A triangle has two sides of lengths 5 and 13. What value could the length of
the third side be? Check all that apply.
A. 5
B. 24
C. 8
D. 2
O E. 19
F. 10
>
SUBMIT

Answer:  

Step-by-step explanation:

The degree is 4 the leading coefficient is even/positive.  There are 3 distinct real 0's and 3 relative extreme values

Explanation:

4th degree.   Degree is the highest exponent.  The number of 0's (times it hits the curve)tells you the degree.  The curve goes through the x 2 times, which means 2 x's. Then it bounces off x 1 time which means there are 2 x's there too but because this one bounces off it means it's not a distint solution it's a multiplicity ex (x-3)².  So that accounts for 4 solutions

Even/positive coefficient.  That's the first number in the equation.  Because it's facing up it's a positive but all the ends are both facing up so that tells you it's even.  Think of a parabola that is an even function, this follows those rules too.

3 distinct zeroes.    This is explained in 4th degree.   Zeroes are solutions, when it hits x axis.  Goes through x 2 times and bounces once.  So there are 3 distinct zeroes

3 relative extreme values. This is how many "mini" max and mins you have.  

Using sine law and cosine law, the value of the missing sides are

B = 17.94°, C = 124.03° and c = 403.57m

To solve the missing side, we have to use the sine angle formula.

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

The formula is given as;

a / sin A = b / sin B

A = 38° 18' = 38.03°

Substituting the values into the formula

300 / sin 38.03 = 150 / sin B

sin B = 150 * sin 38.03 / 300

sin B = 0.3080

B = sin⁻¹(0.3080)

B = 17.94°

From the sum of angles in a triangle;

A + B + C = 180°

38.03 + 17.94 + C = 180

C = 124.03°

Using cosine rule;

c² = a² + b² - 2(a)(b)cos C

c² = 300² + 150² - 2(300)(150)cos 124.03°

c² = 162866.422

c = √162866.422

c = 403.57m

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Answer:

68.75 square yards (rounded to the nearest hundredth).

Step-by-step explanation:

To find the area of a right triangle, we can use the formula:

Area = (1/2) * base * height

Given the height of 6 and one fourth yards (6 1/4) and a base of 22 yards, we can calculate the area as follows:

Area = (1/2) * 22 * (6 1/4)

To simplify the calculation, we can convert the mixed fraction 6 1/4 to an improper fraction:

6 1/4 = (4 * 6 + 1) / 4 = 25 / 4

Now we can substitute the values into the area formula:

Area = (1/2) * 22 * (25/4)

Next, we can simplify the expression by multiplying the numbers:

Area = (11/1) * (25/4)

Multiplying the numerators and denominators:

Area = (11 * 25) / (1 * 4)

= 275 / 4

To convert the fraction to a mixed number, we can divide the numerator by the denominator:

275 ÷ 4 = 68 remainder 3

Therefore, the area of the right triangle is:

Area = 68 3/4 square yards or 68.75 square yards (rounded to the nearest hundredth).

Among the options provided, the closest match is "sixty-eight and three fourths yds2".

Answer:

68.75 square yards

Step-by-step explanation:

Alright, so let's assume your phone number has no repeated digits. The first task is to select the first digit of the two-digit number. Since phone numbers don't start with zero, you have 9 choices (1 through 9).

The next task is to select the second digit. Because we've already used one digit, and we're assuming there are no repeats in the phone number, we have 9 choices left (0 and the 8 digits that were not selected first).

That gives us a total of 9 * 9 = 81 possible two-digit numbers.

Now, your phone number has a specific first two digits, right? There's only one such combination that matches your phone number.

So the probability that the two-digit number you've selected matches the first two digits of your phone number is 1 in 81, or 1/81.

Think of it this way, my friend: Imagine you have a bag with 81 marbles, each marble has a unique two-digit number on it. You close your eyes and reach into the bag to pick a marble. The chance that you'll pick out the marble with your phone number's first two digits is just like finding one special marble in a bag of 81. It's quite the quest, isn't it? But that's what makes the game of probability so interesting!

Answer:

see explanation

Step-by-step explanation:

the x- intercepts are the values of x where the graph crosses the x- axis

these occur at x = - 2 and x = 2

then x- intercepts are x = - 2 , x = 2

the y- intercept is the value of y where the graph crosses the y- axis

this occurs at y = 4

then y- intercept is 4

x intercept of a graph is the point(s) of the graph that intersects x-axis , y intercept of a graph is the point(s) of the graph that intersects y-axis .

x and y intersepts vary from graph to graph , a graph may have various x and y intersepts , a graph may have one x and y intersepts , or may don't have none of them , or may have only one of the intersepts

_______________________

In this graph

there are two x intersepts and one y intersept

x intersepts :

( 2 , 0 )

( -2 , 0 )

y intersept :

( 0 , 4 )

The value of y for the right triangle is equal to 48, which makes the first option correct.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

60/x = 36/60 {opposite/hypotenuse}

x = (60 × 60)/36 {cross multiplication}

x = 100

by Pythagoras rule the unlabeled side of the entire triangle is calculated as:

√(100² - 60²) = 80

so;

y/80 = 60/100 {opposite/hypotenuse}

y = (60 × 80)/100 {cross multiplication}

y = 48

Therefore, the value of y for the right triangle derived to be 48.

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The total area of the composite figure is 51.5 square yards

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

The composite figure

The total area of the composite figure is the sum of the individual shapes

So, we have

Surface area = 9 * 2 + 2 * 3 + 1/2 * (3 + 8) * 5

Evaluate

Surface area = 51.5

Hence. the total area of the figure is 51.5 square yards

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The statement about the points (0, 3), (2, 8), (8, 2), and (0, 1) that is true is All but one of the points are in Quadrant I. Option C

The first quadrant, positioned at the upper-right area of the Cartesian plane, involves coordinates that have favorable values for both x and y.

The coordinates (0,3), (2,8), and (0,1) all fall under quadrant I since their x and y values are positive.

The point located in Quadrant IV can be identified as (8, 2) due to its positive x-coordinate and negative y-coordinate.

Hence, it can be said with precision that Quadrant I contains all but one point.

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[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=280 \end{cases}\implies 280=2\pi r\implies \cfrac{280}{2\pi }=r\implies \cfrac{140}{\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{140}{\pi } \end{cases}\implies A=\pi \left( \cfrac{140}{\pi } \right)^2 \\\\\\ A=\pi \cdot \cfrac{140^2}{\pi^2}\implies A=\cfrac{19600}{\pi }\implies A\approx 6238.87~cm^2[/tex]

A preimage includes a line segment with a length of x units and a slope of munits. The preimage is dilated by a scale factor of n.

The length of the corresponding line segment in the image is nx units. The slope of the corresponding line segment in the image is m.

The slope or gradient of a line is described as  a number that describes both the direction and the steepness of the line.

The is very important and tells you how steep a line is, or how much y increases as x increases.

In conclusion, the slope is constant (the same) anywhere on the line.

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Answer:

slope m = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m of the line using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, 2) ← 2 points on the line

m = [tex]\frac{2-3}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]

• Parallel lines have equal slopes

then parallel line will have a slope of - [tex]\frac{1}{3}[/tex]

Answer:

$858

Step-by-step explanation:

You are paying 11 months of rent for 1 year.

11 × $936 = $10,296

The total rent paid in 1 year for 11 months of rent is $10,296.

Divide the total by 12:

$10,296/12 = $858

The monthly amount averages to $858.

The equation of the directrix of the parabola found in part A is [tex]x^2 = -2cy + c^2.[/tex]

The equation of the parabola formed when a cross section is taken through the reflector's central axis is

[tex]y = (1/12)(x - 0)^2 + 0.[/tex]

In this equation, the vertex is at the origin (0, 0) and the coefficient 1/12 determines the shape of the parabola.

The equation implies that the parabola opens upward because the coefficient of [tex]x^2[/tex] is positive.

To find the equation of the directrix, we can use the distance formula. The directrix is a horizontal line that is equidistant from the vertex as any point on the parabola.

Since the parabola is symmetric with respect to the y-axis, the directrix will also be symmetric with respect to the y-axis.

Let's assume that the directrix is a horizontal line with the equation y = c, where c is a constant.

To find the value of c, we need to consider a point (x, y) on the parabola. The distance from the point (x, y) to the directrix y = c should be equal to the distance from the point (x, y) to the vertex (0, 0).

Using the distance formula, the distance from (x, y) to the directrix y = c is given by |y - c|, and the distance from (x, y) to the vertex (0, 0) is given by [tex]\sqrt{(x^2 + y^2)}[/tex]

Setting these distances equal, we have:

[tex]|y - c| = \sqrt{(x^2 + y^2)}[/tex]

Squaring both sides of the equation, we get:

[tex](y - c)^2 = x^2 + y^2[/tex]

Expanding and simplifying the equation, we have:

[tex]y^2 - 2cy + c^2 = x^2 + y^2[/tex]

Simplifying further, we obtain:

[tex]-2cy + c^2 = x^2[/tex]

Rearranging the terms, we get:

[tex]x^2 = -2cy + c^2[/tex]

This equation represents the equation of the directrix of the parabola formed by the reflector.

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The answers to the questions to one significant figure are

a. 4000

b. 2000

c. 10,000

The problem can be solved using calculator

a

= 24 * 65 / 0.37

= 1608 / 0.37

= 4345.946

= 4000 to one significant figure

b. 71 * 8.2 / 0.22

= 2646.364

= 2000 to one significant figure

c. 49.3 * 11.1 / 0.053

= 10325.094

= 10000  to one significant figure

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The estimation of the following numbers rounded to one significant figure are:

a. 4,000

b. 3,000

c. 10,000

[tex] \frac{24 \times 65}{0.37} [/tex]

[tex] = \frac{1560}{0.37} [/tex]

= 4216.216216216216

= 4000 to one significant figure.

[tex] \frac{71 \times8.2 }{0.22} [/tex]

[tex] = \frac{582.2}{0.22} [/tex]

[tex] = 2646.363636363636[/tex]

= 3,000 to one significant figure

[tex] \frac{49.3 \times 11.1}{0.053} [/tex]

[tex] = \frac{547.23}{0.053} [/tex]

[tex] = 10325.09433962264[/tex]

= 10,000 to one significant figure

Significant figures are digits 1 to 9

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Step-by-step explanation:

The quadratic expression f(x) = 2x^2 - 9x - 18 can be factored as (2x + 3)(x - 6). So, the missing values in the given expression (2x + [?])(x - [ ]) are 3 and 6, respectively.

Answer:

(2x + 3)(x -6)

Step-by-step explanation:

2x² -9x -18

2 × -18 = -36

Find factors of -36 which you multiply will give -36 but when same factors are added will give -9.

-12 × 3 = -36

-12 + 3 = -9

2x²-12x +3x -18

2x(x - 6) + 3(x -6)

(2x + 3)(x -6)

The correct option is (a) "If two angles are congruent, then they have the same measure".If a conditional statement and its converse are both true, the statement is said to be biconditional. The biconditional statement is one that can be written in the form “p if and only if q” which means that it is only true when both p and q are true.

The biconditional statement of the given options is "If two angles are congruent, then they have the same measure".

Option a) If two angles are congruent, then they have the same measure is a biconditional statement. This statement is a biconditional because it is true for both its converse and inverse.

If two angles are congruent, they have the same measure and if two angles have the same measure, they are congruent. This statement is true in both directions.

It can be written as:Two angles are congruent if and only if they have the same measure.Therefore, the correct option is (a) "If two angles are congruent, then they have the same measure".

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The kinetic energy of this car is equal to 77160.49 Joules.

In Mathematics, the kinetic energy of a physical object can be calculated by using the following equation (formula):

K.E = 1/2 × mv²

Where:

Note: 50 km/h to m/s = 50 × 1000/3600 = 13.89 m/s

By substituting the given parameters into the formula for the kinetic energy of a physical object, we have the following:

Kinetic energy, K.E = 1/2 × 800 × 13.89²

Kinetic energy, K.E = 400 × 192.90

Kinetic energy, K.E = 77160.49 Joules.

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Complete Question:

An 800 kg car travels at 50 km/h, what will its kinetic energy be?

Answer:

a

Step-by-step explanation:

i did it

The product of 22.12 and 0.6 is indeed 13.272.

To compute the product of 22.12 and 0.6, we can perform the multiplication using the standard algorithm for decimal multiplication.

Multiply the decimal part (the digits after the decimal point) first.

0.12 x 0.6 = 0.072 (Multiply 12 by 6, which gives 72, and then move the decimal point two places to the left.)

Multiply the whole numbers.

22 x 0.6 = 13.2 (Multiply 22 by 6, which gives 132, and then move the decimal point one place to the left.)

Add the results from Step 1 and Step 2.

0.072 + 13.2 = 13.272

Therefore, when multiplying 22.12 by 0.6, the result is 13.272.

To verify the calculation, we can check by using estimation. 22.12 is approximately 22 and 0.6 is approximately 0.6. Multiplying 22 by 0.6 gives 13.2, which is close to our calculated result of 13.272. This further confirms that our multiplication is correct.

Hence, the product of 22.12 and 0.6 is indeed 13.272.

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The solution for the system of equations is (x, y) = B. (3, -5).

The correct option is B. (3, -5).

To find the solution for the system of equations:

{4x + y = 7

{2y + 3 = 3x - 16

We can solve it using the method of substitution or elimination. Let's use the method of elimination:

First, let's multiply the second equation by 2 to eliminate the variable y:

2(2y + 3) = 2(3x - 16)

4y + 6 = 6x - 32

Rearranging this equation, we get:

6x - 4y = 38 ----(1)

Now we have the system of equations:

4x + y = 7 ----(2)

6x - 4y = 38 ----(1)

Next, let's multiply equation (2) by 4 to eliminate the variable y:

4(4x + y) = 4(7)

16x + 4y = 28

Now we have the system of equations:

16x + 4y = 28 ----(3)

6x - 4y = 38 ----(1)

Adding equations (3) and (1) eliminates the variable y:

(16x + 4y) + (6x - 4y) = 28 + 38

22x = 66

x = 66/22

x = 3

Substituting the value of x into equation (2), we can solve for y:

4(3) + y = 7

12 + y = 7

y = 7 - 12

y = -5

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Answer: $204

Step-by-step explanation:

203 plus 195 plus 180 plus 238 equals 816

816 divided by 4 equals 204

203+195=398

398+180=578

578+238=816

816/4=204

The given expression -4x^2 + 2x - 5(1+x) is equivalent to -4x^2 - 3x - 5, not -5 - 5x.

To simplify the expression -4x^2 + 2x - 5(1+x), we can distribute the -5 to the terms inside the parentheses:

-4x^2 + 2x - 5(1+x) = -4x^2 + 2x - 5 - 5x

Next, we can combine like terms:

-4x^2 + 2x - 5 - 5x = -4x^2 + (2x - 5x) - 5

Simplifying further, we have:

-4x^2 + (2x - 5x) - 5 = -4x^2 - 3x - 5

Therefore, the expression -4x^2 + 2x - 5(1+x) is equivalent to -4x^2 - 3x - 5.

It's important to note that when we distribute the -5 to the terms inside the parentheses, we multiply each term by -5. So, the expression becomes -5(1) - 5(x). However, -5(1) simplifies to -5, and -5(x) simplifies to -5x. Hence, the expression simplifies to -5 - 5x.

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The domain of the height function is [0, 2.5]

The range of the height function is [0, 25]

We know that the height is given by the quadratic function:

h(t) = 40t - 16t²

First, the domain. This is the set of possible values of t.

We know that we start at t = 0.

The final value of the domain is t such that the rocket returns to the ground, that is when h = 0.

We can rewrite the function as:

h(t) = 40t - 16t² = t*(40 - 16t)

It is zero when t = 0 (we already know) and when 40 - 16t = 0

Solving the second one we get:

40 - 16t = 0

40 = 16t

40/16 = t

2.5 = t

Then the domain is [0, 2.5]

For the range we need to find the maximum height, we know that the minimum height is h = 0.

The maximum one is when t = (2.5 + 0)/2 = 1.25

Evaluating there we get:

h = 40*1.25 - 16*(1.25)²

h =  25

Then the range is [0, 25]

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Answer: The fuction with the greatest intercept is 0,2

Step-by-step explanation:

None of the answer choices (2,4), (2,-4), (4,2), or (4,-2) are applicable to the function f(x) = 3/(x-4) + 2. The function does not have a center point in the traditional geometric sense. Option E.

he function f(x) = 3/(x-4) + 2 does not have a center in the traditional sense. The concept of a center is typically associated with geometric figures such as circles or ellipses.

The function f(x) = 3/(x-4) + 2 represents a rational function. It does not have a central point or location like a circle, which has a center at (h, k). In this case, we are dealing with a rational expression involving x.

The equation f(x) = 3/(x-4) + 2 describes a vertical shift of the graph of the function 3/(x-4) by 2 units upward. However, this vertical shift does not correspond to a center point.

The function f(x) = 3/(x-4) + 2 does not have a center point. The concept of a center is not applicable in this context as it is commonly associated with geometric figures rather than rational functions. Option E is correct.

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Answer:33

Step-by-step explanation:Range=maximum minus minimum in data set

100 - 67 = 33

Answer:

33

Step-by-step explanation:

67, 88, 90, 98, 100 is the set in order from least to greatest.

Range is the largest number (100) minus the smallest number (67).

100 - 67= 33.

Thus, your answer is 33.

Megan is wrong because the square root of a number can be either smaller or larger, depending on whether the number is less than or greater than 1.

Megan's statement that "when you square root a number, the answer is always smaller" is incorrect.

In fact, the square root of a number can be either smaller or larger than the original number, depending on the value of the number.

To demonstrate that Megan is wrong, let's consider a few examples:

Square root of 4:

The square root of 4 is 2.

In this case, the square root is smaller than the original number.

Square root of 1:

The square root of 1 is also 1.

Here, the square root is equal to the original number.

Square root of 9:

The square root of 9 is 3.

In this case, the square root is larger than the original number.

Square root of 16:

The square root of 16 is 4.

Again, the square root is larger than the original number.

From these examples, we can see that the square root of a number can be smaller, equal to, or larger than the original number.

It depends on the specific value of the number.

Megan's statement oversimplifies the relationship between a number and its square root.

In general, the square root of a number is a value that, when multiplied by itself, gives the original number.

It is not always smaller but rather a value that satisfies the mathematical relationship.

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Answer:

You're multiplying each of those numbers by 3.

Step-by-step explanation:

1 * 3 = 3

3 * 3 = 9

9 * 3 = 27
27 * 3 = 81

81 * 3 = 243

Each number is multiplied by 3.

1 x3=3 -> 3x3=9 -> 9x3=27 -> 27x3=81 and so on.

Happy to help; have a great day! :)

There are 17,576,000 possible license plates that can be issued using this system.

To calculate the number of possible license plates that can be issued using this system, we need to determine the number of options for each character in the license plate.

For the first character, there are 26 letters in the English alphabet. Therefore, we have 26 options for the first character.

Similarly, for the second and third characters, we also have 26 options each.

For the fourth character, there are 10 possible numbers (0-9).

And for the fifth character, we again have 10 possible numbers.

To find the total number of possible license plates, we multiply the number of options for each character together:

Number of possible license plates = Number of options for the first character × Number of options for the second character × Number of options for the third character × Number of options for the fourth character × Number of options for the fifth character

Number of possible license plates = 26 × 26 × 26 × 10 × 10

Calculating this expression gives us:

Number of possible license plates = 17,576,000

Therefore, there are 17,576,000 possible license plates that can be issued using this system.

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