Which Expression Is Equivalent To -28x-35x-7A) (7x-3) (-4x+3)B) (-7x-7) (4x+1)C) (7x+3) (-4x-3)D) (-7x+7) (2024)

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given details

[tex]\begin{gathered} w=g(z)=1+\sqrt{6-z} \\ (z,w)=(5,2) \end{gathered}[/tex]

STEP 2: Explain Tangent line

Tangent Lines:

The tangent line to a function f(x) is a line that touches the graph of the function at one specific point of tangency where it has the same slope as the function at that point.

If x = a is the point of tangency, the tangent line can be written in slope-intercept form as:

[tex]\begin{gathered} y=mx+b \\ where\text{ }m=f^{\prime}(a)\text{ }and\text{ }y|_{x=a}=f(a) \end{gathered}[/tex]

STEP 3: Find the tangent

We can first determine the slope of the tangent line by differentiating the function. Writing the function as:

[tex]g(z)=1+(6-z)^{\frac{1}{2}}[/tex]

We find the derivative using the chain rule:

[tex]\begin{gathered} \mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g' \\ =\frac{d}{dz}\left(1\right)+\frac{d}{dz}\left(\left(6-z\right)^{\frac{1}{2}}\right) \\ \frac{d}{dz}\left(1\right)=0,\frac{d}{dz}\left(\left(6-z\right)^{\frac{1}{2}}\right)=-\frac{1}{2\left(6-z\right)^{\frac{1}{2}}} \\ \\ =0-\frac{1}{2\left(6-z\right)^{\frac{1}{2}}} \\ =-\frac{1}{2\left(-z+6\right)^{\frac{1}{2}}} \\ \\ =-\frac{1}{2}(6-z)^{-\frac{1}{2}} \end{gathered}[/tex]

At the point of tangency, the slope is

[tex]\begin{gathered} g^{\prime}(5)=-\frac{1}{2}(6-5)^{-\frac{1}{2}} \\ g^{\prime}(5)=-\frac{1}{2} \end{gathered}[/tex]

We can begin to write the equation of the tangent line in slope-intercept form

[tex]w=-\frac{1}{2}z+b[/tex]

Substituting both coordinates of the point of tangency allows us to solve for the intercept:

[tex]\begin{gathered} 2=-\frac{1}{2}(5)+b \\ -\frac{1}{2}\left(5\right)+b=2 \\ -\frac{1}{2}\cdot \:5+b=2 \\ -\frac{5}{2}+b=2 \\ \frac{5}{2}+b+\frac{5}{2}=2+\frac{5}{2} \\ b=\frac{9}{2} \end{gathered}[/tex]

The complete equation of the tangent line at (5,2) is then

[tex]w=-\frac{1}{2}z+(\frac{9}{2})[/tex]

Question:

Solution:

The volume of the cone with radius r and height h is given by the following formula:

[tex]V\text{ = }\frac{1}{3}\pi r^2h[/tex]

The data given in the problem are:

Diameter : 17.6 cm, then the radius is 17.6cm / 2 = 8.8 cm

Slant height : 25 cm

Thus, to find the height of the cone we use the Pythagorean theorem:

[tex]h=\text{ }\sqrt[]{25^2-8.8^2}\text{ = 23.4}[/tex]

then we have that the given cone has a height of 23.4 cm and a radius of 8.8cm. So that, replacing these that into the first equation (volume of the cone), we get:

[tex]V\text{ = }\frac{1}{3}\pi(8.8)^2(23.4)\text{ = }1897.6[/tex]

then, we can conclude that the correct answer is:

[tex]V\text{ = }1897.6[/tex]

Let's use the variable L to represent the length and W to represent the width.

