Step-by-step explanation:
In parallelogram RECT is a rectangle,
EC = x + y , RT = 2x - y, RE = 2x + y and TC = 3x - 3
To find, the values of the variable = ?
∵ The opposite sides are equal.
∴ RE = TC and RT = EC
2x + y = 3x - 3
⇒ x - y = 3 .......... (1)
Also,
2x - y = x + y
⇒ x - 2y = 0 .......... (2)
Subtracting (1) from (2), we get
∴ x - y - (x - 2y ) = 3 - 0
⇒ x - y - x + 2y = 3
⇒ y = 3
Put y = 3 in equation (1), we get
x - 3 = 3
⇒ x = 3 + 3 = 6
∴ x = 6 and y = 3
Thus, the values of the variable are 3 and 6.
James, Priya, and Siobhan work in a grocery store. James makes $7.00 per hour. Priya makes 40% more than James, and Siobhan makes 5% less than Priya. How much does Siobhan make per hour?
Siobhan makes $
per hour.
Answer:
The per hour income of Siobhan is $9.31 per hour.
Step-by-step explanation:
Working in a grocery store James makes $7.00 per hour. Priya's hourly income is 40% more than James, and Siobhan's hourly income is 5% less than Priya.
Therefore, using formula of percentage, the per hour income of Priya will be
[tex]7.00(1 + \frac{40}{100}) = 7 \times 1.4 = 9.8[/tex] dollars per hour.
Again, the per hour income of Siobhan is [tex]9.8(1 - \frac{5}{100}) = 9.8 \times 0.95 = 9.31[/tex] dollars per hour. (Answer)
John measures the angle of elevation to the top of a cliff to be 23 degrees. He walks 720 metres horizontally towards the cliff and finds the angle of elevation has doubled. What is the height of the cliff to the nearest metre ?
Answer:
The answer to this question is 1,495 ft
Step-by-step explanation:
Hope this helps
the total yearly cost to rent a trumpet is $114. The montly cost is constant with no initial fee
Answer:
$9.5 is the cost of 1 month.
Step-by-step explanation:
the total yearly cost = 12 months = $114
Cost of per month = 1 month = $114 / 12 = $9.5
hcf and lcm 112 and 46 using prime factorisation
Answer:
HCF of 112 and 46 = 2
Step-by-step explanation:
HCF/GCD/GCF all mean the same. They are the highest common factor of two or more numbers.
Step 1: First you extract all the 'Prime' factors of each number.
The ladders on the image show that you are dividing each number with the smallest prime number. You keep doing it till you reach 1 .
Step 2: Then you write the factors of each.
Step 3: You choose the common factors.
Step 4: Multiply the common factors (if any) and then you have your answer.
Answer:
HCF: 2
LCM: 2576
Step-by-step explanation:
Prime factorizations:
112 = 2×2×2×2×7
46 = 2×23
HCF: 2 (only common factor)
LCM: 2×2×2×2×7×23 = 2576
100 points gor correct answer Identify the base of a triangle in which h=(3x+15) ft and A=(15x+75) ft^2.
b = 30 ft
b = 5x ft
b = 10 ft
Answer:
b = 10
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here h = 3x + 15 and A = 15x + 75, thus
[tex]\frac{1}{2}[/tex] × b × (3x + 15) = 15x + 75
Multiply both sides by 2 to clear the fraction
b(3x + 15) = 30x + 150
Divide both sides by (3x + 15)
b = [tex]\frac{30x+150}{3x+15}[/tex] ← factor numerator and denominator
= [tex]\frac{30(x + 5)}{3(x+5)}[/tex] ← cancel the factor (x + 5) on numerator/denominator
= [tex]\frac{30}{3}[/tex]
= 10
Answer:
b = 10ft
Step-by-step explanation:
Area = ½ × base × height
15x + 75 = ½ × base × (3x + 15)
30x + 150 = base × (3x + 15)
10(3x + 15) = base × (3x + 15)
base = 10
what is the third quartile of this data set?
20, 21, 24, 25, 28, 29, 35, 37, 39, 42, 44
Answer:
39
Step-by-step explanation:
Answer:
39
Step-by-step explanation:
How much 5/16 are in 1 7/8
Answer:
convert 1 7/8 to an improper fraction.
1 times 8 is 8 plus 7 is 15.
1 7/8 = 15/8
15/8=30/16
30/16 divided by 5/16 is 6.
six 5/16 are in 1 7/8
if the ratio of the two numbers is7:8and theri sum 135 find the numbers
Answer:
63 and 72
Step-by-step explanation:
Sum the parts of the ratio, 7 + 8 = 15 parts
Divide the sum by 15 to find the value of one part of the ratio
135 ÷ 15 = 9 ← value of 1 part of the ratio, thus
7 parts = 7 × 9 = 63
8 parts = 8 × 9 = 72
The numbers are 63 and 72
Is -38,-68,-98,-128,... arithmetic
Answer:
yes
Step-by-step explanation
the common difference is -30
Final answer:
The sequence -38, -68, -98, -128,... is an arithmetic sequence because the common difference between consecutive terms is consistent, which is -30.
Explanation:
The student has asked whether the sequence -38, -68, -98, -128,... is arithmetic. To determine if a sequence is arithmetic, we need to check if the difference between any two consecutive terms (also known as the common difference) is the same.
Let's calculate the difference between the first two terms:
-68 - (-38) = -68 + 38 = -30
Now, let's calculate the difference between the second and the third terms:
-98 - (-68) = -98 + 68 = -30
Similarly, the difference between the third and the fourth terms is:
-128 - (-98) = -128 + 98 = -30
Since the common difference is the same (-30) for all consecutive terms mentioned, the sequence is indeed an arithmetic sequence.
The average yearly rainfall in Lakeview is 21.55 inches. What is the total amount of rainfall in inches in Lakeview in 5.75 years? A 1,239.125 B 12.39125 C 123.9125 D 27.3
Answer:
123.9125
Step-by-step explanation:
The total amount of rainfall in Lakeview in 5.75 years is approximately 123.9125 inches. The correct answer is option C.
Lakeview gets 21.55 inches of rain per year on average.
To find the total amount of rainfall in Lakeview in 5.75 years, we can multiply the average yearly rainfall by the number of years.
Average yearly rainfall: 21.55 inches
Total rainfall in 5.75 years: 21.55 inches/year * 5.75 years
Calculating the result:
= 21.55 x 5.75
≈ 123.9125
Therefore, the total amount of rainfall in Lakeview in 5.75 years is approximately 123.9125 inches.
The correct answer is option C.
Learn more about averages here:
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The bench below is a rectangular prism on top of two cubes. The total height of the bench is
8 inches. What is the volume of this bench?
- 25 inches
4 inches
4 inches
4 inches
424 cubic inches
464 cubic inches
228 cubic inches
528 cubic inches
WILL GIVE BRAINLIEST AND A THANKS
Question:
The image of the question is attached below.
Answer:
Volume of the bench = 528 cubic inches
Solution:
Side of the cube = 4 inch
Volume of a cube = side × side × side
= 4 inch × 4 inch × 4 inch
Volume of a cube = 64 cubic inches
Volume of 2 cubes = 2 × 64 cubic inches
Volume of 2 cubes = 128 cubic inches
Length of the prism = 25 inch
Breadth of the prism = 4 inch
Height of the prism = 8 – 4 = 4 inch
Volume of the rectangular prism = length × breadth × height
= 25 inch × 4 inch × 4 inch
Volume of the rectangular prism = 400 cubic inches
Volume of the bench = volume of 2 cube + volume of the rectangular prism
= 128 cubic inches + 400 cubic inches
Volume of the bench = 528 cubic inches
Hence volume of the bench is 528 cubic inches.
Answer:528
Step-by-step explanation:
2 Points
Kendra took out a loan for $750 at an 8.4% APR, compounded monthly, to buy
a stereo. If she will make monthly payments of $46.50 to pay off the loan,
which of these groups of values plugged into the TVM Solver of a graphing
calculator could be used to calculate the number of payments she will have
to make?
O
O
A. N=;1% = 0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12;
PMT:END
B. N=;1% = 0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12;
PMT:END
C. N=;1% = 8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12;
PMT:END
D. N=;1% = 8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12;
To calculate the number of payments for Kendra's loan using a TVM Solver, the correct setup includes an APR of 8.4% converted to a monthly rate of 0.7%, with matching payment and compounding frequencies, making Option A the accurate choice.
Explanation:When Kendra takes out a loan to buy a stereo, calculating the number of payments she will have to make involves understanding the terms used in Time Value of Money (TVM) calculations. The correct set of values must account for the annual percentage rate (APR) being compounded monthly, which requires converting the APR to a monthly rate, and ensuring the payment and compounding periods match.
