If r^n=a, then which of the following are true statements? Check all that apply.

a. a^1/n=r b. a^r=n c. n sq a =r d. n^1/r=a

The slope of the line given the points (-2, 6) and (0, 4) is -1. The correct answer would be option (A).

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

We have to determine the slope of the line given the points (-2, 6) and (0, 4)

Plugging in the given points, we get:

m = (4 - 6) / (0 - (-2)) = -2 / 2 = -1

So, the slope of the line is -1.

Hence, the correct answer would be an option (A).

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The value of unknown variable x in the right angled triangle is equal to approximately 20 units.

To find the value of x using the concept of similar triangles,

Use the property that in a right triangle, the altitude drawn from the right angle to the hypotenuse creates three similar triangles.

In triangle QRS, m∠R = 90°.

RS = x (unknown).

RT is an altitude on hypotenuse QS.

ST = 9.

QT = 16.

Now, set up the following ratios for the similar triangles:

In triangle QRT:

QR / QT = RT / ST

In triangle QRS:

QR / QS = RS / ST

Since triangle QRS is a right triangle, we can use the Pythagorean Theorem to find the value of QR:

QR² + RS² = QS²

QR² + x²= (QT + ST)²

QR² + x² = (16 + 9)²

QR²+ x² = 25²

Now, let's use the first similarity ratio to find QR in terms of ST:

QR / QT = RT / ST

QR / 16 = RT / 9

QR = (RT × 16) / 9

Since triangle QRT is also a right triangle, we can use the Pythagorean Theorem again:

QR² + RT² = QT²

((RT × 16) / 9)² + RT² = 16²

(RT² ×256) / 81 + RT²= 256

(RT² ×256 + 81 × RT²) / 81 = 256

(RT² × 337) / 81 = 256

RT² = (256 ×81) / 337

RT² ≈ 61.771

RT ≈ √61.771

RT ≈ 7.859

Now, substitute RT back into the expression for QR:

QR = (RT× 16) / 9

QR = (7.859 × 16) / 9

QR ≈ 13.927

Finally, substitute QR into the Pythagorean Theorem equation we obtained earlier to find the value of x:

QR² + x² = 25²

(13.927)² + x² = 625

193.931 + x² = 625

x² = 625 - 193.931

x² ≈ 431.069

x ≈ √431.069

x ≈ 20.059

Therefore, the value of x in the right triangle is approximately 20 units.

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The answer is B. He will pay $431.

The estimated standard error for the mean difference between two samples with sizes of 5 and 10 respectively, and a pooled variance of 30, is calculated using the standard error formula. The standard error is 3.

The question you've asked falls under the realm of statistics, in specific it involves the calculation of the estimated standard error for differences between two sample means (one with n=5 scores and the second with n=10 scores) given a pooled variance of 30.

The formula to find the estimated standard error for a difference between two sample means is:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

Where s1^2 and s2^2 are the variances of the two samples and n1 and n2 are the sizes of two samples respectively. As we do not know the variances for the individual samples, we can use the pooled variance as an estimate. The pooled variance can be considered as s1^2 = s2^2 = 30.

Now substitute these values in the equation, we get:

SE = sqrt[(30/5) + (30/10)] = sqrt[6+3] = sqrt[9] = 3

So, the estimated standard error for the mean difference between these two samples is 3.

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divide total paid by number of pencils for price of 1 pencil

4.50 / 18 = 0.25 for 1

 so you would put a dot at (1, 0.25) (2,0.5) (3,0.75) etc and draw a line through the dots

 see attached picture:

Answer:   3x=10

Step-by-step explanation:

x +80 >-3x

add 3x to each side

4x+80 >0

 subtract 80 from each side

4x>-80

divide both sides by 4

x > -80/4

x>-20

A line segment or ray that is perpendicular to the segment at its midpoint is called perpendicular bisector.

A straight line that forms a 90° angle with another line is said to be perpendicular. A small square is placed between two perpendicular lines, as seen in the illustration, to indicate a right angle, also known as a 90° angle. The two lines in this instance are considered to be perpendicular to one another because they intersect at a straight angle.

A line that divides a line segment into two equal halves and forms a 90° angle at the place of intersection is called a perpendicular bisector. In other words, a perpendicular bisector splits a line segment at its halfway, creating a 90° angle.

Therefore, a line segment or ray that is perpendicular to the segment at its midpoint is called perpendicular bisector.

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Answer: The area of the parallelogram with the given vertices=238 square units.

Step-by-step explanation:

Let CD be the base of the parallelogram ABCD is given by distance formula

CD=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} =\sqrt{(-12-2)^2+(-5-(-5))^2} =\sqrt{196} =14[/tex]units[or you can count distance by using graph as ordinates of C and D are same to we can count the distance of x from C to D]

Now consider P a point on CD such that AP become the height of the parallelogram which is given by (from the graph attached)=17 [as abscissa of P and A are same to we can count the distance of y from A to P]

Area of parallelogram = base × height=14×17=238 square units.

When Lisa purchased her house, the mortgage lender required her homeowner's insurance to cover 100% of the loan amount. After many years, Lisa paid off her mortgage. If Lisa decided to comparison shop for homeowner's insurance now, then the insurance coverage amount be based on the cost to rebuild the house.

The question involves understanding square roots and cube roots in mathematics. The square root of 16 is 4 and of 4 is 2. The cube root of 4 is about 1.587 and of 16 is approximately 2.52.

The question is related to the concept of roots, specifically square roots and cube roots. A square root of a number is a value that, when multiplied by itself, gives the original number. The square root of 16 is 4 because 4*4 equals 16. Similarly, the square root of 4 is 2 because 2*2 equals 4.

On the other hand, the cube root of a number is a value that, when multiplied by itself twice, gives the original number. The cube root of 4 is approximately 1.587 because 1.587*1.587*1.587 is roughly equal to 4. The cube root of 16 is approximately 2.52 because 2.52*2.52*2.52 is roughly equal to 16.

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since the known angle is 45 degrees both the height and the base are equal

 so y = 6

the hypotenuse (x) on a 45 degree triangle = the side time sqrt(2)

 so x = 6sqrt(2)

Phoebe got £180, Andy got £60 and Polly got £30

The amount shared is given as:

Amount = £270

Represent Phoebe's share with x, Andy's with y and Polly's with z.

From the question, we have:

x = 3y

y = 2z

So, we have:

x : y : z = 3y : 2z : z

This gives

x : y : z = 6z : 2z : z

When £270 is shared in the above ratio, we have:

x : y : z = 180 : 60 : 30

Hence, Phoebe got £180, Andy got £60 and Polly got £30

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The value of solution of quadratic equation 5x² + 10x - 5 = 0 is,

⇒ x = - 1 ± √2

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

Equation is,

5x² + 10x - 5 = 0

Now, We can solve by using quadratic formula as;

⇒ x = - 10 ± √10² - 4×5×- 5 / (2×5)

⇒ x = - 10 ± √100 + 100 / 10

⇒ x = - 10 ± √200 / 10

⇒ x = - 1 ± √2

Thus, The value of solution of quadratic equation 5x² + 10x - 5 = 0 is,

⇒ x = - 1 ± √2

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Answer:

mine is 6.7

Step-by-step explanation:

I would say they are not a function

 looking at the x values

2-1 =1

4-2=2

6-4=2

they aren't all the same

 now the Y's

4- -1 = 5

6-4 =2

8-6 =2

they are not all the same either

Answer:

36

Step-by-step explanation:

took it