Susan made 168 cupcakes and gave some to her 21 students.
She then had 1/2 of her cupcakes left. On average, how many
cupcakes did she give to each of the 21 students?

Answer:

x = 10

Step-by-step explanation:

Simplifying

8x + -3 = 6x + 17

Reorder the terms:

-3 + 8x = 6x + 17

Reorder the terms:

-3 + 8x = 17 + 6x

Solving

-3 + 8x = 17 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation.

-3 + 8x + -6x = 17 + 6x + -6x

Combine like terms: 8x + -6x = 2x

-3 + 2x = 17 + 6x + -6x

Combine like terms: 6x + -6x = 0

-3 + 2x = 17 + 0

-3 + 2x = 17

Add '3' to each side of the equation.

-3 + 3 + 2x = 17 + 3

Combine like terms: -3 + 3 = 0

0 + 2x = 17 + 3

2x = 17 + 3

Combine like terms: 17 + 3 = 20

2x = 20

Divide each side by '2'.

x = 10

Simplifying

x = 10

Answer:

The correct options are;

3 Congruent sides

Corresponding congruent Angle-Side-Angle

Corresponding congruent Side-Angle-Side

Corresponding congruent Side-Side-Angle

Step-by-step explanation:

The conditions for congruency are;

Two triangles are congruent when

AAS which is the acronym for corresponding Angle-Angle-Side are congruent

SAS  which is the acronym for corresponding Side-Angle-Side are congruent

SSS which is the acronym for corresponding Side-Side-Side are congruent

ASA which is the acronym for corresponding Angle-Side-Angle are congruent.

The criteria that always proves triangles

are congruent are;

Option A; Corresponding congruent Angle-Side-Angle

Option A; Corresponding congruent Angle-Side-AngleOption B; Corresponding congruent Side-Angle-Side

Option A; Corresponding congruent Angle-Side-AngleOption B; Corresponding congruent Side-Angle-SideOption D: 3 congruent sides

There are some congruence theorems that prove that two triangles are congruent and they are;

1) SSS; This means Side - Side - Side and it denotes that the 3 corresponding sides of both triangles are congruent.

2) SAS; This denotes Side - Angle - Side and it denotes that the 2 corresponding sides and the included corresponding angle are congruent.

3) ASA; This denotes Angle - Side - Angle and it means that the 2 corresponding angles and the included corresponding side are congruent.

4) AAS; This denotes Angle - Angle - Side and it denotes that the 2 corresponding angles and corresponding non-included side are congruent.

In conclusion, from the options, options A, B & D.

Read more at; https://brainly.com/question/10533727

Answer:

40.021

Step-by-step explanation:

Unlimited calls = $40

Text message = $0.021

NOTE:There is a difference between the value you gave for cost of text messages in the question and the values given in the group of answers. I will use $0.021 for cost of text messages since it is common to all answer choices.

Total cost = Cost of unlimited calls + cost of text messages

C = $40 + $0.021

= $40.021

Therefore, the equation which represent the total cost in dollars for a month is 40.021

A. 40.021

Answer:

maluna1999live is correct the answer is 40.021 so if your going to give someone the brailest then it should be maluna1999live

Step-by-step explanation:

Answer:

Step-by-step explanation:

As per definition of the package

Given the value of g

So the value of l should be

To be considered a package the length to be less than 46 in

Answer:

D'( -6 , 4).

Step-by-step explanation:

In rotation through 90 degrees from the origin

P(x,y) - P'(-y , x)

D(4 , 6) - D'( -6 , 4).

It's simple

Answer:

6

Step-by-step explanation:equals 6

Answer:

5-2x>10x

Step-by-step explanation:

Answer:

bruh just reading this question hurts my head

i guess you could say the first number is 8 and the second number is 1, but jeez bro

Step-by-step explanation:

Answer:

A(-3,0)

B(6,1)

C(15,0)

Step-by-step explanation:

To find the three new coordinates A,B,C we have to find out the equation of the original curve y=f(x) which is shown in the figure. We find that equation by using the turning point (2,1) which is point B and take any other point either A or C which intercept's the x-axis, i took C. We put both these points into the completing square formula of the curve.

