What is the value of k?

Please answer ASAP, Thank you :)

Answer:

x = 2

x = -4

x = -3/2

Step-by-step explanation:

We need to find the roots of the equation

2x^3 + 7x^2 – 10x – 24 = 0

We can factorize the equation into

(x-2)(x+4)(2x + 3) = 0

Roots

x = 2

x = -4

x = -3/2

The answer to your question is also attached in the images below

Answer:

x=2 ; x=-4 or x=-3/2

Step-by-step explanation:

We are given a cubic polynomial

[tex]2x^3+7x^2-10x-24=0[/tex]  

Here as we are having a cubic equation to factorize, we have to find some value of x such that when we put that value in place of x , it gives us a 0. We have to try it randomly like first we try it for x=1 then x=2 and so on.

On trying for x=2 , we see that the equation becomes 0=0 and hence x=2 is one of the solution. And also as x=2 is one of the solution, (x-2) must be one of the factor. Now we use this property to determine the other factor like this.

[tex]2x^3+7x^2-10x-24=0[/tex]

Adding and subtracing [tex]4x^2[/tex] to [tex]2x^3[/tex] we get

[tex]2x^3-4x^2+4x^2+7x^2-10x-24=0[/tex]

Now we take out [tex]2x^2[/tex] as GCF

[tex]2x^2(x-2)+11x^2-10x-24=0[/tex]

Now subtracting and adding [tex]22x[/tex] to [tex]11x^2[/tex]

[tex]2x^2(x-2)+11x^2-22x+22x-10x-24=0[/tex]

taking [tex]11x^2[/tex] as GCF out  

[tex]2x^2(x-2)+11x(x-2)+22x-10x-24=0[/tex]

[tex]2x^2(x-2)+11x(x-2)+12x-24=0[/tex]

[tex]2x^2(x-2)+11x(x-2)+12(x-2)=0[/tex]

Now taking [tex](x-2)[/tex] out as GCF

[tex](x-2)(2x^2+11x+12)[/tex]

Now we need to split the middle term of [tex](2x^2+11x+12)[/tex] to factorize it in such a way that their product is 2*12 and sum is 11. We have 8 and 3 as these factors.

Hence it can be factored like this

[tex](2x^2+11x+12)\\2x^2+8x+3x+12\\2x(x+4)+3(x+4)\\(2x+3)(x+4)[/tex]

Hence our answer will be

[tex](x-2)(2x+3)(x+4)=0[/tex]

And thus the solutions will be

x-2=0 : x=2

x+4=0 ; x=-4

2x+3=0 ; x=-[tex]\frac{3}{2}[/tex]

Answer:

Just take out the two lines and make it stay a negative number!

Which is (c) -11

2 bar represents absolute value which is positive value of passed number.

so |-6| will give positive of 6 that it 6.

so after taking absolute value now you have a nagetive sign in front of value we obtained. so your number now become negative.

so

- (|-11| )= -(11) = -11

so answer is option C

Answer:

it might be d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

hi

Answer:

[tex]7+6\times(14-9)=37[/tex]

Step-by-step explanation:

The given expression is

[tex]7+6\times14-9[/tex]

If we evaluate the expression as it is  we will get;

[tex]7+84-9=82[/tex]

But we want to insert parenthesis so that we will use PEDMAS to obtain 37 as the result.

The only way this can be achieved is when we insert the parenthesis as shown below;

[tex]7+6\times(14-9)=7+6(5)=7+30=37[/tex]

Answer:

Step-by-step explanation:

We graph the function.

Final answer:

Plotting points that satisfy an equation or inequality creates a graph representing their relationship, with lines or curves like parabolas depending on the equation type.

Explanation:

When we plot all the points that satisfy an equation or inequality, we create a visual representation of the relationship between variables that are described by that equation or inequality. For instance, if the equation is linear and we plot its solutions on a graph, we will see a line. The y-intercept is an important feature of this line, indicating the point where the plot crosses the y-axis. In the case of a quadratic equation, plotting its solutions results in a parabola. If we want to determine whether the plot crosses a particular axis, such as the t-axis, we may need to analyze the discriminant (D) of the quadratic equation, which tells us whether the equation has real roots and, consequently, intersects with the axis.

