Which could be the first step in simplifying this expression? Check all that apply.

Answer:

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Step-by-step explanation:

C = 2P  .....equation 1

4C + 2P = 20  .....equation 2

Substituting eqn 1 into eqn 2, we have;

4(2P) + 2P = 20

8P + 2P = 20

10P = 20

P = 20/10

Pie, P = $2

Next, we would determine the cost of a cake;

From equation 1;

C = 2P

Substituting the value of "P" we have;

C = 2 * 2

Cake, C = $4

Therefore, we would have the following answers;

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Check:

From equation 2;

4C + 2P = 20

4(4) + 2(2) = 20

16 + 4 = 20

20 = 20

Answer:

6x+20

Step-by-step explanation:

F(x) = 6x+2

f(x+3) means replace x with x+3

F(x+3) = 6(x+3)+2

         = 6x+18+2

         = 6x+20

Answer:

A; F(x+3) = 6x^2 + 20x + 6

Step-by-step explanation:

To find it you just would multiply F(x) onto the other side. So it would look like this:

           F(x+3) = 6x + 2 (x+3)            

          F(x+3) = 6x^2 + 2x + 18x + 6            *combine like terms getting you

           F(x+3) = 6x^2 + 20x + 6    

Hope this helped!!

Answer:

Step-by-step explanation:20

20  130  3  8.12 - 1) 2:2  12-1  21=-11 # 1 - 2 1212 II + 3) 472 I + 3 2(1 - 1) -1 2:2 3(12 - 1) 32 – 23– 3+.

Answer: 0.667

Step-by-step explanation:

6/9 ⇔ Given

2/3 ⇔ Simplify fraction

0.666... (repeating) ⇔ Convert fraction to decimal

0.667 ⇔ Round to 3 decimal (Since 6 is more than 5, thus we need to

               rounding up)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Answer is A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer is C because if swimmer A does 14 laps to start an 3 laps every day after that and on the chart swimmer B does 11 laps to start and 2 laps every day after that you would compare.

on day 3 swimmer B has 17 (shown on chart)

on day 3 swimmer A has 23 (14, 17, 20, 23)

if you would want it to complicate it 14:3 and 11:2

14 ÷ 14 is 1

3 ÷ 14 is .214

11 ÷ 11 is 1

2 ÷ 11 is .181

Answer:

21

Step-by-step explanation:

5×5-4 you replace the z with the 5 then multiply by 5 and subtract by 4

Answer:

21

Step-by-step explanation:

5×5-4 you replace the z with the 5 then multiply by 5 and subtract by 4

Answer:

D

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

7.2 is rounded down to 7, 7.3 is rounded down to 7, 6.9 is rounded up to 7, and 6.8 is rounded up to 7. Then you can add 7+7+7+7 to get an estimation of 28.

Answer:

the constant is the number without an x attaches to it.

Ex:

y = 2x + 9

9 is a constant because it is not attached to any x

y = x^3 + 2x^2 + 10x + 19

19 is a constant because it is not attached to any x

Answer:

only the third answer is right.

Step-by-step explanation:

to solve it, we need to bring everything to the same denominator (the expression below the division line) or eliminate it completely.

how do we do it ? by multiplying everything with the same expression, so that we can eliminate the denominator for every term.

when looking for the best option I see that

(x² + 5x + 6) = (x + 2)×(x + 3)

that is great, because this covers all 3 denominators in our main expression.

so, we multiply everything by ((x+2)×(x+3)) and eliminate the denominators and the corresponding part of our multiplier.

that leaves us with

x×(x+3) + 2 = 5×(x+2)

now we simply simplify the expression

x² + 3x + 2 = 5x + 10

x² - 8x - 8 = 0

a squared equation has typically 2 solutions. and they are defined as

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case

a = 1

b = -8

c = -8

x = (8 ± sqrt(64 + 32)) / 2 = (8 ± sqrt(96))/2 =

= (8 ± sqrt(16×6))/2 = (8 ± 4×sqrt(6))/2 = 4 ± 2×sqrt(6)

x1 = 4 + 2×sqrt(6)

x2 = 4 - 2×sqrt(6)

both solutions are different from -2 or -3, therefore -2 and -3 are not solutions at all, and they cannot be extraneous solutions either for that reason.

and since we have 2 perfectly fine solutions, the answer options work no or only one solutions are wrong too.

Answer: y = 5x

Step by step process: Use the slope form and then substitute in the equation y = mx + b.

