y=f(x) = (1/2)
Find f(x) when x = 1

Answer:

Correct Pairs:

E(4, 4), F(8, 3), G(10, 6), and H(8, 6) ⇒ a translation 7 units right

E(3,4), F(-1,3), G(-3, 6), and H(-1,6) ⇒ a reflection across the y-axis

E(-3,-4), F(1,-3), G(3,-6), and H(1,-6) ⇒ a reflection across the x-axis

E(-3,-1), F(1,-2), G(3, 1), and H(1,1) ⇒ a translation 5 units down

Step-by-step explanation:

In Mathematics Geometry, translation just means 'moving'. A move without altering the size, rotation or anything else. When you perform a translation on a shape, the coordinates of that shape will change.

Translation right means you would add the translated unit to the x-coordinates of the of the point, let say P(x, y), in the original object.

Translation down means you would subtract the translated unit from the y-coordinates of the of the point, let say P(x, y), in the original object.

In Mathematics, a reflection just means a 'flip' over a line.

A reflection across x axis means, if a point P(x, y) is reflected across the x-axis, the x coordinate remains the same, while y coordinate changes its sign. i.e. the point (x, y) is changed to (x, -y).

A reflection across y axis means, if a point P(x, y) is reflected across the y-axis, the y coordinate remains the same, while x coordinate changes its sign. i.e. the point (x, y) is changed to (-x, y).

Now, lets head towards the solution:

Analyzing "a translation 7 units right"

As the given ABCD Quadrilateral has vertices as A (-3, 4),  B (1, 3), C (3, 6) and D (1, 6).

As EFGH is congruent to ABCD.

And

A translation of ABCD 7 units right would bring the following transformation:

A (-3, 4),  B (1, 3), C (3, 6) and D(1, 6) ⇒ A'(4, 4), B'(8, 3), C'(10, 6), and D'(8, 6)

As EFGH ≅ ABCD

So,

Here are the matching vertices when a translation 7 units right is made:

E(4, 4), F(8, 3), G(10, 6), and H(8, 6) ⇒ a translation 7 units right

Analyzing "a reflection across the y-axis"

As the given ABCD Quadrilateral has vertices as A (-3, 4),  B (1, 3), C (3, 6) and D (1, 6).

As EFGH is congruent to ABCD.

And

A reflection of ABCD across the y-axis would bring the following transformation:

A(-3, 4), B (1, 3), C(3, 6) and D(1, 6) ⇒ A' (3, 4), B'(-1, 3), C'(-3, 6) and D'(-1, 6)

As EFGH ≅ ABCD

So,

Here are the matching vertices when a reflection across the y-axis is made:

E(3,4), F(-1,3), G(-3, 6), and H(-1,6) ⇒ a reflection across the y-axis

Analyzing "a reflection across the x-axis"

As the given ABCD Quadrilateral has vertices as A (-3, 4),  B (1, 3), C (3, 6) and D (1, 6).

As EFGH is congruent to ABCD.

And

A reflection of ABCD across the x-axis would bring the following transformation:

A(-3, 4), B (1, 3), C(3, 6) and D(1, 6) ⇒ A' (-3, -4), B'(1, -3), C'(3, -6) and D'(1, -6)

As EFGH ≅ ABCD

So,

Here are the matching vertices when a reflection across the x-axis is made:

E(-3,-4), F(1,-3), G(3,-6), and H(1,-6) ⇒ a reflection across the x-axis

Analyzing "a translation 5 units down"

As the given ABCD Quadrilateral has vertices as A (-3, 4),  B (1, 3), C (3, 6) and D (1, 6).

As EFGH is congruent to ABCD.

And

A translation of ABCD 5 units down brings the following transformation:

A (-3, 4),  B (1, 3), C (3, 6) and D(1, 6) ⇒  A' (-3, -1),  B'(1, -2), C'(3, 1) and D'(1, 1)

As EFGH ≅ ABCD

So,

Here are the matching vertices when a translation 5 units down is made:

E(-3,-1), F(1,-2), G(3, 1), and H(1,1) ⇒ a translation 5 units down

Here is summary of matched Pairs:

E(4, 4), F(8, 3), G(10, 6), and H(8, 6) ⇒ a translation 7 units right

E(3,4), F(-1,3), G(-3, 6), and H(-1,6) ⇒ a reflection across the y-axis

E(-3,-4), F(1,-3), G(3,-6), and H(1,-6) ⇒ a reflection across the x-axis

E(-3,-1), F(1,-2), G(3, 1), and H(1,1) ⇒ a translation 5 units down

Keywords: reflection, translation, transformation

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Answer:

The second choice

Step-by-step explanation:

Answer:

|4x-2| = -6

Step-by-step explanation:

recall that the absolute value of anything must be greater or equal to zero (i.e 0 or positive).

in the first option, we can see that the absolute value of the expression (4x-2) gives a negative number. This violates our definition above hence it cannot be true.

