The vertices of ABC are A(-2,2), B(6,2), and C(0,8). The perimeter of ABC

Answer:

c

Step-by-step explanation:

Answer:

C. The number is even or less than 12.

Step-by-step explanation:

Let's analyze each event:

A. The number is greater than 2.

This doesn't cover the case when we get number 2. Because 2 is equal to 2, not greater.

B. The number is not divisible by 5.

10 and 5 are divisible by 5, so this doesn't cover the entire sample space.

C. The number is even or less than 12.

Let's notice that every number from {2, 3, 4, ... 10} is less than 12, so the even part of the event doesn't play any role. This covers the entire sample space.

D. The number is neither prime nor composite.

The definition of prime number is exactly the opposite of composite number, so there can't be a number that's neither both. This event doesn't cover any number of the set.

E. The square root of the number is less than 3.

This doesn't cover number 10, because the square root of 10 is approx. 3,16 that's greater than 3.

Answer:

c=15.50+0.08t

Step-by-step explanation:

Sandra's total monthly cost for her cell phone, represented by C, consists of a fixed rate of $15.50 for unlimited minutes and an additional $0.08 per text message. The formula to calculate her total cost is C = 15.50 + 0.08t, where t is the number of text messages.

The total monthly cost, C, for Sandra's cell phone is composed of a fixed monthly charge plus a variable charge that depends on the number of text messages she sends.

The fixed charge is her unlimited minutes plan which costs $15.50 per month.

On top of that, each text message costs $0.08, so if we let t represent the number of texts she sends, the variable cost will be 0.08t.

Therefore, the equation to model Sandra's total monthly cost would be:

C = 15.50 + 0.08t

We can confidently state that this equation represents how Sandra's monthly expenses on her cell phone will add up depending on the number of texts, t, she sends in a month.

Answer:

B.   3x^2 - 2x - 1.

Step-by-step explanation:

(f + g)x = f(x) + g(x)

= -4x + 3 + 3x^2 + 2x - 4

Adding like terms we get the answer:

= 3x^2 - 2x - 1.

The answer is:

B. [tex](f+g)(x)=3x^{2} -2x-1[/tex]

To solve the problem, we need to add/subtract like terms. The like terms are the terms that share the same variable and the same exponent.

For example:

[tex]x^{2} +3x^{2} +5x^{3}=4x^{2}+5x^{3}[/tex]

We were able to add the terms that were squared since both shares the same variable and the same exponent.

So, we are given the functions:

[tex]f(x)=-4x+3\\g(x)=3x^{2} +2x-4[/tex]

Now, we are asked to calculate (f+g)(x) which is also equal to f(x) + g(x).

Then, calculating we have:

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

Hence, the answer is:

B. [tex](f+g)(x)=3x^{2} -2x-1[/tex]

Have a nice day!

2.14 is the answer!!!

Answer:

Step-by-step explanation:

3*5 / 7 is the way I'm guessing it is.

15/7  one way it can be represented.

2 1/7 is another way.

2.1428 is yet another way.

Answer:

9000 milligrams

Step-by-step explanation:

1 gram = 1000 milligrams

( × 9 on both sides to get 9 grams )

9 grams = 9000 milligrams

Answer:

9000 milligram

Step-by-step explanation:

multiply the mass value by 1000

There is 1 17-year-old player on the varsity basketball team whose height is 74 inches or less. The correct option is B.

In a scatter plot, each dot represents one player, with the x-axis typically representing age and the y-axis representing height. By examining the data points corresponding to 17-year-olds, we find only one dot where the height is 74 inches or less.

This analysis involves visually inspecting the scatter plot and identifying the specific data points that satisfy the criteria mentioned in the question. The correct answer, therefore, reflects the count of such data points, and in this case, it is one.

Answer:

2

Step-by-step explanation:

IF YOU LOOK AT THE CHART, YOU WILL SEE THATTHE NUMBER OF 17 YEAR OLDS THAT ARE 74 INCHES AND UNDER ARE 2

Answer:

(1/6)π(7²) = (49/6)π square inches

= about 25.66 square inches

Answer:

It has to be 25 it is the middle number

Answer:

C which is 30.

Consecutive terms differ by 1.5, so this is an arithmetic sequence given by

[tex]\begin{cases}a_1=19\\a_n=a_{n-1}+1.5&\text{for }n>1\end{cases}[/tex]

So we have

[tex]a_2=a_1+1.5[/tex]

[tex]a_3=a_2+1.5=a_1+2\cdot1.5[/tex]

[tex]a_4=a_3+1.5=a_1+3\cdot1.5[/tex]

and so on, up to

[tex]a_n=a_1+1.5(n-1)=17.5+1.5n[/tex]

The sum of the first [tex]N[/tex] terms is 10,900:

[tex]\displaystyle\sum_{n=1}^Na_n=\sum_{n=1}^N(17.5+1.5n)=17.5N+1.5\dfrac{N(N+1)}2=10,900[/tex]

[tex]\implies17.5N+0.75N(N+1)=10,900[/tex]

[tex]\implies0.75N^2+18.25N-10,900=0[/tex]

[tex]\implies N=109[/tex] (we ignore the negative solution)

so there are 109 terms in the series.

