lynomials and Linear Factors
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Write the polynomial function y = (x + 5) (x - 1)(x - 2) in
standard form.

Answer:

90 recipes

Step-by-step explanation:

we know that

Fiona posted a total 216 recipes in 36 weeks

using proportion

Find out  how many recipes did she upload in 15 weeks'

Let

x -----> the number of recipes

[tex]\frac{216}{36}\frac{recipes}{weeks}=\frac{x}{15}\frac{recipes}{weeks} \\\\x=216*15/36\\\\x= 90\ recipes[/tex]

Answer:

Variability is when there is no consistency.

Step-by-step explanation:

Variation in data can be due to various factors. Variability can also be called the spread of data.

Standard deviation is a measure of variability as standard deviation measures the spread of data.

!!

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ \cline{1-1} B=\stackrel{183\times 183}{33489}\\ h=110 \end{cases}\implies V=\cfrac{1}{3}(33489)(110)\implies V=1227930[/tex]

Answer:

V =1127930 m^3

Step-by-step explanation:

The volume is

V = 1/3 B h

where B is the area of the base

B = area of the square

B = 183*183 since it is a square

B = 33489

V = 1/3 *(33489) * 110

V =1127930 m^3

Answer:

27/1000

Step-by-step explanation:

To solve this, you would distribute the power 3 to the numerator and denomerator. 3^3 is 27 and 10^3 is 1000. So you get 27/1000

Answer:

the value is 27/1000 in other words the answer to your question is B

The Addition Property of Equality allows us to add the same amount to both sides of an equation, so if x = 5, by adding 3 to both sides, x + 3 would be 8.

The Addition Property of Equality is a principle of mathematics that states: if you add the same amount to both sides of an equation, the equation remains balanced. So, if we take the equation x = 5, according to the Addition Property of Equality, we can add 3 to both sides of the equation. This will give us: x + 3 = 5 + 3. Therefore, x + 3 = 8.

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Answer:

you are correct

Step-by-step explanation:

area = 6 × 3 = 18 in²

Answer:

Yes!You got it correct!

Step-by-step explanation:

Good job!

Answer:

x=8 ?

Step-by-step explanation:

Answer:5x2+12x-14

Step-by-step explanation:

(5x2+11x-9)-(2x-3x+5)

5x2+11x-9-2x+3x-5

5x2+12x-14

[tex](5x^2 + 11x - 9) - (2x - 3x + 5)=5x^2+11x-9-2x+3x-5=5x^2+12x-14[/tex]

-------------------------------------------------

[tex](5x^2 + 11x - 9) - (2x^2 - 3x + 5)=5x^2+11x-9-2x^2+3x-5=3x^2+14x-14[/tex]

Answer:

The vertical distance from the ground to the bird's eyes is 47.67 m

Step-by-step explanation:

* Lets explain the situation of the problem

- There is a bird on the top of  a tree

- The bird looks down on a field mouse at an angle of depression of 50°

- The field mouse is 40 meters from the base of the tree

* Consider that the vertical distance from the ground to the bird's eyes,

 the distance from the field mouse to the base of the tree distance

 from the bird eyes to the field mouse formed a right triangle

- The hypotenuse is the distance from the bird eyes to the field mouse

- The horizontal side is the distance from the field mouse to the base

 of the tree

- The angle between the hypotenuse and the horizontal side is the

 angle of depression which = 50°

- The opposite side to the angle of measure 50° is the vertical distance

 from the ground to the bird's eyes

* Lets use trigonometry functions to find the vertical distance

∵ The length of the adjacent side to the angle of measure 50° is 40 m

∵ The length of the opposite side to the angle of measure 50° is h m

∵ tan Ф = opposite side to Ф ÷ adjacent side to Ф

∵ Ф = 50°

∴ tan 50° = h/40 ⇒ by using cross multiplication

∴ 40 tan 50° = h

∴ h = 47.67 m

* The vertical distance from the ground to the bird's eyes is 47.67 m

Answer:

(8,-10)