The total surface area of a square pyramid with a side length of 4 feet and a height of 6 feet is 64 square feet.

To find the total surface area of a square pyramid, we need to calculate the area of the base and the area of all four triangular faces. The area of the base (a square) can be found using the formula side². In this case, that's 4² which equals 16 square feet. To find the area of a triangular face, we use the formula 0.5 * base * height. Since we have 4 identical triangular faces, we calculate this once and then multiply by 4. The base of each triangle is the side of the square, which is 4 feet, and the height is given as 6 feet. Plugging these values into the formula we get 0.5 * 4 * 6 = 12 square feet for one triangular face. Since there are 4 of these faces, the total surface area of the faces is 4 * 12 = 48 square feet. Adding this to the area of the base, we find the total surface area of the pyramid is 16 + 48 = 64 square feet.

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To find the total area of a square pyramid, calculate the area of the base and the area of the four triangular faces. The total area is 64 square feet.

To find the total area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces. Since the base is a square with sides measuring 4 feet, its area is 4 x 4 = 16 square feet.

To find the area of each triangular face, you can use the formula for the area of a triangle: (base x height) / 2.

In this case, the base of each triangular face is 4 feet and the height is 6 feet, so the area of each face is (4 x 6) / 2 = 12 square feet. Since there are 4 triangular faces, the total area of these faces is 4 x 12 = 48 square feet.

Finally, you can find the total area of the pyramid by adding the area of the base and the area of the faces: 16 + 48 = 64 square feet.

Therefore, the total area of the square pyramid is 64 square feet.

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9x= 4x +35

5x=35

x=6

ask if u need explanation

To find the value of x that makes the equation true, you need to solve the equation 9x = 4x + 25 by subtracting 4x from both sides and then dividing by 5 to find x = 5.

Value of x: To find which value of x makes the equation 9x = 4x + 25 true, you need to solve the equation.

Step-by-step explanation:

Subtract 4x from both sides: 9x - 4x = 25

This simplifies to 5x = 25

Divide by 5 to solve for x: x = 5

Therefore, the value 5 makes the sentence 9x= 4x+ 25​ true.

Answer: [tex]x=-8\\y=0[/tex]

Step-by-step explanation:

You can apply the elimination method:

- Multiply the first equation by -2.

- Add both equations to cancel out the variable x.

- Solve for y:

[tex]\left \{ {{(-2)(x-4y)=-8(-2)} \atop {2x-3y=-16}} \right.\\\\\\\left \{ {{-2x+8y=16} \atop {2x-3y=-16}} \right.\\ ------\\5y=0\\y=0[/tex]

- Substitute y=0 into any of the original equations ans solve for x. Then:

[tex]x-4(0)=-8\\x=-8[/tex]

The answers are:

[tex]x=-8\\y=0[/tex]

Since we have to equations, first we need to isolate one variable, and then substitute it into the other equation.

So, isolating x from the first equation we have:

[tex]x-4y=-8\\x=-8+4y[/tex]

Then, substituting "x" into the second equation, we have:

[tex]2(-8+4y)-3y=-16\\-16+8y-3y-=-16\\5y=-16+16\\5y=0\\y=\frac{0}{5}=0[/tex]

Therefore, substituting "y" into the first equation, we have:

[tex]x-4(0)=-8\\x-0=-8\\x=-8[/tex]

So, the solutions for the system of equation are:

[tex]x=-8\\y=0[/tex]

Have a nice day!

Answer:

750 sq. ft

Step-by-step explanation:

To understand the area of a triangle, we can start with the area of a rectangle. The area of a rectangle with some length (which I'll call L) and some width (which I'll call W) is just the product of those two values, L × W. How does this carry to triangles? Well we can take any triangle we want and draw a rectangle around it, using the base of the triangle as one of the rectangle's sides.

Now, the key here is to cut that original rectangle into two smaller ones, starting at the top point of the triangle. Notice now that half of the left rectangle is taken up by the orange triangle, and half of the right one as well. Putting those two together, we can say that the big orange triangle takes up exactly half of the green rectangle, or in other words, its area is (L × W) ÷ 2. Of course, when we talk about triangles, we use the words "base" (B) and "height" (H) rather than length and width, so you could also say that the area of a triangle is (B × H) ÷ 2.

Taking this into our problem, we're given a base of 100 ft and a height of 15 feet; using our newly-discovered equation, we find its area to be

(100 × 15) ÷ 2 = 1500 ÷ 2 = 750 sq. ft.

Circumference is found by multiplying the diameter by PI,

so a circumference of 6PI means the diameter is 6 inches.

Area is found using the formula PI x r^2

r = 1/2 the diameter

r = 6/2 = 3

The area becomes 3^2 x PI = 9PI inches.

The answer is C.

Answer:

[tex]d = \sqrt{164} = 12.8[/tex]

Step-by-step explanation:

We can find the distance using the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We then substitute (2,-3) as [tex](x_1,y_1)[/tex] and (10,7) as [tex](x_2,y_2)[/tex].

[tex]d=\sqrt{(10-2)^2+(7--3)^2} \\d=\sqrt{(8)^2+(10)^2} \\d=\sqrt{64+100}\\d=\sqrt{164}=12.8[/tex]

Applying the angle bisector theorem, the value of x is: B. 5.3.

An angle bisector divides an angle into two congruent halves. According to the angle bisector theorem, an angle bisector of a triangle divides the interior angles opposite sides in such a way that the corresponding lengths are proportional to each other. This means that the corresponding sides have ratios that are equal.

In the image given, applying the angle bisector theorem, we have the following proportion which we can use to find the value of x in the triangle given above:

6/x = 9/8 [according to the angle bisector theorem]

Cross multiply

(9)(x) = (6)(8)

9x = 48

Divide both sides by 9

9x/9 = 48/9

x = 5.333

Thus, to the nearest tenth, the value of x is approximately calculated as: B. 5.3

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Answer:

A- Students who do not act

B- Every 4th student selected from an alphabetical register of the club

E- Students whose names are randomly selected from a hat

Step-by-step explanation:

A drama teacher wants to decide where the drama club should go to celebrate their performance.

We are to determine whether which of the options is not a representative sample.

By definition, a sample which is the subset of the bigger population reflecting the characteristics is said to be a representative sample.

So the correct options are:

A- Students who do not act

B- Every 4th student selected from an alphabetical register of the club

E- Students whose names are randomly selected from a hat

Answer:

Step-by-step explanation:

The objective is to determine where the drama club should go to celebrate their final performance.

In orther to achieve that objective, the sample must be representative. For example, the sample must be formed by students that actually acts.

Therefore, A, B and E are not representative samples because they don't act, every 4th student selected doesn't imply that all of them act, and selecting randomly names won't represents students that actually acts.

Answer:

Step-by-step explanation:

Payment Shock is when there is a risk that future periodic payments of a loan increases and thus may put the borrower at risk of defaulting on the loan.

It can occur for many reasons, such as:

People are usually attracted to these mortgages because low initial monthly payments. But sometimes, these backfire on them because of reasons stated above and put them at risk when monthly payments rise above being comfortable.

Answer:

-22

Step-by-step explanation:

Answer:

-22

Step-by-step explanation:

got it right on test

The given points have the same Y value.

Find the distance between the X values -3 to 1 is 4 units.

All sides of a square are the same length so the other points must be 4 units away.

Add 4 units to the Y values:

(-3,2) = (-3,(2+4)) = (-3,6)

(1,2) = (1,(2+4)) = (1,6)

Two other points to make a square could be (-3,6) and (1,6)

Answer:

This graph is a line passing for the points (15/4,0) and (0,-5)

Step-by-step explanation:

It doesnt matter other options, the system represents a line, so you all need to do is graph a line according to the given equation.

