Answer:
P = 84
Step-by-step explanation:
Area = length* width or A = lw
We know that the length is 5 times its width which can also mean
[tex]l = 5*w[/tex] or [tex]l=5w[/tex]
Use the formula for area and replace [tex]l[/tex] with [tex]5w[/tex] and the total area with 245
[tex]A = lw\\245=5w(w)[/tex]
Multiply:
[tex]245=5w^{2}[/tex]
Divide by 5
[tex]49=w^2[/tex]
Square root of [tex]w^2[/tex]
[tex]\sqrt{49}=\sqrt{w^2}[/tex]
Simplify
[tex]7=w[/tex]
Now that we know w = 7 we can input this into the Perimeter formula
(P = 2l +2w)
P = 2(5*7)+2(7) // Note: Remember [tex]l[/tex] = 5*w and w = 7
P = 84
There is also a formula for this type of problem, but this explanation is for when you forget. Hope that explains things :)
There are 7 highway routes from City A to City B, 8 highway routes from City B to City C, and 10 highway routes from City
C to City D. How many different highway routes are there if you want to travel to City A, B, C, and D in that order?
highway routes from City A to City D.
There are how many highway routes from city a to city d
The number of highway routes from A to D is 560
Number of highway routes from A to B = 7 highways
Number of highways routes from B to C = 8 highways
Number of highways routes from C to D = 10 highways
Number of routes from A to D = Number of highway routes from A to B × Number of highways routes from B to C × Number of highways routes from C to D
Here we have to use multiplication
Substitute the values in the equation
Number of routes from A to D = 7 × 8 × 10
= 560 highways
Hence, the number of highway routes from A to D is 560
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Find the equation for a polynomial f(x) that satisfies
▪ Degree 5
▪ Root of multiplicity 2 at x =
= -4
▪ Root of multiplicity 1 at x = -1
■ Root of multiplicity 2 at x = -2
▪y-intercept of (0, 128)
The polynomial function that has the degree of 5 is written as f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128
Polynomial function:
The equations formed with variables, exponents and coefficients are known as the polynomial equations. And it can have different exponents, where the higher one is called the degree of the equation.
Given,
Here we have the following things,
Degree = 5
Root of multiplicity 2 is x = -4
Root of multiplicity 1 at x = -1
Root of multiplicity 2 at x = -2
y-intercept of (0, 128)
Here we need to find the polynomial equation of the function.
According to the given roots of multiplicity, we have the factors of the polynomials are,
=> (x + 4)² (x + 1) (x + 2)²
So, the general form of the polynomial function can be written as,
=> f(x) = A (x + 4)² (x + 1) (x + 2)²
In order to find the 5 degree polynomial function, we have to calculate the value of A.
To Find the value of A, we have to apply the y - intercept point on the equation then we get,
=> 128 = A (0 + 4)² (0 + 1) (0 + 2)²
=> 128 = A (4)² (1) (2)²
=> 128 = A (16 x 1 x 4)
=> 128 = 64A
=> A = 2
Now, the polynomial function is written as,
=> f(x) = 2 (x + 4)² (x + 1) (x + 2)²
When we expand this one then we get,
=> f(x) =2 [x⁵ + 13x⁴ + 64x³ + 148x² + 160x + 64]
Therefore, the resulting polynomial function is,
=> f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128
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X-y=3 determine the x and y intercepts of linear equations
Answer:
y-intercept (0,-3)
x-intercept (3,0)
Step-by-step explanation:
Let x = 0
-y =3
y = -3
(0,-3)
Let y = 0
x = 3
(3,0)
the product of two and a number, divided by five 5
The expression of the given statement is [tex]\frac{2x}{5}[/tex] .
What is algebraic expression?
When terms are combined using operations like addition, subtraction, multiplication, division, etc., the result is an algebraic expression (or variable expression). Let's look at the formula 5x + 7 as an illustration. Consequently, we can state that 5x + 7 is an illustration of an algebraic statement. Here are some more examples: 5x + 4y + 10
Here the given product of two and a number. Lets us take number as x. Then ,
=> 2*x= 2x
Product of two and a number divided by 5. Then,
=> [tex]\frac{2x}{5}[/tex]
Hence the algebraic expression of the given statement is [tex]\frac{2x}{5}[/tex] .
