Area if this figure

Answer:

simultaneous equations

Step-by-step explanation:

phils age =7x

Peter age=x

scenario 2

phils age = 4(7x)

Peter age= 2x-2

[tex]7x + x = 4(7x) + 2x - 2[/tex]

Answer:

x = 7/2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj side / hypotenuse

cos 45 = x / 7 sqrt(2) /2

7 sqrt(2)/2 cos 45 = x

7 sqrt(2)/2 (1/ sqrt(2))= x

7/2 = x

Answer:

sin^2 A

Step-by-step explanation:

first expand the trigonometry

1(1-cosA)+cosA(1-cosA)

=1-cosA+cosA-cos^2 A

= 1-cos^2 A

from trigonometric identity sin^2 A + cos^2 A= 1

sin^2 A= 1- cos^2 A

=sin^2 A

Answer:

total surface area  = 298.45105 m2

lateral surface area = 141.37155 m2

top surface area = 78.53975 m2

bottom surface area = 78.53975 m2

Step-by-step explanation:

Joanna will need approximately 298.3 square inches of frosting to cover the entire cake.

To calculate the amount of frosting Joanna will need for the entire cake, we first need to find the surface area of the cylindrical cake.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr² + 2πrh

Where r is the radius of the base and h is the height of the cylinder.

Given that the diameter of the cake is 10 inches, we can find the radius by dividing it by 2: r = 10/2 = 5 inches.

Plugging in the values, we have:

Surface Area = 2π(5)² + 2π(5)(4.5)

Simplifying the equation:

Surface Area = 2π(25) + 2π(22.5)

Surface Area = 50π + 45π

Surface Area = 95π

To find the actual numerical value, we can approximate π as 3.14:

Surface Area ≈ 95 * 3.14

Surface Area ≈ 298.3 square inches

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Answer:

D

Step-by-step explanation:

R: (50, 450)

Answer:

D

The R (range) is: (50, 450)

Answer= decreasing annual profit in the business

are $13200.

Answer:

[tex]P = 44,000(.97)^{t}[/tex]

P=Profit

t=years

Step-by-step explanation:

[tex]P = 44,000(.97)^{t}[/tex]

P=Profit

t=years

Answer:

7.5 Imperial Gallons = 30 Imperial Quarts

Hi there!  

»»————-　★　————-««

I believe your answer is:  

30 qt.

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

7.5 * 4 = 30

7.5 gal. = 30 qt.

⸻⸻⸻⸻

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Hope this helps you. I apologize if it’s incorrect.  

i think it 10 because the angle your looking at is x is 7

Answer:

ax + b + y^2 + 2yx + x^2

Step-by-step explanation:

(y+x)^2

= (y+x)(y+x)

= y^2 + 2yx + x^2

y^2 + 2yx + x^2 + (ax+b)

= ax + b + y^2 + 2yx + x^2

Answer:

2*sqrt(5)

Step-by-step explanation:

By using Pythagoras theorem, we have

4^2+2^2=(the third side)^2

16+4=(the third side)^2

Third side=sqrt(20)=2*sqrt(5)

real numbers, integers, rational numbers

=========================================================

Explanation:

So far in your studies, every number is a real number. This is assuming your teacher hasn't introduced complex or imaginary numbers yet.

So that's why -12 is a real number.

Choice A is one of the answers

---------------

The set of whole numbers is {0,1,2,3,4,...} so we aren't including negative values here, which rules out choice B. However, the set of integers does include negative values

{..., -3, -2, -1, 0, 1, 2, 3, ...}

That makes -12 an integer

Choice C is one of the answers

----------------

The value -12 is not irrational because we can write it as a fraction of two integers. Eg: -12 = -12/1

This shows that -12 is rational and why choice F is one of the answers and allows us to rule out choice D.

------------------

We can rule out choice E because the set of natural numbers is {1,2,3,4,...} basically the set of whole numbers but we kicked out 0.

The requried, -12  is an element of sets of real numbers, integers, and rational numbers. Options A, C, and F are correct.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

Here,

Only sets that consist of negative values are, real numbers, integers, and rational numbers.