Step-by-step explanation:

step 1

Find the slope of line KL

K(-6,8),L(6,0)

m=(0-8)/(6+6)

m=-8/12=-2/3

step 2

Find the slope of the line that is parallel to KL

we know that

If two lines are parallel , then their slopes are the same

therefore

The slope of the parallel line to KL is m=-2/3

step 3

Find the equation of the line parallel to KL that pass through the point M

M(-4,-2)

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

substitute

y+2=-(2/3)(x+4)

step 4

Verify the points

we know that

If the point lie on the line, then the point must satisfy the equation of the line

case a) (-10,0)

substitute the value of x and the value of y in the equation and then compare the result

-10+2=-(2/3)(0+4)

-8=-8/3 -----> is not true

therefore

The point is not on the line

case b) (-6,2)

substitute the value of x and the value of y in the equation and then compare the result

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

4=4/3 -----> is not true

therefore

The point is not on the line

case c) (0,-6)

substitute the value of x and the value of y in the equation and then compare the result

-6+2=-(2/3)(0+4)

-4=-8/3 -----> is not true

therefore

The point is not on the line

case d) (8,-10)

substitute the value of x and the value of y in the equation and then compare the result

-10+2=-(2/3)(8+4)

-8=-8 -----> is true

therefore

The point is on the line

Answer:

C. 40°

Step-by-step explanation:

From the diagram, in triangle XYZ, XY=XZ=6 units. This means triangle XYZ is isosceles triangle with base YZ.

In isoscels triangle angles adjacent to the base are congruent, so

∠ZYX=∠YZX=70°

The sum of all interior angles in triangle is always 180°, so

∠ZYX+∠YZX+∠ZXY=180°

∠ZXY=180°-70°-70°

∠ZXY=40°

∠ZXY is ∠X, so ∠X=40°

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - [tex]\frac{5}{2}[/tex] and (a, b) = (- 6, 2), so

y - 2 = - [tex]\frac{5}{2}[/tex] (x - (- 6)), that is

y - 2 = - [tex]\frac{5}{2}[/tex] (x + 6) ← in point- slope form

An equation in point slope form for this line y - 2 = -5/2  (x + 6) .

The point slope form of a straight line in geometry is used to represent the equation of a straight line using its slope 'm' and a point(x, y) that lies on the given line.

equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Now,  m = - 5/2

and (a, b) = (- 6, 2)

So, the equation of line be

y-2=  -5/2 (x+6)

Hence,

y - 2 = -5/2  (x + 6) in point- slope form.

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Answer:

yes! total calories= 535

Step-by-step explanation:

answer:

Donna Dieter is trying to keep her lunches under 600 calories. Today she had a peanut butter sandwich, one cup of vegetable soup, an apple, and a glass of milk. Did she stay under her goal?

YES

Answer:

46%

Step-by-step explanation:

440 + 480 = 920

2000 / 920 =46%

Answer:

One cinnamon chip scone provides 46% of the daily recommended calorie intake of 2000 calories for an adult woman.

Step-by-step explanation:

Consider the provided information.

The Starbucks cinnamon chip scone has 480 calories-more calories than a 440 calorie McDonald's double cheeseburger.

First calculate the calories in Starbucks cinnamon chip scone .

Starbucks cinnamon has 480 calories-more than a 440 calorie cheeseburger.

The calories in Starbucks cinnamon = 480+440 = 920

Now we need to find the One cinnamon chip scone provides what percent of the daily recommended calorie intake of 2000 calories for an adult woman.

Find what percentage of 2000 is 920 as shown.

[tex]\frac{920}{2000}\times 100[/tex]

[tex]\frac{920}{20}[/tex]

[tex]46\%[/tex]

Hence, One cinnamon chip scone provides 46% of the daily recommended calorie intake of 2000 calories for an adult woman.

The problem is solved by calculating that there are 24 nickels and 12 dimes to make a total of $2.40, given that there are twice as many nickels as dimes.

