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Two triangles A B C and A D E. Triangle A B C is on top of Triangle A D E at point A. Side A C is smaller than A E and side A B is smaller than side A D. Side C B has a length of three. Side E D has a length of x. Side A B has a length of nine. Segment B D has a length of six. Angle A B C and A D E are both ninety degrees.
A
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E
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D
D
B
B
C
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9
9
3
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6
6
x
x

The perpendicular bisector of the line segment with endpoints (6, -5) and (-2, -9) is 7x,2y = 6.

Therefore,

The coordinates of the end points:

(6, -5) and (-2, -9)

((6, -5) +(-2, -9))/2

= ((6,-9)/2, (-2, -5)/2)

= (1.5, 3.5)

The difference in endpoint coordinates will be;

(Δx, Δy) = (9-(-5), (-2)-6) = (14, 8)

Then the ratio of these values, so we need to divide both by the common factor of 2:

(Δx, Δy) = (7, 2)

A line perpendicular to this segment through the point (h, k) can be written as;

Δx·x +Δy·y = Δx·h +Δy·k

7x ,2y = 7(2) 2(4)

7x, 2y = 6 .

Hence the standard form equation for the perpendicular bisector will be;  7x ,2y = 6 .

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When the circumference of a circle is 19π cm the area of the circle is

28.27 square centimeters

Information given in the question include

The circumference of a circle is 19π cm

Area of a circle is given by

π r^2

where r = radius

π = constant = 3.124

circumference of a circle is given by 2πr

2πr = 19

πr = 9.5

r = 3.024

r = 3 cm

The area is solved as

= π * 3^2

= 28 .27square centimeters

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The car travels 30 miles in 45 minutes with the speed 40 miles/hour with the constant speed.

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. The distance traveled by a moving object in a specific amount of time is its speed. How quickly something is moving is determined by its speed. The distance traveled by an object in a given amount of time divided by the time gives the object's average speed.

Here,

45 minutes/60 minutes= .75 hours (this gives you the amount of time in hours)

time x speed = distance

.75 hours time x 40 mph speed = 30 miles distance

With a constant speed of 40 miles per hour, the car covers 30 miles in 45 minutes.

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Answer: The sum of two prime numbers is always even (which is composite).

Hope this helped :)

The probability that exactly four of the selected bulbs from the pack of 10 bulbs is defective is 1/120.

For the given question;

Thus, the probability that exactly four of the selected is defective.

P = ⁴C₄  / ¹⁰C₃

P = 1/120

Thus, the probability that exactly four of the selected is defective is 1/120.

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Answer:

175

how will convert it in mixes fraction when there is no division number

By simplifying 2/5  + [tex]a^{2/2}[/tex] C we get the solution as (2a + 5C) / 5.

Given equation ,

2/5  + [tex]a^{2/2}[/tex] C

We know that ,  [tex]a^{2/2}[/tex]  = a

So the equation becomes ,

2/5 a + C

By simplifying,

2a / 5 + C

= 2a / 5 + 5C / 5

By combining fractions ,

(2a + 5C) / 5

Thus solution is (2a + 5C) / 5 .

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~16 - (-16)~~)^2 + (~~4 - 11~~)^2} \implies d=\sqrt{(16 +16)^2 + (4 -11)^2} \\\\\\ d=\sqrt{( 32 )^2 + ( -7 )^2} \implies d=\sqrt{ 1024 + 49 } \implies d=\sqrt{ 1073 }\implies d\approx 32.76[/tex]

Yes, a baseball fit in box A.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc.

Volume is simply the amount of space a three-dimensional solid takes up. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.

Given:

The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches.

So, the maximum value of Circumference

2πr = 9.5

r= 9.5/ 2 x 3.14

r = 1.472 inch

So, Volume of ball = 4/3 πr³

Volume of ball = 4/3 x 3.14 x (1.472)³

Volume of ball = 13.36 inch³ < 64 inch³

Hence, it will fit inside the box.

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Answer:

d

Step-by-step explanation:

Because answer would be 4/10 or 5/10

The equivalent expressions using only positive exponents are 1/(7x⁵y⁸)⁵ and (5y³/x⁶)⁵

Expression 1

From the question, the expression is given as

(49x¹⁰y¹⁶)⁻⁵/²

Express the radicals as roots

So, we have

(49x¹⁰y¹⁶)⁻⁵/² = √[(49x¹⁰y¹⁶)]⁻⁵

Take the square root of each of the factor in the bracket

This gives

(49x¹⁰y¹⁶)⁻⁵/² = (7x⁵y⁸)⁻⁵

Apply the negative exponent rule of indices

So, we have

(49x¹⁰y¹⁶)⁻⁵/² = 1/(7x⁵y⁸)⁵

Expression 2

From the question, the expression is given as

(125x⁻¹⁸y⁹)⁵/₃

Express the radicals as roots

So, we have

(125x⁻¹⁸y⁹)⁵/₃ = ∛[(125x⁻¹⁸y⁹)]⁵

Take the cube root of each of the factor in the bracket

This gives

(125x⁻¹⁸y⁹)⁵/₃ = (5x⁻⁶y³)⁵

Apply the negative exponent rule of indices

So, we have

(125x⁻¹⁸y⁹)⁵/₃ = (5y³/x⁶)⁵

Hence, the equivalent expression is  (125x⁻¹⁸y⁹)⁵/₃ = (5y³/x⁶)⁵

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The number of books bought by the school is 92.

Here it is given that the school spend $925 to buy new books for the library.

The cost of each book is $9.95

So we have to find the number of books that can be bought.

By dividing the total money spent by the cost of each book we get the number of books bought.

Let n be the number of books bought.

n × 9.95 = Total money spend on the books

As we know the total money spend on the books is $925.

So we get:

925 = n × 9.95

n = 925/ 9.95

= 92

Therefore the total number of books bought is 92.

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Answer:

-7,7

Step-by-step explanation:

The fraction 7/2a+4/a*a can be written as (7 + 8a) / 2a

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are in spoken common English. In other words, a fraction indicates the components of a whole or group of items.

Solution Explained:

First, we simplify the equation

=  [tex]\frac{7}{2a} + \frac{4}{a} X a[/tex]

=  [tex]\frac{7}{2a} + 4[/tex]

= [tex]\frac{7 + 8a}{2a}[/tex]

Therefore, the equation can be written as (7 + 8a) / 2a

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You can see pic..

The linear equation parallel to 8y=6x+5  is:

y = (3/4)*x - 4

Remember that two linear equations are parallel if and only if both lines have the same slope and different y-intercept.

Here we want to find a line parallel to:

8y = 6x + 5

Rewriting this in slope-intercept form we get:

y = (6x + 5)/8

y = (3/4)*x + 5/8

Then a parallel line to this one will be:

y = (3/4)*x + b

To find the value of b, we use the fact that this line must pass through the point (-8, -10).

-10 = (3/4)*(-8) + b

-10 = -6 + b

-10 + 6 = b

-4 = b

Then the linear equation is:

y = (3/4)*x - 4

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Answer:

4:1

Step-by-step explanation:

12÷3=4

3÷3=1

white to blue

12 : 1

Answer: angle 1 and 4

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

x + 12 = 90

x = 78

The minimum score needed to receive a grade of 'a' is 87.92

Given that,

At a nearby university, a professor noticed that her students' exam results were regularly distributed, with a mean of 73 and a standard deviation of 11. 8.75 percent of the professor's students achieved grades of A, she told us.

Mean = μ = 73

Standard deviation = σ =  11

Using the standard normal table,

⇒ P(Z > z) = 8.75%

⇒ 1 - P(Z < z) = 8.75%

= 1 - P(Z < z) = 0.0875

= P(Z < -1.36) =1- 0.0875

= P(Z < 1.3563) =0.9125

∴ Z = 1.3563                              ( Using standard normal z-table )

Using z-score formula ;

x= z * σ + μ

x=1.3563 * 11 + 73

x=87.92

So, the minimum score needed to receive a grade of 'a' is 87.92

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The graph of the inequality is attached below.

We are given an inequality. The inequality is linear in nature. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. The inequality is given below.

y < 2x - 3

We need to graph the inequality. The first step is to find out the corresponding equation of the straight line. The equation is found by replacing the greater-than or less-than sign with the equal-to sign. The equation is given below.

y = 2x - 3

We plot this equation on the graph with a dotted line. Now we shade the area that satisfies the given inequality. The graph is given below.

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Answer:

Step-by-step explanation: I think it could be 5,0000

Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

What is an Algebraic Expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. For example, 3x² − 2xy + c is an algebraic expression.

Given,

Total money Preston have = $15

He buys the ticket for = $6.50

And, two snacks = $1.75 each

so the cost of two snacks is = 1.75 * 2 = $3.5

Total cost for ticket and snacks = $3.5 + $6.50 = $10

Now, he spent money on snacks and ticket $10 and he have total money $15 so,

Preston left with = $15 - $10

                           = $5

Therefore, Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

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Answer:

D

Step-by-step explanation:

Multiply both sides by 3

x − 1 = 9

Add 1 to both sides

x = 10

Answer:

Step-by-step explanation:

5.40/12= 0.45

6.72/16=0.42

Answer:

The 16 pack

Step-by-step explanation:

Pack 1: $5.40 for 12

Pack 2: $6.72 for 16

Therefore the 16 pack is the better buy because you purchase an extra 4 sodas for $0.03 less.

To select the community, there are 20 ways available.

What is Combination?

A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant.

Solution:

Since 2 particular students are to be included,

we have to arrange 3 students from 6 students.

nCr = n! / (n-r)!*r!

6C2 = 6!/ (6-3)! 3!

6C2 = 6*5*4*3!/ 3! * 3*2

6C2 = 5*4 = 20

Thereofre, there exists 20 ways of doing the above mentioned.

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Answer:

A

Step-by-step explanation:

the arithmetic sequence is the one in which the difference between the one and the next term is a constant.

0,7,14,21,28,35,42...

this is an arithmetic sequence with a common difference of [7]

The proportion of bottles that will have more than 18 ounces dispensed into them is 0.0228

Proportion relationship:

Proportion means a relationships between two variables where their ratios are equivalent and it is the way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

Given,

A company that manufactures and bottles apple juice uses a machine that automatically fills 20-ounce bottles. there is some variation, however, in the amount of liquid dispensed into the bottles. the amount dispensed has been observed to be approximately normally distributed with mean 20 ounces and standard deviation 1 ounce.

Here we need to determine the proportion of bottles that will have more than 18 ounces dispensed into them and round the answer to the four decimal places.

Here we have to use tables to determine the proportion of bottles that will have more than 18 ounces dispensed into them.

Let us consider X denote the amount of juice dispensed.

Then it can be written as,

P (X >18) = P (Z > (20 - 18)/1)

=> P (X >18) = P (Z > 2)

=> 1 - Ф(2)

=> 1 - 0.9772

=> 0.0228

Hence the proportion of the bottles that will have more than 18 ounces dispensed into them is 0.0228.

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