So - 12 is a negative number that belongs to the set of real numbers, integers, and rational numbers.

Thus, the requried, -12  is an element of sets of real numbers, integers, and rational numbers. Options A, C, and F are correct.

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Refer to the attachment

Answer:

It is not because the half the perimeter is not only one side but another half side of the triangle, and the distence between two points in a triangle can never become longer then the length of one side.

Step-by-step explanation:

The math part I am unsure of because you did say prove but let me know if this helps. Thanks!

Answer:

y - 5 = -1/6 (x - 4)

Step-by-step explanation:

y = 6x - 1          y = -1/6x + b

y - 5 = -1/6 (x - 4)

Answer:  Choice B

1 & 3/4

=============================================

Explanation:

Rewrite 1/2 into 4/8 so that it has the same denominator as 7/8.

Now that the denominators are the same, we focus on the numerators. This is because the equal denominators cancel out when we divide the fractions later on.

We'll divide the numerators 7 and 4 to get

7/4 = (4+3)/4

7/4 = (4/4) + (3/4)

7/4 = 1 + (3/4)

7/4 = 1 & 3/4

Meg can get 1 & 3/4 servings from the jug.

Answer:

13. 1

14. 42

15. 65

Step-by-step explanation:

13.

If the average of two numbers is 1, then the sum of those two numbers is 2. As 2*1 is 2, and the average is found by dividing the sum by the amount of numbers.

Only one number is an integer and has a reciprocal that is an integer, the number being 1.

1/1 = 1

1/1 = 1

Average:

1+1 = 2

2/1 = 1

Therefore the answer is 1.

14.

If we multiply everything by 7x, we'd get

7 + x = 49

subtract 7 on both sides

x = 42

15.

If

pg = 50 and gr = 15

then

pg + gr = 65

factoring that would give you

g(p+r) = 65

I can't see 16 but good luck!

Answer:

In agreement to your twister question, a spinner can randomly select whether they want to put an arm or a leg, meaning this choice is entirely upon them. The color choice is also independent, so spinners are allowed to choose freely, whichever color as well as limb they want to move in the game of twister.

See the attached image for step by step explanation of the final probability

Answer:

x=11

Step-by-step explanation:

5x+7=62

5x=62-7

5x=55

x=11

Answer: there is no picture attached or equation? what's the question?

Step-by-step explanation:

ok, what do you need help with?

the answer to this question is the slope is 43

Answer:

Therefore, the slope is 3/4

Step-by-step explanation:

An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)

Likewise, an

y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)

Now we have two points(4,0) (0,-3)

To find the slope given two points, we use the formula

rise÷run , or y2−y1÷x2−x1 .

Plug in the given points into the formula

-3-0/0-4

-3/-4

3/4

Therefore, the slope is 3/4

Hope this helps!

Answer:

$15 and 3600ft^2

Step-by-step explanation:

C) There are 16 white tiles used. The unit cost of a white tile=240/16=$15

E) The cafeteria area consists of 36 tiles of dimensions 10 ft x 10 ft, so the area of the floor is 3600ft^2

Answer:

Martin family: 20 hours

Lewis family: 35 hours

Step-by-step explanation:

Let's say that the Lewis family sprinklers were out for L hours and the Martin family's sprinklers were out for M hours. We know that for each hour that the Lewis family sprinkler was on, 30L of water was put out. We can thus write the Lewis family sprinkler water output as 30L per each hour of L = 30 * L. Similarly, the Martin family sprinkler water output = 15 * M .

We know that the total hours for the sprinklers is 55, so L + M = 55. The total water output for the sprinklers is the sum of the sprinkler outputs, so 30 * L + 15 * M = 1350

L + M = 55

30 * L + 15 * M = 1350

One way to solve this would be to solve for L in the first equation and substitute that into the second

subtract M from both sides in the second equation

55 - M = L

30 * (55-M) + 15 * M = 1350

30 * 55 - 30 * M + 15 * M = 1350

1650 - 15M = 1350

subtract 1650 from both sides to isolate the M and its coefficient

-15M = -300

divide both sides by -15 to isolate M

M = 20

L = 55-20 = 35

Answer:

think this one

Step-by-step explanation:

the answers there

i think

Answer:

Step-by-step explanation:

a) [tex]t_{n}[/tex] = 2n - 3

[tex]t_{1}=2*1-3 = 2-3=-1\\\\t_{2}=2*2-3=4-3=1\\\\t_{3}=2*3-3=6-3=3\\\\t_{4}=2*4-3=8-3=5\\\\S_{4}=t_{1}+t_{2}+t_{3}+t_{4}\\\\= -1 + 1 + 3 + 5 \\\\= 8[/tex]

d)

[tex]t_{n}=\frac{2n-1}{2n+1}\\\\\\t_{1}=\frac{2-1}{2+1}=\frac{1}{3}\\\\t_{2}=\frac{4-1}{4+1}=\frac{3}{5}\\\\t_{3}=\frac{6-1}{6+1}=\frac{5}{7}\\\\t_{4}=\frac{8-1}{8+1}=\frac{7}{9}\\\\[/tex]

[tex]S_{n}=\frac{n}{2}(a+l)\\\\S_{4}=\frac{4}{2}(\frac{1}{3}+\frac{7}{9})\\\\=2*(\frac{1*3}{3*3}+\frac{7}{9})\\\\=2*(\frac{3}{9}+\frac{7}{9})\\\\=2*\frac{10}{9}\\\\=\frac{20}{9}[/tex]

Answer:

y = -2x +13

Step-by-step explanation:

you know the point is (5,3) and slope is -2

sub into the linear equation y=mx+b

3 = -2(5) +b

rearrange and solve for b

b= 3 + 10

b = 13

Answer:

24.68 gram

Step-by-step explanation:

Given that :

Volume = 182.8 ml

Density of liquid = 0.135 gram/ml

Recall :

Density = mass (g/ml) / volume (ml)

Substitute the value into the equation :

0.135 = mass / 182.8

Mass = 0.135 * 182.8

Mass = 24.678 gram

Hence, weight = 24.678 grams

Answer:

The slope is -3/4 and the y intercept is 5

Step-by-step explanation:

- 3x - 4y= -20

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

Solve for y

Add 3x to each side

- 3x - 4y+3x=3x -20

-4y = 3x-20

Divide by -4

-4y/-4 = 3x/-4  -20/-4

y = -3/4 x+5

The slope is -3/4 and the y intercept is 5

Answer:

Slope: [tex]\displaystyle-\frac{3}{4}[/tex]

Y-intercept: 5

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.

[tex]-3x-4y=-20[/tex]

To find the slope and y-intercept of the given line, rearrange the equation into slope-intercept form. We can do this by isolating y.

Add 3x to both sides:

[tex]-3x-4y+3x=-20+3x\\-4y=3x-20[/tex]

Divide both sides by -4:

[tex]y=\displaystyle -\frac{3}{4} x+5[/tex]

Now, we can identify [tex]\displaystyle-\frac{3}{4}[/tex] to be in place of m, the slope, and 5 to be in place of b, the y-intercept. Here is a comparison:

[tex]y=\displaystyle -\frac{3}{4} x+5[/tex]

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

I hope this helps!

Answer:

I think it is 0.909090909090. Hope this helped.

Step-by-step explanation:

Answer:

Step-by-step explanation: 10 meters/3 meters =x/4.5 meters

Where x = the maximum distance the projector can be placed that can produce an image 4.5 meters high

3x = 10 (4.5)

3x = 45

X= 45/3

X= 15 meters

So, the maximum distance that the projector can be placed from the screen which produces an image 4.5 meters high is 15 meters.

Answer: B

No, because y does not change by 5 every time x changes by 1

Step-by-step explanation:

rate of change is basically slope

if the rate of change of the function of 5, then the slope will be 5/1

The x changes by 1 every time y changes by 4

so the slope of the function is 4