Solution :

[tex]$y=x^{3/2}, \ \ y =8, \ \ x=0$[/tex]

[tex]$v=2 \pi \int_0^4 x (8-x^{3/2}) \ dx$[/tex]

 [tex]$= 2\pi \left(\frac{8x^2}{2}-\frac{x^{7/2}}{7/2}\ \left|_0^4[/tex]

 [tex]$=2\pi \left( 4x^2-\frac{2}{7}x^{7/2}\ |_0^4$[/tex]

 [tex]$=2\pi \left( 64-\frac{2}{7} \times 32 \times 4 \right)$[/tex]

  [tex]$=2\pi \left(1-\frac{4}{7} \right) 64$[/tex]

  [tex]$=128 \pi \times \frac{3}{7}$[/tex]

 [tex]$=\frac{384 \pi}{7}$[/tex]

Answer:

Step-by-step explanation:

so just solve this as if it's

-5= 2x+3

and

2x+3 = 7 ( be careful not to switch sides or the arrow switches too)

the the top equation looks like

-8=2x

-8/2 = x

-4 =x

the bottom equation looks like

2x = 4

x = 4/2

x = 2

now put it back together with the arrows in the same direction :) ( we don't have to worry about switching directions of the arrows b/c we didn't switch side,  multiply or divide by a negative, so all good :P)

-4<x<=2

Answer:

360 cm^2

Step-by-step explanation:

Find the area of each face of the triangular prism.

Imagine the triangular prism as its net, it is composed with 2 triangular faces (these are tye bases of the prism) and 3 rectangular faces.

Areas of the 2 triangular bases (they are similar triangles):

1/2 x 8 cm x 6 cm = 24 cm^2

24 x 2 = 48 cm^2

Area of the rectangular face:

8 x 13 = 104 cm^2

Area of another rectangular face:

6 cm x 13 cm = 78 cm^2

Area of another rectangular face:

13 cm x 10 cm = 130 cm^2

Add up all the areas of all faces:

48 + 104 + 78 + 130 = 360

So the SA is 360 cm^2

Answer:

2.65

Step-by-step explanation:

15.00 - 12.35 = 2.65

...I don't really know how do explain it but yeah thats the answer.

Hope it helps c:

Answer:

y = -4x + 29

Step-by-step explanation:

-3 = -4(8) + b

-3 = -32+b

29=b

The equation whose slope is -4 and passes through (8,-3) is y=-4x+29 where slope is -4.

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

We have been given slope of line being -4 and point through which it passes (8,-3) and we have to find the equation of line.

The equation from two points can be calculated through the following formula:

y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]) and slope is m.

Putting the values of points and slope in the formula given above.

y-(-3)=-4(x-8)

y+3=-4(x-8)

y+3=-4x+32

y=-4x+32-3

y=-4x+29

Hence the equation is y=-4x+29 where slope is -4.

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Answer:

See Below.

Step-by-step explanation:

We want to prove that:

[tex]x^3-13x-12\text{ is divisible by } x^2-x-12[/tex]

We can factor the divisor:

[tex]x^2-x-12=(x-4)(x+3)[/tex]

According to the Factor Theorem, if we have a polynomial P(x) divided by a binomial in the form of (x - a) and if P(a) = 0, then the binomial is a factor of P(x).

Our two binomial factors our (x - 4) and (x + 3). Thus, a = 4 and a = -3.

Evaluate the polynomial for both of these factors:

[tex]P(4)=(4)^3-13(4)-12=0[/tex]

And:

[tex]P(-3)=(-3)^3-13(-3)-12=0[/tex]

Since both yielded zero, the original polynomial is divisible by both (x - 4) and (x + 3) or x² - x - 12. Hence:

[tex]x^3-13x-12\text{ is indeed divisible by } x^2-x-12[/tex]

Here

[tex]\\ \sf\longmapsto \frac{7}{x} = \frac{15}{10} \\ \\ \sf\longmapsto 7 \times 10 = 15x \\ \\ \sf\longmapsto 15x = 70 \\ \\ \sf\longmapsto x = \frac{70}{15} \\ \\ \sf\longmapsto \boxed{ \sf x = 4.6cm}[/tex]

Answer:

i can help you i know this answer

Answer:

T = -t / 4 + T0   where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature

This is a linear equation in T and t

(-1 / 4 represents -5 deg / 20 min  = - 1 deg / 4min

The given situation is linear equation in T and t. so option D is correct option.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given situation:

The temperature of a cup of coffee decreases by 5 F every 20 minutes.

T = -t / 4 + T0  

where t is the temperature in minutes elapsed.

T is the final temperature.

T0 is the initial temperature.

We need to find the type of model best fits the given situation.

(-1 / 4 represents -5 deg / 20 min  = - 1 deg / 4min

Therefore, The given situation is linear equation in T and t. so option D is correct option.