For Kendra's loan:
APR is 8.4%, implying a monthly interest rate (I%) of 0.7% (8.4% divided by 12).The present value (PV) of the loan is -$750, indicating an outflow of cash.Her monthly payment (PMT) is $46.50, aimed at reducing the loan balance.The future value (FV) she aims for is $0, meaning she intends to fully repay the loan.P/Y (Payments per year) and C/Y (Compounding periods per year) both should match the monthly nature of the loan, hence should be 12.Given these conditions, the only option that correctly configures all elements for a TVM Solver is Option A:
N=; I% = 0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
This configuration accurately reflects the loan's terms, allowing the calculation of the number of payments (N) Kendra will need to make.
The correct answer is: D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END. Option A uses annual percentage rate (APR), while option D uses the periodic interest rate (monthly rate). Given that the interest rate is compounded monthly, it's more appropriate to use the periodic interest rate (option D).
To calculate the number of payments Kendra will have to make to pay off the loan, we can use the Time Value of Money (TVM) Solver feature of a graphing calculator. We need to set up the values correctly to solve for the number of payments (N).
Let's go through the options:
A. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
B. N=; I% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=; 1% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
Let's analyze each option:
A. This option has the correct annual interest rate (8.4%), correct present value (loan amount), correct payment amount, and correct compounding periods per year. Hence, it's a potential correct option.
B. This option has the interest rate incorrectly set as 0.7%. It should be 8.4%, not 0.7%. Hence, it's incorrect.
C. Similar to option B, this option has the interest rate incorrectly set as 0.7%. Hence, it's incorrect.
D. This option has the correct interest rate (8.4%), correct present value, correct payment amount, and correct compounding periods per year. Hence, it's a potential correct option.
So, options A and D are potential correct options. Both have the correct interest rate and payment amount. The difference lies in how the interest rate is represented: option A uses annual percentage rate (APR), while option D uses the periodic interest rate (monthly rate).
Given that the interest rate is compounded monthly, it's more appropriate to use the periodic interest rate (option D). Therefore, option D is the most suitable choice.
Complete Question:
Kendra took out a loan for $750 at an 8.4% APR, compounded monthly, to buy a stereo. If she will make monthly payments of $46.50 to pay off the loan, which of these groups of values plugged into the TVM Solver of a graphing to make?
A. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
B. N=; I% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=; 1% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
(3+4) + (4x+56) - (5x+3) = 45
Will Mark Brainliest
Answer:
X=21
Step-by-step explanation:
(7)+ (4x+56) - (5x+3)=45
7+4x+56-5x+3=45 add similar numbers
56+7+3=66
4x-5x= -x
-x+66=45
-66 -66
-x=-21
divide by - and x=21
find the mean of 37.5, 25.5, 30.5, 41.5, 52.5, 28.25, 30.5
Answer:
35.1785714286
Step-by-step explanation:
To find the mean you have to add all numbers. After you have added all numbers, you must divide the sum by the number of how many points you have.
Answer:
35.18
Step-by-step explanation:
Given the above scores .
Mean
= sum of scores/ number of scores
37.5 + 25.5 + 30.5 +41.5 +52.5 + 28.25 + 30.5 /7
246.25/7
35.18
What’s the answers please help
The product of 7/10 and another factor
is greater than 7/10. Which could be
the other factor?
A. 4/3
B. 5/9
C. 10/12
D. 7/7
Answer:a
Step-by-step explanation:Because four divide by three is one point and thirty three
Final answer:
To find a factor that when multiplied with 7/10 results in a greater number, the factor must be greater than 1. The only option greater than 1 is 4/3. Therefore, the correct answer is A. 4/3.
Explanation:
The question is asking to find a factor that when multiplied with 7/10, results in a product that is greater than 7/10. To have a resulting product greater than 7/10, the other factor must be greater than 1, as multiplying by a number greater than 1 increases the value of the original number. Let's evaluate the options:
A. 4/3 - This fraction is greater than 1 because 4 divided by 3 is approximately 1.33.B. 5/9 - This fraction is less than 1 because 5 divided by 9 is approximately 0.56.C. 10/12 - This fraction simplifies to 5/6, which is less than 1.D. 7/7 - This fraction simplifies to 1, which would mean the product is the same as the original number (7/10).Therefore, the correct answer is A. 4/3, since it is the only option greater than 1 and will result in a product greater than 7/10 when multiplied together.
You are selling concessions at a local swim meet. Hot dogs are being sold for $1.00 and soda is being sold for $0.50. At the end of the day you made $150. Let x represent the number of hotdogs sold and y represent the number of sodas sold. Write an equation that can be used to find the number of hotdogs and sodas sold at the swim meet
Answer:
1x + 0.5y = $150
Step-by-step explanation:
x = hot dog and each hot dog is sold for $1. We will multiply each hot dog sold by $1.
y = soda and each soda is sold for $0.50. We will multiply each soda sold by $0.50.
A single sheet of 20-pound bond paper is about a tenth of a millimeter thick. Each time you fold an ordinary sheet of paper in half, you double the thickness. What would be the thickness in kilometers if you were physically able to fold it 50 times? Note: For comparison, the distance from Earth to the Sun is about 149,600,000 kilometers. (Round your answer to the nearest kilometer.)
The paper would be 112589991 km thick if folded 50 times.
Step-by-step explanation:
Step 1; The sheet is [tex]\frac{1}{10}[/tex]mm thick which equals 0.1 mm. Every time it is folded it doubles in thickness. So if folded once it becomes 0.2 mm thick, if folded thrice it becomes 0.4mm thick.
Thickness if folded once = [tex]2^{1}[/tex] × 0.1 mm
thickness if folded twice = [tex]2^{2}[/tex]× 0.1 mm
Thickness if folded thrice = [tex]2^{3}[/tex] × 0.1 mm.
So if the paper is folded nth fold it would be [tex]2^{n}[/tex] × 0.1 mm thick.
Step 2; Using the above formula, if the paper is folded 50 times the thickness would be equal to [tex]2^{50}[/tex] × 0.1 mm = 112,589,990,684,262.4 mm.
1 km is equivalent to [tex]10^{6}[/tex]mm so 112,589,990,684,262.4 mm = 112,589,990.6842624 km which is rounded off to 112589991 km.
what is the slope of (-1,0) (0,-1)
Answer:
-1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-0)/(0-(-1))
m=-1/(0+1)
m=-1/1
m=-1
Rob cuts a 15-foot wire into 8 equal pieces.About how long is each piece in fractions
Answer:
1 7/8
Step-by-step explanation:
15/8= 15/1 * 1/8
15/8
Simplify that and you get 1 7/8.
Hope it helps!
Answer:
1 7/8
Step-by-step explanation:
Length of wire= 15foot
Cut into 8 equal pieces
Length of each piece = 15/8
1 7/8 foot each
which equation is equivalent to 3 = 87 ÷ h
Answer
3h=87 or h=87/3
Step-by-step explanation:
Answer:
Let's see...
Step-by-step explanation:
Equation formats:3h = 873 = 87/hh = 87/3I hope this helps!
- sincerelynini
(UPLOADED AGAIN) Please give the answer and how you got it
Answer:
B.
Step-by-step explanation:
B. <b and <A are complementary - remember that complementary angles means that the 2 angles will add up to 90 degrees, and in this case, they add up to 180 degrees.
I don't know how to do it?
Answer:
130°
Step-by-step explanation:
A hexagon's angels should be 720°.
so we need to substract the outer angels to find the interior angels.
180-75=105
180-38=142
180-42=138
180-65=115
180-90=90
then we add them up with x and equal it to 720
105+142+138+115+90+x=720
720-590=x
x=130
a=130
Answer:
a = 130°
Step-by-step explanation:
The interior angle of a polygon is calculated as
180° - exterior angle, thus
180° - 75° = 105°
180° - 42° = 138°
180° - 65° = 115°
180° - 90° = 90°
180° - 38° = 142°
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 6, thus
sum = 180° × 4 = 720°
Sum the interior angles and equate to 720
105 + 138 + 115 + 90 + 142 + a = 720, that is
590 + a = 720 ( subtract 590 from both sides )
a = 130
(5x2 - 13x + 3) +(x-3)
Answer:
5x^2 - 13x + 3 + x - 3
5x^2 - 12x
I’ve been stuck on this someone please help me solve this question
Answer:
part A) [tex]f=2.75p[/tex]
par B) [tex]38.5\ cups\ of\ flour[/tex]
Step-by-step explanation:
Part A)
Let
p ----> the number of pounds of cake
f ----> the number of cups of flour
we know that
A relationship between two variables, p, and f, represent a proportional variation if it can be expressed in the form [tex]k=\frac{f}{p}[/tex] or [tex]f=kp[/tex]
Find the value of k
For p=3, f=8.25 ----> [tex]k=\frac{8.25}{3}=2.75[/tex]
therefore
The linear equation is
[tex]f=2.75p[/tex]
Part B) we have
For p=14
substitute in the equation and solve for f
[tex]f=2.75(14)=38.5\ cups[/tex]
What is the solution of the equation 3x + x + 8 = 4?
a. -1 c. 2
b. 1 d. 4
Answer:
a. -1
Step-by-step explanation:
Simply the equation: 3x+x+8=4
1st step: 4x+8=4
2nd step: 4x=4-8
3rd step: x=[tex]\frac{-4}{4}[/tex]
4th step: x= -1
David is making a wall out of bricks. Each brick is 2/3 foot long. There are 20 bricks lined up end to end to make the wall. What is the total length of the wall in inches?