[tex]y=a(x-h)^2+k[/tex]

where (h,k) are the turning points (2,1) respectively and C (5,0) corresponds to (x,y)

so the equations becomes

[tex]0=a(5-2)^2+1\\0=a(3)^2+1\\0=9a+1\\-1=9a\\a=\frac{-1}{9}[/tex]

So our equation y=f(x) becomes

[tex]y=-\frac{(x-2)^2}{9}+1[/tex]

now for

[tex]y=f(\frac{x}{3} )[/tex]

we replace the x in the original equation above with x/3 which changes the equation to

[tex]f(\frac{x}{3} )=-\frac{(\frac{x}{3}-2)^2}{9} +1[/tex]

and now we sketch the curve we have our hints for the new points A,B,C our hint is that the original points A and C are the x-intercepts so the new A and C lets name them A' and C' must be the x-intercepts as well and B is the turning point of y=f(x) so the new point B' must be the turning point of y=f(x/3)

so we simply sketch the curve y=f(x/3) use an online graph plotter if you know how to sketch it to save time or if you don't know you can ask me and i'll teach you cause learning to sketch isn't in the question so furthermore we sketch the curve i attached the figure in an image you check it out and the new points as well.

Answer:

d

Step-by-step explanation:

g

Answer:

C

Step-by-step explanation:

They are all more in the modern era

Answer:$14.75 for bananas and oranges

Step-by-step explanation:

You have to Add to get your answer.I'll show you how I got $14.75:

4.50+4.50=$9

9+2=$11

11+0.75=$11.75

11.75+3=14.75

Your answer is:$14.75

hope this was helpful:)

Answer:

g(f(5)) = - 61

Step-by-step explanation:

Evaluate f(5) then substitute the value obtained into g(x) , that is

f(5) = - 4(5) - 7 = - 20 - 7 = - 27 , then

g(- 27) = 2(- 27) - 7 = - 54 - 7 = - 61

Answer:

Translation

Step-by-step explanation:

[tex] - 9 {x}^{2} + 3x = 0 [/tex]

[tex]3x( - 3x + 1) = 0[/tex]

[tex]3 x = 0 \\ x = 0[/tex]

And

[tex] - 3x + 1 = 0 \\ - 3x = - 1 \\ x = \frac{ - 1}{ - 3} \\ x = \frac{1}{3} [/tex]

So the x-intercepts are :

[tex]x = 0 \: \: \: \: \: and \: \: \: \: \: x = \frac{1}{3} \\ [/tex]

Answer:

3 test tubes

Step-by-step explanation:

First one took 2 so 8-2=6 so 6 left for the other 2 tests then 6 divided by 2 is 3

Answer:

a

Step-by-step explanation:

Here all the given equations are in the form of

[tex]ax^2+bx+c=0[/tex]

The value of [tex]x[/tex] can be determined by the perfect square method as follows:

[tex]ax^2+bx+c=0[/tex]

[tex]\Rightarrow x^2+\frac{b}{a}+\frac{c}{a}=0[/tex]

[tex]\Rightarrow x^2+2\times\frac{b}{2a}+\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2+\frac{c}{a}=0[/tex]

[tex]\Rightarrow \left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2-\frac{c}{a}[/tex]

[tex]\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\;\cdots(i)[/tex]

Now, for [tex]x^2+3x-4=0[/tex]

[tex]a=1, b=3, c=-4[/tex]

So, from equation (i)

[tex]x=\frac{-3\pm\sqrt{3^2-4\times1\times(-4)}}{2\times1}[/tex]

[tex]\Rightarrow x=\frac{3\pm\sqrt{9+16}}{2}[/tex]

[tex]\Rightarrow x=\frac{3\pm5}{2}[/tex]

[tex]\Rightarrow x=\frac{3+5}{2},\frac{3-5}{2}[/tex]

[tex]\Rightarrow x= 4, -1[/tex]

Similarly, for [tex]9x^2+12x+4=0[/tex]

[tex]a=9, b=12, c=4[/tex]

So, from equation (i)

[tex]x=\frac{-12\pm\sqrt{12^2-4\times9\times4}}{2\times9}[/tex]

[tex]\Rightarrow x=\frac{-12\pm0}{18}[/tex]

[tex]\Rightarrow x=\frac{-2}{3}[/tex]

For [tex]x^2-2x-3=0[/tex]

[tex]a=1, b=-2, c=-3[/tex]

[tex]x=\frac{-(-2)\pm\sqrt{(-2)^2-4\times1\times(-3)}}{2\times1}[/tex]

[tex]\Rightarrow x=\frac{2\pm\sqrt{16}}{2}[/tex]

[tex]\Rightarrow x=\frac{2\pm4}{2}[/tex]

[tex]\Rightarrow x=\frac{6}{2},\frac{-2}{2}[/tex]

[tex]\Rightarrow x=3.00, -1.00[/tex]

