The equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.
There is a rectangular garden with an area of 24 square feet
The garden is 2 feet longer than it is wide
Let the width of the garden be x
Then, the length of the garden is x + 2
The area of a rectangular garden = length of the garden x width of the garden
24 = x (x + 2)
x² + 2x - 24 =0
x² + 6x - 4x - 24 = 0
x(x + 6) -4(x + 6) = 0
(x - 4)(x + 6) = 0
x - 4 = 0
x = 4
Width of the rectangular garden is 4 feet
Length of the rectangular garden is (4 + 2) feet = 6feet
Therefore, the equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.
To learn more about area refer here
https://brainly.com/question/25292087
#SPJ9
Me podrían ayudar a contestar estas preguntas, por favorspeak spanish
En un parallelogramo, los lados opuestos son paralelos. De la misma forma, los angulos opuestos son iguales y los angulos adjacentes suman 180 grados.
Con ello, podemos decir que:
a. Los lados RS y UT son paralelos.
b. Los lados RU y ST son paralelos.
c. El angulo en U es igual al angulo en S pues son opuestos
d. Los angulos en S y T son adjacentes . Esto quiere decir que, su suma es igual a 180 grados.
e. El angulo en R es igual al angulo en T pues son opuestos.
f. De forma similar al caso d, los angulos U y R son adjacentes, su suma es 180 grados.
Graph y < -1 in a coordinate plane. And Label the Axis
Answer:
Explanation:
Given the below inequality;
[tex]y<-1[/tex]To graph the above, we have to note that since we have the less than sign without an inequality sign, the line will be broken lines and we'll shade the downward part of the graph as shown below;
for every dollar of revenue the government takes in, it pays 5 cents in interest on its debtwhat is the ratio of debt interest to total revenue a. 1:4b. 1:5c. 1:10d. 1:20
Answer;
D. 1:20
Explanation
According to the question, we are given the following
Total revenue = 1 dollars
Debt interest = 5cents
Ratio of debt interest to total revenue = 5cents : 1 dollar
Since 1 dollar = 100cents
ratio of debt interest to total revenue = 5cents : 100cents
ratio of debt interest to total revenue = 5/100 = 1/20
Hence the ratio of debt interest to total revenue is 1:20
Neil and Tom love to collect baseball cards. Neil has 83 more baseball cards than Tom. Neil has 517 baseball cards,How many baseball cards does Tom have?
We start by labeling the number of cards of each. The number of cards that Neil has will be "N", and the number of cards that Tom has will be "T".
We are told that Neil has 83 more baseball cards than Tom, this can be represented in an equation:
[tex]N=T+83[/tex]In this expression, we say that the number of cards that Neil has is equal to the number of cards that Tom has plus 83 more cards.
Since the problem also indicates that Neil has 517 baseball cards:
[tex]N=517[/tex]And we can combine the two equations we have as follows:
[tex]T+83=517[/tex]With this last equation, we will be able to find the number of baseball cards that Tom has, by solving for T.
To solve for T, we subtract 83 to both sides of the equation:
[tex]T+83-83=517-83[/tex]On the left side +83-83 cancel each other:
[tex]T=517-83[/tex]And making the subtraction on the right side, we get the value of T:
[tex]T=434[/tex]Tom has 434 baseball cards.
Answer: 434
Issaiah Jones Unit Rate, Reasoning Down Dec 06, 7:36:45 PM Watch help video HII Julian earned $437.00 at his job when he worked for 19 hour he earn each hour
EXPLANATION
Let's see the facts:
Julian Earns--> $437.00
Worked--> 19 hours
Unit rate=
[tex]Unit_{}-rate=\frac{437\text{ dollars}}{19\text{ hours}}=23\text{ \$/h}[/tex]Find the solution set of each linear system3x+2y+z=8x+y+2z= 44x+y+z= y
Answer:
x=0, y=4 and z=0.
Explanation:
Given the system of linear equations:
[tex]\begin{gathered} 3x+2y+z=8 \\ x+y+2z=4 \\ 4x+y+z=y \end{gathered}[/tex]From the third equation:
[tex]\begin{gathered} 4x+y-y+z=0 \\ 4x+z=0 \\ z=-4x \end{gathered}[/tex]Substitute z=-4x into the first and second equations.
[tex]\begin{gathered} 3x+2y-4x=8 \\ -x+2y=8 \\ \text{Second Equation} \\ x+y+2z=4 \\ x+y+2(-4x)=4 \\ x+y-8x=4 \\ -7x+y=4 \end{gathered}[/tex]Solve the two results simultaneously.
[tex]\begin{gathered} -x+2y=8\implies x=2y-8 \\ -7x+y=4 \\ -7(2y-8)+y=4 \\ -14y+56+y=4 \\ -13y=4-56 \\ -13y=-52 \\ y=-\frac{52}{-13} \\ y=4 \end{gathered}[/tex]Substitute y=4 to solve for x.
[tex]\begin{gathered} -7x+y=4 \\ -7x+4=4 \\ -7x=4-4 \\ -7x=0 \\ x=0 \end{gathered}[/tex]Finally, recall that: z=-4x
[tex]z=-4(0)=0[/tex]Therefore x=0, y=4 and z=0.
Determine the amount of an investment if $100 is invested at an interest rate of 5.5% compounded semi-annually for 6 years.
We have an investment that is compounded semi-anually.
The equation for the future value of an compounded interest investment is:
[tex]FV=PV(1+\frac{r}{m})^{n\cdot m}[/tex]where:
FV is the future value.
PV is the present or initial value of the investment (PV=100).
r is the annual nominal interest rate (r=5.5%=0.055).
m is the number of capitalization subperiods in the year. In this case, as it is semiannually, m=12/6=2.
n is the number of yearly periods that the investment last (n=6 years).
Then, we can replace the variables with the values and calculate:
[tex]\begin{gathered} FV=100\cdot(1+\frac{0.055}{2})^{2\cdot6} \\ FV=100\cdot(1+0.0275)^{12} \\ FV=100\cdot1.0275^{12} \\ FV\approx100\cdot1.3848 \\ FV\approx138.48 \end{gathered}[/tex]Answer: the value of the investment after 6 years is $138.48.
Amber rolls a 6-sided die. On her first roll, she gets a "4". She rolls again.(a) What is the probability that the second roll is also a "4".P(4 | 4) =(b) What is the probability that the second roll is a "1".P(14)
The outcome of the second roll is independent from the previous outcome. The probability of getting any given number from 1 to 6 is always the same: 1/6.
Therefore, the answers are:
a) The probability that the second roll is also a 4 is 1/6.
b) The probability that the second roll is a 1 is 1/6.
The Washington Monument, in Washington, D.C., is 555 feet 5% inches tall and weighs 90,854 tons. The monument is topped by a square aluminum pyramid. The sides of the pyramid's base measure 5.6 inches, and the pyramid is 8.9 inches tall. Estimate the slope that a face of the pyramid makes with its base. Round to the nearest tenth.
Sides of the pyramid are:
5.6 inches base
Height of the pyramid is:
8.9 inches
Let's recall the formula of the slope:
Slope = Change in y/Change in x
Let x = 8.9 or change in vertical distance
Let y = 2.8 or change in horizontal distance
Slope = 8.9/2.8
Slope = 3.1785
Slope = 3.2 rounding to the next tenth
CR. 4: Two spinners-One 5 and one 6. What is the probability that you will spin thesame number on both spinners twice. What is the probability that you get two numbersthat have the SUM of 5? What is the probability that you land on an even number?Lastly, what is the probability that you will get one 2 and one 3 when you spin?(OR NewSpinners)
We will denote the first spinner as S5 and the second one as S6.
1) Probability spin the same number is both spinners twice
The probability of landing in a given number using S5 is equal to 1/5, while when using the S6 the probability is 1/6.
First, we get the same result twice using S5, this probability is given by:
[tex]P(S5_{\text{twice}})=\frac{1}{5}\cdot\frac{1}{5}=\frac{1}{25}[/tex](An specific number, of the 5 available, twice) Notice that the result we obtain with S5 does not affect what we obtain with S6.
