18. Find the measure of angle STP.

The sum of all angles in a triangle = 180 degree

So :

Angle x + Angle 5x + 72 = 180

x + 5x + 72 = 180

6x = 180 - 72

6x = 108

Divide both side by 6 :

6x/6 = 108/6

x = 18

x = 18

since all the angles are less than 90 degree so the triangle is an acute triangle,

as 5x = 90 thus one angle is of 90 degree

Thus triangle is Acute Right angle triangle

Answer : x = 18, acute right angle triangle

Answer is 35 degrees

Step-by-step explanation:

Y=4(5)-9

=11

you must follow the formula given

Answer:

y=11

Step-by-step explanation:

y=mx-b

mx-b=y

4 * 5 - 9 = y

20 - 9 = y

11 = y

An open circle is used to represent x > 4 as we do not want to include 4 in our solution set.

Treat the <, ≤, >, or ≥  as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.

Using the open instructions when we plot the inequality we see that x > 4 has an open circle at 4.

This indicates that we do not want to include 4 in our solution set.

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The length of A'B' = 5 units

The line segment AB is of 5 units. AB is then transformed through translation of 3 units to the right.

The translation only means change through a straight line. This transformation does not change the length of a line segment.

So the length of A'B' will also be 5 units.

But the position of A'B' will be different from that of AB on the co-ordinate plane. To be exactly, A'B' would be 3 units right to the position of AB on the co-ordinate plane.

Also the co-ordinates of A'B' will be different. Still their lengths will be same.

Thus the length of A'B' = 5 units

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Answer:

8x+7

Step-by-step explanation:

Use the given functions to set up and simplify  

(f+g)(x)

Answer:

8x + 7

Step-by-step explanation:

(f+g)(x)= f(x) +g(x) = 3x + 10 + 5x - 3 = 8x + 7

seen you with ur ex

Answer:

300 in.³

Step-by-step explanation:

We find the volume of 1 prism and multiply it by 2.

V = BH

where V = volume of prism, B = area of the base of the prism, H = height of the prism

V = ½bh × H

V = ½(5 in.)(6 in.) × 10 in.

V = 150 in.³

That is the volume of one triangular prism. Now we multiply it by 2.

volume = 2 × 150 in.³ = 300 in.³

The minimum score required to be considered as a part of the 2% is 99.7

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

Mean = 100

Standard deviation = 15

Error percentage = 2%

The minimum score is calculated as

Minimum = Mean - Standard deviation * Error percentage

Substitute the known values in the above equation, so, we have the following representation

Minimum = 100 - 15 * 2%

Evaluate

Minimum = 99.7

Hence, the minimum is 99.7

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Answer:

60 and

x=4

Step-by-step explanation:

Answer:

37cm = 370 millimeters

37cm = 0.37 meter

37cm = 0.00037 kilometers

Step-by-step explanation:

\(1cm = 10 millimeters \\\\1 cm = \frac{1}{100} meter\\\\1cm = \frac{1}{100000} kilometer\\\\\)

37cm = 370 millimeters

37cm = 0.37 meter

37cm = 0.00037 kilometers

Therefore , the solution of the given problem of percentage comes out to be 38 years old is the median age.

In statistics, a "a%" is a figure or statistic that is expressed as a percentage of 100. The words "pct," "pct," but instead "pc" are also not frequently used. However, the sign "%" is frequently used to represent it. The percentage sum is flat; there are no dimensions. Percentages are truly integers because their numerator almost always equals 100. Either the % symbol (%) or the additional term "fraction" must come before a number to denote that it is a percentage.

Here,

The following algorithm must be used to determine the mean age:

=> mean = (all years added together) / (total number of persons)

The representative age for each age group is the age that falls in the middle of the range. With this approach, we can determine the total age as follows:

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

=> 162 + 644 + 924 + 2970 + 4636 + 2688 + 1152 + 1520 + 272.25

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

According to the information provided, there are 460 people in total.

=> mean = 17745.25 / 460

=> mean = 17745.25 / 460

As a result, the average lifespan is roughly 38.552 years.

The age category in this instance with the highest frequency has a midpoint of 38 and a frequency of 122. As a result, 38 years old is the median age.

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Answer: 60 inches in 5 feet

Step-by-step explanation:

5X12=60

Step-by-step explanation:

The roots of the equation 25x^2 + 60x + 37 = 0 can be found using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 25, b = 60, and c = 37. Substituting these values into the formula, we get:

x = (-60 ± sqrt(60^2 - 4(25)(37))) / 2(25)

x = (-60 ± sqrt(3600 - 3700)) / 50

x = (-60 ± sqrt(-100)) / 50

Since the discriminant (b^2 - 4ac) is negative, the roots will be complex conjugates in the form a + bi, where a and b are real numbers. We can simplify the expression by factoring out the square root of -1 as i:

x = (-60 ± 10i) / 50

x = (-6 ± i) / 5

Therefore, the roots of the equation in simplest a + bi form are (-6 + i)/5 and (-6 - i)/5.

Answer:

\(\displaystyle x=-\frac{6}{5}\pm\frac{i}{5}\)

Step-by-step explanation:

Complete the square on LHS and solve for x

\(\displaystyle 25x^2+60x+37=0\\\\25x^2+60x+36=-1\\\\(5x+6)^2=-1\\\\5x+6=\pm i\\\\5x=-6\pm i\\\\x=-\frac{6}{5}\pm\frac{i}{5}\)

There will be  2850 of the 3000 random samples will contain the population mean.

If 95% confidence intervals are computed for each sample, it means that we expect approximately 95% of the intervals to contain the population mean.

In the case of 3000 random samples, we can estimate the number of intervals that will contain the population mean by multiplying 3000 by the percentage of intervals that are expected to contain the mean.

Approximately, 95% of the 3000 random samples will contain the population mean. So, the estimated number of intervals that will contain the population mean is:

Estimated number = 0.95 * 3000 = 2850

Therefore, approximately 2850 of the 3000 random samples will contain the population mean.

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Answer:

5

Step-by-step explanation:

-8x + 25 = -15

                 -25 = -40  then

-40 divide -8 to get 5

Answer: x = 5

The first step of the inverse operation is to subtract 25 on both sides of the equation to cancel out the 25 from the left side:

-8x+25 (-25) = -15 (-25)

-8x = -40

Next, you need to divide -8 on both sides to isolate the variable, which would give you the answer to x. The negatives would cancel out, leaving you with: x = 5

hope that helps :)

Answer:

Step-by-step explanation:

angle L is 106 degrees

x= 2

angle LMK is 37 degrees

its equal, you can check by adding up all the angles to 360 degrees

Answer: B to the 5 power

Step-by-step explanation: hope this helps :)

Answer:

Step-by-step explanation:

Given

b³·b²

=\(b^{3+2} \\\)

=\(b^{5}\)

hope it helps :)

Answer:

12

Step-by-step explanation:

Write down multiples of each number:

3, 6, 9, 12 . . .

4, 8, 12 . . .

6, 12 . . .

The first one they all have is the LCM.

Answer:

12

Step-by-step explanation:

Think of it this way. Simplifying 3, 4 and 6 into their simplest factors:

\(3=3\)

\(4=2*2\)

\(6=3*2\)

6 is a multiple of both 3 and 2, which are both represented by the factors of 3 and 4. Thus, as it is doubled in these, it is not necessary to find the lowest common multiple of the numbers.

Now the LCM can be multiplied with the factors of the remaining numbers:

LCM\(=3*2*2\)

Notice the first two numbers equal 6, the second and third equal 4, and the first only equals 3. This means the three numbers are represented in the LCM.

\(3*2*2=24\)

And that is the LCM, so we are done. QED

Answer: D

Step-by-step explanation: reflecting about the line y=-1, followers by translating 8 units to the right

Answer:

Step-by-step explanation:

Since this is a test/homework I'll give a hint.

For a linear equation, you have no idea what x and y is, but thats ok! The test itself has already given you 4 options, so you can just input the x/y coordinates, and if they fit, good for you! If they don't, you may need to try again. There are other more complex and faster ways, but they are (a) more complex.

Hope this helps!

The missing number is 5. The polyhedron has 5 faces.

Euler's formula for polyhedra states that the number of faces (F), edges (E), and vertices (V) of a polyhedron are related by the equation:

F + V = E + 2

In this case, we are given the number of edges (E) as 9 and the number of vertices (V) as 6.

We need to find the number of faces (F).

Using Euler's formula, we can substitute the given values:

F + 6 = 9 + 2

Simplifying the equation:

F + 6 = 11

Subtracting 6 from both sides of the equation:

F = 11 - 6

F = 5.

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Answer:

0.21

Step-by-step explanation:

Answer:

The correct answer is: A 2-column table with 3 rows. Column 1 is labeled x with entries negative 5, 0, 3. Column 2 is labeled y with entries negative 18, negative 2, 10.

To create the table, you can plug in each value of x into the equation -2 + 4x = y, then simplify to find the corresponding value of y. Here are the steps:

When x = -5:

-2 + 4(-5) = y

-2 - 20 = y

y = -22

When x = 0:

-2 + 4(0) = y

-2 + 0 = y

y = -2

When x = 3:

-2 + 4(3) = y

-2 + 12 = y

y = 10

So the table has 3 rows, with x-values of -5, 0, and 3, and corresponding y-values of -22, -2, and 10.

Answer:

rational

irrational

rational

Step-by-step explanation:

2 × 2 = 4 rational

2 × √2 = 2√2  irrational

√2 × √2 = √4 = 2 rational

Answer:

-6 is the y coordinate

Step-by-step explanation:

False. The given statement is not a valid proof of the theorem because it is circular.

The proof starts with the assumption that there exists an integer k such that n < k < n^2 and then uses this assumption to conclude that the theorem is true. However, this does not actually prove the existence of k, it simply restates the theorem. A valid proof would need to start with some other set of premises and use logical deduction to arrive at the conclusion that such a k exists. The given statement is not sufficient to establish the truth of the theorem.

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