-6+ (-20) + (-40) + 3d

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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The cost of the paint needed to give the entire wall a good coverage of paint is $22

Firstly, we need to calculate the equivalent areas

Mathematically, we know that 1 ft is 12 inches

So to calculate the area of the wall in square inches, we have;

Now let us calculate the area of the test;

We have this as;

Now, we know that1 ounce is okay for the test, the number of ounces okay for the main wall would be;

So, 100.60 ounces of paint would be enough to cover the wall

Finally, we proceed to get the cost of this as follows;

Mathematically, 1 ounce is 0.0078125 gallons

So, the number of ounces would be;

From the question, the cost per gallon is $28

So, the cost in 0.786 gallons would be;

According to the z-score distribution table, we find out that the p-value is 0.0752 for the given test statistic of z = 1.438 which is accurate to four decimal places.

It is given to us that -

A study is conducted to see if the probability of catching the flu this year is significantly more than 0.23

The sample data produces the test statistic

The value of z = 1.438

We have to find out the p-value accurate to four decimal places.

We know that the p-value is known as the decimal value which can be expressed from 0 to 100%. This p-value is important in hypothesis testing in order to establish the significance of the results expected.

We are given that the test statistic, z = 1.438 and we know that this is a two-tailed test.

So, we can obtain the p-value from the z distribution table.

P-value = 2P (Z<1.438)

=> P-value = 0.0752       [Value from z-score table]

Thus, from the z-score distribution table, we find out that the p-value is 0.0752 which is accurate to four decimal places.

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Answer:

1) 2.009

2) 2.098

3) 2.90

Step-by-step explanation:

Answer:

2.098, 2.009, 2.90

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

Step-by-step explanation:

The domain includes all x values, and here, it is [-2, 4].

The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

\(P(C\ or\ D) = 1\)

Step-by-step explanation:

Given

\(P(C) = \frac{3}{7}\)

\(P(D) = \frac{4}{7}\)

Required

\(P(C\ or\ D)\)

Since the events are mutually exclusive, then:

\(P(C\ or\ D) = P(C) + P(D)\)

So, we have:

\(P(C\ or\ D) = \frac{3}{7} + \frac{4}{7}\)

Take LCM

\(P(C\ or\ D) = \frac{3+4}{7}\)

\(P(C\ or\ D) = \frac{7}{7}\)

\(P(C\ or\ D) = 1\)

Answer:

I can try to help!

(:

Step-by-step explanation:

Answer: d. 25

Step-by-step explanation: This is correct because the graph starts at 75 and then jumps to 100. 75 + 25 is 100. This then goes from 100 to 125. Again, 100 + 25 is 125. Finally, it goes from 125 to 150. 125 + 25 equals 150. The final answer is 25 because each time the line increases, it increases by 25.

Let me know if this helped in the comments.

Answer:

Multiplication sorry I late

Step-by-step explanation:

Answer: Multiplication property of equality

The points (-3, 9), (-1, 1), (0, 0), (1, 1) and (3, 9) lie on the graph of the function y = x²

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation y = x²

When x = -3; y = (-3)² = 9

When x = -1; y = (-1)² = 1

When x = 0; y = (0)² = 0

When x = 1; y = (1)² = 1

When x = 3; y = (3)² = 9

The points (-3, 9), (-1, 1), (0, 0), (1, 1) and (3, 9) lie on the graph of the function y = x²

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Answer:

In 28 minutes the car will travel  18.67 miles

in 1 hour the car will travel 40 miles

Step-by-step explanation:

ʕ•ᴥ•ʔ

Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer:

\(\sin(\theta) = \frac{5}{27}\)

Step-by-step explanation:

Given

\(\csc(\theta) = \frac{27}{5}\)

Required

Determine \(\sin(\theta)\)

In trigonometry identity;

\(\sin(\theta) = \frac{1}{\csc(\theta)}\)

So, we have:

\(\sin(\theta) = \frac{1}{\frac{27}{5}}\)

Take inverse of the fraction

\(\sin(\theta) = \frac{5}{27}\)

Answer: 10/40 or 1/4

Step-by-step explanation:

Add up all the amount of rolls, so 10+6+4+8+6+6=40

then add the probability of rolling a 3 or 6 = 10

divide that quantity out of the whole

answer is 10/40 and simplified is 1/4

hope it helps

288 ounces of water are left in the water tank.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots

Here, we have

Given: Tom has a water tank that holds 5 gallons of water. tell me this is water for my footing to fill six bottles they each hold 16 ounces and a picture that holds one over 2 gallons.

