Question:
A width of a rectangular painting is 3 in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting
a. write an expression for the combined area of the painting and frame.
b. use the expression to find the combined area when the height of the painting is 12 in.
c. use the expression to find the combined area when the height of the the painting is 15 in.
Answer:
a) (h + 5)(2h + 8) is the expression for the combined area of the painting and frame
b) The combined area when h = 12 is 544 square inches
c) The combined area when h = 15 is 760 square inches
Solution:
Given that,
A frame that is 2.5 inches wide goes around the painting
The frame will go around all 4 sides of the painting.
That means that the length of each side of the painting will increase by 2.5 inches
Therefore,
The height of painting and frame is:
h = h + 2.5 + 2.5
h = h + 5
(2.5 inches on the top and the bottom)
Also given that,
Width of a rectangular painting is 3 inches more than twice the height
w = 3 + 2h
Now the width of painting and frame is:
w = 3 + 2h + 2.5 + 2.5
(Again, 2.5 inches on the top and the bottom)
w = 2h + 8
Thus the combined area of the painting and frame is:
[tex]Combined\ area = (h+5)(2h+8)[/tex]
B) Substitute h = 12 inches
[tex]Combined\ area = (12+5)(2(12)+8)\\\\Combined\ area = 17 \times (24+8) = 17 \times 32\\\\Combined\ area = 544[/tex]
Thus the combined area when h = 12 is 544 square inches
C) Substitute h = 15 inches
[tex]Combined\ area = (15+5)(2(15)+8)\\\\Combined\ area = 20 \times (30+8) = 20 \times 38\\\\Combined\ area = 760[/tex]
Thus combined area when h = 15 is 760 square inches
Please help I’ll give 50 points
The question is down below with the fractions please answer as fast as you can
Answer:
C
Step-by-step explanation:
(4√6)/(5√6)
= 6^(¼) ÷ 6^(1/5)
= 6^(1/4 - 1/5)
= 6^[(5-4)/20]
= 6^(1/20
When dividing roots, multiply them together: 4 x 5 = 20
Invert the product: 1/20
Raise the number under the root by that
Answer = 6 ^ 1/20
Kyle is purchasing a refurbished phone. He is looking at the phone models 4, 5, and 6, with a protective case in red (R), blue (B), or camo (C). What are all of the different choices he has? A) {4, 5, 6} B) {4R, 5B, 6C} C) {4R, 4B, 4C, 5R, 5B, 5C} D) {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}
Answer:
The choices Kyle has are option D.) {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}
Step-by-step explanation:
The choices available to Kyle either of the models 4, or 5 or 6 and each model can have a protective case which can be either red(R) or blue(B) or camo(C).
So Kyle can have model 4 in red protective case, 4R, or model 4 in blue protective case(4B), or model 4 in camo protective case (4C) or
Kyle can have model 5 in red protective case, 5R, or model 5 in blue protective case(5B), or model 5 in camo protective case (5C) or
Kyle can have model 6 in red protective case, 6R, or model 6 in blue protective case(6B), or model 6 in camo protective case (6C).
So the choices Kyle has are option D.) {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}
Answer:
D
Step-by-step explanation:
How many times greater is the 5 in
458,039 than the 5 in 271,145?
A. 10
B. 100
C. 1,000
D. 10,000
Answer:
D.
Step-by-step explanation:
The 5 in 458,039 is 100 times greater than the 5 in 271,145 because it represents 50,000 while the 5 in 271,145 represents 500. This can be determined by understanding place values, as each digit's value depends on its position in the number.
Explanation:The 5 in 458,039 is in the ten thousands place, meaning it represents 50,000. The 5 in 271,145 is in the hundreds place, meaning it represents 500. To understand how many times greater one is than the other, we would divide 50,000 by 500. The result is 100, therefore, the 5 in 458,039 is 100 times greater than the 5 in 271,145. So, the answer is B. 100.
This problem involves place values in numbers, where each digit in a number has a different value depending on its position.
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How can this 12×2+2³ make 120
Step-by-step explanation:
[tex]12\times(2+2^3)\qquad\text{use PEMDAS}\\\\\text{first power}\\\\=12\times(2+8)\\\\\text{next addition in parentheses}\\\\=12\times10=120[/tex]
A survey of all beings on planet Pib found 20% preferred umpt juice to all other juices. if 6 brings preferred umpt juice, how many beings were surveyed altogether?
Answer:
30 people.
Step-by-step explanation:
In a survey it is found that 20% of the people preferred umpt juice to all other juices.
Now, if 6 of the surveyed people are being preferred umpt juice, then we have to find the total number of people that were surveyed altogether.
So, 20% of the people being surveyed is equal to 6 people.
Therefore, 100% of the people is equal to [tex]6 \times \frac{100}{20} = 30[/tex] people. (Answer)
URGENT!!