On the other hand, the probability of getting any number twice in a row, using S6, is:
[tex]P(S6_{\text{twice}})=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}[/tex](An specific number, of the 6 available, twice) In case the problem refers to the probability of spinning S5 once, then S6, and obtaining the same number:
First, notice that there are a total of 5 results that satisfy this condition
(1,1),(2,2),(3,3),(4,4),(5,5)
And there is a total of 5*6=30 possible combinations. 30 different pairs (S5,S6).
So, the probability is the number of positive cases divided by the total amount of cases:
[tex]P(S5=S6)=\frac{5}{30}=\frac{1}{6}[/tex]This is the probability of getting the same number if you spin S5 and S6 once each.
2) Probability getting two numbers which SUM is equal to 5
Let's suppose that the problem refers to spinning once each one of the spinners and then adding the results.
First, we need to get the pairs that add up to 5
(S5,S6)
(1,4),(4,1)(2,3),(3,2). These are the only pairs that satisfy the condition.
And remember that, when spinning S5 and S6 once each, there are 30 possible combinations. So, the probability we are looking for in part 2 is:
[tex]P(SUM(5))=\frac{4}{30}=\frac{2}{15}\approx0.1333\ldots[/tex]3) Landing on an even number
In the case of S5, there are 2 even numbers:2,4 and 5 numbers on which the spinner can land:1,2,3,4,5.
So, the probability is:
[tex]P(S5_{\text{even}})=\frac{2}{5}=0.4[/tex]On the other hand, the probability of getting an even number with S6 is:
[tex]P(S6_{\text{even}})=\frac{3}{6}=0.5[/tex]We can even find the probability of spinning S5 once, then S6, and get an even number. Since the events are independent, that probability is:
[tex]P(S5_{\text{even}})\cdot P(S6_{\text{even}})=0.4\cdot0.5=0.2=\frac{1}{5}[/tex]d) Get one 2 and one 3.
Once again, there is a total of 2 pairs that satisfy this condition: (2,3) and (3,2), and there is a total of 30 combinations when we spin S5 and S6. So,
[tex]P(2and3)=\frac{2}{30}=\frac{1}{15}\approx0.0666[/tex]And that's the answer to the fourth question
Find the slope of a line a. parallel and b. perpendicular to the line y = - 3x + 8.a. Parallel:b. Perpendicular:
The slope of a line parallel to the given line is -3
The slope of the line perpendicular to the given line is 1/3
Explanation:
Given:
y = -3x + 8
To find:
a) slope of a line parallel to the given line
b) slope of a line perpendicular to the given line
a) For two lines to be parallel, their slopes will be the same
From the given equation, we will get the value of the slope
[tex]\begin{gathered} linear\text{ equation: y = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \\ \\ comparing\text{ y = mx + b with y = -3x + 8}: \\ mx\text{ = -3x} \\ m\text{ = -3} \end{gathered}[/tex]The slope of a line parallel to the given line is -3
b) For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the other line
The slope from the line given is -3
reciprocal of the slope = 1/-3 = -1/3
negative reciprocal = -(-1/3) = 1/3
The slope of the line perpendicular to the given line is 1/3
Determine if the triangles are similar; if they are then what is the reason?
From the given triangles,
[tex]\frac{OP}{PN}=\frac{RS}{SQ}[/tex][tex]\angle OPN=\angle RSQ=89^O[/tex]Thus the triangles are similar by SAS property.
The relation is SAS: two sides+included angle congruent.
Combine Like Terms -8w + 16x + 20w – 40x
Answer:
12w - 24x
Step-by-step explanation:
-8w + 16x + 20w - 40x
20w - 8w = 12w
-40x + 16x = 24x
Answer:
12w - 24xStep-by-step explanation:
Start by grouping terms that are alike. You can identify such terms by looking at the variables. Anything associated with x is considered a like term to another number associated with x.[tex]-8w+16x+20w-40x\\-8w+20w+16x-40x[/tex]
Add both like elements for each side.[tex]-8w+20w=12w\\12w+16x-40x\\16x-40x=-24x\\\bold{=12w-24x}[/tex]
Hope this helps!
