To translate the point P(x,y) , a units left and b units down, use P'(x−a,y−b) .
Write an equation Y=|x| 10 units down?y=|x-10|-3
Inside, is opposite. So therefore, to move it right 10 units, you subtract ten. However, outside of the absolute value, it is normal, so to move it down 3 units, you subtract 3.The number –45.3 is 45.3 units away from zero and the number 10 is 10 units away from zero. Therefore, the absolute value of any number is really a positive number (or zero).As we know that absolute value means remove the negative sign from the number and make it positive. So we get the absolute value of -10 as 10. So we get the absolute value of 10 as 10. Hence absolute value of -10 and 10 is 10 and 10 respectivelyTo know more about units visit:
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Complete the square for the expression. Then factor the trinomial.
x2 - 6x
Expression:
Factored form:
Expression: x² - 6x + 9
Factored form: (x - 3)²
Using the concept of factorization.
What is factorization?The breaking or breakdown of an entity (such as an integer, a matrix, or even a polynomial) into such a combination of some other unit, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.
Similarly to this, factoring is a very useful technique in algebra that is utilized at all levels. Additionally, to, of course, simplify complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.
Factor the expression, put each factor equal to 0, and then solve each equation to solve a quadratic equation by factoring. To do this, rearrange all terms on one side of the equation such the other side equals 0.
Given that,
x² - 6x
Now, to find the value of c = (b/2)²
divide the coefficient of x by 2.
So, divide 6 by 2 we get: ( -1.3)²
Next, multiply -1 by 3: (-3)²
Now, raise -3 to the power of 2, we get: 9
So, the expression becomes: x² - 6x + 9
Factorized form: (x - 3) (x -3)
or we can write (x - 3)²
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Math- algebra 1 - please help
For both pizzas A and B to cost the same, there must be 5 toppings. Equations can be categorized as identities or conditional equations.
what is equation ?The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two equilateral triangles and an equivalent sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear model is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables.
given
number of toppings be x
number of toppings for pizza A = $10 + x*$1.5
number of toppings for pizza B = $12.5 + x*$1
10 +1.5x = 12.5 + x
10 -12.5 = x- 1.5x
-2.5 = - 0.5x
x = 5
For both pizzas A and B to cost the same, there must be 5 toppings.
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Suki is trying to solve the equation 62.75 + x = 92.
Determine whether Suki could use each statement below to reason and solve the equation.
Choose Yes or No for each statement.
A) Suki can add 62.75 to both sides of the equation.
[ Select ]
B) Suki asks, "What number can be added to 62.75 to get 92?"
[ Select ]
C) Suki thinks, "x is the difference between 92 and 62.75."
[ Select ]
D) Suki can divide 92 by x to get a value equal to 62.75.
[ Select ]
E) Suki knows that 62.75 + 0.25 = 63 and 63 + 29 = 92, so x must be 29.25.
[ Select ]
Answer:
A) Technically he/she can, but they shouldn't really.
B) Yes
C) Yes
D) Yes he/she can but is not necessary to solve the equation
E) Yes
2 alien spaceships are traveling toward each other from space stations that are 7100 km apart at speed of 110000 km
It would take 116.18 seconds for the space stations that are 7100 km apart at speed of 110000 km to meet
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
The speed of an object is the ratio of the total distance travelled to the total time taken. It is given by:
Speed = distance / time
Distance = Speed * time
The spaceships are moving at 110000 km/h
The distance covered by each in x hours is:
Distance = 110000 * x = 110000x
Since they are 7100 km apart, hence:
110000x + 110000x = 7100
220000x = 7100
x = 0.03227 hours = 116.18 seconds
It would take 116.18 seconds for the spaceships to meet.
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State how many negative real roots there may be for the function.
f(x) = x³ +7x² - 5x + 19
4 or 2 or o negative real roots
2 or o negative real roots
3 or 1 negative real roots
1 negative real root
There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
The function f(x) = x³ +7x² - 5x + 19 is a polynomial function of degree 3, which means it has 3 roots (also known as zeros or solutions) that could be real or complex.