For [tex]x^2-6x+9=0[/tex]

[tex]a=1, b=-6, c=9[/tex]

[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4\times1\times9}}{2\times1}[/tex]

[tex]\Rightarrow x=\frac{6\pm0}{2}[/tex]

[tex]\Rightarrow x=3.00[/tex]

For [tex]2x^2-4x-3=0[/tex]

[tex]a=2, b=-4, c=-3[/tex]

[tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4\times2\times(-3)}}{2\times2}[/tex]

[tex]\Rightarrow x=\frac{4\pm\sqrt{40}}{4}[/tex]

[tex]\Rightarrow x=\frac{4\pm2\sqrt{10}}{4}[/tex]

[tex]\Rightarrow x=\frac{4+2\sqrt{10}}{4},\frac{4-2\sqrt{10}}{4}[/tex]

[tex]\Rightarrow x=2.58, -0.58[/tex]

Answer:

f(x)=(x-1)(x+1)^2(x-4)^3

Step-by-step explanation:

The zeros of the function are x=-1, x=1, and x=4, so its factors are x+1, x-1, and x-4.

The graph touches, but doesn’t cross, the x-axis at x=-1. So the factor x+1 is a repeated factor with an even multiplicity.

The graph crosses the x-axis at x=4, but with a little curve before and after it meets this point. So the factor x+4 is a repeated factor with odd multiplicity.

The graph crosses the x-axis at x=1 with no curve before or after. So the factor x-1 is not a repeated factor.

Therefore, function f is defined by f(x)=(x-1)(x+1)^2(x-4)^3.

The sixth-degree polynomial that shows in the graph is [tex]\rm f(x) = (x+1)(x-1)^2(x-4)^3[/tex] and this can be determined by evaluating the x-intercept of the given graph.

Given :

Sixth-degree polynomial -- [tex]\rm f(x) = (x-b)(x-c)^2(x-d)^3[/tex]

The following steps can be used in order to determine the value of b, c, and d:

Step 1 - Write the given sixth-degree polynomial.

[tex]\rm f(x) = (x-b)(x-c)^2(x-d)^3[/tex]

Step 2 - Observe the given graph and determine the x-intercept of the graph of the sixth-degree polynomial.

Step 3 - So, the x-intercepts that are the values of b, c, and d is given below:

b = -1

c = 1

d = 4

Step 4 - Substitute the values in the given sixth-degree polynomial.

[tex]\rm f(x) = (x+1)(x-1)^2(x-4)^3[/tex]

For more information, refer to the link given below:

https://brainly.com/question/14375099

Answer:

G(x) = 3x +2

Step-by-step explanation:

I do not know what the problem is asking for, but if it's asking for the function, here you go.

Answer:

shbdhsjdcjsvdbssegehehhehehejrjehe

9514 1404 393

Answer:

Step-by-step explanation:

The signs of the terms are + - - +. There are two sign changes, so 0 or 2 positive real roots.

Negating the signs of the odd-degree terms, the signs are + + + +. There are no sign changes, so 0 negative real roots.

For x=0, the value of the quartic is +3. For x=1, the value is -3, so we know there are 2 positive real roots, one of which lies in the interval (0, 1).

The 4th-degree polynomial equation must have 4 roots, so the other two must be complex.

_____

The roots are approximately 0.489999841592, 2.06573034434, −0.777865092969 ± 1.53582061225i

Answer:

-20x.....

Step-by-step explanation:

–4(5x)

-20x

Gradient = Slope = coefficient of x

Thus ;

Gradient = Slope = 5

_________________________________

Vertical axis = y -axis

To find the y-intercept of the equation we must put zero instead of x .

Let's do it.....

[tex]y = 5x + 30[/tex]

[tex]y = 5(0) + 30[/tex]

[tex]y = 30[/tex]

So the y-intercept is 30 .

_________________________________

And we're done.....♥️♥️♥️♥️♥️

Answer:

-493

Step-by-step explanation:

Answer:

-493:) brainly?

Step-by-step explanation:

Answer:

m-7 2

Step-by-step explanation:

I very much agree-_-

Answer:

  the marked answer is correct

Step-by-step explanation:

The desired end result is an identity matrix in the first three columns. The diagonal values are 1, as needed, so what remains is to eliminate the off-diagonal values. In row 2 that can be done by adding row 3 to it.

The next step should be to add rows 2 and 3 and replace row 2 with that sum.

Answer:

2b + 4 = 22

b= 9, the cost of each game is $9

Step-by-step explanation: