Nita Graft A System Of Equations On The Graph Below. Y= -3(x+2) Y=-3x-6 (2024)

the greatest common factor is 2x²

Explanation:[tex]\begin{gathered} The\text{ given expression:} \\ 14x^2+24x^3-16x^6 \end{gathered}[/tex]

We find the factors common to each of the term. Then we will factorise it out:

[tex]\begin{gathered} 14x^2\text{ = 2 }\times\text{ 7 }\times\text{ x }\times\text{ x} \\ 24x^3\text{ = }2\text{ }\times\text{ 2 }\times\text{ 2 }\times\text{ 3}\times x\text{ }\times x\times x \\ 16x^6=2^{}\text{ }\times\text{ 2 }\times\text{ 2}\times\text{ 2 }\times x\text{ }\times x\times x\times x\text{ }\times x\times x \end{gathered}[/tex][tex]\begin{gathered} we\text{ check the factors common to all thre}e\text{:} \\ 2\text{ }\times x\times x=2x^2 \end{gathered}[/tex][tex]\begin{gathered} 14x^2+24x^3-16x^6\text{ = }2\text{ }x^2(\text{7})\text{ + }2^{}x^2\text{ }\times(12x)-2\text{ }x^2(8x^4)\text{ } \\ 14x^2+24x^3-16x^6=2x^2(7+12x-8x^4) \end{gathered}[/tex]

Hence, the greatest common factor is 2x²

SOLUTION

We want to solve

moving -3/x to the other side we have

[tex]\begin{gathered} \frac{x+5}{x^2-x}=\frac{1}{x-1}+\frac{3}{x} \\ adding\text{ the other side by LCM, we have } \\ \frac{x+5}{x^2-x}=\frac{x+3(x-1)}{(x-1)x} \\ expanding\text{ we have } \\ \frac{x+5}{x^2-x}=\frac{x+3x-3}{x^2-x} \\ \frac{x+5}{x^2-x}=\frac{4x-3}{x^2-x} \end{gathered}[/tex]

Continuing we have

[tex]\begin{gathered} \frac{x+5}{x^2-x}=\frac{4x-3}{x^2-x} \\ cancelling\text{ common denominators, we have } \\ x+5=4x-3 \\ collecting\text{ like terms } \\ 5+3=4x-x \\ 8=3x \\ x=\frac{8}{3} \end{gathered}[/tex]

Hence the answer is 8/3

let

w = width

length = l

l = 3w - 5

area of the rectangle = 28 meter squared

The dimension are solved below

[tex]\text{area}=lw[/tex][tex]undefined[/tex]

The triangle given in the problem is a right triangle. Given its hypotenuse c and the length of one side a, the other side of the triangle can be computed using the Pythagorean theorem wherein

[tex]\begin{gathered} c^2=a^2+b^2 \\ b^2=c^2-a^2 \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]

Just substitute the value of c (hypotenuse) and a (length of one side) on the equation above and compute, we get

[tex]\begin{gathered} b=\sqrt[]{(17cm)^2+(8cm)^2_{}} \\ b=\sqrt[]{289cm^2+64cm^2} \\ b=\sqrt[]{353cm^2} \\ b=18.79\operatorname{cm}\approx19\operatorname{cm} \end{gathered}[/tex]

Hence, the length of the other side of the right triangle is 19 cm.

Answer: c) 19 cm

Answer:

[tex]\text{ a}_n=-2.(5)^{n-1}[/tex]

Explanation:

Here, we want to write the explicit formula for the given sequence

Looking at the sequence, we can see that:

[tex]\frac{-10}{-2}\text{ = }\frac{-50}{-10}\text{ = }\frac{-250}{-50}\text{ = 5}[/tex]

What this simply means is that we have to multiply the preceding term by 5 to get the succeeding term

Now, we have the explicit formula as follows:

We have deduced that the sequence is geometric. So we have the explicit formula as:

[tex]\text{ a}_n=-2.(5)^{n-1}[/tex]

where n is the term number

PART 1

To traslate a point 4 units to the left, we substract 4 from the x-coordinate. Similarly, to traslate it 8 units up we add 8 to the y-coordinate.

This way, the rule for translating a point 4 units left and 8 units up is:

[tex](x,y)\rightarrow(x-4,y+8)[/tex]

PART 2

Let's apply the traslation to each of the vertex:

[tex]\begin{gathered} A(7,5)\rightarrow(7-4,5+8)\rightarrow A^{\prime}(3,13) \\ B(2,9)\rightarrow(2-4,9+5)\rightarrow B^{\prime}(-2,14) \\ C(1,3)\rightarrow(1-4,3+8)\rightarrow C^{\prime}(-3,11) \end{gathered}[/tex]

This way, we can conclude that the new set of vertex is:

[tex]\begin{gathered} A^{\prime}(3,13) \\ B^{\prime}(-2,14) \\ C^{\prime}(-3,11) \end{gathered}[/tex]

PART 3

By definiton, the rule to reflect a point over the y-axis is:

[tex](x,y)\rightarrow(-x,y)[/tex]

PART 4

We apply this transformation to each of the new vertex:

[tex]\begin{gathered} A^{\prime}(3,13)\rightarrow A´´(-3,13) \\ B^{\prime}(-2,14)\rightarrow B´´(2,14) \\ C^{\prime}(-3,11)\rightarrow C´´(3,11) \end{gathered}[/tex]

This way, we can conclude that the new set of vertex is:

[tex]\begin{gathered} A´´(-3,13) \\ B´´(2,14) \\ C´´(3,11) \end{gathered}[/tex]

PART 5

We can conclude that A HAS NOT returned to its original location.



The table that shows a ratio of y to x as 8:1 is C.

This comes from the fact every value of y is 8 times the value of x given.

The Solution:

Given:

99.7% of the data.

Required:

By the Empirical Rule:

99.7% of the data falls three standard deviations from the mean.

Thus, the correct answer is [option A]

We have the following:

we can calculate the function as follows:

the first thing is to calculate the slope of the function

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

replacing:

[tex]\begin{gathered} m=\frac{63-35}{9-5} \\ m=7 \end{gathered}[/tex]

Therefore, the function is:

[tex]y=7x[/tex]

Therefore, the cost of movie ticket is $7

The midpoint between two complex numbers x+yi and u+vi is given by:

[tex]\frac{x+u}{2}+\frac{y+v}{2}i[/tex]

Plugging the values of the numbers given we have:

[tex]\frac{3+7}{2}+\frac{-12+6}{2}i=\frac{10}{2}-\frac{6}{2}i=5-3i[/tex]

Therefore the value of b is -3

Notice that the given points are in polar coordinates.

Recall that the distance between two points (r₁,θ₁) and (r₂,θ₂) in polar coordinates is given by the distance formula:

[tex]d=\sqrt[]{r^2_1+r^2_2-2r_1r_2\cos (\theta_2-\theta_1)}[/tex]

Substitute (r₁,θ₁)=(4,200º) and (r₂,θ₂)=(2,140º) into the formula:

[tex]d=\sqrt[]{4^2+2^2-2\cdot4\cdot2\cos (140-200)}[/tex]

Simplify the expression on the right:

[tex]d=\sqrt[]{16+4-16\cos(-60)}=\sqrt[]{20-16(\frac{1}{2})}=\sqrt[]{20-8}=\sqrt[]{12}=2\sqrt[]{3}[/tex]

Express the number as a decimal to the nearest tenth as required:

[tex]2\sqrt[]{3}\approx3.5[/tex]

Hence, the distance between the points is about 3.5 units.

Function, domain and range

x = 1. 2. 3. 2

y = 1. 4. 9. -4

THEN analyze table

If in a table, x values are REPEATED, then this table does NOT represent a function

For example, in this case ,number 2 is repeated two times

Then, for this reason, this table IS NOT a function

EXPLANATION

The mean formula is given by the following expression:

[tex]\text{Mean}=\frac{\sum ^{}_{}X}{N}[/tex]

Where X represents each individual value and N the number of values.

