find the slope of the lines that passes through the points (1, -4) and (3, -1)​

Sue's statement is incorrect. The decrease in length by 15% and width by 10% does not necessarily result in a 25% decrease in the perimeter of the rectangle.

When the length of the rectangle decreases by 15%, it becomes 60 cm - (15% of 60 cm) = 60 cm - 9 cm = 51 cm. Similarly, when the width decreases by 10%, it becomes 40 cm - (10% of 40 cm) = 40 cm - 4 cm = 36 cm.

The new perimeter of the rectangle can be calculated as 2 * (length + width) = 2 * (51 cm + 36 cm) = 2 * 87 cm = 174 cm.

Comparing this to the original perimeter of 2 * (60 cm + 40 cm) = 2 * 100 cm = 200 cm, we find that the new perimeter is 174 cm, which represents a decrease of (200 cm - 174 cm) / 200 cm ≈ 13%. Therefore, the actual decrease in the perimeter is approximately 13%, not 25% as Sue claimed.


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Step-by-step explanation:

Simple

Total no of marbles = 6 + 4 + 8 = 18

Probability of red marble = 6 / 18 = 1/ 3

Answer:

A ) -5

B) -4

C) -9

D) -12

\( \)

The general form of the equation of the circle is\(x^2 + y^2 + 4x - 2y - 4 = 0\). The general form of the equation of a circle is given by

\((x - h)^2 + (y - k)^2 = r^2\)  where (h, k) represents the center of the circle, and r represents the radius.

To rewrite

\(x^2 + y^2 + 4x - 2y - 4 = 0\)

into the general form, we need to complete the square on x and y terms. So, we will start by grouping the x and y terms separately as shown below:

\(x^2+ 4x + y^2 - 2y - 4 = 0\)

Rearranging terms, we have

\((x^2 + 4x) + (y^2 - 2y) = 4\)

Now, we complete the square on the x-term as follows:

\((x^2 + 4x + 4) + (y^2 - 2y) = 4 + 4= 8\)

Simplifying, we have

\((x + 2)^2+ (y - 1)^2 = 8\)

which is in the general form of the equation of a circle as required. Therefore, the center of the circle is (-2, 1) and its radius is

\(\sqrt{8} = 2\sqrt{2} .\)

The standard form of a circle is

\((x-a)^2 + (y-b)^2 = r^2\)

, where the center is (a, b) and the radius is r. In order to derive the general form of a circle, we square the terms on the left-hand side to get \(x^2 + 2ax + a^2 + y^2 + 2by + b^2 = r^2.\)

By rearranging the terms, we arrive at

\(x^2 + y^2 + 2ax + 2by + (a^2 + b^2 - r^2) = 0\).

The coefficients of x and y in this equation are used to find the center of the circle, while the radius is obtained by taking the square root of

\((a^2 + b^2 - r^2).\)

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The location of the treasure on the treasure map is (b) (7.6,8.8)

The ratio is given as:

\(m : n = 5 : 9\)

The coordinates of the rock and the tree are:

\(Rock =(3,2)\)

\(Tree = (16,21)\)

The x and y coordinates of the location of the treasure are:

\((x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\)

So, we have:

\((x,y) = (\frac{5 \times 16 + 9 \times 3}{5 + 9},\frac{5 \times 21 + 9 \times 2}{5 + 9})\)

\((x,y) = (\frac{107}{14},\frac{123}{14})\)

\((x,y) = (7.6,8.8)\)

Hence, the location of the treasure is (b) (7.6,8.8)

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The solution set to the given inequality is

(-∞, -4) U (2,∞)

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

5(x – 2)(x + 4) > 0

First we solve for x, we replace the inequality sign by = sign

5(x – 2)(x + 4) = 0

Divide both sides by 5

(x – 2)(x + 4) = 0

Now we set each factor =0  and solve for x

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we use number line and make three intervals

First interval -infinity to -4

second interval -4 to 2

third interval 2 to infinity

Now we check each interval with our inequality

First interval -infinity to -4, pick a number in this interval and check with our inequality. lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

second interval -4 to 2, pick a number in this interval and check with our inequality. lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval 2 to infinity, pick a number in this interval and check with our inequality. lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

solution set are the intervals that make the inequalities true

(-∞, -4) U (2,∞)

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Question:

What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

Option A is the correct answer because the missing step in the two column proof is;

Statement: XW/UT = XV/UV Reason: Corresponding sides of similar triangles are proportional

Similar triangles are defined as triangles that have the same shape, but then their sizes may vary. Thus, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Now, we see from the two column proof that ΔTVU ∼ ΔWVX. This means that corresponding sides of both triangles are proportional or have corresponding proportions.