Learn more about equations here;

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Answer:

There is no valid value for b

Step-by-step explanation:

We solve the above question using the law of cosines

b² = a² + c² - 2ac × Cos B

B = 42°, a = 6, c = 4

b² = 6² + 4² - 2 × 6 × 4 × Cos 42

b =√6² + 4² - 2 × 6 × 4 × Cos 42

b = √36 + 16 - 48 × Cos 42

Solving the above question, there is no valid value for b

Answer:

z = -i

Step-by-step explanation:

1 - iz=-1 +iz

Add iz to each side

1 - iz+iz=-1 +iz+iz

1 = -1 +2iz

Add 1 to each side

1+1 = -1+1 +2iz

2 = 2iz

Divide by 2

2/2 = 2iz/2

1 =iz

Divide by i

1/i = iz/i

1/i =z

Multiply the left by i/i

i/i^2 = z

i/-1 =z

-i =z

Answer:

12

Step-by-step explanation:

The interquartile range is the difference between the lower quartile and the upper quartile

We can find the quartiles at the beginning and the end of the box

At the beginning of the box, we have the lower quartile, while at the end, we have the upper quartile

from what we have ;

The lower quartile is 29 while the upper quartile is 41

So the difference between the two which is the interquartile range is ;

41-29 = 12

Answer:

12

Step-by-step explanation:

Answer: IT IS CONGRUENT BY ASA POSTULATE.

Step-by-step explanation:

ACCORDING TO THE GIVEN IMAGE

CONSIDER TRIANGLE 1 AS TRIANGLE ABC AND TRIANGLE 2 AS TRIANGLE PQR

IN TRIANGLE ABC AND PQR

ANGLE B = ANGLE C ( 90 DEGREES )

AC = PR ( GIVEN IN FIGURE )

A TRIANGLE HAS SUM OF INTERIOR ANGLES AS 180 DEGREES

IF ANGLE B AND ANGLE Q ARE 90 DEGREES, ANGLE A + ANGLE C = ANGLE P + ANGLE R

WE HAVE ALREADY PROVED THAT AC = PR

If two triangles have one angle equal to one angle, two sides adjoining the equal angles equal, namely, one side adjoining the equal angles, and one opposite the equal angles, and the remaining angles either both less or both not less than a right angle, then the remaining side equals the remaining side and the remaining angles equal the remaining angles.

SO ANGLE A = ANGLE P

THEREFORE BY ASA CONGRUENCY TRIANGLE ABC IS CONGRUENT TO TRIANGLE PQR

HOPE IT HELPS YOU......

(IF I HAVE MADE ANY MISTAKES PLS COMMENT BELOW)

Answer:

(−3)(+2)(3+2)

Step-by-step explanation:

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(32+8+4)

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(+2)(3+2)

Answer:

Step-by-step explanation:

To answer this, we need only solve for x and then use Pythagorean's Theorem to find z. We have the length of the hypotenuse which is 15, and we also have the base angle of 60. To solve for x we can use the trig ratio

[tex]cos60=\frac{x}{15}[/tex] and

x = 15cos60 which gives us that

x = [tex]\frac{15}{2}[/tex]

Now we can use Pythagorean's Theorem to find z, the other leg of the big triangle.

[tex](\frac{15}{2})^2+z^2=15^2[/tex] and

[tex](\frac{225}{4})+z^2=225[/tex] and

[tex]z^2=225-\frac{225}{4}[/tex] and getting a common denominator:

[tex]z^2=\frac{900}{4}-\frac{225}{4}[/tex] and

[tex]z^2=\frac{675}{4}[/tex] now we take the square root by simplifying the radical to get

[tex]z=\frac{15\sqrt{3} }{2}[/tex]

and that's what goes into the blanks there, one number per blank.

Answer:

Step-by-step explanation:

You have it right it is 6^x -3

You have the right idea, but you don't need to type in the "y=" portion since that is already taken care of. So you just need to type in -3 + 6^x

Answer:

16.  25/45 ; 18/45

17  4/7; 4/7

Step-by-step explanation:

5/9 and 2/5

The common denominator is 45

5/9 * 5/5 = 25/45

2/5 *9/9 = 18/45

4/7  and 12/21

Simplify 12/21 by dividing by 3 in the numerator and denominator

12/21 = 4/7

4/7; 4/7

The common denominator is 7

16:25/45;18/45

17: 4/7;4/7

Answer:

16:5/9;2/5

Common denominator is 9*5=45

now

make a equal denominator

5/9=5/9*5/5=25/45

2/5=2/5*9/9=18/45

and

17: 4/7;12/21

common denominator =7

4/7

12/21=4/7