plssss help!!!! Right triangle RST is drawn below. A square is drawn on to each leg of the triangle, and a square is drawn onto the hypotenuse of the triangle. The area of square A is 25 cm² . The area of square B is 144 cm². Determine the length in centimeters of x, the hypotenuse of the right triangle.O 13 cmO 17 cm O 169 cmO 119 cm

Consider that the equation of a line with slope 'm' and y-intercept 'c' is given by,

Consider the given equation of line,

Comparing the coefficient, it is found that the slope of the given line is 3,

Let 's' be the slope of the line which is perpendicular to this line.

Consider that two lines will be perpendicular if their product of slopes is -1,

So the slope of the perpendicular line is given by,

Now, it is given that this line passes through the point (-2,5), so it must satisfy the equation of the line,

Substitute the value of 'c' to get the final equation,

Thus, the required equation of the perpendicular line is x + 3y = 13 .

we know that

In this problem

that means

ANSWER

Option D - The area of this triangle is one-half of that of a square that has area of 12 square units

EXPLANATION

We want to the best description of the area of the triangle given.

To do this, we have to first find the area of the triangle.

The area of a triangle is given as:

Where b = base and h = height

From the diagram, we have that:

b = 4 units

h = 3 units.

Therefore, the area of this triangle is:

Checking through the options, we see that the only correct option is Option D.

This is because the area of this triangle (6 square units) is one-half of that of a square that has area of 12 square units

Given:

Rectangle CARD: {length = 2x-5 and width = 6x+10}

Triangle BEST: {length = 10x+3 and width = 4x-7}

To find the differnce, let's first the perimeter of both.

Perimeter of rectangle CARD: 2(length + width)

= 2(2x - 5 + 6x + 10)

= 2(2x + 6x - 5 + 10)

= 2(8x + 5)

= 16x + 10

Perimeter of triangle BEST: 2(length + width)

2(10x + 3 + 4x - 7)

= 2(10x + 4x + 3 - 7)

= 2(14x - 4)

= 28x - 8

Therfore, the difference between both of them is calculated below:

(28x - 8) - (16x + 10)

= 28x - 8 - 16x + 10

= 28x - 16x - 8 10

= 12x - 18

ANSWER:

12x -

We have to find the probaiblity of winning a split bet in roulette.

Then, we will have 2 numbers that will make us wind the bet out of 37 numbers that make the sample space.

We can then calculate the probability of winning the split bet as the quotient between the number of success outcomes (2) and the number of possible otucomes (37):

We can transform this into the odds of winning by taking into account that if 2 are the success outcomes, then 37-2 = 35 are the failure outcomes.

Then, the odds of winning are 2:35.

We now have to calculate the expected value for a $1 bet.

We know the probabilities of winning and losing, but we don't know the value or prize for winning.

The payout for a split bet is 17:1, meaning that winning a split bet of $1 has a prize of $17.

Then, we can use this to calculate the expected value as:

This means that is expected to win $0.9189 per $1 split bet.

Answer:

Probability of winning: 2/37 ≈ 0.054

Odds of winning: 2:35

Expected value of $1 split bet (17:1 payout): $0.9189

In general, a function f(x) means that the input is x and the output is f(x) (or simply f).

Therefore, in our case, the input is the length of the race and the outcome is the time.

Answer:

1040 × 33.0 =

33,280

tenths= 33.3km\s

Substitute arbitrary values of x for which -10 < h(x) < 10.

In this instance, we can use x = 1, and x = -1

Therefore, the points that fits in the grid in the function h(x) are (1, -0.625) and (-1, 0.625).

Answer:

a) Corresponding

b) Congruent, since they have the same measure.

c) p = 32

d) 90º

Step-by-step explanation:

Corresponding angles:

Two angles that are in matching corners when two lines are crossed by a line. They are congruent, that is, they have the same measure.

Item a:

Corresponding

Item b:

Congruent, since they have the same measure.

Item c:

They have the same measure, the angles. So

3p - 6 = 90

3p = 96

p = 96/3

p = 32

Item d:

The above is 90º, and the below is the same. So 90º

The binomials x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.