-3y=15-4x which can be written as y=-5+x*4/3

This equation have one crossing point with y axis (15/4,0) and other at (0,-5)

So just put a line passing these points and you are good to go.

4= 1/4

1/4x1/4 = 1/16

Answer: the person who answered this is wrong it’s 1/12.

1/4 divided by 3 (4 x 3=12, so 1/12)

Step-by-step explanation:

Answer:

70 degrees

Step-by-step explanation:

Answer:

70°

Step-by-step explanation:

(a) Calculate the value of x

∠A +   ∠B     +   ∠C    = 180

40 + 2x - 30 + x + 20 = 180

Combine like terms

3x + 30 = 180

Subtract 30 from each side

3x = 150

Divide each side by 3

x = 50

(b) Calculate m∠B

m∠B = 2x - 30 = 2×50 - 30 = 100 - 30 = 70°

The total number of paper airplanes Fiona and her family made can be represented by the numerical expression: (12 + 8) x 2 + 3.

The total number of paper airplanes Fiona and her family made can be represented by the numerical expression: (12 + 8) x 2 + 3. The expression uses parentheses to indicate that the addition of 12 and 8 should be done first. Then, the result is multiplied by 2 to account for the doubling of planes in the afternoon. Finally, 3 is added to account for the extra planes made by Fiona's little brother. This expression represents the total number of paper airplanes made by Fiona and her family without simplifying it.

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ A=5\\ b=x\\ h=x-9 \end{cases}\implies 5=\cfrac{1}{2}(x)(x-9)[/tex]

Answer:

$4779

Step-by-step explanation:

First you need to write an equation to model this situation. In this case it's f(x)=1000(1.12)^x. College usually lasts 4 years, so to find the total amount of money they need to budget, you need to find the sum of f(0), f(1), f(2), and f(3).

This is roughly equivalent to 1000+1120+1254+1405, which equals 4779.

Answer: A

Step-by-step explanation:

It looks like its A to me but I actually am not 100% on this one

Answer:

6. x=10

8. B

Step-by-step explanation:

6.  The x intercept is when y=0

Let y=0

4x -5(0) = 40

4x = 40

Divide by 4

4x/4 = 40/4

x = 10

The x intercept is 10

8.  f(0) means x=0

The point on the y axis is B

Answer: 12cm

Work is shown in the attached sheet! :)

Answer:

12

Step-by-step explanation:

Answer:

[tex] 4x^3 + 2x^2 + 2x[/tex]

Step-by-step explanation:

The functions are [tex]f(x) = 9x^3 + 2x^2 -5x + 4[/tex] and [tex]g(x) = 5x^3 - 7x + 4[/tex]. Find the equation when g is subtracted from f and combing like terms. Remember like terms are terms with the same base and exponent.

[tex](9x^3 + 2x^2 -5x + 4) - (5x^3 - 7x + 4)\\f(x) - g(x) = 9x^3 + 2x^2 -5x + 4 -5x^3 + 7x -4\\f(x) - g(x) = 4x^3 + 2x^2 + 2x[/tex]

Answer:

3 in

Step-by-step explanation:

A cubes sides are all the same length. The volume is 27. We take the cube root of the volume to find one length. the cube root of 27 is 3 so one side length is 3.

Answer:

Step-by-step explanation:

It is unknow. This is because x can be any number.

Answer:

the answer is c, squared

Step-by-step explanation:

The units for surface areas will always be squared.

Thus, option (3) is correct.

The units for surface areas are always squared because they represent the measure of a two-dimensional space.

As, to calculate the surface area of an object, determining the total area of all its exposed sides, which involves measuring length and width (or height) and multiplying them together.

As a result, the units of surface area are expressed in square units, such as square inches (in²), square meters (m²), or square centimeters (cm²).

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Answer:

The result is 7.8 * 10^3

Step-by-step explanation:

When we are dividing in scientific notation, divide the numbers in front

7.8/1 = 7.8

Subtract the exponents on the powers of 10

10^(7-4) = 10 ^3

The result is 7.8 * 10^3