If the length is 3 yd less than double the width, we can write the following equation:

[tex]L=2W-3[/tex]

If the area is equal to 14 yd², we have this equation:

[tex]L\cdot W=14[/tex]

Let's use the value of L from the first equation into the second one, then we solve the resulting equation for W:

[tex]\begin{gathered} (2W-3)\cdot W=14 \\ 2W^2-3W=14 \\ 2W^2-3W-14=0 \\ W=\frac{-(-3)\pm\sqrt[]{(-3)^2-4\cdot2\cdot(-14)}}{2\cdot2} \\ W=\frac{3\pm\sqrt[]{9+112}}{4} \\ W=\frac{3\pm11}{4} \\ W_1=\frac{3+11}{4}=\frac{14}{4}=3.5 \\ W_2=\frac{3-11}{4}=-\frac{8}{4}=-2 \end{gathered}[/tex]

Since a negative value for the width is not valid, we have W = 3.5 yd.

Now, calculating the length, we have:

[tex]\begin{gathered} L=2W-3 \\ L=2\cdot3.5-3 \\ L=7-3 \\ L=4\text{ yd} \end{gathered}[/tex]

Therefore the length is 4 yards and the width is 3.5 yards.

[tex]2x-5=x+1[/tex]

we need to put on one side all the terms with x and on the other side all the terms without x

[tex]\begin{gathered} 2x-x=1+5 \\ x=6 \end{gathered}[/tex]

the value of x=6

We have to replace A= 25 mg in the equation and solve for t. Doing so, we have:

[tex]\begin{gathered} 25=50(0.9217)^t\text{ } \\ 0.5=(0.9217)^t\text{ (Dividing by 50 on both sides of the equation)} \end{gathered}[/tex]

[tex]\begin{gathered} \log _5(0.5)=\log _5(0.9217)^t(\text{ Taking the logarithm base 5 of both sides of the equation)} \\ \log _5(0.5)=t\cdot\log _5(0.9217)\text{ (Using the power rule of logarithms)} \\ -0.431=t\cdot(-0.0507)\text{ (Finding the logarithms for each case)} \\ 8.50=t\text{ (Dividing by }-0.0507\text{ on both sides of the equation)} \end{gathered}[/tex]

The answer is 8.50 hours (Rounding to two decimal places)

Write an explict formula for the sequence 7,2,-3,-8,-13​

we have

a1=7

a2=2

a3=-3

a4=-8

a5=-13

Find the commom difference d

d=a2-a1=2-7=-5

d=a3-a2=-3-2=-5

d=a4-a3=-8-(-3)=-5

d=a5-a4=-13-(-8)=-5

so

d=-5

In this problem we have an artithmetic sequence

so

an=a1+d(n-1)

we have

a1=7

d=-5

substitute

an=7+(-5)(n-1)

an=7-5n+5

an=12-5n

therefore

the answer is

an=12-5n

Solution

The answer is

For this question you just have to susbtitute 4 wherever you see an i, doing that we get

[tex]a_4=7+2(4+1)\text{ = 7+2}\cdot5=17[/tex]

In order to find which function will have the greatest value at x = 8, let's calculate the value of each function with this value of x:

[tex]\begin{gathered} y=3x \\ y=3\cdot8 \\ y=24 \\ \\ y=x^2-13x+60 \\ y=8^2-13\cdot8+60 \\ y=64-104+60 \\ y=20 \\ \\ y=1.11^x \\ y=1.11^8 \\ y=2.3 \end{gathered}[/tex]

So the correct option is the first one.

D; The function is decreasing in the interval;

[tex](-\infty,\infty)[/tex]

Here, we want to interpret the given rate of change of the function

From what we have, coming from negative infinity, we can see that there is a decrease in the rate of change of the function. As we move closer to zero, we can see a decrease in the range value of the function

Now, moving away from zero, we can see that there is a continuous decrease as we move towards positive infinity. We can therefore conclude that there is a continuous decrease from the point x = 0 towards the point x = positive infinity

So, the correct choice here is that the function is decreasing in the interval negative infinity to positive infinity

Polynomials in standard form are arranged in decreasing power of x.

Therefore,

[tex]x^3+x^4-3x^5+10[/tex]

in standard, is written as:

[tex]-3x^5+x^4+x^3+10[/tex]

Answer:

The vertices of the image are:

[tex]\begin{gathered} N^{\prime}(-1,-2) \\ M^{\prime}(-4,1) \\ O^{\prime}(-3,3) \end{gathered}[/tex]

Step-by-step explanation:

Remember that the general rule to reflect over a vertical line in the form:

[tex]x=a[/tex]

is:

[tex](x.y)\rightarrow(-x-2a,y)[/tex]

For x = 3, we'll have that the general rule is:

[tex](x,y)\rightarrow(-x-6,y)[/tex]

We'll apply this transformation to the vertices, as following:

[tex]\begin{gathered} N(-5,2)\rightarrow N^{\prime}(-1,-2) \\ M(-2,1)\rightarrow M^{\prime}(-4,1) \\ O(-3,3)\rightarrow O^{\prime}(-3,3) \end{gathered}[/tex]

Therefore, the vertices of the image are:

[tex]\begin{gathered} N^{\prime}(-1,-2) \\ M^{\prime}(-4,1) \\ O^{\prime}(-3,3) \end{gathered}[/tex]

Answer:

N: (-1, 2)

M: (-4, 1)

O: (-3, 3)

x represents the amount of portion in millimeters

y represents the time she was invisible

Write out an equation to show the variation relationship

Since the variation is direct

Then

[tex]\begin{gathered} x\propto y \\ x=k\times y \end{gathered}[/tex]

To get the value of k

when x= 1 mm, y = 5 minutes

[tex]\begin{gathered} k\text{ = }\frac{x}{y} \\ =\frac{1}{5}\text{ mm/min} \end{gathered}[/tex]

The relationship between x and y will be

[tex]\begin{gathered} \text{substitute k in x=}ky \\ x=\frac{1}{5}\times y \\ x=\frac{y}{5}\text{ (this is the relationship)} \end{gathered}[/tex]

ln x + ln x^2 = 3

log property:

ln (x*x^2 ) = 3

ln x^3 = 3

3 ln x = 3

Divide both sides by 3

(3 ln x ) /3 = 3/3

ln x = 1

e^lnx = e^1

x= e = 2.71828182

Part A

The most likely value of the correlation coefficient can be obtained by examining if there is an existing relationship between Time(x) and Radius(y) from the given table.

From the table, as time increases from 1 to 4 days, the radius increases by two times. As we progress from 4 to 7 days, this change in radius is reduced.

Hence, the correlation coefficient is 0.94

The relationship between time and radius of the algae can be explained thus: for every increase in time (days), the radius of the increases but not steadily.

Part C

The data in the table does not indicate causation. It rather shows correlation.

This is because the change in the radius of the algae is not a result of the change in time.

ANSWER and EXPLANATION

A. First, we have to find the number of people that liked white bread only and wheat bread only.

To find the number of people that liked white bread only, subtract the number of people that liked both from the number of people that liked white bread:

[tex]\begin{gathered} n(white\text{ }bread\text{ }only)=40-35 \\ n(white\text{ }bread\text{ }only)=5 \end{gathered}[/tex]

To find the number of people that liked wheat bread only, subtract the number of people that liked both from the number of people that liked wheat bread:

[tex]\begin{gathered} n(wheat\text{ }bread\text{ }only)=75-35 \\ n(wheat\text{ }bread\text{ }only)=40 \end{gathered}[/tex]

Now, we can draw the Venn diagram:

B. The total number of people interviewed is the sum of all the numbers on the Venn diagram.

Therefore, the total number of people interviewed is:

[tex]\begin{gathered} n(total)=5+35+40+15 \\ n(total)=95 \end{gathered}[/tex]

That is the total number of people that were interviewed.

To find the total amount that the sandwich shop paid, multiply the total number of people interviewed by $2:

[tex]\begin{gathered} Total\text{ }amount\text{ }paid=2*95 \\ Total\text{ }amount\text{ }paid=\$190 \end{gathered}[/tex]

That is the total amount that the sandwich shop paid for the interviews.