Thus, we can say that;

XW/UT = XV/UV

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There are 97 people who rent umbrellas.


Step 1: Find the number of people who rent only chairs.
Since there are 72 people who rent both chairs and umbrellas, there must be 125 - 72 = 53 people who rent only chairs.

Step 2: Find the total number of people who rent only chairs or only umbrellas.
Since there are 150 customers in total, there must be 150 - 72 = 78 people who rent either only chairs or only umbrellas.

Step 3: Find the number of people who rent only umbrellas.
Since we know that 53 people rent only chairs from Step 1, there must be 78 - 53 = 25 people who rent only umbrellas.

Step 4: Find the total number of people who rent umbrellas.
Since there are 72 people who rent both chairs and umbrellas and 25 people who rent only umbrellas, there are 72 + 25 = 97 people who rent umbrellas.

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Answer:

17.5%

Step-by-step explanation:

1879/10730=17.5%

Answer:

18%

Step-by-step explanation:

Locate the "receives aid" column and "graduate" row. The value 1879 is in this row and column combo.

There are 10730 students total as shown in the bottom right hand corner.

Roughly 1879/10730 = 0.1751 = 17.51% of the students are graduates who receive aid. This rounds to 18%

The required side length of the variable "x" is 12.8 units for the given figure.

When a line parallel to one side of a triangle intersects the other two sides in distinct spots, the other two sides are separated in the same ratio.

As we can see that both are similar quadrilaterals,

According to Thales's Theorem,

5:8 = 8:x

So, 5/8 = 8/x

Apply the cross-multiplication, and we get

5x = 8 × 8

x = 64/5

Apply the division operation, and we get

x = 12.8

Thus, the required side length of the variable "x" is 12.8 units.

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Answer:

Step-by-step explanation:

5, 5, 5, 16, 16, 28, 29, 32, 35, 48

Mode: 5, 16

Median: 44/2 = 22

range: 48 - 5 = 43

mean: (5 + 5 + 5 + 16 + 16 + 28 + 29 +32 + 35 + 48)/10 = 219/10 = 21.9

Answer:

245, 3, 453

Step-by-step explanation:

-11 squared = 121

121 multiplied by 2 = 242

242 + 3 = 245

0 squared is 0

0 multiplied by 2 = 0

0 + 3 = 3

15 squared is 225

225 multiplied by 2 = 450

450 + 3 = 453

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9514 1404 393

Answer:

  (-5,1)

Step-by-step explanation:

To eliminate x, multiply the first equation by 3 and add 2 times the second equation.

  3(-2x +7y) +2(3x -4y) = 3(17) +2(-19)

  -6x +21y +6x -8y = 51 -38

  13y = 13

  y = 1 . . . . . matches the third answer choice

  (x, y) = (-5, 1)

Answer:

Solution given:

\( \frac{1 + {4}^{2} \times 3}{7} \)

\( \frac{1 + 16 \times 3}{7} \)

\( \frac{1 + 48}{7} \)

\( \frac{49}{7} \)

7 is a required expression.

Answer: 0.25 or 25%

Step-by-step explanation: The probability of getting heads in a coin flip is 0.5, or 50%. In order to account for the two times we flip the coin, we multiply that by two. 0.5(2)=0.25 or 25%.

Step-by-step explanation:

Two flips has  2^2 = 4 possible outcomes

  ONE of which is   Heads - Heads

    one out of 4     =   1/4 = .25

H H

H T

T H

T T

Answer:

step one is the identitey  property step 2 is the communative property step 3 is the associative property

Step-by-step explanation:

The given equations of planes are: 15x - 3y + 12z = 2  & 2y = 10x - 8z

To determine whether these planes are parallel, perpendicular or neither, we need to compare the normal vectors of the planes. The normal vector of a plane is given by the coefficients of x, y and z in the equation of the plane.

The normal vector of the first plane (1) is [15, -3, 12] and the normal vector of the second plane (2) is [10, 2, -8/2] = [10, 2, -4].

Now, to check if the planes are parallel or perpendicular, we can take the dot product of the normal vectors. If the dot product is 0, then the planes are perpendicular, and if it is non-zero, then the planes are parallel.

The dot product of the normal vectors of the given planes is:

[15, -3, 12] · [10, 2, -4] = (15)(10) + (-3)(2) + (12)(-4) = 0

Since the dot product is zero, the planes are perpendicular to each other.

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According to the question we have the solution of the  given differential equation initial value problem is: g(x) = (3/4)x^4 - x + 9/4 .

To solve the given initial value problem, we need to integrate both sides of the differential equation. We have:

g'(x) = 3x(x^2 - 1/3)

Integrating both sides with respect to x, we get:

g(x) = ∫[3x(x^2 - 1/3)] dx

g(x) = ∫[3x^3 - 1] dx

g(x) = (3/4)x^4 - x + C

where C is the constant of integration.

To find the value of C, we use the initial condition g(1) = 2. Substituting x = 1 and g(x) = 2 in the above equation, we get:

2 = (3/4)1^4 - 1 + C

2 = 3/4 - 1 + C

C = 9/4

Therefore, the solution of the given initial value problem is:

g(x) = (3/4)x^4 - x + 9/4

In more than 100 words, we can say that the given initial value problem is a first-order differential equation, which can be solved by integrating both sides of the equation. The resulting function is a family of solutions that contain a constant of integration. To find the specific solution that satisfies the initial condition, we use the given value of g(1) = 2 to determine the constant of integration. The resulting solution is unique and satisfies the given differential equation as well as the initial condition.

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30 is the correct value of the expression in linear equation .

What in mathematics is a linear equation?

The error starts from here- 36-10 + 4

If we are doing addition or subtraction start from left

=36−10+4

=26+4

= 30

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Answer:

See explanation

Step-by-step explanation:

The discriminant is \({b^{2}-4ac }\)

1. 9² - 4(1)(20) = 81 - 80 = 1 so there are 2 solutions

2. (-9)² - 4(3)(-13) = 81 + 156 = 237, so there are 2 solutions

3. The first answer is correct

4. The third answer is correct

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer: x = 4/3 or x = 1.3 or x = 1 1/3

Step-by-step explanation: you have to move everything that does Not have A Variable to the right and solve the equation

9x + 12 = 24

9x = 24 - 12

    = 12

x = 12/9

I am confused too. This is the best I can do :(

Answer:

add 21 to both sides to get everything on one side

x^2 - 10x + 21 = 0

do factorization, guess and check

(x - 7) (x -3) = 0

x =7, and x =3

Answer:

x= 7,3

Step-by-step explanation:

Move all terms to the left side and set equal to 0. Then set each factor = to 0

Hope this helps please make me brainliest!

Answer: The value of x in trapezoid ABCD is 15

Step-by-step explanation: The trapezoid as described in the question has two bases which are AB and DC and these are parallel. Also it has sides AD and BC described as congruent (that is, equal in length or measurement). These descriptions makes trapezoid ABCD an isosceles trapezoid.

One of the properties of an isosceles trapezoid is that the angles on either side of the two bases are equal. Since line AD is equal to line BC, then angle D is equal to angle C. It also implies that angle A is equal to angle B.

With that bit of information we can conclude that the angles in the trapezoid are identified as 3x, 3x, 9x and 9x.

Also the sum of angles in a quadrilateral equals 360. We can now express this as follows;

3x + 3x + 9x + 9x = 360

24x = 360

Divide both sides of the equation by 24

x = 15

Therefore, in trapezoid ABCD

x = 15  

Answer:

x=15

Step-by-step explanation:

Answer:

equal parts of this story is the order I am the first thing to say about this

Answer:

The toy falls at a rate of at least a Negative one-half meter per second.

Step-by-step explanation:

Answer:

the awnser is a or the pool is 1 meter deep

Step-by-step explanation:

i am smart and i got it right when i did it

4.208 + 2.482= 6.69 so rounding that would be 7                                      

4.208 + 2.482 = 6.69

When we round it to the nearest, it becomes 7.

Hope it helps you..

Answer:

1/6, 1/13, and 2

Step-by-step explanation:

The reciprocal of a number is simply "1" divided by that number.

Reciprocal of 6 = 1/6

Reciprocal of 13 = 1/13

Reciprocal of 1/2 = 2

Therefore, the reciprocals of 6, 13, and 1/2 are 1/6, 1/13, and 2

Hope this helps!

Answer:

1/6, 1/13, 2

Step-by-step explanation:

The reciprocal of a number is the inverse of that number.

6 is the same as 6/1, and the inverse (formed by basically flipping the fraction) is 1/6

Then, for 13, we can do the same thing. 13/1 inverted is 1/13, and 1/2 inverted is 2/1, or just 2.

Hope that helps :)