Herein we know the x-values of a polynomial such that the expression is equal to zero. Mathematically speaking, these x-values are known as roots and the mathematical expressions that contain them are known as factors, which are represented by binomials of the form:

a · r - b = 0

Where a, b are real coefficients.

If we know that x₁ = 4, x₂ = - 1, x₃ = 3 / 2, then the factors of the polynomials are listed below:

x₁ = 4:

x - 4 = 0

x₂ = - 1:

x + 1 = 0

x₃ = 3 / 2

2 · x - 3 = 0

x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.

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Let's make a diagram to represent the situation

The tower angle is found by using the interior angles theorem

It is important to know that the given directions are about the North axis, that's why we have to draw a line showing North to then find the interior angles on the base of the triangle formed.

To find the distance between the fire and Station B, we have to use the law of sines.

Then, we solve for x

Answer:

H = 32 cm

Explanation:

The area of a cylinder is given by

Now solving for h gives

Now V = 438.08 π and r = 3.7 cm. Putting these values in the above equations gives

which is our answer!

We have the function d, representing the distance from the ground of a person riding on a Ferris wheel:

If we consider the position of the person at t = 0, which is:

This position, for t = 0, will be the same position as when the argument of the sine function is equal to 2π, which is equivalent to one cycle of the wheel. Then, we can find the value of t:

Then, the wheel will repeat its position after t = 60 seconds.

Answer: 60 seconds.

Answer:

Yes

Step-by-step explanation:

The equations need to be in slope intercept form. The first equation is but the second one isn't. Solve the second equation for y to put it in slope intercept form.

x + y = 17

x - x + y = 17 - x

y = -x + 17

To determine if they are parallel the slopes need to be the same.

y = -1x + 3

y = -1x +17

The slope are both -1, so they are parallel

Answer:

Yes

Step-by-step explanation:

Answer:

10.8 hours or 648 minutes

Step-by-step explanation:

1. Find a factor of 15 and 18 kilometers. A similar factor is 3.

2. Find how long it will take the turtle to swim 3 kilometers.

3. Divide 9 by 5 which is how long it takes to swim three hours. (Keep it in a fraction for now)

4.Multiply 9/5 by 6 to get 18 hours; which is 10.8 hours.

Given trhat a car used 15 gallons of gasoline to cover 315 miles.

The expression that will be used to determine the unit rate of miles per gallon of gasoline is:

ANSWER:

You have the following expression:

3x + 2y = 12

the best method to graph the previous expression is by intercepts.

In this case, you make one of the variables zero and solve for the other one. Next, repeat the procedure wi

Two or more expressions with an Equal sign is called as Equation. x is -6 and 7 for equations y = x² + 4x and y = 2x² + 3x - 6

Two or more expressions with an Equal sign is called as Equation.

The given two equations are

y = x² + 4x

y = 2x² + 3x - 6

Let us simplify these equations as below.

x² + 4x-y=0..(1)

2x² + 3x -y= 6..(2)

subtract equations (2) from (1)

x² + 4x-y-2x² - 3x+y=-6

-x² +x=-6

x(-x+1)=-6

x=-6

and -x+1=-6

Subtract -1 from both sides

-x=-7

x=7

Hence solution of x is -6 and 7 for equations y = x² + 4x and y = 2x² + 3x - 6

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Below question can be answered by finding the quotient of :

C. Jared has of an hour left to finish making goodie bags. It takes him of an hour to make each goodie bag. How many goodie bags can he make?

In arithmetic, a quotient is a number obtained by dividing two numbers. A quotient is widely used throughout mathematics and is often referred to as the whole number or fraction of a division or  ratio.

The number we get when we divide a number by another is the quotient. For example,  8 ÷  = 2; here the result of  division is 2, so it is a quotient. 8 is the dividend and  is the divisor.