Answer:

8 inches

Step-by-step explanation:

90 miles -------------> represented by 3 inches

1 mile -------------> represented by 3/90 inches

240 miles ----------> represented by 3/90 x 240 = 8 inches

To determine the length of a line segment that represents 240 miles on a scale drawing, set up a proportion using the information given. The line segment would be 8 inches long.

To determine the length of a line segment that represents 240 miles on a scale drawing, we can set up a proportion using the information given. The scale in the drawing states that 3 inches represent 90 miles. We can cross-multiply and solve for the unknown length as follows:

3 inches / 90 miles = x inches / 240 miles

To solve for x, we can multiply both sides of the equation by 240 and then divide by 90:

x inches = (3 inches / 90 miles) * 240 miles

x inches = 8 inches

Therefore, a line segment that represents 240 miles on the scale drawing would be 8 inches long.

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Answer:

1.35

Step-by-step explanation:

$9=100%

15%        x

-----  =   ----

100%     9

Cross multiply:

100x=135

Solve:

x=1.35

15% of $9 is $1.35

:)

Answer: $1.35

Step-by-step explanation: To find 15% of $9, first write 15% as a decimal by moving the decimal point 2 places to the left to get .15.

Next, "of $9" means times 9 so we multiply .15 times 9 or (.15)(9) which gives us 1.35. So 15% of $9 is $1.35.

Answer:

data collection error

Answer:

B. Data Collection Error.

Step-by-step explanation:

Answer: c  

Step-by-step explanation:

Answer:

f(x)=3/2(8/7)^-x

Step-by-step explanation:

If you turn the fractions into decimals ([tex]\frac{3}{2}(\frac{8}{7} )[/tex]^-x = 1.5(1.14)^-x), put that number into y= in your graphing calculator and press graph you will be able to see, verses the other functions, that the line decreases.

Answer:

[tex]\frac{(\frac{3}{5}*1000) }{6}[/tex]

Step-by-step explanation:

First, let's find out how many words Maria has left to write. If she has already finished 2/5 of her essay, she has 3/5ths left to write. We can do 3/5 times 1000 to find out how many words are left.

[tex]\frac{3 }{5} * \frac{1000}{1}[/tex]

[tex]\frac{3000}{5}[/tex]

[tex]600[/tex]

Thus, there are 600 words left to write.

Now to find the amount of time, we can find how take to write 600 words at a pace of 6 words per minute by dividing 600 by 6.

[tex]\frac{600}{6}[/tex]

[tex]100[/tex]

It will take 100 minutes for Maria to write the rest of her essay. Now let's think about an expression that tells us this information. It sounds like your questions is supposed to have options, but I doesn't seem like you've posted them, no worries however.

So first, the amount she has left to write.

[tex](\frac{3}{5} * 1000)[/tex]

We know this is 600, but we don't have to simplify it for the expression.

Now thinking back to how we found the time, we can divide this '600' by 6.

[tex]\frac{(\frac{3}{5}*1000) }{6}[/tex]

This is the expression that shows the amount of time it will take to write the rest of the essay.

[tex]\frac{((1-(\frac{2}{5})*1000) }{6}[/tex] is also a valid solution.

Final answer:

Maria has 600 words left to write in her essay, and at 6 words per minute, it will take her 100 minutes to finish writing the remaining part.

Explanation:

Maria has written 2/5 of her essay, which means she has written 400 words (2/5 of 1,000 words). To find out how long it will take her to write the remaining 3/5 of her essay, we need to calculate 3/5 of 1,000 words, which is 600 words. If she writes at a pace of 6 words per minute, we can find the time by dividing the remaining number of words by her writing pace.

The expression that shows the amount of time it will take her to finish the essay is:
 (Total remaining words) / (Words per minute)
 = (3/5  of 1,000) / 6
 = 600 / 6
 = 100 minutes

1st draw probability = 5/8

2nd draw probability = 4/7

probability of drawing two blue cards: 5/8 x 4/7 = 5/14

answer: 5/14

Write an algebraic expression that is the quotient of a variable term and a constant

The algebraic expression that is the quotient of a variable term and a constant is [tex]quotient = \frac{x}{5}[/tex]

In arithmetic, a quotient is the quantity produced by the division of two numbers

Here given in question that quotient of a variable term and a constant

So the quotient produced by division of variable term and constant

A variable is a special type of amount or quantity with an unknown value. Though it can be anything, you often see letters like x or y as variables in algebraic equations

Let the variable term be "x"

Constants are the terms in the algebraic expression that contain only numbers

Let the constant be "5" (Note that it can be any number, here we choose 5)

So the quotient of a variable term and a constant is:

An algebraic expression is a mathematical expression that consists of variables, numbers and operations.

[tex]quotient = \frac{\text{ variable term}}{constant}[/tex]

[tex]quotient = \frac{x}{5}[/tex]

[tex]quotient = x \div 5[/tex]

Each side of a square has a length of 5x. Use your area expression to find the area of the square when x = 2.2 centimeters. Show your work.

The area of square is 121 square centimeter

Solution:

Given that each side of square has length of 5x

The area of square is given as:

[tex]\text{ area of square }= (side)^2[/tex]

[tex]\text{ area of square} = (5x)^2\\\\\text{ area of square} = 25x^2[/tex]

Given x = 2.2 centimeter

[tex]\text{ area of square} = 25(2.2)^2 = 25 \times 4.84 = 121[/tex]

Thus area of square is 121 square centimeter

Final answer:

An algebraic expression x/3 is provided as an example, and the area of a square with side length 5x is calculated when x = 2.2 cm.

Explanation:

Algebraic expression: An example of an algebraic expression that is the quotient of a variable term and a constant is x/3, where x is the variable term and 3 is the constant.

Finding the area of a square: Given that each side of a square is 5x, the area is found by squaring the side length. So, Area = (5x)^2 = 25x^2.

Calculating the area when x = 2.2 cm: Substituting x = 2.2 into the area expression gives 25*(2.2)^2 = 25*4.84 = 121 cm².

Answer:

all work is shown and pictured

Answer:

Hence Cos X = 40/41 .

Step-by-step explanation:

Given-   X Y = 41 units, Y Z = 9 units, X Z = 40 units, ∠ Z= 90°,

∵ ∠ Z = 90°, so Δ XYZ is a right triangle.

∴ By Pythagorean Theorem-

Cos X = [tex]\frac{Base}{Hypotenuse}[/tex]

Cos X = [tex]\frac{X Z}{X Y}[/tex]

Cos X = [tex]\frac{40}{41}[/tex]

Answer:

Step-by-step explanation:

-9z=-207

Dividing each term by -9

z = -207/-9

z = 23

Answer:

23

Step-by-step explanation:

-9z=-207

divide by 9 on both sides

z=23

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Final answer:

To find the inverse of a matrix, follow these steps: 1. Check if the matrix is square and has a non-zero determinant. 2. Use the formula for finding the inverse of a 2x2 matrix. 3. For larger matrices, use row reduction or the adjugate matrix.

Explanation:

To find the inverse of a matrix, follow these steps:

Check if the matrix is square (the number of rows equals the number of columns). If it is not, then the matrix does not have an inverse.

Calculate the determinant of the matrix. If the determinant is 0, then the matrix does not have an inverse.

If the matrix is square and has a non-zero determinant, use the formula for finding the inverse of a matrix. For a 2x2 matrix:

A-1 = 1/det(A) * [d -b;
-c a]

where A is the original matrix, A-1 is the inverse matrix, det(A) is the determinant of A, and a, b, c, and d are the entries of A.

If the matrix is larger than 2x2, you can use methods such as row reduction or the adjugate matrix to find the inverse.

Answer:

One (1) significant figure.

Step-by-step explanation:

All non zero digits are always significant zeros. Since there is no decimal point, the 0 is a trailing zero, and does not count as a significant figure.

Answer:

y=2/3x+2

Step-by-step explanation:

2x-3y=12

3y=2x-12

y=2/3x-12/3

y=2/3x-4

----------------

y-y1=m(x-x1)

y-(-2)=2/3(x-(-6))

y+2=2/3(x+6)

y=2/3x+12/3-2

y=2/3x+4-2

y=2/3x+2

Answer:

-7 feet above the ground

Step-by-step explanation:

Answer:

508.8 seconds (8.48 minutes)

Step-by-step explanation:

Final answer:

The question involves an algebraic expression defining Y in terms of x in Mathematics.

Explanation:

The subject of this question is Mathematics.

To define the expression given, Y is equal to 2 plus the product of 3 and x, it can be represented as: Y = 2 + 3x.

This is a basic algebraic expression where Y depends on the value of x.

D. x = –2, x = 2, and x = 3

Please correct me If I'm wrong, I did the math myself and this is what I got.

Answer:

The 3rd picture.

Hope this helps :)

Answer:

yeah its the third picture hope this helped you

Answer:

$1,330.26

Step-by-step explanation:

The solution is, Devonte’s actual account balance is $1,330.26.

A checking account gives smooth get admission to your money on your everyday transactional needs and facilitates keeping your coins cozy. clients can commonly use a debit card or exams to make purchases or pay payments. money owed may have special alternatives to help keep away from the month-to-month provider fee.

here, we have,

A transaction account, also called a bank account, chequing account, present-day account, call for a deposit account, or share draft account at credit score unions is a deposit account held at a financial institution or other monetary organization.

given that,

Devonte is balancing his checking account. His account statement does not include a deposit of $107.00 that he made on November 1st.

from the given data ,

so, we get,

Devonte’s actual account balance is $1,330.26.

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Answer:

A: 34574+3280x-24x^2

Answer:

A

Step-by-step explanation:

took test

Answer:

B.

Step-by-step explanation:

Try solving:

13x - 5 = - 5 + 13x

13x - 13x = -5 + 5

0 = 0.

Therefore it is an identity.

We could make x any real value and the identity would hold.

The given equation 13x - 5 = -5 + 13x is an identity with infinite solutions. The option B is correct.

The given equation is 13x - 5 = -5 + 13x. To determine what kind of solution this equation has, we should simplify and solve for x. Starting by adding 5 to both sides of the equation to cancel out the -5, we get 13x = 13x. This results in the terms involving x on both sides of the equation being identical. Hence, no matter what value of x we substitute, the equation will always hold true.

Therefore, the equation represents an identity, meaning that it is true for all real numbers and there are infinite solutions. This is because subtracting or adding equal amounts on both sides of an equation does not change its solutions, leading to an expression of an identity.

Answer:

[tex]y=5x+7[/tex]

Step-by-step explanation:

step 1

Find the slope of the line parallel to the given line

we know that

If two lines are parallel, then their slopes are equal

The equation of the given line is [tex]y=5x+4[/tex]

The slope of the given line is [tex]m=5[/tex]

so

The slope of the line parallel to the given line is also [tex]m=5[/tex]

step 2

Find the equation of the line parallel to the given line

The equation of the line in point slope form is

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=5[/tex]

[tex]point\ (-1,2)[/tex]

substitute

[tex]y-2=5(x+1)[/tex]

step 3

Convert to slope intercept form

Isolate the variable y

[tex]y-2=5x+5[/tex]

[tex]y=5x+5+2[/tex]

[tex]y=5x+7[/tex]

Answer:

The slope will be 2/2 which is equal to 1.

Answer:

Step-by-step explanation:

The slope is 2/2 which equals to 1.

Answer:

684 tickets were sold for each performance

Step-by-step explanation:

8,208 divided by 12 = 684

Answer:

684 tickets

Step-by-step explanation:

having been sold out means that all seats for 12 nights were sold with none left over.

given a total of 8,208 tickets were sold out for 12 nights,

number of tickets sold each night

= 8208 ÷ 12

= 684 tickets

Answer:

The length of the ladder is 9.2 meters

Step-by-step explanation:

Given as :

The angels of elevation of a ladder against a wall = 60°

The Distance of the foot of the ladder fro the wall = d = 4.6 meters

Let The length of the ladder = h meters

Now, According to question

cos angle = [tex]\dfrac{\textrm base}{\textrm hypotenuse}[/tex]

Or, cos 60° = [tex]\dfrac{\textrm d}{\textrm h}[/tex]

Or, 0.5 = [tex]\dfrac{\textrm 4.6}{\textrm h}[/tex]

∴  h = [tex]\dfrac{\textrm 4.6}{\textrm 0.5}[/tex]

i.e h = 9.2

So,The length of the ladder = h = 9.2 meters

Hence The length of the ladder is 9.2 meters Answer

Answer:

-(x^2+4)

Step-by-step explanation:

Answer:

(-x-2i)(x-2i)

Step-by-step explanation:

All you must do is multiply 4 by 1 and 1/4, so 5 total pounds.

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