Match The Graph With The Correct Equation. A. Y-5=-(x+3)B. Y-3=(x+5)C. Y-3=-(x+5)D. Y+3=-(x+5) (2024)

Given:

The first fund earns $600 and the second fund earns $800.

Let x% be the lower rate of interest.

And x+4% be the higher rate of interest.

The difference between the amounts is,

[tex]800-600=200[/tex]

It means,

[tex]\begin{gathered} 4\text{ percent of n =200} \\ \text{Where n is the amount invested. } \\ \frac{4}{100}\times n=200 \\ n=\frac{200\times100}{4} \\ n=5000 \\ It\text{ gives } \\ \text{x percent of }5000=600 \\ \frac{x}{100}\times5000=600 \\ x=\frac{600}{50} \\ x=12 \\ \text{Same way,} \\ \text{x percent of }5000=800 \\ \frac{x}{100}\times5000=800 \\ x=\frac{800}{50} \\ x=16 \end{gathered}[/tex]

Alternative way,

For the first fund. let a be the lower rate and a+4 be the higher rate.

[tex]ax=600[/tex]

For second fund,

[tex]\begin{gathered} x(a+4)=800 \\ ax+4x=800 \\ 600+4x=800 \\ 4x=800-600 \\ x=\frac{200}{4} \\ x=50 \end{gathered}[/tex]

So,

[tex]\begin{gathered} ax=600 \\ 50a=600 \\ a=\frac{600}{50} \\ a=12 \\ \Rightarrow a+4=12+4=16 \end{gathered}[/tex]

Answer: The lower rate of interest is 12%

To write a fraction as a percentage, you need to obtain the result of the division of 3 by 5 (this will be a decimal expression), and then multiply the result by 100. Then, we have:

[tex]\frac{3}{5}=0.6[/tex]

Therefore:

[tex]P=0.6\cdot100\Rightarrow P=60[/tex]

That is, 3/5 can be written as 60%. In other words, 3 is 60% of 5.

Solution

[tex]undefined[/tex]

Option B

[tex]undefined[/tex]

The final answer

Option B

In your graphic, you can choose some points: A(5,9) and B(3,5).

To find the slope, you have to divide the difference of the y-coordinates of 2 points by the difference of the x-coordinates of those same 2 points.

[tex]\text{slope = }\frac{\Delta y}{\Delta x}[/tex]

Using the 2 points:

[tex]\text{slope = (9-5)/(5-3)}[/tex][tex]\begin{gathered} \text{slope = 4/2} \\ \text{slope = 2} \\ \end{gathered}[/tex]

We have tjhe general rule for dilations:

[tex]D_k(x,y)=(kx,ky)[/tex]

where k is the scale factor.

In this case, we can take the points (10,0) and the dilated point (8,0) to find the scale factor like this:

[tex]\begin{gathered} D_k(10,0)=(10k,0k)=(8,0) \\ \Rightarrow10k=8 \\ \Rightarrow k=\frac{8}{10}=\frac{4}{5} \\ k\text{=}\frac{4}{5} \end{gathered}[/tex]

therefore, the scale factor is k=4/5

In order to get the number of free throws each player will make, we simply have to multiply each probability by the total number of attempts which is 80.

The equation for the best player would then be:

[tex]\begin{gathered} 85\%\times80=x \\ or \\ \frac{85}{100}\times80=x \\ or \\ \frac{85}{100}=\frac{x}{80} \end{gathered}[/tex]

After multiplying, we can say that estimatedly, the best player will make about 68 free throws.

[tex]\begin{gathered} \frac{85}{100}=\frac{x}{80} \\ Cross-multiply. \\ \frac{85\times80}{100}=x\Rightarrow\frac{6800}{100}\Rightarrow x=68 \end{gathered}[/tex]

On the other hand, for the second best player, we

We have the following function for the amount of carbon dioxide in moles produced in a chemical reaction:

[tex]f(t)=0.02t^2[/tex]

And we also have that it is a function of time (t), and we need to find the rate of production of carbon dioxide after two seconds.

1. To find the rate of production, we need to find the derivative for the function since it will give us the instant rate of change for the chemical reaction. Then we have:

[tex]\frac{df(t)}{dt}=\frac{d}{dt}(0.02t^2)[/tex]

2. And now, applying the derivative rules for a constant, and for a power, we have:

[tex]\begin{gathered} \frac{d}{dt}(0.02t^2)=0.02*\frac{d}{dt}(t^2)=0.02*2*t=0.04*t \\ \\ \text{ Therefore, the derivative is:} \\ \\ 0.04*t \end{gathered}[/tex]

3. Then after 2 seconds, we have that the rate of production of carbon dioxide is:

[tex]0.04(2)=0.08\frac{\text{ mol}}{s}[/tex]

Therefore, in summary, the rate of production of carbon dioxide after two seconds is 0.08 mol/s (option c).

