure is 4x+34.
b. The total area of figure is 24x+40.
Step-by-step explanation:
Given,
Length of figure = 12
Width of figure = x+5+x = 2x+5
a. Perimeter = Length + Length + Width + Width
Perimeter = [tex](12)+(12)+(2x+5)+(2x+5)[/tex]
Perimeter = [tex]12+12+2x+5+2x+5 = 4x+34[/tex]
The perimeter of the figure is 4x+34.
b. Total area = Length * Width
Total area = [tex]12(2x+5) = 24x+60[/tex]
The total area of figure is 24x+40.
Keywords: area, perimeter
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Julie is 6 feet tall. If she stands 15 feet from the flagpole and holds a cardboard square, the edges of the square line up with the top and bottom of the flagpole. Approximate the height of the flagpole
Answer:
43.5 ft
Step-by-step explanation:
Given: Julie is 6 feet tall
She stands 15 feet from the flagpole.
The edges of the square line up with the top and bottom of the flagpole.
Picture drawn to show side and angle formed by Julie and flagpole.
Lets assume the height of flagpole be "h".
As given, the edges of the square line up with the top and bottom of the flagpole.
∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.
Now, finding the height of flagpole by using tangent rule.
we know, [tex]tan\theta= \frac{Opposite}{adjacent}[/tex]
Remember, both the angle are equal.
∴ Ratio of opposite and adjacent leg for both right angle triangle= [tex]\frac{6}{15} : \frac{h-6}{15}[/tex]
We can put it; [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Solving the equation now
⇒ [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Multiplying both side by 15
⇒[tex]6 = \frac{15\times 15}{h-6}[/tex]
Multiplying both side by (h-6)
⇒ [tex]6\times (h-6) = 15\times 15[/tex]
Distributive property of multiplication
⇒ [tex]6h-36= 225[/tex]
Adding both side by 36
⇒[tex]6h= 225+36[/tex]
Dividing both side by 6
⇒[tex]h= \frac{261}{6}[/tex]
∴ [tex]h= 43.5\ feet[/tex]
Hence, the height of flagpole is 43.5 feet.
The height of the flagpole is given by the length of the hypotenuse side
formed by the right triangle Julie forms with the cardboard.
Response:
Height of the flagpole is 17.4 feetWhich method is used to calculate the height of the flagpole?The triangle formed by the edges of square lined up with the top and
bottom of the flagpole is a right triangle.
The altitude of the right triangle formed with the height of the flagpole as the base = 15 feet
Length of a leg of the right triangle = √(15² + 6²) = 3·√(29)
The other angle formed by the right triangle = (90° - arctan(15/6))
h × sin(arctan(15/6)) = 3·√29
[tex]h = \mathbf{\dfrac{3 \cdot \sqrt{29} }{sin(arctan(15/6))} } = 17.4[/tex]
Height of the flagpole, h = 17.4 feet
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Want three fractions are the same2/4 4/6 5/8 3/6 2/3 6/9
Answer:
2/4 . 4/6 . 2/3
Step-by-step explanation:
Answer:
Step-by-step explanation:
2/4=1/4
4/6=2/3
5/8
3/6
6/9=3/6
Land in a development is selling for $60,000 per acre. If Jack purchase 1 ¾ acres, how much will he pay?
Answer:
The total cost is calculated to be $105,000.
Step-by-step explanation:
Here,
The cost of per acre land= $60,000
Jack is willing to purchase= 1 ¾acres = [tex]\frac{4*1+3}{4} =\frac{7}{4}=1.75[/tex] acres
Then,
By unitary method,
The cost of one acre land is $60,000 .
The cost of 1.75 acres is = $[tex]1.75*60,000[/tex]
The total cost of land is =$105,000.
So, Jack has to pay $105,000 to purchase 1.75 acres of land.
To find the total cost of 1 ¾ acres of land purchased at $60,000 per acre, multiply the price by the number of acres. Jack will pay $105,000 for the land.
