A solid right prism $ABCDEF$ has a height of $16,$ as shown. Also, its bases are equilateral triangles with side length $12.$ Points $X,$ $Y,$ and $Z$ are the midpoints of edges $AC,$ $BC,$ and $DC,$ respectively. A part of the prism above is sliced off with a straight cut through points $X,$ $Y,$ and $Z.$ Determine the surface area of solid $CXYZ,$ the part that was sliced off.

11 students could sell 1870 cookies.

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.

Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.

An expression is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in certain ways. Language phrases can comprise actions on their own, but they do not make up complete sentences.

=  10 X 17

=  170 X 11

= 1870

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There were 64 calls that Anna answered in this algebra question,

What is Answered calls?

Total engaged calls, another name for answered calls, is a measurement of all incoming calls that were handled by an agent during regular business hours.

Solution:

If Ana answers more calls than Darryl does, then let D be the number of calls Darryl Answered.

A + D = 80

A = 4D

4D + D = 80

5D = 80

D = 80 / 5

    = 16

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According to the algebra, Ana answered 16 calls,

The area of mathematics known as algebra is used to represent situations or problems using mathematical expressions. In algebra, we use numbers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine numbers with variables like x, y, and z.

Solution:

Let D be the number of calls Darryl answered if Ana answers more calls than he does.

A + D = 80

A = 4D

4D + D = 80

5D = 80

D = 80 / 5

   = 16

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Answer:

[tex]volume = \frac{1}{3} \pi {r}^{2} h \\ = \frac{1}{3} \times 3.14 \times {(14.3)}^{2} \times 3.9 \\ = 834.73 \: cubic \: in[/tex]

Answer:835.2

Step-by-step explanation:

Answer:

3.1354776 m2

Step-by-step explanation:

Answer: 33.75

Step-by-step explanation:

5 times 3 is 15 and 15 times 2 1/4 is 33.75

The true statement is 6 less than 10

From the question, we have the following parameters that can be used in our computation:

(-2) (-3) less greater than equal than 8- (-2)

We start by evaluating each expression

So, we have the following representation

(-2) (-3) = 6

8- (-2) = 10

Substitute the known values in the above equation, so, we have the following representation

6 less greater than equal than 10

6 is less than 10

So, we have

6 less than 10

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Answer: 495 people

Step-by-step explanation:

As this involves the population in a future year, you can use the future value model for this:

= Population * ( 1 + rate of increase) ^ number of years

Number of years = 2020 - 2011

= 9 years

Rate of increase will be negative to show that it is a decrease.

= 567 * ( 1 - 1.5%) ⁹

= 494.9

= 495 people

An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.

a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.

A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."

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Answer:

X=8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

17x−30+7x+18=180

17x+−30+7x+18=180

(17x+7x)+(−30+18)=180(Combine Like Terms)

24x+−12=180

24x−12=180

Step 2: Add 12 to both sides.

24x−12+12=180+12

24x=192

Step 3: Divide both sides by 24.

X=8

Answer:

184cm

Step-by-step explanation:

to find the area of the triandles

4 times (half of 6 ) 3 = 12 divided by 2 = 6 + 6 ( because there are two right triangles making up one side ) so one side is 12cm add the other side 12 +12 = 24cm

To find the left and right sides mutipy length times width 10 x 5 = 50 add the oher side 50 + 50 = 100

To fide the bottom rectangle do the same thing but 10 x 6 = 60

so add everything together 24+100+60 = 184cm

Answer:

x+7

Step-by-step explanation:

Remove Parentheses

Collect like terms

Calculate

Answer: x+7

Step-by-step explanation: distribute the -2 first

3x - 2x + 8 - 1

simplify (combine like terms )

3x-2x= x

8-1= 7

x+7  

Hope this helps (^_^)

Answer:

3x-2y+2z

Step-by-step explanation:

Answer:

28 ft

Step-by-step explanation:

112 ft / 4 sides (since it is a square background)

112/4 = 28 ft/side length.

Answer:

x = 15

y = -26

Step-by-step explanation:

x + y = -11

x - y = 41

let x = 41 + y

substitute:

41 + y + y = -11

2y = -52

y = -26

x -26 = -11

x = 15

The Trigonometric inequality Sec (x)< cot(x) will hold true in π/2 < x < π.

How can a trigonometric inequality be expressed?

The intervals where the trigonometric inequality sec (x) cot (x) always holds true are what we are looking for.

This can also be expressed as: 1/cos (x) < 1/tan (x)

Now, this is only possible in the fourth quadrant, where cos x is positive and tan (x) is negative, where: π/2 < x < π.

The values for sin, cos, and tan are all positive in the first quadrant.

Only positive values for sin are present in the second quadrant.

The tan values in the third quadrant are all positive.

Only positive values for cos are present in the fourth quadrant.

Therefore the inequality Sec(x) < cot(x) will hold true in π/2 < x < π.

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Answer:

C = 18π m

Step-by-step explanation:

The circumference (C) of the circle is calculated as

C = 2πr ( r is the radius ) , then

C = 2π × 9 = 18π

Answer:

36°, 72°, and 72°

Step-by-step explanation:

The interior angles of a triangle will always add to 180°.

Let's say the smallest angle is x, then the other two angles are both 2x.

x+2x+2x=180

5x=180

x=36

If our angles are x, 2x, and 2x, and we know x is 36, then the answer is:

36°, (2*36)°, and (2*36)°, which equals

36°, 72°, and 72°

Check: 36+72+72=180

To determine if three measures can make a triangle, use the Triangle Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side.

for example

side 1 = 6

side 2 = 8

side 3 = 10

6 + 8 = 14 > 10,

therefore the three sides can make a triangle.

1. Gather the three measures of the triangle.

2. Add the two smallest side lengths together.

3. Compare the sum of the two smallest sides to the longest side.

4. If the sum of the two smallest sides is greater than the longest side, then the three measures can make a triangle.

5. If the sum of the two smallest sides is not greater than the longest side, then the three measures cannot make a triangle.

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Answer:

x > - 3

Step-by-step explanation:

x + 2[tex]\frac{1}{2}[/tex] > - [tex]\frac{1}{2}[/tex]      First turn 2[tex]\frac{1}{2}[/tex] into an fraction since its easier. So it becomes [tex]\frac{5}{2}[/tex]

x + [tex]\frac{5}{2}[/tex] > - [tex]\frac{1}{2}[/tex]

  - [tex]\frac{5}{2}[/tex]     - [tex]\frac{5}{2}[/tex]         Do inverse operations, so subtract [tex]\frac{5}{2}[/tex] from both sides.

    x > - [tex]\frac{6}{2}[/tex]          Combine  - [tex]\frac{5}{2}[/tex] with - [tex]\frac{1}{2}[/tex], which gives us - [tex]\frac{6}{2}[/tex]

    x > - 3          Since we know that 6 divided by 2 is 3.

This would not allow me to attach an image so I am going to type a visual representation f what the graph would look like below)

<-------------O--------------------------------------------------->

-5    -4     -3      -2       -1     0     1     2    3    4     5

So, the number line would be a solid line rather than dashed (but I was not able to attach an image so I kind of had to improvise). When using ≥ ≤ sings the circle of the point is closed. When using < and > signs, the circle of the point is open. Thus, in this scenario since he sign is >, then the circle of the point is open. The direction of the arrow and ray for this equality is going to the right because the answer is that x is greater than - 3, Therefore any values greater than - 3 are a possibility which is why the arrow goes on indefinitely.

Answer:

The value of x is 2/7 or 0.285

Step-by-step explanation:

Here, we will make equivalent expressions in the equation that all have equal bases.

6²⁽⁶ˣ⁻¹⁾ = 6⁵ˣ

Since, The bases are the same i.e., 6. So, exponent are also same

2(6x - 1) = 5x

Solve for x

12x - 2 = 5x

12x - 5x - 2 + 2 = 5x - 5x + 2

7x = 2

7x/7 = 2/7

x = 2/7 = 0.285

Thus, The value of x is 2/7 or 0.285

For verification

36⁶ˣ⁻¹ = 6⁵ˣ

36⁶⁽⁰°²⁸⁵⁾ ⁻ ¹ = 6⁵⁽⁰°²⁸⁵⁾

36¹°⁷¹ ⁻ ¹ = 6¹°⁴²⁵

36⁰°⁷¹ = 6¹°⁴²⁵

12.7 = 12.7

Hence, L.H.S = R.H.S

VERIFIED!!

Answer:

4/8

Step-by-step explanation:

Answer:

B. 10°, 10°, 160°

Step-by-step explanation:

The rule with triangles is that the angles combined may only ever add to 180°

So, lets add to be sure.

A. 90° + 45° + 46° = 181°

B. 10° + 10° + 160° = 180°

C. 28° + 12° + 120° = 160°

Therefore, option B

Answer:

33 degrees

Step-by-step explanation:
Angle 1 and 2 add up to a right angle which is 90 degrees. To find 2, subtract 57 from 90

90-57=33

Therefore 33 degrees is the answer

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Answer:

5/12

Step-by-step explanation:

Add both fractions and divide by 2 to find the one right in between.

3/8+11/24=5/6

then divide by two

(5/6)/2=5/12

=5/12

It is recommended that when an ambulance arrives at an accident scene, it should park a safe distance away from the scene, at least 500 feet away.

This is to ensure the safety of the paramedics and other emergency responders, as well as to ensure that the ambulance does not impede the movement of other emergency vehicles. Additionally, it is also to protect the privacy of the individuals involved in the accident and ensure that the scene is not tampered with.

It is also important to follow any additional instructions given by the police or fire department at the scene, as they may have specific parking instructions based on the situation.

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Answer:

54

Step-by-step explanation:

6x + 5x = 99

11x = 99

x=99/11

x=9

6x = 6x9 = 54

5x = 5x9 = 45

ans: 54

Answer:

[tex](x+5)^2+(y-6)^2=41[/tex]

Step-by-step explanation:

Hi there!

Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at [tex](h,k)[/tex] and r is the radius

1) Plug in the center (-5,6)

[tex](x-(-5))^2+(y-6)^2=r^2\\(x+5)^2+(y-6)^2=r^2[/tex]

2) Plug in the given point (-1,1) and solve for r²

[tex](-1+5)^2+(1-6)^2=r^2\\(4)^2+(-5)^2=r^2\\16+25=r^2\\41=r^2[/tex]

Therefore, r² is 41. Plug this back into [tex](x+5)^2+(y-6)^2=r^2[/tex]:

[tex](x+5)^2+(y-6)^2=41[/tex]

I hope this helps!

Answer:

Step-by-step explanation:

7,80

The corresponding element in the range when 7 is an element  in the domain is f(7)=33

Step-by-step explanation:

Given that the 7 is an element in the domain of f(x)

The function f is defined by f(x)=6x-18/2

To find the corresponding element in the range:

That is put x=7 in the given function f(x)

Therefore f(x) becomes

f(7) = 6(7)-18/2

      =42-18/2

      =42-9

      =33

Therefore corresponding element in the range when 7 is an element  in the domain is f(7)=33

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Answer:

y=-2/3x+4

Step-by-step explanation:

slope intercept form = y=mx+b

y=-2/3x+4