Solve for the variables: 2x+5y=37 11-2x=y

Answer:

w = -7z/2

Step-by-step explanation:

Our goal is to isolate w

1. subtract 3w from both sides to get 2w+9z = 2z

2. Subtract 9z from both sides to get 2w = -7z

3. Divide both sides by 2 to get w = -7z/2

We cannot simplify further, so this is our answer.

Answer:

35/42 = b/7    and b= 35/6

Step-by-step explanation:

Our base is unkhown so it will be the variable in our equation :

so b is 35/6 cm

Answer:

m = 2

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug our coordinates into the slope formula and solve for m:

m = (5 - 3)/(4 - 3)

m = 2/1

m = 2

Answer:

Step-by-step explanation:

Let the points be A and B

A( 3 , 3 ) -----> ( x1 , y1 )

B(4 , 5 ) ------>( x2 , y2 )

Now,

finding the slope,

Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]

[tex] = \frac{5 - 3}{4 - 3} [/tex]

[tex] = \frac{2}{1} [/tex]

[tex] = 2[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

676

Step-by-step explanation:

Convert the percentage to a decimal.

30% = 0.3

Multiply the number by the decimal.

520 × 0.3 = 156

Add this number by the number given.

520 + 156 = 676

Answer:

slope is m=1. y-intercept is -1

Answer:

Slope is 1 and intercept is -1. Slope can be found by taking the rise and run of 2 points on a graph. and intercept is just when x = 0

Answer: 11:16

Step-by-step explanation: 11 ounces of blue paint: the total number ounces of paint (adding blue and yellow)

Answer:

5:16

Step-by-step explanation:

The amount of blue paint is 5 oz

The total amount of paint is 16 oz

Make these numbers a ratio of blue to total

Answer:

9.110434

Step-by-step explanation:

√83 ≈ 9.110434

Answer:

9.

Step-by-step explanation:

You would have to find the area of the triangle which is 1/2(bh) which would give you 9. So you would 9 feet of outdoor carpet. Which is actually already given to you as the area inside the triangle.

Answer:

9

Step-by-step explanation:

I finally got it!

Answer:

3 meters

63 meters

Step-by-step explanation:

In order for his two breaks to occur after even distances, simply divide his total path in three:

[tex]B = \frac{9}{3}\\ B=3\ meters[/tex]

He will reach his first break after 3 meters.

If he can only take 9 pieces at a time the number of trips required is:

[tex]n=\frac{36}{9}\\ n=4[/tex]

Note that he will have to back to the back yard for the first three trips (traveling back the 9 meters path). The total distance traveled is:

[tex]d= 3*(9+9)+9\\d=63\ meters[/tex]

He will travel 63 meters.

Answer:

Result = 9b/25 or 36b/100

Step-by-step explanation:

The number is b

step 1

b is decreased by 40%

value of 40% of b = 40/100 *b = 4b/10

New value after this change = b - 40% decreased value of b = b -4b/10

= (10b-4b)/10 = 6b/10

Step 2 The new value obtained is again decreased by 40%

value of 40%  number found in step 1 =  40% of value found in step 1

value of 40%  number found in step 1 =  40/100 * 6b/10 = 24b/100

This value (24b/100) is subtracted from value found in step 1(6b/10) as given that  value obtained is decreased by 40%

new value found after 40% decrease = 6b/10 - 24b/100

new value found after 40% decrease = 60b/100 - 24b/100= 36b/100

new value found after 40% decrease =  36b/100 = 9b/25

Thus, the result of b is decreased by 40% and decreased again by 40% is 9b/25

Answer:

yes

Step-by-step explanation:

2b+b=3b because2+1 = 3

Answer:

the answer is yes

Step-by-step explanation:

yes it is equivalent expression because 2b+b and 3b have the same value and length or numerator which equals yes.

Answer: 4 wholes and 1/5 is 4.20 and you need something greater than that but less than 4.25 which still has only 2 decimals.

Answer:

The height of triangle is 12cm.

The base of triangle is 25 cm.

The area of triangle is 150cm².

Step-by-step explanation:

Given that the area of triangle is Area = 1/2×base×height. So you have to substitute the values into the formula :

[tex]area = \frac{1}{2} \times base \times height[/tex]

[tex]let \: base = 25 \\ let \: height = 12[/tex]

[tex]area = \frac{1}{2} \times 25 \times 12[/tex]

[tex]area = \frac{1}{2} \times 300[/tex]

[tex]area = 150 \: {cm}^{2} [/tex]

Answer:

Negative Binomial

Step-by-step explanation:

The girl receives only 5% of mail which are addressed to her. Rest of 95% mails belong to other family members.

P (X) = 5%

P (X) = 95 / 5

P (X) = 19

The family receives 19 mails out of which only 5% will address the girl. The all other mails belong to the other family members.

