Solve Using Elimination.10x 10y = 1010x + 8y = 8 (2024)

5. The two triangles are similar. The value of x = 12.

6. The information cannot be used to show that the triangles are similar triangles.

How to Determine if two Triangles are Similar?

Two triangles are similar to each other if they have the same shape but different sizes, in order words, they must have the same corresponding angle measures but different corresponding side lengths that are proportional to each other.

5. In the first figure, we see that there are two pairs of corresponding congruent angles (a pair of right angles and a pair of vertical angles in both triangles), but different corresponding side lengths.

Therefore, based on the AA similarity theorem that says two triangles are similar of they have two pairs of congruent sides, we can prove that both triangles are similar to each other.

Therefore:

x/9 = 20/15

15x = (9)(20)

15x = 180

15x/15 = 180/15

x = 12

6. The second image shows that the two triangles share a common side, which means they have a pair of corresponding sides that are congruent. Therefore, the information given cannot be used to prove they are similar triangles.

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The probability of getting a green of a yellow marble can be determined like this:

Probability = (yellow marbles + green marbles) / total number of marbles

Probability = (1 + 4) / 10

Probability = 5 / 10

Probability = 1/2

By multiplying the given probability by the number of times a marble will be drawn, we get how many times we can predict that a green or a yellow marble will be picked, then we get:

Number of predictions = 150 × 1/2

Number of predictions = 75

Then, the answer is 75 times

Answer:

75 times.

Step-by-step explanation:

There are a total of 10 marbles in the bag.

Probability a green marble is drawn (in 1 draw) = 4/10 = 2/5.

In 150 draws you can expect to draw 150* 2/5 = 60 green marbles.

Probability a yellow marble is drawn (in 1 draw) = 1/10.

In 150 draws you can expect to draw 150* 1/10 = 15 yellow marbles.

So, the number of times for a green or yellow marble

= 60+15= 75.

Based on the scores that Jenna received on her quizzes, the lower quartile can be found to be 12

How to find the lower quartile?

To find the lower quartile, use the formula:

= (Number of scores + 1) x 1/4

But before that, you need to arrange the scores that Jenna received, from ascending order:

11, 12, 16, 16, 17, 18, 20

Then use the formula to find the position of the lower quartile:

= (7 + 1) x 1/4

= 8 x 1/4

= 2

It is in the second position. The lower quartile score is therefore 12.

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Based on the scores that Jenna received on her quizzes, the lower quartile would be; 12

What is quartile?

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

To determine the lower quartile, use the formula as;

= (Number of scores + 1) x 1/4

But before that, we need to arrange the scores that Jenna received, from ascending order which is;

11, 12, 16, 16, 17, 18, 20

Thus, use the formula for the position of the lower quartile:

= (7 + 1) x 1/4

= 8 x 1/4

= 2

Hence, It's in the second position. The lower quartile score is; 12.

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There are 240240 possible permutations of choosing 5 shows from 14 available shows. It can be obtained by applying the formula of permutation.

What is permutation?

In mathematics, it is the number of ways in which given number of items can be arranged in different orders.

Here, we need to select 5 iteams from the given 14 iteams.

[tex]P(14,5)=\frac{14!}{(14-5)!}\\=\frac{14!}{(9!)}\\=\frac{(14)(13)(12)(11)(10)(9!)}{(9!)}\\=(14)(13)(12)(11)(10)\\=240240[/tex]

Hence, there are 240240 possible permutations of choosing 5 shows from 14 available shows.

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If the liquid flows out of the tank at a rate of 40 cubic inches per minute, the height of the liquid will decrease at rate 0.0318 in./minute

Referring to the attached picture, the two triangles in a cone are similar. Hence,

r/h = 48/24

or

r = 2h.

The volume of the liquid is given by:

V = 1/3 . πr²h

Substitute r = 2h,

V = 1/3 . π(2h)²h = 4/3 . πh³

Take the derivative with respect to t

dV/dt = 4/3 . 3πh² . dh/dt

dV/dt = 4 . πh² . dh/dt

Substitute dV/dt = -40 and h = 10

-40 = 4 . π(10)² . dh/dt

dh/dt = - 0.0318 in./minute

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The values of the angles for the two parallel lines will be ∠1 = 115°, ∠2=115°, ∠3=148°, and ∠4 = 148°.

