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:

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:

-4.62962962963

Step-by-step explanation:

Answer: 15,000

Step-by-step explanation:

40 percent *37500

= (40/100)*37500

= (40*37500)/100

= 1500000/100 = 15,000

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:

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:

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:

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

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:

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:

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

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

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:

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.

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

Hope this can help ! :)

Answer:

The answer is in the picture above

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:

-32.9985652798%

Step-by-step explanation:

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:

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:

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:

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

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:

n = -11

Step-by-step explanation:

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

5 + 4n + 36 = -3,

41 + 4n = -3,

4n = -44,

n = -11

Answer:

Step-by-step explanation:

-1