please help:
show that two quadrilaterals are congruent​

Step-by-step explanation:

First, you should translate everything into math. So,

"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)

"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)

Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:

(3C + 2) + C = 90

4C + 2 = 90

4C = 88

C = 22

Plugging C = 22 back into either equation (1) or (2) gives us

B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)

Thus, ∠B = 68º; ∠C = 22º

hope this helps

The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.

How to solve function?

h(x) = −3|x − 1| + 4

Substitute x = -5

h(-5) = −3|(-5) − 1| + 4

= -3|-6| + 4

= -18 + 4

= -14

h(-5) = -14

Hence, The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.

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The ball reached its maximum height at a time of 1 second.

In this problem we have the case of a ball that experiments a free fall, that is, a case of an uniform accelerated motion due to gravity. The position of the ball as a function of time is represented by a quadratic equation:

y' = y + v · t + 0.5 · g · t²

Where:

And to determine the time related to the highest point, we need to rearrange the expression into its standard form:

y' - k = C · (t - h)²

Where:

First, write the quadratic equation:

y' = y + v · t + 0.5 · g · t²

y' = 10 + 16 · t - 8 · t²

Second, complete the square until the standard form is found:

y' - 10 = 16 · t - 8 · t²

y' - 10 = - 8 · (t² - 2 · t)

y' - 18 = - 8 · (t² - 2 · t + 1)

y' - 18 = - 8 · (t - 1)²

The ball takes a time of 1 second to reach its maximum height.

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Let the cost of each gift card be x.

Three of them will cost 3x.

We need the total cost be no more than $2 above or below $60.

This can be represented as:

and

or as combined inequality:

Answer:

B second one

Step-by-step explanation:

2000-750/5=250

In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

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Answer:

x = -4

Step-by-step explanation:

(4x-5)/(3x+5) = 3

1. Multiply both sides by 3x+5

  4x-5 = 3(3x+5)

2. Expand

   4x-5 = 9x+15

3. -4x from both sides

   -5 = 5x+15

4. -15 from both sides

  -20 = 5x

   x = -4

It is greater than 3

x = 4

We can solve the equation as

(4x-5) = (3x+5)*3

4x-5=9x+15

x = 4

Hello,

I hope you and your family are doing well!

To simplify the expression, you can combine like terms and simplify:

[tex](2x^2+x+1)-(x^2-x+7)-(4x^2+2x+8)[/tex]

[tex]= 2x^2+x+1 - x^2+x-7 - 4x^2-2x-8[/tex]

[tex]= (2x^2 - x^2 - 4x^2) + (x - x - 2x) + (1 - 7 - 8)[/tex]

[tex]= -3x^2 - 3x - 14[/tex]

Therefore, the simplified expression is [tex]-3x^2 - 3x - 14[/tex]

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Happy Holidays!

There are 1240 students in the school.

What is Proportionalities (Ratios)?

It is possible to represent absolute connections using ratios or proportions, independent of the variables' actual raw values. For instance, if your business always produces widgets packaged in bundles of 20 widgets each, you will always have a 20 widgets to 1 bundle ratio regardless of how many bundles you produce. Accordingly, if you produce 100 bundles per day, you will have produced 2000 widgets in a single day.  The proportion of widgets to bundles is constant and does not change. As long as the other ratio factor quantity is known or can be known, the ratio or proportion can then be used as a conversion factor to calculate the number of an unknown quantity of one ratio factor.

In our problem, we know that there are 11 boys : 9 girls in the school. We also know that there are 124 more boys than girls.

If we let x equal the number of girls in the school, the number of boys will then be x+124. We know the ratio of boys to girls and produce a conversion factor to determine the number of girls present in the school:

( number of boys)[tex]$\left(\frac{\text { girls }}{\text { boys }}\right)=$[/tex] number of girls

[tex](x+124)\left(\frac{9}{11}\right)=x[/tex]

Note that since we are looking to find the number of girls, it appears in the numerator of the conversion factor and boys in the denominator. If we were looking for the number of boys, we would flip the conversion factor to have the number of boys in the numerator and girls in the denominator.

Now let's simplify the equation and solve for x :

[tex]\begin{aligned}(x+124)\left(\frac{9}{11}\right) & =x \\\frac{9 x+1116}{11} & =x \\9 x+1116 & =11 x \\1116 & =11 x-9 x \\1116 & =2 x \\\frac{1116}{2} & =x=558\end{aligned}[/tex]

If we have 558 girls, the number of boys is then:

x+124=558+124=682boys

Adding the number of boys and girls together, we will have the total number of students in the school: 558+682=1240 students

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Sean's real average speed was less than his predicted 40 mph.

Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time.

Hence, Sean's real average speed was less than his predicted 40 mph.

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The number of feet of light used by Chad is 176 feet

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

Length = 55 feet

Width = 48 feet

We start by calculating the distance from the end of the width till the beginning of the length

This is represented by the following Pythagoras theorem

Distance = √(Length² + Width²)

So, we have

Distance = √(55² + 48²)

Evaluate

Distance = 73

The number of feet is then calculated as

Feet = Length + width + distance

So, we have

Feet = 55 + 48 + 73

Evaluate

Feet = 176

Hence, the total distance is 176 feet

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Answer:

∠ 1 = 25° , ∠ 2 = 155°

Step-by-step explanation:

∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is

x - 6 + 5x = 180

6x - 6 = 180 ( add 6 to both sides )

6x = 186 ( divide both sides by 6 )

x = 31

Then

∠ 1 = x - 6 = 31 - 6 = 25°

∠ 2 = 5x = 5 × 31 = 155°

The axis of symmetry of equation y = 3x² - 18x + 5 is x = 3.

The object's shape becomes symmetrical when a straight line acts as the axis of symmetry. Each side of the axis of symmetry produces a perfect reflection of the other. It can be lateral, vertical, or any combination of the three.

Given equation:

y = 3x² - 18x + 5

The line symmetry of y =  [tex]ax^2+bx+c = 0[/tex]  is x = -b / 2a,

Hence, x = -(-18) / 2 × 3

Therefore, x = 3 is the axis of symmetry of equation y = 3x² - 18x + 5.

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Step-by-step explanation:

so pretty much replace -3, 0 and 3 into the equation

-3 to the power of 2 is 9 and 9(3) is 27. 27-(-3) is 27+3, 30

0 squared is 0 so the 2nd one would be 0

3 squared times 3 is 27 and subtracted by 3 is 24.

Answer:mutplion

Step-by-step explanation:

The probability that either of spin two wheel lands on an odd value is 1.

For the stated question-

Total number marked on the wheel (1 to 6) = 6 numbers.

Total odd number (1, 3, 5) = 3 numbers

Probability of of getting odd number on one wheel = 3/6 = 1/2.

Let the probability of of getting odd number on one wheel P(A).

Then, Probability of of getting odd number on second wheel P(B).

Then,

Only only wheel have the odd number,

P(A∩B) = 0.

Thus,

Probability that either wheel lands on an odd value;

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 1/2 + 1/2 - 0

P(A∪B) = 1

Thus, probability that either wheel lands on an odd value is 1.

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35 is  diagonals does a convex decagon have .

What does a pentagon basic definition entail?

A geometric figure with five sides and five angles is called a pentagon. Here, "Penta" stands for five, while "gon" is an angle.

                      One of the different kinds of polygons is the pentagon. For a standard pentagon, the total internal angles come to 540 degrees.

There are a total of  ¹⁰C₂  ways to connect two different vertices. But connecting neighbouring vertices doesn't count, so we have to exclude the sides from our consideration. There are 10 sides, so we need to take away 10 ways from the 45 ways possible to get the number of diagonals.

 Number of diagonals in a decagon = 35

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Answer: It's in the picture.

Step-by-step explanation:

The weight of all of the rocks to the nearest tenth is 6.085 pounds .

Given :

in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks if necessary, round your answer to the nearest tenth.

Let x be the total weight or all the weight of rocks .

3 = 49.3 % * x

3 = 49.3 * 1 / 100 * x

3 * 100 = 49.3 * x

300 = 49.3 * x

divide with 49.3 on both sides

300 / 49.3 = 1 * x

x = 300 / 49.3

= 6.085 pounds

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Answer: n= 1

Step-by-step explanation:

8n+7=-4n+19

First, subtract 7 from both sides

8n = 4n +12

Then add 4n from both sides

12n = 12

Then divide by 12 from both sides

n= 1

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Answer: n = 1

Step-by-step explanation:

First, you could start off by bringing the -4n to the left side:

8n + 7 = -4n+19  →  12n + 7 = 19

Next, you take the 7 on the left side of the equals sign and subtract it from the 19:

12n + 7 = 19 → 12n = 12

Finally, you divide the 12 on the right by the 12 on the left:

12n = 12  →  n = 12/12

A number over itself will always be 1, so n = 1.

Check the picture below.

so hmmm let's only find the lines in red and add them up all

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-4}) ~\hfill d1=\sqrt{(~~ 1- (-2)~~)^2 + (~~ -4- (-1)~~)^2} \\\\\\ ~\hfill d1=\sqrt{( 3)^2 + ( -3)^2} \implies d1=\sqrt{ 18 }[/tex]

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill d2=\sqrt{(~~ 2- 1~~)^2 + (~~ 0- (-4)~~)^2} \\\\\\ ~\hfill d2=\sqrt{( 1)^2 + ( 4)^2} \implies d2=\sqrt{ 17 } \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{4~~ + ~~4~~ + ~~3~~ + ~~\sqrt{18}~~ + ~~\sqrt{17}} ~~ \approx ~~ \text{\LARGE 19.4}[/tex]

The fraction of the cake that was ron's pieces is 1/5.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Since Mrs Jones gave 1/5 of a cake to her neighbour, the remaining fraction will be:

= 1 - 1/5

= 4/5

The fraction of the cake that was ron's pieces will be:

= 2/(1+3+4) × 4/5

= 2/8 × 4/5

= 8/40

= 1/5

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Answer:y= -2/3+3 is the answer since you are just flipping the same line and move down by 1

Step-by-step explanation:

Answer: 108

Step-by-step explanation:

We find the number of boys by taking 300 timed 0.32 = 96 boys

Then we subtract 300 from 96 = 204 girls

Then we removed 204 by 96 = 108

So there are 106 girls more than boys

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Answer: 108

Step-by-step explanation: There are 300 teenagers in all. To find how many boys they are, multiply 32/100 times 300/1. You get 96, so there are 96 boys. This means that there are 204 girls. There are 108 more girls than boys. Hope this helps!

Answer:

6

Step-by-step explanation:

RS and QT are parallel because it is a trapezoid. This means that the transversal applies. Look at the picture attached to understand what I mean.

So, we know that 18x - 13 = 180(degree of a line)-85. Then, solve the equation.

18x-13=95

18x=108

x=6

the area will be fall in between 100≤ 20x ≤1000.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,A quadrilateral should be closed shape with 4 sides

All the internal angles of a quadrilateral sum up to 360°.

The area of a rectangle is A = a*b

Here in the figure the length is given 4x and the breadth is 5.

The area is given in between 100≤A≤1000

So this area will be A = 5x*4 = 20x

Now the area will be lie in between 100≤ 20x ≤1000

hence, the area will be fall in between 100≤ 20x ≤1000.

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Answer:

$227

Step-by-step explanation: if the console gets marked downed $25 it will be $200 then the 12% increase which it $27 so that will be $227

Answer:

The series -1+2+(-4)+8+... is an arithmetic series because it has a common difference between consecutive terms. Specifically, the common difference is -4 - 2 = -6.

To determine whether the series is convergent or divergent, we need to find its sum. The sum of an arithmetic series is given by the formula:

sum = (n/2)(a1 + an)

where n is the number of terms in the series, a1 is the first term, and an is the nth term.

Since the series is infinite, we cannot determine its sum using this formula. However, we can determine its sum by taking the limit as n approaches infinity. Using the formula above, we find that the sum is equal to:

sum = (infinity/2)(-1 + infinity)

Since the series contains an infinite number of negative terms, it is divergent.