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if ally worked 20.56 hours , and makes $10 an hour . how much is pay check? show work.
Answer:
$205.6
Step-by-step explanation:
20.56hours × $10/hour = $205.6
cannot decide which of two washing machines to buy. The selling price of each is $550. The first is marked down by 40%. The second is marked down by 30% with an additional 10% off. Find the sale price of each washing machine. Use pencil and paper. Explain why should buy the first washing machine rather than the second if the machines are the same except for the selling price.
The selling price of the two washing machies are
first washing machine is $330second washing machine is $346.5I will buy the first because it has a lower selling price
How to determine the best washing machine to buyThe question is a percentage problem
The first washing machine has a mark down by 40%
= 40 percent
= 40 / 100
= 0.4
marked down factor = 1 - 0.4 = 0.6
selling price of the first machine = 550 * 0.6 = 330
the second washing machine has mark down of 30%
30% = 0.3
marked down factor = 1 - 0.3 = 0.7
selling price of the second washing machine at first mark down
= 550 * 0.7 = 385
marked down again
10% = 0.1
the factor here is = 1 - 0.1 = 0.9
selling price of the second washing machine at second mark down
= 385 * 0.9 = 346.5
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Solve for x. Round to the nearest tenth, if necessary.
Answer:
46.9
Step-by-step explanation:
sin54=x/58
58sin54=46.922
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume days in a year.
P = 7000$, r = 7.5%,15 t = months
The simple interest owned for the use of the money is $2625.
What is Simple Interest?
Simple interest is a quick and simple way to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest. A loan is a sum of money that someone borrows from a bank or other financial institution to cover expenses. Home loans, auto loans, student loans, and personal loans are a few instances of loans.
In the given question we have:
Principal amount = 7000$,
Rate of interest r = 7.5%,
Time t = 15 months;
So, applying the formula to calculate simple Interest:
S.I = [tex]\frac{PRT}{100}[/tex]
S.I = [tex]\frac{7000 \times 7.5 \times 15}{ 12 \times 100}[/tex]
S. I = $2625;
Hence, The Simple Interest owed for the use of the money. is $ 2625.
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A. x² +5
B. +5X
C.X + 5
D.5X
The expression that represents the quotient of given model is x + 5
The correct answer is an option (C)
In this question, we have been given a synthetic division of x^2 + 5x and x
We need to find the quotient.
x + 1 + 1 + 1 + 1 + 1
x) x^2 x x x x x
- x^2
0 x
- x
0 x
- x
0 x
- x
0 x
- x
0 x
- x
0
Therefore, the expression that represents the quotient of given model is x + 5
The correct answer is an option (C)
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Lisa wants to buy a hat that costs 114 Argentine Pesos.She has $25.Does she have enough money to buy the hat?
Answer:
150
Step-by-step explanation:
I had this on one of my quizzes, hope this helps :D
Please I need help I don’t understand
For give expression Ben's work is correct.
In this question, Ben and Jerry both simplified the expression √24x⁵y³
where x > 0, y > 0
We need to determine which student is correct.
First we simplify given expression.
√24x⁵y³
= √(2)(2)(2)(3)(x)(x)(x)(x)(x)(y)(y)(y)
= √(2²)(2)(3)(x²)(x²)(x)(y²)(y)
= √(2²) * √(2) * √(3) * √(x²) * √(x²) * √(x) * √(y²) * √(y) ...(seperate the radical symbol)
= 2 * √(2) * √(3) * x * x * √(x) * y * √(y) ...........exponent rule
= 2x²y√(2)(3)(x)(y) ........(combine terms with same powers)
= 2x²y √6xy
So, Ben's work is correct.
We observe that by rule of exponents, the fourth step in Jerry's work is incorrect.
Therefore, Ben's work is correct.
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QUESTION 1 1 POINT
Jason bought new shoes priced at $75 and sales tax is 6%. What is the total cost of the shoes after-tax?
Provide your answer below:
The total cost of the shoe after tax is $79.50
Calculating total cost after sales taxFrom the question, we are to determine the total cost of the shoes after tax.
