The two trapezoids are congruent. What is the value of x?

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Answer: negative one third

Answer:

-1/3

Explanation:

There's a formula that I'll use to find the slope - it's called the slope formula.

\(\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

Plug in the data:

\(\sf{m=\dfrac{8-4}{-4-8}}\\\\\sf{m=\dfrac{4}{-12}\)

Simplify:

\(\sf{m=-\dfrac{4}{12}}\)

\(\sf{m=-\dfrac{1}{3}}\)

Hence, the slope is negative one-third.

The probability that neither student and parent don't get picked is equal to the value 2/5.

Probability is simply the likelihood of something occurring. When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how likely they are. Statistics is the study of events governed by probability.

Given, there are 5 students 7 parents and 8 teachers in a room.

Total members in the room = 5+7+8

Total members in the room = 20

Total mem = 20

Probability of neither student and parent get picked = Probability of Teacher getting picked

Probability = Needed ones / Total members

Probability = 8 / 20

Probability = 2/5

Therefore, the probability that neither student and parent don't get picked is equal to the value 2/5.

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Answer:

Step-by-step explanation:

4(x+2)+3(2x+5)

4x+8+6x+15

10x+23

Answer:

It is 10x + 23

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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Additional Perspectives. A pair of supplementary angles are two angles whose sum measures 180°. A 110° angle and a 70° angle are two examples of supplementary angles

1) 4x+ 6 = 130

        x= 31

2) 9x +36+45 =180

   x=11

1) 4x+ 6 = 130

        x= 31

2) 9x +36+45 =180

   x=11

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Since the angles are supplementary, their measures add to 180°. In other words: 2x+(2x–2)=180. Solving this equation gives the value of x. In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown." x is a variable in x + 2 = 7.

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Answer:

No, it is not a good test point to choose since it's on the boundary.

(0,0) is a better choice

See graph below.

=======================================================

Further Explanation:

The given point (-3,3) has x = -3 and y = 3 pair up together.

Plug those coordinates into the boundary line equation.

y = (4/3)*x + 7

3 = (4/3)*(-3) + 7

3 = -4 + 7

3 = 3

The fact we get a true statement at the end proves that (-3,3) is on the boundary line y = (-4/3)x+7

So the question is: which side of the boundary do we shade? The test point (-3,3) is literally on the fence, and it's indecisive on which side to pick. This is exactly why (-3,3) is a bad choice.

A better choice would be to use (0,0) since 0 is an easy number to work with and because the origin is not on the boundary line. See note below.

Let's plug x = 0 and y = 0 into the inequality.

y < (4/3)x + 7

0 < (4/3)*0 + 7

0 < 0 + 7

0 < 7

The last inequality is true, so (0,0) is in the shaded region. This means we shade everything below the dashed boundary line of y = (4/3)x+7 since (0,0) is below the boundary line.

The graph is shown below.

Side note: The origin is the first choice I'd go for as long as the origin point is not on the boundary. If it is on the boundary, then pick something else on the y axis such as (0,1) as a test point.

Answer:

64in cubed

Step-by-step explanation:

Because if the vase if half full, half of 8 is 4. To find the volume of a cube is l x W x H. So 4 x 4 x 4= 64.

Answer:

can you take a picture of you problem

By solving a system of equations, we conclude that Kelli's speed on still water is 6.1km/h

Let's say that the speed of Kelli in still water is S. And we know that the speed of the river is 5km/h.

When she swims upstream, her velocity is:

(S - 5km/h)

When she swims downstream, her velocity is:

(S + 5km/h)

With the given information, we can write for a distance D:

(S - 5km/h)*1h = D

(S + 5km/h)*6min = D

First, let's rewrite 6 minutes into hours.

1 hour = 60min

6 min = 6/(60) hours = 0.1 hours

Then the system of equations that we need to solve is:

(S - 5km/h)*1h = D

(S + 5km/h)*0.1h = D

D is the same distance in both cases, then we can write:

(S - 5km/h)*1h = (S + 5km/h)*0.1h

Now we can solve this for S.

S*1h - 5km = S*0.1h + 0.5km

S*1h - S*0.1h = 5km + 0.5km

S*(0.9h) = 5.5km

S = 5.5km/0.9h = 6.1km/h

Kelli's speed on still water is 6.1km/h

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Answer: 1/32 pounds

Step-by-step explanation:

1/4 divided by 8 = 1/32

Answer:

1/32

Explanation:

1/4 / 8 = 1/32

The expected value for the number of siblings of a randomly chosen student is 1.11.

"In a probability distribution, the weighted average of possible values of a random variable, with weights given by their respective theoretical probabilities, is known as the expected value".

For the given situation,

The table shows the probability distribution of siblings of students in a high school with 1500 students.

For number of siblings = 0, Probability = 0.18.

For number of siblings = 1, Probability = 0.65.

For number of siblings = 2, Probability = 0.09.

For number of siblings = 3, Probability = 0.05.

For number of siblings = 4, Probability = 0.02.

For number of siblings = 5, Probability = 0.01.

The formula for expected value mean, E(x) = ΣxP(x)

\(E(x)=(0)(0.18)+(1)(0.65)+(2)(0.09)+(3)(0.05)+(4)(0.02)+(5)(0.01)\)

⇒ \(E(x)=1.11\)

Hence we can conclude that the expected value for the number of siblings of a randomly chosen student is 1.11.

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Given addition:

(I). → {4(2/3)} + {1(1/6)}

= {(12+2)/3}+{(6+1)/6}

= (14/3)+(7/6)

Take the LCM of 3 & 6 is 6.

= {(14×2 + 7×1)/6}

= {(28+7)/6}

= 35/6

= {5(5/6)}.

(ii).→ {5(3/5)} + (3/10)

= {(25+3)/5} + (3/10)

= (28/5) + (3/10)

Take the LCM of 5 & 10 is 10.

= {(28×2 + 3×1)/10}

= {(56 + 3)/10}

= (59/10)

= {5(9/10)}.

(iii).→ {3(5/8)} + {1(5/12)}

= {(24+5)/8} + {(12+5)/12}

= (29/8) + (17/12)

Take the LCM of 8 & 12 is 24.

= {(29×3 + 17×2)/24}

= {(87 + 34)/24}

= 121/24

= {10(1/12)}.

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Given the following sum of mixed fractions, we are to find the resulting value:

1) \(4\frac{2}{3} + 1\frac{1}{6} \)

Convert to improper fractions

\(=\frac{14}{3}+\frac{7}{6} \\ =\frac{28+7}{6} \\ =\frac{35}{6}\\ =5 \frac{5}{6} \)

2)Given the sum of fractions \(5\frac{3}{5} +\frac{3}{10}\\ \)

\(=\frac{28}{5}+\frac{3}{10} \\ =\frac{56+3}{10} \\ =\frac{59}{10}\\ =5 \frac{9}{10} \)

3) Given the sum of fractions

\(=8\frac{5}{8} +1\frac{5}{12} \\ ==\frac{69}{8}+\frac{17}{12} \\ =\frac{207+34}{24} \\ =\frac{241}{24}\\ =10 \frac{1}{24}\)

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Answer:

b. 5 meters

Step-by-step explanation:

1 meter = 1000 millimeters

5 meter = 5000 millimeters

Which is longer 5 meters or 400 millimeters?

5000 > 400

So, the answer is b. 5 meters.

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer:

Step-by-step explanation:

I suppose the question is to solve the equation

\(2x+3y+1+3ix=x-2y+(3+y)*i\\\\2x+3y+1+3ix-x+2y-3i-iy=0\\\\x+5y+1+i(3x-y-3)=0\\\\\Longrightarrow\\\\\left\{\begin{array}{ccc|c|c|}x+5y&=&-1&-3&1\\3x-y&=&3&1&5\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}-16y&=&6\\16x&=&14\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&\dfrac{14}{16}\\\\y&=&\dfrac{-6}{16} \\\end{array}\right.\\\)

The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

At 2 hours before sunset, the temperature is 0°F.

And,  At 2 hours after sunset, the temperature is −4°F.

Now,

Let the temperature in degrees Fahrenheit = y

So, We can formulate;

⇒ y = - 4°x + 0°

Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

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Answer:

given;

previous year price of gas= $4.35

price of gas has been increased by 30%

now,price of gas in present year=?

we have;

price of gas in present year=priceof

previous year+30%of price of previous year.

so ,price of gas in present year=4.35+30%of4.35

=$4.35+30/100×4.35

=$4.35+1.305

= $5.655. ans....

therefore, the price of gas in present year is ;$5.655.

Answer:

337.35 mi/h^2

Step-by-step explanation:

Given the equation;

v= u +at

v= final velocity = 51 mi/h

u= initial velocity = 23 mi/h

t = time = 5 mins or 0.083 hours

a = acceleration, the unknown

51 = 23 + 0.083a

51 - 23 = 0.083a

a= 51 - 23/0.083

a= 337.35 mi/h^2

Answer:

A sample of 796 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In this question, we have that:

\(\pi = 0.53\)

91% confidence level

So \(\alpha = 0.09\), z is the value of Z that has a pvalue of \(1 - \frac{0.09}{2} = 0.955\), so \(Z = 1.695\).

How large should a sample be if the margin of error is .03 for a 91% confidence interval

We need a sample of n, which is found when \(M = 0.03\). So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.695\sqrt{\frac{0.53*0.47}{n}}\)

\(0.03\sqrt{n} = 1.695\sqrt{0.53*0.47}\)

\(\sqrt{n} = \frac{1.695\sqrt{0.53*0.47}}{0.03}\)

\((\sqrt{n})^2 = (\frac{1.695\sqrt{0.53*0.47}}{0.03})^{2}\)

\(n = 795.2\)

Rounding up

A sample of 796 is needed.

Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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The total surface area of the pyramid from the net is 286 square cm

To calculate the total surface area of a pyramid from its net, you need to add up the areas of all its faces.

The net of a pyramid is a two-dimensional representation of the pyramid, where the edges of the net represent the edges of the pyramid.

In this case, the nets are

Using the above as a guide, we have the following:

Area = 10 * 7 + 2 * (1/2 * 10 * 12.5 + 1/2 * 7 * 13)

Evaluate

Area = 286

Hence, the surface area is 286 square cm

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Answer:

Auto Credit Express, Carvana, Capital one auto loan

Answer:

D is correct

Step-by-step explanation:

Answer: D) 72.22

Step-by-step explanation: Hope you have a great day soldiers

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

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Answer:

See explanation

Step-by-step explanation:

It appears that the second graph is better since it seems to be rather consistent. The graph of the first one seems out of place. Therefore it seems to be confusing and could be misleading.

Answer:

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?

Answer:

4

Step-by-step explanation:

Area of a triangle = bh/2

B = 2h

16 = 2h × 2/2

h×2 = 16

2h = 16

* put a square root on both sides then u will get the answer which is

Height of the triangle = 4