2.
Consider the following graph and rotate point P 90° counterclockwise
around two points: the origin and (-2,4). Sketch both points on the
graph.

If the function f be defined by f(x) =5x – 2a, then the value of a is 5.

Let the function f be defined by f(x) =5x – 2a

The value of f(10)

f(x) =5x – 2a

f(10) = 5(10) - 2a

f(10) = 50 - 2a

The value of f(10)

f(x) =5x – 2a

f(5) = 5(5) - 2a

f(5) = 25 -2a

f (10) + f (5) = 55,

50 - 2a + 25 - 2a = 55

-4a = 55 - 75

4a = 20

a = 5

Therefore, if the function f be defined by f(x) =5x – 2a, then the value of a is 5.

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\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's solve ~

By using distance formula :

\(\qquad \sf  \dashrightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } \)

\(\qquad \sf  \dashrightarrow \: \sqrt{(4 - ( - 1)) {}^{2} + (4 - ( - 1)) {}^{2} } \)

\(\qquad \sf  \dashrightarrow \: \sqrt{(4 + 1) {}^{2} + (4 + 1) {}^{2} } \)

\(\qquad \sf  \dashrightarrow \: \sqrt{2(5) {}^{2} } \)

\(\qquad \sf  \dashrightarrow \: 5 \sqrt{2 }\: \: units\)

\( \rm{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }\)

Proof:

\( \rm{Let \: X'OX \: and \: YOY' \: be \: the \: z-axis \: and \: y-axis \: respectively. Then, O \: is \: the \: origin.}\)

\( \rm{Let \: A(x_1,y_1) \: and \: B(x_2,y_2) \: be \: the \: given \: points.}\)

\( \rm{Draw \: AL \perp \: OX, BM \perp \: OX \: and \: AN \perp BM }\)

Now,

\( \rm{OL=x_1,OM=x_2,AL=y_1 \: and \: BM=y_2}\)

\(\rm\therefore{AN=LM=(OM-OL)=(x_2-x_1)}\)

\( \: \: \: \: \rm{BN=(BM-NM)=(BM-AL)=(y_2-y_1)}\)

\( \rm{In \: right \: angled \: \triangle ANB, by \: Pythagorean \: theorem,}\)

We have,

\( \: \: \: \: \rm{AB^2=AN^2+BN^2}\)

\( \rm{or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2}\)

\( \rm\therefore AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \)

The Given question,

Find the distance of AG if A (4,4) and G (-1,-1).

Solution,

The given points are A(4,4) and G(-1,-1).

Then,

\( \rm{(x_1=4,y_1=4) and (x_2=-1,y_2=-1)}\)

We know that,

The distance formula,

\( \rm{AG= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }\)

\( \: \: \: \: \: \: \: \: = \sqrt{ {( - 1 - 4)}^{2} + {( - 1 - 4)}^{2} } \)

\( \: \: \: \: \: \: \: \: = \sqrt{ {( - 5)}^{2} + {( - 5)}^{2} } \)

\( \: \: \: \: \: \: \: \: = \sqrt{25 + 25} \)

\( \: \: \: \: \: \: \: \: = \sqrt{50} \)

\( \: \: \: \: \: \: \: \: = \sqrt{(2)(25)} \)

\( \: \: \: \: \: \: \: \: = \sqrt{(2)(5)(5)} \)

\( \: \: \: \: \: \: \: \: = \sqrt{(2)( {5}^{2}) } \)

\( \rm \: \: \: \: \: \: \: \: = 5 \sqrt{2} \: units\)

Answered by:

\(\frak{\red{moonlight123429}}\)

Answer: 102

Step-by-step explanation:

Michael had 72 books before he acquired the 10 additional books.

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The abelian groups (up to isomorphism) of order 360 are:

1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.

First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.

In this case, we can form the following abelian groups of order 360:

C360: This is the cyclic group of order 360 itself.

C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.

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Answer:

2) RC = OG

3) ‹Q

4) m‹A = 73°

5) m‹B = 65°

6) m‹C = 42°

7) AC = 3.5 cm

8) DE = 26 cm

Answer:

Within 10 feet of a fire hydrant

Step-by-step explanation:

Answer:

10 feet.

Step-by-step explanation:

The area of a rectangle is given by the product of its dimensions.

If this rectangle has a length of 2x + 7 and a width of x + 4, its area is:

The perimeter is the sum of all side lengths, so we have:

When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is   \(\\26 \frac{2}{5}\).

What is improper fractions?

An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

12 times 120% + 12

12*120%+12

\($$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$\)

Follow the PEMDAS order of operations

Multiply and divide (left to right) \($12 \times \frac{6}{5}: \frac{72}{5}$\)

\(=\frac{72}{5}+12$$\)

Add and subtract (left to right) \($\frac{72}{5}+12: \frac{132}{5}$\)

\(=\frac{132}{5}$$\)

Convert improper fractions to mixed numbers: \($\frac{132}{5}=26 \frac{2}{5}$\)

\(=26 \frac{2}{5}$$\)

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Answer:

17m³

Step-by-step explanation:

==>Given:

Prism with right triangular base with the following dimensions:

Height = 17m

Base area = area of the right triangle = ½×2×1 = 1m²

==>Required:

Volume of prism

==>Solution:

Volume of prism = Base area × height of prism

Volume of prism = 1m² × 17m

Volume = 17m³

Answer:

It is irrational.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

A

Step-by-step explanation:

The minus sign is not needed.

