Answer:
Below is the step-by-step explanation.
Step-by-step explanation:
To determine:
Construct a triangle ABC
Information Fetching and Information Steps:
From the given data,
[tex]BC\:=\:4\:cm[/tex][tex]B=60^{\circ }[/tex][tex]AB+AC=6\:cm[/tex]Procedure:
First draw a line segment [tex]BC\:=\:4\:cm[/tex]Then construct angle of [tex]m[/tex] ∠ [tex]60^{0}[/tex] at [tex]B[/tex] on [tex]BC[/tex].Taking [tex]B[/tex] as center with [tex]6\:cm[/tex] radius, draw an arc which cuts the ray of [tex]m[/tex] ∠ [tex]60^{0}[/tex] at [tex]X[/tex].Then Join [tex]X[/tex] and [tex]C[/tex].The draw a perpendicular bisector of [tex]XC[/tex].Wherever this perpendicular bisector intersect [tex]BX[/tex], name that point as [tex]A[/tex]Join [tex]A[/tex] and [tex]C[/tex].Thus, ∆ [tex]ABC[/tex] will be a required triangle.
Keywords: triangle, perpendicular bisector, angle
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At the fair, you spend $6 for food, then use the rest of your $20 to buy ride tickets. You have
enough money to buy 56 tickets. How much does each ticket cost?
a. $ 0.20 c. $0.35
b. $0.25 d. $ 0.48
Add. What is the answer
(5b^2-3b+2)+(2b-4)
Answer:
5b²-1b-2
Step-by-step explanation:
-3b and +2b are like terms so you combine them together -3b+2b= -1b
+2 and -4 are like terms so +2-4= -2
5b² has no like terms
then you put your answers together to simplify the equation
5b²-1b-2
The polynomials added together give the result 5b^2 - b - 2. The addition is done by combining like terms in the given polynomials.
Explanation:To add these polynomials, you combine like terms. Like terms are the terms in the polynomial that have the same variable and exponent. Here, our terms are 5b^2, -3b, 2, 2b, and -4.
The term 5b^2 does not have a like term, so it remains as is. The terms -3b and 2b add up to -b because -3b + 2b = -b. And finally, the constants 2 and -4 add up to -2. When we combine these results, we have the final answer: 5b^2 - b - 2.
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What place is the 4 at in the number 562,347
Answer: tenth place
Step-by-step explanation:
Answer:
The tens place.
Step-by-step explanation:
In order, the numbers would go as follows:
7 would be in the ones place.
4 would be in the tens place.
3 is in the hundreds place.
2 is in the thousands place.
6 is in the hundred thousands place.
5 is in the millions place.
how do you do linear models?
Answer:
Identify the input and output values.
convert the data to do coordinate pairs.
find the slope.
write the linear model.
use the model to make a prediction by evaluating the function at the given x-value.
use the model to identify an x value that results in a given y value.
Four more than half of the students in Bryan’s homeroom have tickets to attend the school’s musical. 20 students have tickets. Select all the equations that can be used to find the number of students in Bryan’s homeroom.
The equation formed by the given problem statement is 0.5*x + 4 = 20, solving this gives x = 32. Hence, there are 32 students in Bryan’s homeroom.
Explanation:The problem statement says that 'Four more than half of the students in Bryan’s homeroom have tickets to attend the school’s musical' and '20 students have tickets'. If we denote the total number of students in Bryan’s homeroom by x, we can write the statement as an equation: 0.5*x + 4 = 20. Simplifying this equation gives us 0.5*x = 20 - 4 = 16, so x = 16 * 2 = 32. Hence, there are 32 students in Bryan’s homeroom.
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What ratio is equivalent to 2:9
Answer:
8:36
Step-by-step explanation:
Factors: 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36
GCF: 4
8 ÷ 4 = 2 36 ÷ 4 = 9
a hose is coiled into circular loops about 30 inches in diameter. the length of each loop is about...
a. 7 ft
b. 8 ft
c .9ft
D. 10ft
Answer:
b. 8 ft
Step-by-step explanation:
We use the formula for the circumference of a circle to find the length of each loop.
Circumference of a circle = 2πr or Dπ
Where: π = pi
r = radius of the circular loops
D = Diameter
π = [tex]\frac{22}{7}[/tex]
D = 30 inches
Use Circumference of a circle = Dπ
Circumference of a circle = 30 x (22/7)
= 30 x 3.142857143
= 94.28571429 inches
Convert 94.28571429 inches to feet (ft)
12 inches = 1 ft
94.28571429 inches = 94.28571429/12
= 7.857142858 ft
≈ 8 ff
3 1/2, 3 5/6, 4 2/12, ………………, 4 5/6
What is the missing term?
