People leaving an ice cream store were asked to name their favorite flavor of ice cream. Fifty-one people said chocolate was their favorite flavor. If 68% of the people surveyed said chocolate, how many people were surveyed?

Answer:

1) Expression is

[tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]

2) The standard form of the expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

3) The expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

Where [tex](n+1)^3[/tex] is the cube of the middle integer

Step-by-step explanation:

1) Given three consecutive integers are n. n+1, and n+2

Now multiplying the three consecutive integers

[tex](n)(n+1)(n+2)=(n^2+n)(n+2)[/tex]

[tex]=n^3+2n^2+n^2+2n[/tex]

[tex]=n^3+3n^2+2n[/tex]

Therefore [tex](n)(n+1)(n+2)=n^3+3n^2+2n[/tex]

Now adding the middle integer to the result of the multiplication.

ie, adding (n+1) to the result of the multiplication [tex]n^3+3n^2+2n[/tex]

[tex](n+1)+(n^3+3n^2+2n)=n+1+n^3+3n^2+2n[/tex]

[tex]=3n+1+n^3+3n^2[/tex]

Therefore [tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]

2) Expression is [tex]n^3+3n^2+3n+1[/tex]

Now we simplify the above expression

[tex]n^3+3n^2+3n+1=n^3+3n^2(1)+3(n)(1)^2+1^3[/tex]

[tex]=(n+1)^3[/tex]      (by using [tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]  , Here a = n and b=1)

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

3) The expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

Where [tex](n+1)^3[/tex] is the cube of the middle integer.

ie, expression is equivalent to the cube of the middle integer

Answer:

x>5

Step-by-step explanation:

-3(2x+5)<-45

2x+5<-45/-3

2x+5<15

2x<15-5

2x<10

x<10/2

x<5

x>5

Answer:

Step-by-step explanation:

g(h(x))=g(3x + 7). Since h(x)=3x + 7

g(h(x))= 2(3x + 7) - 5

g(h(x))= 6x + 14 -5

=6x +9

Answer:

6

Step-by-step explanation:

all you have to do is split the shape in half to create a square and a triangle then for the triangle the equation would be 2*2=4 then divide by 2 witch is 2 the do the square witch is 2*2=4 then you add 4+2=6 and i'm only in 7th grade.

Answer:

The area of cardboard required is 40750 cm².

Step-by-step explanation:

Given:

Length (L) = 25 cm

Width (W) = 5 m = 5 × 100 = 500 cm

Height (H) = 15 cm

Area of the cardboard is same as the total surface area of the closed rectangular box.

Total surface area of the rectangular box is given as:

[tex]SA=2(LW+WH+LH)\\\\SA=2(25\times 500+500\times 15+15\times 25)\\\\SA=2(12500+7500+375)\\\\SA=2\times 20375=40750\ cm^2[/tex]

So, the area of cardboard required is 40750 cm².

Answer: Robert has 22 video games.

Step-by-step explanation:

Let be "r" the number of video games that Robert has and "s" the the number of video games that Samuel has.

Set up a system of equations:

[tex]\left \{ {{r=5s+7} \atop {r+s=25}} \right.[/tex]

You can use the substitution method to solve the system:

- You need to substitute the first equation into the second equation and solve for "s":

[tex](5s+7)+s=25\\\\6s=25-7\\\\s=\frac{18}{6}\\\\s=3[/tex]

- Finally you must substitute the value of "s" into the first equation and evaluate:

[tex]r=5(3)+7\\\\r=22[/tex]

Answer:3

Step-by-step explanation:

5x+7=25

So lets subtract 7 from 25 to get 5x alone...

5x=18

5x/5=x

18/5=3.3

You cant have 0.3 of a video game so the answer is 3

Answer:

x=-5, x=9

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

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

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2} -8x-90[/tex]  

equate to zero

[tex]2x^{2} -8x-90=0[/tex]  

so

[tex]2=-1\\b=-8\\c=-90[/tex]

substitute in the formula

[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(2)(-90)}} {2(2)}[/tex]

[tex]x=\frac{8\pm\sqrt{784}} {4}[/tex]

[tex]x=\frac{8\pm28} {4}[/tex]

[tex]x=\frac{8+28} {4}=9[/tex]

[tex]x=\frac{8-28} {4}=-5[/tex]

therefore

The solutions are x=-5, x=9

Answer:

answer is y-5=-3(x-3)

Step-by-step explanation:

your y-coordinate is 5 s you would write y-5 and your slope is -3 with your x-coordinate as 3 so that would be written as -3(x-3).  The equation put together correctly would be y-5=-3(x-3)

Answer:

y-5=-3(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-3)

The equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have given:

Length of Mother manatee = 12 feet.

Let's suppose the length of a baby manatee is 'x'.

So the equation can be framed as:

3x = 12

x = 4 feet

The length of blue whale is = 9(length of mother manatee)

The length of blue whale is = 9(12) = 108 feet

Thus, the equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

Answer:

$114

Step-by-step explanation:

Sales price = Original Cost - $35

Sales price - $35 = Original Cost

Substitute in known values

$149 - $35 = Original Cost

$114 = Original Cost

Hope this helps :)

Answer:

0.60

Step-by-step explanation:

Again, we have a 10x10 space, which means there are 100 squares.

