f(x) = x² + 2ax + a² - a
g(x) = 4 - x²

Let variable a be a real number. Find the range of values of a such that the equation f(x) = g(x) has two different solutions.

***The answer should be -2 < a < 4, but I don't know why.

Answer:

[tex]16x {y}^{2} + 10xy \\ = 2xy(8y + 5) \\ 2xy = 0 \: or \: 8y + 5 = 0 \\ y = - \frac{5}{8} [/tex]

Answer:

C. QR = 2 • PR

Step-by-step explanation:

According to given information we can draw a right triangle with angle measures as follows :

30-60-90 and for this special right triangle the side length would follow as:

The side length that sees angle measure 30 = a

The side length that sees angle measure 60 = a[tex]\sqrt{3}[/tex]

The side length that sees angle measure 90 = 2a

following this information the:

PR(sees 30 degrees) = a (can be represented as PR in this case)

and so

QR(sees 90 degrees) = 2a (2*PR  in this case)

PQ(sees 60 degrees) = a[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] *PQ in this case)

The correct option is C. QR = 2 • PR

Answer:

72 women

Step-by-step explanation:

sorry it let me answer now

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

Work Shown:

m = number of men

w = number of women

The ratio of men to women is 5 to 4, which means m/w = 5/4

We can cross multiply and solve for m like so

m/w = 5/4

4m = 5w

m = 5w/4

m = 1.25w

Because there are 162 people total, we then can say:

m+w = 162

1.25w + w = 162

2.25w = 162

w = 162/(2.25)

w = 72

There are 72 women at this company and m = 1.25w = 1.25*72 = 90 men

m+w = 90+72 = 162

m/w = 90/72 = (5*18)/(4*18) = 5/4

Both of those two equations above help confirm our answer.

Answer:

117600

Step-by-step explanation:

50 x 49 x 48 = 117,600 ways

You have 50 possible for 1st, 49 for 2nd, 48 for 3rd

or

Permutations 50P3 = 117,600

There are total 59280 ways that can the runners finish first, second and third in a race.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]

Where,

[tex]nP_{r}[/tex] is permutation.

n is total number of objects.

r is number of objects selected.

According to the given question

Total number of runners, n = 40

Total number of runners to be selected for first, second and third position  is 3 i.e. r = 3

Therefore,

The number of ways can the runners finish the first, second and third is given by

[tex]40P_{3} = \frac{40!}{((40-3)!} =(40)(39)(38)=59280[/tex]

Hence, there are total 59280 ways that can the runners finish first, second and third in a race.

Learn more about Permutation here:

https://brainly.com/question/2295036

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Answer: 15,000

Step-by-step explanation:

40 percent *37500

= (40/100)*37500

= (40*37500)/100

= 1500000/100 = 15,000

Answer:

75

Step-by-step explanation:

divide 4 by 300 and then you will get the answer of 75. I'm so sorry if this is wrong

Answer:

x=20

Step-by-step explanation:

It all equals 360º and there are two of each angle. So, we can add 5x+5x+(3x+20)+(3x+20)=360º. Subtracted 40 and simplify. So 16x=320.So divide by 16 and you get that x=20.

Answer:

n = -11

Step-by-step explanation:

5 + 4(n + 9) = -3,

5 + 4n + 36 = -3,

41 + 4n = -3,

4n = -44,

n = -11

Answer:

-32.9985652798%

Step-by-step explanation:

maybe -10.8 cuz it looks like u gotta multiply by 10 to get the full shape

Answer:

-4.62962962963

Step-by-step explanation:

Answer:

Goran: $54

Juan: $18

Mai: $12

Step-by-step explanation:

Please leave “thanks” heart

Answer:

yeah f(x) = 2

Step-by-step explanation:

because there is no x and f(x) is on positive 2

Answer:

24 units^2

Step-by-step explanation:

bc=6

ab=8

area of a triangle: b*l/2

6*8/2=24

Answer: Area of the figure = 24

Concept:

Here, we need to know how to find the area of a triangle.

Area (triangle) = (1/2) · b · h

b = base

h = height

Solve:

Given coordinates on the graph

A (-5, 5)

B (-5. -3)

C (1, -3)

To find the value of the height, we need to know the value of a vertical line, meaning the [x] value of the points on the line is equal. As we can see from the given coordinates, point A and point B has the same [x] value. The value of the height equals the difference between A and B's [y] value

A (-5, 5)

B (-5, -3)

5 - (-3) = 5 + 3 = 8

To find the value of the base, we need to know the value of a horizontal line, meaning the [y] value of the points on the line is equal. As we can see from the given coordinates, point B and point C has the same [y] value. The value of the base equals the difference between B and C's [x] value

B (-5, -3)

C (1, -3)

1 - (-5) = 1 + 5 = 6

Given expression

A = (1/2) · b · h

Substitute values into the expression

A = (1/2) · (6) · (8)

Simplify by multiplication

A = (1/2) · (48)

[tex]\boxed{A =24}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

362.984 could be the answer but don't judge me I could be wrong.

Step-by-step explanation:

I'm not 100% sure.

From what I've been taught, they're asking for the amount of snow in cm that is melting per minute.

What I did:

I input 17 where r is in the equation for Volume. I solved it and got the answer: 20579.52628 > Rounded to nearest 10th > 20579.5

I then took that number and multiplied it by 0.1 and got: 2057.95

This is most likely incorrect based on the numbers that were given, but it should help to know that how to solve for Volume.

Answer:

Step-by-step explanation:

-1

Answer:

[tex]f(x) = 2x - 1 \\ g(x) = 3x \\ h(x) = {x}^{2} + 1 \\ f( g(x)) = 2(3x) - 1 = 6x - 1 \\ f( g( - 3)) = 6( - 3) - 1 = - 19 \\ h(f(x)) = {(2x - 1)}^{2} + 1 \\ h(f(0)) = {(2(0) - 1)}^{2} + 1 \\ h(f(0)) = 2[/tex]

Answer:

The answer is in the picture above

Here is how your graph should look. Make sure to plot (0,-8) as your y-intercept.

Hope this can help ! :)

Answer:

p= 6.33333333333

Step-by-step explanation:

U divide 19/3 to get the value of p

Hope this helps :)

Can u plz mark me as brainliest plz? :)

Answer:

6y + 3

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

15+40+10+40+30=135.

135÷5 I.e the total average of the number.

135÷5=27

Answer:

27

Step-by-step explanation:

15+40+10+40+30=135

135/5

Because 5 is the number of numbers

=27

Answer:

3 feet 6 inches

Step-by-step explanation:

If we add those inches together, we get 42 inches. Turn that to feet (12 in in a foot) and we get 3.5 feet, or 3 feet and 6 inches.

Answer:

its B

Step-by-step explanation:

X:2

Y:4

Z:6

The values that best complete the chart as per the concept of ratio are X:2, Y:4, and Z:6.

To determine the correct values for the chart, let's analyze the given information about an object moving at a constant acceleration:

The first column represents time in seconds (0, 1, 2, 3).

The second column represents velocity in meters per second (0, X, Y, Z).

Since the object is moving at a constant acceleration, its velocity is changing by the same amount in equal time intervals.

We can use the formula for constant acceleration:

Velocity (V) = Initial Velocity (U) + (Acceleration × Time)

Given that the object starts from rest (initial velocity, U = 0), we can deduce the following:

At time 1 second (T = 1), the object's velocity is X m/s.

At time 2 seconds (T = 2), the object's velocity is Y m/s.

At time 3 seconds (T = 3), the object's velocity is Z m/s.

Based on this information, the correct values for the chart are:

X: 2 (Velocity at 1 second is 2 m/s)

Y: 4 (Velocity at 2 seconds is 4 m/s)

Z: 6 (Velocity at 3 seconds is 6 m/s)

To learn more about the ratio;

https://brainly.com/question/13419413

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Answer:

m < U = 65°

Step-by-step explanation:

Given that m < PTU° = 115°, and that it is a supplement to < UTV, then we can establish that m < UTV = 65° because their angles must add up to 180°.

From this point forward, we'll name < UTV as < T of △VUT.

Now that we have the measure of < T, we can find out the value of the missing angle, < VUT, through the following equation:

180° = m < V° + m < T° + m < U°

180° =  m < 50° + m < 65° +  x

180° =  m < 115° +  x

Subtract m < 115 from both sides to isolate x:

180° -  m < 115° =  m < 115° - m < 115° +  x

65° = x

To verify that we have the correct answer, we'll add up all the measures of the three angles of the triangle to see if it sums up to 180°:

180° = m < V° + m < T° + m < U°

180° = m < 50° + m < 65° + m < 65°

180° = m < 50° + m < 65° + m < 65°

180°  = 180°  (True statement).

Therefore, the measure of the missing angle, < U = 65°

Answer:

Don't quite see how this should fall into the mathematics category