summarize how you can find the slope of a perpendicular line.

Please provide your question with a math problem in the form of an image or text.

The rate of change of surface area is 524.02 square kilometers per minutes.

The total space occupied by a three-dimensional square prism is called surface area.

Given, the decreasing rate of the base side with respect to time, ds/dt = 7 km/min

the increasing rate of height with respect to time, dh/dt = 10 km/min

At a time, t, base side, s = 4 km

and height, h = 9 km

we need to determine the rate of change of surface area with respect to time, d A/dt

from the differentiation chain rule, d A/ dt = d A /dt × ds /ds

                                                        d A /dt = d A/ ds × ds /dt ... equation 1

we know that the surface area for prism, A = 2s² + 4sh

if we differentiate with respect to s then we find d A /ds

  d/ds (A) = d/ ds (2s² + 4sh)

d A /ds = 4s + 4h +4s dh/ds ......  equation 2

now dh /ds = dh /ds × dt /dt [ using differentiation chain rule]

dh/ds = dh/ dt× dt/ds

d h/ ds = dh/dt × 1/ ds/dt

it stated earlier that dh/ dt = 10 and ds /dt = 7

dh / ds = 10/7

putting this value in equation 2, we get

d A /ds = 4s +4h + 4s ×10/7

as we know at time t, s= 4 and h = 9

d A /ds = 4 × 4 + 4 ×9 +4×4 ×10 /7

d A /ds = 74.86

putting the value  d A /ds in equation 1, we get

d A /dt = d A /ds × ds/ dt

d A/ dt = 74.86 × 7

d A /dt = 524.02 km² / min

hence, the rate of change of surface area = 524.02 square kilometers per minutes

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Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.

We suppose a general triangle, for which:

The lengths and the sine of the angles are proportionally related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The segments in this problem are given as follows:

Hence it can be affirmed that:

BC > AB.

As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.

As for segment AC, we need the measure of angle B, hence nothing can be affirmed.

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Answer:

Step-by-step explanation:

Let's assume that,

→ Length = 2x

→ Width = x

→ Perimeter = 30

Perimeter of rectangle formula,

→ P = 2(L + W)

Now the value of x will be,

→ P = 2(L + W)

→ 2(2x + x) = 30

→ 2 × 3x = 30

→ 6x = 30

→ x = 30/6

→ [ x = 5 ]

Then required dimensions are,

→ Length = 2x = 2 × 5 = 10

→ Width = x = 5

Hence, these are the dimensions.

Length = 10

width = 5

Given-

Perimeter =30

l=2b........................................................ i

so

P =2(l+b)

here

30 = 2(2b +b)... ... ..............         as l=2b from i

30 = 2*3b

30 = 6b

b= 5

which implies l= 2*5 --->10............................................ from i

so

Length = 10

width = 5

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On solving the provided question we cans ay that - here in linear equation, y = 3 and x = -1/2

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y = 2x + 1 - linear equation.

value of y;

[tex]x = 0\\y = 2(0) + 1\\y = 2 + 1\\y = 3[/tex]

value of x;

[tex]y = 0\\0 = 2x + 1\\2x = -1\\x = -1/2[/tex]

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The amount of rain required would be 2.5 inches.

What is the addition?

Addition is a mathematical operation that represents the process of combining two or more numbers together. The result of this operation is called the sum. The addition operation is often represented using the symbol "+", and it can be used to add any two or more numbers together.

To beat the record by one-tenth of an inch, an additional 0.1 inches of rain must fall.

Currently, the average amount of rain per day is 12 inches / 5 days = 2.4 inches per day.

So, the amount of rain that must fall on Friday to beat the record by one-tenth of an inch is 2.4 inches + 0.1 inches = 2.5 inches

Hence, the amount of rain required would be 2.5 inches.

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Answer:

The 4th one

Step-by-step explanation:

Right on edge!

Answer: Tonya's calculation is incorrect because she mixed units of measurement. She used feet to measure one dimension of the room (10 feet) and inches to measure the other dimension (120 inches) and then calculated the area as 10 x 120 = 1200 square feet.

Area is a measure of the amount of space inside a two-dimensional shape, and it's typically measured in square units. To calculate the area of a rectangular room, you multiply the length of the room by the width of the room,

However in this case, Tonya used different units of measurement for length and width (feet and inches), and therefore the answer is incorrect.

You would need to convert inches to feet before multiplying 10 feet by 120 inches to get the area.

120 inches = 10 feet

So, the correct calculation of the area would be 10 feet * 10 feet = 100 square feet

It's worth mentioning that before calculating any area or volume, it's important to make sure that all units of measurement are consistent and the same.

Step-by-step explanation:

In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.

the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.

A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.