Answer:

Step-by-step explanation:

[tex]19,\ 20.5,\ 22,\ 23.5,\ ...,\ 181\\\\\text{It's the arithmetic sequence with:}\\\\a_1=19,\ a_n=181.\\\\\text{The sum of n terms of this sequence is equal to 10,900.}\\\\\text{the formula of a sum of n terms of an arithmetic sequence:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\text{Substitute:}\ S_n=10,900,\ a_1=19,\ a_n=181:\\\\\dfrac{19+181}{2}\cdot n=10,900\\\\\dfrac{200}{2}n=10,900\\\\100n=10,900\qquad\text{divide both sides by 100}\\\\n=109[/tex]

Answer:

f(x) = x^3 - x^2 -2x

Step-by-step explanation:

If x = a is a zero of a polynomial, then x-a is a factor of the polynomial. Given the factors of a polynomial, the polynomial can be obtained by multiplying the factors.

The factors of the given polynomial are;

x - 2

x + 1

x

Multiplying the first two factors;

(x-2)(x+1) = x^2 + x -2x -2

              = x^2 -x -2

We finally multiply this result by x to obtain our polynomial;

f(x) = x ( x^2 -x -2)

      = x^3 - x^2 -2x

which is a cubic polynomial since it has 3 roots.

Answer:

f(x) = x³ - x² - 2x

Step-by-step explanation:

given a polynomial with zeros x = a, x = b, x = c

Then the factors are (x - a), (x - b) and (x - c)

and the polynomial is the product of the factors, that is

f(x) = k(x - a)(x - b)(x - c) ← where k is a multiplier

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

Here the zeros are x = 2, x = - 1 and x = 0, thus the factors are

(x - 2), (x + 1) and (x - 0) , thus

y = kx(x - 2)(x + 1) ← let k = 1 and expand factors

 = x(x² - x - 2) = x³ - x² - 2x

Hence a possible polynomial is

f(x) = x³ - x² - 2x

what expression?

if you have an expression then I could probably help you.

Answer:

b

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Well first I found the area of the big rectangle which is lxw which will be equal to 12. while the small rectangle the area will be equal to 3. Finally, I added the 2 areas and I got 15. I hope this helped you.

Answer:

[tex]33\ ft[/tex]

Step-by-step explanation:

Let

y-----> the height of the telephone pole

we know that

In the right triangle of the figure

The sine of angle of 67 degrees is equal to divide the opposite side of angle of 67 degrees by the hypotenuse

[tex]sin(67\°)=\frac{y}{36}[/tex]

solve for y

[tex]y=(36)sin(67\°)=33\ ft[/tex]

Answer:

15%

Step-by-step explanation:

15% of 40 is 6.

Answer:

the definition is two of the same kind

An ordered pair is a set of coordinates or points on a graph. In order, they would be the x coordinate and the y coordinate. The ordered pair would look like this (x, y). For example, on a graph, the ordered pair of a point that is 3 over and 4 up would look like this: (3, 4), as the x value is 3 and y value is 4. The x value always comes before the y value in an ordered pair.

Answer:

Its A) 23

Step-by-step explanation:

Its right, trust me

The possible value of the third side of the triangle is 23.

The range of third side c when two sides a and b of a triangle are known is given by the inequality:

[tex]a-b < c < a+b[/tex]

It is given that:

a =15

b = 9

So, by the triangle inequality

[tex]15-9 < c < 15+9[/tex]

6 <c <24

The third side will take the value between 6 and 24.

so, the possible value of the third side of the triangle i.e. c is 23.

Therefore, the possible value of the third side of the triangle is 23.

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Hi, if we are using the quadratic formula to solve this, then here is a good answer.

The solution to the equation 7/3x = 2/(x+5) is found by cross-multiplication and simplifying, ending with the result x = -35.

To solve the given equation 7/3x = 2/(x+5), the first step is to cross-multiply. This gives us 7*(x+5) = 2*3x. Simplifying this results in 7x + 35 = 6x. Subtract 6x from each side and you get x + 35 = 0. And thus, x = -35 is the solution of the equation.