7. Use the quadratic formula to solve the equation.4x + x-9-0-11 1722-82908-111454-11 145B
Use the quadratic formula, given by:
[tex]x=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]where a, b and c are the coefficients of the equation:
ax² + bx + c = 0
By comparing the given equation 4x² + x - 9 = 0, with the previous general form, you have:
a = 4
b = 1
c = -9
replace the previous values of the parameters into the quadratic formula:
[tex]\begin{gathered} x=\frac{-1\pm\sqrt[\square]{(1)^{2}-4(4)(-9)}}{2(4)} \\ x=\frac{-1\pm\sqrt[]{145}}{8} \end{gathered}[/tex]The previous expression contains the solutions to the given quadratic equation.
2221. Admission to a science museum is $22for an adult. The cost for a child is $5 lessthan the cost for an adult. What would bethe total cost of admission for 12 adultsand 15 children? Explain.
the cost for an adult admission is 22 $
cost for child is 22 - 5 = 17 $
total cost for 12 adults is 12 x 22 = 264
total cost for 15 children is 15 x 17 = 255
so the total cost of admission for 12 adults and 15 children is,
= 264 + 255
= 519 $
so the answer is 519 $
These are some unfinished calculations. Complete them to find each difference
for 2nd question
[tex]\begin{gathered} 9\frac{4}{8}-5\frac{1}{8}=\frac{76}{8}-\frac{41}{8} \\ =\frac{76-41}{8}=\frac{35}{8}\text{ or 4}\frac{3}{8} \end{gathered}[/tex]for 3rd question,
[tex]\begin{gathered} 9\frac{4}{8}-3\frac{5}{8}=\frac{76}{8}-\frac{29}{8} \\ =\frac{76-29}{8}=\frac{47}{8}\text{ or 5}\frac{7}{8} \end{gathered}[/tex]for 4th question,
[tex]\begin{gathered} 5\frac{1}{8}-3\frac{5}{8}=\frac{41}{8}-\frac{29}{8} \\ =\frac{41-29}{8}=\frac{12}{8}=\frac{3}{2}\text{ or 1}\frac{1}{2} \end{gathered}[/tex]Jenna, a 40-year-old female, bought a $650,900, 20-year life insurance policythrough her employer. Jenna is paid weekly. How much is deducted from each of herpaychecks? (use the table) Round answer to the hundredths place. If the answerdoesn't have a hundredths place then use zeros so that it does.
ANSWER:
$120
STEP-BY-STEP EXPLANATION:
Jenna is a 40-year-old woman and her policy is for 20 years, so according to the table, for every $1,000, $9.60 per year is deducted.
Now, Jenna's policy is $650,900, therefore, the annual deduction in her case taking into account her rate would be:
[tex]\begin{gathered} \frac{650900}{1000}=650.9\cong650 \\ \\ \text{ Therefore:} \\ 650\cdot9.6=6240 \end{gathered}[/tex]Now, this is the annual result, but since the payments are weekly and we know that there are 52 weeks in a year, then:
[tex]\begin{gathered} d=\frac{6240}{52} \\ \\ d=\text{ \$120} \end{gathered}[/tex]Which means that in each payment they deduct $120
Write the polynomial in factored form as a product of linear factors:g(t)=t^3+2t^2−10t−8
Okay, here we have this:
We need to write the following polynomial in factored form as a product of linear factors:
[tex]\begin{gathered} g\mleft(t\mright)=t^3+2t^2-10t-8 \\ =\mleft(t+4\mright)\mleft(t^2-2t-2\mright) \end{gathered}[/tex]Now, let's solve the following polynomial using the general formula for equations of the second degree:
[tex]\begin{gathered} (t^2-2t-2)=0 \\ t_{1,\: 2}=\frac{-\left(-2\right)\pm\sqrt{\left(-2\right)^2-4\cdot\:1\cdot\left(-2\right)}}{2\cdot\:1} \\ t_{1,\: 2}=\frac{-\left(-2\right)\pm\:2\sqrt{3}}{2\cdot\:1} \\ t_1=\frac{-\left(-2\right)+2\sqrt{3}}{2\cdot\:1},\: t_2=\frac{-\left(-2\right)-2\sqrt{3}}{2\cdot\:1} \\ t=1+\sqrt{3},\: t=1-\sqrt{3} \end{gathered}[/tex]Finally, we obtain the following polynomial:
[tex]g(t)=(t+4)(t-1-\sqrt{3})(t-1+\sqrt{3})[/tex]The initial balance of a savings account was $676. After which transactions will the balance of the savings account be the same as the initial balance? A. A withdrawal of $45, followed by a withdrawal of $45 Vocabulary Box: B. A deposit of $36, followed by a withdrawal of $36 Initial balance: starting amount ($$) C. A withdrawal of $67, followed by a deposit of $45 Transactions: deposits or withdrawals D. A deposit of $168, followed by a deposit of $168 Deposit: Put money in (+) please help
ANSWER
B
EXPLANATION
The intial balance of the savings account was $676.