1 gallon = 128 ounces, 2 gallon = 256 ounces

6 bottles × 16 ounces = 96 ounces

2 gallon + 96 ounces = 256 + 96 ounces = 352 ounces

5 gallon = 5 × 128 = 640 ounces

= 640 - 352 = 288 ounces

Hence,  288 ounces of water are left in the water tank.

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Answer:

Step-by-step explanation:

22.5q - 40

Notice that the number in in front of the q is +. That's because there are two minus signs multiplied and that makes a plus.

There is only 1 minus sign in front of 2.5 * 16 and that makes 40 minus.

Answer:

14%

Step-by-step explanation:

Answer: 88

The mode is the value that appears most frequently in a data set.

The mode of the given data set will be 88.

The mode is the value that appears most often in a set of data values.

We have,

Data set            100, 98, 95, 92, 88, 85, 80, 75.

Frequency           1,     2,   2,   4,   7,    3,   5,    1

So,

As mentioned in the statement above,

Mode is the value that appears most often in a set of data values.

So,

We can see from the given table

i.e.

Frequency of 88 is maximum,

So,

The mode of the given data is 88.

Hence, we can say that the mode of the given data set will be 88.

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Evelyn needs 123 in. of white ribbon for the 82 in. of blue ribbon, so the white color of ribbon she will run out of the first.

It is a basic operation of arithmetic in which you divide a number into smaller parts.

Given:

Evelyn uses 6 in. of blue ribbon for every 9 in. of white ribbon,

So for 1 in. of blue ribbon, she needs 9 / 6 in. of white ribbon,

And for the 82 in of blue ribbon, she needs 9 / 6 × 82 in. of white ribbon

Hence, she needs 123 in. of white ribbon for the 82 in. of blue ribbon,

Therefore, The white color of ribbon she will run out of the first.

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Answer: x = -3 or if not solving for x then -2x -6

Step-by-step explanation:

1 - 2x - 7 = 0

-6 - 2x = 0

add 2x on both sides

-6 = 2x

divide 2 on both sides

-6/2 = x

x = -3

The weighted average length of a nail from the carpenter's box is 3.5 centimeters.

Different from calculating the average, the weighted average implies considering the frequency or abundance percentage. Now, to calculate the average weighted we will need to multiply the length of each type of nail by the abundance and finally, we will need to add the results obtained. The process is shown below:

Short nail: 2.5 cm x 70.5%= 1.7625 cm

Medium nail: 5.0 cm x (19% = 0.95 cm

Long nail: 7.5 cm x 10.5% = 0.7875 cm

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

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Resolving the expression into a system of linear equations, the value of x and y are 5 and 15 respectively

Expanding the given equation, we get:

\((3x - y)^2 + (x - 5)^2 = 0\\9x^2 - 6xy + y^2 + x^2 - 10x + 25 = 0\\10x^2 - 6xy + y^2 - 10x + 25 = 0\)

To solve for x and y, we need another equation that relates them. However, since the given equation has no real solutions (as the sum of two squares cannot be zero unless both squares are zero), we can conclude that there are no real values of x and y that satisfy the equation.

Alternatively, we could write the given equation as:

(3x - y)² = (5 - x)²

Taking the square root of both sides, we get:

3x - y = ±(5 - x)

Now we have two equations:

3x - y = 5 - x ...eq(i)

3x - y = x - 5 ...eq(ii)

solving for both x and y in the system of linear equations

x = 5 and y = 15

Therefore, the solution to the given equation is:

x = 5, y = 15

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