Find the length of the third side. If necessary, round to the nearest tenth.

The slopes of GH, HI, IJ, and JG include the following:

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope GH = (-3 + 9)/(-4 + 7)

Slope GH = 6/3

Slope GH = 2.

Slope HI = (5 + 3)/(-6 + 4)

Slope HI = -8/2

Slope HI = -4.

Slope IJ = (-1 - 5)/(-9 + 6)

Slope IJ = -6/-3

Slope IJ = 2.

Slope JG = (-9 + 1)/(-7 + 9)

Slope JG = -8/2

Slope JG = -4.

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Option B and option C are true when the blank is filled with the number 16.

What is an equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it contains no "equal to" symbol. It will be regarded as a phrase.

Given options are

A)  8(___ + 3) = 32 + 24

B)  8(2 + 9) = ___ + 72

C) 4(7 + 4) = 28 + ___

D) 8(5 + 6) = 40 + ___

Putting 16 in the blank space:

8(16 + 3) = 32 + 24

8×19 = 56

152 = 56 (False)

Putting 16 in the blank space:

8(2 + 9) = 16 + 72

8×11 = 88

88 = 88 (True)

Putting 16 in the blank space:

4(7 + 4) = 28 + 16

4×11 = 44

44 = 44 (True)

Putting 16 in the blank space:

8(5 + 6) = 40 + 16

8×11 = 56

88 = 56 (False)

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Answer:

487

or

4870

Step-by-step explanation:

(I might not have done it right)

is it 24,354 / 5 or 2,435 / 5?

Because I got 487

But to check an answer you must multiply

When I multiplied 5 x 487 the answer is 2,435

But 5 x 4870 is 24,350

It has to be one of these

Answer:

Step-by-step explanation:

First substitue the coordinates to the equation so

x=9, y=2

you would get

2=-3/7(9) + b

we put b because we are trying to find the new slope

multiply the two numbers above

2=-3/6/7 + b

subtract the whole number from both sides

b= 5/6/7

in equation would be

y= -3/7 + 5/6/7

Let me know if there is an error.

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

The equation \(\frac{5-3-2}{1+4+6+7+8+9}\)  = 0 is true

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.

Using digits 0 to 9, no more than once each.

we want to place them in such a way that the division will be zero.

As we know that a quotient is equal to zero iff the numerator is equal to zero and the denominator other than zero.

So if we put some numbers on the numerator in such a way by adding them gives 0.

So, 5 - 3 - 2 = 0

Use all the other numbers in the denominator.

\(\frac{5-3-2}{1+4+6+7+8+9}\)  = 0

which is true.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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a) The actual distance between towns K and L is: 100 km

b) As shown in the attached file

c) The bearing of town L from town K is 117 degrees.

The scale of the map is given as:

1 cm to represent 50 km

Now, when we measure the distance between K and L on the map, we see that it gives us a distance of 2 cm.

Using the scale of 1 cm: 50 km, we can say that:

Actual distance between towns K and L = (2 * 50)/1 = 100 km

b) Using a compass and it’s 3cm aiming down {South} as seen in the attached photo. Then a line was drawn aiming {South} with a ruler. On the end of the line the (x) point was put there to get the mark.

c) Measuring the angle gives the bearing of town L from town K which is 117 degrees.

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Answer:

6+ 10h =31

Step-by-step explanation:

That's your equation. You have to then subtract six from the six and 31. Which would get you 10h=25. Divide 10 from both sides and get h=2.5. They rented a canoe for 2 and a half hours.

Answer:

Step-by-step explanation:

since its a horizontal parabola opening to the right we use a formula for the directrix

 x=h-p 4p=5/4 p=5

X= -3 v(h,k)=(2,0)

After w weeks, the expression for the total cost of games is 250 + 4000w.

What is Expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1.

As an illustration, while x is a variable raised to the first power, x2 is a variable raised to the second power. An illustration of a constant is 5.

Linear expressions are what the two expressions are. One variable raised to the power of one makes up a linear expression.

250 + 1000g.

Where: g(w) = 4w.

250 + 1000(4w).

250 + 4000w.

Therefore, number of games produced in w weeks is 250 + 4000w.

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The absolute relative percent error for the first derivative approximation with O(h²) is 181.4%, while the O(h¹) approximation yields an error of 19.1%. For the second derivative, both approximations have an error of approximately 4.1%.

To estimate the derivatives of the given function, we can use centered difference approximations. For the first derivative, we can use the formula:

f'(x) ≈ (f(x + h) - f(x - h)) / (2h)

For the second derivative, we can use the formula:

f''(x) ≈ (f(x + h) - 2f(x) + f(x - h)) / (h²)

For h = 0.10, let's calculate the approximations:

Using O(h²) approximation:

f'(2) ≈ (-0.702 - (-0.818)) / (2 * 0.10) ≈ 0.58

f''(2) ≈ (-0.702 - 2(-0.818) + (-0.951)) / (0.10²) ≈ -0.68

Using O(h¹) approximation:

f'(2) ≈ (-0.818 - (-0.702)) / (2 * 0.10) ≈ -0.58

f''(2) ≈ (-0.951 - 2(-0.818) + (-0.702)) / (0.10²) ≈ -0.68

To compute the derivatives analytically, we first find the function's derivative:

y' = -ed√x - 0.5ex√x + 4

For x = 2:

y'(2) = -e - 0.5e + 4 ≈ -0.717

y''(2) = -0.5e - 0.25e + 0 ≈ -0.709

To calculate the absolute relative percent error (ARPE), we use the formula:

ARPE = |(approximation - analytical) / analytical| * 100

For the first derivative:

ARPE (O(h²)) = |(0.58 - (-0.717)) / (-0.717)| * 100 ≈ 181.4%

ARPE (O(h¹)) = |(-0.58 - (-0.717)) / (-0.717)| * 100 ≈ 19.1%

For the second derivative:

ARPE (O(h²)) = |(-0.68 - (-0.709)) / (-0.709)| * 100 ≈ 4.1%

ARPE (O(h¹)) = |(-0.68 - (-0.709)) / (-0.709)| * 100 ≈ 4.1%

Therefore, the absolute relative percent error for the first derivative approximation with O(h²) is 181.4%, while the O(h¹) approximation yields an error of 19.1%. For the second derivative, both approximations have an error of approximately 4.1%.

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The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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Answer:

2^17

Step-by-step explanation:

the indices are added when the integers are multiplied. the integer, however, does not need to be changed since it is already the same.

Answer:

Thaey are proportional

Step-by-step explanation:

Answer:

\(60+10x=6\)

Step-by-step explanation:

Hi there!

\(4+\displaystyle \frac{2}{3} x=\frac{2}{5}\)

To get rid of the fraction \(\displaystyle \frac{2}{3}\), multiply both sides of the equation by 3 (the denominator):

\(3(4+\displaystyle \frac{2}{3} x)=3(\frac{2}{5})\\\\3*4+\frac{3*2}{3}x =\frac{3*2}{5} \\\\12+2x =\frac{6}{5}\)

To get rid of the fraction \(\displaystyle \frac{6}{5}\), multiply both sides of the equation by 5 (the denominator):

\(\displaystyle 5(12+2x) =5(\frac{6}{5})\\\\5*12+5*2x=\frac{5*6}{5} \\\\60+10x=6\)

I hope this helps!

Answer:

theleangreenbear has the correct answer, but it could be reduced from

60 + 10x = 6 to

30 + 5x = 3

Step-by-step explanation:  divide both sides by 2

From rectangle P and Q, the ratio of x to y is 25/18

An equation is an expression used to show the relationship between two or more numbers and variables.

Area of P = 40 * x = 40x cm²

Area of Q = y * (1.25 * 40) = 50y cm²

Given that area of Q = 90% if P = 0.9(40x) = 36x cm²

50y cm² = 36x cm²

x/y = 50/36 = 25/18

From rectangle P and Q, the ratio of x to y is 25/18

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to get the slope of any straight line, all we need is two points off  of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{1}{4}\)

Answer:

        y - 8.3 = 6.5(x + 3.4)     {the point-slope form of the equation}

        y = 6.5x + 30.4            {the slope-intercept form of the equation}  

        65x - 10y = - 304            {the standard form of the equation}

Step-by-step explanation:

The point-slope form of equation is: y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope.

m = 6.5

(-3.4, 8.3)    ⇒   x₀ = -3.4,  y₀ = 8.3

The point-slope form of the equation:

y - 8.3 = 6.5(x + 3.4)

So:

y - 8.3 =  6.5x + 22.1         {add 8.3 to both sides}

y = 6.5x + 30.4             ←  the slope-intercept form of the equation

 y - 6.5x = 30.4                   {multiply both sides by (-10)}

65x - 10y = - 304               ←  the standard form of the equation

For the random sample, the test statistic is -3.88.

The hypothesis to be tested can be expressed as follows:

H0: p1 ≤ p2, or equivalently p1 - p2 ≤ 0 (null hypothesis)

HA: p1 > p2, or equivalently p1 - p2 > 0 (alternative hypothesis)

where p1 is the true proportion of vehicles exceeding the pollution standard at low altitudes, and p2 is the true proportion of vehicles exceeding the pollution standard at high altitudes.

The test statistic to test this hypothesis is given by:

z = (p1 - p2) / sqrt(p(1 - p) * (1/n1 + 1/n2))

where p1 and p2 are the sample proportions of vehicles exceeding the pollution standard at low and high altitudes, respectively, p = (x1 + x2) / (n1 + n2) is the pooled sample proportion, x1 and x2 are the numbers of vehicles exceeding the pollution standard in the two samples, and n1 and n2 are the sample sizes.

For the given data, we have:

x1 = 41, n1 = 310, p1 = 41/310 ≈ 0.1323, x2 = 21, n2 = 95, p2 = 21/95 ≈ 0.2211, p = (x1 + x2) / (n1 + n2) ≈ (41 + 21) / (310 + 95) ≈ 0.1521

Substituting the values, we get:

z = (0.1323 - 0.2211) / sqrt(0.1521 * 0.8479 * (1/310 + 1/95))≈ -3.88

The test statistic is approximately -3.88.

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Answer:

y = 2 * 4^x

Step-by-step explanation:

We could define a wide variety of rules!

It turns out that any set of n (x, y) pairs can be modeled by a singular polynomial of degree (n-1) or less, and by infinitely many polynomials of degree n or more! And we're only talking polynomials!

Let's input it into a polynomial interpolation calculator:

\((27 x^4)/4 - (63 x^3)/2 + (225 x^2)/4 - (51 x)/2 + 2\)

Well I don't love this.

Let's try to actually look for patterns. We see that the function is rapidly increasing. More and more, actually. Let's look for the ratios of each next y

8/2 = 4

32/8 = 4

128/32 = 4

512/128 = 4

BINGO!

So we can define the rule as:

y = 2 * 4^x

Answer:

the x-intercepts are -5 and 2

Step-by-step explanation:

\(y=2x^2+6x-20\)

x-intercept is when y is set equal to zero

So, y = 0

\(0 = 2x^2+6x-20\)

\(2x^3+6x-20 = 0\\Taking \ 2 \ common\\2(x^2+3x-10) = 0\\Dividing \ both \ sides \ by \ 2\\x^2+3x-10 = 0\\Using \ mid\ term \ break \ formula\\x^2+5x-2x-10 = 0\\x(x+5)-2(x+5)=0\\Taking \ (x+5) \ common\\(x+5)(x-2) = 0\)

Either,

x+5 = 0     OR    x-2 = 0

x = -5       OR       x = 2

So, the x-intercepts are -5 and 2

Answer:

The x-intercepts would be (2, 0) and (-5, 0).

Step-by-step explanation:

To find the x-intercepts, substitute in 0 for y and solve for x.

0 = 2x^2 + 6x - 20.

Solve the equation.

x = 2, -5.

Answer:

fghjgfvgh

yguhyu

Step-by-step explanation:

Answer:

frank traveled 2760-1400 = 1360 miles

traveled 16 hours

This means he drove: 1360 miles / 16 hours = 85 miles per hour.

Answer:

Then the black cards=12

Step-by-step explanation:

N of red=3

N of black=10

and we have ratio 3:10

think when we ⇒ add 2 to red, will be 5:10= 1:2 not equal to 1:3

                   ⇒add 1 to red and 1 to black, the ratio will be 4:11 not equal to 1:3

                   ⇒add 2 to black, the ratio will be 3:12 = 1:3

Then the black cards=12

hope this helps!

Answer:

Either

(1) there were originally 60 black cards, and 2 red cards were added, or

(2) there were originally 20 black cards, and 1 red card and 1 black card were added.

Step-by-step explanation:

The ratio of red cards to black cards is 3:10.

Since we don't know the actual numbers of red and black cards, we can write the ratio of red to black cards as

3k/10k

After adding 2 cards, the ratio of red cards to black cards becomes 1:3.

There are 3 ways of adding 2 cards: (A) both red, (B) 1 red and one black, (C) both black.

Possibility A: add two red cards

(3k + 2)/(10k) = 1/3

10k = 9k + 6

k = 6

3k/10k = 3(6) / 10(6) = 18/60

There were originally 60 black cards.

Possibility B: add 1 red card and 1 black card

(3k + 1)/(10k + 1) = 1/3

10k + 1 = 9k + 3

k = 2

3k/10k = 3(2) / 10(2) = 6/20

There were originally 20 black cards.

Possibility C: add two black cards.

(3k)/(10k + 2) = 1/3

10k + 2 = 9k

k = -2

3k/10k = 3(-2) / 10(-2) = -6 / -20

We cannot have a negative number of cards.

No solution.

Answer: Either there were originally 60 black cards, and 2 red cards were added, or there were originally 20 black cards, and 1 red card and 1 black card were added.

Answer:

Step-by-step explanation:

Let the miles is x:

It seems incorrect but Alex can drive 4 miles

Answer:

The answer is C

Step-by-step explanation:

25^2 = 625

20^2 = 400

625+400 = 1025

sqrt(1025) is the answer

Answer:

i am not sure

Step-by-step explanation:

Answer:

a

Step-by-step explanation: