From the first line of the table, it shows
[tex]f(-2)=-12[/tex]This means that
when x = -2, y = -12,
so
[tex]a=-2[/tex]Now,
Can I Plss get some help on this (Number 50)
EXPLANATION:
Given;
We are given a rectangle with sides as indicated.
Required;
We are required to find the area and the perimeter from the dimensions provided.
Step-by-step solution;
We shall begin by reconstructing the rectangle and show the missing sides. This is done below;
Take note that we can extract one of the triangles and use the dimensions to calculate the missing side. This is also shown below;
Observe that we now have a triangle with sides 17 units and 16 units.
We draw a perpendicular and we effectively split the triangle into two right angled triangles. We can now solve for the side x using the Pythagoras' theorem.
[tex]\begin{gathered} c^2=a^2+b^2 \\ Where: \\ c=hypotenuse \\ a,b=other\text{ }sides \end{gathered}[/tex]We substitute these into the formula above;
[tex]\begin{gathered} 17^2=x^2+8^2 \\ \\ 289=x^2+64 \end{gathered}[/tex]Subtract 64 from both sides;
[tex]225=x^2[/tex]Take the square root of both sides;
[tex]\begin{gathered} \sqrt{225}=\sqrt{x^2} \\ \\ 15=x \end{gathered}[/tex]Let us now reconstruct the quadrilateral with the new dimension calculated.
We now have the Length and Width of the rectangle and we can now calculate the area and perimeter.
[tex]\begin{gathered} AREA\text{ }OFA\text{ }RECTANGLE: \\ Area=l\times w \\ \\ Area=30\times16 \\ \\ Area=480 \end{gathered}[/tex][tex]\begin{gathered} PERIMETER: \\ Perimeter=2(l+w) \\ \\ Perimeter=2(30+16) \\ \\ Perimeter=2(46) \\ \\ Perimeter=92 \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} Area=480units^2 \\ \\ Perimeter=92units \end{gathered}[/tex]Samuel invested $210 per acre for seed, fertilizer, fuel, depreciation, and land use. If he grosses$220 per acre this year, what percent return does he earn on his investment?
Let's begin by identifying key information given to us:
Amount invested (Initial Value) = $210 /acre
Gross income (Final Value) = $220 /acre
The percentage return is given by:
[tex]\begin{gathered} Return=\frac{FinalValue-InitialValue}{InitialValue} \\ Return=\frac{220-210}{210}=\frac{10}{210} \\ Return=0.04762\approx4.76\approx4.8 \\ Return=4.8\text{\%} \end{gathered}[/tex]Therefore, the return on investment is 4.8%
A garden table and a bench cost $669 combined. The garden table costs $81 less than the bench. What is the cost of the bench?
Given:
The cost of garden table and bench is, 669.
The garden table costs 81 less than bench.
Let us take x as the cost of the bench and y as the cost of the table. Then we have,
[tex]\begin{gathered} x+y=669\ldots\text{.}.(1) \\ y=x-81\ldots.(2) \end{gathered}[/tex]Now, substituting the value of y in equation 1, we get,
[tex]\begin{gathered} x+x-81=669 \\ 2x=669+81 \\ 2x=750 \\ x=\frac{750}{2}=375 \end{gathered}[/tex]Thus, the cost of bench is 375.
What is the area of rectangle with a length of 24 meters and a height of 7 meters?A84 square meters84 square metersB600 square meters600 square metersC168 square meters168 square metersD300 square meters
Answer: C. 168 m²
Explanation
The area of a rectangle (A) is given by:
[tex]A=l\cdot h[/tex]where l represents the length and h represents the height.
Then, in our case, l = 24m and h = 7m. By replacing the values and simplifying we get:
[tex]A=24m\cdot7m[/tex][tex]A=168m^2[/tex]it doesn't matter which of the two points on a line you choose to call (x1,y1) and which you choose to call (x2,y2) to calculate the slope of the line . true or false.
True
Explanation
the slope of a lines is the change in y over the change in x
[tex]\text{slope}=\frac{change\text{ in y}}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]where
[tex]\begin{gathered} \text{P1}=(x_1,y_1) \\ P2=(x_2,y_2) \end{gathered}[/tex]Step 1
Now, to prove , make
[tex]\begin{gathered} P1(x_2,y_2) \\ P2(x_1,y_1) \\ \end{gathered}[/tex]now, replace
[tex]\begin{gathered} \text{slope}=\frac{y_1-y_2}{x_1-x_2} \\ \text{slope}=\frac{y_1-y_2}{x_1-x_2}=\frac{-(y_2-y_1)}{-(x_2-x_1)}=\frac{(y_2-y_1)}{(x_2-x_1)} \end{gathered}[/tex]and we get the same slope, it does not matter wich one of the two points we choose to call P1 and P2.
True
I hope this helps you
There are 15 members of the show choir. In how many different ways can you arrange any 8 members in the front row?
We have the following:
The first chair can be any of the 15.
For each of those ...
The second chair can be any of the 14.
For each of those ...
And so on until choosing 8 chairs
.
.
.
The eighth chair can be any of 8.
For each of those ...
Number of ways to fill the 8 chairs = (15 x 14 x 13 x 12 x 11 x 10 x 9 x 8) = 259,459,200
But in each group of 8 people you can sit on (8 x 7 x 6 x 5x 4 x 3 x 2 x 1) = 40,320 orders.
So each group of 40,320 people is represented 24 times out of 259,459,200
Therefore, the answer is:
[tex]\frac{259459200}{40320}=6435[/tex]6435 sets of 8 members, in any order.
graph the inequality x-2y less than or equal to 0
To graph the inequality, we can do the following steps.
Step 1: We rearrange the equation so y is on the left and everything else is on the right.
[tex]\begin{gathered} x-2y\le0 \\ \text{ Subtract x from both sides} \\ x-2y-x\le0-x \\ -2y\le-x \\ \text{ Divide by -2 from both sides} \\ \frac{-2y}{-2}\le\frac{-x}{-2} \\ y\ge\frac{x}{2} \end{gathered}[/tex]Step 2: We plot the line associated with the inequality. For this, we choose two values of x and replace them in the below equation.
[tex]\begin{gathered} x=2 \\ $$\boldsymbol{y=\frac{x}{2}}$$ \\ y=\frac{2}{2} \\ y=1 \\ \text{ Then, the lines passes through the point (2,1).} \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ y=\frac{x}{2} \\ y=\frac{4}{2} \\ y=2 \\ \text{ Then, the lines passes through the point (4,2).} \end{gathered}[/tex]Since inequality has the symbol ≥, we make a solid line.
Step 3: Since inequality has the symbol ≥, we shade above the line. Therefore, the graph of the inequality is:
o points earned 21 Sally borrowed $500 to help pay for a car repair. The interest rate is 16% and the length of the loan is 30 months. How much money will Sally owe in total at the end of 30 months? Do not enter any spaces.
Answer:
$700
Explanation;
Givern the following
Amount borrowed = $500 (Principal)
Rate = 16%
Time = 30months = 30/12 yrs
Get the interest
Interest = PRT/100
Interest = 500*16*30/12*100
Interest = 5*16*30/12
Interest = $200
Amount owed at the end of 30months = Principal + Interest
Amount owed at the end of 30months = $500 + $200
Amount owed at the end of 30months = $700
Rihanna‘s yacht holds 70 passengers. Each hour he stops at the Marnie to let some passengers off and on. The scatterplot shows how many passengers are on board during each hour of boating. Usually given line of best fit the approximate the rate of change relative to the scatterplot. Pick a point along the line and use the coordinates X, Y to plug into the X equals MX plus be equation in sulfur M. Your rate of change! What is the passengers per hour?
5
1) Examining the scatterplot we can pick two points along the best line of fit. (7,60) and (1,30)
2) So now, we can plug these points into the slope formula:
[tex]m=\frac{30-60}{1-7}=\frac{-30}{-6}=5[/tex]3) Since this is a line of best fit, we can tell that the rate of change relative is (approximately) 5.
geometry, please give answer i know how to I think I did the steps wrong
We get that
[tex]\begin{gathered} m\angle1+m\angle4=180\rightarrow \\ 10x+2+5x+13=180 \\ 15x+15=180 \\ 15x=165 \\ x=\frac{165}{15}=11\rightarrow \\ m\angle1=10\cdot11+2=112 \end{gathered}[/tex]1. A function is given by the set of ordered pairs {(2,5),(4,9), (6,13), (8,17)). Write its domain and rangein roster form.Domain:Range:
The domains are:
{2, 4, 6, and 8}
The range are {5, 9, 13 and 17}
EXPLANATION
Given:
{(2,5),(4,9), (6,13), (8,17))
The above is given in the form (x, y)
where x is the domain and y is the range.
The domains are:
{2, 4, 6, and 8}
The range are {5, 9, 13 and 17}
what is 2÷0+3×5÷5÷2000÷1000÷399
Answer:
It's basically infinity.
Step-by-step explanation:
If you just add lots of numbers along with the equation it will sometimes be infinity
How much pesticide is need to treat 80,000 square feet at 2 pints/1000 square feetrate
2 pints ----> 1000 square feet
x pints ----> 80000 square feet
[tex]\begin{gathered} x\times1000=2\times80000 \\ 1000x=160000 \\ \frac{1000x}{1000}=\frac{160000}{1000} \\ x=160 \end{gathered}[/tex]answer:
160 pints is need to treat 80000 square feet
5 + kx = 17Solve for x
1) To solve for x, is to leave the x on the left side the other variables on the right along with the constants, like this
[tex]\begin{gathered} 5\text{ +kx =17} \\ kx\text{ =17-5} \\ x=\frac{17-5}{k} \end{gathered}[/tex]Note that, we subtracted 5 and then divided by x.
Answer:
5+kx=17
kx=17-5
kx=12
x= 12/k
These marbles are placed in a bag and twoof them are randomly drawn.What is the probability of drawing twoyellow marbles if the first one is placed backin the bag before the second draw?Give your answer as a ratio, reduced tosimplest terms.Hint: Multiply the probability of the 1st Event by theprobability of the 2nd Event to get your answer.
step 1
Find the probability that the first marble is yellow
P=2/10 ------> P=1/5
step 2
Find the probability the the second marble is yellow
P=2/10 -----> P=1/5
therefore
P=(1/5)(1/5)
P=1/25
answer is 1/25Michelle sells new and used kayaks. She makes a 10.5% commission on every kayak she sells and she also gets paid $495.50 per week. a) Develop an equation for the way Michelle is paid. b) Last month, the total value of the kayaks she sold was $19 425. Use the equation you’ve developed to find out how much Michelle was paid for that month.
Michelle was paid for that month is $ 4021.625
A linear equation is an algebraic equation of the form y=mx+b. regarding only a regular and a first-order (linear) time period, in which m is the slope and b is the y-intercept. on occasion, the above is called a "linear equation of two variables," where y and x are the variables.
Calculation:-
Percentage of commission = 10.5%
per week paid = $495.50
a. Equation of Michelle paid = 10.5/100X + 495.50
b. The total value of the kayaks she sold was $19 425.
Michelle was paid for that month = 19 425 × 10.5/100 + 4 × 495.50
= 2039.625 + 1982
= $ 4021.625
A linear equation bureaucracy is an immediate line on a graph. A nonlinear equation paperwork an S-curve, bell curve, or any other nonlinear form on a graph. experts in mathematics and physics view linear equations as simple. specialists in mathematics and physics view nonlinear equations as complex.
A linear equation in a single variable is an equation wherein there is handiest one variable present. it is of the form Ax + B = 0, wherein A and B are any real numbers and x is an unknown variable that has the handiest one answer. for instance, 9x + 78 = 18 is a linear equation in one variable.
Learn more about linear equations here:-https://brainly.com/question/2030026
#SPJ1
The equation m = 5b represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
Determine the constant of proportionality.
10
5
1
one fifth
The constant of proportionality for the equation m = 5b is 5.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
We have,
The equation m = 5b represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
Now,
The equation:
m = 5b can be written as m ∝ b
m ∝ b
m = 5b
Where 5 is the constant of proportionality.
Thus,
The constant of proportionality for the equation m = 5b is 5.
Option B is the correct answer.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Answer: 5
Equation of a Proportional Relationship
m = 5b
the 5 represents the constant of proportionality
the m represents the dependent variable, or y-coordinate in an ordered pair
the b represents the independent variable, or x-coordinate in an ordered pair
The annual interest on a $2000 investment exceeds the interest earned on a $1000 investment by $55.The $2000 is invested at a 0.5% higher rate of interest thanthe $1000. What is the interest rate of each investment?
from the question;
The annual interest on $2000 ivestment exceeds the interest earned on $1000 investment by $55 and the $2000 is invested at a 0.5% higher rate of interest than the $1000
let P = principal
I = interest
R = interest rate
first
[tex]\begin{gathered} \text{Let} \\ P_1=\text{ \$1000 investment} \\ I_1\text{ = x} \\ R_1\text{ = r\%} \end{gathered}[/tex]given the above information on $1000 investment above and the information above
[tex]\begin{gathered} \text{let } \\ P_2\text{ = \$2000 investment} \\ I_2\text{ = x + 55} \\ R_2\text{ = (r + 0.5)\%} \end{gathered}[/tex]applying the formula for Interest
[tex]\text{Interest I = }\frac{P\text{ }\times T\text{ }\times\text{ R}}{100}[/tex]for $1000 investment
[tex]\begin{gathered} u\sin g\text{ the interest formula and inserting the appropriate values} \\ we\text{ get} \\ x\text{ = }\frac{1000\text{ }\times\text{ 1 }\times\text{ r}}{100} \\ x\text{ = 10r -------- (1)} \end{gathered}[/tex]for $2000 investmet
[tex]\begin{gathered} u\sin g\text{ the interest formula and applying the appropriate values} \\ we\text{ get} \\ x\text{ + 55 = }\frac{2000\text{ }\times\text{ 1 }\times\text{ (r + 0.5)}}{100} \\ x\text{ + 55 = 20(r + 0.5)} \\ x\text{ + 55 = 20r + 10} \\ x\text{ - 20r = 10 - 55} \\ x\text{ - 20r = -45 ----------(2)} \end{gathered}[/tex]combine the two equations;
[tex]\begin{gathered} x\text{ = 10r -------------(1)} \\ x\text{ - 20r = - 45 ---------(2)} \end{gathered}[/tex]substitute x=10r into equation 2; we get
[tex]\begin{gathered} 10r\text{ - 20r= -45} \\ -10r\text{ = - 45} \\ \text{divide both sides by -10} \\ \frac{-10r}{-10}\text{ = }\frac{-45}{-10} \\ r\text{ = 4.5} \end{gathered}[/tex]Therefore,
the interest rate on $1000 investment = 4.5%
The interest rate on $2000 investment is (4.5 + 0.5)% = 5.0%
Can someone please help me? I’ll give brainly :) question is in photo
Answer:
Step-by-step explanation:
So basically you would cut the block in half however you'd like but this is how I did it- first you would multiply one side the side I chose has the numbers 7*15*10 so you multiply those getting 1050 then set that aside and do the other side with the numbers of 6*5*10 which if you multiply you would get 300 then you add the first number 1050+300 = 1350 •tbh this might not be correct I tried•
Instructions: Factor the polynomial expression.7x²-13x +6Answer:
Explanation
Given the polynomial
[tex]7x^2-13x+6[/tex]We can find its factors below.
[tex]\begin{gathered} 7x^2-13x+6 \\ =7x^2-7x-6x+6 \\ =7x(x-1)-6(x-1) \\ =(7x-6)(x-1) \end{gathered}[/tex]Answer: (7x-6) and (x-1)
Look at the graphs and their equations below. Then in the information about the ABCand D
Given:
Given a graph and their equations. Then in the information about the A,B, Cand D
Required:
To fill the blanks.
Explanation:
(a) For each coefficient choose whether it is positive or negative :
A : It has positive coefficient.
B : It has positive coefficient.
C : It has negative coefficient.
D : It has negative coefficient.
(b) Choose the coefficient with the least value:
The graph D.
(c)
2. A blanket is 4 feet wide. It is 3 times as long as it is wide. Draw a diagram of the blanket, and label its dimensions. b. Find the perimeter and area of the blanket.
the width of the blanket is 4 ft
it is given that length is 3 times of width so the length is 3 * 4 = 12 ft
part b)
so the blanket is rectangular.
the perimeter of the blanket is
2(4+12) = 32
area of the blanket is
length x width
12 x 4 = 48 square ft
part a)
the diagram of the blanket is given as follows,
I need help with number 13 and can you please write your answer using only positive exponents
Answer:
[tex]\frac{1}{x^{45}}[/tex]Explanation:
The given expression is
[tex](x^{-5})^9[/tex]In this case, we can multiply the exponents to get
[tex]x^{-5\cdot9}=x^{-45}[/tex]Then, to use positive exponents, we need to write it as a fraction
[tex]\frac{1}{x^{45}}[/tex]Therefore, the answer is
[tex]\frac{1}{x^{45}}[/tex]find the prime factorization ofa) 2205 and b)2525
(a) 2205.
The prime factorization consist in finding prime numbers which multiplication gives the initial number, to find those prime numbers, we divide the number by 2, 3, or 5, depending on the case. Let's do it.
2205 | 5
441 | 3
147 | 3
49 | 7
7 | 7
1
So, the prime factorization is
[tex]2205=5\times3\times3\times7\times7[/tex](b) 2525.
Let's repeat the process as we did with (a).
2525 | 5
505 | 5
101 | 101
1
So, the prime factorization is
[tex]2525=5\times5\times101[/tex]A car with a 15-gallon gas tank can go 22 miles on 1 gallon of gas. If the tank is full at the beginning of a 377-mile trip, how many times does the driver have to refill the gas tank?
Consider that the car can go 22 miles on 1 gallon of gas, therefore the amount of gas required for the 377 mile trip is calculated as,
[tex]\frac{377}{22}\approx17.136[/tex]So the car needs 17.136 gallons of gas to complete the trip.
Since the capacity of the tank is 15 gallons, so the driver has to fill the tank two times.
First time for the full 15 gallons refill, and the second tme for the remaining 2.136 galllons fuel refill.
Thus, the driver has to refill the gas tank 2 times, to complete the trip.
If the scale factor is 5:8, and the actual width of the model is 20 feet, what is the model width?
If the scale factor is 5:8, it is the same as 5/8.
In order to calculate the width of the model, just multiply its actual width by the scale factor, as follow:
width of the model = (20 ft)(5/8) = 12.5 feet
Hence, the width of the model is 12.5 feet
suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the sof its height. suppose also that a beam 6 inches wide, 2 inches high, and 12 feet long can support a maximum of 14 tons. what is the maximum weight that could be supported by a beam that is 4 inches wide, 3 inches high and 14 feet long
Step 1
Write the formula connecting all variables.
Weight = w
Length = L
Width = b
Height = H
k = constant
[tex]w\text{ = }\frac{kbH^2}{L}[/tex]Step 2
Use the values below to find the constant k.
b = 6
H = 2
L = 12
W = 14
[tex]\begin{gathered} 12\text{ = }\frac{k\text{ }\times\text{ 6 }\times2^2}{12} \\ 14\text{ = }\frac{24k}{12} \\ \text{Cross multiply} \\ 24k\text{ = 14 x 12} \\ 24k\text{ = 1}68 \\ k\text{ = }\frac{168}{24} \\ k\text{ = }7 \end{gathered}[/tex]Step 3
Find the unknow
W = ?
b = 4
H = 3
L = 14
[tex]\begin{gathered} W\text{ = }\frac{kbH^2}{L} \\ W\text{ = }\frac{7\text{ }\times\text{ 4 }\times3^2}{14} \\ W\text{ = }\frac{7\text{ }\times\text{ 4 }\times\text{ 9}}{14} \\ W\text{ = }\frac{252}{14} \\ W=\text{ 18 tons} \end{gathered}[/tex]The maximum weight = 18 tons
Dave wants to borrow $22,000 from first finance bank. the bank will give him a 15 year loan at an interest rate od 4.85 % how mich will he pay the bank in interest over the life of the loan? Round to the nearest hundred dollar ?
Problem 7:
We determine the time as follows:
*We can proceed using the following expression:
[tex]t=\frac{\ln (\frac{m}{p})-\ln (\frac{m}{p}-\frac{r}{n})}{n\ln (1+\frac{r}{n})}[/tex]Here, t is the time it will take to pay, m is the maximum she can afford to pay each month, p is the base loan value, r is the interest rate, n is the number of periods. Now we replace:
[tex]t=\frac{\ln(\frac{500}{20000})-\ln(\frac{500}{20000}-\frac{0.071}{12})}{12\ln(1+\frac{0.071}{12})}\Rightarrow t\approx3.8[/tex]So, she will take approximately 3.8 years to pay up the loan.
Problem 8:
We determine the time he has as follows:
We use the expression:
[tex]t=\frac{\ln (\frac{m}{p})-\ln (\frac{m}{p}-\frac{r}{n})}{n\ln (1+\frac{r}{n})}[/tex]Here, t is the time it will take to pay, m is the maximum he can afford to pay each month, p is the base loan value, r is APR, n is the number of periods. Now we replace:
[tex]t=\frac{\ln(\frac{400}{14000})-\ln(\frac{400}{14000}-\frac{0.068}{12})}{12\ln(1+\frac{0.068}{12})}\Rightarrow t\approx3.3[/tex]So, he will take approximately 3.3 years to pay the loan.
Problem 10:
We determine the amount he will have to pay as follows:
*We use the following expression:
[tex]V=P(1+n)^t[/tex]Here V is the value to obtain, P is the original amount, n is the interest rate and t is the number of periods, now we replace:
[tex]V=(22000)(1-0.0485)^{15}\Rightarrow V\approx44766.09[/tex]So, after 15 years he will have to pay approximately $44766.09.
Let X represent number of sundaes sold and y represent the number of banana splits sold.Sundaes are sold for $2 each and banana splits for $3 each. They made a total of $150. Equation____________The number of sundaes sold is 5 times more than the number of banana splits sold. Equation________Solve the system of problem questions by substitution
Given that the total income was $150 by selling 'x' sundaes and 'y' banana splits,
[tex]\begin{gathered} \text{Total Cost}=\text{ Cost per sundae}\cdot\text{ Number of sundae}+\text{ Cost per banana splits}\cdot\text{ Number of banana splits} \\ 150=2x+3y \\ 2x+3y=150\ldots(1) \end{gathered}[/tex]Also given that the number of sundaes sold is 5 times more than the number of banana splits sold,
[tex]\begin{gathered} x=y+5y \\ x=6y\ldots(2) \end{gathered}[/tex]Substitute this value in equation (1),
[tex]\begin{gathered} 2(6y)+3y=150 \\ 12y+3y=150 \\ 15y=150 \\ y=10 \end{gathered}[/tex]The corresponding value of 'x' is calculated by using equation (2) as,
[tex]\begin{gathered} x=6(10) \\ x=60 \end{gathered}[/tex]Thus, the solution to the system of problem
a cylinder has a volume of 105 and a radius of eight what is the height of the cylinder give an exact answer or approximation to three decimals
We are asked to determine the height of a cylinder given its radius and its volume. To do that we will use the formula for the volume of a cylinder:
[tex]V=\pi r^2h[/tex]now, we solve for the height, we get:
[tex]\frac{V}{\pi r^2}=h[/tex]Now, we plug in the values:
[tex]\frac{105}{\pi(8)^2}=h[/tex]Solving the operations:
[tex]0.522=h[/tex]Therefore, the height is 0.522.