Let us check the options A to D to see which of them is going to leave the same amount as the initial amount.
A. A withdrawal of $5 followed by a withdrawal of $45.
A withdrawal means money was taken so, the final balance will be:
$(676 - 45 - 45)
= $586
The final is not the same as the initial.
B. A deposit of $36, followed by a withdrawal of $36.
A deposit means money was added to the account, so the final balance is:
$(676 + 36 - 36)
= $676
The final amount is the same as the initial.
C. A withdrawal of $67, followed by a deposit of $45.
So, the final balance will be:
$(676 - 67 + 45)
= $654
The final amount is not the same as the initial.
D. A deposit of $168, followed by a deposit of $168.
So, the final balance will be:
$(676 + 168 + 168)
= $340
The final amount is not the same as the initial.
So, the correct choice is B because the final amount is the same as the initial amount
151617= 1819Write an equation in slope-intercept form for the line with slope 5 and y-intercept - 1.00=0:Х?
The slope-intercept format of a line is given as y=mx+c where m is the slope and c is the intercept.
Since m=5 and c=-1
Therefore the equation of the line is y = 5x-1
At the Avonlea Country Club, 54% of the members play bridge and swim, and 89% of the members play bridge. If a member is selected at random, what is the probability that the members swims, given that the member plays bridge?
ANSWER
[tex]P(S|B)=0.61[/tex]EXPLANATION
We are given that 54% of the members at the club play bridge and swim, and 89% of the members play bridge.
[tex]\begin{gathered} P(\text{BnS)}=0.54 \\ P(B)=0.89 \end{gathered}[/tex]To find the probability that the member swims given that he/she plays bridge, we have to apply conditional probability.
The probability that the member swims given that he/she plays bridge is gotten by dividing the probability that the member plays bridge and swims by the probability that the member plays bridge:
[tex]\begin{gathered} P(S|B)=\frac{P(B\cap S)}{P(B)} \\ \Rightarrow P(S|B)=\frac{0.54}{0.89} \\ P(S|B)=0.61 \end{gathered}[/tex]That is the answer.
To support the high school, the local businesses will donate $2 for every ticketsold at the homecoming game. If 113 student, 158 home and 52 visitor ticketswere sold, how much did they donate?
we know that
to find out the total amout donate, multiply the total tickets sold by $2
so
step 1
Find the total tickets sold
adds
113+
1. A taxi company charges an $8 fee for picking you up, plus an additional $1.75 for each mile that you travel. The last customer to use the company was charged 34.25 for their taxi ride. How many miles did they travel in the taxi?
they travelled 15 miles
Explanation:let the number of miles = m
The total charge per ride= $8 + (amount for each mile × number of miles)
amount for each mile = $1.75
The total charge = $8 + ($1.75 × m)
The total charge per ride = 8 + 1.75m
Last customer paid $34.25
34.25 = 8 + 1.75m
collect like terms:
34.25 - 8 = 1.75m
26.25 = 1.75m
divide both sides by 1.75:
26.25/1.75 = 1.75m/1.75
m = 15
Hence, they travelled 15 miles
V8 to the nearest tenth is about ?
Show all work to receive credit. Write verbal questions in at least one complete sentence.For each of the following questions, decide if the data is qualitative or quantitative. If it is quantitative, decide if it’s discrete or continuous. Explain the reason for your answer. a)Janelle is collecting data on the number of ounces of water drank by college students during a typical math class. What type of data is this?
To answer this question let's remember the definitions of qualitative and quantitative data:
• Qualitative data is data that describes the attributes or properties of what we are studying.
