Choose the system of equations that best represents the situation below:
The sum of two numbers is 25 choose the system that best represents the situation below and their difference is 7. Find the two numbers.
A. x + y = 18

B.x + y = 25
2 + y = 7

C. x - y = 25
2 - y = 7

D. x+y= 25
x - y = 7

Answer:

base= 9 ft

height= 36 ft

Step-by-step explanation:

Area of triangle= ½ ×base ×height

Let the base and the height of the triangle be b and h ft respectively.

162= ½ ×b ×h

Given that h= 4b,

162= ½ ×b ×4b

162= ½(4b²)

162= 2b²

Divide both sides by 2:

b²= 81

Square root both sides:

b= 9

h= 4b

h= 4(9)

h= 36

Thus, the lengths of the base and height are 9 and 36 ft respectively.

Answer:

27.8 nearest tenth pints

To find, divide the value by 16

[tex](a+b)^3 -(a-b)^3\\\\=(a+b-a+b)[(a+b)^2 + (a+b)(a-b) +(a-b)^2]\\\\=2b(a^2+b^2+2ab+a^2-b^2 +a^2 +b^2 -2ab)\\\\=2b(3a^2+b^2)[/tex]

Answer:

Step-by-step explanation:

(a + b)³ - (a - b)³ = a³ + 3a²b + 3ab² + b³ - [a³ - 3a²b + 3ab² -b³]

                         = a³ + 3a²b + 3ab² + b³ - a³  + 3a²b - 3ab² + b³

                         = a³ - a³  + 3a²b + 3a²b  + 3ab² - 3ab² + b³ + b³

Here, the underlined terms will be cancelled.

                         = 6a²b + 2b³

                        = 2 * 3 *a²*b  + 2*b³

                        = 2b* (3a² + b²)

Prime

Hope it helps.

Do comment if you have any query.

Answer:

prime

Step-by-step explanation:

I tried to delete my answer

Answer:

check the attachment and explanation below

Step-by-step explanation:

Explanation for statement 3 :

Suppose The number of shoppers on Saturday is 100 and the number of shoppers on Sunday is 200

Total number of shoppers = 300

On Saturday :

Q₃ = 70 then 25% of shoppers spent more then $70

then 25 shopper spent more then $70

On Sunday:

M’ = 70 then 50% of shoppers spent more then $70

then 100 shopper spent more then $70

On both days:

(100+ 25) shopper spent more then $70

Then 125 shopper spent more then $70

But 125 is not 75% of 100+200=300

Answer:

The base is a triangle with a base length of 11 m and a corresponding height of 7 m. The height of the prism is 14 m. 12.

Answer: the person above is wrong

Step-by-step explanation: Some ratios are not fractions.

and All fractions are ratios

Answer:

Multiply the grade on the assignment by the grade weight. In the example, 85 times 20 percent equals 17, and 100 times 80 percent equals 80.

Step-by-step explanation:

Answer:

2/15

Step-by-step explanation:

3/9*2/5=

1/3*2/5=

2/15

Answer:

answer is 4

have a nice day

The solution to maria’s equation [tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex] by using the properties of the logarithm is 5/4.

A logarithm is the exponentiation inverse function that can be expressed by the exponent or power to which a base must be raised to yield a number.

It is given that

[tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex]

Using properties of a logarithm, we get

[tex]\rm log x + log y=logxy[/tex]

[tex]\rm log[\frac{x}{2} \times\frac{20}{x^{2} }] = log8\\\rm log[\frac{10}{x}] = log8[/tex]

on comparing

10/x = 8

x = 10/8

x = 5/4

Hence, the solution to maria’s equation [tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex] is 5/4.

Learn more about logarithm;

https://brainly.com/question/20785664

Answer:

C

Step-by-step explanation:

C) 5/4

Answer:

Below in bold.

Step-by-step explanation:

Radius of the pizza = 1/2 * 8 = 4 in.

Area of the whole pizza = π r^2

=  π * 4^2

= 8 π

So if you take 1/8 away

the area left = 7/8 * 8 * π

= 7π

Taking π to be 22/7:

= 7 * 22/7

= approximately 22 in^2.

Solution:

D. y = –0.5x + 5

In this chart, the slope, (m):

[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\hookrightarrow \sf \frac{-6-0}{-2-0}[/tex]

[tex]\hookrightarrow \sf \frac{-6}{-2}[/tex]

[tex]\hookrightarrow \sf 3[/tex]

Equation:

[tex]\sf y_1-y= m(x_1-x)[/tex]

[tex]\hookrightarrow \sf y-(-6)= 3(x-(-2))[/tex]

[tex]\hookrightarrow \sf y+6= 3x+6[/tex]

[tex]\hookrightarrow \sf y+6-6= 3x+6-6[/tex]

[tex]\hookrightarrow \sf y= 3x[/tex]  

⇒ Thus we found in the chart, the slope is 3 and y-intercept : 0

From this D only has the greatest y-intercept than the chart.

