Find the prime factorization of 42.Use the multiplication sign, ×, instead of the letter x to separate the factors. It can be found on the keyboard provided below.

First we are going to mention the postulate. It is going to be the SAS theorem.

As we can see in the image both triangles share one side, and since it is a parallelogram the hypotenuse is equal for both. So, we have 2 equal sides. And we can see each triangle has one right angle. So , the conditions of the SAS theorem are fulfilled.

Given: The penny size d is given by the equation

where n is the length of the nail.

Required: a) To solve the equation for n

b) To use the equation to find out the length of the nail with the following penny sizes: 3, 6, and 10.

Explanation: The given equation can be solved for n as follows

Now putting the value of d=3 we get

Again putting d=6 we get

Finally putting d=10 we get

Final Answer: a) The equation for n is

b) The length of the nail with penny sizes 3,6, and 10 is 5/4, 2, and 3 respectively.

Let the height of the beanstalk be h

from the diagram,

Also,

We need to create a table as follows:

Yellow pieces Green pieces Yellow/Green

5 50 - 5 = 45 5/45 = 0.11

10 50 - 10 = 40 10/40 = 0.225

15 50 - 15 = 35 15/35 = 0.4286

25 50 - 25 = 25 25/25 = 1

35 50 - 35 = 15 35/15 = 2.333

45 50 - 45 = 5 45/5 = 9

We define the number of yellow pieces, then we calculate the number of green pieces taking into account that the sum of yellow and green is 50.

Finally, we found the relation between yellow and green pieces. The answer is going to be the row where the division between the yellow and green pieces is 9. Because that division tells us how many Yellow pieces are for every green piece.

Answer: 45 yellow pieces

Since the shape of the frame is a square we know that its area is given as:

where l is the length of each side, plugging the value of the area into the equation and solving for l we have:

Therefore we notice that the length of the sides is between 11 and 12 inches, hence the answer is C.

Answer: The length of the photo frame is between the 11 inches and 12 inches.

Step-by-step explanation: 123 square root = 11.0905

Solve the equation;

The solution is, x = 3

Given data:

The given expression is 10-x +y/2.

The given value of x is x=5.

The given value of y=2.

Substitute the given values in the expression.

Thus, the value of the given expression is 6.

Let n be the number of nickels

Let d be the number of dimes

There are 31 coins in your pocket:

You have in total $2.65:

Use the two equations above a system of linear equations to solve the variables n and d:

1. Solve n in the fist equation:

2. Use the value of n=31-d in the second equaiton:

3. Solve d:

4. Use the value of d=22 to solve n:

Solution:

Weakest correlation states that a linear relationship is indicated by a correlation coefficient equal to 0 or if the value is nearest to 0, then it also represents the weakest correlation.

Thus, the nearest value to zero in the option is 0.1

In general, the simple interest formula is

Thus, in our case,

Therefore, finding A,

The exact answer is $2208.275

ANSWER:

24 miles

STEP-BY-STEP EXPLANATION:

The first thing is to make a graph of the situation, like this:

Therefore, the function of total cost will be:

To minimize we must calculate the derivative of the function, like this:

Now we set the derivative equal to 0 and solve for d, like this:

Distance from terminal the two types of pipe meet is 29 - x, therefore would be:

Answer

Area = 314 square inches

Explanation

The area of a circle is given as

Area = πr²

π = pi = 3.14

r = radius of the circle = ½ (Diameter) = ½ (20) = 10 inches

Area = πr²

Area = 3.14 × (10²)

Area = 314 square inches

Hope this Helps!!!

According to the problem, the recursive rule is

This means the first term of the sequence is 15.

So, for n = 2, we have

But, we know that f(1) = 15, so

The second term is 9.

For n = 3.

But, we know that f(2)=9, so

The roman number for 1000 is M.

The roman number for 600 is DC. (In this case we have to remember that the D represents 500 and C represents 100, then their sum 600 is DC).

The roman number for 30 is XXX. (X represents 10, then 30 is represented by XXX).

Therefore, the roman numeral for 1630 is MDCXXX

We are given various skateboard kicker ramp with different height and base

For the first triangle,

The heigth = 3 ft

Base = 12 ft

The ratio of height to base = 3/12

= 1 : 4..

Second figure,

The height = 1 ft

Base = 1.5 ft

Only the first figure and the second figure will give you 4 : 1 as the ratio of hei

To find the fraction form of 2.2

First separate, the whole number 2 from the decimal

Then write ;

since there is only one number after the decimal point, we will multiply the numerator and denominator by 10

That is;

Join the fraction and the whole number part together

His first step should be subtracting 3 from both sides of the equation(Subtraction property of equality).

The multiplication property of equality states that when we multiply both sides of an equation by the same number, the 2 sides remain the same.