C. To find the percentage of people that liked either white bread or wheat bread, find the sum of people that liked white bread only, wheat bread only, and both types of bread, divide it by the total number of people interviewed and multiply by 100:

[tex]\begin{gathered} \Rightarrow\frac{5+35+40}{95}*100 \\ \\ \Rightarrow\frac{80}{95}*100 \\ \\ \Rightarrow84.2\% \end{gathered}[/tex]

That is the percent of people that like either white or wheat bread.

Let n be the number of nickels

Let d be the number of dimes

There are 31 coins in your pocket:

[tex]n+d=31[/tex]

You have in total $2.65:

[tex]0.05n+0.10d=2.65[/tex]

Use the two equations above a system of linear equations to solve the variables n and d:

[tex]\begin{gathered} n+d=31 \\ 0.05n+0.10d=2.65 \end{gathered}[/tex]

1. Solve n in the fist equation:

[tex]\begin{gathered} n+d-d=31-d \\ \\ n=31-d \end{gathered}[/tex]

2. Use the value of n=31-d in the second equaiton:

[tex]0.05(31-d)+0.10d=2.65[/tex]

3. Solve d:

[tex]\begin{gathered} 1.55-0.05d+0.10d=2.65 \\ 1.55+0.05d=2.65 \\ 1.55-1.55+0.05d=2.65-1.55 \\ 0.05d=1.1 \\ \frac{0.05}{0.05}d=\frac{1.1}{0.05} \\ \\ d=22 \end{gathered}[/tex]

4. Use the value of d=22 to solve n:

[tex]\begin{gathered} n=31-d \\ n=31-22 \\ n=9 \end{gathered}[/tex]Then, you have 9 nickels and 22 dimes in your pocket

Answer:

0,4,2

Step-by-step explanation:

all you have to do is divide the y value with the x value and I got these solutions

We can divide the figure into two triangles.

As you can observe, both triangles are equal, their base is 3 units long and their height is 5 units long. The height is outside the triangle because it's an obtuse triangle. First, let's use the area formula for triangles.

[tex]A=\frac{bh}{2}[/tex]

Where b = 3 and h = 5. Let's find the area of one triangle.

[tex]A=\frac{3\cdot5}{2}=\frac{15}{2}[/tex]

Then, we multiply this area by 2 because there are two triangles.

[tex]A_{\text{total}}=2\cdot\frac{15}{2}=15[/tex]Therefore, the area of the shape is 15 square units.

Set up a proportion:

height / shadow

6 / 7 = x / 36

Solve for x:

(6/7) 36 = x

x = 30.9 ft

ANSWER

3(x + 3)

EXPLANATION

We have the expression:

3x + 9

To factorise it, we wll use a number that is a factor of the two numbers in the expression.

We have:

3x + 9

= 3(x + 3)

That is the expression in factored form.

the sum of the intern angles of a triangle must be 180°

First we need to find the value of x

(2x-8)+(x+44)+x=180

4x+36=180

4x=180-36

4x=144

x=144/4

x=36

angle P=2(36)-8=64°

angle Q=36+44=80°

angle R=36°

#7

(a)

To find values of the function h at different x values, we go straight to that x value and find the corresponding y value of the graph.

From the graph, we have:

[tex]\begin{gathered} h(-2)=1 \\ h(0)=-1 \\ h(2)=3 \\ h(3)=4 \end{gathered}[/tex](b)

The domain of a function is the set of x-values for which the graph of the function is defined.

The range of a function is the set of y-values for which the graph of the function is defined.

Looking at the graph, we see that from

x = - 3 to x = 4, the function is defined.

Also, from

y = - 1 to y = 4, the function is defined.

Thus, we can write the domain and range as >>>>>

[tex]\begin{gathered} D=-3\leq x\leq4 \\ R=-1\leq y\leq4 \end{gathered}[/tex]

(c)

h(x) = 3 means y = 3

We will draw a horizontal line at y = 3 and see the points at which that line and curve crosses. Then, we will draw a perpendicular from that point to the x-axis. These are the values of x for which y = 3.

