21.(03.02)
If f(x) = 7x – 1, what does f(12) represent?

Answer:

y = 3/4( x+5)( x+4) ( x-1)

Step-by-step explanation:

The formula for the polynomial is

y = c( x- a1)( x- a2) ( x-a3)  where c is a constant and a1,a2,a3 are the zeros

We have zeros -5,-4 and 1

y = c( x- -5)( x- -4) ( x-1)

y = c( x+5)( x+4) ( x-1)

We have a y intercept of -15

That means x=0 and y = -15

-15 = c ( 0+5)( 0+4) ( 0-1)

-15 = c( 5) ( 4) (-1)

-15 = c( -20)

Divide each side by -20

-15/-20 = c

3/4 =c

The equation is

y = 3/4( x+5)( x+4) ( x-1)

Answer:

106°

Step-by-step explanation:

Given that the points B, C and D are colinear, it means that

2x + 40 = 5x + 10

collecting like terms

40 - 10 = 5x - 2x

3x = 30

x = 10

Hence the angle ∠E

= 5(10) + 10

= 60°

∠BCE = X + 4

= 10 + 4

= 14°

Given that the sum of angles in a triangle is 180°

∠D + 14 + 60 = 180

∠D = 180 - 74

= 106°

Answer:

x=-7  x=4

Step-by-step explanation:

(X-2)(x+5)=18

FOIL

x^2 +5x -2x-10 =18

Combine like terms

x^2 +3x -10 = 18

Subtract 18 from each side

x^2 +3x -10 -18 = 0

Combine like terms

x^2 +3x -28 =0

Factor

What two numbers multiply to -28 and add to 3

7*-4 = -28

7+-4 = 3

( x+7) ( x-4) =0

Using the zero product property

x+7 =0  x-4=0

x=-7  x=4

The solution is where the two red lines cross. This is the point (3,-4)

If you knew the equation of each red line, you can plug (x,y) = (3,-4) into each equation. You should find the two equations lead to true statements.

Answer:

10 cm overlap required to make a 30 cm long strip.

Step-by-step explanation:

Given:

Four paper strips of the same length.

Two of them glued together with a 4 cm overlap to make a new strip which is 36 cm long.

To find:

Overlap required to make a strip which is 30 cm long = ?

Solution:

First of all, let us understand the concept of overlap.

Please refer to the attached image.

Let length of each strip be [tex]x[/tex] cm.

Given that there is 4 cm overlap resulting in new strip of length 36 cm.

The overlapping length is counted only once as clear from the figure attached.

So, Let us try to find the equation:

[tex]x +(x-4) = 36\\\Rightarrow 2x=40\\\Rightarrow x = 20\ cm[/tex]

i.e. each strip length is 20 cm.

Now, let us assume, an overlap of 'y' cm is to be made to make a new strip of 30 cm.

The equation will be:

[tex](20-y)+20 =30\\\Rightarrow y = 40-30\\\Rightarrow y = 10\ cm[/tex]

Answer:

answer is 1 answer is 4-5 = 1 is 3-6 answer is only 3

Answer:

y = 9x^2 + 12x - 12.

Step-by-step explanation:

y = (3x - 2)(3x + 6)

y = 9x^2 - 6x + 18x - 12

y = 9x^2 + 12x - 12.

Hope this helps!

Answer:

0.8185 or 81.85%

Step-by-step explanation:

The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.

The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive  and if the raw score is below the mean the z sore is negative. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.

For 8 inches:

[tex]z=\frac{x-\mu}{\sigma}=\frac{8-11}{1.5}=-2[/tex]

For 12.5 inches:

[tex]z=\frac{x-\mu}{\sigma}=\frac{12.5-11}{1.5}=1[/tex]

From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1)  - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%

Answer:

I would say the answer is C.

Answer:

I hope it will help you...

Answer:

(x-9)(x-6)

x= 9, x= 6

Step-by-step explanation:

Factored, and roots are:

Answer:

8: 1721 m

9: 1173 m

Step-by-step explanation:

8:

[tex]d = v_{i} t + \frac{1}{2}at^{2}[/tex]

because initial velocity is 0:

[tex]d = \frac{1}{2} at^{2} = \frac{1}{2}(3.2m/s^2)(32.8 s)^2 = 1721.344 m[/tex]

9:

[tex]v_f^2 = v_i^2 + 2ad[/tex]

because velocity initial is 0:

[tex]v_f^2 = 2ad[/tex]

[tex]d = \frac{v_f^2}{2a} = \frac{(88m/s)^2}{2(3.3 m/s^2)} = 1173.3333 m[/tex]

Answer:

do it youself

Step-by-step explanation:

Answer:

A: 39.1304348% OR 39%

B: 33.3%

Step-by-step explanation:

Part A:

find the total amount of children: 90+20+80+40=230

90-20=50

i got this from taking away the amount that like watching tv and not reading so from this you know 50 of those 90 that like watching tv also like tv and reading.

