The legs of a right triangle are 3 and 6. Find the length of the hypotenuse

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

y = 4x - 11

Step-by-step explanation:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:

1 = 4(3) + b

1 = 12 + b

-11 = b

Thus, the y-intercept is -11.

Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11

The answer is:

Work/explanation:

First, we will write the equation in point slope:

\(\sf{y-y_1=m(x-x_1)}\)

where m = slope;

(x₁,y₁) is a point on the line.

Plug in the data:

\(\sf{y-1=4(x-3)}\)

Simplify

\(\sf{y-1=4x-12}\)

Add 1 on each side

\(\sf{y=4x-12+1}\)

\(\sf{y=4x-11}\)

Answer:

0.66

Step-by-step explanation:

Because PI=180 degrees

38 degrees= PI/180 degrees x 38 degrees=0.66

Answer:

A. 64

Step-by-step explanation:

In this problem, you're trying to find out what b is.

With the information that you have, you know that the answer will be 16, and your denominator (what you'll be dividing by) is 4. What you got wrong in this was thinking of it as "what times 4 equals 16", to which you got the answer 4 because 4*4=16. But, that's not exactly what you're supposed to be doing.

If we looked at it like that in this problem, you'd have b=4, making the equation then look like 4/4=16. This isn't true because 4/4=1.

Instead, to get the correct answer, you'll be multiplying 4, the denominator, by 16, our solution. With this, you'll get the answer A. 64.

If you have any more questions, feel free to reach out for help.

Answer:

We are given an equation of \(\frac{b}{4} = 16\) and we need to determine what b is.  The way that we would do this is what you did and we would multiply both sides by 4 which would get rid of the 4 in the fraction and this would end up multiplying 16 by 4 giving us \(b=64\).  This would best match with option A which is 64.

Hope this helps!  Let me know if you have any questions

By using the properties of angle, it can be concluded that

\(\angle QPS\) and \(\angle TSP\) are consecutive interior angle

What is angle?

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

\(\angle QPS\) and \(\angle TSU\) are not consecutive interior angle as \(\angle PST\) falls in between

\(\angle QPS\) and \(\angle RSU\) are not consecutive interior angle as \(\angle RSU\) is an exterior angle

\(\angle QPS\) and \(\angle TSP\) are consecutive interior angle

\(\angle QPS\) and \(\angle OPN\) are not consecutive interior angle as \(\angle OPN\) is an exterior angle

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By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

sorry is i m wrong hope this will help you

Step-by-step explanation:

z²-12z+24=0

z²-6x-6z+36-12=0

z(z-6)-6(z-6)-12=0

(z-6)(z-6-12)=0

(z-6)(z-18)=0

either

z-6=0

z=6

or

z-18=0

z=18

Answer:

40 cm

Step-by-step explanation:

57600 is the volume here

Because "was filled with 57600cm of water."

36 x 40 x n = 57600

n = 40

For least amount of fencing, length and width of rectangular area should be 14 feet and 7 feet respectively.

Let us consider length and width are l and w respectively.

Area of rectangular region = l x w

l x w = 98

w = 98/l

Since, no fencing needed along the river.

So, perimeter of rectangular region, P = 2w + l

Substituting the value of w in above expression.

We get,    

P = 2(98/l) + l

= 196 /l + l

For least amount of fencing, perimeter should be minimum

Differentiate perimeter expression with respect to length l.

dP/dl = -196/l^2 +1 =0

l^2 = 196

l= sqrt(196)

l= 14 feet

so, w= 98/14

w = 7

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There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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Answer:

m>11

Step-by-step explanation:

2*(m+3)-(-5+3*m)<0

STEP1:

2 • (m + 3) -  (3m - 5)  < 0

STEP2:

11 - m  < 0

STEP3:

Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

     m-11  > 0

The rate of the passenger's train is given as follows:

60 miles per hour.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

For the passenger train, the equation is given as follows:

v = 240/t.

vt = 240

t = 240/v.

For the freight train, the velocity is 20 miles slower than for the passenger train, hence:

v - 20 = 160/t

v = 160/t + 20.

Replacing the first equation into the second, the rate of the passenger train is obtained as follows:

v = 160v/240 + 20

v = 2v/3 + 20

v/3 = 20

v = 60 miles per hour.

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Answer:

333234

Step-by-step explanation:

333234$ for the next 4 years and the ecvation is 69$+-2$

Answer:

He read 1/3 of the book on the second day

He didn't finish the book in two days.

Step-by-step explanation:

Lets find 3/5 of 5/9

If we said, find 3/5 of x, the answer would be 3/5x.

3/5*x = 3/5x

In the same way, \(\frac{3}{5} *\frac{5}{9} = \frac{15}{45} = \frac{1}{3}\)

He read 1/3 of the book on the second day

Does 5/9 + 1/3 equal to 1?

1/3 = 3/9

5/9 + 3/9 = 8/9

He didn't finish the book in two days.

Hope this helps :)

Have a nice day!

Using the z-distribution, as we have the standard deviation for the population, to test the hypothesis, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

At the null hypothesis, it is tested if the mean time is of 28 minutes, that is:

\(H_0: \mu = 28\)

At the alternative hypothesis, it is tested if the mean time is greater than 28 minutes, that is:

\(H_1: \mu > 28\).