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Answer:

x = - 2

Step-by-step explanation:

0.5x = - 1

(0.5/0.5 ) x = -1/0.5

Use your calculator

1

÷

0.5

=

You should get 2. But there is a minus sign on the right. The answer is -2

Answer:

50%=250

20%=50

40%=80

50=60

so she kept $60

Step-by-step explanation:

Answer:

$60

Step-by-step explanation:

Winning = $500

Mildred  = 50% of $500 = 0.5 x $50 = $250

Left = $500 - $250 = $250

Berice = 20% of $250 = 0.2 x $250 = $50

Left = $250 - $50 = $200

Alice = 40% of $200 = 0.4 x $200 = $80

Left  = $200 - $80 = $120

Bea = 50% of $120 = 0.5 x $120 = $60

Left = $120 - $60 = $60

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=14\pi \\ r=12 \end{cases}\implies 14\pi =12\theta \implies \cfrac{14\pi }{12}=\theta \\\\\\ \stackrel{\textit{radians}}{\cfrac{7\pi }{6}}=\theta ~\hspace{10em}\stackrel{\textit{in degrees}}{210^o}[/tex]

The radius is 3.

Because the diameter is 3•2=6

Hope this helps.

Answer:

3

Step-by-step explanation:

The diameter of the circle is 2 times the radius

d = 2r

6 = 2r

Divide each side by 2

6/2 =2r/2

3=r

The radius is 3

Answer:

Area 6

Hope This Helps!  Have A Nice Day!!

Area 6

Hope This Helps!  Have A Nice Day!!

Answer:

Part a) The volume of the pill is [tex]603\ mm^{3}[/tex]

Part b) [tex]1.7\frac{mg}{mm^{3}}[/tex]

Part c) [tex]215\ mg[/tex]

Step-by-step explanation:

Part a) Find the volume of the pill in cubic millimeters

we know that

The volume of the pill is equal to the volume of the cylinder plus the volume of a sphere (two hemisphere is equal to one sphere)

so

[tex]V=\frac{4}{3}\pi r^{3}  +\pi r^{2}h[/tex]

we have

[tex]r= (18-11)/2=3.5\ mm[/tex]

[tex]h=11\ mm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(3.5)^{3}  +(3.14)(3.5)^{2}(11)[/tex]

[tex]V=603\ mm^{3}[/tex]

Part b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per  cubic millimeter?

Divide 1,000 milligrams by the volume

[tex]1,000/603=1.7\frac{mg}{mm^{3}}[/tex]

Part c) Another pill that is entirely spherical has a diameter of 10 millimeters and contains 1.5 milligrams of  vitamin C per cubic millimeter. How much less vitamin C does this second pill contain, rounded to the

nearest milligram, than the one pictured?​

step 1

Find the volume of the sphere

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=10/2=5\ mm[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(5)^{3}[/tex]

[tex]V=523.33\ mm^{3}[/tex]

step 2

Multiply the volume by 1.5 milligrams of  vitamin C per cubic millimeter

so

[tex]523.33*1.5=785\ mg[/tex]

step 3

Find the difference

[tex]1,000-785=215\ mg[/tex]

Answer: 42

Step-by-step explanation:

The different types of one-topping pizzas that they serve are 196.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

where,

n is the number of choices available,

r is the choices to be made.

As the size of the pizzas that are available is of 3 different types, therefore, the number of choices for the size of the pizza is 3, which can be written as,

[tex]\text{Choices of Pizza}=^3C_1[/tex]

The number of toppings that are available is 14, therefore, the number of choices for pizza toppings can be written as,

[tex]\text{Choices of Toppings}=^{14}C_1[/tex]

Now, the different types of one-topping pizzas that they serve are,

[tex]= \text{Choices of Pizza} \times \text{Choices of Toppings}\\\\= ^3C_1 \times ^{14}C_1\\\\=3 \times 14\\\\= 196[/tex]

Hence, the different types of one-topping pizzas that they serve are 196.

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Line DF is parallel

In triangle ABC with midpoints D, E, and F on sides AB, BC, AC, respectively, segment DF is parallel to BC based on the Midline Theorem

In triangle ABC, if D, E, and F are the midpoints of sides AB, BC, and AC, respectively, then the line segment DE is parallel to BC as per the Midline Theorem.

This theorem states that if a line segment connects the midpoints of two sides of a triangle, that segment is parallel to (and half the length of) the third side of the triangle.

Considering our given scenario, the midpoints of AB and AC are D and F and the line segment formed is DF.

Following the Midline Theorem, this segment DF would be parallel to the third side of the triangle, i.e., BC.

So, the answer to the question 'which segment is parallel to BC?' is DF.

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The probable question may be:

In triangle ABC, Point D, E and F are midpoint of triangle ABC.

which segment us parallel to BC?

