Prove the following statement using the given pieces of information.2Given: ZGPS = ZJPS, PS_L_GJProve: ASJP – ASGPZGPS ZJPSbecause perpendicular lines form right angles, and all right anglès are congruent.PS and PS arethe two pairs of congruent angles.Click to select your answer(s).

For 12 to be the GCF (Greatest common factor) between 36 and 60, means that the greatest number that can divide both 36 and 60 at the same time is 12.

We need to come up with a question involving the graph.

Very simple!

We can ask how much time in a day Cal spends for different activities.

We can say:

According to the graph, how much time of the day does Cal spend studying and sleeping?

answering this question:

After calculating some basic arithmetic we have come to find that, 12 pounds of more cheese  should be added to the scale to get the amount that Veronica needs which 23 pounds.

Using the four operations, arithmetic is a branch of mathematics that deals with the characteristics of numbers.

Division, multiplication, and subtraction are the four operations. The rules for each operation are very detailed.

As an illustration of arithmetic, one of the rules of addition and subtraction is that addition increases the overall value of a number while subtraction decreases the overall value of a number.

Veronica needs to buy 13 pounds of cheese

Cheese in a container weighs = 1 pounds

Mass of cheese clerk needs to add = 13 - 1

                                                            = 12 pounds

                                                             (as 1 pound is already there)

Thus, 12 pounds of more cheese  should be added to the scale to get the amount that Veronica needs which 23 pounds.

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If M is a centroid of triangle WOR and YR =16, the length of WR

side will be WR = 48.

The ratio of the two sides will be given here as:

WY/ YR = 2/1

Determine the value of YR to determine the value of WR.

WY/16 = 2/1

WY = 32

WR will have the following value:

WR = WY+ YR

WR = 32+ 16

WR = 48

As a result, the value of the side WR is 48.

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The value of the composite function (f o g)(x) is 8x - 17

The definition of the functions are given as

f(x) = 4x - 1

g(x) = 2x - 4

The composite function definition is given as

(f o g)(x)

This composite function is calculated using the following composite function formula

(f o g)(x)= f(g(x))

Substitute the known values in the above equation

So, we have the following equation

(f o g)(x) = 4(g(x)) - 1

So, we have the following equation

(f o g)(x) = 4(2x - 4) - 1

Open the brackets

(f o g)(x) = 8x - 16 - 1

Evaluate

(f o g)(x) = 8x - 17

Hence, the composite function is (f o g)(x) = 8x - 17

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Answer:

1. -6 + 10x

Step-by-step explanation:

The expression 10x – 6 is the same as adding -6 to 10x, or 10x + -6. Since addition equations can be rearranged, 10x + -6 can also be written as -6 + 10x.

Answer:

[tex] \sf{ \large{ - 6 + 10x}}[/tex]

Step-by-step explanation:

10x - 6

note: there is a plus sign at 10x

+10x - 6

so when you switch it will be like this

-6 + 10x

SOLUTION:

Step 1:

In this question, we are given the following:

Bismuth-210 has a half-life of about 6 days.

After 21 days, how many milligrams of a 1,220 mg sample will remain?

Round answer to the nearest tenth place.

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is:

Given

Variables

Find

Which variable being tested in an experiment

Explanation

The dependent variable is the variable that is being measured or tested in an experiment

response variable is often referred as dependent variable.

Final Answer

hence , the correct option is A.

0.0058

The given scientific notation is:

This can also be written as:

Therefore 5.8 x 10^-3 in standard form is 0.0058

Answer:

16.56

Step-by-step explanation:

9.66/7

=1.38 each

1.38x12=16.56

Answer:

16.56

Step-by-step explanation:

The mathematical expression 8z - 2 can be phrased as:

The difference between 8 times the variable z and 2.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Any mathematical object has a symbol, and that symbol is called a variable. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

Consider the mathematical expression,

8z - 2

The expression can be defined as 2 less than the product of 8 and variable z.

The expression can also be rephrased as:

The difference between 8 times the variable z and 2.

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Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x > −2

Interval Notation:

(−2, ∞)

X is greater than -2

There are 35 natural numbers that are greater than 64.

Natural numbers:

Natural number are the numbers that start from 1 and end at infinity. In other words, they are counting numbers and they do not include 0 or any negative values.

Given,

Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.

Here we need to find the numbers that satisfied the given condition and that is also greater than 64.

We know that, two digit natural numbers range from 10 to 99.

Since there are replacement take place, then each number formed from 10 to 99 is valid in this exercise.

Now, we have to move on to the other thing that is, those number are greater than 64,

Then we have to calculate it as,

=> 99-64 = 35 are greater than 64.

And those number are 65,66,67,68,69,...,98,99.

Finally, we have identified that there are 35 number are greater than 64.

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A) 8 cents

Explanation

Step 1

find the rate

cost

hence

total cost = time*rate*consume

now, to convert from dollars to cents, multply by 100

I hope this helps you

From the graph, x coordinate 3 mean it takes 3 seconds to travels 15 miles.

Option B is the correct answer.

Given,

The expression is,

Substracting 4 from both sides then,

Substracting 6n from both sides then,

Multiplying both sides by 1/3 then,

Hence, the solution for n is n<= (-10/3).

we know that

the formula is equal to

P(n,r) = n! / (n-r)!

we have that

nPr = n!/(n-r)!

we have

11P0

so

n=11

r=0

= 11!/(11-0)!

=11!/11!

=1

Part a: The missing length =  28 units.

Part b: The missing length =  25 units, for the given similar triangle.

Part a: For the similar triangles.

Let the unknown value be x.

The, using the similarity of the triangle,

63/x = 27/12

x = (63×12)/27

x = 28 units.

The missing length is 28 units.

Part b:  For the similar triangles.

Let the unknown value be x.

The, using the similarity of the triangle,

21/15 = (10 + x)/x

21x = 150 - 15x

6x = 150

x = 25

The missing length is 25 units.

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Answer:

there is none so it would be 62

Step-by-step explanation:

Solution

For this case we can use the compound interest formula given by:

and for this case A= 5000, r = 0.06, t= 4 and n = 1 ( compounded yearly)

and the interest would be:

Number of large boxes will be 65.

Number of small boxes will be 70.

What is mathematical expression?

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

Given that;

The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each.

There are 135 boxes in all.

If the truck is carrying a total of 4350 pounds in boxes.

Let number of large boxes = x

Number of small boxes = y

Since, There are 135 boxes in all.

So, We get;

x + y = 135  ... (i)

And, The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each and the truck is carrying a total of 4350 pounds in boxes.

So, we can formulate;

40x + 25y = 4350  ... (ii)

Solve equation (i) and (ii) as;

Multiply 40 by (i) and subtract by (ii) we get;

40x + 40y - 40x - 25y = 5,400 - 4,350

15y = 1,050

y = 70

And, x + y = 135

x + 70 = 135

x = 135 - 70

x = 65

Thus, Number of large boxes will be 65.

Number of small boxes will be 70.

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Answer:

B and C are correct

Step-by-step explanation:

[tex]\cfrac{6^3\cdot 15^3}{(7^0)^3}\implies \cfrac{(6\cdot 15)^3}{(1)^3}\implies \cfrac{90^3}{1}\implies 729000[/tex]

Given,

The expression for function P(x) is | x |.

The expression for function I(x) is | x |/2.

Required:

The graph of the function.

The graph of the function is,

The function P(x) is represented by black line.

The function I(x) is represented by Red line.

Hence, option A is correct.

From the table it can be observed if we multiply the number of boxes by 9, then it gives total number of pounds for the corresponding number of boxes.

As 4 multiply by 9 is 36, which is total number of pounds for 4 boxes. In similar manner total number of pounds can be obtained for different number of boxes.

So answer is,

Option B is correct.

We have the following:

We apply the distributive property that tells us that the multiplication of a number by a sum is equal to the sum of the multiplications of said number by each of the addends.

Therefore:

The bag has 5 marbles

3 yellow marbles

2 red marbles

"Glen chooses a marble first and then Kris chooses one" You have to determine the probability of Kris choosing a yellow marble if Glen chooses a yellow one first.

1. First you have to determine the probability that Glen choose a yellow marble first.

To do so, you have to calculate the quotient between the number of yellow marbles on the bag and the total number of marbles on the bag:

2. and 3.

After Glen takes the first yellow marble from the bag, the total number of marbles is reduced by one and so is the number of yellow marbles on the bag, so:

New total: 4 marbles

Number of yellow marbles: 2

4.

To determine the probability of Kris choosing a yellow marble, you have to use the data on the remaining marbles on the bag. And calculate the quotient between the remaining number of yellow marbles and the remaining number of marbles:

Solution

For this case we can use the Pythagoras theorem and we have:

And solving for x we got:

Then the answer is:

14.25