To determine the number of negative real roots, we can use the fact that a cubic function has at least one real root.
x³ +7x² - 5x + 19
the first coefficient is positive, the second is positive, the third is negative, and the fourth is positive.
There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"
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if june 13 was on monday what day will it be on june 13 math
Answer:
Monday??????
SteP-by-step explanation:
Question 5(Multiple Choice Worth 2 points)
(Sample Spaces LC)
A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. List the sample space when choosing one marble.
A s= (1, 2, 3, 4, 5, 6
B s=(purple, pink, red, blue, green, orange, yellow}
C s=(g. r, b. y. o, p)
D s= (green, blue, yellow, orange, purple, red)
The sample space when choosing one marble will be B s=(purple, pink, red, blue, green, orange, yellow}
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample space may contain a variety of outcomes.
A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. The sample space when choosing one marble will be all the colors. The correct option is B.
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16. The side length of a square ABCD is 18 inches. What is the side length of the square formed by joining the
midpoints of the sides of ABCD, to
the nearest tenth?
Therefore , the solution of the given problem of square comes out to be the ABCD square is 18 inches
what is the side of length of square ABCD?The side length of a square ABCD is 18 inches Each side of square ABCD is 18 inches The midpoints of ABCD are joined to form a square MNOP The figure is attached below
Here,
We need to find the side length of square MNOP
AMN form a Right angle triangle
We know AM =9 and AN= 9
To find MN , use Pythagoreans theorem
MN2=AM2+AN2
MN2=9square+9 square
MN2=162
Take square root on both sides
MN=9 root 2
so the side of the square MNOP is 9 square root 2 inches
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profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, what were profits last year.
The profits last year were $2041.66
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here, profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, then let the profit last year be x then we have 2.4x=4900
x=4900/2.4
x=2041.66
Hence, The profits last year were $2041.66
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Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).
Considering the definition of a line, the linear function that represents the total cost when x tickets are ordered is c= 20.5x + 5.50.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Total cost in this caseIn this case, you know:
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. This is, as service fee is a single fee applied to the total, no matter the number of tickets purchased, the value of "b" is 5.50.The total cost in dollars for ordering 5 tickets is $108.00Being Total cost= set price per ticket× amount of tickets + 5.50, then:
108=set price per ticket× 5 + 5.50
108 - 5.50= set price per ticket× 5
102.5= set price per ticket× 5
102.5÷5= set price per ticket
20.5= set price per ticket
Finally, the total cost is Total cost= 20.5× amount of tickets + 5.50.
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Answer:
Its letter A
Step-by-step explanation:
A boat is purchased for $51,000 and has a resale value of $42,000 after a useful life of 6 years. Using a book value depreciation chart, calculate the number of years until the book value of the boat is $48,000.
The number of years until the book value of the boat is $ 48, 000, can be found to be 2 years
How to find the number of years ?To find the number of years till the book value of the boat is $ 48, 000, you first need to find the depreciation rate per year by the formula :
= ( Purchase price of boat - Resale value ) / Useful life
= ( 51, 000 - 42, 000 ) / 6
= 9, 000 / 6 years
= $ 1, 500 per year
In the first year, the value of the boat would depreciate to:
= 51, 000 - 1, 500
= $ 49, 500
In the second year, the value would depreciate to:
= 49, 500 - 1, 500
= $ 48, 000
It therefore takes 2 years for the book value to be $ 48, 000.
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Can someone help me with this? I'm stressed out and its urgent.
Gross pay is $360, Health insurance is $50.40, Pension deduction is $21.60, Total deductions is $173.85 and net pay is $186.15.
What is gross Earnings?Gross pay or gross earnings is the amount of money an employer earn before all the tax and other deductions and benefits.
Employee works for 40 hours at a rate of $9.00 per hour.
Gross pay = 40 × 9 = $360
Health insurance = 14% of gross earnings
= 14% × 360
= 0.14 × 360
= $50.40
Pension deduction = 6% of gross earnings
= 0.06 × 360
= $21.60
Total deductions = $55.00 + $21.80 + $25.05 + $50.40 + $21.60
= $173.85
Net pay = Gross earnings - Total deductions
= $360 - $173.85
= $186.15
Hence the amount of gross pay is $360, and net pay is $186.15.
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Terrence made a scale drawing of a boarding school. The scale he used was
7 centimeters: 3 meters. If the actual length of a building at the school is 300 meters, how
on is the building in the drawing?
The building in the drawing is 700 centimeters or 7 meters.
Define the unitary method.The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What are ratios and proportions?An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Given 3 meters on real is equal to 7 centimeters on drawing
i.e. 3 meters=7 centimeters
or, 1 meter = 7/3 centimeters
We need to find reading for 300 meters so,
or, 300 meters=7/3*300 centimeters
=700 centimeters or 7 meters
Therefore the building in the drawing is 700 centimeters or 7 meters.
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Select the correct answer from each drop-down menu.
A town's population was 10,000 in 2005. The population has increased by 10% per year since 2005.
This situation represents
The rate of growth or decay, r, is equal to ____. So each year the number of residents in the town is ___ times the number in the previous year.
There were around 14,641 residents in the town ___ years after 2005.
The rate of growth or decay, r, is equal to 0.10.
What is population?Population in math refers to the set of all items of interest in a given context. It is the target or focus of a statistical study, and the objects described by the population's characteristics are known as population elements. It is important to define the population in detail before analyzing data and drawing conclusions. Examples of populations can include all students at a school, all people living in a particular country, or all people who bought a particular product.
So each year the number of residents in the town is 1.10 times the number in the previous year.
There were around 14,641 residents in the town 14 years after 2005.
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Bethany and Samuel are buying a new house. They have $25,000 saved for a down payment and know that they can afford a monthly payment of $1,500 or less. They also know that the best interest rate they can get is 5.1% annually and they want to sign a 30-year mortgage.
1. This equation is used to find the monthly payment, m, given the monthly interest rate, i, the principal, P, and the number of interest periods, n, in months:
Using the equation, find the largest possible principal P for their situation. In other words, what is the largest amount of money they can borrow? (Hint: To answer the question, you must rearrange the equation.)
The largest amount of money they can borrow is $$276.268.65
How to calculate the largest amount?The main formula used in this problem is the Present Value of an annuity Formula:
P = R[1-(1+i)⁻ⁿ]/i
Where;
P: present value (the mortgage value)R: periodic paymentt: time (in years)r: annual interest ratem: number of compounding per yeari=r/m (rate per period)n=mt the total number of paymentsThe maximal monthly payment that Bethany and Samuel can afford is $1,500.
The best interest rate is %5.1 annually, and they want to sign a 30-year mortgage.
This implies that
R=1,500
t=30
r=%5.1 = 5.1 /100 = 0.051
m=12, because they make the payments monthly
i=r/m=0.051/12=0.00425
n=mt = 12*30=360
That is,
i) they will make 360 monthly payments,
ii) the largest amount of money they can borrow can be found using the formula:
P = R[1-(1+i)⁻ⁿ]/i
Substituting the known values:
P = 1500[1-(1+0.00425)⁻³⁶⁰]/0.00425
Therefore, $276.268.65 is the largest possible principal for the situation
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4 less than three sevenths as an algebraic expression
simplify the expression 14+5(x+3) - 7x
Answer:
- 2x +29
Step-by-step explanation:
Open up the parenthesis, then simplify
14 + 5x + 15 - 7x
5x - 7x + 14 + 15
-2x + 29
[tex]14+5(x+3) - 7x[/tex]
Distribute:
[tex]14+(5)(x)+(5)(3)-7x[/tex]
[tex]14+5x+15-7x[/tex]
Combine Like Terms:
[tex](5x-7x)+(14+15)[/tex]
[tex]\fbox{-2x + 29}[/tex]
Jim made 45 treats for his birthday. He gave 5 away tohis family before taking the rest to school. What percent did he give away to his family?