The total length of wall is 160 inches
Solution:
Given that,
[tex]Length\ of\ each\ brick = \frac{2}{3}\ foot[/tex]
1 feet = 12 inches
Therefore,
[tex]Length\ of\ each\ brick = \frac{2}{3} \times 12\ inches = 8\ inches[/tex]
There are 20 bricks lined up end to end to make the wall
To find: Total length of wall in inches
[tex]Total\ length\ of\ wall = \text{length of each brick } \times \text{ total number of bricks}[/tex]
Thus we get,
[tex]Total\ length\ of\ wall = 8 \times 20\\\\Total\ length\ of\ wall = 160\ inches[/tex]
Thus total length of wall is 160 inches
First: State the degree and tell which monomial (term) you determined to be the one as the greatest degree. Second: Classify each of the 2 polynomials. If it is NOT a polynomial, explain why you think it is not a polynomial. For example you may say: Polynomial # 4. has degree of 5 and is classified as a quintic polynomial of 4 terms. We covered this in class (see below). Explain in sentences how you determined degree and "name" or why it is NOT a polynomial. 1. 7x^4 + 5x^2 + x − 9 2. 7x^6 − 4x^3 + 1/x
Answer:
As the degree of the polynomial is said to be the highest degree of any of the terms. Therefore, the degree of [tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex] is 4The expression [tex]7x^6\:-\:4x^3\:+\:1/x[/tex] is not a polynomial as the term [tex]\frac{1}{x}[/tex] is not a polynomial as the the variable [tex]x[/tex] is in the denominator.Step-by-step explanation:
Considering the given expressions
[tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex][tex]7x^6\:-\:4x^3\:+\:1/x[/tex]As we know that
A polynomial is considered to be the sum of monomials where each monomial is said to be a term.The degree of a polynomial is the considered to be the greatest degree of its terms.A polynomial is normally written with the term with the highest exponent of the variable first and afterwards decreasing from left to right.The first term of a polynomial is said to be the leading coefficient.The degree of the polynomial is said to be the highest degree of any of the terms.Now, considering the expression
[tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex]Here, the first term (monomial) i.e. [tex]7x^4\:[/tex] has the highest exponent of the variable. Here, the highest exponent is 4.
As the degree of the polynomial is said to be the highest degree of any of the terms.
Therefore, the degree of [tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex] is 4.
The polynomial [tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex] can also be called a quadrinomial as it has four terms.
Also considering the second expression
[tex]7x^6\:-\:4x^3\:+\:1/x[/tex]This expression is not a polynomial.
For an expression to be a polynomial, it must must have to carry
no square roots of variables. For example, [tex]\sqrt{y}[/tex] is not a polynomial as the variable y is inside a radical. no fractional or negative powers on the variables, For example, [tex]5x^{-3}[/tex] is not a polynomial as the x variable has a negative exponent.and no variables in the denominators of any fractions. For example, [tex]\frac{1}{x}[/tex] is not a polynomial as the the variable x is in the denominator.Therefore, the expression [tex]7x^6\:-\:4x^3\:+\:1/x[/tex] is not a polynomial as the term [tex]\frac{1}{x}[/tex] is not a polynomial as the the variable x is in the denominator.
Keywords: degree, monomial, polynomial, expression
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2> n +0.8 I don’t understand
Answer:
1.2 > n
Step-by-step explanation:
Step 1: Solve for n
2 > n + 0.8
2 - 0.8 > n + 0.8 - 0.8
1.2 > n
Answer: 1.2 > n
Is 2,509 less than 2,590
Answer:
Yes
Step-by-step explanation:
Answer:
Yes, 2,509 is less than 2,590
Step-by-step explanation:
When comparing 2509 to 2590, you first look at the first number on the left. In our case it is 2, then you look at the second number, which is 5, then you look at the third number which is 0 and 9, since the 9 is bigger that makes 2590 bigger than 2509, or 2509 less than 2590
Hope this helps ;)