From the given information,
Jason bought new shoes priced at $75
and
The sales tax is 6%
The total cost of the shoe = Price of the shoe + Sales tax
Sales tax = 6% of $75
Sales tax = 0.06 × $75
Sales tax = $4.50
Thus,
Total cost of the shoe = $75 + $4.50
Total cost of the shoe = $79.50
Hence, the total cost is $79.50
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What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
x^2+32+116=12x
Answer:
Below
Step-by-step explanation:
x^2 + 32 + 116 = 12x 1st intermediate step: put everything on one side
x^2 -12x + 148 = 0 2nd intermediate step : re-arrange with constant on R
x^2 -12x = -148 3 rd intermediate step : take 1/2 of the 'x' coefficient
square it and add to both sides
x^2 -12x + 36 = -148 + 36 4th intermediate step : simplify
(x-6)^2 = -112
Area of a Circle Ji-Min needs to replace a circular window having a diameter of 5 ft. She decides to use double strength glass costing $ 3 per square foot. Find the total cost for the glass.
Ji-Min will spend a total of $235.62 to fence or cover the area of the circular window.
Area of a CircleWhat is the area of the a circle?
The area of circle is equal to pi times square of its radius, i.e. πr². To find the area of circle we have to know the radius or diameter of the circle.
Let's find the area of the circle first;
radius = diameter / 2
radius = 5 / 2
radius = 2.5ft
The area of the circle is;
A = πr²
A = π * 5²
A = 25π
A = 78.54ft²
For every square foot, the glass cost $3, this implies that 3 * 78.54 will be the total cost to cover the window.
cost = 3 * 78.54 = $235.62
She will spend $235.62 to fence the window
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If she decides to use double strength glass costing $ 3 per square foot. the total cost for the glass is $58.88.
How to find the total cost?Given data:
Diameter = 5ft
Glass costing = $3 per square foot
Hence,
Let the radius be 5/2 feet
Area = π × (5/2)²
Area = 25π /4 ft²
So,
Total cost = ( π × 25 /4 × $3)
Total cost = $58.875
Total cost = $58.88
Therefore $58.88 is the total cost.
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Which fractions have a LCD of 84?
100 Point's 50 points each have a blessed day
The fractions have a LCD of 84 is option C, 2/21,1/4,1/3.
Given:
3/14,1/42,1/6
= 3/14 + 1/42 + 1/6
= 9+42+7 / 42
The LCD is 42 not 84.
2/84,1/16,1/42
= 6+21+8 / 336
The LCD is 336 not 84
2/21,1/4,1/3
= 8+21+28 / 84
The LCD is 84
2/3,1/6,1/7
= 28+7+6 / 42
The LCD is 42 not 84
Therefore the fractions have a LCD of 84 is option C, 2/21,1/4,1/3.
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Answer:
[tex]\textsf{C)} \quad \dfrac{2}{21}, \dfrac{1}{4}, \dfrac{1}{3}[/tex]
Step-by-step explanation:
The least common denominator (LCD) is the smallest number that is exactly divisible by each denominator of a set of fractions.
To find the LCD of a set of fractions, reduce the fractions to their smallest equivalent, list the multiples of each denominator, then locate the smallest common number.
[tex]\textsf{A)} \quad \dfrac{3}{14}, \dfrac{1}{42}, \dfrac{1}{6}[/tex]
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, ...
Multiples of 42: 42, 84, 126, 168, 210, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Therefore, the LCD is 42.
[tex]\textsf{B)} \quad \dfrac{2}{84}, \dfrac{1}{16}, \dfrac{1}{42}=\dfrac{1}{42}, \dfrac{1}{16}, \dfrac{1}{42}[/tex]
Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, ... , 336, ...
Therefore, the LCD is 336.
[tex]\textsf{C)} \quad \dfrac{2}{21}, \dfrac{1}{4}, \dfrac{1}{3}[/tex]
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ... , 84, 88, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ... , 84, 87, ...
Therefore, the LCD is 84.
[tex]\textsf{D)} \quad \dfrac{2}{3}, \dfrac{1}{6}, \dfrac{1}{7}[/tex]
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ... , 42, 45, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, ...