What rule can you create for this pattern?
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
The sequence is [tex]3\frac{1}{2}, 3\frac{5}{6}, 4\frac{2}{12}, .... , 4\frac{5}{6}[/tex].
So, we have to find the missing term.
The sequence can be written in improper fraction as [tex]\frac{7}{2}, \frac{23}{6}, \frac{25}{6}, ... , \frac{29}{6}[/tex].
Therefore, the sequence is in A.P. as the consecutive numbers in the sequence are increasing by [tex]\frac{1}{3}[/tex].
As, [tex](\frac{23}{6} - \frac{7}{2}) = \frac{1}{3} = (\frac{25}{6} - \frac{23}{6})[/tex].
Therefore, the missing number is [tex](\frac{25}{6} + \frac{1}{3}) = \frac{27}{6} = \frac{9}{2} = 4\frac{1}{2}[/tex]. (Answer)
1.
What is the unit price of shampoo if a
15-ounce bottle costs $2.79?
Answer:
$2.79 per bottle$0.186 per ounceStep-by-step explanation:
When you talk about "unit price," you need to define the unit of interest. Unit prices on grocery store shelves don't always use the same unit, even for like items. Here it might be convenient to use any of the following as the "unit":
1 bottle1 ounce1 pint (16 ounces)1 cup (8 ounces)The "unit price" is computed as ...
unit price = (price for some number of units)/(the number of units)
The "number of units" may be larger, smaller, or equal to 1.
Then the price per cup (8 ounces) would be ...
unit price = (price for 15 oz)/(15/8 cups) = ($2.79)(8/15)
= $1.488 per cup
__
The price per ounce would be ...
unit price = ($2.79)/(15 oz) = $0.186/oz
__
We assume that the unit of interest is probably 1 ounce, but it could be something else. Your grader may expect the value to be rounded to the nearest cent, $0.19 per ounce.
The unit price of shampoo is approximately $0.186 per ounce.
Explanation:To find the unit price of shampoo, divide the cost of the bottle by the number of ounces it contains. In this case, the cost is $2.79 and the bottle is 15 ounces. So, the unit price can be calculated as $2.79 divided by 15 ounces, which gives us approximately $0.186 unit price per ounce.
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What does 7 1/2 - 2 3/16 - 1 5/8= as a fraction?
Answer:
3 11/16
Step-by-step explanation:
7 1/2 - 2 3/16 - 1 5/8
turn all to same fractions using multiplication
by this i mean to only multiply the fractions (both numerator and denomenator)
7 8/16 - 2 3/16 - 1 10/16
Turn them into improper fractions
120/16 - 35/16 - 26/16 =
And solve
3 11/16
A cantaloupe weighs 1/2. A watermelon weighs four times as much as the cantaloupe, how much does the watermelon weighs?
Answer:2
Step-by-step explanation: 1/2=0.5 0.5x4=2
Find 987 divided by 47 using the most efficient strategy you can. Show your work
The quotient of 987 divided by 47 is found to be 21 using estimation and step-by-step long division.
Explanation:The question asks to find 987 divided by 47 using an efficient strategy and show the work. To solve this, we can perform long division.
First, we see how many times 47 goes into 987. Since 47 is close to 50 and we know that 50 times 20 is 1000, which is just above 987, we can start by estimating around 20.20 times 47 is 940. We subtract this from 987 to get a remainder of 47.Since we see that 47 goes into 47 exactly once more, we add this to our previous quotient of 20.The final answer is 21 because 47 goes into 987 exactly 21 times. The most efficient strategy here was to use estimation and subtraction to find the quotient step-by-step.
Hahn passes the 0 point running 5 meters per second to the right. where will he be 6 seconds later
Answer:
30 meters away
Step-by-step explanation:
each second is equal to 5 meters, hence meters per second
what is the product of 2/5 and 2/3
Answer:
4/15 or in decimal form its 0.26
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.26
Tim would like to buy a video game that costs $27. He has not saved any money. His parents are willing to pay him $3 for every 2 chores, but will also pay him for completing single chores.
Tim would have to do 18 chores (2 chores 9 times or 1 chore 18 times) to be able to buy the video game.
Step-by-step explanation:
Step 1; Tim's parents will give him $3 for every two chores. This equals $1.50 for a single chore. He wants to save up $27 so that he can buy the video games he wants.