,• Quantitative data that describes certain quantity or amount. It is usually express by numbers with some unit associated it with it and it can be discrete or continuous. Discrete data is described by particular numbers in a range and continuos data is described by any number in any range.
With this in mind we conclude that Janelle is measuring qualitative data, since she is measuring the amount of water the student takes, furthermore this is continuous data since each student can drink any amount of water, that is, we can even divide the ounces in any decimal.
evaluate. Reduce your answer to lowest terms.2 1/5-10×(3/5)2
8 1/3% Convert each percent to a fraction and a decimal.
We must convert the percentage 8 1/3% to:
0. a fraction,
,1. a decimal.
First, we rewrite the number 8 1/3 in the following way:
[tex]8\text{ 1/3 }=8+\frac{1}{3}=8\cdot1+\frac{1}{3}=8\cdot\frac{3}{3}+\frac{1}{3}=\frac{8\cdot3+1}{3}=\frac{25}{3}\text{.}[/tex]Now, we have that:
[tex]8\text{ 1/3 \% }=\frac{25}{3}\text{ \%.}[/tex]1) Because 8 1/3 % is 8 1/3 per 100, we have that:
[tex]8\frac{1}{3}％=\frac{8\frac{1}{3}}{100}=\frac{\frac{25}{3}}{100}=\frac{25}{3\cdot100}=\frac{25}{3\cdot4\cdot25}=\frac{1}{12}\text{.}[/tex]2) Using a calculator, we have:
[tex]8\frac{1}{3}％=\frac{1}{12}\cong0.083.[/tex]Answer
• 8 1/3% as a ,fraction, is ,1/12,,
,• 8 1/3% as a ,decimal, is ,0.083,.
john wants to purchase a boat that costs $1,500. He signs an installment agreement requiring a 20% down payment. How much will john need for the down payment
Answer:
$300 down payment
Step-by-step explanation:
John wants to purchase a boat that costs $1,500. He signs an installment agreement requiring a 20% down payment. How much will john need for the down payment
20% = 0.20
0.20 * 1,500 = $300 down payment
CourcesKhan AcademyEmpirical ruleYou might need: CalculatorThe lifespans of seals in a particular zoo are normally distributed. The average seal lives 13.8 years, the standarddeviation is 3.2 years,ALCROLUse the empirical rule (68 - 95 - 99.7%) to estimate the probability of a seal living less than 7.4 years.Asi%Show CalculatorTATUSCoReport a problemStuck? Watch a video or use a hint.SAPro
Probability of a seal living less than 7.4 years, P(X < 7.4) = 0.023
Explanations:The distribution is said to be a normal distributuion.
For a normal distribution, you first calculate the z value.
[tex]\begin{gathered} \text{Average life, }\mu\text{ = 13.8} \\ \text{Standard Deviation, }\sigma\text{ = 3.2} \\ \text{The observed value, x = 7.4} \end{gathered}[/tex]The z value is calculated as:
[tex]\begin{gathered} \text{z = }\frac{\text{x -}\mu}{\sigma} \\ z\text{ = }\frac{7.4-13.8}{3.2} \\ z\text{ = }\frac{-6.4}{3.2} \\ z\text{ = -2} \end{gathered}[/tex]The probability of a seal living less than 7.4 years can be represented mathematically as:
P ( X < 7.4) Which can be interpreted as P(z < -2)
Checking this is in standard normal table:
P( z < -2) = 0.02275
Approximating to 3 decimal places, P(z < -2) = 0.023
Therefore, P ( X < 7.4) = 0.023
Two step equations 0=4+n/5
SOLUTION
We want to solve the equation
[tex]0=4+\frac{n}{5}[/tex]This means we should solve for n or find n. This becomes
[tex]\begin{gathered} 0=4+\frac{n}{5} \\ \text{moving 4 to the other side of the equation, we have } \\ -4=\frac{n}{5} \\ \text{Hence } \\ \frac{n}{5}=-4 \\ m\text{ultiplying both sides of the equation by 5, we have } \\ \frac{n}{5}\times\frac{5}{1}=-4\times5 \\ n=-20 \end{gathered}[/tex]Hence, the answer is n = -20