These triangles are similar looking at the angles.
True or false
Answer:
False
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
a jar of peanut butter contains 452 with a standard deviation of 10.4 g assuming a normal distribution find the probability that a jar contains less than 449 grams
Answer:
0.3859
Step-by-step explanation:
Assuming on the average, a jar of peanut butter contains 452 grams, with a standard deviation of 10.4 grams.
Then we have
[tex] \mu = 452 \: and \: \sigma = 10.4[/tex]
We want to find the probability that a jar contains less than 449 grams.
We first determine the z-score of x=449 grams using:
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
We plug in these values to get:
[tex]z = \frac{449 - 452}{10.4} [/tex]
[tex]z = \frac{ - 3}{10.4} = - 0.29[/tex]
Now we read from the standard normal distribution table the area that corresponds to a z-score of -0.29
P(X<449)=0.3859
To find the probability that a jar contains less than 449 grams, calculate the z-score and use a standard normal distribution table or calculator.
Explanation:To find the probability that a jar contains less than 449 grams, we can use the standard normal distribution and the z-score formula. The z-score is calculated as (X - mean) / standard deviation. In this case, X = 449, mean = 452, and standard deviation = 10.4. By substituting these values into the formula, we can find the z-score, and then use a standard normal distribution table or calculator to find the probability.
1. Calculate the z-score: (449 - 452) / 10.4 = -0.2885
2. Use a standard normal distribution table or calculator to find the probability associated with a z-score of -0.2885. The probability is approximately 0.3830, or 38.30%.
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Combine like terms to create an equivalent expression 2/5m - 4/5 - 3/5m
Answer:
-1/5m-4/5
Step-by-step explanation:
2/5m-4/5-3/5m
2/5m-3/5m-4/5
-1/5m-4/5
Is -8-2(3+2n) + 7n equivalent to -30-13n? Explain why or why not.
Read this scene from The Miracle Worker Act 2.
(ANNIE insists, and HELEN gets rid of ANNIE’S hand by jabbing it with the needle. ANNIE gasps and moves to grip HELEN’S wrist; but KATE intervenes with a proffered sweet, and HELEN drops the card, crams the sweet into her mouth, and scrambles up to search her mother’s hands for more.)
How do these stage directions add meaning to the play?
The stage directions explain the characters’ facial expressions.
The stage directions illustrate the appearance of the room.
The stage directions describe how characters react to Helen.
The stage directions reveal Annie’s manner of speaking.
Answer:
The stage directions describe how characters react to Helen.
Step-by-step explanation:
In the given scene, the different characteristics of Helen as well as how other characters react when they see Helen is depicted in the scene. Other characters in the scene react differently to Helen when they come in contact with her. This is the main objective of the stage direction. It shows the interaction between Helen and others.
The stage directions represent the additions of the meaning to the play in terms of the stage directions describe how characters react to Helen.
The following information should be considered:
In the given situation, there is various characters of Helen and how the other character react at the time of seeing when Helen represent in the scene. The other characters scene react in a different way at the time of contacting. It represents the main aim of the stage directon. Also, it shows the interaction that lies between Helen and others.Learn more: brainly.com/question/17429689
Which of the following is equal to one million three hundred thousand?
A 1.3×106
B 1.3×109
C 1.03×106
D 1.03×109
1 million is 1*10^6
300 thousand is 3*10^5
Since 300,000 is one power of ten below 1 million, it's either A or B.
The correct choice is A, however, because of 1 million being 10^6. We choose the biggest value we get.
Hope this helped!
F is directly proportional to a.
If F = 24 when a = 8 find,
a when F = 18
Answer:
K = 3
a = 6
Step-by-step explanation:
F is directly proportional to a
That’s F = Ka
K is the constant
Divide both sides by a to get the constant k
K = F/a
When F = 24 and a =8
K = 24/8
= 3
When F = 18
a = ?
F = Ka
18 = 3 x a
18 = 3 x a
Divide both sides by 3
18/3 = 3 x a /3
6 = a
a = 6
An object is launched from a platform.
Its height (in meters), x seconds after the launch, is modeled by:
h(x)=-5x2verb +20x+60
What is the height of the object at the time of launch?
Answer:
60 feet
Step-by-step explanation:
The height, h (in meters), of the object launched from a platform is represented by the equation
[tex]h=h(x)=-5x^2+20x+60[/tex]
where x is the time (in seconds) passed after the launch.
The time of launch is [tex]x=0[/tex] (0 seconds passed after the launch)
Substitute [tex]x=0[/tex] to find the height:
[tex]h=h(0)=-5\cdot 0^2+20\cdot 0+60=60\ feet[/tex]
Mrs. Rivera ate 3/8 of a
pizza and Ms. Carter ate 4/8
of a pizza. How much pizza
did they eat altogether?
Answer:
They ate 7/8 of a pizza altogether.