Answer:

D

Step-by-step explanation:

Sorry if I'm late for the party, hope this helps anyways! :)

Answer:

y = 2x - 4

Step-by-step explanation:

y = ax + b

a = slope

b = y-int

so, in y = 2x - 4

a = slope = 2

b = y-int = -4

Answer:

n=9M, when m is 6,n=18

Step-by-step explanation:

If n is proportional to M

n=kM

27=3k

k=27/3

k=9

the formula on terms of n and M is

n= 9M

2) If m= 6,

n= 3M

n=3(6)

n=18

Answer:

n = 108

Step-by-step explanation:

given n is proportional to m² then the equation relating them is

n = km² ← k is the constant of proportion

to find k use the condition n = 27 when m = 3 , then

27 = k × 3² = 9k ( divide both sides by 9 )

3 = k

n = 3m² ← equation of proportion

when m = 6 , then

n = 3 × 6² = 3 × 36 = 108

Answer:

Step-by-step explanation:

given that a bag contains 6 balls labelled A to F.

Given that a ball is drawn at random and its letter is recorded as outcome.

Since each ball is equally likely to be drawn the sample space for one ball drawing is

S = {A,B,C,D,E,F} and n(S) = 6

Let G be the event of choosing a lable from D to F

G = The event of choosing a label from D to F= {D,E,F}  n(A) = 3

A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.

i.e. the sample space while flipping a coin is: {H,T}

The sample space while tossing a six-sided die is: {1,2,3,4,5,6}

Here it is given that:

A bag has six balls labeled:  A,B,C,D,E,F

One ball will be randomly picked, and its letter will be recorded as the outcome.

       This means that the sample space is given by:

                     Sample space={ A,B,C,D,E,F}

Now, when the event is choosing a letter from   D to F.

            Then the sample space is:

                     Sample space= {D,E,F}

Answer: It is the third to the top

Step-by-step explanation:

90's block each other out add you rotate it 180 degrees you get this.  

Answer:

C.

Step-by-step explanation:

Answer:

v > - 78

Step-by-step explanation:

Version 1.

   v

-----------  < 92

-6 + 79

    v

------------  <  92

    73

    v

------------  <  92(73)

    73(73)

v < 6716

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

Version 2

    v

------------ + 79 <  92

    -6       -79      -79

        v

(-) ------------  <  13(6)

        6(6)

-v < 78

÷-1   ÷-1

v > -78

I hope this helps!

Answer:

Step-by-step explanation:

(1 , -2)   x₁ =1 & y₁ = -2

(-3,10)  x₂= -3 & y₂ = 10

First we need to find the slope.

[tex]\boxed{Slope = $\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}[/tex][tex]\boxed{Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]

          [tex]=\dfrac{10-[-2]}{-3-1}\\\\\\=\dfrac{10+2}{-4}\\\\\\=\dfrac{12}{-4}\\\\\\= - 3[/tex]

m = -3

Equation of the line: y = mx + b

y = -3x + b

To find the value of b, take one of the point and substitue in the above equaiton.

(1 , -2)

-2 = -3*1 + b

-2 = -3 + b

-2 + 3 = b

b = 1

Equation of the line:

y = -3x + 1

Using the Newton's law of cooling, the time it takes to cool to 100°F is 116 mins.

According to the Newton's law of cooling, the when an object is exposed to the surrounding it looses heat rapidly untill it is at a thermal equilibrium with the suurroundings.

Now;

T(t) = T(s) + (To - Ts)e^-kt

T(t) = temperature at time T

To = initial temperature

Ts = temperature of the surrounding

k = colling constant

t = time taken

200 = 68 + (230 - 68)e^-15k

200 = 68 + 162e^-15k

200 - 68/162 = e^-15k

ln(0.815) = -15k

k = ln(0.815)/-15

k = 0.014 min-1

Now;

100 = 68 + (230 - 68)e^-( 0.014t)

100 -68/162 = e^-( 0.014t)

0.198 =e^-( 0.014t)

ln(0.198) = -( 0.014t)

t = ln(0.198)/-0.014

t = 116 mins

Learn more about newtons law of cooling: https://brainly.com/question/14643865:

Answer:

15.

Step-by-step explanation:

1) property:

m(∠B)+m(∠D)=180°;

2) according to the property:

3x+9x=180°; ⇒ x=15°

The value of x is 15 degree in the trapezoid ABCD.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles

A trapezoid is a quadrilateral with one pair of opposite sides parallel.

ABCD is a trapezoid.

We have to find the value of x in the given quadrilateral.

The sum of opposite angles of a quadrilateral is 180 degrees.

m(∠B)+m(∠D)=180°

From the figure m(∠B) is 3x and m(∠D) is 9x

3x+9x=180°

Combine the like terms

12x=180

x=15 degrees.

Hence, the value of x is 15 degree in the trapezoid ABCD.

To learn more on Quadrilateral click:

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#SPJ5

Answer:

option c 16x²+24x+9

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Answer:✨Samantha✨

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

8+4=12

12-6=6

Answer:

given :-

for rectangular part: length=12in, breadth=8in

for triangular part:base=8in, height=3in

area of the given fig:

area of the given fig:area of 2 triangles +area of rectangle

[tex]→2( \frac{1}{2} \times b \times h) + l \times b \\ →2( \frac{1}{2} \times 8 \times 3) + 12 \times 8 \\ →24 + 96 \\ → {120in}^{2} [/tex]