In the given image, you have the following:

- side OP (first triangle) is congruent to side QR

- angle N is congruent to angle S

- angle O is congruent to angle Q

if angles N and S, and O and Q are equal, it is necessary that angles P and R are equal. Do to all interioir angles are equal, it is necessary that all sides of both trangles have the same length (beacuse one of such sides is equal to one side of the other triangle.)

Hence, you can conclude that both triangles are congruent:

ΔOPN ≅ ΔQRS

moreover, the specific theorem to express the congruent of both triangles is:

AAS

The scale drawing of the float is shown to be 14 inches long. The actual float has its length as 10 feet long. That means the scale used is;

[tex]\begin{gathered} \text{Scale}=\frac{14}{120} \\ \text{Note that 10 f}eet\text{ equals (10 x 12) 120 inches } \\ \text{Scale}=\frac{7}{60} \\ \text{For the width of the scale drawing, we use the scale as follows;} \\ \text{Scale}=\frac{7}{60}\times\text{actual} \\ \text{Scale}=\frac{7}{60}\times72 \\ \text{Scale}=\frac{7}{5}\times6 \\ \text{Scale =}\frac{42}{5} \\ \text{The width of the scale drawing is 8}\frac{2}{5} \\ \text{The approx}imate\text{ width therefore is 8 inches} \\ \text{This is because }\frac{2}{5}\text{ or 0.4 cannot be approx}imated\text{ to a whole number} \end{gathered}[/tex]

Given a circle with d = 6 in.

Circunference:

C = π × d

C = π × 6 in

C = 18.85 in

Area:

A = π × r²

A = π × 3²

A = 28.27 in²

ANSWER

circumference = 18.85 in

area = 28.27 in²

It is important to note the following:

• If the slopes of the two lines are equal, they are parallel.

,

• If the slopes of the two lines are negative reciprocal of each other, they are perpendicular.

Let's now calculate the slope of each line. Use the formula:

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

Let's start with line 1.

[tex]m=\frac{1-13}{-8-1}\Rightarrow m=\frac{-12}{-9}\Rightarrow m=\frac{4}{3}[/tex]

The slope of line 1 is 4/3.

Let's move on to line 2.

[tex]m=\frac{\frac{5}{3}-(-1)}{5-3}\Rightarrow m=\frac{\frac{8}{3}}{2}\Rightarrow m=\frac{4}{3}[/tex]

The slope of line 2 is also 4/3.

Since the slopes of the two lines are the same, then the two lines are parallel.

First, we find how many numbers are divided by 4:

[tex]\frac{100}{4}=25[/tex]

Now, we find how many numbers are divided by 9:

[tex]\frac{99}{9}=11[/tex]

Adding these two results:

[tex]25+11=36[/tex]

Finally, we find how many numbers are divided by both 4 and 9:

[tex]36\text{ and }72[/tex]

That is, there are two numbers. We subtract 2 from 36 and we obtain 34 numbers.

Answer: 34 numbers

Answer:

Explanation:

We'll use the below formula to solve the given question;

[tex]undefined[/tex]

Assume the equation to solve is:

[tex]N-\mleft(-13\mright)=24[/tex]

We distribute the minus sign and make

Step 1

see the figure below to better understand the problem

Step 2

Applying the law of sines

Find out the area of triangle ABC

[tex]\begin{gathered} A=\frac{1}{2}(3.1)(6.9)sin(112^o) \\ A=9.916\text{ yd}^2 \end{gathered}[/tex]

Step 3

Applying the law of cosines

Find out the length of the side AC

[tex]\begin{gathered} AC^2=3.1^2+6.9^2-2(3.1)(6.9(cos112^o) \\ AC=8.6\text{ m} \end{gathered}[/tex]

Step 4

Applying the law of cosines

Find out the measure of angle D

[tex]AC^2=AD^2+DC^2-2(AD)(DC)cosD[/tex]

substitute given values

[tex]\begin{gathered} 8.6^2=10.6^2+9.6^2-2(10.6)(9.6)cosD \\ solve\text{ for cosD} \\ cosD=\frac{10.6^2+9.6^2-8.6^2}{2(10.6)(9.6)} \\ \\ angle\text{ D}=50.1^o \end{gathered}[/tex]

Step 5

Applying the law of sines

Find out the area of the triangle ADC

[tex]\begin{gathered} A=\frac{1}{2}(10.6)(9.6)sin(50.1^o) \\ \\ A=39.03\text{ yd}^2 \end{gathered}[/tex]

The area of the quadrilateral is equal to

[tex]\begin{gathered} A=9.92+39.03 \\ A=48.95\text{ yd}^2 \end{gathered}[/tex]The area is 48.95 square yards (rounded to two decimal places)

Answer:

Define a periodic function:

A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals o radians, are periodic functions.

