The 220 cm (2.2 m) perimeter of the tiles and the 9.6 meter side length of the square floor gives equations with the following solutions;
(a) The dimensions of the tiles are;
Width = 0.3 meters
Length = 0.8 meters
(b) 384 tiles are needed
(c) The fitting cost of the tiles is Kshs 51,000
What is an equation?An equation is a mathematical statement that consists of two expressions connected with an equals sign
Shape of the floor = Square
Shape of the tiles = Rectangular
Perimeter of the tiles = 220 cm = 2.2 m
The number of tiles in each row = 20 + The number of tiles in each column
Length of the floor = 9.6 m
(a) Let w represent the width of the tiles, the length l is found using the equation;
[tex]l = \dfrac{2.2 - 2\cdot x}{2} = 1.1 - x[/tex]
Let n represent the number of tiles in each row, which gives;
The number of tiles in each column = 20 + n
(20+n)·x = n·(1.1 - x)
Which gives;
[tex]x = \dfrac{1.1\cdot n}{2\cdot n+20}[/tex]
The side length of the square floor, s = 9.6
(20+n)·x = n·(1.1 - x) = 9.6
Which gives;
[tex]n\cdot \left(1.1 - \dfrac{1.1\cdot n}{2\cdot n+20}\right) = 9.6[/tex]
Which gives;
0.55·n² - 1.4·n -96 = 0
n = 12 or n ≈ -14.5
The number tiles in each roe, n = 20
Which gives; n·(1.1 - x) = 9.6
20 × (1.1 - x) = 9.6
x = 0.3
The width of each tile, x = 0.3 m
The length of each tiles = 1.1 m - 0.3 m = 0.8 m
(b) The number of tiles in each row, n = 20
The number of tiles in each column = n + 20, which gives;
Number of tiles in each column = 12 + 20 = 32
The number of tiles needed = 12 × 32 = 384
(c) The cost of a dozen tiles = Kshs 1,500
The labour cost = Kshs 3,000
Number of dozens of tiles = 384 ÷ 12 = 32
The cost of the tiles C = Kshs 1500 × 32 = Kshs 48000
The total cost = Kshs 48,000 + Kshs 3,000 = Kshs 51,000
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Please HELP 7 B(x)*C(x)
Answer: dont be rude
Step-by-step explanation:
Write one quadratic equation that forms a graph through the points (−4,2) and (2,2) and has a
maximum value at the vertex.
Explain please
Quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.
Given,
Quadratic equation passes through the points (-4,2) and (2,2)
(x₁, y₁) =(-4,2)
(x₂ ,y₂) = (2,2)
Here,
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
⇒(y - 2) / (x + 4) = (2 - 2) / (2 + 4)
⇒ (y-2) / (x+4) =0
⇒y -2 =0
⇒y = 2
Quadratic equation formed from the given points (-4,2) and (2,2) is y =2.
Which represents the horizontal line and does not have any vertex.
Therefore, quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.
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Find the values of x and y
X= 20 & Y= 70 in right-angled triangle .
What is right angle triangle?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The longest of the three sides, known as the hypotenuse, is the third side.2X + 140 = 180
2X = 40°
X = 20°
X + Y = 90°
Y = 70°
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Use PMT=
nearest dollar.
-nt
to determine the regular payment amount, rounded to the
The price of a home is $210,000. The bank requires a 15% down payment and one
point at the time of closing. The cost of the home is financed with a 30-year fixed-
rate mortgage at 6.5%.
a. Find the required down payment.
b. Find the amount of the mortgage.
c. How much must be paid for the one point at closing?
d. Find the total cost of interest over 30 years, to the nearest dollar.
B)
OA) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $2100
d. total cost of interest over 30 years: $196,167
a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $1785
d. total cost of interest ver 30 years: $227,667
Oc) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $2100
d. total cost of interest over 30 years: $227,667
OD) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $1785
d. total cost of interest over 30 years: $406,167
Answer:
B
a. down payment: $31,500b. amount of mortgage: $178,500c. points paid at closing: $1785d. total cost of interest over 30 years: $227,667Step-by-step explanation:
You want to know the 15% down payment, the mortgage amount, the value of 1 point, and the total interest cost for a 6.5% 30 year loan on a $210,000 home.
Look at the Answer ChoicesThe answer choices all have the down payment as $31,500 and the loan value as $178,500. A "point" is one percent of the loan value (not the home value), so ...