Answer:

The second answer is correct because his answer is closer to his experimental probability.

9000 ways to create 4-digit passwords using digits from 0 to 9 that the first character can't be 0, but not using the digit 0 as the first character.

We have to see how many different 4-digit passwords we can create by using digits from 0 to 9, such that the first character can't be 0.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

Here we have 4 selections.

Now let's find the number of options for each of these:

First character = 9 options {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Second character = 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Third character = 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Fourth character = 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The total number of different combinations is just the product of these 4 numbers:

C = 9×10×10×10 = 9,000

So, we can conclude that the correct option is D.

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Answer:

d

Step-by-step explanation:

trust

The number that satisfies the given condition is 8. When we multiply 8 by 3 and add 5, we get 29, which is equal to 8 plus 21.

To find the number that satisfies the condition of its triple plus 5 being equal to the number plus 21, we can set up an equation. Let "x" be the number we are looking for, then the equation would be:

3x + 5 = x + 21

Now, let's solve the equation to find the value of "x". We subtract "x" from both sides of the equation:

2x + 5 = 21

Next, we subtract 5 from both sides of the equation:

2x = 16

Finally, we divide by 2 to isolate "x":

x = 8

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Answer:

4 miles

Step-by-step explanation:

2/3 x 6= 4

To find the percentages of U.S. presidents who were lawyers, we can divide the number of presidents by the total number of presidents and then multiply by 100 to get the answer as a percentage.

Given the information, we have:

Number of presidents who were lawyers = 29

Total number of presidents = 42

So, the percentages of presidents who were lawyers is:

(29 / 42) * 100 = 69%

Therefore, 69% of the first 42 U.S. presidents were lawyers.

A percentage is a number or ratio expressed as a fraction of 100. It represents a portion of a whole and is often used to describe parts of a larger quantity in terms of 100. For example, if a student scored 80 out of 100 on a test, their score can be expressed as 80%, which means they answered 80 out of 100 questions correctly. The symbol for percentage is "%". To convert a fraction or decimal to a percentage, it is multiplied by 100.

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Answer:

the four consecutive numbers are   89, 90, 91, 93.

Step-by-step explanation:

let the four consecutive numbers be x, x+2, x+4, x+6

according to the condition in the question

x+x+2+x+4+x+6=368

4x+12=368

4x=356

x= 89

So,  the numbers are   89, 90, 91, 93.

hope this will help :)

Answer: 7

Step-by-step explanation:

i wish i knew why

Using the line plot, the difference in miles between the student who live closet and further away is: 2.75 miles.

A line plot, also known as a line graph or line chart, is a type of data visualization that represents data points using a series of connected line segments. It is commonly used to display the trend or pattern of data over time or another continuous variable.

The missing line plot is shown in the image attached below. It shows that:

the miles for the student who live closest is 5.

the miles for the student who live further is 7.75.

The difference = 7.75 - 5 = 2.75 miles.

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Answer: The probability of the first player being the center fielder is 1 out of 9 because there is only one center fielder on the team.

After the center fielder is chosen, there are 8 players remaining, and the probability of the second player being the shortstop is 1 out of 8 because there is only one shortstop on the team.

To calculate the probability of both events occurring in order, we multiply the individual probabilities:

Probability = (1/9) * (1/8) = 1/72

Therefore, the probability that the first two players in the lineup will be the center fielder and the shortstop, in that order, is 1 out of 72.

Answer:

4

Step-by-step explanation:

lol

Answer:

-42

Step-by-step explanation:

Hope it helps!

If you take the point on the bridge directly beneath the lowest point on the cable to be the origin, then the parabola has equation

\(y = ax^2+bx+10\)

300 ft to either side of the origin, the parabola reaches a value of y = 90, so

\(a(300)^2+b(300)+10 = 90 \implies 4500a+15b = 4\)

\(a(-300)^2+b(-300)+10 = 90 \implies 4500a-15b = 4\)

Adding these together eliminates b and lets you solve for a :

\((4500a+15b)+(4500a-15b)=4+4 \\\\ 9000a = 8 \\\\ a = \dfrac1{1125}\)

Solving for b gives

\(4500\left(\dfrac1{1125}\right)+15b=4 \\\\ 4+15b = 4 \\\\ 15b=0 \\\\ b=0\)

So the parabola's equation is

\(y = \dfrac{x^2}{1125}+10\)

150 ft away from the origin, the cable is at a height y of

\(y = \dfrac{150^2}{1125}+10 = \boxed{30}\)

ft above the bridge.

The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

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Answer:

E. 3i√3

Step-by-step explanation:

√-27 is √27 times √-1

√-1 is i, so i√27

√27 = 3√3, and then we have:

3i√3 as our answer

Slope intercept form of equation of a line is described by y - y1 = m(x - x1)

The are three kinds of equation of a line

a) point intercept form

b) slope point form

c) point point form

The formula y - y1 = m(x - x1) is usually described as the 'point-slope form' for the equation of a line.

where m represents the slope of the line and x1 and y1 is the point given through which the line passes.

It is useful when one point on a certain line and the slope of that certain line is known, then the equation of the line can be structured using this form.

Thus, the slope intercept form of equation of a line is described by y - y1 = m(x - x1)

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b.) Given:

To determine whether the pair of the equations parallel perpendicular or neither:

Let us write it in slope intercept form,

The slopes are,

Since,

Hence, the lines are neither parallel nor perpendicular.

So, the answer is neither.