The next step is the Multiplication property of equality

His error is that the Multiplication Property of equality came before the Subtraction property of equality. The subtraction property of equality should come first.

Answer:

180 miles

Explanation:

The distance can be calculated as the speed times the number of hours.

So, the distance is equal to:

Therefore, the distance traveled by car was 180 miles.

Answer:

32,767 pennies

Explanation:

The number of pennies saved by Joe for the first four days forms the sequence below:

We want to determine the total size of Joe's collection on the 15th day.

The sequence above forms a geometric sequence in which:

• The first term, a1 = 1

• The common ratio, r = 2/1=4/2=2

The sum of a geometric sequence is determined using the formula:

On the 15th day: n=15

If Joe continues with this pattern, he will have 32,767 pennies on the 15th day.

Given the question:

what is the perimeter of square HIJK?​

Let the square has a side length = x

The perimeter will be = 4x

Answer:

Machikna randi ko chalo

b³ - 2ac + d²

a = 2

b = -3

c = 4

d = -5

In order to evaluate the given polynomial, we need to replace each letter by its corresponding value:

b³ - 2ac + d²

(-3)³ - 2 * 2 * 4 + (-5)²

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

9 * (-3) - 16 + 25 , because the product of two negative numbers equals a positive number

-27 - 16 + 25

-27 + 9

-18

Answer:

(1,-1)

Step-by-step explanation

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places.

Therefore, the image of (-1,1) is (1,-1)

Let x be the cost before the sale, since during the sale you can at least save $50, the cost before the sale was

Therefore, the suit cost before the sale was

that is, it costs greater or equal to $299

The formula for calculating binomial probability is expressed as

P(x) = nCx * p^x * q^(n - x)

where

n represents number of trials

p represents probability of success

q represents probability of failure

x represents number of successes

From the information given,

n = 5

p = 0.479

q = 1 - p = 1 - 0.479 = 0.521

For x = k = 0,

P(x = k = 0) = 5C0 * 0.479^0 * 0.521^(5 - 0)

P(x = k = 0) = 0.0384

For x = k = 1,

P(x = k = 1) = 5C1 * 0.479^1 * 0.521^(5 - 1)

P(x = k = 1) = 0.1765

For x = k = 2,

P(x = k = 2) = 5C2 * 0.479^2 * 0.521^(5 - 2)

P(x = k = 2) = 0.3245

For x = k = 3,

P(x = k = 3) = 5C3 * 0.479^3 * 0.521^(5 - 3)

P(x = k = 3) = 0.2983

For x = k = 4,

P(x = k = 4) = 5C4 * 0.479^4 * 0.521^(5 - 4)

P(x = k = 4) = 0.1371

For x = k = 5,

P(x = k = 5) = 5C5 * 0.479^5 * 0.521^(5 - 5)

P(x = k = 5) = 0.0252

Answer

Tan (7π/3) = √3

csc (-330°) = 2

Explanation

tan (7π/3) Note: π radians = 180°

tan [(7 x 180°)/3]

tan 420° = tan (420 - 360)° = Tan 60°

tan 60° = √3

∴ tan (7π/3) = √3

csc (-330°) = csc (-330° + 360°)

csc (30°) = 1/sin (30°) = 1 ÷ 1/2 = 2

∴ csc (-330°) = 2

In the given question we are asked to pick what described line GI.

Explanation

In the question, we are given four possible options which are

1) Perpendicular bisector of FH

2) Angle bisector of G

3) Median of triangle FGH

4) Altitude of triangle FGH

Considering options 1. 2, 3, we should note that the trio of options will require a confirmation that angle G is truly bisected by GI. Since there is no indication of that on the image, it implies that the only accurate option is

Answer: Altitude of triangle FGH

ollo

Here we have:

m(x) = 5 - x

which is: y = m(x) = 5 -x

To solve this, substitute each value given for x in the equation.

The height of the 7 box tower is 161 centimeter.

Given,

The number of boxes Mary used to make a tower = 5

The height of the tower = 115 cm

Number of boxes Mary puts again on the pile = 2

We have to find the height of the new tower.

Here,

Height of one box = Height of tower / number of boxes used

= 115/5

= 23 cm

Height of one box is 23 cm.

Height of new tower = height of old tower + (number of boxes added × height of one box)

= 115 + (2 × 23)

= 115 + 46

= 161

Therefore,

The height of the 7 box tower is 161 centimeter.

Learn more about height of box here;

https://brainly.com/question/12246051

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Given

The Arithmetic sequence,

25, 31, 37, 43.

To find:

The commen difference of the arithmetic sequence.

Explanation:

It is given that,

The Arithmetic sequence,

25, 31, 37, 43.

That implies,

Hence, the common difference is 6.

Solution;

This means the concert ticket costs less per ticket and the difference is,

The concert ticket costs $0.20 less than the movie ticket