The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

The parameters are:

In this problem, the values of the parameters are given by:

\(\overline{x} = 32, \mu = 28, \sigma = 5, n = 10\)

Hence:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{32 - 28}{\frac{5}{\sqrt{10}}}\)

\(z = 2.53\)

Considering that we have a right-tailed test, as we are testing if the mean is greater than a value, with a standard significance level of 0.05, the critical value is of \(z^\ast = 1.645\).

Since the test statistic is greater than the critical value, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

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Answer:

59/1

Step-by-step explanation:

Answer:

5.6 miles

Step-by-step explanation:

From the question, we can infer that this is an inversely proportionality question.

Let us represent Miles per hour = N

Depth of snow = s

Where k is proportionality constant.

dN/ds = k/s

dN = ds .k/s

Integrating this

∫dN = ∫k/s ds

N = k In s + C

Step 1

We find k

From the question, we are told that:

Given that 20 miles per hour are cleared when the depth of the snow is 2.5 inches

11 miles per hour are cleared when the depth of the snow is 7 inches,

20 = k ln 2.5 + C ..... Equation 1

11 = k ln 7 + C...... Equation 2

11 = k ln 7 + 20 - k ln 2.5

Collect like terms

k ln 2.5 - k ln 7 = 20 - 11

k( In 2.5 - In 7) = 9

k = 9/( In 2.5 - In 7)

k = 9/ -1.0296194172

k = -8.7410938932

Step 2

We find C

20 = k ln 2.5 + C ..... Equation 1

C = 20 - k ln 2.5

C = 20 -(-8.7410938932 In 2.5)

C = 20 + 8.7410938932 In 2.5

C = 20 + 8.0093833208

C = 28.0093833208

Step 3

how many miles of road will be cleared each hour when the depth of the snow is 13 inches

N = k In s + C

= -8.7410938932 ln 13 + 28.0093833208

= -22.420463165 + 28.0093833208

= 5.5889201559

Approximately= 5.6 miles

Therefore, 5.6 miles of road will be cleared each hour when the depth of the snow is 13 inches.

we have the new function

The vertex of this function is the ordered pair (0,3)

The coordinates of the second point

(2,2) ------------> (2,f(2))

Find the value of f(2)

the new coordinates of point (2,2) are (2,13/3)

see the attached figure

Answer:

y intercept = -41/9

Step-by-step explanation:

y = mx + b

y = -1/9x + b

-5 = -1/9(4) + b

-5 = -4/9 + b

add 4/9 to both sides

-45/9 + 4/9 = b

-41/9 = b

the y intercept is equal to -41/9

linear equation: y = -1/9x - 41/9

Answer:

\(B.(2,1)\)

Step-by-step explanation:

The graph shows that Connor traveled a total of seven blocks from his house to the store and then from the store to the bank.

Graph is a data structure used to represent data in a visual way. It is composed of a set of nodes and edges, where each node represents an object and each edge represents a connection between two objects. Graphs can be used to represent a variety of data structures, such as a network of roads, a family tree, or a list of friends. Graphs are powerful tools for understanding complex relationships in data.

It also shows that he stayed at the store and the bank for five and seven minutes respectively. After leaving the bank, he drove the remaining four blocks back home.

The graph also reveals that Connor was driving at a steady pace between the store and the bank and that the total journey time was twenty-two minutes. This time could have been reduced if he had driven faster. However, it is possible that he was being cautious due to the traffic or other conditions.

Overall, the graph provides a visual representation of Connor's journey and his decisions along the way. It also provides insight into his driving habits, as well as his ability to manage his time. Based on this data, it is clear that Connor was able to complete his errands in an efficient manner.

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Answer:

The value of MA in third class lever is always less than one because the load arm is greater than the effort arm.

Step-by-step explanation:

As we know that when the load arm is greater than the effort arm, the mechanical advantage will always be lesser than one, which results in gain in speed.

Answer:

1.99%. (2% rounded)

Step-by-step explanation:

The total number of ways to select 4 children out of 40 is given by the combination formula:

C(40,4) = 40! / (4! * (40-4)!) = 91,390

The number of ways to select 4 girls out of 16 is given by the combination formula as well:

C(16,4) = 16! / (4! * (16-4)!) = 1,820

Therefore, the probability of selecting 4 girls out of the group of 40 children is:

P(4 girls) = C(16,4) / C(40,4) = 1,820 / 91,390 ≈ 0.0199 or 1.99%

So the probability that all 4 helpers will be girls is approximately 1.99%

Hope this helps!.

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.

To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:

Area = (1/2) * a * b * sin(C),

where a and b are the lengths of the two sides adjacent to the given angle C.

In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:

c² = a² + b² - 2ab * cos(C),

where C is the angle opposite side c. Rearranging the formula, we have:

b² = a² + c² - 2ac * cos(C),

b² = 86² + 37² - 2 * 86 * 37 * cos(128°).

By substituting the given values and calculating, we find b ≈ 63.8.

Now, we can calculate the area using the formula:

Area = (1/2) * a * b * sin(C),

Area = (1/2) * 86 * 63.8 * sin(128°).

By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.

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