Answers
Answer:
A = 252Step-by-step explanation:
It's a trapezoid.
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
b₁, b₂ - bases
h - height
(look at the picture)
Use the Pythagorean theorem to calculate the length x:
[tex]x^2+12^2=15^2[/tex]
[tex]x^2+144=225[/tex] subtract 144 from both sides
[tex]x^2=81\to x=\sqrt{81}\\\\x=9[/tex]
Substitute:
[tex]b_1=9+12+9=30\\b_2=12\\h=12[/tex]
[tex]A=\dfrac{30+12}{2}\cdot12=(42)(6)=252[/txt]
Related Questions
The ratio of Alex’s toy cars to Jim’s toy cars is 8:3. How many toy cars do they have altogether, if Alex has 40 more cars than Jim.
Answers
[tex]\bf \cfrac{\textit{Alex's cars}}{\textit{Jim's cars}}=\cfrac{8}{3}\qquad \qquad \cfrac{\stackrel{\textit{40 more than \underline{j}}}{j+40}}{j}=\cfrac{8}{3}\implies 3j+120=8j \\\\\\ 120=5j\implies \cfrac{120}{5}=j\implies 24=j \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Jim}}{j = 24}\qquad \qquad \stackrel{\textit{Alex}}{24+40\implies 64}\qquad \qquad \stackrel{\textit{altogether}}{24+64\implies 88}[/tex]
The total number of cars that Alex and Jim have altogether is 84 cars.
What is a ratio?A ratio is a quantitative relationship between two different numbers that express the number of times in which a number is divisible within the other number. Sometimes ratios can be expressed in fraction form.
From the given information:
The ratio of Alex to Jim's toy is 8 : 3If Alex has more toys than Jim, i.e Jim = x and Alex = x + 40.Then, we can express them in fraction form as:
[tex]\mathbf{\dfrac{8}{3} = \dfrac{x +40}{x}}[/tex]
8x = 3(x +40)
8x = 3x + 120
8x = 3x = 120
5x = 120
x = 120/5
x = 24
Jim = x = 24 cars
Alex = x + 40 = 24 + 40 = 64 cars.
The total number of cars they have altogether is 24+64 = 84 cars.
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today Kylee put a kitchen table on layaway by making a down payment of 120 and agreeing to pay $48 a month starting next month for 24 months when will I receive the kitchen table
Answers
Answer:
2 1/2 months by the 3rd month
Step-by-step explanation:
Answer:
Kylee will receive the table in 24 months.
Step-by-step explanation:
Layaway is a type of purchasing method where the buyer places a deposit on an item to secure it or lay it aside. The buyer will pick up the item later when he pays the full balance.
This system allows the buyer to make smaller payments on the item until the full amount has been paid off.
So, if Kylee put the kitchen table on layaway, and agrees to pay $48 a month starting next month for 24 months. She will get the table in 24 months after completing her payment.
Which ratio is not equivalent to 5/3
Answers
4/3 I hope this helps
Select all the correct answers.
An architect is designing a swimming pool with a base in the shape of a right triangle. According to the architect, the pool’s depth should be 6 feet less than its length, x, and its width should be 8 feet less than its length. The volume of water in the pool cannot exceed 1,680 cubic feet. Which statements about the pool are true?
The water level in the pool cannot exceed 14 feet.
The water level in the pool cannot exceed 20 feet.
The inequality x3 − 14x2 + 48x − 1,680 ≥ 0 can be used to find pool’s length.
The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.
The inequality x3 − 14x2 + 48x − 3,360 ≤ 0 can be used to find pool’s length.
Answers
Answer:
The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.
⇒The water level in the pool cannot exceed 14 feet.
Step-by-step explanation:
The question is on inequalities
Given;
Length= x ft
depth= x-6 ft
Width= x-8 ft
volume ≤ 1680 ft³
Forming the inequality to find length x of the pool
Volume= base area × depth
base area × depth ≤ volume
x(x-8) × (x-6) = 1680
(x²-8x )(x-6) = 1680
x(x²-8x) -6 (x²-8x)=1680
x³-8x²-6x²+48x=1680
x³-14x²+48x=1680
x³-14x²+48x-1680 ≤ 0
⇒The water level in the pool cannot exceed 14 feet...why?
taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;
d=x-6 = 17-6=11 ft
⇒11 ft is less than 14ft
what’s the MAD of 7 20 9 35 12 15 7 10 20 25
Answers
Answer:
Population size:10
Mean (μ): 16
Mean Absolute Deviation (MAD): 7.2
Step-by-step explanation:
Mean absolute deviation (MAD) Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. ... Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.