Step 2; The number of times he has to do the chores to be able to but the video game is a division between the money he wants to save up by the money he gets for the chores.
Number of 2 chores he needs to do = Amount of money he wants to save up / money he gets for doing two chores
= $27 / $3 = 9 times.
Number of single chores he has to do =Amount of money he wants to save up / money he gets for doing two chores
$27 / $1.50 = 18 times
An Expression is shown.
1 3 a 2 + b ÷ 2
What is the value of the expression if a = 3 and b = 8?
Answer:
If you're supposed to be multiplying the first four numbers, the answer is going to be 13.
Step-by-step explanation:
A farmer had a total of 995 horses and cows. After selling some of the horses and cows, he had 510 horses and 390 cows left. How many horses and cows did he sell altogether?
Answer: 95 sold
Step-by-step explanation:
995 horses and cows - 510 horses and 390 cows left = 95 sold
Answer:
95
Step-by-step explanation:
add 510 + 390 to find out the total number of horses and cows he has left. this equals 900
then you subtract the total of horses and cows he started with by what he has left to find out how many he sold
995-900=95
cual es factor de 8
Answer:
ocho es 8
Step-by-step explanation:
si quieres a saver mas solo necesitas a preguntar ;)
solo estoy jugando no mi mesajas yo no te quiero solo estoy jugando otra ves si te quiero como un amigo
A spherical ball with a volume of 2,304π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?
Answer:
Therefore the volume of the box is 13824 in³
Step-by-step explanation:
Given:
A spherical ball with is packaged in a box that is in the shape of a cube.
Volume of ball = 2304π in³.
Let 'r' be the radius of sphere
To Find:
Volume of Cube = ?
Solution:
Volume of sphere is given by
[tex]\textrm{Volume of sphere}=\dfrac{4}{3}\pi r^{3}[/tex]
Substituting the values we get
[tex]2304\pi=\dfrac{4}{3}\pi r^{3}\\\\\therefore r^{3}=1728\\\\Cube\ Rooting\\\\r=12\ in[/tex]
Now we know that diameter is given by
[tex]diameter=2\times r=2\times 12=24\ in[/tex]
it is given that,
The edge length of the box is equal to the diameter of the ball.
Therefore the length of cube = 24 in
Now the volume of the cube is given by
[tex]\textrm{Volume of cube}=(edge)^{3}[/tex]
substituting the values we get
[tex]\textrm{Volume of cube}=(24)^{3}=13824\ in^{3}[/tex]
Therefore the volume of the box is 13824 in³
Buying a Car Math Quiz
QUESTION 2 of 10: According to AAA the average monthly maintenance cost on a used car is 75 per month. You are looking to pay cash for
the exact same Jeep at two different dealers. Dealer "A' wants $4.995.00. Dealer "B" wants 55,595.00 with free maintenance coverage for
one year. Which is the best deal?
Answer:
Dealer B
Step-by-step explanation:
Maintenance cost per year = 75$
Dealer "A' wants $4.995.00.
Dealer "B" wants 55,595.00 with free maintenance cover for a year.
It is obvious that the best deal is what dealer B is offering, with free maintenance cover per year. for example, if i pick dealer A, calculate the maintenance cover for 3years = $2700
whereas for dealer B, a whole year maintenance cost is free, it implies that one will start paying the next coming year i.e a year lesser than dealer A. by that time the one who picked dealer A must have paid $3600 for maintenance while the one who picked dealer B will about to pay $1800.
The best deal is what dealer B is offering coupled with the free maintenance cover for 1year.
Final answer:
After calculating the total costs for one year, Dealer B offers a better deal on the Jeep by saving $300, as it includes free maintenance, contrasting with Dealer A which results in higher overall costs after adding maintenance payments.
Explanation:
To determine which car deal from the dealers is the better option, we need to calculate the total cost of each option over the course of one year, including the average monthly maintenance cost on a used car. According to AAA, this cost is $75 per month.
For Dealer A, the cost of the car is $4,995 with no free maintenance, so the total cost after one year is the price of the car plus 12 months of maintenance:
Cost of the car: $4,995
12 months of maintenance: 12 * $75 = $900
Total cost for Dealer A after one year: $4,995 + $900 = $5,895
For Dealer B, the car costs $5,595 but comes with free maintenance for one year, which means:
Total cost for Dealer B after one year: $5,595
Comparing these totals, we see that Dealer B offers the better deal, with the overall savings being:
Savings: $5,895 - $5,595 = $300
Find the final price on a $1,049 television
that is on sale for 12% off of the sales tax is
4.5%
Answer:
$883.40
Step-by-step explanation:
Calculate the amount of money needed to pay after the discount.n
$1049 × 88% = $923.12
Calculate the amount of money needed to pay after the tax.
$923.12 × 104.5% = $883.3684210526
=$883.40(rounded off to nearest cents)
hope this helps
To find the final price of the television on sale, calculate the discount amount, subtract it from the original price, and then add the sales tax amount.
Explanation:To find the final price of the television, we first need to find the discount amount by multiplying the original price ($1,049) by the discount percentage (12%).
Discount amount = $1,049 × 0.12 = $125.88
Next, subtract the discount amount from the original price to get the sale price:
Sale price = $1,049 - $125.88 = $923.12
Finally, add the amount of sales tax to the sale price. To find the sales tax amount, multiply the sale price by the sales tax rate (4.5%):
Sales tax amount = $923.12 × 0.045 = $41.54
Final price = Sale price + Sales tax amount = $923.12 + $41.54 = $964.66
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Can you help solve this please
50 points for all questions
9) Volume of the cone: [tex]9152 mm^3[/tex]
10) New volume of the cone: [tex]339 mm^3[/tex]
11) The volume of the cone shrinks by a factor of [tex]3^3=27[/tex]
12) Volume of the composite figure: [tex]15 ft^3[/tex]
Step-by-step explanation:
9)
The volume of a cone is given by the equation
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
where
[tex]\pi r^2[/tex] is the area of the base, where
r is the radius of the cone
h is the height of the cone
For the cone in this problem, we have:
r = 18 mm (radius)
h = 27 mm (height)
Therefore, the volume of this cone is
[tex]V=\frac{1}{3}\pi (18)^2 (27)=9152 mm^3[/tex]
10)
In this second exercise, the radius and the height of the cone are divided by 3. Therefore we have:
[tex]r'=\frac{r}{3}=\frac{18}{3}=6 mm[/tex] is the new radius of the cone
[tex]h'=\frac{27}{3}=9 mm[/tex] is the new height of the cone
Therefore, the new volume of the cone is
[tex]V=\frac{1}{3}\pi r'^2 h'[/tex]
And substituting, we find
[tex]V=\frac{1}{3}\pi (6)^2 (9)=339 mm^3[/tex]
11)
We can understand what happened to the volume of the cone after dividing its dimensions by 3 by calculating the ratio of the original volume to the new volume:
[tex]\frac{V}{V'}=\frac{9152}{339}=27[/tex]
This means that the new volume of the cone is 27 times smaller than the original volume.
We see that this "factor of shrinking" corresponds to the total factor of shrinking ofits dimensions, to the power of 3. In fact:
- Each the radius and the height of the cone has shrunk by a factor of 3
- However, the cone is a figure in 3 dimensions, so the total factor of shrinking of its volume is [tex]3^3 = 27[/tex]
12)
The composite figure consists of a squared pyramid + a parallelepiped.
The volume of the square pyramid is given by:
[tex]V_1 = \frac{1}{3}Lwh[/tex]
where
L = 5 ft is the length of the base
w = 1 ft is the width of the base
h = 6 ft is the height of the pyramid
Substituting,
[tex]V_1 = \frac{1}{3}(5)(1)(6)=10 ft^3[/tex]
The volume of the parallelepiped is given by
[tex]V_2=Lwh[/tex]
where
L = 5 ft is the length of the base
w = 1 ft is the width of the base
h = 1 ft is the height
Substituting,
[tex]V_2 = (5)(1)(1)=5 ft^3[/tex]
So, the total volume of the composite figure is
[tex]V=V_1+V_2=10+5=15 ft^3[/tex]
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Answer:
9) Volume of the cone: 9152 mm^3
10) New volume of the cone: 339 mm^3
11) The volume of the cone shrinks by a factor of 3^3=27
12) Volume of the composite figure: 15 ft^3
Step-by-step explanation:
jake made some tarts. He sold 3/5 of them and gave 1/4 of the remainder to his friends. If he had 150 tarts left, how many did he sell?
Answer: 90 tarts
Step by Step: 150/5 = 30
30 multiplied times 3 = 90
Final answer:
Jake initially had 750 tarts, sold 450 of them, and had 150 tarts remaining after giving some to his friends.