The subject of this question is Mathematics, specifically dealing with simple money-based equations. In the problem you're presented with, you've been asked to figure out the number of nickels and dimes that make up $2.40, given that there are twice as many nickels as there are dimes.

First, we can start by understanding the value of each coin. A nickel is worth $0.05, and a dime is worth $0.10. With the condition expressed in the problem, let's express the number of dimes as x, thus the number of nickels would then be 2x.

Because of their respective values, the total value of the dimes would be 0.10x and the total value of the nickels would be 0.05 × 2x or 0.10x. Adding both together, we'd have 0.10x + 0.10x = 0.20x, which we know equals $2.40 from the problem. Solving the equation 0.20x = 2.40 gives us x = 12. That's your number of dimes. The nickels would be 2 × 12 = 24. So, the answer to your problem would be 24 nickels and 12 dimes.

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Answer:

1/32768

Step-by-step explanation:

First, solve the parenthesis:

2^3 = 2 * 2 * 2 = (2 * 2) * 2 = (4) * 2 = 8

Next, solve the outer power. Note that it has a negative sign, which means that after you solve for the power sign, you have to put the number under 1.

(8)^-5 = 1/(8 * 8 * 8 * 8 * 8) = 1/32768

1/32768 is your answer.

~

Answer:

A) 1/2^15

Step-by-step explanation:

edge2021

Answer:

Q1. The solution for the quadratic equation on a graph is same as the value of x-intercept(zeros)

Q2. discriminant(b^2-4ac) when y=ax^2 + bx + c

there are 3 situations:

1. discriminant > 0 → 2 real solutions(2 x-intercepts/zeros)

2. discriminant = 0 → 1 real solution(1 x-intercept/zero)

3. discriminant < 0 → 0 real solution(0 x-intercept/zero) → also 2 imaginary solution

Hope it helped!

Step-by-step explanation:

Answer:

1) You find the solution by identifying the x-intercepts.

2) Possible real solutions:

- One real solution.

- Two distinct real solutions.

Step-by-step explanation:

1) The graph of a quadratic equation is a parabola.

By definition, the x-intercepts (Where [tex]y=0[/tex]) are the solutions of the quadratic equation .

2) Given a quadratic equation [tex]ax^2+bx+c=0[/tex], you can know the number of real solutions by using this formula to find the Discriminant :

[tex]D=b^2-4ac[/tex]

If  [tex]D=0[/tex], then there is one real solution with multiplicity two.

If  [tex]D>0[/tex], then there are two distinct real solutions.

On a graph:

-If the graph has two x-intercepts, then the quadratic equation has two real solutions.

 -If the graph has one x-intercept , then the quadratic equation has one real solution.

Step-by-step explanation:

[tex]1 \div 2 \times base \times height = area[/tex]

[tex]1 \div 2 \times x \times 42.2 = \ 369.25 \[/tex]

[tex]x = 369.25 \div 21.1[/tex]

[tex] = 17.5[/tex]

Answer:

Base = 17.5 inches.

Step-by-step explanation:

Given  : A triangle has an area of 369.25 square inches. The height of the triangle is 42.2 inches.

To find : What is the length of the base of the triangle.

Solution : We have given

Area of triangle = 369.25 square inches.

Height =  42.2 inches.

Area of triangle = [tex]\frac{1}{2}*base*height[/tex].

Plugging the values.

369.25 =  [tex]\frac{1}{2}*base*42.2[/tex].

On multiplying both sides by 2

369.25 * 2 = base * 42.2

738.5 = base * 42.2

On dividing both sides by 42.2

Base = 17.5 inches.

Therefore, Base = 17.5 inches.

The best name for the part of the figure identified by the arrow is line of symmetry.

The best name for the part of the figure identified by the arrow is line of symmetry. It refers to a line that divides a figure into two equal halves, which are mirror images of each other.

The line of symmetry can be identified by the arrow in the figure where the reflection occurs.

For example, in the letter 'A', the line through the middle vertically is the line of symmetry, as both sides of the letter are identical when folded along that line.