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Using the combination formula, it is found that:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials. It is used when the order in which the elements are chosen does not matter.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In the context of this problem, we have that seven tablets are chosen from a set of 28 tablets, hence the number of selections that can be made is given by:

[tex]C_{28,7} = \frac{28!}{7!21!} = 1,184,040[/tex]

For two defective tablets, the selections are given as follows:

Hence the number of selections is calculated as follows:

[tex]C_{23,5}C_{5,2} = \frac{23!}{5!18!} \times \frac{5!}{2!3!} = 336,490[/tex]

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start at 4 on the positive y axis, then go up 3 and 5 to the left

All real numbers (In interval form (-∞,∞) )

Given,

From the graph,

To find the domain of the function.

Now,

We know that a domain of a function is the set of the all the x-values for which the function is defined.

By looking at the graph of the function we see that it is a graph of a upward open parabola and the graph is extending to infinity on both the side of the x-axis this means that the function is defined all over the x-axis i.e. for all the real values.

Also, we know that the function will be a quadratic polynomial since the equation of a parabola is a quadratic equation and as we know polynomial is well defined for all the real value of x.

The domain of the function is:

Hence,  All real numbers (In interval form (-∞,∞) )

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We have to write the equation of the line that passes through (0,7) and (4,2) in point-slope form.

We start by using the points to calculate the slope m:

Then, if we use point (0,7), we can write the equation in point-slope form as:

Answer: the equation is y = -(5/4)*x + 7

The given expression is

Let's replace z = 12.8.

Using the normal distribution and the central limit theorem, it is found that:

a) The distribution is approximately N(145, 1.71).

b) P(143 < X < 148) = 0.8389.

c) The 70th percentile of the distribution is of 145.90 minutes.

d) The median is of 145 minutes.

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In the context of this problem, the parameters are defined as follows:

[tex]\mu = 145, \sigma = 12, n = 49, s = \frac{12}{\sqrt{49}} = 1.71[/tex]

The distribution of sample means is approximately:

N(145, 1.71) -> Insert the mean and the standard error.

The normal distribution is symmetric, hence the median is equal to the mean, of 145 minutes.

For item b, the probability is the p-value of Z when X = 148 subtracted by the p-value of Z when X = 143, hence:

X = 148:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (148 - 145)/1.71

Z = 1.75

Z = 1.75 has a p-value of 0.9599.

X = 143:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (143 - 145)/1.71

Z = -1.17

Z = -1.17 has a p-value of 0.1210.

Hence the probability is:

0.9599 - 0.1210 = 0.8389.

The 70th percentile is X when Z has a p-value of 0.7, so X when Z = 0.525, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

0.525 = (X - 145)/1.71

X - 145 = 0.525(1.71)

X = 145.90 minutes.

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Answer

Expected number of paintings that a randomly chosen exhibit has = 40.3

Explanation

The expected value of any distribution is calculated as the mean of that distribution.

The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.

Mean = (Σx)/N

x = each variable

Σx = Sum of the variables

N = number of variables

Σx = (9 × 2) + (21 × 1) + (40 × 1) + (46 × 3) + (52 × 1) + (67 × 2)

Σx = 18 + 21 + 40 + 138 + 52 + 134

Σx = 403

N = 2 + 1 + 1 + 3 + 1 + 2 = 10

Mean = (Σx)/N

Mean = (403/10) = 40.3

Hope this Helps!!!

The graph is

its a upword parabola and vertex of graph is (0,1)

the point on a graph x=-2

so graph of function is :

(B)

the coordinate of graph then x=1

the value of y is 2 then value of x=1

Answer:

The number of boys in the school is;

Explanation:

Given that the ratio of boys to girls in a school is 5:4;

And there are 500 girls in the school.

The number of boys in the school will be;

Therefore, the number of boys in the school is;

A matrix being in row echelon form means that Gaussian elimination has operated on the rows.

A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions:

- It is in row echelon form.

-The leading entry in each nonzero row is a 1 (called a leading 1).

-Each column containing a leading 1 has zeros in all its other entries.

The matrix presented on the problem satisfies all conditions, therefore, the matrix is indeed in reduced row-echelon form.

ANSWER

g'(0.1) = 4

EXPLANATION

As stated, g(x) is a composition of two functions: f(x) and 2x. To find its derivative, we have to use the chain rule,

So, the derivative of g(x) = f(2x) is twice the derivative of f(x) and, therefore,

Hence, g'(0.1) = 4.