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Answer:

---------------------------

Slope-intercept form:

Point-slope form:

Use the point-slope form to find the equation and then convert it to slope-intercept form:

The value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.

What is the triangle translation?

In mathematics, a triangle translation refers to the geometric transformation in which a triangle is moved to a new position without rotating or scaling it. The triangle is simply slid along a straight line in a certain direction, and the new position of the triangle will be parallel to the original one.

Given that ΔABC translates to ΔA'B'C', we can assume that the measures of the angles are the same in both triangles. Therefore, if we know the measure of an angle in one triangle, we can assume that the measure of the corresponding angle in the translated triangle is the same.

Given:

m∠A = y

m∠A' = 2x + 5

m∠C = 3x-y

m∠C' = 4

Since opposite angles in a rectangle are congruent, m∠A=m∠C' and m∠C = m∠A'

Therefore,

y = 4

3x-y = 2x + 5

Solving this equation gives us:

x = y + 5 = 4 + 5 = 9

y=4

m∠C = 3x - y = 3(9) - 4 = 25

m∠A' = 2x + 5 = 2(9) + 5 = 23

Hence, the value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.

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Step-by-step explanation:

1

We can see that RS divides ∆PQS into two equal parts

So,

PR = RQ

Therefore

RQ = 5.1

Now

PQ = PR + RQ

=> PQ = 5.1 + 5.1

=> PQ = 10.2

2

Here

KM is the angle bisector

So

JM = ML

JM = 46

(1). ΔIJH ≅ ΔKHJ, by SSS criterion,

and (2) we need,  ΔTNS and ΔUHS are right-triangles and S is the mid-point to prove  ΔTNS ≅ ΔUHS, by HL criterion.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

We have the triangle:

ΔIJH ≅ ΔKHJ.

To prove the congruent by SSS:

We have to show that three sides of the triangle are congruent to three sides of  the other triangle.

Here,

IJ ≅ KH.

IH ≅ JH, Given.

And both triangles share the same side JH.

So,

JH ≅ JH

So, ΔIJH ≅ ΔKHJ, by SSS criterion.

ΔTNS ≅ ΔUHS.

To prove the congruent by HL:

We have to show that the triangles are right-triangle and one leg and hypotenuse of the triangle is congruent to one leg and hypotenuse of the other triangle.

So, we need;

ΔTNS and ΔUHS are right-triangles.

S is the mid-point.

So,

SN ≅ SH.

ST ≅ US

So, ΔTNS ≅ ΔUHS, by HL criterion.

Therefore, ΔIJH ≅ ΔKHJ, by SSS criterion and we need;

ΔTNS and ΔUHS are right-triangles and S is the mid-point.

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Answer:

8.5

Step-by-step explanation:

there's a rule to get the distance between 2 points

√((1st x- 2nd x)²+(1st y- 2nd y)²)

√((-6-(-6))²+(5-(-3.5))²)

=√((-6+6))²+(5+3.5))²)

you can just type that on your calculator and you'll get the result

√((-6+6))²+(5+3.5))²)

=√((5+3.5))²)

= √((8.5))²)

the root goes away with the power (exponent)

so it equals 8.5

The proof that the angles m<1 = m<4 is shown below

From the question, we have the following parameters that can be used in our computation:

Measure of angles

The angle measurements are then given as

m<1 + m<2 = 90 and m<3 + m<4 = 90

The relationship to prove is also given as

m<1 = m<4

Using the above as a guide, we have the following:

Subtract the equations m<1 + m<2 = 90 and m<3 + m<4 = 90

This gives

m<1 + m<2 = 90

-(m<3 + m<4 = 90)

Evaluate the difference

m<1 + m<2 = m<3 + m<4

When both sides of the angle equations are compared, we have:

m<1 = m<4

m<2 = m<3

Ignoring the second equation, we have

m<1 = m<4

Hence, the measure of the angles has been proved

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Step-by-step explanation:

please refer to sketch for detail

A'(-2, -3) would result if A (2, -3) was reflected over the x axis. Point (2,3)'s representation under the x-axis is (2,-3). from the y-axis P image (-a,b).

Changing the sign of the value on the opposite axis, in this case the y-value, is all that is required to reflect a point such as (-2,3) across the x-axis in a question. As a result, this location has a y-value of 3. A positive number, this. A negative sign produces a result of -3.

While the Y coordinate remains the same when you reflect across the Y-axis, the X coordinate changes sign. Determining the reflection of (2, 3) across the Y-axis is therefore (-2, 3). The Y-coordinate of each point must be negative while reflecting across the X axis, but the X value must remain constant.

Therefore the correct answer is option a ) A'(-2, -3)

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Answer:

- 4s - q + r

Step-by-step explanation:

that's right. You do not put the p since 3p and -3p cancel out to give zero. I'll solve the question for you:-

⇒3p-3p+2s-6s+2q-3q+8r-7r

add or subtract the like terms(terms having same variables), then out of the two like terms, put the sign of the greater number, for e.g. 2q-3q = -1q

⇒0 - 4s - 1q + 1r

⇒- 4s - q + r Answer

hope that helps...

After constructing the frame of the sides 5.25 and sandbox, there is 10 inches of wood left over.

A square is a closed, two-dimensional shape that has four equal sides and four vertices. Parallel to one another are its opposing sides. A square is also equivalent to an equal-length and-width rectangle. A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is a two-dimensional shape with four equal-length sides. A square's opposing sides are parallel to one another, and its four internal angles are all right angles.

given,

The total amount of wood.

= 4 x 65.5

= 262 inches.

Frame:

Side = 5.25 inches

The perimeter of the frame.

= 4 x 5.25

= 21 inches

Now,

Sandbox:

The wood used for the sandbox.

= 11 x 21

= 231 inches

The remaining wood.

= 262 - (21 + 231)

= 262 - 252

= 10 inches

The wood left over after making the frame of sides 5 .25 inches and the sandbox is 10 inches.

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Answer:

12 bananas

9 apples

18 pears

Step-by-step explanation:

You are tripling the recipe.

10 x 3 = 3

4 x 3 = 12

3 x 3 = 9

6 x 3 = 18

The present value of the tax benefits from depreciation which is a non cash expenditure under capital budgeting decisions is $10432.80

According to the prudence concept of accounting convention, Depreciation is a non cash expenditure that has been charged against the profit. Depreciation is value that amortized over useful life of tangible fixed asset. The absolute decline in the value of asset due to obsolesce, usage of asset, wear & tear of fixed asset is referred as depreciation.

As per accounting standard on property, plant & equipment depreciation can be computed by straight line method and written down value method.

While analyzing the capital budgeting decision from the equipment to be acquired the cash inflows and outflows during the currency of the project shall be accounted for.

The tax benefit from depreciation expenses will be consider as cash inflow. The same shall be calculated by the present value annuity factor for the as follows:

cost of capital = 12 %

Depreciation = $10000

Life of the project = 8 years

Tax rate = 21%

Present value annuity factor (PVAF) at 12% for 8 years will be:

0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404

Grand total of the (PVAF) at 12% = 4.968

Now multiply the PVAF with depreciation amount

Present Value of Depreciation = 4.968 × 10000 = $49,680

Tax benefit from depreciation = $49,680 × 21% = $10432.8

Thus the tax Tax benefit from depreciation is $10432.80

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Answer

A(-10, 9), A'(-4, 9)

B(-4, 2), B'(-10, 2)

C(-7, 9), C'(-7, -4)

Example 3:

A(-3, 5), A'(3, 5)

B(-3, 0), B'(3, 0)

C(-3, 5), C'(-3, -10)

Exact Circumference = 4pi feet

Approximate Circumference = 12.56 feet (when using pi = 3.14)

======================================================

Explanation:

The larger circle has a 3 foot radius.

The inner circle has a 3-1 = 2 foot radius.

Let's find the circumference of the smaller inner circle, which represents the glass window and ignores the metal frame surrounding it.

C = 2pi*r

C = 2pi*2

C = 4pi

The exact circumference is 4pi feet. This is the perimeter around the circle.

If you wanted, you can use an approximation like pi = 3.14 to find that 4pi = 4*3.14 = 12.56 feet is the approximate circumference.

Check the picture below.

Answer:

No Solutions

Step-by-step explanation:

Hello!

We can solve for a by isolating the variable.

Since -29 cannot be equal to -9, there are no solutions for this equation.

The equation of the line is y = 4x + 1 , where the slope of the line is m = 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the number of blocks be y

Let the stage number be x

Let the first point be represented as P = P ( 1 , 5 )

Let the second point be represented as Q = Q ( 2 , 9 )

Now , the slope of the line between the points be

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 9 - 5 ) / ( 2 - 1 )

Slope m = 4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = 4 ( x - 1 )

On simplifying the equation , we get

y - 5 = 4x - 4

Adding 5 on both sides of the equation , we get

y = 4x + 1

Therefore , the value of A is y = 4x + 1

Hence , the equation of line is y = 4x + 1

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Step-by-step explanation:

a) x+20+x+90=180 [sum of 3 angel of triangle]

2x + 110 = 180

2x = 180- 110

2x = 70

x = 70÷2

x = 35

b) 2y + y + y = 180

4y = 180

y = 180÷4

y= 45

c) 4z-30 + 2z = 180

6z = 180 + 30

6z = 210

z = 35