The area of a rectangle is (4x2 − 49y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely.

Answer:

the answer is 91

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

non terminating recurring. i think option c must be the answer

Answer:

y = -4/3x -46/3

Step-by-step explanation:

The question tells us to write an equation that is:

- parallel to the given line

- goes through the point (-7, -6)

Parallel lines will have the same slope, because if the slope was different, they would eventually intersect and not be parallel lines anymore.

We are going to use the point-slope form to find the other line.

Point-slope form uses a point that the graph will cross through and the slope of the graph to find the graph in y = mx + b form (also called slope-intercept form).

(I attached the point-slope form as an image below)

m = slope

x1 = x coordinate of the point

y1 = y coordinate of the point

We are going to substitute our slope into the form first:

y - y1 = (-4/3)(x - x1)

Next let's put in our point (-7, -6):

(Remember! -7 is our x coordinate & -6 is our y coordinate :-) )

y - (-6) = -4/3(x - (-7))

(cancel out the negatives to make them positive)

y + 6 = -4/3 (x +7)

Now solve for x using basic algebra:

y + 6 = -4/3 (x +7)

(distribue the -4/3)

y + 6 = -4/3x - 28/3

(subtract 6 from both sides)

y = -4/3x -46/3

That's your answer!

Hope it helps (●'◡'●)

Answer:

Step-by-step explanation:

y + 6 = -4/3(x + 7)

y + 6 = -4/3x - 28/3

y + 18/3 = -4/3x - 28/3

y = -4/3x - 46/3

Answer:

1/4 = x

Step-by-step explanation:

x - 2( 3x - 1 ) = 3x

Step 1 :- Distribute 2

x - 2 × 3x - 2 × 1 = 3x

x - 6x + 2 = 3x

Step 2:- Combine like terms

-5x + 2 = 3x

Step 3 :- Add 5x to both sides

-5x + 5x + 2 = 3x + 5x

2 = 8x

Step 4 :- Divide both side by 8

2/8 = 8x / 8

1/4 = x

Answer:

Step-by-step explanation:

The key is to find out the entire volume the tank can hold when it is full, then take 2/3 of that amount. The volume of a cylinder is

[tex]V=\pi r^2h[/tex] and filling in:

[tex]V=3.14(3)^2(3)[/tex] (if the diameter is 6 m, the radius is 3) so

V = 84.78 m³ when it is full all the way. If we need the amount that makes up 2/3 of that:

[tex]\frac{2}{3}(84.78)=56.52m^3[/tex]

Answer:

B is the answer

the graph is shifted up +3

the graph is curving upward, so the power has to be positive

Answer:

you mean the mean not the meaning right?

The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.

Answer:

16 guests

Step-by-step explanation:

Firstly, we know Sidney's retirement party costs a starting amount of $28. We also know that she can only spend $44 on her retirement party. The easiest way to do it in my opinion is subtract 28 from 44, giving you 16. Since we know that each guest is only $1, we know that the maximum number of guests Sidney can afford is 16 guests. I hope this helped and please don't hesitate to ask for clarification!

$44-$28=$16

$16÷$1=16 guests at most

Answer:

y = 75.5

Step-by-step explanation:

Reference angle (θ) = 49°

Hypotenuse = 100

Opposite = y

Apply trigonometric function, SOH. Which is:

Sin θ = Opp/Hyp

Plug in the values

Sin 49 = y/100

100*Sin 49 = y

y = 75.5 (nearest tenth)

Answer:

16

Step-by-step explanation:

[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]

                   [tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]

The value of x^2-2xy+y^2

will be 16 .

Explanation is in the attachment .

hope it is helpful to you ☺️

Answer:

The probability that in a sample of 400 registered voters at least 290 voted in their most recent local elections is:

= 72.5%

Step-by-step explanation:

Sample of registered voters = 400

Sample of voters that actually voted = 290

Probability = 290/400 * 100

= 72.5%

b) This result above gives the statistic that for every 100 registered voters, 72.5 voters voted.  Probability measures the chance of an event occurring given other events.  Therefore, one can conclude that the voting was at least 72.5%.  Inversely, 27.5% of the registered voters did not participate or cast their ballots in the local elections.

Answer: 113.01m - You are almost right

Step-by-step explanation:

Simply by using pir^2, you get the number you calculated, but it is asking for at least 2 decimal places. So it would be "113.01"

Answer: [tex]x\in (0,1)\cup (4,\infty)[/tex]

Step-by-step explanation:

Given

In equality is [tex]x^3+4x>5x^2[/tex]

Taking terms one side

[tex]\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0[/tex]

Using wavy curve method

[tex]x\in (0,1)\cup (4,\infty)[/tex]

Answer:

7 sq unit

Step-by-step explanation:

Area of triagle ABC = Area of rectangle mnBp - Area of trangle AmC - Are of triangle CnB - Area of triangle ABp

Area of rectangle mnBp = 5x3 = 15 sq unit

Area of trangle AmC = 4x2 /2 = 4 sq unit

Are of triangle CnB = 5x1 /2 = 2.5 sq unit

Area of triangle ABp = 3x1 /2 = 1.5 sq unit

I believe you can work out thd answer from the above

Answer:

1,773.33 Mexican pesos

Step-by-step explanation:

Create a proportion where x was how many Mexican pesos it was worth:

[tex]\frac{1}{0.075}[/tex] = [tex]\frac{x}{133}[/tex]

Cross multiply and solve for x:

133 = 0.075x

1773.33 = x

So, it was worth approximately 1,773.33 Mexican pesos

Answer:

Test statistic = - 2.71

Step-by-step explanation:

Table of the sample data is attached below :

Using a dependent sample t test :

H0 : μd = 0

H0 : μd ≠ 0

The difference in the 6th and 13th date data is :

Difference, d = -4, -6, -3, -1, 1, -7

The sample size, n = 6

The mean of d ; μd = Σd/ n = - 3.667

Standard deviation of difference, Sd = 3.011

The test statistic : μd/(Sd/√n)

Test statistic = - 3.33 / (3.011/√6)

Test statistic = - 3.33 / 1.2292356

Test statistic = - 2.709

Test statistic = - 2.71

Answer:

The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].

Step-by-step explanation:

Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.

Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].

Given:

[tex]\phi=1.618[/tex]

22nd number in Fibonacci sequence = 17,711

To find:

The 23rd number in the Fibonacci sequence.

Solution:

The nth term of a Fibonacci sequence is:

[tex]f_n=\dfrac{\phi^n-(1-\phi)^n}{\sqrt{5}}[/tex]

Substituting [tex]\phi=1.618, n=21[/tex], we get

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=10941.1724024[/tex]

[tex]f_{21}\approx 10941[/tex]

Now,

[tex]f_{23}=f_{21}+f_{22}[/tex]

[tex]f_{23}=10941+17711[/tex]

[tex]f_{23}=28652[/tex]

It is about 28,656. Therefore, the correct option is D.

Answer:

(-3,4)

Step-by-step explanation:

A system of equations is given to us. The given equations are ,

[tex]\implies 2x - 3y = -18[/tex]

[tex]\implies 3x + y =-5[/tex]

We need to plot the graph and find the solution of the given system . For that refer to attachment . The point at which both the lines of the graph will intersect each other will be the solution of the given system of equations .

From the graph we can see that it intersect at (-3,4) . Therefore the Solution is ,

[tex]\longrightarrow \underline{\underline{ Solution = (-3,4)}}[/tex]

Answer: If you graphing it’s (-6, 13) or (3, 4)

Step-by-step explanation:

21 - 3y = -18- y = 13

3x + y = -5- x = -6

Step-by-step explanation:

we cannot see the diagram, so we don't know how many layers of bricks are used. and therefore it is impossible to tell the height of the wall.

9514 1404 393

Answer:

  x = 36°

Step-by-step explanation:

The exterior angle is equal to the sum of the remote interior angles. A linear pair is supplementary. So, you can find x either of two ways:

  2x = x + (180 -4x)   ⇒   5x = 180   ⇒   x = 36

Or ..

  4x = x + (180 -2x)   ⇒   5x = 180   ⇒   x = 36

The value of x is 36°.

Answer:

c. both of the above statements are false

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Distribution skewed to the right

This means that the Empirical Rule is not applicable, and the two statements are false, and thus, the correct answer is given by option c.

The first would be false nonetheless, but the second would be true if the distribution was normal.

Answer:

3x2−2x+6/x2

Step-by-step explanation:

have a great day <33333

Answer:

The p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.

Step-by-step explanation:

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before.

At the null hypothesis, we test if the two means are equal, that is, the subtraction of them is 0.

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

At the alternative hypothesis, we test if the two means are different, that is, the subtraction of them is different of 0. So

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789.

Considering a standard significance level of 0.02789, the p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.

Answer:

The answer is a

Step-by-step explanation:

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Answer:

Step-by-step B represents the $14 John earned in the 2 hours he worked.

explanation:

Answer:

c. 4 and 42

Step-by-step explanation:

Given

[tex]p = 4[/tex] -- independent variables

[tex]n = 47[/tex] ---- observations

Required

The numerator and denominator degrees of freedom

The denominator degrees of freedom is:

[tex]df =n - p - 1[/tex]

[tex]df =47 - 4 - 1[/tex]

[tex]df =42[/tex]

For the numerator, we have:

[tex]df = p[/tex]

[tex]df = 4[/tex]

Answer:

2.113

Step-by-step explanation:

               [tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]