In this case, there are 60 shaded squares. This gives the probability of [tex]\frac{60}{100}[/tex] which simplifies to 0.60

Answer:

0.60

Step-by-step explanation:

Because there are 100 squares and 60 out of it is shaded if you chose a random point amongst these 100 square the probability of choosing a shaded one is 60/100 which is equal to 0.60.

Answer:

The centroid is located at (3,3)

Step-by-step explanation:

Centroid Of A Triangle

The centroid of a triangle is the point where its three medians intersect. It is also the center of gravity of the triangle. The medians are lines that go from each vertex to the midpoint of the opposite side.

Given A(ax,by), B(bx,by), C(cx,cy) the points of the vertices, then the coordinates of the centroid [tex]P(x_c,y_c)[/tex] are

[tex]\displaystyle x_c=\frac{ax+bx+cx}{3}[/tex]

[tex]\displaystyle y_c=\frac{ay+by+cy}{3}[/tex]

The vertices are  (0,1) (2,6) (7,2), thus

[tex]\displaystyle x_c=\frac{0+2+7}{3}=3[/tex]

[tex]\displaystyle y_c=\frac{1+6+2}{3}=3[/tex]

The centroid is located at (3,3)

The coordinates of centroid are (3,3)

Step-by-step explanation:

The coordinates of centroid of a triangle are calculated by finding average of x-coordinates of vertices and the average of y-coordinates of vertices.

Given vertices are:

(0,1) (2,6) (7,2)

So,

x-coordinate of centroid:

[tex]x = \frac{0+2+7}{3}\\=\frac{9}{3}\\= 3[/tex]

y-coordinate of centroid:

[tex]y = \frac{1+6+2}{3}\\=\frac{9}{3}\\= 3[/tex]

Hence,

The coordinates of centroid are (3,3)

Keywords: Triangle, centroid

Learn more about triangle at:

#LearnwithBrainly

Answer:

Step-by-step explanation:

Equation for line: y=mx+b where m is the slope and b is the y-intercept

We have the slope. We just need to find the y-intercept. Plug in the point and the slope and solve for b.

y=mx+b

1=4(-5)+b

b=21

Answer: y=4x+21

By completing the square, the equation x²- 20x + 100 = 0, we get, (x-10)²=0

Here, we have,

To rewrite the equation x² - 20x + 100 = 0 by completing the square, we can follow these steps:

Step 1: Move the constant term to the right side of the equation:

x² - 20x = -100.

Step 2: Take half of the coefficient of the x-term (-20/2 = -10) and square it to get (-10)² = 100.

Step 3: Add the result from step 2 to both sides of the equation:

x² - 20x + 100 = -100 + 100.

Simplifying:

x² - 20x + 100 = 0.

Step 4: Factor the left side of the equation. In this case, the left side is a perfect square trinomial:

(x - 10)² = 0.

Therefore, by completing the square, the equation x²- 20x + 100 = 0,

we get, (x-10)²=0

To learn more on equation click:

https://brainly.com/question/14468218

#SPJ6

Final answer:

The equation [tex]x^2 - 20x + 100 = 0[/tex] is already a perfect square and does not need to be completed. However, completing the square involves moving the constant to the other side, squaring half the coefficient of x, and solving for x, which leads us back to the original equation [tex](x - 10)^2 = 0[/tex] and reveals that x = 10.

Explanation:

The equation given is [tex]x^2 - 20x + 100 = 0[/tex]. This equation appears to already be a perfect square, as the constant term (100) is the square of half the coefficient of the x term (which is 10), thus completing the square is actually not needed. However, to illustrate the method of completing the square, let's ignore for a moment that it's already a perfect square and proceed with the steps:

We've found that x = 10 is the solution to the equation, which is the same result you would get by recognizing the equation was already a perfect square in its original form.

Answer:

A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

Step-by-step explanation:

find the number line best shows how to solve −8 − (−6)

In the number line first we start with -8 . negative and negative becomes positive

from -8 move 6 units to the right. So it ends at -2

A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

Answer:

C. (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

Step-by-step explanation:

The function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The parent function is:

g(x) = IxI

And we have:

f(x) = I6x - 2I - 7

Rearranging the function:

f(x) = 6Ix - 1/3I - 7

Then, now let's define some transformations:

If we start with g(x), a translation of N units to the right is:

f(x) = g(x - N)

if we start with g(x), a translation of N units up is:

f(x) = g(x) + N

A translation down would be:

f(x) = g(x) - N

And a vertical dilation of scale factor A is written as:

f(x) = A × g(x)

Then in this case we have:

A translation to the right of 1/3 units.

A dilation of scale factor 6.

A translation down of 7 units.

And the axis of symmetry will be when the absolute value part is equal to zero, or when

6Ix - 1/3I = 0

And that is when x = 1/3.