Percentage of chocolates Jim given to his family is 11.11%.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Jim made 45 treats for his birthday. He gave 5 away to his family before taking the rest to school.
Now, percentage of chocolates Jim given to his family
= 5/45 ×100
= 0.1111 ×100
= 11.11%
Therefore, percentage of chocolates Jim given to his family is 11.11%.
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Ifn(r'ns')+ n(r'ns)=3 n(r n s) = 4 & n(s'nr)= 7 find n(u).
Answer:
14
Step-by-step explanation:
You want to know the size of the universal set if ...
n(r'∩s') +n(r'∩s) = 3n(r∩s) = 4n(s'∩r) = 7UniverseThe given sets are mutually exclusive and exhaustive, so the sum of their sizes is the size of the universal set:
n(u) = 3 + 4 + 7
n(u) = 14
__
Additional comment
(r'∩s') ∪ (r'∩s) = r'∩(s' ∪ s) = r' . . . . n(r') = 3
(r∩s) ∪ (r∩s') = r∩(s ∪ s') = r . . . . . . n(r) = 4 +7 = 11
Then r' ∪ r = u, the universal set. . . . . n(u) = 3 +11 = 14
What is the vertext of the following parabola: x^2 - y + 6x + 8 = 0
Answer: y=(x+3)2−17
Step-by-step explanation:
Write three ratios that are equivalent to 75% and three
ratios that are equivalent to 100%.
The three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4 and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.
What is ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
First we have to write the equivalent ratios for 75%.
Since, 75% can be written as,
75/100
Simplifying this, 15/20
Again simplifying this, 3/4
Hence, the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4.
Now to write the equivalent ratios for 100%.
Since, 100% can be written as,
100/100
Simplifying this, 20/20
Again simplifying this, 4/4
Hence, the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.
Therefore, the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4 and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.
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Locating Fractions on a Number Line
A B
Hot
-2
-1
Intro
C
D
+++++
0 1 2
Use the drop-down menus to label the points on the
number line.
Point A is at
Point B is at
Point C is at
Point D is at
<
Done
On solving the provided question we cans ay that - order when writing it on the number line: = -1.25, -0.75, 0.25, 1.5, 2
what is number line?A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.
The numbers on the number line must be
[tex]6/3 = 2\\-3/4 = -0.75\\1.5 = 1.5\\0.25 = 0.25\\-5.4 = -1.25\\[/tex]
In ascending order, t
[tex]-1.25 = -5/4\\-0.75 = -3/4\\0.25\\1.5\\2 = 6/3[/tex]
order when writing it on the number line:
-1.25, -0.75, 0.25, 1.5, 2
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You're fitting a pipe into an existing fitting. The fitting allows a diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005", What's the maximum allowable pipe diameter? a. 0.496, b.0.501, c. 0.499, d. 0.541
The maximum allowable pipe diameter is given as : 0.501. Option B
How to solve for the diameterFrom the question the interior diameter of the pipe is said to be 0.49
The pipe is said to have the thickness of 0.005 inches.
The exterior diameter of the pipe would be solved as 0.49 + 2 * 0.005
= 0.49 + 0.01
= 0.5
The questions said the variance in the diameter of this pipe is 0.001
Then the maximum allowable pipe diameter would be solved as: 0.001 + 0.5 = 0.501
The diameter of the pipe that is allowable is 0.501
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Write the two equations for each problem and explain please, thank you
1. Victoria has a total of 65 dimes and quarters worth $10.70. How many of each type of coin does she have?
2. Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the
weekend he worked for a total of 14 hours and made a total of $192. How many hours did he work for each job?
Answer:
1) Let D be the number of dimes and Q be the number of quarters. We can set up the following system of equations to represent the given information:
D + Q = 65
0.1D + 0.25Q = 10.70
The first equation represents the total number of coins Victoria has, and the second equation represents the total value of those coins in dollars. Solving this system of equations will give us the number of dimes and quarters Victoria has.
2) Let M be the number of hours Max spends mowing lawns and T be the number of hours he spends tutoring. We can set up the following system of equations to represent the given information:
M + T = 14
12M + 15T = 192
The first equation represents the total number of hours Max worked over the weekend, and the second equation represents the total amount of money he made during that time. Solving this system of equations will give us the number of hours Max spent on each job.
I just need help with question A
Suppose your cousin missed class and asks you, “Why do we plug in 0 for x to find y-intercepts and 0 for y to find x-intercepts? That doesn’t make sense to me.” Explain to your cousin WHY this process works. Use the line
5x+4y=14 as an example.
A) A description in words why this works
The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.
How to find the x and y intercepts?The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.
Now, we are given the equation of the line as;
5x + 4y = 14
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Rewriting the equation of the line in slope intercept form is;
y = -⁵/₄x + ⁷/₂
Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.
Similarly, the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.
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Find the trigonometric ratios for both acute angles in fraction and decimal form to the nearest ten-thousandths when appropriate.
The trigonometric functions are sin A = 12/13, sin B = 5/13, cos A = 5/13, cos B = 12/13, tan A = 12/5, and tan B = 5/12 as fractions.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric functions are given in the question
Apply the sine ratio on the given right triangle
⇒ sin(θ) = Perpendicular/hypotenuse
sin A = BC/AB
sin A = 12/13
sin B = AC/AB
sin B = 5/13
Apply the cosine ratio on the given right triangle
⇒ cos(θ) = Base/hypotenuse
cos A = AC/AB
cos A = 5/13
cos B = BC/AB
cos B = 12/13
Apply the tangent ratio on the given right triangle
⇒ sin(θ) = Perpendicular/Base
tan A = BC/AC
tan A = 12/5
tan B = AC/BC
tan B = 5/12
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A two story building measures 21 ft from the ground. A scale model shows the building to be 3 inches taller. How many inches would an 84 foot building be in the model?
Answer:
The scale of the model is (21 ft / 3 in) = 7 ft / 1 in. So an 84 foot building would be (84 ft / 7 ft) * 1 in = 12 inches tall in the model.
Step-by-step explanation:
hope it helps
Answer:
588 inches
Step-by-step explanation:
First, find the scale factor of the model by dividing the height of the real building by the height of the model: 21 ft / 3 inches = 21/3 = 7
7 inches/ft
Then, multiply the scale factor by the height of the 84 foot building to find the height of the model: 7 inches/ft * 84 ft = 7*84 = 588
588 inches
(4 x 5) + ( 4 x 2) = 4 x (5 + n)
Answer:
Step-by-step explanation:
1. (4x5) is 20
2. (4x 2) is 8
3. 20 plus 8 is 28
4. 28= 4x (5+n)
5. isolate n by dividing 4 on both sides= 28/4= 4+n
6. subtract 4 on both sides to get 7-4=n
7. n=3
Any help would be awesome
Answer: 72 square units
Step-by-step explanation: It is 72 square units because if you count the sides p and q you get 9 and the same with sides q and r you get 8 and if you multiply them together you get 72.
write each percent as a fraction and
as a decimal.
7/100%
I NEED THIS BY 2:30PM
7/100% can be written as a fraction as 7/100, and as a decimal as 0.07.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{7}{100}\%}[/tex]
[tex]\mathsf{= \dfrac{7}{100} \div 100}[/tex]
[tex]\mathsf{= \dfrac{7}{100}\times \dfrac{1}{100}}[/tex]
[tex]\mathsf{= \dfrac{7(1)}{100(100)}}[/tex]
[tex]\mathsf{= \dfrac{7}{1,000}}[/tex]
[tex]\mathsf{= 0.0007}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{7}{1,000} \ \& \ 0.0007}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]