Plugging in the numbers into the expression:

[tex]\text{Mean = }\frac{60+57+86+26+128+82}{6}=\frac{439}{6}=73.1666\ldots\approx73.2[/tex]

In conclusion, the mean is 73.2

STEP - BY - STEP EXPLANATION

What to find?

Determine whether the given series converge or diverge.

Given:

Step 1

Determine the common ratio.

[tex]\begin{gathered} \frac{16}{27}\times\frac{9}{4}=\frac{4}{3} \\ \\ \frac{4}{9}\times\frac{3}{1}=\frac{4}{3} \\ \\ \frac{1}{3}\times\frac{4}{1}=\frac{4}{3} \end{gathered}[/tex]

It is enough to see that it is a geometric series.

Step 2

List out the conditions for convergence /divergence of a geometric series.

• If the absolute value of the ,common ration, i.e, |r| is less than 1,, the the series ,converges,.

,

• If, |r| > 1, then the series, diverges.

Clearly, 4/3 > 1

This implies |r| >1, hence the series diverges.

ANSWER

The series diverges.

The series is geometric and the absolute value of the common ratio is greater than 1.

Answer:

$5904

Explanation:

• The purchase value of the car = $21,500

,

• The rate of depreciation = 35%.

To find the resale value of the car after a certain number of years, we use the depreciation formula below:

[tex]A(t)=A_o(1-r)^t[/tex]

• The initial value, Ao = 21,500

,

• The rate, r = 35% =0.35

,

• The time, t (in years) = 3

Substitute these values into the formula:

[tex]\begin{gathered} A(3)=21500(1-0.35)^3 \\ =21500(0.65)^3 \\ =5904.44 \\ \approx\$5904 \end{gathered}[/tex]

The resale value of the car after 3 years is $5904 (correct to the nearest dollar).

The constant acceleration of a ball shot up from the ground is a = -32 ft/sec^2.

The acceleration is defined as the instant rate of change of the velocity:

[tex]a=\frac{dv}{dt}[/tex]

Integrating this equation, we have:

[tex]v=\int a\cdot dt[/tex]

Since the acceleration is a constant function:

[tex]\begin{gathered} v=\int-32\cdot dt \\ \\ v=-32\int dt \\ \\ v=-32t+v_o \end{gathered}[/tex]

The initial velocity is 48 ft/s, thus

[tex]v=48-32t[/tex]

The ball will stop and return to the ground when the velocity is 0:

[tex]48-32t=0[/tex]

Solving for t:

[tex]t=\frac{48}{32}=1.5[/tex]

Now we find the displacement function by integrating the velocity:

[tex]d=\int(48-32t)dt[/tex]

Integrating:

[tex]\begin{gathered} d=48t-\frac{32t^2}{2}+d_o \\ \\ d=48t-16t^2+d_o \end{gathered}[/tex]

The ball was shot from the ground, so do = 0:

[tex]d=48t-16t^2[/tex]

When t = 0, the position is d = 0.

When t = 1.5 seconds, the position is:

[tex]\begin{gathered} d=48\cdot1.5-16(1.5)^2 \\ \\ d=72-36 \\ \\ d=36 \end{gathered}[/tex]

The ball goes up to 36 feet

Solution:

Given the scatterplot below:

where the line of best fit is expressed as

[tex]y=0.91x+7.99[/tex]

A) Predicted hourly rate for cashier with 9 years of experience:

Thus, we have

[tex]x=9[/tex]

By substituting the value of 9 for x into the equation, we have

[tex]\begin{gathered} y=0.91\left(9\right)+7.99 \\ =\$16.18 \end{gathered}[/tex]

B) Predicted hourly rate for cashier with no experience:

This implies that

[tex]x=0[/tex]

By substitution, we have

[tex]\begin{gathered} y=0.91(0)+7.99 \\ \Rightarrow y=\$7.99 \end{gathered}[/tex]

C) Predicted increase in the hourly rate for an increase of one year of experience:

Recall that the equation of a line is expressed as

[tex]\begin{gathered} y=mx+c \\ where \\ m\Rightarrow slope \\ m=\frac{increase\text{ in y}}{increase\text{ in x}} \end{gathered}[/tex]

From the equation of the line of best fit, by comparison, we have

[tex]\begin{gathered} slope=0.91 \\ where \\ slope=\frac{incresre\text{ in hourly pay}}{increase\text{ in year of experince}} \\ \Rightarrow0.91=\frac{increase\text{ in hourly pay}}{1} \\ thus,\text{ we have} \\ predicted\text{ increase in hourly pay = \$0.91} \\ \end{gathered}[/tex]

The slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

The given equation is

18x - 13y = 11

We would re-arrange the equation so that it takes the slope intercept form. It becomes

18x - 13y = 11

13y = 18x - 11

Dividing both sides of the equation by 13, it becomes

y = 18x/13 - 11/13

The equation in slope intercept form is

y = 18x/13 - 11/13

The coordinates of the vertices of figure A'B'C'D" will be A''(4,4),B''(13,4),C''(13,1) and D''(4,1).

What is geometric transformation?

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that, Rani dilates figure ABCD to form figure A'B'C'D'. She uses a scale factor of and a center of dilation at the origin. Then she translates the image up to 7 units to form figures A"B" C" and D".

The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.

Thus,,the coordinates of the vertices of figure A'B'C'D" will be A''(4,4),B''(13,4),C''(13,1) and D''(4,1).

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Given:-

Marty's friend Tom makes and hourly wage of $15.00 per hour. Using that there are 40 hours in a standard work week, there are 52 weeks in a year, Social Security Tax is $6.20 for every $100 earned, Medicare Tax is $1.45 for every $100 earned.

To find:-

A. Tom's annual income tax.

B. Tom's net annual income.

C.Tom's net monthly income .

So toms wage per week is,

[tex]40\times15=600[/tex]

So wage per week is $600.

So total income tax is,

[tex]6(6.20+1.45)=6\times7.65=45.9[/tex]

So the annual income tax is,

[tex]52\times45.9=2366[/tex]

So the required income tax is $2366.

Tom's net annual income is,

[tex]52\times600=31200[/tex]

So toms net annual income is $31200.

Tom's net monthly income is,

[tex]600\times4=2400[/tex]

So net monthly income is $2400.

Finance charge be on a $500 balance for just 1month is equal to $20.79.

APR stands for the annual percentage rate on a loan which is the interest rate on a one year loan. To calculate the monthly rate r, we know that:

49.9 / 100 / 12 * $500 = $20.79

The finance charge is $20.79.

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

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Time: 3hr and 10 minutes

Distance: 14.32 km

Apply the next formula:

Speed: Distance/ time

First, convert the time into hours:

60 min = 1 hour

10 min = 10/60 = 0.167 hours

3+0.167 = 3.167 hours

Back with the formula:

Speed: 14.32/3.167 = 4.52 km/h

Simplify the fractions.

OPTION A

[tex]\begin{gathered} \frac{88}{92}=\frac{44}{46} \\ =\frac{22}{23} \end{gathered}[/tex]

Not equivalent of fraction 45/46.

OPTION B

[tex]\begin{gathered} \frac{135}{138}=\frac{45\cdot3}{46\cdot3} \\ =\frac{45}{46} \end{gathered}[/tex]

Fraction 135/138 is simplify to 45/46. So fraction 135/138 is equivalent to 45/45.

OPTION C

[tex]\begin{gathered} \frac{90}{93}=\frac{30\cdot3}{31\cdot3} \\ =\frac{30}{31} \end{gathered}[/tex]

Fraction 90/93 is not equivalent to 45/46.

OPTION D

[tex]\begin{gathered} \frac{170}{178}=\frac{85\cdot2}{89\cdot2} \\ =\frac{85}{89} \end{gathered}[/tex]

Fraction 170/178 is not equivalent to 45/46.

So answer is OPTION B.

