At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x-axis?
-5
-2
Ο Ο Ο Ο
2
5

Answer:

4(-2) + 8(4) / 7 - (-2)²

-8 + 32 / 7 - 4

24 / 3

= 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

18

Answer:

Step-by-step explanation:

P(x)= x^2-5x+c=0

P (-2)= (-2)^2-5 (-2)+c=0

= 4+10+c=0

=14+c=0

C=(-14)

Answer:

[tex]\fbox{\begin{minipage}{4em}c = -14\end{minipage}}[/tex]

Step-by-step explanation:

Given:

A quadratic equation: [tex]x^{2} - 5x + c = 0[/tex], with [tex]x =-2[/tex] is a solution.

Solve for:

Value of c

Step 1: define the problem

If [tex]x = -2[/tex] is a solution of equation [tex]f(x) = 0[/tex], then [tex]f(-2) = 0[/tex]

Step 2: Perform the calculation

Substitute [tex]x = -2[/tex] into original quadratic equation, we have:

[tex](-2)^{2} - 5(-2) + c = 0[/tex]

Perform the square and multiplication:

[tex]4 + 10 + c = 0[/tex]

Transfer all of numbers to the right side, except c:

(notice for the change in sign of numbers)

[tex]c = (-4) + (-10)[/tex]

Perform the sum on the right side to get c:

[tex]c = -14[/tex]

Hope this helps!

:)

Answer:

B:(x-2)^2+(y-1)^2=64

Step-by-step explanation:

center is (2,1), point is (2,9)

so the radius=9-1=8

(x-2)^2+(y-1)^2=64

Answer: a+b = 12

Los triangulos verdes son semejantes entre si por tener dos lados proporcionales y el angulo comprendido respectivamente iguales. De igual forma los triangulos azules son semejantes por tener dos lados proporcionales y el angulo comprendido respectivamente iguales. En general el factor de proporcionalidad de los triangulos es 1:2 siendo en ambos casos el grande el doble del pequeño. Por tanto

a+2 = 2(3)

a=4

10 = 2(b-3)

b=8

Luego a+b = 12

Answer:

40 millimetres

Answer:

40

Step-by-step explanation:

Answer:

12.5 cm

Step-by-step explanation:

Find the height of a prism in the following way:

height = Volume divided by Area of cross section.

Substitute the values and so you have:

1500 divided by 120 = 12.5

Answer:

Y = 0

Step-by-step explanation:

Y = -1/2 x²

To find y-intercept, substitute X = 0

Solve the equation for y

Y = 0

Answer:

x = 7.5

Step-by-step explanation:

Given BE is parallel to CD and intersects the other 2 sides, it divides those sides proportionally, that is

[tex]\frac{AE}{ED}[/tex] = [tex]\frac{AB}{BC}[/tex] , substitute values

[tex]\frac{10}{8}[/tex] = [tex]\frac{x}{6}[/tex] ( cross- multiply )

8x = 60 ( divide both sides by 8 )

x = 7.5

Answer:

alternate exterior angles

Step-by-step explanation:

The two horizontal lines are simply two lines.

The other line is a transversal since it intersect the two lines at two different points.

Angles 1 and 8 are on two different sides of the transversal. That makes them alternate angles. They are on the outside of the two lines. That makes them exterior angles. Put the two things together and they are:

alternate exterior angles

Answer:

(-2,0.5)

Step-by-step explanation:

1st set of Point=(-5,-2)

2nd set  of Point=(1,3)

Midpoint=(X1+X2/2 , Y1+Y2/2)

=(-5+1/2 , -2+3/2)

=(-2,0.5)

Answer:

Step-by-step explanation:

If point D is located on the segment CE, then point C, D and E lies on the same line i.e they are collinear. Mathematically, CD+DE = CE

Given CD = 24 and DE = x and CE = 5x, on substituting this values in the equation we have;

[tex]24+x = 5x\\5x-x = 24\\4x = 24\\x = 24/4\\x = 6[/tex]

Since CE = 5x, CE = 5(6) = 30

The measure of segment CE is 30

Answer: 48 red drops

Step-by-step explanation:

ratio of yellow food drops to red food drops is 8:12

8:12 simplifies to 2:3

2:3 = 2/5:3/5

2x/5 = 32 = # of yellow drops (where x is the total # of drops)

2x/5 = 32

2x = 160

x = 80

Since there are 80 total drops and 32 yellow drops, there must be 48 red drops (80-32=48)

Reasoning:

'a' is less than 0, so we write a < 0

Since a < 0, this means a^4 > 0. Raising a negative to an even exponent will make the result positive. Example: (-2)^4 = 16

Applying the cube root to some positive number leads to some other positive number.

So far we see that the expression    a^(4/3)   is positive

The final result however is negative because the negative out front flips things from positive to negative.

It turns out it doesn't matter if 'a' is positive or negative. As long as 'a' is nonzero, then   -a^(4/3)   is negative. If a = 0, then the whole thing is 0.

Answer:

y= 71   Reason: alternate angle to 71 degrees

z = 44

Step-by-step explanation:

You already solve for x.

y = 71 because it is alternate to 71 degrees you see up there.

For z:

all angles inside a triangle sum upto 180

z=180-(71+65) = 44

Answer:

x=10

Step-by-step explanation:

x-4=6

To isolate x, you can add 4 to both sides of the equation:

x-4+4=6+4

x=10

Hope this helps!

Step-by-step explanation:

x=10

In this problem, we have a pair of like terms in our x terms.

3x and -2x are like terms because they are exactly alike except for the coefficients or the numbers in front of the variables.

______________________________

Hey!!

3x and -2x are the like terms.

Explanation:

To add and subtract the algebraic expression, there should be the like and unlike terms.Unlike terms are those which do not have the same base and like terms are those which have the same base.

Hope it helps

Good luck on your assignment

_____________________________

Answer:

4 11/12

Step-by-step explanation:

x2−4x−12<0

x2+10x−24<0

x−1=2y

x=−5912

Decimal Form:

x=−4.91¯6

Mixed Number Form:

x=−4 11/12

Answer:

There is no solution to this.

Step-by-step explanation:

Maybe check for a typo?

you would first need to calculate the discriminant, D= b^2-4 a c

D= (-12)^2 -4*1*59

Simplify

D=-92

Since D<0, the quadratic equation has no real solutions.

Unfortunatly brainly does not provide me with graphics support.

First thing to realise is that we are dealing with inequality which essentially means that the solution will be an interval or more specifically a possibly constrained set of value.

Here is the inequality:

[tex]

350 > 125 + 15r

[/tex]

If we subtract 125 and then divide by 15 on both sides we get:

[tex]

r > 15

[/tex]

This notation essentialy means that inequality is true for any r smaller than 15. We can write that as r being in some set of numbers that represents the possibilites:

[tex]r\in\{14,13,12,\dots,-\infty\}[/tex]

In interval notation that is:

[tex]r\in(-\infty,15)[/tex]

Answer:

Step-by-step explanation:

[1,2]

local maxima means curve is curved downwards.

in [1,2] it is curved downward.

Answer:

The answer is [1,2]

Step-by-step explanation:

Do you understand now.

Feel free to ask for further explanation

Answer:

a7=1458

Step-by-step explanation:

2; -6; 18... a geometric progression

a1=2; a2=-6; a3=18

r=a2/a1=-6/2

r= -3

a7=a1*r⁶

a7=2*(-3)⁶=2*729

a7=1458

Answer:

1/3 I think I am not sure tho.

btw I know st math I used to do that to! LOL!

Step-by-step explanation:

If I am please mark me BRAINLIEST!

Answer: 60 kids, 180 adults

Step-by-step explanation:

Let x be the number of children and y be the number of adults eating.

If they have 240 people eating then x+y=240.

If they have to fundraise 1200 then 2x+6y=1200.

Solving the system of equations, we can multiply the first equation by 2 to get 2x+2y=480. Then subtract the two equations and get -4y=-720, so y=180. Substitute y=180 back in to get x=60.

Hope that helped,

-sirswagger21

Answer:

Angle measure two is equal to 75º and Angle measure one is equal to 105º

Step-by-step explanation:

I know this because angle one is alternate exterior angle with angle 7 and angle seven forms a staight line with angle 75 so to find angle 7 you have to do 180-75 and that would equal 105.

for angle two it is interior angles with angle 75 so this means that are congruent angles which means they both have the same measure

Answer: <2 is 75 degrees & <1 is 105 degrees

Step-by-step explanation:

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]4(x + 2) = 2x + 10[/tex]

Distribute 4(x+2).

[tex]4x+8 = 2x + 10[/tex]

Subtract 2x and 8 from both sides.

[tex]4x-2x=10-8[/tex]

[tex]2x=2[/tex]

Divide both sides of the equation by 2.

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

[tex]x=1[/tex]

Answer:

x = 1

Step-by-step explanation:

4(x + 2) = 2x + 10

You start by expanding 4(x +2)

i.e. 4x + 8 = 2x + 10

Then, subtract 2x from both sides of the equation

4x + 8 - 2x = 2x + 10 - 2x

4x - 2x + 8 = 2x - 2x + 10

2x + 8 = 10

Subtract 8 from both sides of the equation

i.e. 2x +8 - 8 = 10 - 8

2x = 2

Divide both sides of the equation by the coefficient of x above(which is 2)

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

x = 1

Hope this helps :))

Answer:

see below

Step-by-step explanation:

a) They could be congruent because having the same angles doesn't necessarily mean that they are congruent.

b) These triangles are  congruent by ASA because using the sum of angles in a triangle they have the same angles and one congruent side.

Answer:

a) F

b) C

Step-by-step explanation:

Brainliest please?

For a) it only tells you all the angles, which makes them similar triangles, but none of the sides are given, so it cannot be determined whether they are congruent.

For b) it is not to scale and using a little subtraction, you can quickly use the fact that there are 180 degrees in a triangle, you can determine that the 2 triangles have the same angles, with the side with 9.2 cm between 58 and 68 degree vertices on both triangles, making the 2 triangles congruent by ASA.

QED

Answer:

40 pages

Step-by-step explanation:

240/12 = 20 = pages read in 1 hour

20 x 2 = 40 = pages read in 2 hours

Answer:

Los triangulos son iguales porque tienen dos lados y el angulo comprendido  respectivamente iguales, por tanto

[tex]3x = x+8\\2x=8\\x=4\\[/tex]

Answer:

A and D

Step-by-step explanation:

We have to create a perfect square. To make x^2+bx+c into a perfect square, c has to be (b/2)^2. In this case, b is -10. so, c has to be (-10/2)^2, which is 25. To make the left hand side 25, we would have to add 30 to both sides.

This leads to a new equation:

x^2 - 10x + 25 = 9+30

x^2 - 10x + 25 = 39

Now, we can change the left hand side to a perfect square.

(x-5)^2 = 39. (the -5 is b/2)

Then we square root both sides;

x-5 = +/- sqrt39. (When you square root an expression, remember that you need to include both the positive AND negative)

x = 5-sqrt39 or 5+sqrt39