Step-by-step explanation:
So, you know Mrs. Rivera ate 3/8 of a pizza and Ms. Carter ate 4/8 of a pizza.
You add 3/8 + 4/8 and you get 7/8.
The ate 7/8 of a pizza altogether.
The quantity of pizza that Mrs. Rivera and Ms. Carter ate altogether is equal to [tex]\frac{7}{8}[/tex]
Given the following data:
Fraction Rivera ate = [tex]\frac{3}{8}[/tex]Fraction Carter ate = [tex]\frac{4}{8}[/tex]To calculate how much (quantity) pizza they ate altogether:
A fraction can be defined as a numerical quantity that isn't a whole number.
Hence, a fraction is simply a part of a whole number.
In this exercise, we would add up the two fractions, so as to calculate how much (quantity) pizza they ate altogether.
[tex]Total \;quantity = \frac{3}{8} + \frac{4}{8}[/tex]
Lowest common multiple (LCM) = 8
[tex]Total\;quantity = \frac{4\;+\;3}{8} \\\\Total\;quantity = \frac{7}{8}[/tex]
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What is 4,095 divisible by
Answer:
5
Step-by-step explanation:
the answer would be 819
Answer: 5
Step-by-step explanation:
Friday, a store sold 10 blue shirts and 20 white shirts. what percentage of the shirts sold were blue? give answer to the ones place
Answer:
10+20=30
10 is what percent of 30?
10 is 1/3 of 30
Step-by-step explanation:
10 is 33.33% of 30
so 33% of the shirts sold were blue
33.33% of the shirts sold were blue.
Given that, Friday, a store sold 10 blue shirts and 20 white shirts.
We need to find out what percentage of the shirts sold were blue.
What is the percentage?The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now, 10+20=30
We need to calculate 10 is what per cent of 30.
Let the percentage be x.
So, x% of 30=10
⇒x/100 × 30=10
⇒3x/10=10
⇒3x=100
⇒x=33.33%
Therefore, 33.33% of the shirts sold were blue.
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Use the remainder to divide 5x^2+9x-2 by x+3. What is the remainder?
Answer:
16
Step-by-step explanation:
Using the Remainder theorem
f(x) divided by (x + h) then the remainder is the value of f(- h)
here the divisor is (x + 3), thus remainder is f(- 3)
remainder = 5(- 3)² + 9(- 3) - 2 = 5(9) - 27 - 2 = 45 - 29 = 16
For each set of three measures determine if they can be angle measures of a triangle
The options that can be angle measures of a triangle is
2. Set: 25°, 130°, 25°
How to find measure of triangle
To determine whether a set of three angle measures can be the angle measures of a triangle, you can use the sum of internal angles of a triangle which is 180 degrees
Let's analyze each set of three angle measures:
1. Set: 41°, 112°, 52°
41 + 112 + 52 = 205
This cannot be a triangle
2. Set: 25°, 130°, 25°
25 + 130 + 25 = 180
This can be a triangle
3. Set: 30°, 40°, 90°
30 + 40 + 90 = 160
This cannot be a triangle
4. Set: 132°, 141°, 31°
132 + 141 + 31 = 304
This cannot be a triangle
What is the value of t in the following equation? t + 14 = 2 712
Answer: t = 2698
Step-by-step explanation: Subtract 14 from 2712 to get the value of t
15 POINTS PLEASE HELP PPLESSE
Step-by-step explanation:
Hope it helps you in your learning process.
34. If each interior angle has a measure of 175.2°, how many sides does the polygon have?
Answer:
75 sides when the interior angle is 175.2
Step-by-step explanation:
these problems are all done the same way. Subtract the interior angle from 180 and divide the result into 360
360/(180 - 175.2)
360 / 4.8
75 sides
Write an equivalent expression for 20(x-5)
Answer:
40(x-10)
Step-by-step explanation:
Please show work for both problems
Answer:
3) x = 15; 95 and 85 4) x = 12; 98 for both angles
Step-by-step explanation:
2x + 65 + 3x + 40 = 180 Set the equations equal to 180
5x + 105 = 180 Combine like terms
- 105 - 105 Subtract 105 from both sides
5x = 75 Divide both sides by 5
x = 15
Plug 15 into both equations
2(15) + 65 = 95
3(15) + 40 = 85
4) 5x + 38 = 9x - 10 Set the equations equal to each other
- 5x - 5x Subtract 5x from both sides
38 = 4x - 10
+ 10 + 10 Add 10 to both sides
48 = 4x Divide both sides by 4
12 = x
Plug 12 into both equations
5(12) + 38 = 98
9(12) - 10 = 98
Eric worked for 13 hours each day For 6 days hen the next day he worked 5 hours How many hours did Eric work in complete Answer ASAP
Answer:
83 Hours
Step-by-step explanation:
First do 13x6=78
then add 5 hours to 78 hours and you get 83
A runner increased her distance from 9 miles to 12.5 miles a week. Find the percent increase in mileage.