Take for instance a sine function below

Step 2:

Define the amplitude of a function:

The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine.

[tex]\begin{gathered} From\text{ the sine function, the amplitude is represented as} \\ =A \end{gathered}[/tex]

Step 3:

Define the period of a function:

The Period goes from one peak to the next (or from any point to the next matching point):

This is the time it takes complete one cycle

From the equation of a sine function,

The period is represented below as

[tex]Period=\frac{2\pi}{B}[/tex]

TAKE FOR EXAMPLE ,

The sine equation given below

[tex]\begin{gathered} y=2sin(4(x-0.5))+3 \\ Amplitude=A=2 \\ period=\frac{2\pi}{B}=4 \\ period=B=\frac{\pi}{2} \end{gathered}[/tex]

The graph will be given below as

If x is the number of tickets the seventh grade students sold, then you have:

tickets sold by seventh grade students = x

tickets sold by seventh grade students = x

This situation does not represent a proportionality relation because the ratios are different.

This comes from the fact that:

[tex]\frac{18}{3}=6[/tex]

and

[tex]\frac{40}{5}=8[/tex]

Therefore the ratios are different.

As the rick is thrown straight up in the air and the function of its displacement is quadratic it means that the rock traveled a distance up to its maximum and then down to the ground. Then, the function value in the maximum is half the distance traveled by the rock.

[tex]f(t)=-2t^2+15.7t[/tex]

Use the next formula to find the time (t) in the maximum point of quadratic function:

[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \\ x_{max}=-\frac{b}{2a} \end{gathered}[/tex][tex]t_{max}=-\frac{15.7}{2(-2)}=-\frac{15.7}{-4}=3.925[/tex]

Evaluate the function for t=3.925 to find the maximum value:

[tex]\begin{gathered} f(3.925)=-2(3.925)^2+15.7(3.925) \\ f(3.925)\approx-2(15.4056)+61.6225 \\ f(3.925)\approx-30.8112+61.6225 \\ f(3.925)\approx30.8113 \end{gathered}[/tex]

Multiply the maximum value by 2 to get the total distance traveled by the rock:

[tex]30.8113*2\approx61.62[/tex]Then, the total distance traveled by the rock when it reaches the ground is 61.62metersAnswer: C

First let's start with the graph of y = x:

Then, let's apply the "absolute value" operator: y = |x|

Then, we have an horizontal translation of 2 units to the left: y = |x + 2|:

Then, a vertical stretch by a factor of 1/2: y = (1/2)|x + 2|:

Finally, a vertical translation of 1 unit down: y = (1/2)|x + 2| - 1:

Explanation: The rate of change of a given function is the slope. Once we are given an equation, it is important to know the slope -ntercept form of a function that is represented below

[tex]y=mx+b[/tex]

As we can see above, m represents the slope of the function.

Step 1: To find the rate of change we just need to compare our equation to the slope-intercept form given above as follows

As we can see above rate of change = slope= m = 1

Final answer: So the final answer is 1.

Number of golfers that didn't qualify = 30

Explanation:

Total number of golfers = 80

The percentage that qualified for the next round = 62.5% = 0.625

Number that qualified = 80 * 62.5%

= 80 * 0.625

Number of golfers that qualified = 50

Number of golfers that didn't qualify = Total number of golfers - Number of golfers that qualified

= 80 - 50

Number of golfers that didn't qualify = 30

We have to calculate the monthly deposit in order to achieve a certain amount after certain number of years.

The amount is P = $210,000 and the number of years is n = 8 years.

Each deposit will increase a capital that will be compounding the interest, which has a annual rate of r = 10.2%.

As the deposits are made monthly (and we assume this is also the compounding period), we have a number of subperiods m = 12 subperiods per year.

We can use the annuity formula to find the monthly payment M so as to have a future value of FV = 210000:

[tex]M=\frac{FV*\frac{r}{m}}{(1+\frac{r}{m})^{n*m}-1}[/tex]

We can replace with the values and calculate the amount as:

[tex]\begin{gathered} M=\frac{210000*\frac{0.102}{12}}{(1+\frac{0.102}{12})^{8*12}-1} \\ M=\frac{210000*0.0085}{(1.0085)^{96}-1} \\ M\approx\frac{1785}{2.25365-1} \\ M\approx\frac{1785}{1.25365} \\ M\approx1423.84 \end{gathered}[/tex]

2) We have to calculate how much they deposit into the account.

As they deposit monthly during 8 years, the amount of deposits will be 12*8 = 96 deposits.

We can then multiply by the deposit amount and obtain:

[tex]\begin{gathered} TP=M*(n*m) \\ TP=1423.84*96 \\ TP=136688.64 \end{gathered}[/tex]

Answer:

1) Monthly payment = $1,423.84

2) $136,688.64

He needs 1 350 sq ft of hardwood

Explanation:

Data:

Kitchen's measurements: 25 ft by 25 ft

Bedroom's measurements: 25 ft by 20 ft

Excess wanting to purchase: 20% => 1.20

Formula:

Area of the kitchen: A(k) = side * side

Area of the bedroom: A(b) = side * side

Total Area: A = A(k) + A(b)

Amount of sq. ft of hardwood neede: T(h) = A + (A * 20%) = A + (A * 20 / 100) = A * 1.20

Solution:

A(k) = 25 * 25 = 625 sq. ft

A(b) = 25 * 20 = 500 sq. ft

A = 625 + 500 = 1 125 sq. ft

T(h) = 1 125 * 1.20 = 1 125 + ( 1 125 * 20 / 100 ) = 1 350 sq. ft

f(x) = 2 (x + 2)^2 + 8

Transformation 1: If we start with y = x^2 and replace x by x + 2, it has the effect of shifting the graph 2 units to the left.

Transformation 2: Then if we multiply the right side by 2, it turns the parabola upside down and gives a vertical expansion by a factor of 2.

Transformation 3: Finally, if we add 8 to the right side, it shifts the graph to 8 units up.

We need to determine which of the given equations has solution x = 12.

We can do so by replacing x with 12 on the left side of an equation and comparing the result to the right side. If they are equal, then x = 12 will be a solution to that equation.

We have:

[tex]12-12=0\ne4[/tex][tex]48\div12=4\ne12[/tex][tex]12+4=16\ne12[/tex][tex]12(12)=144[/tex]

Therefore, x = 12 is a solution to the last equation.

Answer: 12 x = 144

Bill monthly salary is $2100 plus an additional $100 for every copy of history is fun

We set S to represent his total monthly salary and N the total number of copies that he sells

Therefore, 2100 is an independent value and 100 depends on the number of sells

then, the equation is:

[tex]S=2100+100N[/tex]

To graph the equation, we need to find the x-intercept and y-intercept:

To find the y-intercept, set x=0:

In this case, x is represented by N, and y is represented by S:

[tex]S(0)=2100+100(0)[/tex][tex]s(0)=2100[/tex]

So the graph starts at S=2100, point (S,N) = (2100, 0)

Then,

when he sells one book

N=1

[tex]S=2100+100(1)=2200[/tex]

Y = 2200

-When he sells 2 books

N =2

[tex]S=2100+100(2)=2300[/tex]

S=2300

- When he sells 3 books

N =3

[tex]S=2100+100(3)=2400[/tex]

then, S=2400

- When he sells 4 books

N = 4

[tex]S=2100+100(4)=2500[/tex]

Then, S=2500

Therefore, his salary depends on how many books he sells, then change the N value to find all the points of the graps

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

Given:

[tex]\begin{gathered} \operatorname{mean}\text{ = 77.3} \\ \text{standard deviation = 4.8} \end{gathered}[/tex]

From the given curve, we can assume the extreme values are three standard deviations of the mean since the shaded area covers almost all parts of the curve i.e :

[tex]z\text{ =3 or -3}[/tex]

Using the formula for z-score, we can find the extreme points:

[tex]\begin{gathered} z\text{ = }\frac{x-\psi}{\sigma} \\ \text{where }\psi\text{ is the mean and} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]

Substituting we have:

[tex]\begin{gathered} 3\text{ =}\frac{x_1-77.3}{4.8} \\ x_1-77.3=14.4 \\ x_1\text{ =91.7} \end{gathered}[/tex][tex]\begin{gathered} -3\text{ = }\frac{x-77.3}{4.8} \\ x-77.3\text{ = -14.4} \\ x\text{ =62.9} \end{gathered}[/tex]

Hence,

The percentage of total area shaded is 99.7%

The left and right values are 62.9 and 91.7 respectively

Solve for x:

[tex]12(1+x)=4x+28[/tex]

As a first step, use distributive multiplication:

[tex]12+12x=4x+28[/tex]

Then, we can use inverse operations to solve equations:

[tex]\begin{gathered} 12x-4x=28-12 \\ 8x=16 \\ x=\frac{16}{8} \\ x=2 \end{gathered}[/tex]

We determine that by calculating the cost of buying one Oz for each case, that is:

[tex]p_1=\frac{1\cdot3}{12}\Rightarrow p_1=\frac{1}{4}\Rightarrow p_1=0.25[/tex][tex]p_2=\frac{1\cdot4}{8}\Rightarrow p_2=\frac{1}{2}\Rightarrow p_2=0.5_{}[/tex]

Here p1 and p2 represent the cost of 1 Oz for the 12 Oz and 8 Oz scenarios given, from this we have that is better to buy a 12 Oz box of cereal for $3 since we would be buying 1 Oz for $0.25.