Therefore, the LCD is 42.
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −43, ordered pair: (0,−25)
Answer:
[tex] \huge{ \bold{y = - 43x - 25}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is given by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = - 43
In order to find c we substitute the point (0,−25) into the equation y = mx + c
That's
[tex] - 25 = - 43(0) + c \\ - 25 = 0 + c \\ c = - 25[/tex]
We now substitute m and c into the equation
We have the final answer as
[tex] \bold{y = - 43x - 25}[/tex]
Hope this helps you
Write the equvalent fractions using 35 as a common denominater
The equvalent fractions of 5/7 using 35 as a common denominator is 25/35.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, it should be noted that the fraction given is 5/7.
The equivalent fraction will be:
= 5/7 × 5/5
= 25/35
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Complete question
Write the equvalent fraction of 2/5 using 35 as a common denominater
How many cubic inches are in an aluminum can with a 2 3/5 diameter and 5 1/4 in height?
According to the volume of cylinder formula, an aluminum can with a 2 3/5 diameter and 5 1/4 in height are in 27.86 cubic inches.
Volume of Cylinder
The formula to calculate the volume of the cylinder is
Volume of a cylinder = πr²h cubic units.
where
r refers the radius
h refers the height.
Given,
Here we have an aluminum can with a 2 3/5 diameter and 5 1/4 in height and now we have to find the volume in cubic inches.
While we looking into the given question, we know the following values,
Diameter = 2 3/5
When we simplify it, then we get the value of diameter as
d = 13/5 or 2.6
Similarly, the value of height is rewritten as,
h = 5.25
So, based on the formula of volume of cylinder,
We get the value as,
=> V = π x (2.6/2)² x 5.25
Apply the value of π as 3.14, then we get,
=> V = 3.14 x (1.3)² x 5.25
=> V = 16.485 x 1.69
Therefore, the volume in cubic inches is 27.86 cubic inches.
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find the slope of (-4,4) (0,0)
The slope for the following question is = 4.
What is slope?Slope is used to describe the steepness of a line. The definition of slope is the rise of a line over the run of a line, or the change in the vertical direction (y) over the change in the horizontal direction (x). When one thinks of skiing down a hill or climbing up a mountain, the angle at which they are descending or ascending is the slope. Sometimes the slope can be fairly flat or very steep depending on what it is.The slope of an object indicates how steep it is. Slope knowledge is crucial for daily decision-making. For instance, understanding a roof's slope enables builders to determine whether specific construction materials are required for shingling projects. Since there must be sufficient grade for water to pass through the tile, slope is crucial in agriculture when tiling a field. Slope can also be calculated using elevation points on a GIS, a type of digital map that can highlight areas with sharp elevation changes in the ground.acc to our question-
the two y's are 0 and 4 so its 0-4then the two x's are0 and one so its 0-10-4/0-1 is -4/-1 which when simplified the negatives cancel out leaving you with a positive 4hence the value of slope=4
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Simplify: (x^5) ^5?
Answer:
x^25
Step-by-step explanation:
The simplified expression is x²⁵.
Given is an expression (x⁵)⁵, we need to simplify the expression.
To simplify the expression (x⁵)⁵, we need to apply the exponentiation rules.
The exponent outside the parentheses should be distributed to each term inside the parentheses.
In this case, the exponent outside is 5, and the term inside the parentheses is x⁵.
To distribute the exponent, we multiply the exponents together.
Applying the rule, we get:
(x⁵)⁵ = x⁵⁽⁵⁾ = x²⁵
Therefore, the simplified expression is x²⁵.
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Please help I was sick and missed out on class.Thank you
Answer:
slope = (1/3)
Step-by-step explanation:
(-8, 2), (-11, 3)
(x₁, y₁) (x₂, y₂)
m = slope
y₂ - y₁ 3 - 2 1 1
m = ------------ = -------------- = ----------- = -------
x₂ - x₁ -11 - (-8) -11 + 8 3
I hope this helps!
What are the zeros of the function f(x)=x²-x² - 2?
O +3, ti
O +2, ti
O +√2 ti
O+√3, ti
The zeros of the function f(x) = x⁴− x² − 2 are ±√2 or x = ±i option third positive or negative square root of 2, ±i is correct.