A. 28%
B. 39%
C. 58%
D. 42%
Answer:
39 percent is increase in mileage.
Thus, the correct option is B. 39%.
Step-by-step explanation:
Given:
A runner increased her distance from 9 miles to 12.5 miles a week.
Now, to find percent increase in mileage.
Previous mileage = 9 miles.
Present mileage = 12.5 miles.
Mileage increase = 12.5 - 9 = 3.5 miles.
Now, to get the percent increase in mileage:
[tex]\frac{Mileage\ increased}{previous\ mileage} \times 100[/tex]
[tex]=\frac{3.5}{9} \times 100[/tex]
[tex]=\frac{350}{9}[/tex]
[tex]=38.88\%.[/tex]
Approximately the percent increase = 39%.
Therefore, 39% is increase in mileage.
Thus, the correct option is B. 39%.
7 + (5 – 9)2 + 3(16 ÷ 8).
Answer:
5
Step-by-step explanation:
7 + (5 - 9)2 +3(16/8)
7 + (-4)2 +3(2)
7+(-8) +6
7 -8 +6
7 -2
5
Write a ratio as a ratio of whole numbers in lowest terms
$1.00 to $1.50
Answer:
Step-by-step explanation:
50
The ratio of the whole numbers in its lowest term is ratio $2 to $3 i.e. [tex]\mathbf{\dfrac{2}{3}}[/tex]
A ratio of two integers a and b can be represented into a fraction as numerators and denominators.
[tex]\mathbf{\dfrac{a \to numerator}{b \to denominator}}[/tex]
To recognize and determine the ratio of the whole numbers in their lowest terms, we will multiply both the numerator and the denominator by 10.
i.e.
[tex]\mathbf{=\dfrac{1.00}{1.50}}[/tex]
[tex]\mathbf{=\dfrac{1.00\times 10}{1.50 \times 10}}[/tex]
[tex]\mathbf{=\dfrac{10}{15}}[/tex]
DIvide both the numerator and denominator by 5;
[tex]\mathbf{=\dfrac{2}{3}}[/tex]
Therefore, we can conclude that the ratio of the whole numbers in its lowest term is ratio $2 to $3 i.e. [tex]\mathbf{\dfrac{2}{3}}[/tex]
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A bag contains 6 gray tiles and 3 blue tiles. Jenny reached into the bag and picked a tile
randomly, and then without replacing it, picked a second tile.
What is the probability that she
picked a gray tile with her second pick given that she picked a blue tile with her first pick?
Answer:
The probability that Jenny picked a gray tile with her second pick given that she picked a blue tile with her first pick = 0.25
Step-by-step explanation:
i.) there are 6 gray tiles and 3 blue tiles
ii) the probability that Jenny picked a blue tile first is given by
[tex]\frac{number\hspace{0.1cm} of \hspace{0.1cm} blue\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm} of \hspace{0.1cm}tiles\hspace{0.1cm} } = \frac{3}{9} = \frac{1}{3}[/tex]
iii) the probability that Jenny picked a gray tile with her second pick without replacing the first tile[tex]\frac{number\hspace{0.1cm} of \hspace{0.1cm} blue\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm} of \hspace{0.1cm}tiles\hspace{0.1cm} } \times \frac{number\hspace{0.1cm} of \hspace{0.1cm} gray\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm } of \hspace{0.1cm}tiles\hspace{0.1cm} - 1 } = \frac{3}{9} \times \frac{6}{8} = \frac{1}{3} \times \frac{3}{4} = \frac{1}{4} = 0.25[/tex]
The probability that Jenny picked a gray tile with her second pick given that she picked a blue tile with her first pick = 0.25
what is the measurement of
Answer: Angle A = 120° and angle C = 45°
Step-by-step explanation: The first thing to note at the back of our minds is that the sum of the interior angles of a triangle equals 180°. Given that the three angle are available, we can start by adding them all together. Hence,
{12x + 12} + 15 + {3x + 18} = 180
12x + 12 + 15 + 3x + 18 = 180
By collecting like terms, we arrive at,
12x + 3x + 12 + 15 + 18 = 180
15x + 45 = 180
Subtract 45 from both sides of the equation
15x = 135
Divide both sides of the equation by 15
x = 9
At this point, we can now substitute for the value of x = 9 in the expressions representing angles A and C.
Angle A = 12x + 12
= 12(9) + 12
= 108 + 12
= 120
Angle A = 120°
Angle C = 3x + 18
= 3(9) + 18
= 27 + 18
= 45
Angle C = 45°
To make a ribbon and bow for a hat, Stacey needs 5/6 yard of black ribbon and 2/3 yard of red ribbon. How much total ribbon does she need