Rewrite as a simplified fraction.
__
0.612 = ?
Answers
Final answer:
To convert the decimal 0.612 to a fraction, express it as 612/1000 and then divide both the numerator and the denominator by their greatest common divisor, which is 4, to get the simplified fraction 153/250.
Explanation:
To rewrite 0.612 as a simplified fraction, one can first recognize that it's equivalent to 612/1000. After realizing that, we can simplify the fraction by finding the greatest common divisor (GCD) of both the numerator and the denominator. In this case, the GCD of 612 and 1000 is 4. Hence, we can divide both numerator and denominator by 4 to simplify the fraction.
Dividing both 612 and 1000 by 4, we obtain 153/250. So, 0.612 as a simplified fraction is 153/250.
Some doctors recommend that men drink 3 liters of water every day . There are approximately 29.6 milliliters in 1 fluid ounce. Which measurement is closest to the number of fluid ounces in 3 liters ?
Answers
Answer:
[tex]\boxed{\text{101 fl oz}}[/tex]
Step-by-step explanation:
Step 1. Convert litres to millilitres
[tex]\text{V} = \text{3 L} \times \dfrac{\text{1000 mL}}{\text{1 L}} = \text{3000 mL}[/tex]
Step 2.Convert millilitres to fluid ounces
[tex]\text{v} = \text{3000 mL} \times \dfrac{\text{1 fl oz}}{\text{29.6 mL}} = \boxed{\textbf{101 fl oz}}[/tex]
How many different sandwiches with one meat, one cheese, and one type of bread can be made if there are 3 choices of meat, 2 choices of cheese, and 4 choices of bread?
Answers
Answer:
24
Step-by-step explanation:
⇒The question is on probability, to be specific its about counting principal
⇒You need to understand the counting rule where we multiply events together to get the total number of outcomes .
⇒In general if we have an event t and another event s the total outcome for the events is given by t×s
⇒In this question you multiply the number of ways we can make the different sandwiches
Given
meat=3 choices
cheese=2 choices
bread=4 choices
Outcomes= 3×2×4=24
The total number of sandwiches that can be made = 24
There are 24 different sandwiches that can be made with 3 choices of meat, 2 choices of cheese, and 4 choices of bread.
Explanation:The subject of this question is related to combinatorics, a topic in mathematics. The question asks, 'How many different sandwiches with one meat, one cheese, and one type of bread can be made if there are 3 choices of meat, 2 choices of cheese, and 4 choices of bread?'.
To find the answer, you would use the fundamental principle of counting which states that if there are n ways to do one thing and m ways to do another thing, then there are n * m total ways to perform both actions. In this case, we multiply the number of options together:
There are 3 choices for the meat.There are 2 choices for the cheese.There are 4 choices for the bread.Hence, the total number of different sandwiches that can be made is given by 3 (choices of meat) * 2 (choices of cheese) * 4 (choices of bread), which equals 24 different sandwiches.
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If an equation is an identity, then how many solutions does it have?
Answers
Identities have INFINITE solutions.
Hope I could help! :)
Answer:
Infinite solution
Step-by-step explanation:
We are given an equation is identity
We have to find that how many solutions equation have
Identity equation:Identity equation is that true equation in which no matter what value is substitute for variable .It is always true statement.
Suppose that we have an identity equation
[tex]x=x[/tex]
[tex]x-x=0[/tex]
[tex]0=0[/tex]
If this type of condition is obtained then we have infinite solutions.
So, if an equation is identity then the equation have infinite solutions.
Evaluate 4 · 1 + 6 · 16 + 0
a) 8
b) 0
c) 100
d) 185
Answers
4+96=100 when you follow PEMDAS
Answer:
c) 100
Step-by-step explanation:
We want to evaluate
[tex]4\times1+6\times 16+0[/tex]
We use the order of operations, PEDMAS to solve this problem.
The first step here is to multiply to get:
[tex]4+96+0[/tex]
We now add to obtain:
[tex]100[/tex]
The correct answer is C) 100
what is 0.007÷0.0435
Answers
Answer:0.16091954023
Step-by-step explanation:
Answer: Based on the calculator it’s...
0.16091954023
Step-by-step explanation:
Jeff has a cube train that is 22 inches long. he removes 8 inches of cubes from the train. How long is Jeff's cube train now?
Answers
Answer:
14 inches long
Step-by-step explanation:
Answer:
14 inches long
Step-by-step explanation:
When a warehouse opened, it had an inventory of 6,000 items. Every month, the inventory increases by 3,000 items.
Which graph has the most appropriate scales and units for this situation?
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x----> the time in months
y ----> the total inventory of the warehouse
we know that
The linear equation that represent this situation is equal to
[tex]y=3,000x+6,000[/tex]
using a graphing tool
see the attached figure
Answer: Guessing this is off the test.
The graph with
6
12
18
21
30 should be correct.
Step-by-step explanation:
How do you get to 5,652 using 12 + something?
Answers
"Something" is a variable. A variable is a number that we do not know. The variable will be x.
5,652 is the total; the total is 12 plus x.
5652 = 12 + x
Subtract 12 from each side
5652 - 12 = 12 + x - 12
5640 = x
change it around
x = 5640.
5640 is your answer
Sarah Saver writes a $40 check which is returned by her bank with additional charges. If the company she wrote the check to, Johnson Plumbing, also charges $25 for returned checks, which of the following represents the amount Sarah must have to balance her debts?
Answers
Answer: $65 dollars to johnson plumbing
Step-by-step explanation:
she would owe johnson plumbing 40 for the check plus the returned check fee of 25
$40 + $25 = $65 to johnson plumbing
plus whatever her bank charged ( i did not see that amount listed)
Final answer:
Sarah Saver must have enough money to cover the original $40 check, the $25 fee from Johnson Plumbing, and any additional bank charges. The expression representing the total amount needed is $40 + $25 + B, where B represents the bank's charges.
Explanation:
The student is asking about the total amount Sarah Saver must have to balance her debts after writing a $40 check that was returned with additional charges and a $25 fee for the returned check from the company. To find the total amount Sarah owes, you need to sum the amount of the check and the additional fees charged by her bank and Johnson Plumbing.
Add the original check amount: $40.
Add the fee charged by Johnson Plumbing for the returned check: $25.
Add any additional charges by her bank (the question doesn't specify an amount, so let's denote this amount as B).
The total amount Sarah needs to settle her debts will be $40 + $25 + B.
Therefore, without knowing the specific bank charges, we cannot provide a numerical answer, but the expression $40 + $25 + B represents the total amount Sarah needs to cover her debts, with B being the additional bank charges.
Which of the following is a feature of a credit card?
A: more flexibility
B: purchases are automatically deducted
C: requires a linked bank account
D: similar to cash
Answers
Credit cards offer more flexibility compared to other payment methods.
The correct answer is
A: more flexibility.
A: more flexibility - Credit cards provide users with the flexibility to make purchases without needing to have the full amount of money upfront. Instead, they can borrow funds up to a certain limit, known as the credit limit, and repay them later, often with interest. This flexibility allows cardholders to manage their cash flow more effectively and make purchases even when they may not have sufficient funds available in their bank account.
B: purchases are automatically deducted - This feature describes a debit card rather than a credit card. With a debit card, purchases are automatically deducted from the linked bank account at the time of the transaction, meaning that the cardholder needs to have sufficient funds available in their account to cover the purchase.
C: requires a linked bank account - While credit cards may require applicants to have a bank account for verification purposes, they do not necessarily need to be linked to a specific bank account for transactions to be processed. Credit cards operate on a revolving line of credit extended by the issuer, allowing cardholders to borrow money up to a certain limit regardless of their bank account balances.
D: similar to cash - Credit cards are not similar to cash. Unlike cash, which involves immediate payment and does not incur any interest charges, credit cards allow users to defer payment for purchases and may accrue interest if the balance is not paid in full by the due date. Additionally, credit cards offer various benefits such as rewards, cashback, and purchase protection, which are not typically associated with cash transactions.
Therefore the correct option is A: more flexibility
Complete question
Which of the following is a feature of a credit card?