1 point = 0.01 × $178,500 = $1785 . . . . . . eliminates choices A and C
The difference between choices B and D is in the value of the interest paid. Your experience with 30-year loans in this interest rate range tells you that the interest paid is between 1 and 2 times the loan value. That is, the chice $227,667 is more likely correct than the choice $406,167.
Comparing these two numbers, we see they differ by 178,500, which is the value of the loan. That is, we can guess that 406,167 is the total amount repaid, not just the interest.
Answer choice B is the only one that makes sense.
Work the problemIf you like, you can work the problem.
down payment = 15% × $210,000 = $31,500
loan amount = $210,000 -31,500 = $178,500
one point = 0.01 × $178,500 = $1785
The monthly payment is found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
A = 178500(0.065/12)/(1 -(1 +0.065/12)^(-12·30)) ≈ 1128.24
The monthly payment amount is about $1128.
So, the total repaid is 360 payments of $1128.24, or $406,167.
The interest paid is this amount less the principal:
interest paid = $406,167 -178,500 = $227,667
Let's play a game where I flip a coin. If the coin lands on Heads you win a $1, if it lands on Tails you lose a $1. I flip a coin 8 times and here is the results Tails Tails Tails Tails Tails Tails Tails Tails So you lost 8 times in a row and thus lose $8.00.
Part1: Would you like to continue this game. Why or why not.
Part 2: Calculate the P-value of getting 8 tails in a row assuming the coin is fair. Is it a big number or small?
Part 3: Based on the P-value you got above what would you conclude about your initial hypothesis that the coin is fair.
Using the z-distribution to test the hypothesis, it is found that:
1. You would not like to continue the game, as in each trial you are losing.
2. The p-value is of 0.0023.
3. The low p-value means that there is enough evidence to conclude that the coin is biased.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the coin is biased, that is, the proportion of heads is of 0.5, hence:
[tex]H_0: p = 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the coin is biased, that is, it has a proportion of heads lower than 0.5, hence:
[tex]H_1: p_1 < 0.5[/tex]
What is the test statistic?The test statistic is given by the equation as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the variables are listed and explained as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters are given as follows:
[tex]\overline{p} = \frac{0}{8} = 0, n = 8, p = 0.5[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0 - 0.5}{\sqrt{\frac{0.5(0.5)}{8}}}[/tex]
z = -2.83.
P-value and conclusionUsing a z-distribution calculator, and considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -2.83, the p-value is of 0.0023.
Since this p-value is less than the standard significance level of 0.05, it means that there is enough evidence to conclude that the coin is biased towards tails.
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The graph of the absolute value parent function, f(x) = |x), is stretched
horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
OA. g(x)= x+3|
OB. g(x) = 31x1
C. g(x) = 13x1
OD. g(x)= |||
Answer:
OB. g(x) = 31x1
C. g(x) = 13x1
Step-by-step explanation:
The ratio of teachers to students is 1 to 26. Find an equivalent ratio
Answer:
2:52
Step-by-step explanation:
Multiply by 2
A university reported that its enrollment increased from 11,937 students in 2005-2006 to 12,256 students in 2006-2007.
a. What is the ratio of the number of students in 2006-2007 to the number of students in 2005-2006?
b. From your result in part a, determine the growth factor. Write it in decimal form to the nearest thousandth.
c. By what percent did the enrollment increase?
a.
The ratio of the number of students in 2006-2007 to the number of students in 2005-2006 is = 12,256 : 11,937
b.
Growth factor = (12256-11937)/11937
= 0.02672.
c.
Increase in percent = 100* (12256 - 11937)/11937
= 100 * 0.02672
= 2.672%
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Three middle schools in a city had enrollments of 296,315 and 278 what was the total middle school enrollment
The total middle school enrollment is 889 for the given city.
According to the question,
We have the following information:
Three middle schools in a city had enrollments of 296,315 and 278.
Now, the total middle school enrollment can be easily found by adding the enrollments in three middle schools of the city.
So, we have the following expression:
Total middle school enrollment = 296+315+278
(We already know that the digits are first added from the right hand side and then we move to the left hand side.)
Total middle school enrollment = 889
Hence, the total middle school enrollment is 889 for the given city.
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Hello, I need help with this math exercise.
John buys 7 apples and 4 pears for $7.25. At the same prices, Hayley buys 5 apples and 9 pears for $10.40. What is the price of one pear? Use Cramer’s Rule to solve.
The price of one pear is $0.85
How to use Cramer’s Rule to solve the price of one pear?
Cramer's rule is one of the useful methods used for solving a system of equations. In this method, the values of the variables in the system are to be calculated using the determinants of matrices. Thus, Cramer's rule is also known as the determinant method.