The graph:

We see from the graph drawn that for x = - 3, x = 2, and x = 4, the value of the function h is 3.

So,

[tex]x=-3,2,4[/tex]

(d)

The values of x for which the function is ≤ 3 can be found by again drawing a line y = 3 and finding the places where the graph is BELOW that line.

Graph:

So, we can see that from x = - 3 to x = 2, the function is less than or equal to 3.

Thus,

[tex]-3\leq x\leq2[/tex]

(e)

From x = - 3 to x = 3, the function changes several values. But the net change can be found by finding the respective values of the function at x = - 3 and at x = 3 and finding the difference.

At x = - 3, the function has a value of "3".

At x = 3, the function has a value of "4".

Thus, the net change is 4 - 3 = 1

Net Change = 1

Explanation

Given

[tex]\begin{gathered} Amount=$ \text{ \$}500,000 $ \\ Time=30years \\ rate=4\text{\%} \\ principal=? \\ n=12 \end{gathered}[/tex]

We can use the formula below to find how much would you need to deposit now into the account to reach your retirement goal.

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \end{gathered}[/tex]

Therefore;

[tex]\begin{gathered} 500000=P(1+(\frac{4}{100}\div12))^{12\times30} \\ 500000=P(1+(\frac{4}{100\times12}))^{360} \\ 500000=P(1+0.0033333)^{360} \\ 500000=P(1.0033333)^{360} \\ Switch\:sides \\ P\left(1.0033333\right)^{360}=500000 \\ Divude\text{ both sides by }1.0033333^{\left\{360\right\}} \\ \frac{P\cdot\:1.0033333^{360}}{1.0033333^{360}}=\frac{500000}{1.0033333^{360}} \\ P=150899.7373 \end{gathered}[/tex]

Answer:

[tex]\begin{equation*} 150899.7373 \end{equation*}[/tex]

Let's begin by identifying key information given to us:

[tex]\begin{gathered} W=4.8in, \\ X=7.2in, \\ Y=9.3in \\ \end{gathered}[/tex]

Let's draw a diagram of the question

We have 3 known sides & 1 unknown angle. We will use Law of cosines

[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ 2bc\cos A=b^2+c^2-a^2 \\ \cos A=\frac{b^2+c^2-a^2}{2bc} \\ A=\cos ^{-1}(\frac{b^2+c^2-a^2}{2bc}) \\ a=w,b=x,c=y \\ W=\cos ^{-1}(\frac{7.2^2+9.3^2-4.8^2}{2(7.2)(9.3)}) \\ W=\cos ^{-1}(\frac{115.29}{133.92}) \\ W=\cos ^{-1}(0.8609) \\ W=30.58\approx31 \\ W=31^{\circ} \end{gathered}[/tex]

Given that a state fair gives free admission to every 187th person that enters the fair.

We have the find the number of people who received free admission.

On Saturday, 5619 people attended the fair. The number of free admissions is equal to the quotient when 5619 is divided by 187.

The quotient is 30. So, on Saturday, the free admissions are 30.

On Sunday, 9257 people attended the fair. The number of free admissions is equal to the quotient when 9257 is divided by 187.

The quotient is 49. So, on Sunday, the free admissions are 49.

Thus, 79 people received free admission over two days.

The expression

[tex]3\times4^2+8-(\frac{6}{2})[/tex]

is equivalent to

[tex]3\times16+8-3[/tex]

since 3x16=48, we get

[tex]48+8-3[/tex]

since 48+8=56, we have

[tex]56-3[/tex]

Therefore, the expression is equal to 53.

Let's go!

So, it's

[tex]-1\text{ }\leq\text{ x }<3[/tex]

Because the interval is closed on the -1, meaning it is a part of it and opened in 3, meaning it is not.

x greater or equal to -1 and less than 3 (the way you read it)