Jack purchased 1 ¾ acres of land at $60,000 per acre. To calculate the total cost, multiply the price per acre by the total number of acres:
Total Cost = Price per acre x Number of acres
Total Cost = $60,000 x 1.75 = $105,000
If gas costs $4 per gallon, how much will gas cost Sally per day just to get to and from Job A per day? per week? per year?
To find the cost of gas for Sally's commute, you would multiply the number of gallons she uses daily by the cost per gallon. Assuming a daily use of one gallon at $4 per gallon, Sally would spend $4 per day, $20 per week (5-day workweek), and $1,040 per year (52 workweeks). This does not account for variable factors such as days off or gas price changes.
Explanation:The student is asking about the cost of gasoline for commuting to and from a job. Since we do not have the exact distance Sally travels or the efficiency of her vehicle, we cannot compute the exact cost per day, week, or year. However, if we assume Sally uses one gallon of gas per day at a cost of $4 per gallon, here's how you calculate the costs:
Per day: Sally would spend $4 each day on gas.Per week: Assuming she works 5 days a week, Sally would spend 5 days x $4/day = $20 per week on gas.Per year: If Sally works 52 weeks a year, she would spend 52 weeks x $20/week = $1,040 per year on gas.These calculations are based on the premise of daily one-gallon gas usage and do not take into account vacations, days off, or possible fluctuations in gas prices.
5+10+13+?13+10+5 Which of the following symbols curly completes this com perforation
2.4 X 10 -1 in standard form
Answer:
Step-by-step explanation:
0.24
Rewrite 3/4x+2=9/10 so that it doesn’t have fractions
The equation with no fractions is:
30x + 80 = 36
Solution:
Given that the equation is:
[tex]\frac{3}{4}x+2=\frac{9}{10}[/tex]
We have to rewrite the equation such that there is no fraction
From given expression,
[tex]\frac{3}{4}x+2=\frac{9}{10}[/tex]
Simplify the left hand side of equation
[tex]\frac{3x+8}{4} = \frac{9}{10}[/tex]
Cross multiply to get a simpler equation
[tex]10(3x+8) = 9 \times 4\\\\Simplify\ the\ above\ expression\\\\30x + 80 = 36[/tex]
Thus the equation is rewritten with no fractions
To rewrite the equation 3/4x + 2 = 9/10 without fractions, we multiply every term by the lowest common denominator (20) to get 15x + 40 = 18. Then, we isolate x by subtracting 40 from both sides to get 15x = -22. We solve for x by dividing both sides by 15, resulting in x = -22/15.
Explanation:The aim is to rewrite the equation 3/4x + 2 = 9/10 without fractions. To get rid of the fractions, we'll multiply each term by the lowest common denominator (LCD). In this case, the LCD is 20 because it's the smallest number both 4 and 10 can both go into. The equation thus becomes: 20*(3/4x) + 20*2 = 20*(9/10)
This simplifies to: 15x + 40 = 18
Now, to isolate x, we start by subtracting 40 from both sides:
15x + 40 - 40 = 18 - 40
So, 15x = -22. Finally, to solve for x, we divide by 15:
x = -22/15
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The perimeter of this hexagon is 52in. Each longer side measure 1 in. less than 4 times the length of a shorter side. Find the length of the labeled x.
Answer:
x=4.5 inches
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The perimeter of a hexagon is the sum of its six length sides
Let
x ----> the length of a shorter side
y ---> the length of a longer side
The perimeter of the hexagon is equal to
[tex]P=4x+2y[/tex]
[tex]P=52\ in[/tex]
so
[tex]52=4x+2y[/tex] ---->equation A
Each longer side measure 1 in. less than 4 times the length of a shorter side
so
[tex]y=4x-1[/tex] ----> equation B
substitute equation B in equation A
[tex]52=4x+2(4x-1)[/tex]
Solve for x
[tex]4x+8x=52+2\\12x=54\\x=4.5\ in[/tex]