Explanation:
Jake initially had a total number of tarts. He sold 3/5 of them and then gave 1/4 of the remainder to his friends. If he had 150 tarts left, we need to calculate the number he sold. Let's denote the total number of tarts as T. After selling 3/5 of T, Jake would have 2/5T left. Then, he gives away 1/4 of 2/5T, which means he's giving away 1/4 * 2/5T = 1/10T. So, he is left with 2/5T - 1/10T = 1/5T. We know that 1/5T equals 150, so T equals 150 * 5 = 750. Jake sold 3/5 of these, which is 3/5 * 750 = 450 tarts.
there are 5 pink shirts and 9 green shirts. If there are 27 green shirts,how many pink shirts are there?
Answer:
Step-by-step explanation:
5 pinks =9 greens
x pinks = 27 greens
Cross multiply
5pinks × 27 greens =x pinks × 9greens
Divide both side by 9green
5 pinks × 27 greens / 9greens =x pinks
Then green cancel greens
x pink = 15 pinks
Then, 27 greens implies 15 pinks
Your bedroom ceiling is 10 feet high and is 2/3 as high as the living room ceiling. Write and solve an equation to find the height of the living room ceiling
The height of living room ceiling is 15 feet.
Step-by-step explanation:
Given,
Height of ceiling in bedroom = 10 feet
This is 2/3 height of living room ceiling.
Let,
x be the height of living room ceiling.
2/3 of x = 10
[tex]\frac{2}{3}x=10[/tex]
Multiplying both sides by 3
[tex]3*\frac{2}{3}x=10*3\\2x=30[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{30}{2}\\x=15[/tex]
The height of living room ceiling is 15 feet.
Keywords: fraction, division
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The height of the living room ceiling is 15 feet.
Explanation:To find the height of the living room ceiling, we can start by letting 'x' represent the height of the living room ceiling.
Since the bedroom ceiling is 2/3 as high as the living room ceiling, we can write the equation:
10 = (2/3)x
To solve for x, we can multiply both sides of the equation by 3/2:
(3/2)(10) = (3/2)((2/3)x)
15 = x
Therefore, the height of the living room ceiling is 15 feet.
Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10
Given ⇒ 2(x − 4) + 6x = 9x − 10
Step 1 ⇒ 2x − 8 + 6x = 9x − 10
Step 2 ⇒ 2x + 6x − 8 = 9x − 10
Step 3 ⇒ 8x − 8 = 9x − 10
Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Step 5 ⇒ 0 − 8 = x − 10
Step 6 ⇒ −8 = x − 10
Step 7 ⇒ −8 + 10 = x − 10 + 10
Step 8 ⇒ 2 = x + 0
Step 9 ⇒ 2 = x
Which step in solving this equation is justified by the Distributive Property?
A) Step 1 ⇒ 2x − 8 + 6x = 9x − 10
B) Step 2 ⇒ 2x + 6x − 8 = 9x − 10
C) Step 3 ⇒ 8x − 8 = 9x − 10
D) Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Answer:
A I think is the right one
The maximum volume of a cylindrical tank measures 3rs/4 liters. What is one-third of the tank's maximum volume? (1/3)x(3rs/4) (3rs/4) / 1/3 (3rs/4) / 3 9rs/4 rs/4
there is not any slope for this mathematical equation
To find one-third of the tank's maximum volume, multiply the maximum volume by one-third: 1/3 * 3rs/4 = 3rs/12.
Explanation:To find one-third of the tank's maximum volume, we can multiply the maximum volume by one-third:
1/3 × 3rs/4 = 3rs/12
So, one-third of the tank's maximum volume is 3rs/12 liters.
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45.6 x 10 to the 2nd power
4,560
10 to the 2nd power is = 100
so 100 × 45.6 =
What is the absolute value of | 56-12 |?
Answer: 44! Hope this helps :D
Step-by-step explanation:
Answer:
Step-by-step explanation:
56 - 12 is 44
Which Fraction is less than 3/5 3/10 3/4 2/3 or 5/3
Answer:
The fraction less than [tex]\frac{3}{5}[/tex] is [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
Given fractions are
[tex]\frac{3}{5} ,\frac{3}{10} ,\frac{3}{4}, \frac{2}{3}, \frac{5}{3}[/tex]
[tex]\frac{3}{5} =0.6\\\\\frac{3}{10}= 0.3\\\\\frac{3}{4} =0.75\\\\\frac{2}{3}=0.66 \\\\\frac{5}{3}=1.66[/tex]
Arranging the fraction in increasing order of their value
[tex]\frac{3}{10}= 0.3<\frac{3}{5} =0.6<\frac{2}{3}=0.66<\frac{3}{4} =0.75<\frac{5}{3}=1.66[/tex]
So,the fractions less than [tex]\frac{3}{5}[/tex] is [tex]\frac{3}{10}[/tex]