2) I have a line with a slopeof -7 and the line crosses they-axis at positive 9. Writethe equation for this line inslope-intercept form (y=mx+b).

The sum between n = 1 and n = 5 is 15.5, so the correct option is the second one.

Here we have the summatory:

\(\sum^{5}_{n = 1} 2^{n - 2}\)

So we just need to add the 5 terms (between n = 1 and n = 5)

So we will get the sum:

S = [ 2¹⁻² + 2²⁻² + 2³⁻² + 2⁴⁻² + 2⁵⁻²]

S = [2⁻¹ + 2⁰ + 2¹ + 2² + 2³]

S = [0.5 + 1 + 2 + 4 +8]

S = 15.5

So the correct option is the second one.

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Answer:

y intercept is 4

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

21+0

Answer:

97.5 kgs

Step-by-step explanation:

130÷100= 1.3

1.3×25= 32.5

130-32.5= 97.5

Answer: The cost of milk at Target is 3 standard deviations above the mean = $3.05.

Step-by-step explanation:

Given: Mean price of a gallon of milk = $2.60

Standard deviation =  $0.15

The cost of milk at Target is 3 standard deviations above the mean = Mean + Standard deviation

= $ (2.60+3(0.15))

=-$(2.60+0.45)

= $ 3.05

Hence, the cost of milk at Target is 3 standard deviations above the mean = $3.05.

The book value at the end of year 2 of the equipment depreciated using the sum-of-the-years’-digits method is $65,560.

Depreciation is a method used to expense the cost of an asset. Book value is the cost of the asset less the accumulated depreciation.

Sum-of-the-year digits = (remaining useful life / sum of the years ) x  (Cost of asset - Salvage value)

Depreciation expense in year 1:

Sum of the years = 1 +2 +3 +4 + 5 + 6 + 7 + 8 + 9 + 10+ 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 210

Undepreciated life of the asset = 20

(20 / 210) x ($79,600 - 4,000) = 7200

Depreciation expense in year 2:

19 / 210 x ($79,600 - 4,000) = 6840

Book value = 79600 - 7200 - 6840 = $65,560

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Answer: No

Step-by-step explanation: a rectangle can be a parallelogram because it qualifies to be a parallelogram however a parallelogram can’t be a rectangle because a rectangle has all 90 degree angles and that opposite sides can be equal and parallelograms come in different forms

Answer:

width = 17 m ; length = 31 m

Step-by-step explanation:

w = width

l = length

perimeter of a rectangle = (length + width) * 2

l = 14 + w

(14 + w + w) * 2 = 96

(14 + 2w) * 2 = 96

28 + 4w = 96

4w = 68

w = 17 m

l = 14 + 17 = 31 m

Answer:

If they're in fraction form, set them equal to each other to test if they are proportional. Cross multiply and simplify. If you get a true statement, then the ratios are proportional!

Answer:

Cross multiply

Step-by-step explanation:

Convert into fraction form, make them equal to each other using cross multiplication.

Answer:

Step-by-step explanation:

The position vector of point P, MP, is given by MP = 6i - j.

To find the position vector of point P, which is the midpoint of NO, we can use the midpoint formula.

The midpoint formula states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:

Midpoint (Mᵖ) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's find the position vector of point P using the given information:

Point N: N = 4i - 5j

Point O: O = 8i + 3j

Using the midpoint formula, we can find the coordinates of point P:

x-coordinate of P: (x₁ + x₂) / 2 = (4i + 8i) / 2 = 12i / 2 = 6i

y-coordinate of P: (y₁ + y₂) / 2 = (-5j + 3j) / 2 = -2j / 2 = -j

Therefore, the position vector of point P, MP, is given by:

MP = 6i - j

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The given system of equation is

x + 2y + 0z = 3

- x + y + z = 2

0x + y - 2z = - 3

The augumented matrix is formed by using the coefficient of the variables. The required matrix is shown below

The correct option is the second one

The side a = 65.19 approximately to two decimal places using the cosine rule.

In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Considering the ∆ABC, line a is calculated with cosine rule as follows;

a² = b² + c² - 2(b)(c)cosA

a² = 35² + 31² - 2(35)(31)cos162°

a² = 1225 + 961 + 2063.7926

a² = 4249.7926 {take square root of both sides}

a = 65.1904

With proper application of the cosine rule, we can conclude the value of the side a of the triangle ABC is approximately 65.19 to 2 decimal place.

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Answer:Expanded Notation Form:

 80,000  

+ 6,000  

+ 400  

+ 20  

+ 5  

Step-by-step explanation:

Expanded Exponential Form:

8 × 104

+ 6 × 103

+ 4 × 102

+ 2 × 101

+ 5 × 100

Step-by-step explanation:

hope it helps u...........

The result of the formula  \(12 - 3y2 + (v=4) / (2y - 2)\) for y = 3 is  \(-29/2\)  .

When \(y = 3\) is used, the value of the expression \(12 - 3y2 + (v=4) / (2y - 2)\)  has a value of  \(-29/2\) .

To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.

If  \(y = 3\) , we can insert it into the expression & simplify as follows to evaluate   \(12 - 3y2 + (v=4) / (2y - 2)\) for  \(y = 3\)  .