What are lines and angles?

Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point.

Given that the lines s and t are parallel to each other. The values of the different angles will be:-

∠1 = 115° Exterior angle property

∠2 = 115° Vertically opposite angle

The value of angle ∠3 will be calculated by the supplementary angle property.

∠3 = 148°

The value of angle ∠4 is 148 by vertically opposite angle property.

∠4 = 148°

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If a rectangle has an area of A and sides b and h, then:

[tex]A=b\cdot h[/tex]

Solving for the base:

[tex]b=\frac{A}{h}[/tex]

Basically, the sides b and h could have any value provided that b*h=A.

Nevertheless, this problem seems to want from us to factorize the expression:

[tex]x^2-5x-300[/tex]

So that each side is a binomial.

Part a)

To factorize that expression, find two numbers so that if they are added up, the sum is equal to -5, and if they are multiplied, the product is equal to -300.

Since the product is negative, one number must be negative. Since the sum is negative, the biggest number should be the negative one.

Consider the factors of 300:

[tex]300=2\cdot2\cdot3\cdot5\cdot5[/tex]

Using those factors, we can find pairs of numbers that give 300 as a result from multiplying.

After a bit of trial and error, notice that 15*20=300. If we choose 20 as the negative number, then 15*(-20)=-300 and 15+(-20)=-5. Therefore:

[tex]x^2-5x-300=(x+15)(x-20)[/tex]

So, we can choose the width and the height to be those factors. Since (x+15) is greater then (x-20), then:

[tex]\begin{gathered} \text{Width}=x+15 \\ \text{Height}=x-20 \end{gathered}[/tex]

Part b)

If x=45, then:

[tex]\begin{gathered} \text{Width}=60feet \\ \text{Height}=25feet \end{gathered}[/tex]

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Since angle D is 50, E is 80, we can add those two for now, 50+80=130, to make it 180, we can do 180-130 which gives us 50. So the value of x is 5. Sorry that its pretty confusing

ok

Equations : 4x + y = 2 x - y = 3

Equation 1 4x + y = 2 x - y = 3

x y x y

-2 10 -2 -5

-1 6 -1 -4

0 2 0 -3

1 -2 1 -2

2 -6 2 -1

The point where both lines cross is (1, -2) so it is the solution.

When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 1/2.

Given,

An envelope contains 8 bills;

Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.

When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.

Total outcomes = 2 x 2 x 2 x 2 = 16

Total possible outcomes, more than 20;

(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases

That is,

The total possible outcomes is 8.

Now,

The probability of bill to be $20 or more = Possible outcome / Total outcome

Probability = 8/16 = 1/2

That is,

When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 1/2.

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In order to determine the value of the missing length b, use the Pithagorean theorem, given by:

h² = a² + b²

where:

h = 6.5 mm

a = 2.5 mm

solve the previous equation for b, as follow:

b = √(h² - a²)

b = √(6.5² - 2.5²)mm

b = √36 mm

b = 6 mm

Hence, the value of the missing length is 6 mm

( x - 2) ( x - 4 ) is function which is equal to g(x) .

In the simplest terms, what is a function?

As a set of inputs with one output for each, a function is defined as a relationship between them. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

f(x) = x² - 1

f( x - 3 ) = ( x - 3 )² - 1

= x² + 9 - 6x -1

= x² -6x + 8

= x² -4x -2x + 8

= x( x - 4 ) -2( x - 4)

= ( x - 2) ( x - 4 )

g(x) = f(x - 3)

= ( x - 2) ( x - 4 )

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Given:

Alvin paddled for 2 hours with a 5-km/h current to reach a campsite.

Let n be the speed of boat.

Distance is calculated as,

[tex]\begin{gathered} d=rt \\ d=2\mleft(n+5\mright) \end{gathered}[/tex]

The return trip against the same current took 7 hours.

[tex]\begin{gathered} d=rt \\ d=7(n-5) \end{gathered}[/tex]

Equate both the equations,

[tex]\begin{gathered} 2(n+5)=7(n-5) \\ 2n+10=7n-35 \\ 7n-2n=10+35 \\ 5n=45 \\ n=\frac{45}{5} \\ n=9 \end{gathered}[/tex]

Answer: the speed of the boat is 9 mph.

Let

number of children admitted = x

number of adult admitted = y

Total number admitted = 335

[tex]\begin{gathered} x+y=335 \\ 1.5x+4y=940 \\ x=335-y \\ 1.5(335-y)+4y=940 \\ 502.5-1.5y+4y=940 \\ 502.5+2.5y=940 \\ 2.5y=940-502.5 \\ 2.5y=437.5 \\ y=\frac{437.5}{2.5} \\ y=175 \\ x+y=335 \\ x+175=335 \\ x=335-175 \\ x=160 \end{gathered}[/tex]

number of children = 160

number of adult = 175

[tex]25\pi[/tex]

1) The area of a sector of a circle can be found with the following formula:

[tex]\begin{gathered} A_S=\frac{\alpha}{360}\cdot\pi r² \\ A_s=\frac{90}{360}\dot{\cdot\pi(10)²} \\ A=\frac{\dot{100\pi}}{4} \\ A=25\pi \\ \end{gathered}[/tex]

2) Thus the area of the sector is 25π cm²

Kadeem takes 0.5 hours to travel 25 miles, and Quinn 0.33 hours, so Kadeem takes longer.

Who takes longer to drive 25 miles?

Remember the relation:

Speed*time = distance.

Notice that if the distance is fixed, then for a longer speed the time needed will be smaller.

Here we know that:

Kadeem drives at a constant speed of 50mi/h

Quinn drives at a constant speed of 75 mi/h.

Replacing that in the equation:

Kadeem's case:

(50 mi/h)*t = 25mi

t = (25 mi)/(50 mi/h) = 0.5 hours.

Quinn's case:

t = (25mi)/(75 mi/h) = 0.33 hours.

So Kadeem takes longer.

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Larger number: 12

Smaller number: 1

Let Statements:

Let x = the larger number

Let 1/2x - 5 = the smaller number

Equation:

x + (1/2x - 5) = 13

1.5x - 5 = 13

1.5x = 18

x = 12

Solutions:

The larger number = x = 12

The smaller number = 1/2x - 5 = 1/2(12) - 5 = 6 - 5 = 1

Both Sheila and Bob together can wash the car in 10 minutes

Calculating work :

The formulas to find work and time is given by

Time Taken = 1 / Rate of Work

Rate of Work = 1 / Time Taken

If a work can be done in x number of days, then the work can be done in one day = 1/x

Total Work done = Number of Days × Efficiency ( of the person or machine )

Given that,

Sheila can wash her car in 15 minutes

Let us consider washing the car is 1 unit of work

Then the work can done by Sheila in 1 minute = 1/15

Bob take twice as long as Sheila to wash the same

Bob can wash the same car in 30 minutes

Then the work can done by Bob in 1 minute = 1/30

From above calculation,

The work can be done by Sheila and Bob = (1/15 + 1/30)

= (2+1) /30 = 3/30 = 1/10

So the efficiency of Both Sheila and Bob per minute = 1/10

Let Both can complete the work in x minutes

As we know Total Work done = time × Efficiency

⇒ 1 = x × 1/10

⇒ x = 1 × 10

⇒ x = 10 minutes

Therefore,

Both Sheila and Bob together can wash the car in 10 minutes

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[tex]4x-5(2x-1)\le7\mleft(2x+3\mright)[/tex][tex]\begin{gathered} 4x-10x+5\le14x+21 \\ -6x+5\le14x+21 \\ -6x-14x\le21-5 \\ -20x\le16 \\ x\ge\frac{16}{-20} \\ x\ge-\frac{4}{5} \end{gathered}[/tex]

Answer:

Step-by-step explanation:

-1>-4>-6

-1 is the greatest number.

Answer:

50 degrees

Step-by-step explanation:

Line CDF is 180 degrees

76 and 54 and some part of the 180 degrees

1. add 76+54 = 130

2. subtract 180-130 = 50

⇒Mathematically this means

[tex]\frac{1}{4} (r+10)= r-4\\\frac{r}{4} +\frac{10}{4} =r-4\\\frac{r}{4}(4) +\frac{10}{4} (4)=r(4)-4(4)\\r+10=4r-16\\r-4r=-16-10\\-3r=-26\\\frac{-3r}{-3} =\frac{-26}{-3} \\r=\frac{26}{3}[/tex]

Attached is the solution.

If arthur walks 3 km north, and then turns east and walks 4 km. The distance traveled is 7km and his displacement is 5km.

Distance travelled and displacement

Distance traveled:

Distance traveled = Km north + East Km

Distance traveled = 3 km + 4 km

Distance traveled = 7 km

Displacement

Using Pythagoras theorem to determine or find the displacement

B² = A ²+AB²

B² = 3 ² +4 ²

B = 9+16

B = √ 25

B = 5 km

Therefore the 7km is the distance and 5km is the displacement.

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The property used here is the distributive property of the multiplication.

What property is being used?

Here we have the expression:

5*23 = 5*20 + 5*3

This is the distributive property of the multiplication, it says that:

A*(B + C) = A*B + A*C

Now, the original expression can be rewritten as:

5*23 = 5*(20 + 3)

And now we apply the above property to get:

5*23 = 5*(20 + 3) = 5*20 + 5*3

5*23 = 5*20 + 5*3

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Expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.

As given in the question,

Number of art electives students = 3

Number of history electives students = 4

Number of computer electives students = 5

Choosing an art electives students = ³C₁

Choosing an history electives students = ⁴C₁

Expression represents the probability that a student chooses an art elective and a history elective

= (³C₁⁴C₁) / ¹²C₂

Therefore, expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.

The complete question is:

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.

Which expression represents the probability that a student chooses an art elective and a history elective?

a. ⁷C₂ / ¹²C₂

b. ⁷P₂ / ¹²P₂

c. (³C₁⁴C₁) / ¹²C₂

d. (³P₁⁴P₁) / ¹²P₂

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the answer would be (0,5)

No. of ways of selecting the 5 member committee by combination= 1981

What are the number of ways of selecting the 5 member committee ?

No. of women faculty in the mathematics department = 7

No. of men faculty in the mathematics department = 7

Total number of faculty members = 14

Condition - at least one woman must be on the committee

No. of ways of selection = C (14, 5) - C (7, 5)

We know that combination C(n , r) = [tex]\frac{n!}{(n-r)!r!}[/tex]

Consider the total combination C (14, 5),

[tex]C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002[/tex]

Consider the combination of men C (7, 5) ,

[tex]C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21[/tex]

No. of ways of selection = C (14, 5) - C (7, 5)

= 2002 - 21

=1981

No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981

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Answer:

1.25 hours.

68.75 miles from the city

Step-by-step explanation:

Eltan's train (E) is travelling 65mph west.

Dmitri's train (D) is travelling 55mph west.

In terms of vectors, we can write E as 65E and D as 55W

The miles travelled by each is a function of time, T, in hours.

Each train's distance is:

E: T*65E

D: T*55W

They are 150 miles apart. They will meet with the combined miles travelled is 150 miles.

150 miles = T*65E + T*55W

150 miles = T(120 miles/hour)

T = (150 miles/120 miles/hour)

T = 1.25 hours

Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.

They will have travelled the following miles in 1.25 hours:

Demitri: (1.25hr)(55 m/hr) = 68.75 miles

Eitan: (1.25hr)(65 m/hr) = 81.25 miles

Total = 150 miles

Dimitri is headed away from the city. After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city. They meet 68.75 miles from the city.

Answer:

question one is B and question 2 is C

Step-by-step explanation:

The following table shows how the relation is a function when t is the independent variable and not a function when t is the dependent variable:

t 0 1 2 3 4 5

v 0 1 2 3 4 5

A vertical line drawn from the independent variable axis (x-axis) meets the function graph only once because a function is a relationship between an input and an output in which each input has just one output.

The independent variable is the input, while the dependent variable is the output.

Filling out the table in such a way that when t is the independent variable, the relationship is a function, and when t is the dependent variable, the relation is not a function, results in the following table:

t 0 1 2 3 4 5

v 0 1 2 3 4 5

Given that each value of the independent variable t has a corresponding value of the velocity v, the aforementioned is a function.

However, when t is the dependent variable, the independent variable value of 1 produces two outputs of 1 and 5, which results in the following table:

t 0 1 2 3 4 5

v 0 1 2 3 4 5

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Answer:

The percent change in attendance from the 2014 to 2015 school year is a 11.5385% decrease, or 12% when rounded.

Make sure to mark as Brainliest if this is correct so others know that this is the correct answer.

Answer:

r u cheating or just need "HELP"

Step-by-step explanation: