4y+4x=8 solving by slope intercept form

Based on the given values above which is 2 inches: 1 foot, given that the mantel in the room has an actual width of 8 feet, this would mean that the width of the mantel in the blueprint would be 16 inches. 8 times 2 is 16.

To know more about dimension visit :

https://brainly.com/question/14917338

#SPJ9

a) She can make 400 milliliters of the fizzy drink.

b) The change does not affect the greatest amount of drink.

We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.

If we divide the total amount of apple juice in 7 parts, then each part has:

280ml/7 = 40ml

Then we need 3 parts of 40ml of the lemonade, this is:

3*40ml = 120ml

Then the total amounf of drink fizz that she can make is:

280ml + 120ml = 400ml.

b) Now she has  160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.

Learn more about quotients:

https://brainly.com/question/629998

#SPJ1

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

For more such questions on rank

https://brainly.com/question/28839672

#SPJ8

Answer:

2/35

Step-by-step explanation:

\(\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}\)

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

Learn more about Law of Cosines here: brainly.com/question/9261858

#SPJ1

Answer:

1.39285714286

Step-by-step explanation:

\(1\frac{1}{3} + 2\frac{1}{4} = \frac{3*1+1}{3} + \frac{4*2+1}{4} = \frac{4}{3} + \frac{9}{4} = \frac{4*4}{3*4} + \frac{9*3}{4*3} = \frac{16}{12} + \frac{27}{12} = \frac{16+27}{12}=\frac{23}{12} = 1\frac{11}{12}\)

Answer:

64

Step-by-step explanation:

Since one of the 3 identical factors is 4, then the number is 4×4×4, or 4³

Answer:

m  (parallel)  = 3 /4

Step-by-step explanation:

on the graph Y will start on two

Answer: its 2

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.

It took Lin's dad about 3.6 miles for him to meet up with his family.

Speed is the ratio of total distance travelled to total time taken. It is given by:

Speed = distance / time

Let d represent the distance travelled by Lin to meet up with his family. Hence:

Total time for Lin's Dad = d/0.24 + 5

Total time for Lin = d/0.18

Hence:

d/0.24 + 5 = d/0.18

100d/24 + 5 = 100d/18

1800d + 2160 = 2400d

d = 3.6 miles

Find out more on Speed at: https://brainly.com/question/4931057

Answer:

mean 74.714285714286

median 72

mode 72

range 34

Step-by-step explanation:

Answer:

Mean: 74.71

Median: 72

Mode: 72

Range: 34

Step-by-step explanation:

First, let's define what each of these terms mean:

Mean: the average of the data

Median: the number in the middle after being put in ascending order

Mode: the number listed the most

Range: the highest number minus the smallest number

To find the mean, just add up all the numbers and divide by how many there are. First, add up all the numbers in the set. This should give you 1,046. Next, divide by how many terms there are. Since there are 14 terms in this set, we'll be dividing 1,046 by 14. This will give us a mean of 74.71 or 75 if you're rounding up.

To find the median, you'll first need to put the terms in ascending order, meaning from lowest to highest. Luckily, the set is already in ascending order, so that step is not necessary here. Next, you're going to find the number in the middle of the set. However, since there are an even number of terms, we have two numbers in the middle: 72 and 72. To find the median with two numbers in the middle, just add both terms up and divide by 2. However, since both terms are 72, this step is also not necessary. Our median is simply 72.

To find the mode, you're just looking for the number that appears the most. In this case, it would be 72 since it appears more than any other number in the set (5 times.)

Last, to find the range, just subtract the lowest number from the highest number in the set. With the highest number being 93 and the lowest being 59, just do 93 - 59 for a range of 34. Please let me know if you have any further questions!

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

To know more about PEMDAS, visit:

https://brainly.com/question/345677

#SPJ1

The meters of fabric worth d is 1347.36

what is profit and loss?

Here a full roll of fabric contains d meters.

when 18m have been sold, then the value of the remaining faric = 25600

Therefore, d-18m = 25600

selling price of 1m = 25600 ÷ (d - 18m)

1m+18m = 25600 ÷ d

19m × d = 25600

Threfore d = 25600 ÷ 19

d = 1347.36

To learn more about profit refer to;

https://brainly.com/question/1078746

#SPJ4

Answer:

3x

Step-by-step explanation:

If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.