\(12 - 3(3)^2 + (√4) / (2(3) - 2)\) (y = 3 replacement)

\(12 - 27 + 2 / 4\s-15 + 1/2\s-29/2\)

Therefore, The result of the formula  \(12 - 3y2 + (v=4) / (2y - 2)\) for y = 3 is  \(-29/2\)  .

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\(\frac{7}{8} (-32-48x) + 36 = \frac{2}{3} (-33x-18) -10x\)

\(\frac{7}{8} (-32)+\frac{7}{8} (-48)+36=\frac{2}{3} (-33x)+\frac{2}{3} (-18)-10x\)

\(-28-42+36=-22x-12-10x\)

\(22x+10x=28+42-36-12\)

\(32x=22\)

\(x=\frac{22}{32} =\frac{11}{16} =0,6875\)

Answer: x = 0.6875

Ok done. Thank to me :>

Answer:

x = 2

Step-by-step explanation:

7/8 (-32-48x) + 36 = 2/3 (-33x-18) - 10x

Multiply,

7(-32-48x)/8 + 36 = 2(-33x-18)/3 -10x

Simpliy,

-336(3x+2) + 864 = -48(11x+6) - 240x

Expand,

-1008x + 192 = -768x - 288

Simplify,

-1008x = -768x -480

Simplify,

-240x = -480

Simplify,

x = -480/-240

Answer,

x = 2

Answer: The Silo is 44 meters tall

Step-by-step explanation:

To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)

The quantity 2a 2c corresponds to the rate of change of the surface area with respect to a. So, Correct option is C.

When considering a rectangular prism with dimensions a, b, and c, there are three different measures that we can associate with the dimensions: the length, width, and height. These measures are important in determining both the volume and the surface area of the prism.

In this problem, we are given a quantity 2a 2c and asked to determine which measure of the rectangular prism it corresponds to. We can do this by considering the formulas for the volume and surface area of the prism, and taking the partial derivatives with respect to each of the three dimensions.

The volume of a rectangular prism is given by:

V = abc

Taking the partial derivative of this expression with respect to a, we get:

\(\frac {\partial v} {\partial a}\) = bc

This is not equal to 2a 2c, so we can eliminate the possibility of the quantity corresponding to the rate of change of the volume with respect to a.

Taking the partial derivative of the volume with respect to b and c gives:

\(\frac {\partial v} {\partial b}\) = ac

\(\frac {\partial v} {\partial c}\) = ab

Again, neither of these expressions is equal to 2a 2c, so we can eliminate the possibilities of the quantity corresponding to the rate of change of the volume with respect to b or c.

Next, we can consider the surface area of the prism, which is given by:

A = 2ab + 2ac + 2bc

Taking the partial derivative of this expression with respect to a, we get:

\(\frac {\partial v} {\partial a}\) = 2b + 2c

Substituting 2a 2c for 2b + 2c, we get:

\(\frac {\partial A} {\partial a}\) = 2a 2c

This is the same expression as the given quantity, so we can conclude that the quantity 2a 2c corresponds to the rate of change of the surface area with respect to a.

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Answer:

10is the answer

Step-by-step explanation:

\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108\)

The Pythagorean triples here are; 3, 4, 5. Option 1

We define a Pythagorean triple as a^2+b^2 = c^2 where a, b and c are the three positive integers. Given that we can find the Pythagorean triple from; (x2 - y2)2 + (2xy)2 = (x2 + y2)2

Where; x = 2, y = 1

Substituting values have;

(2^2 - 1^2)^2 + (2*2*1)^2 = (2^2 + 1^2)^2

This results to;

3^2 + 4^2 = 5^2

9 + 16 = 25

25=25

Therefore the Pythagorean triples here are; 3, 4, 5. Option 1

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Answer:

x=-24 is the correct answer

Answer:

Step-by-step explanation:

Area of a triangle is given by

\(A = \frac{1}{2} bh\)

where

b is the base

h is the height

From the question

Area = 21 m²

The statement

The height of a triangle is 8 m more than the length of the base is written as

h = 8 + b

Make b the subject

That's

b = h - 8

Substitute the expression into the above formula and solve for the height

That's

\(21 = \frac{1}{2} (h - 8)h\)

Multiply through by 2

h² - 8h = 48

h² - 8h - 48 = 0

(h + 4)(h - 12) = 0

h + 4 = 0 h - 12 = 0

h = - 4 h = 12

Since the height cannot be a negative number we have the final answer as

Hope this helps you

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Amount Invested or Borrowed is equivalent to

PRINCIPAL

The second option is the correct answer

Answer:

Step-by-step explanation:

Using

Point A: x= 1 and y=3

And point B: x=-2 and y=-6

use equation of slope and substitute the values

Slope= YB-YA/Xb-Xa

= -6-3/-2-1

=3

Answer:

.1113490364

Step-by-step explanation:

this is the answer.

Answer:

The answer is (2,16)

Step-by-step explanation:

graphing

In order to determine the volume of the square pyramid, use the following formula:

V = 1/3 B·h

where:

B: area of the base = (2 cm)² = 4 cm²

h: height = 2 cm

replace the previous values into the formula for V:

V = 1/3 (4 cm²)(2 cm)

V = 8/3 cm³

V ≈ 2.7 cm³

Hence, the volume of the given square pyramid is approximately 2.7 cm³