Answer:

(√77) / 22

Step-by-step explanation:

To rationalize the fraction we must multiply the entire fraction by √11 / √11. Note that the 2 is not important because it's not a radical. This gives us √77 / 22.

Answer:

There is enough evidence to support the claim that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Step-by-step explanation:

The question is incomplete:

"A national computer retailer believes that the average sales are greater for salespersons with a college degree. A random sample of 32 salespersons with a degree had an average weekly sale of $3599 last year, while 35 salespersons without a college degree averaged $3311 in weekly sales. The standard deviations were $468 and $642 respectively.

Required:

Is there evidence at the 5% level to support the retailer's belief?"

This is a hypothesis test for the difference between populations means.

The claim is that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

The significance level is 0.05.

The sample 1 (college degree), of size n1=32 has a mean of 3599 and a standard deviation of 468.

The sample 2 (non-college degree), of size n2=35 has a mean of 3311 and a standard deviation of 642.

The difference between sample means is Md=288.

[tex]M_d=M_1-M_2=3599-3311=288[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{468^2}{32}+\dfrac{642^2}{35}}\\\\\\s_{M_d}=\sqrt{6844.5+11776.114}=\sqrt{18620.614}=136.4574[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{288-0}{136.4574}=\dfrac{288}{136.4574}=2.11[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=32+35-2=65[/tex]

This test is a right-tailed test, with 65 degrees of freedom and t=2.11, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>2.11)=0.019[/tex]

As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Hey there! :)

Answer:

2nd choice. (x - 2)

Step-by-step explanation:

Given in the question:

(x²-4) ÷ (x + 2) = x-2

This is an example of difference of squares.

We can rearrange the equation by multiplying both sides by (x+2) to become:

(x² - 4) = x - 2 (x + 2)

Therefore, the binomial that must be multiplied by (x+2) is the second choice, x-2.

Answer: B

Step-by-step explanation:

Answer:

3 8/9

Step-by-step explanation:

1.) Convert each fraction from a mixed number to a improper fraction (to do that multiply the denominator with the whole number then add the numerator, the improper fraction denominator will remain the same as the mixed number denominator):

14/3 ÷ 6/5

2.) Solve

a. To divide the fractions, Flip the reciprocal, and multiply the fractions

14/3 x 5/6

b. Check if you can reduce the numbers, which you can 14 and 6 can be both divided by 2:

7/3x5/3

c. Multiply fractions (simply by multiplying across):

35/9

3.) Simplify numbers into mixed fraction (or decimal):

3 8/9

Answer:

(1,1)

Step-by-step explanation:

x=1

y=1

6(1) + 1=7

6+1=7

Answer:

x=1, y=1

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

[tex] \because \triangle ACB \cong \triangle DCE... (given) \\

\therefore \angle A \cong \angle D... (c.a.c.t)\\

\therefore m\angle A = m\angle D\\

\therefore 50\degree = 10x\\\\

\therefore x = \frac{50\degree}{10}\\\\

\huge \orange {\boxed {\therefore x = 5\degree}} [/tex]

Answer:

7.22?

Step-by-step explanation:

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The average college major requires 34 credit hours to complete, with a standard deviation of 3 hours. A college's academic advisors conduct a study to see how many credit hours a sample size of 50 students will need to take to complete their majors.

They calculate:

μx = μ = 34

σx = μ/√n = 34/√50 = 4.81

What did they do wrong?

Answer:

The sample mean will be the same as the population mean

μx = μ = 34

Whereas the standard deviation of the sample would be

σx = σ/√n

σx = 3/√50

σx = 0.424

Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.

Step-by-step explanation:

From the given information we know that,

The population mean is

μ = 34 credit hours

The population standard deviation is

σ = 34 credit hours

The college's academic advisors take a sample size of 50 students so

sample size = n = 50

Since the sample size is quite large then according to the central limit theorem,

The sample mean will be the same as the population mean

μx = μ = 34

Whereas the standard deviation of the sample would be

σx = σ/√n

σx = 3/√50

σx = 0.424

Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.

Answer:

csc∅ = 25/7

sec∅ = 25/24

cot∅ = 24/7

Step-by-step explanation:

Cosecant (csc) is 1/sin∅ or hypotenuse over opposite

Secant (sec) is 1/cos∅ or hypotenuse over adjacent

Cotangent (cot) is 1/tan∅ or adjacent over opposite

Answer:

  see below

Step-by-step explanation:

There are a couple of ways to go about this.

The general form of a conic equation is ...

  Ax^2 +Bxy +Cy^2 +Dx +Ey +F = 0

For AC > 0, this is the equation of an ellipse or circle. (AC < 0, hyperbola; AC = 0, parabola)

So, from the coefficients of the given equation, AC = 2·5 = 10, you know the equation is of an ellipse.

__

The rotation matrix for Cartesian coordinates tells you ...

  x = x'·cos(θ) +y'·sin(θ)

  y = -x'·sin(θ) +y'·cos(θ)

For θ = 45° the values of these trig functions are all (√2)/2. That is, there is no way to get coefficients in the rotated equation that involve √3. This eliminates choice 2.

The only remaining viable choice is choice 4.

__

If you like, you can substitute for x and y using the above relations. You will find that the result differs from any of the answer choices. The rotated figure will have the equation ...

  [tex]5x^2-6xy+9y^2+10\sqrt{2}x+2\sqrt{2}y-80=0[/tex]

For example, the x and y terms become ...

  [tex]6x-4y=6(x'\cos{(45^{\circ})}+y'\sin{(45^{\circ})})-4(-x'\sin{(45^{\circ})}+y'\cos{(45^{\circ})})\\\\=10x'\dfrac{\sqrt{2}}{2}+2y'\dfrac{\sqrt{2}}{2}\\\\\text{Multiplying this by 2 gives $\dots$}\\\\10x'\sqrt{2}+2y'\sqrt{2}[/tex]

Note that this is not the 10√2x' -10√2y' shown in choice 4.

__

Another way to look at this is to look at the angle of rotation relative to alignment with the x- and y-axes. That angle α is given by ...

  cot(2α) = (A -C)/B

For the original ellipse, the rotation angle is ...

  α = arccot((2 -5)/2)/2 ≈ -16.85°

For the transformed ellipse of choice 4, the rotation angle is ...

  α = arccot((9 -5)/6)/2 ≈ 28.15°

This is 45° more*, as it should be, indicating choice 4 is the better of the offered choices.

__

If you do the angle calculation for the 2nd answer choice, you will find it has no relation to a 45° rotation of the original ellipse.

_____

* While the computed rotation angle is as expected, the fact that the x^2 and y^2 coefficients have been swapped means that the long and short axes of the ellipse have been swapped. That is, the long axis of the ellipse has been rotated 45° in the wrong direction by the equation given in the answer choices. The second attachment shows the original ellipse (red), the properly rotated ellipse (dashed red) and the ellipse of choice 4 (blue).

its congruent by HL or RHSaxiom

Answer:

HL

Step-by-step explanation:

[tex] In\: right \triangle 's DAB \: \&\: CBA\\

\angle DAB \cong \angle CBA... (each 90\degree) \\ hypotenuse \: DB \cong hypotenuse \: CA. (given) \\

side AB \cong side BA.. (common) \\

\therefore \triangle DAB \cong \triangle CBA.. (By \: RHS\: or \: HL \: Postulate) [/tex]

Multiply both sides of the ODE

[tex]x'+2tx+5t[/tex]

by [tex]e^{t^2}[/tex]:

[tex]e^{t^2}x'+2te^{t^2}x=5te^{t^2}[/tex]

Now the left side can be condensed as the derivative of a product:

[tex]\left(e^{t^2}x\right)'=5te^{t^2}[/tex]

Integrate both sides, then solve for x :

[tex]e^{t^2}x=\dfrac52e^{t^2}+C[/tex]

[tex]\implies x(t)=\dfrac52+Ce^{-t^2}[/tex]

Given that x(0) = 8, we find

[tex]8=\dfrac52+Ce^0\implies C=\dfrac{11}2[/tex]

so that the particular solution to this IVP is

[tex]\boxed{x(t)=\dfrac{5+11e^{-t^2}}2}[/tex]

Answer:

[tex]\frac{1}{9^3}[/tex] or [tex]\frac{1}{729}[/tex]

Step-by-step explanation:

When we have an exponent that is a negative, it is the same thing as 1 over the positive exponent. So, we move 9^-3 into 1/9^3 and then we evaluate the exponent to get our answer.

Answer:

[tex]3x - 4y = 17ndx - y = 3 \\ 3x - x - 4y + 44y = 17 - 3 \\ 3x - x = 17 - 3 \\ 2x = 17 - 3 \\ 2x = 14 \\ x = 7 \\ \\ 7 - 4y = 3 \\ - 4y = - 4 \\ y = 1[/tex]

Answer:

x = 7

y = 1

Step-by-step explanation:

3x - 4y = 17

x - 4y = 3

Solve x in the second equation.

x = 3 + 4y

Put x as 3 + 4y in the first equation and solve for y.

3(3 + 4y) - 4y = 17

9 + 12y - 4y = 17

9 + 8y = 17

8y = 17 - 9

8y = 8

y = 8/8

y = 1

Put y as 1 in the second equation and solve for x.

x = 3 + 4(1)

x = 3 + 4

x = 7

Answer:The first one

Step-by-step explanation:

V rectangular prism = Area of the base *5