Therefore, the function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

To learn more about the function;

brainly.com/question/28303908

#SPJ5

Answer:

initial value=2

Step-by-step explanation:

equation of line,

y-[tex]y_1[/tex]=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex][tex](x-x_1)[/tex]..............(1)

put co ordinate (0,3) and (2,7) in the equation (1)

y-3=[tex]\frac{7-3}{2-0}[/tex](x-0)

y-3=2x

y=2x+3

rate of change of linear equation=[tex]\frac{\partial (2x+3)}{\partial x}[/tex]

[tex]\frac{\partial y}{\partial x}[/tex]=2

hence, initial value=2 answer

Answer:

w=12.6

Step-by-step explanation:

2w+2(w+3.8)=58

2w+2w+7.6=58

4w+7.6=58

4w=58-7.6

4w=50.4

w=50.4/4

w=12.6

Answer:

y=x/2−1/2

Step-by-step explanation:

Answer:

x<=5

Step-by-step explanation:

Two things

Answer:

B

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line

m = [tex]\frac{-4-8}{2+1}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 → B

Answer:

The slope of the given line is -4.

So, option (B) is correct.

Step-by-step explanation:

We know that, slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is given by,

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Now, the given line passes through the point (-1, 8) and (2,-4).

So, (x₁, y₁) = (-1, 8) and (x₂, y₂) = (2, -4)

So, by using the above formula, we get

Slope(m) of the given line passing through (-1, 8) and (2, -4) is given by,

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-4-8}{2-(-1)}[/tex]

[tex]\implies\;m = \frac{-12}{3}=-4[/tex]

∴The slope of the given line is -4.

Hence, option (B) is correct.

The bearing of A from B according to the diagram is 82.86°

Using trigonometric relations ;

B = bearing of A from B

Now we have;

Tan B = 40 /5

Tan B = 8

Take the inverse value of the tangent ;

[tex]B = Tan^{-1} (8) [/tex]

B = 82.86°

Hence, the bearing of A from B is 82.86°

Answer:

Answer 1.) f(x)=0x-4

Answer 2.) f(x)=2/3x+4

Answer 3.) i don't really get this one so sorry

Answer 4.) f(x)= -1/5x+2

hope this helped it took me a while to figure out this but looks like the guy ahead of me beat me to it

Step-by-step explanation:

Answer:

The value of each share decreased by $8.

Step-by-step explanation:

Number of shares of a certain stock Linda owned = 4

Total value of shares went down by = $32

So find the change in value of each share.

Solution:

Let the total value of each share in dollars be = [tex]x[/tex]

Value of 4 shares in dollars will be = [tex]4x[/tex]

The total value of shares went down by $32

So, new value of 4 shares = [tex]4x-32[/tex]

New value of each share = [tex]\frac{New\ value\ of\ total\ shares}{4}[/tex]

⇒ [tex]\frac{4x-32}{4}[/tex]

Splitting the denominators.

⇒ [tex]\frac{4x{{4}-\frac{32}}{4}[/tex]

⇒ [tex]x-8[/tex]

Original value of each share in dollars was = [tex]x[/tex]

New value of each share in dollars = [tex]x-8[/tex]

Thus, we can see that the value of each share decreased by $8.

Each point listed is of the form (x,y). The x coordinate is always listed first. We dont have any repeat x values, so this is enough to conclude we have a function.

If you wanted to, you could graph each point given on the same coordinate grid. Note how none of the points stack on top of each other. Or put another way, note how it is impossible to draw a single straight line through more than one point graphed. This graph passes the vertical line test.

A function is where plugging in any x value leads to exactly one y value.

If you had two points like (5,2) and (5,7) then the input x = 5 leads to more than one output y = 2 and y = 7 at the same time, making this example not a function.

If the area is 10 square meters than double that is area of a rectangle with height = 5m and base of 4m because height • base should produce 20m^2.

Hope this helps.

Answer: base length = 4 metres

Step-by-step explanation:

A = ½bh

10m² = ½ * b * 5m

10 = 5b/2

Cross multiply

20 = 5b

b = 4m

Answer:

16 serving.

Step-by-step explanation:

Given: 3/4 cup servings.

Now, computing the number of serving in 12 cups of cherries.

Using unitary method to solve.

∴ Number of serving= [tex]total\ cups \times number\ of\ serving\ per\ cup[/tex]

Number of serving in one cup is [tex]\frac{4}{3}[/tex]

Number of serving in 12 cups = [tex]12\times \frac{4}{3} = 16 \ serving[/tex]

Number of serving in 12 cups= [tex]16\ serving[/tex]

∴ There are 16 serving is possible in 12 cups of cherries.

Final answer:

To calculate the number of 3/4 cup servings in 12 cups of cherries, divide 12 by 3/4, which equals 16 servings.

Explanation:

To determine how many 3/4 cup servings are in 12 cups of cherries, we can divide the total number of cups by the size of one serving.

First, we express the serving size and the total amount in the same units: 3/4 cup and 12 cups.

Next, we divide the total amount of cherries by the serving size: 12 cups ÷ 3/4 cup.

To perform the division, we can multiply 12 by the reciprocal of 3/4, which is 4/3 (12 × 4/3 = 16).

The result is that there are 16 servings of 3/4 cup in 12 cups of cherries.