What is a complex number?
It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a function:
f(x) = x⁴− x² − 2
Assume u = x²
f(x) = u² - u - 2
(u + 1)(u - 2)
(x² + 1)(x² - 2)
x² = -1
x = √1
x² = 2
x = √2
x = ±√2 or x² = -1 ⇒ x = ±i
Thus, the zeros of the function f(x) = x⁴− x² − 2 are ±√2 or x = ±i option third positive or negative square root of 2, ±i is correct.
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sorry i put the wrong pic in here my question i do need help so im putting in more point
Answer:
A. (10x^2) / (5x + 4y)
B. (8xy) / (4y + 5x)
Step-by-step explanation:
A. Factor the numerator and denominator, then cancel out like terms
(10x^2(2a + 3b)) / (2a(5x + 4y) + 3b(5x + 4y))
(10x^2(2a + 3b)) / ((2a + 3b)(5x + 4y))
(10x^2) / (5x + 4y)
B. Factor the numerator and denominator, then cancel out like terms.
(8xy(3p - 4q)) / (3p(5x + 4y) - 4q(4y + 5x))
(8xy(3p - 4q)) / ((3p - 4q)(4y + 5x))
(8xy) / (4y + 5x)
if I have 10 pancakes and I give 5 to jimmy how many pancakes do I have
Answer: 5 is the ancer
Step-by-step explanation:!
Help find intercept and the slope of the line?
slope= -3/2, y-intercept=8
y=mx+b m is the slope while b is the y-inteecept
Question 8
Angel Garcia deposited his $750 federal income tax refund check into his savings account.
The account pays 5% and he made no other deposits or withdrawals. How much is in the
account after 3 months?
O $937.50
$787.50
O $759.38
1 pt
O $752.12
The amount his account will have after 3 months be $ 759.38.
Given, Angel Garcia deposited his $750 federal income tax refund check into his savings account. The account pays 5% and he made no other deposits or withdrawals.
we have to find the amount in the account after 3 months,
So, the amount he made is,
Amount = 750(1 + 5/100)^0.25
Amount = 759.38
So, the amount his account will have after 3 months be $ 759.38.
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77 is 0.7% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 77, slightly less
77, slightly greater than 77, or a lot greater than 77? Explain.
77 is 0.7% of 11000
this number is a lot greater than 77.
Let 77 is 0.7% of m
0.7 percent of m = 77
(0.7/100) * m = 77
m = 77 * (100/0.7)
m = 11000
Therefore, 77 is 0.7% of 11000
this number is a lot greater than 77.
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1. Mark is going to a carnival. He is anxiously looking forward to riding as many rides as possible. In order to enter the park each person is charged a $3 admission fee. The tickets for the rides are $0.75 each.
Match the following number of rides (x) and the total cost with admission (y) for Mark's trip to the carnival for 0 to 4 rides.
1 --> $3.00
2 --> $4.50
4 --> $3.75
3 --> $6.00
0 --> $5. 25
2. Write an equation that describes the relationship between the number of rides (x) and the total cost (y).
3. Use your equation from question #2, to determine the cost of 100 tickets.
4. If Mark's grandmother gave him $50, how many rides could be ridden? (no decimals)
Answer: hi
Step-by-step explanation:
this is it
can someone help with this
Answer:
z=38
Step-by-step explanation:
Using the fact that angles on a straight line add to 180°, the interior angles of the triangle are 86°, (180-3z)°, and (180-4z)°.
Angles in a triangle add to 180°, so:
[tex]86+180-3z+180-4z=180 \\ \\ 86-3z+180-4z=0 \\ \\ 266-7z=0 \\ \\ 7z=266 \\ \\ z=38[/tex]
What’s the answer by chance
The sales tax rate of the cocktail table is 0.055
What is sales tax ?A sales tax is a consumption tax imposed by the government on the sale of goods and services
The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:
Sales tax = list price * sales tax rate
Therefore,
sale tax rate = sales tax / list price
sales tax = $13.75
list price = $250
sale tax rate = 13.75 / 250
sales tax rate = 0.055
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