80-40=40

(same explanation as 90-20=50)

then do 50 +40 which equals 90

now you need to turn it into a percentage.

90/230=

9/23

=39.1304348%

if you need round it, do so!

Part b:

40+20=60

20/60= 2/6

=1/3

=33.3%

Answer:

Hey there!

Marked down by 20 percent is equal to 80 percent of the original value.

4.5(0.8)=3.6

9 percent sales tax

3.6(1.09)=3.92

Hope this helps :)

Answer:

$3.92

Step-by-step explanation:

I took the test

Answer:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given function;

y = 5 + x - x²

To find the maximum value, follow these steps

(i) Find the first derivative (which is the slope) of the given function with respect to x. i.e;

[tex]y^{'}[/tex] = [tex]\frac{dy}{dx}[/tex] = [tex]\frac{d(5 + x - x^2)}{dx}[/tex]

[tex]y^{'}[/tex] = [tex]1 - 2x[/tex]

(ii) From the result in (i) determine the value of x for which the slope is zero. i.e.

x for which

1 - 2x = 0

=> 1 = 2x

=> x = [tex]\frac{1}{2}[/tex]

Therefore, the value of x for which the function is maximum is [tex]\frac{1}{2}[/tex]

Answer:

x = 1/2

Step-by-step explanation:

The standard equation of a quadratic function is given by:

y = ax² + bx + c, If a > 0 then the graph has a minimum but if a < 0, then the graph has a maximum. To find the maximum or minimum, we differentiate the function with respect to x and equate to zero that is y'(x) = 0.

For the function y = 5 + x - x², a = -1 < 0, therefore it has a maximum.

Differentiating with respect to x:

y'(x) = 1 - 2x

Equating to zero

-2x + 1 = 0

-2x = -1

x = -1/ -2

x = 1/2

The function has a maximum at x = 1/2

Answer:

We have the problem:

|3r−15| if r<5

First we see the equality, if r = 5 we have:

I3r - 15I = I3*5 - 15I = I0I = 0.

Then the only restriction that we have is:

I3r - 15I > 0.

now, we could simplify it a bit further:

if r < 5, then the thing inside the absolute value will always be negative:

Then we can write:

I3*r - 15I = -(3*r -15) > 0

multiplying by -1 in both sides

(3r - 15) < 0.

if we keep simplifying this, we will get our initial restriction:

3r - 15 < 0

3r < 15

r < 15/3 = 5

r < 5

Answer:

c.6

Step-by-step explanation:

I would estimate 6.12 to 6 and 38.064 because I know 36 is a common denominator of 6. 36/6=6

Hope this helps.

Answer:

The slope is 2/3

Answer:

2/3

Step-by-step explanation:

This is written in point slope form

y - y1 = m(x-x1)

3(y - 1) = 2x + 2​

Divide each side by 3

(y - 1) = 1/3(2x + 2)

Factor out a 2

(y - 1) = 2/3(x -  -1)

​​The slope is 2/3

Answer:

93107

Step-by-step explanation:

add all of the numbers together

divide by 5 since there are 5 numbers

you would get 92106.8

so round that up since you cannot have 1/8 of a squirrel

Hope this helps!!

Answer:

(-5,0)

Step-by-step explanation:

In case when you tracking the finger across the line, at which there is an increase or decrease in y axis so this is we called intervals. Moreover, the interval notation is also necessary as it depicts the beginning and ending points. In this, the first number denotes the minimum number while the second number denotes the maximum number

For Decreasing:

(-8,-5)

(4,8)

For Increasing:

(-5,0)

Answer:

80 = EG

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

40 = 1/2 EG

Multiply each side by 2

80 = EG

Answer:

80 deg

Step-by-step explanation:

Theorem:

The measure of an inscribed angle is half the measure of the intercepted arc.

m<EFG = (1/2)m(arc)EG

40 deg = (1/2)m(arc)EG

m(arc)EG = 2 * 40 deg

m(arc)EG = 80 deg

Answer: 2.5

Step-by-step explanation:

To find a mean, the average, we have to add everything together.

