Look at the figure. Name the postulate or theorem
you can use to prove the triangles congruent.

SSS Postulate
SAS Postulate
ASA Postulate
AAS Theorem

Answer:

The length of the altitude PM is 3.5 cm.

Step-by-step explanation:

We are given that QT and PM  are the altitudes of the triangle PQR. Also, QR = 8 cm, PR = 7 cm and  QT = 4 cm.

We have to find the length of the altitude PM.

As we know that the area of the triangle is given by;

Area of triangle =  [tex]\dfrac{1}{2} \times \text{Base} \times \text{Height(Altitude)}[/tex]

Here, in [tex]\triangle[/tex]PQR; Base = PR = 7 cm

Height(Altitude) = QT = 4 cm

So, the area of the triangle PQR =  [tex]\frac{1}{2} \times 7 \times 4[/tex]

                                                       =  14 sq cm.

Similarly, the area of the triangle can also be;

Area  =  [tex]\frac{1}{2} \times \text{QR} \times \text{PM}[/tex]

Here, QR = Base of triangle PQR = 8 cm

PM = the required altitude

So, Area of triangle  =  [tex]\frac{1}{2} \times 8\times \text{PM}[/tex]

              [tex]14 =4 \times \text{PM}[/tex]

             PM  =  [tex]\frac{14}{4}[/tex]  = 3.5 cm

Hence, the length of the altitude PM is 3.5 cm.

Answer:

yes

Step-by-step explanation:

Answer:

Yes, the heat that flows into the system is used to change the internal energy of the gas and becomes work done by the piston.

Step-by-step explanation:

I took the K12 test :)

Answer:

x=1.

Step-by-step explanation:

2x + 1 = -x + 4

+x - 1 = +x - 1

3x. = 3

3/3. = x

1. = x

Answer:

Point B of 4the quertant

Answer:

HEY!

your answer is

it would be best to use litres

this is because a litre is 1000 millilitres and a swimming pool is a large amount of water.

Step-by-step explanation:

hope this helps

pls put brainliest

Answer:

The answer is 4.25*10^−4

Step-by-step explanation:

First convert 2.5*10^-5 into decimal form

That's

2.5*10^-5 = 0.000025

0.00045 - 0.000025 = 0.000425

= 4.25*10^−4 in scientific notation

Hope this helps

Answer:

4.25*10^−4

Step-by-step explanation:

khan

Answer:

A.

Step-by-step explanation:

When you multiply the two binomials using distributive property, you get the answer A. I could display the steps since it did not let me.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

The slope is -2/3

Step-by-step explanation:

We find the slope by using the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -1 -3)/( 3- -3)

   = -4 /( 3+3)

   = -4 / 6

   = -2/3

The slope is -2/3

Answer:

-2/3

Step-by-step explanation:

To find the slope, use 2 points and the slope formula:

Points are: (-3, 3) and (3, -1)

The slope is -2/3

Step-by-step explanation:

x² -6x+8=0

x²-4x-2x+8=0

x(x-4)-2(x-4)=0

(x-2)(x-4)=0

x = 2 OR 4

hence ox = 4,2

Answer: There are no real roots.

Step-by-step explanation:

To find the roots of the function

f(x) = (2^x − 1) - (x2 + 2x − 3) with x ∈ R.

First open the bracket

2^x - 1 - x^2 - 2x + 3 = 0

Rearrange and collect the like terms

2x^2 - x^2 - 2x + 3 - 1= 0

X^2 - 2x + 2 = 0

Factorizing the above equation will be impossible, we can therefore find the root by using completing the square method or the quadratic formula.

X^2 - 2x = - 2

Half of coefficient of x is 1

X^2 - 2x + 1^2 = -2 + 1^2

( x - 1 )^2 = - 1

( x - 1 ) = +/- sqrt(-1)

X = -1 + sqrt (-1) or -1 - sqrt (-1)

The root of the function is therefore

X = -1 + sqrt (-1) or -1 - sqrt (-1)

Since b^2 - 4ac of the function is less than zero, we can therefore conclude that there is no real roots

Answer:

It's pretty easy! You can manipulate the numbers to match the equation.

For example,

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

The other equivalent expressions that are equal to 7x - y​ could be; x + 8y + 6x - 9y = 7x - y, 5x + 2x - 2y + y = 7x - y and 10x + 7y - 3x - 8y = 7x - y

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; that can also be used to indicate the logical syntax's order of operations and other features.

We have been given the expression as;

6x + 7y + x-8y = 7x - y

When someone asks to solve an equation, then it usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

The other equivalent expressions that are equal to 7x - y​ could be;

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

To know more about an expression follow;

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▹ Answer

(x, y) = (14/5, 87/20)

▹ Step-by-Step Explanation

8x - 4y = -4 - 3x + 4y = 5

8x - 4y = 5

-4 - 3x + 4y = 5

8x - 4y = 5

-3x + 4y = 9

5x = 14

x = 14/5

-3 * 14/5 + 4y = 9

y = 87/20

(x, y) = (14/5, 87/20)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

11x−8y=−9

Step-by-step explanation:

khan

Answer:

50

Step-by-step explanation:

the missing number is 50

Answer:

50

Step-by-step explanation:

Every number is being multiplied by 10

Hope this helps you out! :)

Answer:

7 Children and 18 Adults.

Step-by-step explanation:

Sorry im late but thats the answer ^

There was 7 children attendee and 17 adult attendee.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

A restaurant catered an event for 25 people.

A child’s dinner cost $5 and an adult’s dinner cost $22.

The party cost $431.

let the number of children attendee be x and adult attendee be y.

So, x+ y = 25..............(1)

and, 5x + 22y = 431.......(2)

Solving the Equation (1) and (2) we get

5(25 - y) + 22y= 431

125 - 5y + 22y= 431

17y = 431-125

17y = 306

y = 18

and, x= 25-18 = 7

Hence, there was 7 children attendee and 17 adult attendee.

Learn more about Equation here:

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I hope this helps you

Answer:

Answer:

so x=8

Step-by-step explanation:

2x+46=7x+6

subtracting 7x on both sides

2x-7x+46=7x-7x+6

-5x+46=6

subtracting 46 on both sides

-5x+46-46=6-46

-5x=-40

5x=40

x=8

i hope this will help you :)

Answer:

x=3

Step-by-step explanation:

f(x) = 2^x

Let f(x) =8

8 = 2^x

Rewriting 8 as 2^3

2^3 = 2^x

The bases are the same so the exponents are the same

3=x

Answer:

A. 3

Step-by-step explanation:

y = 2^x

y = 8

Plug y as 8 in the first equation.

8 = 2^x

Make the left side of the equation with a base of 2.

2^3 = 2^x

Cancel bases.

3 = x

Answer:

(a) t_n = 3n - 9

(b) t_16 = 39

Step-by-step explanation:

(a)

-3 - (-6) = -3 + 6 = 3

The common difference is 3.

t_1 = -6

t_2 = -6 + 3

t_3 = -6 + 3 + 3

t_4 = -6 + 3 + 3 + 3

t_n = -6 + 3(n - 1)

t_n = -6 + 3n - 3

t_n = -9 + 3n

t_n = 3n - 9

The formula is: t_n = 3n - 9

(b) t_16 = 3(16) - 9 = 48 - 9 = 39

Answer:

an = -6 + 3(n - 1)

a(16) = 39

Step-by-step explanation:

Explicit Formula: an = a1 + d(n - 1)

Our d (common difference) is +3

Our a1 (First term) is -6

To find a(16) (the 16th term), plug in 16 for n.

Answer:

B

Step-by-step explanation:

The term 2013 in this context refers to the amount invested.

Mathematically, in finance, we can express the amount to be recouped on an investment, having a particular rate of return over a couple of years using the general formula;

V = P(1+r)^t

Such as in the case of amount obtained in a compound interest formula

Where P is the present value or principal or amount invested

V is the future value

r is the rate of investment

with t being the time taken

Answer:

a=1.5b

Step-by-step explanation:

Add 2b on both sides to get 7a=5a+3b

Subtract 5a

2a=3b

divide by 2

a=1.5b

Answer:

The box-and-whisker plot of this distribution is presented in the attached image to this solution.

Step-by-step explanation:

A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.

A box and whiskers plot shows 5 major information about the distribution of data. It shows:

- The maximum variable.

- The minimum variable.

- The Median.

- The first quartile.

- The third quartile.

Further info such as the range and Inter quartile range can then be obtained from this 5-number summary.

The elements of the box plot are described thus;

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.

The horizontal line inside the box is the median.

The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.

The required boxplot for this question is given in the attached image to this solution.

The median for the boxplot isn't provided, but it was assumed to be midway between the first and third quartile.

Hope this Helps!!!

Answer:

See Explanation

Step-by-step explanation:

The question didn't specify if letter can be repeated or not;

I'll solve for both;

Given

Number of Letters = 26

Number of squared = 4

If Repetition is allowed;

The four squares can take any of the 26 letters in any order

The first letter can be any of 26; Same with the second, third and fourth letters;

Number of Arrangement = 26 * 26 * 26 * 26

Number of Arrangement = 26⁴

Number of Arrangement = 456976

If Repetition is not allowed;

The first square can be filled with any of the 26 letters;

The second can take any of (26 - 1) letters

The third can take any of (26 - 2) letters

The fourth can take any of (26 - 3) letters

Number of Arrangement = 26 * (26 - 1) * (26 - 2) * (26 - 3)

Number of Arrangement = 26 * 25 * 24 * 23

Number of Arrangement = 358800

Answer:

26!/22!

Step-by-step explanation:

I just took the quiz I got it right

Answer:

A

Step-by-step explanation:

The range refers to the possible y-values.  You can assume that values on the right column are the y-values if it is not specifically expressed.  The right column is the output, or y, column.

Since you have a table, you have to state each number.  Put the numbers in numerical order.  This gives you an answer of

{46, 49, 52, 53, 58, 63, 64, 67}

Answer:

15 45 60 30

Step-by-step explanation:

Answer:

15 45 60 30

Step-by-step explanation:

the person above me is right and so am I I promise it's correct just did it on Time 4 Learning

Answer:

Step-by-step explanation:

ε = {x: 2≤ x ≤30}

M = { even numbers} = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

P = { prime numbers} = {2,3,5,7,11,13,17,19,23,29}

T = {odd numbers} = {3, 5, 7, 9, 11,13,15,17,19,21,23,25,27,29}

1. M ∪ P = {2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30}

2. M - T =

n(M) - n(T)

15- 14 = 1

3. P(MT)

(MT) = M ∩ T = 0

P ∪ (M ∩ T ) = {2,3,5,7,11,13,17,19,23,29}

4. P' = not a prime number

T' = not odd number = M

P' ∪(M∩T')

P' ∪ {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

= {2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}

Answer:

The median speed in race A is about 153 miles per hour, and the median speed in race B is about 145 miles per hour.

Step-by-step explanation:

For comparison, we need to analyze and compare both races data which are as follows

For Race A

Maximum range = 170 miles per hour

Minimum  range = 120 miles per hour

First quartile  ≈ 142 miles per hour

Median quartile ≈ 153 miles per hour

It comes from

[tex]= \frac{142\ miles + 165\ miles}{2}[/tex]

= 153 miles

The Third quartile = 165 miles per hour

For Race B

Maximum range  = 165 miles per hour

Minimum range = 125 miles per hour

First quartile  ≈ 139 miles per hour

Median quartile = 145 miles per hour

It comes from

[tex]= \frac{139\ miles + 150\ miles}{2}[/tex]

= 145 miles

The third quartile = 150 miles per hour

Hence, the last option is correct

Hey there! :)

Answer:

(3.5, -1).

Step-by-step explanation:

Use the midpoint formula to solve this problem:

[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Plug in the coordinates given:

[tex](\frac{10-3}{2}, \frac{8-10}{2})[/tex]

Simplify:

[tex](\frac{7}{2}, \frac{-2}{2})[/tex]

Therefore, the coordinates of the mid-point are:

(3.5, -1).

Answer:

$4,523.40

Step-by-step explanation:

The cell phone cost is $124.65 per month. With 12 months in a year, we multiply $124.65 x 12 to get the answer $1,507.80. Since one year equals $1,507.80, we multiply this answer by 3 for 3 years to get $4,523.40. Thus three years of service with $124.65 a month would equal $4,523.40.

Answer:

83/5, 16.6, 16 3/5

Step-by-step explanation:

When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment.

6 times 18 = 5(5+x)

The total secant segment is 6+12=18

so one side = 6 times 8.

The line from the circle (but not inside) is 5.

You don't know the entire segment, but you do know that 5 is part of it. Hence 5 times (5+x).

Sorry for the trashy explanation.

Answer:

Step-by-step explanation:

Answer:

13/3

Step-by-step explanation:

To find the mean of a data set, you must add all the given numbers and then divide the numbers by how many numbers there are.

3+5+4+3+5+6=26/6=4.3333...

When we convert the answer from a decimal to a fraction, we get 13/3.

Hope this helps!!! PLZ MARK BRAINLIEST!!!