Find the midpoint of the line segment with the endpoints A and B.
A(10,4); B(8,2)
The midpoint of the line segment is
(Type an ordered pair.)

Answer:

D. No x-intercept, y-intercept 9

Step-by-step explanation:

The line intercepts at (0, 9)

Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

(a) The average value of f(x) on the closed interval [0, π] is

\(\displaystyle\frac1{\pi-0}\int_0^\pi f(x)\,\mathrm dx = \frac1\pi\int_0^\pi(8\sin(x)-4\sin(2x))\,\mathrm dx = \boxed{\frac{16}\pi}\)

(b) By the mean value theorem, there is some c in the open interval (0, π) such that f(c) = 16/π. Solve for c :

8 sin(c) - 4 sin(2c) = 16/π

8 sin(c) - 8 sin(c) cos(c) = 16/π

sin(c) - sin(c) cos(c) = 2/π

Use a calculator to solve this. You should get two solutions, c ≈ 1.2382 and c ≈ 2.8081.

Answer:

Kevin cycles past his mum who is sitting on a park bench. What is the relative speed if Kevin is cycling at 20 km/h?

Step-by-step explanation:

20 km/h

Answer:

I think this is it.....If not let me know

2x - y = 3

Slope = 2

x - intercept = 3/2 = 1.50000

y - intercept = 3/-1 = -3.0000

x + y = 0

Slope = -2.000/2.000 = -1.000

x - intercept = 0/1 = 0.0000

y - intercept = 0/1 = 0.0000

The first thing you can do is graph each of the equations. To do this, you can write the equations following the form

Where m is the slope of the line and b the intersection point with the y axis. Then

Graphing you have

The solution of the system of equations will be the point at which both lines intersect. Therefore, the solution is (6,2).

Answer: D = √2

(please respond if im wrong)

Step-by-step explanation:

The fold is made along BE. A folds onto A′.

A′B = AB =√2 ⇒ A′C = 1

(by Pythagoras)

ΔA′BC

is therefore a right-angled isosceles triangle.

⇒∠BA′C=45∘ ⇒∠EA′D=45∘

⇒ ED = A′D = √2−1

The amount of time he spent on bicycle is 4.5 hours.

Given Jim began a 145 mile bicycle trip.

The whole trip took 7 hours.

Jim walks at a rate of 4 miles per hour  and rides at 30 miles per hour.

speed = distance / time

time = distance / speed

ride:

d = distance ridden

t = d/30 (given from the problem)

walk:

t = (145 - d)/4 (given from problem)

total trip time:

7 = d/30 + (145 - d)/4.

7 = 4d/120 + 30(145 - d)/120

7×120 = 4d + 30(145 - d)

840= 4d +4350-30d

840 ₋ 4350 = ₋30d ₊ 4d

₋3510 = ₋26d

d = 3510/26

d = 135

d=135 then from here using the formula t = d / s we can solve

t=135/30 = 4.5 hours

hence the amount of time Jim spent on the bicycle is 4.5 hours.

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The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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Applying the two-tangent theorem, the length of AN is: 21 units.

The two-tangent theorem is a geometric theorem that states that if two tangents are drawn to a circle from a point outside the circle, then the lengths of the tangent segments are equal. This theorem is often used in geometry to find the length of tangent segments and to prove the existence of tangents to circles.

More formally, the two-tangent theorem states that if P is a point outside a circle with center O, and if PA and PB are tangents to the circle from point P, then PA = PB. In other words, the lengths of the two tangent segments are equal.

From the image above, AM and AN are two tangents from the same circle. Also, AN is also tangent with 29 - 2y.

This implies that the three tangents are congruent. Therefore:

6y - 3 = 29 - 2y

6y + 2y = 29 + 3

8y = 32

y = 32/8

y = 4

AN = 6y - 3

Plug in the value of y

AN = 6(4) - 3

AN = 21 units.

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Answer:

37

Step-by-step explanation:

Sam's present age is 37.

Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

Answer:

---------------------

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

Based on an equation, the amount that Isabel spent on bread was $2.42.

To solve the equation for the amount spent on bread, we determined the total amount Isabel spent by subtracting the change from the total bills she had.

An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.

The amount Isabel spent on vegetables = $15.91

The amount she spent on fruits = $11.22

Let the amount she spent on bread = x

The total amount she went with = $30 (3 x $10)

The change she got after giving the cashier $30 = $0.45

The total amount Isabel spent for vegetables, fruits, and bread = $29.55 ($30.00 - $0.45)

x = $2.42 ($29.55 - $15.91 - $11.22)

Check:

Vegetables = $15.91

Fruits = $11.22

Bread = $2.42

Total expenses = $29.55

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let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

Robert's dimes are anywhere between 17 and 19.

Nickels

are worth 5 cents, and

dimes

are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.

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Answer:

2x - 3 - (x-1)

2x - 3 -x +1

x-2

Answer:

Answer:

8%

Step-by-step explanation:

We can start solving the problem by using the formula for compound interest:

A =\(P(1+\frac{R}{n})^{nt}\)

Where A is the final amount, P is the initial principal, R is the interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

Given that the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. We can use this information to set up an equation as follows:

\(P(1+\frac{R}{4})^{2}\) = \(1.0816*P(1+\frac{R}{4})\)

We can simplify this equation by canceling out the P and the (1+R/4) on the right side:

\((1+\frac{R}{4})\) = 1.0816

We can then solve for R:

\(\frac{R}{4}\)=\(\sqrt{(1.0816)-1}\)

R = \(4(\sqrt{(1.0816)-1)}\)

R ≈ 0.08, is the exact value of R.

So, Mr. Saver's nominal interest rate is 8%.

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The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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The equation which represents the relationship between X values and Y values can be found by deriving the equation of line using slope intercept form. The equation of line is 3x - 5y = 25.

How to find equation of line using slope intercept form?

Equation of line using slope intercept form is y = mx + b

where m is slope of the line and b is y-intercept

The slope intercept can be used to form equation of line using two points on the line.

According to the given question:

The two points which lie on the line are (x, y) = (5, -2) and (x', y') = (0, -5)

Slope of the line m = y' - y/x' - x

                               = (-5 +2)/(0 - 5)

                               = 3/5

Now y intercept b = y - mx

                              = -2 - (3/5. 5)

                              = -5

Therefore the required equation of line is y = 3/5x - 5

On simplifying further 3x - 5y = 25

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Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

The graph shows that the x-values increase as the y-values increase, which is consistent with the inequality x+4y ≤ 15. The y-values are all greater than or equal to 0, which is consistent with the inequality y ≥ 0.

Inequality is the unequal distribution of resources or opportunities among different individuals, groups, or social classes. It is a situation in which some individuals or groups have significantly more resources or opportunities than other individuals or groups. Inequality can be seen in terms of income, wealth, social class, access to education and health care, political power, or other factors. Inequality can be caused by systemic oppression and discrimination, or by the unequal distribution of resources within a society. It can have a negative impact on the ability of individuals and groups to meet their basic needs and achieve their full potential.

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Answer:

Plato Answer

Step-by-step explanation:

The Explanation of decimal place value is like place value with whole numbers is shown below.

We know,

Each place value to the left of a whole number is multiplied by ten, but a place value to the right of a decimal number is divided by ten.

For example,

We take whole number 254 where place values are

2- Hundred, 5- Tens and 4- Ones

and, take the decimal 2.369 where the place values are

3- Tenth, 6- hundredth and 9- thousandth

So, both decimal and whole number have similar concept of place value but one is multiplied by 10 and other is divided by 10.

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