Solve each system by substitution.
4x + y = 19
6x + 7y=1

Answer:

625

Step-by-step explanation:

250/6 =41.6666666667

41.6666666667x15 = 625

Answer:

2.83 cm

Step-by-step explanation:

The other leg is also 2cm

Pythagorean Theorem

  hypot ^2 = 2^2 + 2^2

  Hypot = sqrt 8 =~ 2.83 cm

Answer:

Step-by-step explanation:

an isosceles triangle where the two legs form a 90-degree angle is an isosceles right triangle. So, the hypotenuse of the triangle is 2√2

The 95% confidence interval for the population mean is approximately $4358.46 to $4441.54. Increasing the sample size is the best alternative to reduce the width of the confidence interval.

a) To make a 95% confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

First, let's calculate the standard error, which is the standard deviation of the sample divided by the square root of the sample size:

Standard error = $900 / √(1800)

≈ $21.21

For a sample size of 1800, the critical value can be found using a t-distribution or approximated using a normal distribution. Since the sample size is large (n > 30), we can use the normal distribution approximation. The critical value for a 95% confidence level is approximately 1.96.

Now, we can calculate the confidence interval:

Confidence interval = $4400 ± (1.96 * $21.21)

Confidence interval ≈ $4400 ± $41.54

b) If the confidence interval obtained in part a is too wide and we want to reduce its width, there are several alternatives to consider:

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The value of the length AB is 8. 66

Trigonometric identities are simply described as equalities that holds true for all the values of the functions in a given equation.

The different trigonometric identities and their ratios are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have;

Opposite = 5. 2

Adjacent = x

Using the tangent identity

tan 31 = 5. 2/x

Cross multiply the values

x = 8. 66

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Answer: The root of -4 is 2, and I'm not sure about 3

Step-by-step explanation:

Using a proportional relationship, the table relating the number of guests and number of tables is given by the image at the end of the answer.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the equation below:

y = kx.

In the context of the problem, the variables are given as follows:

He'll have 4 tables for every 20 guests, hence the constant is given as follows:

k = 4/20 = 1/5 = 0.2.

Hence the relation is:

y = 0.2x.

For 1 table, the number of guests is:

0.2x = 1 -> x = 5.

For 8 tables, the number of guests is:

0.2x = 8 -> x = 8/0.2 = 40.

For 35 guests, the number of tables is:

y = 0.2 x 35 = 7.

For 50 guests, the number of tables is:

y = 0.2 x 50 = 10.

The table with these measures is given by the image at the end of the answer.

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Step-by-step explanation:

To find the mean, you add all the numbers and divide by how many there are.

In this case, you add -54,-32,-70,-25,-65, and -42. Then you divide by 6 because there are 6 numbers.

When you add them all, you get -288.

Now divide.

-288/6=-48

Hope it helps!

Answer:

-48

so you add all the numbers together, which will give you -288

there are 6 terms, so you divide -288 by 6

gives you your answer of -48

Answer:

A

Step-by-step explanation:

         4x + 1             ← quotient

         ----------------------

x + 2 | 4x² + 9x - 34

          4x² + 8x         ← subtract from line above

        -------------------------

                x - 34

               x + 2      ← subtract from line above

        -------------------------

                  - 36    ← remainder

Then

\(\frac{4x^1+9x-34}{x+2}\) = 4x + 1 + \(\frac{-36}{x+2}\)  → A

The solution to the system of equations is (5, 35) and (-4, 8).

The system of equations is given as:

y = x² + 2x    ....(i)

y = 3x + 20   ....(ii)

Substitute the first equation into the second equation to eliminate y and get an equation in terms of x:

x² + 2x = 3x + 20

Simplifying and rearranging:

x² - x - 20 = 0

(x - 5)(x + 4) = 0

So, x = 5 or x = -4.

Substituting each value of x into the first equation to find the corresponding value of y:

When x = 5, y = 35.

When x = -4, y = 8.

Therefore, the solution to the system of equations is (5, 35) and (-4, 8).

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Answer:

what grade

Step-by-step explanation:

to know the rule

Answer:

y=4/3 x+20

Step-by-step explanation:

hope it helps you...

Applying the theorem of angle between intersecting tangents, m<D = 30°.

The theorem states that the angle created by the intersection of two tangent lines at a point outside of a circle is equivalent to half the difference between the measures of the arcs that the tangents intercept.

Given the following:

m<B = 75°

Measure of arc AC = 2(75) [inscribed angle theorem]

Arc AC = 150°

Arc ABC = 360 - 150 = 210°

Based on the theorem of angle between intersecting tangents, we have:

m<D = 1/2(210 - 150)

m<D = 30°

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Answer:

A

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−y+4≥8

Step 2: Subtract 4 from both sides.

−y+4−4≥8−4

−y≥4

Step 3: Divide both sides by -1.

−y

−1

≥

4

−1

y≤−4

Answer:

12

Step-by-step explanation:

| 4-y| ≥8

Separate into two inequalities, one positive and one negative (remembering to flip the inequality)

4-y ≥8 or 4-y≤ -8

Solve

Subtract 4 from all sides

4-y -4 ≥8-4    or 4-y-4≤ -8-4

-y  ≥4    or -y≤ -12

Divide each side by -1, remembering to flip the inequality

y ≤-4  or y ≥12

The smallest positive number is 12

The value of i^32 as shown in the equation is 1

Complex numbers are square root of negative numbers. In complex number;

i^2 = -1

we are to find the value of i^32

i^32 = (i^2)^16

Substitute the value of i^2 into the expression

i^32 = (-1)^16

i^32 = 1

Hence the value of i^32 as shown in the equation is 1

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Given, Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph.Both Jada and Elena start walking along a walking trail at the same time.

Let us determine the distance covered by both of them.Distance travelled by Jada in 3 hours is:Distance = Speed × Time= 3 mph × 3 hours= 9 miles Distance travelled by Elena in 3 hours is:Distance = Speed × Time= 2.8 mph × 3 hours= 8.4 miles Thus, Jada will walk 0.6 miles farther than Elena after 3 hours.

To determine how far Jada will walk after 3 hours, we need to calculate the distance traveled based on her speed.

Jada walks at a speed of 3 miles per hour (mph), so we can calculate her distance using the formula:

Distance = Speed × Time

Plugging in the values, we have:

Distance = 3 mph × 3 hours

Distance = 9 miles

Therefore, Jada will walk a distance of 9 miles after 3 hours.

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The given information is as follows:

Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph. If they both begin walking along a walking trail at the same time.

Therefore, Jada will walk 9 miles after 3 hours.

The distance covered by Jada after 3 hours can be calculated as follows:

Distance = Speed x Time

Since Jada walks at a speed of 3 mph, the distance covered by her in 3 hours can be calculated as:

Distance covered by Jada = 3 mph x 3 hours

= 9 miles.

Therefore, Jada will walk 9 miles after 3 hours.

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Given equation g = x-1/k in terms of x would be x = 1 + gk

for given question,

we have been given an equation g = x-1/k

Dyani began solving the equation g = x-1/k for x by using the addition property of equality.

We solve given equation for x.

⇒ g = x-1/k                      ..........(Given)

⇒ gk = (x - 1/k)k               .........(Multiply both the sides by k)

⇒ gk = x - 1

⇒ gk + 1 = x - 1 + 1           .........(Add 1 to each side)

⇒ gk + 1 = x

⇒ x = 1 + gk

Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk

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The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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Answer:

AIB = 105°

BIC = 130°

CIA = 125°

Step-by-step explanation:

Шаг 1

Находим Угол C

В приведенном выше вопросе нам говорят

Угол A = 80 °

Угол B = 70 °

Сумма углов в треугольнике = 180 °

Угол C = 180 ° - (80 ° + 70 °)

= 180 ° - 150 °

= 30 °

Шаг 2

ABI = ∠IBC = 1/2 ∠B

1/2 × 70 ° = 35 °

∠IAC = ∠BAI = 1/2 ∠A

= 1/2 × 80 ° = 40 °

∠ICB = ∠ACI = 1/2 ∠C

= 1/2 × 30 ° = 15 °

Помните, что сумма углов в треугольнике = 180 °.

∠CIA = 180 ° - ∠IAC - ∠ACI

= 180 ° - 40 ° - 15 °

= 180 ° - 55 °

= 125 °

∠BIC = 180 ° - ∠ICB - ∠IBC

= 180 ° - 15 ° -35 °

= 180 ° - 50 °

= 130 °

∠AIB = 180° - ∠ABI - ∠BIA

=180° - 35° - 40°

=180° - 75°

=105°

9/2 x +48 is an equation to represent the real ashton’s hip between these variables.

To write this type of fraction = 4 + 1/2 - The integer 4 in the expression is the amount of feet of rope that was cut.

Thus to know the number of 1/2 foot pieces produced, let this number be x. Thus, we have 1/2 of x pieces = 2

 x/2 = 4; x = 2x4 = 8

Thus, it has 8 pieces of 1/2 foot long piece each of rope.

9/2 x +48 is an equation to represent the real ashton’s hip between these variables.

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Answer:

8

Step-by-step explanation:

If my calculations are correct the third side is 8

Answer:

No

Step-by-step explanation:

This is because square root of 15 is between 3 and 4, which are not greater than 5. To make a right triangle you could used two 5 for side a and b BUT the longer side of the triangle has to be Greater than a and b

Hope this helped

Answer:  a) 110√2 meters

                b) 2.42 hectares

Step-by-step explanation:

a) Since it is a square, the diagonal cuts the square into two 45-45-90 triangles where the diagonal is the hypotenuse.  Therefore, the sides are length x and the diagonal is length x√2.

\(x\sqrt2=220\\\\\\x=\dfrac{220}{\sqrt2}\\\\\\x=\dfrac{220}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\x=\large\boxed{110\sqrt2}\)

b) Area of a square is side squared.    10,000 meters² = 1 hectare

   \(A=(110\sqrt2)^2\\\\.\quad =(110)^2(\sqrt2)^2\\\\.\quad =12100(2)\\\\.\quad =24200\ \text{meters}^2\\\\.\quad =\large\boxed{2.42\ \text{hectares}}\)

Answer: PART A.

y= remaining height of candle

x= rate the candle burns down in inches per hour

8= original height of candle

the function would be y=8- 0.5x because the candle starts at a height of 8 feet and loses half an inch per hour.

You can use this function to create ordered pairs by putting in number at x which indicates the time:

x=1

y=8- (.5×1)= 7.5

(1, 7.5)

you can then do this for other numbers and get:

(2, 7.0) (3, 6.5) (4, 6.0) (5, 5.5) (6, 5.0)

PART B.

This equation is a function because all of the x-values had different y-values as seen in the coordinates (1, 7.5) (2, 7.0) (3, 6.5) (4, 6.0) (5, 5.5) (6, 5.0)  

PART C.

If the rate was 0.4 inches an hour, it would still be a function because the rate is the only thing that changed making the new function y= 8- 0.4x.This equation would make coordinates of (0,8) (1, 7.6) (2, 7.2) (3, 6.8) and so on with each x value creating a different y value.

Step-by-step explanation: hope this helps

Answer:

are there any more details? cant solve anything from what you have provided

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

5*x+6=36

so 5*6=30

+6=36

Answer:

36

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

42 divided by 2/3 = 7

7 divided by 2/7 = 0.5