A. AB

B. DF

C. AC

D. DE

Answer:

[tex]y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]

Step-by-step explanation:

An equation in the vertex form is written as

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

Where the point (h, k) is the vertex of the equation.

For an equation in the form [tex]ax ^ 2 + bx + c[/tex] the x coordinate of the vertex is defined as

[tex]x = -\frac{b}{2a}[/tex]

In this case we have the equation [tex]y = 9x^2 + 9x - 1[/tex].

Where

[tex]a = 9\\\\b = 9\\\\c = -1[/tex]

Then the x coordinate of the vertex is:

[tex]x = -\frac{9}{2(9)}\\\\x = -\frac{9}{18}\\\\x = -\frac{1}{2}[/tex]

The y coordinate of the vertex is replacing the value of [tex]x = -\frac{1}{2}[/tex] in the function

[tex]y = 9 (-0.5) ^ 2 + 9 (-0.5) -1\\\\y = -\frac{13}{4}[/tex]

Then the vertex is:

[tex](-\frac{1}{2}, -\frac{13}{4})[/tex]

Therefore The encuacion excrita in the form of vertice is:

[tex]y = a(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]

To find the coefficient a we substitute a point that belongs to the function [tex]y = 9x^2 + 9x - 1[/tex]

The point (0, -1) belongs to the function. Thus.

[tex]-1 = a(0 + \frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]

[tex]-1 = a(\frac{1}{4}) -\frac{13}{4}\\\\a = \frac{-1 +\frac{13}{4}}{\frac{1}{4}}\\\\a = 9[/tex]

Then the written function in the form of vertice is

[tex]y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]

Answer:

The vertex form of a parabolic function has the general formula:

f(x) = a(x-h)^2 + k where (h,k) represent the vertex of the parabola.

Therefore, to write the given equation in vertex form, we will need to transform it to the above formula as follows:

y = 9x^2 + 9x - 1  

y = 9(x^2 + x) - 1

y = 9(x^2 + x + 1/4 - 1/4)-1

y = 9((x+1/2)^2 - 1/4)-1

y = 9(x + 1/2)^2 - 9/4 - 1

y = 9(x + 1/2)^2 - 13/4 ..............> The equation in vertex form

Step-by-step explanation:

Hope this helps!!!  Have a great day!!!    : )

Answer:

4 and 5

Step-by-step explanation:

The mode is the value or values which occur most in the data set.

Here 4 occurs 3 times and 5 occurs 3 times, while 7 and 8 only occur once.

Hence there are 2 modes, that is 4 and 5

4 and 5

That’s your answer

Answer:

XY = 5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Calculate the coordinates of X and Y using the midpoint formula

[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂) ]

with (x₁, y₁ ) = A(- 3, 9) and (x₂, y₂ ) = B(- 5, - 3)

X = [[tex]\frac{1}{2}[/tex](- 3 - 5), [tex]\frac{1}{2}[/tex](9 - 3) ] = (- 4, 3)

Repeat with

(x₁, y₁ ) = B(- 5, - 3) and (x₂, y₂ ) = C(7, - 1)

Y = [ [tex]\frac{1}{2}[/tex](- 5 + 7), [tex]\frac{1}{2}[/tex](- 3 - 1) ] = (1, - 2)

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

Calculate the length of XY using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = X(- 4, 3) and (x₂, y₂ ) = Y(1, - 2)

XY = [tex]\sqrt{(1 +4)^2+(-2-3)^2}[/tex]

     = [tex]\sqrt{5^2+(-5)^2}[/tex]

     = [tex]\sqrt{25+25}[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

The area of the right triangle is [tex]43.88\ cm^{2}[/tex]

Step-by-step explanation:

The question in English is

From a right triangle it is known that its hypotenuse measures 20 cm and the sum of the legs measures 24 cm. How much does its area measure?

Let

x-----> the measure of one leg

y----> the measure of the other leg

Assume x is less than y

we know that

Applying Pythagoras Theorem

[tex]20^{2}=x^{2}+y^{2}[/tex] -----> equation A

[tex]x+y=24[/tex]

[tex]y=24-x[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]20^{2}=x^{2}+(24-x)^{2}\\ \\400=x^{2} + 576-48x+x^{2}\\ \\ 2x^{2} -48x+576-400=0\\ \\2x^{2} -48x+176=0[/tex]

Solve the quadratic equation by graphing

The solution is  [tex]x=4.5\ cm[/tex]  

see the attached figure

[tex]x=4.5\ cm[/tex]

[tex]y=24-4.5=19.5\ cm[/tex]

The area is equal to

[tex]A=xy/2=(4.5)(19.5)/2=43.88\ cm^{2}[/tex]