Answer:

3x

Step-by-step explanation:

If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.

Answer:

Proved

Step-by-step explanation:

Given

\((n+5)^2-(n+3)^2\)

Required

Show that \((n+5)^2-(n+3)^2\) is a multiple of 4

Expand each bracket

\((n+5)(n+5)-(n+3)(n+3)\)

Open brackets

\(n^2 + 5x + 5x + 25 - (n^2 + 3x + 3x + 9)\)

\(n^2 + 10x + 25 - (n^2 + 6x + 9)\)

Open bracket

\(n^2 + 10x + 25 - n^2 - 6x - 9\)

Collect Like Terms

\(- n^2 + n^2 - 6n + 10n + 25 - 9\)

\(- 6n + 10n + 25 - 9\)

\(4n + 25 - 9\)

\(4n + 16\)

Factorize

\(4(n + 4)\)

Hence, the multiples of \((n+5)^2-(n+3)^2\) are \(4\) and \((n + 4)\)

Answer:

a) Z = 2.575.

b) Z = 2.327.

c) Z = 1.96.

d) Z = 1.645.

e) Z = 1.88.

Step-by-step explanation:

Question a:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.99}{2} = 0.005\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.005 = 0.995\), so Z = 2.575.

Question b:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.98}{2} = 0.01\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.01 = 0.99\), so Z = 2.327.

Question c:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Question d:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.9}{2} = 0.05\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.

Question e:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.94}{2} = 0.03\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.03 = 0.97\), so Z = 1.88.

Answer:

38 students

Step-by-step explanation:

because 19% of 205 is 38.95, but not fully 39 students, so about 38 students

Answer:

y = 4·0.5^x

Step-by-step explanation:

If x is increased by 1, y is multiplied by 0.5.

x | y

0 | 4

1 | 4·0.5

2 | 4·0.5·0.5

3 | 4·0.5·0.5·0.5

The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

The amount that should be deposited monthly is $286.66.

The monthly deposit is the periodic payment into an investment account that earns interest at a compound rate.

The monthly deposit can be determined using an online finance calculator.

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 6%

PV (Present Value) = $0

FV (Future Value) = $20,000

Results:

Monthly Deposit = $286.66

Sum of all periodic deposits = $17,199.36

Total Interest = $2,800.64

Learn more about periodic deposits at https://brainly.com/question/29003232

#SPJ1

The value of the length x is 2√70. Option C

To determine the value of the length of the triangle, we need to consider the different trigonometric identities, they are;

Now, using the Pythagorean theorem, we have;

17² = x² + 3²

Find the square values and substitute

289 = x² + 9

collect the like terms

x² = 289 - 9

Subtract the values

x² = 280

Find the square root of both sides

x = √280

Find the values

x = √4× 70

x = 2√70

Learn about trigonometric identities at: https://brainly.com/question/22591162

#SPJ1

Answer:

x=0

Step-by-step explanation:

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

To learn more about dilation factor, refer to the link-

https://brainly.com/question/3457976

#SPJ9

Complete Question

The figure has been attached here

The first quantity (45g) as 60 percentage of second (75g).

A part of whole expressed in Hundredth. Percentage is a fraction of a number out of 100%. It can be in fraction or in decimal.

To convert the given percentage value in decimal, divide the given value by 100.

For example:

1. 50% in decimal or fraction will be 50/100 = 0.5.

2. 20% in decimal or fraction will be 20/100 = 0.2.

1. Finding the total amount from which we need to find the percent.

2. Dividing the required amount to find the percentage by total amount.

3. Multiply it by 100.

For example:

1. It rained 10 of the 30 days in April.

Percentage will be 10/30 = (1/3) x 100

Percentage = 33.33%

Here, we have given that:

Total amount = 75g

Required amount for percent = 45g

Now, to find the percentage:

Percentage = 45/75

Percentage = 0.6 x 100

Percentage = 60%

Hence,

The first quantity (45g) as 60 percentage of second (75g).

Learn more about " Percentage " from here: https://brainly.com/question/13450942

#SPJ9

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:

-6

Step-by-step explanation:

6x + y = -1

y = -6x-1

slope which is m is -6