A: more flexibility
B: purchases are automatically deducted
C: requires a linked bank account
D: similar to cash
Help me
Check it for me
Answers
Answer:
£270
Step-by-step explanation:
Works 7.5 hours per shift and there are 5 shifts in a week, hence
hours worked per week = 7.5 × 5 = 37.5
Pay per hour = £7.20, thus
Earnings for a week = 37.5 × 7.20 = £270
The equation of a circle is given below.
(x-20)^{2}+(y-0.05)^{2} = 81(x−20)
2
+(y−0.05)
2
=81left parenthesis, x, minus, 20, right parenthesis, start superscript, 2, end superscript, plus, left parenthesis, y, minus, 0, point, 05, right parenthesis, start superscript, 2, end superscript, equals, 81
What is its center?
((left parenthesis
,,comma
))right parenthesis
What is its radius?
If necessary, round your answer to two decimal places.
Answers
Answer:
Part 1) The center is the point [tex](20,0.05)[/tex]
Part 2) The radius is equal to [tex]r=9\ units[/tex]
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center of the circle
r is the radius of the circle
In this problem we have
[tex](x-20)^{2}+(y-0.05)^{2}=81[/tex]
[tex](x-20)^{2}+(y-0.05)^{2}=9^{2}[/tex]
so
[tex](h,k)=(20,0.05)[/tex]
[tex]r=9\ units[/tex]
multiply (a-2)(2a^2-5a-2)
Answers
Distribute sum groups
a(2a^2 - 5a - 2) - 2(2a^2 - 5a - 2)
Expand
2a^3 - 5a^2 - 2a - (4a^2 - 10a - 4)
Simplify brackets
2a^3 - 5a^2 - 2a - 4a^2 + 10a + 4
Collect like terms
2a^3 + (-5a^2 - 4a^2) + (- 2a + 10a) + 4
Simplify
= 2a^3 - 9a^2 + 8a + 4
Solve for the variable x in the following equation. x2 = 121 x =±
Answers
Answer:
x = ±11
Step-by-step explanation:
x^2 = 121
Take the square root of each side
sqrt(x^2) = sqrt(121)
x = ±11
PLEASE BRANLIESTTT
A pop star is coming for a live concert in your area. The ticket proceeds will benefit a nonprofit organization helping underprivileged children interested in music education. They would like to raise $1,500.
Stage-level seats are on sale for \$10 each and balcony-level seats are on sale for \$5 each. How many of each seat type would need to be sold to reach the goal of \$1,500?
You can set up an equation to help solve this problem. Translate the situation above by letting x represent the number of stage-level seats and by letting y represent the number of balcony-level seats.
Answers
Answer:
You would need to sell 100 of each
Step-by-step explanation:
$5 times 100 people equals $500.
$10 times 100 people equals $1,000.
$1,000+$500=1,500
I hope this helped!
Answer:
100 each
Step-by-step explanation:
I need help please??!!
Answers
Answer:
Step-by-step explanation: (5,-2)
Answer:
(5,-2)
Step-by-step explanation:
Wes lives in Colorado, which has a state income tax rate of 4.63%. He earns $895 weekly. How much state income tax is withheld from each of his paychecks?
Answers
All you must do to find out how much is with held from his paycheck is
solve this
x amount of dollars
÷ = 4.63%
$895
To solve, multiply $895 by 0.0463 (the equivalent of 4.63%)
You get: $41 . 43
That is how much is withheld from Wes' check
The amount of tax withheld from his paychecks is $41.43
What is percentage?Percentage is defined as a given part or amount in every hundred
Income tax rate given in the question = 4.63%
Weekly income given in the question = $895
Tax deducted = (4.63 / 100) * 895 = $41.43
Hence, $41.43 will be deducted from his paychecks every week.
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Find f(t – 3) for f(x) = 4x^2 – 8x + 4.