Given that: John buys 7 apples and 4 pears for $7.25 and at the same prices, Hayley buys 5 apples and 9 pears for $10.40
We will use this given information to form equations in matrices form. Let a and p represent the prices of one apple and one pear respectively.
The equation is:
7a + 4p = 7.25
5a + 9p = 10.40
The matrix formed is:
[tex]C=\left[\begin {array}{ccc}7&4\\5&9\end{array}\right][/tex] , [tex]b=\left[\begin {array}{ccc}7.25\\10.40\end{array}\right][/tex]
Find the determinants,
D = (7 x 9) - (5 x 4) = 43
Da = (7.25 x 9) - (10.40 x 4) = 23.65
Dp = (7 x 10.40) - (5 x 7.25) = 36.55
a = Da/D = 23.65/43 = 0.55
p = Dp/D = 36.55/43 = 0.85
Since p = 0.85. Therefore, the price of one pear is $0.85
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The table shows a proportional relationship between x and y.
x 3.6 12.2 2.1
y 14.4 48.8 8.4
Which of the following correctly describes the graph of the relationship?
OA line that goes through (3.6, 14.4) and (48.8, 12.2)
OA line that goes through (14.4, 3.6) and (12.2, 48.8)
OA line that goes through (0, 0) and (3.6, 14.4)
OA line that goes through (0, 0) and (14.4, 3.6)
The correct answer which define proportional relationship between x and y is OA line that goes through (0, 0) and (3.6, 14.4)
What does proportionality mean to you?
Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
As we can see that in the given question [tex]\frac{x}{y} =\frac{1}{4}[/tex]
and there is only one option which fits this ratio is third one
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Answer:
to simplify the dude aboves' answer its C
Step-by-step explanation:
A line that goes through (0, 0) and (3.6, 14.4)
help with this pls! Lol
Answer:
3y+3y-12
Step-by-step explanation:
we can add the coefficients of y to make 6y-12
And that is equivalent
Hopes this helps please mark brainliest
Movies at the rental store are $3.75 each. Snacks and drinks are $1.89 each. Round each amount to the nearest dollar to estimate the cost to rent 3 movies and buy popcorn, a soda, and a candy bar.
Answer: List all of the solutions.
3.75
=
1.89
=
dollar
=
3
=
Step-by-step explanation:
Identify potential outliers, if any, for the given data. The normal annual precipitation (in inches) is given below for 21 different U.S. cities.
32.4 29.4 34.6 65.3 22.1 31.8 16.6 28.2 36.2 59.4 24.3 47.2 45.6 9.2 27.1 18.9 13.6 31.4 24.2 12.3 35.4
A. none
B. 65.3
C. 9.2; 12.3
D. 9.2; 59.4; 65.3
E. 59.4; 65.3
The potential outliers, given the normal annual precipitation in the different U.S. cities are E. 59.4; 65.3.
What are outliers?Outliers in a data distribution are values or data points that are far from the other points in the data. These can be statistically significant when they distort measures of central tendency such as mean.
In this case, the potential outliers in the normal annual precipitation 59.4 and 65.3 because they are far from the highest annual precipitation (before them) of 47.2 inches. 9.2 inches is quite low but it is close to 12.3 inches and 13.6 inches and so is not an outlier.
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4. The distance needed to stop a car varies directly as the square of its speed. It
requires 120 m to stop a car at 70 km/h. What distance is required to stop a car
at 80 km/h?
Answer:
156.7 m (nearest tenth)
Step-by-step explanation:
Define the variables:
Let d = distance in meters.Let v = speed in kilometers per hour.If the distance needed to stop a car varies directly as the square of its speed:
[tex]\boxed{d \propto v^2 \implies d=kv^2}[/tex]
where k is the constant of proportionality.
Given:
d = 120 mv = 70 km/hTo find the constant of proportionality, k, substitute the given values into the equation:
[tex]\begin{aligned}\implies 120&=k(70)^2\\k&=\dfrac{120}{70^2}\\k&=\dfrac{6}{245}\end{aligned}[/tex]
Substitute the found value of k back into the formula to create an equation for the given relationship:
[tex]\implies d=\dfrac{6v^2}{245}[/tex]
To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:
[tex]\implies d=\dfrac{6(80)^2}{245}[/tex]
[tex]\implies d=\dfrac{6\cdot 6400}{245}[/tex]
[tex]\implies d=\dfrac{7680}{49}[/tex]
[tex]\implies d=156.73469...\; \sf m[/tex]
[tex]\implies d=156.7\; \sf m\; (nearest \;tenth)[/tex]
Therefore, the distance required to stop a car at 80 km/h is:
156.7 m (2 d.p.).If a cone has a volume of 100 cubic inches, what is the length of the radius? Round your answer to the nearest tenth.
The radius of the cone is 10√(3/πh) inches when the volume of the cone is 100 cubic inches.
According to the question,
We have the following information:
Volume of cone = 100 cubic inches
We know that the following formula is used to find the volume of cone:
Volume of cone = π[tex]r^{2}h/3[/tex] where r is the radius of the cone and h is the height of the cone
π[tex]r^{2}h/3[/tex] = 100
Now, using the cross multiplication method:
π[tex]r^{2}[/tex]h = 100*3
Dividing both sides of the equation by πh:
[tex]r^{2}[/tex] = 300/πh
r = 10√(3/πh) inches
We can also solve it further by putting the value of π.
Hence, the radius of the cone is 10√(3/πh) inches when the volume of the cone is 100 cubic inches.
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Question 14 (2 points)
Complete the general form of the equation of a sinusoidal function having an
amplitude of 8, a period of 27, and a phase shift to the left 4 units.
The complete general form of the equation of the given sinusoidal function is y = 8sin[(27/2π)*(x - 4)] + c.
The general form of an equation for a sinusoidal function is presented below.
y = a×sin[b*(x - h)] + c
The variable "a" denotes the amplitude of the equation. The variable "T" represents the time period of the equation, and T = 2π/b. The variable "h" denotes the phase shift of the equation. The variable "c" denotes the vertical shift of the equation. The amplitude, period, and phase shift are 8, 27, and 4 units to the left, respectively. The general form of the equation of a sinusoidal function can be written as given below.
y = a×sin[b*(x - h)] + c
y = 8sin[(27/2π)*(x - 4)] + c
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A pool can be filled by one pipe in 3 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill
the pool?
Answer:
i think it 8h
Step-by-step explanation:
What is the equation of the line that passes through the point (8, 2) and has a slope of -3/4
The equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.
In the given question we have to find the equation of line that passes through the point (8, 2) and has a slope of -3/4.
The given points are (8, 2).
The slope(m) = -3/4
The standard equation of slope intercept form is
y-y(1) = m(x-x(1))
From the question; x(1) = 8 and y(1) = 2.
Putting the value
y-2 = -3/4(x-8)
Add 2 on the both side, we get
y = -3/4(x-8)+2
Hence, the equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.
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High-fiber foods have at least 5 g of fiber per serving. Let f be the
Number of grams of fiber per serving of high-fiber food. Which inequality
Describes this situation?
A.) f > 5
B.) f < 5
C.) f ≤ 5
D.) f≥ 5
A.
B.
C.
D.
The inequality that describes this situation is f ≥ 5
How to calculate the inequality ?
Use the steps below to solve an inequality:
Step 1: Subtract all fractions by multiplying each term by the sum of all fractions' least common denominators.
Step 2: Simplify the inequality by merging like terms on each side.
Step 3: Add or subtract amounts to get the unknown and the numbers on either side.
As per the question it tells the High- fiber should have at least 5g of fiber per serving
f = Number of grams of fiber per serving of high-fiber food
∴ f ≥ 5
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Young Frankenstein has two brothers, Pugsley and Gomez. The sum of their ages is 34. Frankenstein is older than Pugsley, but Pugsley is not the youngest. Gomez is 8 years younger then Frankenstein and Pugsley and Gomez’s ages differ by 5 years. How old are the three brothers?
The age of the three brothers, based on the relationship between the ages of Frankenstein, Pugsley, Gomez, is:
Frankenstein - 15 years Pugsley - 12 years Gomez - 7 yearsHow to find the ages?Frankenstein is older than Pugsley and so is not the youngest. Pugsley is not the youngest according to the question so Gomez must be the youngest.
Assuming Gomez's age is x, the relationship between their ages is:
Gomez age + Pugsley age + Frankenstein age = 34
x + x + 5 + x + 8 = 34
3x + 13 = 34
x = (34 - 13) / 3
x = 7 years
Pugsley's age is:
= x + 5
= 7 + 5
= 12 years
Frankenstein's age is:
= x + 8
= 7 + 8
= 15 years
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2. Write each of the following as a power function in the form f(x) = kx^p.
f(x) = -3/2x^5
The simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .
What is power function ?
A function having a single term that is the sum of a real number, a coefficient, and a variable raised to a fixed real number is called a power function. Consider functions for area or volume as examples (a number that multiplies a variable raised to an exponent is known as a coefficient). A power function is a function where y = x n, where n is any real constant number. In reality, many of our parent functions, including linear and quadratic functions, are power functions.
Here ,
a) f(x) = [tex]\frac{-3}{2x^5}[/tex]
To write in the form of f(x)= [tex]kx^p[/tex]
=> f(x) = [tex]\frac{-3}{2}* \frac{1}{x^5}[/tex]
=> f(x) = [tex]\frac{-3}{2} x^-5[/tex]
b) g(x) = 5[tex]\sqrt[3]{x}[/tex]
Here we know that [tex]\sqrt[n]{a} = a^\frac{1}{n}[/tex] , then
=>g(x)=5[tex]x^\frac{1}{3}[/tex]
Hence the simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .
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Find the amount of money you will have after 20 years if you invest $25,000 at a rate of 12% if interest is compounded a. Quarterly b. Continuously
The compound interest is quaterly then answer is $266,022.2639 and when it is in continuously then answer is $275,579.4095
Quarterly compounding is what?
Compounding quarterly is the term used to describe the amount of interest that is earned on a quarterly basis on a savings account or investment where the interest is also reinvested. As most banks offer interest income on the deposits, which compounds quarterly, this information is useful in computing the fixed deposit income. It can also be used to figure out any revenue from money market instruments or other financial products that pay quarterly income.
What Does Constant Compounding Mean?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. While this is not attainable in practice, the concept of continually compounded interest is crucial in finance. Given that most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.
a) A = P(1 + r/n)nt
P = $25000
r = 12% = 0.12
t = 20 years
n = 4
A = 25000(1 + 0.12/4)(4)(20)
A = $266,022.2639 (Answer)
b) A = Pert
P = $25000
r = 12% = 0.12
t = 20 years
A = 25000e(0.12)(20)
A = $275,579.4095 (Answer)
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I need help on this question and it is the last one please help!
Both function in item I is decreasing, and the function in item II is increasing.
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
What is domain?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
What is range?
The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response.
1) As shown in the I that the function is in 3rd quadrant so thats why it decreases.
2)As show in II figure if ;
x1 = -1 ,y1 = -1
x2 = 0 , y2 =2
x3 = 1, y3 = 5
from the above observation it is clear that ;
x1<x2, y1<y2, x2<x3, y2<y3
So, the II item is increases (monotone increasing)
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Solve for j.
–3(j − 8) + –6 = –9
Answer:
j=3
Step-by-step explanation:
distribute
-3(j-8)+-6=-9
-3j+24-6=9
-3j+18=9
-3j=-9
j=3
Hopes this helps pleae mark brainliest
Answer:
j = 9
Step-by-step explanation:
Let's solve for the value of j,
→ -3(j − 8) + (-6) = -9
→ -3j + 24 - 6 = -9
→ -3j + 18 = -9
→ -3j = -9 - 18
→ j = (-27)/(-3)
→ j = 27/3
→ [ j = 9 ]
Hence, the value of j is 9.
If it takes 1 printer 14 minutes to print a batch of leaflets, how long would it
take 2 printers to print the same number of leaflets?
2 printers takes 7 minutes to print the same number of leaflets.
From the question, we have
1 printers takes 14 minutes to print the leaflets.
2 printers takes = 14/2 = 7 minutes to print the leaflets.
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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Answer: 7
Step-by-step explanation: because 1 printer takes 14 mins but if u have 2 u half the 14 it gives you 7 so it will take 2 printers 7 mins to print the same amount of leaflets. hope this helps.
Which expression is equivalent to 1 2/9 x 6/16
Answer:
0.45833333333 or 11/23
Step-by-step explanation:
1 2/9*6/16 is simply 11/23, cross multiply and simplify
If you roll a die 75 times. How many 1's should you expect to roll?
what digitis in the ten thousands place of 8,675,309
Find point C on the x-axis so that AC + BC is a minimum.
A(-8,4), B(-1,3)
The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).
A(x₁,y₁) = (-8,4)
B(x₂,y₂) = (-1,3)
C(x, y ) = (x ,0)
equation of a line is given as:
y - y₁ = (y₂ - y₁)/ (x₂ - y₁) (x - x₁)
y - 4 = (3 - 4)/(-1 + 8)(x + 8)
y - 4 = -1/7(x + 8)
7(y - 4) = -1(x + 8)
7y - 28 = -x + 8
x + 7y - 36 = 0
when y = 0 then the value of x is given as:
x + 7y- 36 = 0
x + 7(0) - 36 = 0
x = 36
point C on the x-axis (x , 0) = (36,0)
The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).
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