So we add 1 + 4 + 3 + 2, which is equal to 10. The next step to find the average is to divide by the total number of “things” which is the 4 puppeteers.

10/4 is 2.5

==========================================================

Explanation:

Let's say this is a 1 by 1 square. The area is 1*1 = 1 square unit. Whatever the area of the triangle is, we divide it over 1 and it will yield the same value as the area of the triangle. In other words, the area of the triangle will be the answer.

Along the top we have 3 ticks to indicate the top segment has been cut into 3+1 = 4 equal parts. The horizontal distance from the the vertical side of the triangle to the peak of the triangle is 3/4 units. This is because we travel 3 ticks out of 4 total. So this is the height when we consider the vertical segment of the triangle to be the base.

The base is 1 unit as it spans the original square's side length

base = 1

height = 3/4

area of triangle = (1/2)*(base*height)

area of triangle = (1/2)*(1*3/4)

area of triangle = 3/8

ratio of triangle area to square area = (triangle area)/(square area)

ratio of triangle area to square area = (3/8)/1

Answer:

3/8

Step-by-step explanation:

let side of square=x

Area of a square =x^2

height of a triangle= 3x/4  ( 4/4=1/4) since height is only 3x/4 from the square)

( base =x same side as a square)

Area of a triangle=1/2 bh=1/2(x*3x/4)= 3x^2/8

the ratio of shaded triangle to the area= (3x^2/8)/x^2=3x^2/8x^2=3/8

Answer:

Hey there!

Let the cost of one uniform be c, so the expression becomes

c+13+11+18

Thus, we have c+42

Hope this helps :)

Answer:

32

Step-by-step explanation:

13+11+8=32

It seems like information is missing. If so, then please update.

When intersecting a plane and a line, there are two possibilities:

Hey Mate !

Your Answer is given in the snip below !!

Please do mark me as brainliest !!!

(ANSWER=  (D)   [tex]\frac{1}{6}[/tex] )

Explanation

Answer:

You have a standard number cube.

What is the probability of rolling a number less than 3, and then rolling a prime number?

D. 1/6

Answer:

49.87% of the population has a heart rate between 68 and 77.

Step-by-step explanation:

We are given that the mean of the data for the resting heart of adults is 68 beats per minute and the standard deviation is 3 beats per minute.

Let X = the data for the resting heart of adults

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 68 beats per minute

           [tex]\sigma[/tex] = standard deviation = 3 beats per minute

Now, the percentage of the population that has a heart rate between 68 and 77 is given by = P(68 < X < 77)

    P(68 < X < 77) = P(X < 77) - P(X [tex]\leq[/tex] 68)

    P(X < 77) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{77-68}{3}[/tex] ) = P(Z < 3) = 0.9987

    P(X [tex]\leq[/tex] 68) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{68-68}{3}[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50

The above probability is calculated by looking at the value of x = 3 and x = 0 in the z table which has an area of 0.9987 and 0.50 respectively.

Therefore, P(68 < X < 77) = 0.9987 - 0.50 = 0.4987 or 49.87%

Answer:

Angle:

When two lines/rays intersect at a point, they form an angle.

=> Angles may be in radians and degrees.

See the attached file in which two rays intersect to form an angle.

Answer:

[tex]\boxed{\mathrm{view \: explanation \: and \: attachment}}[/tex]

Step-by-step explanation:

Two lines (arms/rays) intersect at one point (vertex) creating an angle.

Answer:

3kg

Step-by-step explanation:

3kg because half of 2 is 1 which then means 2+1 will equal to 3

The total weight of the fish is = 3kg

Weight of an object or a body is the relative mass of that body in Kilogrammes.

The weight of the fish = 2kg + (1/2 × 2kg)

= 2 + 1 = 3kg

Therefore, the total weight of the fish is = 3kg

Learn more about weight here:

https://brainly.com/question/2337612

Answer:

the ansewr is b

Step-by-step explanation:

Answer:

2 CDs and 6 movies

Step-by-step explanation:

Let the number of CD you bought be x, and the number of movies you bought be y.

Since you bought 8 items in total,

x + y = 8 ______(1)

The sum of money spent is 78, so

9x + 10y = 78 ________(2)

From equation (1),

x = 8 - y ________(3)

Substitute (3) into (2),

9 (8-y) + 10y = 78

72 - 9y + 10y = 78

- 9y + 10y = 78-72

y = 6

Now substitute y=6 into (3).

x = 8 - y

x = 8-6

x = 2

Therefore, you bought 2 CDs and 6 movies.