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Answer:

Step-by-step explanation:

First, factor the denominator: (x-5)(x+4)

Since the denominator already has the two values, you only need to multiply it by (x+3), which means you need to multiply the numerator by (x+3):

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

(x-1)(x+3) then simplifies to [tex]x^2+2x-3[/tex]

A = -120

AX = -240

X = 2

Step-by-step explanation:

∵ x + 4y - z = -14

∵ 5x + 6y + 3z = 4

∵ -2x + 7y + 2z = -17

\left[\begin{array}{ccc}1&4&-1\\5&6&3\\-2&7&2\end{array}\right]=\left[\begin{array}{ccc}-14\\4\\-17\end{array}\right]

∴ A = 1(6×2 - 3×7) + (-4)(2×5 - 3×-2) + (-1)(5×7 - 6×-2)

∴ A = 1(12 - 21) + (-4)(10 - -6) + (-1)(35 - -12)

∴ A = -9 + (-4)(16) + (-1)(47) = -9 - 64 - 47 = -120

To find X replace the column of X by the column of the answer

\left[\begin{array}{ccc}-14&4&-1\\4&6&3\\-17&7&2\end{array}\right]

∴ AX = -14(6×2 - 3×7) + (-4)(4×2 - 3×-17) + (-1)(4×7 - 6×-17)

∴ AX = -14(12 - 21) + (-4)(8 - -51) + (-1)(28 - -102)

∴ AX = 126 + (-4)(59) + (-1)(130) = 126 - 236 - 130 = -240

∴ X = AX/A = -240/-120 = 2  

Answer:

A     -120

Ax   -240

Ay    360

Az    -480

x    2

y    -3

z    4

Step-by-step explanation:

Answer:

90-35=55

Hope this helps! <3

Answer:

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume [tex]V[/tex] of a solid pyramid can be given as:

[tex]\displaystyle V = \frac{1}{3} \cdot b \cdot h[/tex],

where

Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be [tex]x[/tex] cm.

As a result, the length of a side of the square will be

[tex]\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x[/tex].

The area of the square will be

[tex]\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}[/tex].

Integrate the area of the horizontal cross-section with respect to [tex]x[/tex]

[tex]\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}[/tex].

In other words, the volume of this pyramid is 16 cubic centimeters.

Answer:

16cm3

Step-by-step explanation:

Answer:

D.

Increase by more than 0.25 dollars.

Step-by-step explanation:

What is the gross margin %?

Margin % = (2.50/1.00) * 100 = 250%

If the cost goes up 0.25 what will the  selling price have to do to maintain a markup of 250%?

250% =(x/1.25) * 100%

Divide by 100%

250 / 100 = x / 1.25

2.5 = x / 1.25  

Multiply both sides by 1.25

2.5 * 1.25 = x

3.125 = x

But that is really not the question. The question is, how much higher is that now than it used to be?

3.125 - 2.50 = 0.625 cents.

So you would have to increase the selling price by more than 0.25

Answer:

Step-by-step explanation:

Slope = y/x

y1-y2/x1-x2=slope of 2 points

8-3/-6-2 = 5/-8 which equals -5/8 or -.625.

The slope of line for the points is -5/8.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

given:

We have the Points (–6, 8), (2, 3).

So, the slope is

m = (3- 8)/ (2- (-6))

m = -5 / (2+6)

m = -5 / 8

Thus, the Slope is -5/8.

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[tex]\bf \begin{cases} f(x)=3x^2\\ g(x)=4x^3+1 \end{cases}\qquad (f\cdot g)(x)\implies f(x)\cdot g(x)\implies [3x^2]\cdot [4x^3+1] \\\\\\ 12x^2x^3+3x^2\implies 12x^{2+3}3x^2\implies \stackrel{\textit{5th degree}}{12x^{\stackrel{\downarrow }{5}}+3x^2}[/tex]

The correct option is:

C. [tex]2(y+1)+y=7[/tex]

To find which of the given options are not the result of a substitution in the given system, we need to isolate the variable in function of the other variable, and then substitute it.

So, substituting and discarding, we have:

- First equation:

[tex]2x+y=7[/tex]

Isolating "y", we have:

[tex]y=7-2x[/tex]

Then, substituting it into the second equation, we have:

[tex]y-x=1[/tex]

[tex]7-2x-x=1[/tex]

We have that it's a result of a substitutiong in the following system (option A)

- Second equation:

[tex]y-x=1[/tex]

Isolating "y", we have:

[tex]y=x+1[/tex]

Then, substituting it into the first equation, we have:

[tex]2x+y=7[/tex]

[tex]2x+(x+1)=7[/tex

[tex]2x+x+=7[/tex

We have that it's a result of a substitution in the following system (option B)

Hence, we have that the option C is not a result of a substitution in the given system of equations since there is not a possible value of the variable "x" that is equal "y+1".

So, the correct option is:

C. [tex]2(y+1)+y=7[/tex]

Have a nice day!

Answer:

C. 2(y + 1) + y = 7​

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2 is the constant of proportionality in the equation y = 2x . When two variables are directly proportional to each others . Where k is called the constant of proportionality . Thus in the question x and y are proportional variables

Answer:

option D: 27.5 square units

Step-by-step explanation:

Divide the polygon in 6 figures

see the attached figure

Area of figure 1 (right triangle)

A1=(1/2)(3)(3)=4.5 units²

Area of figure 2 (rectangle)

A2=(1)(3)=3 units²

Area of figure 3 (rectangle)

A3=(1)(3)=3 units²

Area of figure 4 (right triangle)

A4=(1/2)(3)(3)=4.5 units²

Area of figure 5 (right triangle)

A5=(1/2)(4)(5)=10 units²

Area of figure 6 (right triangle)

A6=(1/2)(1)(5)=2.5 units²

The total area is equal to

At=A1+A2+A3+A4+A5+A6

At=4.5+3+3+4.5+10+2.5=27.5 units²

Answer:

Option D.

Step-by-step explanation:

As we know area of a triangle = [tex]\frac{1}{2}\times Base\times Height[/tex]

1. Area of ΔJKL = [tex]\frac{1}{2}\times(\text{Distance of L from base JK})\times (JK)[/tex]

= [tex]\frac{1}{2}\times (3)\times (5)[/tex]

=7.5 square units

2. Area of ΔIJL = [tex]\frac{1}{2}\times(\text{Distance of J from base IL})\times (IL)[/tex]

=  [tex]\frac{1}{2}\times (3)\times (5)[/tex]

= 7.5 square units

3. Area of triangle IKL = [tex]\frac{1}{2}\times(\text{Distance of H from base IL})\times (IL)[/tex]

= [tex]\frac{1}{2}\times (5)\times (5)[/tex]

= [tex]\frac{25}{2}=12.5[/tex] square units

Now area of ΔJKL + ΔIJL + ΔIKL = 7.5 + 7.5 + 12.5

= 27.5 square units

Option D. is the answer.

Answer:

[tex]{\boxed{\text{A. }\math{k = -7}}[/tex]

Step-by-step explanation:

The general rule for vertical translation of a function ƒ(x) ⟶ ƒ(x) + k .

A positive value of k means that the graph is shifted up by k units.

The graph of ƒ(x) was shifted from (0, 1) to (0, -6).

[tex]\text{The graph was shifted down by seven units, so }{\boxed{\mathbf{k = -7}}[/tex]

The value of k is -7.

Vertical translation refers to the up or down movement of the graph of a function.

Here, the shape of the function remains the same.

It is also known as the movement/shifting of the graph along the y-axis.

In vertical translation, each point on the graph moves k units vertically and the graph is said to translated k units vertically.

The general rule for vertical translation of a function,

f(x)= g(x) + k .

here, the graph is shifted up by k units.

As, seen from the graph of g(x) is shifted from point (0, 1) to (0, -6).

Hence, the graph is shifted by -7 units.

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