135/138

The shape of the corral is rectangle

The length of the corral is twice the width

If x represents the width, and l represents the length

l = 2w

[tex]\begin{gathered} f(x)=-7x+9 \\ h(x)=-5f(x) \end{gathered}[/tex]

First step let us multiply f(x) by -5

[tex]\begin{gathered} h(x)=-5\lbrack-7x+9\rbrack \\ h(x)=(-5)(-7x)+(-5)(9) \\ h(x)=35x+(-45) \\ h(x)=35x-45 \end{gathered}[/tex]

The general form of the linear equation is f(x) = mx + b, where

m is the slope

b is the y-intercept

Since h(x) = 35 x - 45, then

m = 35

b = -45

So:

The slope = 35

y-intercept = -45

Dilation could be an enlargement or a reduction. If line k is mapped to line k', it means that k' is a reduction or an enlargement of k. If point A is common to both lines, then it means that Lines k and k' intersect only at point A.

Thus, the correct option is C

The figure consist of parallelogram, square and right angle triangle.

The dimension of parallelogram is.

Base B= 14

Height H = 5.

The dimension of square is,

side a = 7.

The dimensions of rectangle is,

Base b = 16

Height h = 7 cm

Determine the area of composite figure.

[tex]\begin{gathered} A=B\cdot H+a\cdot a+\frac{1}{2}\cdot b\cdot h \\ =14\cdot5+7\cdot7+\frac{1}{2}\cdot16\cdot7 \\ =70+49+56 \\ =175 \end{gathered}[/tex]

Thus area of composite figure is 175 square centimeter.

[tex]\begin{gathered} \frac{AB}{BC}\text{ = }\frac{PQ}{RQ} \\ \frac{AB}{6}=\text{ }\frac{9}{11} \\ 11AB\text{ = 9}\times6 \\ AB\text{ = }\frac{54}{11}\text{ = 4.9} \\ \\ \text{lets find, AC} \\ \frac{AC}{CB}\text{ = }\frac{PR}{RQ} \\ \frac{AC}{6}\text{ =}\frac{13}{11} \\ 11AC\text{ = 13 }\times6 \\ AC\text{ = }\frac{78}{11}\text{ = 7} \\ \end{gathered}[/tex]

To now find the perimeter of ABC

AB + BC + AC

4.9 +6 +7 = 17.9 approximately 18

Hello

This is a geometric progression and we have the first term and we have to find the common ratio.

first term = a

common ratio = r

[tex]\begin{gathered} a=3 \\ r=\frac{12}{3}=4 \end{gathered}[/tex]

The 5th term would be

[tex]\begin{gathered} T_5=ar^4 \\ T_5=3\times4^4 \\ T_5=3\times256 \\ T_5=768 \end{gathered}[/tex]

The value of the 5th term of the sequence is 768

Answer:

9 is parallel and 10 is perpendicular

Step-by-step explanation:

You find the slope by the change in y over the change in x

Points are in the form(x,y) You take the y numbers on top of the fraction and subtract them and you take the x numbers on the bottom of the fraction and subtract those. Simplify and you have the slope.

(-4,10) (2, -8)

[tex]\frac{-8 - 10}{2 - - 4}[/tex] = [tex]\frac{-18}{2+4}[/tex] = [tex]\frac{-18}{6}[/tex] Divide the top and bottom by 6

[tex]\frac{-3}{1}[/tex] = -3

The slope is -3. Let's compare to the other 2 points.

(1,2) (4, -7)

[tex]\frac{-7 - 2}{4 - 1}[/tex] = [tex]\frac{-9}{3}[/tex] = -3

The slopes are the same. When the slopes are the same, the lines are parallel.

10)

(-3, -7) (3,-3)

[tex]\frac{-3 - -7}{3 - -3}[/tex] = [tex]\frac{-3 + 7}{3 + 3}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

(0,4) (6,-5)

[tex]\frac{-5 -4}{6 - 0}[/tex] = [tex]\frac{-9}{6}[/tex] = [tex]\frac{-3}{2}[/tex]

The slope are opposite reciprocals of each other so they are perpendicular.