a border to surround a picture is to be cut from an 11 1/2 in. by 11 1/2 in. mat board. if the picture is 8 3/4 in. by 8 3/4 in., what is the width of the border?

Given data:

QP = PT and RP = SP

Let us first prove ΔQPR and ΔSPT are congruent.

In ΔQPR and ΔSPT,

QP ≅ TP (Given side)

∠QPR ≅ ∠ SPT (Vertically opposite angles are congruent)

RP ≅ SP (Given side)

Therefore, ΔQPR ≅ ΔSPT (by SAS congruence rule)

By corresponding parts of congruence triangles are congruence,

⇒ ∠Q ≅ ∠T

Hence ∠Q ≅ ∠T.

Answer:

A. 16h+25≤125

Step-by-step explanation:

From the information, the one-time fee is $25.

The rate per hour is $16

Therefore the total cost involved in renting a car is given by:

16h+25

Jamarcus needs to rent a truck and can spend no more than $125.

This implies that:

16h+25≤125

The correct answer is A.

Answer: The speed of the current is 1.5 km/h .

Step-by-step explanation:

Let x = speed of current and y = speed of canoe.

Since  , [tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

As per given , we have

[tex]x+y=\dfrac{12}{2}\\\\ x+y=6......................(1)[/tex]

[tex]y-x=\dfrac{12}{4}\\ y-x=3...............(2)[/tex]

Adding (1) and (2) , we get

[tex]2y=9\\\Rightarrow\ y=\dfrac{9}{2}=4.5[/tex]

Put value of y in (1) , we get

[tex]x+4.5=6\\\Rightarrow\ x=1.5[/tex]

Hence, the speed of the current is 1.5 km/h .

To find the speed of the current, we can use the concept of relative velocity and set up equations for the downstream and upstream journeys.

In order to find the speed of the current, we can use the concept of relative velocity. Let's assume the speed of the canoeist in still water is 'v' km/h and the speed of the current is 'c' km/h.

Downstream journey: The effective speed of the canoeist is 'v + c' km/h. Given that the canoeist took 2 hours to travel 12 km downstream, we can set up the equation:

(v + c) * 2 = 12

Upstream journey: The effective speed of the canoeist is 'v - c' km/h. Given that the canoeist took 4 hours to travel 12 km upstream, we can set up the equation:

(v - c) * 4 = 12

Solving these two equations simultaneously will give us the values of 'v' and 'c', and the value of 'c' will represent the speed of the current.

Answer:

2x = 5

Step-by-step explanation:

If the person in the figure wants his shadow to be 3 feet long, Then he should move to right for 11/3 feet distance.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In this problem Triangle ADF is similar to Triangle

by AA Similarity Theorem

15/6=(10+ED)/ED

Apply cross multiplication

15ED=6(10+ED)

15ED=60+6ED

Subtract 6 ED from both sides

9ED=60

ED=60/9

ED=20/3 ft.

ED is the length

He should move to the right x feet

x=20/3-3

x=11/3 feet

Hence, he should move to right for 11/3 feet distance.

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Answer:

Cannot simplify the fractions further than that

Step-by-step explanation:

The fractions 5/8 and 3/10 have already been simplified so they do not need to be simplified anymore. If you are wanting to put them in decimal form then that is different. All you have to do is plug it in the calculator.

Answer:

70 gallons

Step-by-step explanation:

x gallon of 50%

x * 0.5 + 70 * 0.3 = (x + 70) * 0.4

0.5x + 21 = 0.4x + 28

0.1x = 7

x = 70

To get a mixture that is 40% antifreeze, we need to mix 70 gallons of 30% antifreeze solution with 40 gallons of 50% antifreeze solution. This conclusion is reached by establishing an equation representing the total amount of antifreeze in the mixture before and after and then solving for the unknown.

Your question deals with the concept of a weight ratio in a chemical mixture. Specifically, we're going to solve it using algebra. Let's say you need x gallons of the 50% antifreeze solution. We can work this out by forming an equation based on the information given in the problem:

The total amount of antifreeze in the 70 gallons of 30% solution and x gallons of 50% solution must be equal to the total amount of antifreeze in the (70 + x) gallons of 40% solution.

Therefore, we can write: 0.3 * 70 + 0.5 * x = 0.4 * (70 + x)

Solving the equation above, we find that x equals 40 gallons. So, you would need to mix 40 gallons of a 50% antifreeze solution with 70 gallons of 30% solution to obtain a final solution with a 40% antifreeze concentration.

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49 pieces of string can be cut from a ball of string that has 100 feet

Solution:

Given that, Carle is cutting pieces of string that are exactly 24 3/8 inches long

Therefore,

[tex]Length\ of\ each\ string = 24\frac{3}{8}\ inches = \frac{8 \times 24 + 3}{8} = \frac{195}{8}\ inches[/tex]

How many pieces can she cut from a ball of string that has 100 feet

Total length of string = 100 feet

Convert feet to inches

1 feet = 12 inch

100 feet = 1200 inch

Therefore, number of pieces that can be cut is given as:

[tex]\text{Number of pieces } = \frac{\text{total length of string}}{\text{length of each string}}[/tex]

Substituting the values we get,

[tex]\text{Number of pieces } = \frac{1200}{\frac{195}{8}}\\\\\text{Number of pieces } = 1200 \times \frac{8}{195}\\\\\text{Number of pieces } = 49.2307 \approx 49[/tex]

Therefore, 49 pieces of string can be cut from a ball of string that has 100 feet

Answer:

beggining poit:3   second point (potentially):  1,5

Step-by-step explanation:

in the y intercept 3 is it so which ever has a 3 as the starting point there could be an option

for the 2x part that is the slope otherwise known as rise over run so what you do is that you turn it to a fraction over or under 1 meaning you rise for 2 and go to the right 1

rise 2

      _

run  1

in order to rise 2 you go up 2 from the y intercept(3) and in order to run you go right since its a positive

once you plot those two dots then you draw a line across

Option B: [tex]11,304 \mathrm{mm} ^2[/tex] is the area of the compact disc.

Explanation:

The diameter of the compact disc is [tex]120mm[/tex].

To determine the area of the compact disc, let us substitute the values in the area of the circle formula,

[tex]A=\pi r^2[/tex] where [tex]r=\frac{d}{2}[/tex]

Substituting the value of d in [tex]r=\frac{d}{2}[/tex], we get,

[tex]r=\frac{120}{2} =60[/tex]

Thus, [tex]r=60[/tex] and [tex]\pi=3.14[/tex]. Let us substitute these values in [tex]A=\pi r^2[/tex], we get,

[tex]A=3.14\times(60)^2[/tex]

Simplifying, we have,

[tex]A=3.14\times3600[/tex]

Multiplying, we get,

[tex]A=11304mm^2[/tex]

Thus, the area of the compact disc is [tex]11,304 \mathrm{mm} ^2[/tex]

Hence, Option B is the correct answer.

Answer:

[tex]Area=\frac{5}{12}x^2[/tex]

Step-by-step explanation:

The area of a triangle is given by:

[tex]Area=\frac{1}{2}*base*height[/tex]

From the diagram [tex]base=\frac{5}{6}x,and,height=x[/tex]

We substitute into the formula to get:

[tex]Area=\frac{1}{2}*\frac{5}{6}x*x[/tex]

This implies that:

[tex]Area=\frac{5}{12}x^2[/tex]

Answer:

70

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Answer:

[tex](x^4)^2=x^8[/tex]

Step-by-step explanation:

Because of the power of a power property, which states that [tex](x^n)^m=x^{n\times{m}}[/tex], where m and n are real numbers, the expression you mentioned can be simplified by applying this property like this: [tex](x^4)^2=x^{4\times2}=x^8[/tex]

Answer: 38.47cmsqr

Step-by-step explanation:

The final answer will be rounding it up to $619.

Step-by-step explanation:

4% = 0.04

1 represents 100%

therefore,

(( 1 + 0.04)^3)x 550

= (1.04^3) x 550

= 1.124864 x 550

= $618.6752

The final answer will be rounding it up to $619.

Step-by-step explanation:

[tex] \because \: ( {a}^{m} )^{n} = {a}^{m \times n} \\ \\ \therefore ( {9}^{3} )^{3} = {9}^{3 \times 3} = {9}^{9} \\ [/tex]

64 inches

Step-by-step explanation:

12 inches equals 1 foot so

12*5=60 inches which means it will be bigger than 5 feet.

Answer:

2)  m∠CBD = 60         3) x=15; 95 and 85     4) 12 = x; 98 for both angles

Step-by-step explanation:

2)  2x + 14 + x + 7 = 90       The angles add up to 90 degrees

    3x + 21 = 90                   Combine like terms

          - 21  - 21                    Subtract 21 from both sides

    3x = 69                           Divide both sides by 3

     x = 23

Plug 23 in the equation

2(23) + 14

46 + 14

60

3)  2x + 65 + 3x + 40 = 180       The angles add up to 180 degrees

    5x + 105 = 180                      Combine like terms

          - 105  - 105                      Subtract 105 from both sides

5x = 75                                       Divide both sides by 5

x = 15

Plug in 15 into both equations

2(15) + 65 = 95

3(15) + 40 = 85

4) 5x + 38 = 9x - 10

  - 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 in 12 into both equations

5(12) + 38 = 98

9(12) - 10 = 98

Answer: 49 books

Step-by-step explanation:

Number of books read  by Manuel this year  = 35

Increment in reading rate                                 = 40%

Therefore, we now find 40% of 35 and add it to 35 to know the number of books he had read

Number of books read                                    = 40% of 35

                                                                          = 40/100 x 35

                                                                          = 14 books

Total number of books read                            = 35 + 14

                                                                          = 49 books

Answer:

Step-by-step explanation:

50

Answer:

when [tex]f(x) = 5[/tex], then [tex]x=0[/tex]

Step-by-step explanation:

Considering the expression

[tex]f(x) = 5[/tex]

Rewrite the function as an equation

[tex]y = 5[/tex]

Comparing with slop-intercept form

[tex]y=mx+b[/tex]

So,

[tex]m=0[/tex]

[tex]\mathrm{Axis\:interception\:points\:of}\:5:\quad \mathrm{Y\:Intercepts}:\:\left(0,\:5\right)[/tex]

Therefore, when [tex]f(x) = 5[/tex], then [tex]x=0[/tex]

The graph for  [tex]f(x) = 5[/tex] is also attached below.

Keywords: graph, function

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Answer:

80

Step-by-step explanation:

First recall that:

1 inch=12 feet

The volume of cube-shaped boxes with 12-inch edges is 1 cm³

The volume of a box that is 4

feet tall, 4 feet long, and 5 feet wide is

given by:

[tex]Volume = lwh[/tex]

We substitute l=4ft, w=5ft and h=4ft

To obtain:

[tex]Volume = 4 \times 4 \times 5 = 80 {ft}^{3} [/tex]

Therefore 80 cube-shaped boxes with 12-inch edges can fit into a box that is 4

feet tall, 4 feet long, and 5 feet wide.

Answer:

3

Step-by-step explanation:

n^9/ n^6  = 27

n^9 - 6 = 27

n^3 = 27

n = ∛27

n = 3

Answer:

Pythagoras’ theorem  is a way to find a side or hypothesis when you have 2 sides.  

The formula is:  a^2 + b^2 = c^2

a and b are sides

c is the hypothesis

Ex:  A triangle has a leg that is 5 inches and a leg that is 7 inches.  Find the hypothesis using Pythagoras' theorem.  

A leg is another way of saying a side.

5^2 + 7^2 = c^2

25 + 49 = x^2

sqrt(74) = sqrt(x^2)

sqrt(74) inches = hypothesis

Ex:  A triangle has a leg that is 9 feet and a hypothesis that is 25 feet.  Find the other leg using Pythagoras' theorem.

9^2 + b^2 = 25^2

81 + b^2 - 81 = 625 - 81

sqrt(b^2) = sqrt(544)

b = sqrt(554)

Do you understand more?

The investment will be worth $4686.62 after 5 years.

Step-by-step explanation:

Principal, P = 3700

Rate, r = 4.75% = 0.0475

Number of years, t = 5 years

Number of times compounded, n = 5 times

Amount = P(1 + r/n)^nt

⇒ 3700 (1 + 0.0475/5)^25

⇒ 3700 (5.0475/5)^25

⇒ 3700 (1.0095)^25

⇒ 4686.62

∴ Amount = $4686.62

Answer:

Step-by-step explanation:

as the temp t increases the number of cricket chirps also increases.

1: The complete table is according to the given function :

t  :    40   50   60   70   80   90   100

c :     10   50   90  130  170  210  250

2: It means when the temperature is 60 Fahrenheit then the number of cricket chirps is 90 per minute.

The given function is,

c = 4t - 180

Here t represents the temperature

c represents the cricket chirps per minutes

Now plug in each temperature value and solve for c:

When t = 40:

c = 4(40) - 150

c = 160 - 150

c = 10

When t = 50:

c = 4(50) - 150

c = 200 - 150

c = 50

When t = 60:

c = 4(60) - 150

c = 240 - 150

c = 90

When t = 70:

c = 4(70) - 150

c = 280 - 150

c = 130

When t = 80:

c = 4(80) - 150

c = 320 - 150

c = 170

When t = 90:

c = 4(90) - 150

c = 360 - 150

c = 210

When t = 100:

c = 4(100) - 150

c = 400 - 150

c = 250

Therefore, the complete table is:

t  :    40   50   60   70   80   90   100

c :     10   50   90  130  170  210  250

When the value of t is 60, the value of c is 90.

It means when the temperature is 60 Fahrenheit then the number of cricket chirps is 90 per minute.

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9514 1404 393

Answer:

  A. They form a linear pair.

  B. They are supplementary.

Step-by-step explanation:

An interior angle and its adjacent exterior angle of a polygon are a linear pair. The angles of any linear pair are supplementary.

If he drives 125 miles in 2 1/2 hours, he will drive 125 ÷ 2 1/2 miles per hour.

125 ÷ 2 1/2 = 50 miles

answer: 50 miles per hour

The answer is a. -9, -4, 5, 6.

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

Answer:

Option A:  -9, -4, 5, 6

Step-by-step explanation:

Since the lowest number is -9, it should go first

Since the 2nd lowest number is -4, it should go second

Since the 3rd lowest number is 5, it should go third

Since the 4th lowest number is 6, it should go fourth

Answer:  Option A,  -9, -4, 5, 6

Answer:2,160

Step-by-step explanation:Multiply 20,000 by the percent then multiply the number you get by 3