Question 11 options:
A. 4t^2 – 32t + 64
B. 64
C. 4t^2 – 32t – 64
D. 4t^2 + 32t + 64
Answers
Answer:
A. 4t² - 32t + 64Step-by-step explanation:
Instead of x put (t - 3) in the equation of the function f(x) = 4x² - 8x + 4:
f(t - 3) = 4(t - 3)² - 8(t - 3) + 4
use (a - b)² = a² - 2ab + b² and the distributive property a(b + c) = ab + ac
f(t - 3) = 4(t² - (2)(t)(3) + 3²) + (-8)(t) + (-8)(-3) + 4
f(t - 3) = 4(t² - 6t + 9) - 8t + 24 + 4
f(t - 3) = (4)(t²) + (4)(-6t) + (4)(9) - 8t + 28
f(t - 3) = 4t² - 24t + 36 - 8t + 28
f(t - 3) = 4t² + (-24t - 8t) + (36 + 28)
f(t - 3) = 4t² - 32t + 64
Someone plz help me with this
Answers
Answer:
Step-by-step explanation:
A rectangle is 17 inches long and 7 inches wide. Find its area,
112 square inches
0
59 aquare inches
©
119 square inches
24 square inches
Answers
119 square inches long
Answer:
119
Step-by-step explanation:
(✿◠‿◠)
Which option below correctly lists the domain, range, and a point on the graph of q(x)=x-49?
Domain = All real numbers greater than or equal to 49; Range = All non-negative numbers; (13, 218)
Domain = All real numbers greater than or equal to 49; Range = All non-negative numbers; (50, 1)
Domain = All non-negative numbers; Range = All real numbers greater than or equal to 49; (218, 13)
Domain = All non-negative numbers; Range = All real numbers greater than or equal to 49; (1, 50)
Answers
Answer:
Domain = All non-negative numbers; Range = All real numbers greater than or equal to 49; (1, 50)
Step-by-step explanation:
Answer:
Domain = all real number greater than or equal to 49
Range=all non- negative numbers
point=(50,1)
Step-by-step explanation:
The graph of q(x)=x-49
domain is the collection of numbers which assign for x in the function q(x)=x-49
therefore domain is the collection pf real number which is greater than or equal to 49 .
Range is the collection of numbers whic is obtained after aasignig value of x in the function q(x)=x-49
hence, range is the collection of non negative numbers which is obtained after putting the value of x in the given function q(x)=x-49
when we put x=50 in q(x)=x-49 then we obtain 1
hence, the poin is (50,1) on the given graph.
Original price: $32
Discount: ?
Sale price: $8
Answers
Answer: 75%
Step-by-step explanation:
32 dollars times 75% = 24
32 - 24 = $8
The Discount is of amount $32.
What is Discount?The discount is equivalent to the difference between the purchase price and the par value. A discount is a decrease or deduction in a product's cost price.
Discount = Original price – Sale price.
We have,
Original price: $32
Sale price: $8
So, Discount Price = Original price - Sale price
= 32 - 8
= $24
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Find the volume of the cone with the given dimensions: r = 9 m, h = 13 m
Answers
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=9\\ h=13 \end{cases}\implies V=\cfrac{\pi (9)^2(13)}{3} \\\\\\ V=351\pi \implies V\approx 1102.70[/tex]
Drag each label to the correct location on the figure. Not all labels will be used.
Find the missing angle measurements.
Answers
Answer:
The answers are on the image shown.
remember that all the angles of a triangle add up to 180
Step-by-step explanation:
hope this helps
Answer:
The measure of angle B is 54°. The measure of angle A is 51°. The measure of angle AFE is 47°.
Step-by-step explanation:
According to exterior angle theorem: It a triangle
Exterior angle = Sum of opposite interior angles
In triangle BED,
[tex]\angle AEF=\angle B+\angle D[/tex]
[tex]82=\angle B+28[/tex]
[tex]82-28=\angle B[/tex]
[tex]54=\angle B[/tex]
The measure of angle B is 54°.
In triangle ABC,
[tex]\angle ACD=\angle A+\angle B[/tex]
[tex]105=\angle A+54[/tex]
[tex]105-54=\angle A[/tex]
[tex]51=\angle A[/tex]
The measure of angle A is 51°.
In triangle AEF,
Using angle sum property,
[tex]\angle A+\angle E+\angle AFE=180[/tex]
[tex]51+82+\angle AFE=180[/tex]
[tex]133+\angle AFE=180[/tex]
[tex]\angle AFE=180-133[/tex]
[tex]\angle AFE=47[/tex]
Therefore the measure of angle AFE is 47°.