A transformation T: (x, y) (x + 3, y + 1). For the ordered pair (4, 3), enter its preimage point. (-1, 2) (1, 2) (7, 4)

Answer:

0.001

Step-by-step explanation:

1/1000 is one-thousandths. As a decimal, the first place is the tenth, the second is the hundredths, and the third place is the thousandths. That is three steps away from the decimal point. That's where we put our 1, which gives us 0.001.

1/1000 can be expressed as one-thousandths and in decimal form as 0.001

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point, then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.

As a decimal, the first place is the tenth, the second is the hundredths, and the third place is the thousandths.

1/1000

Which is three steps away from the decimal point 1, gives us 0.001.

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Answer:

m∠8 = 124°

Step-by-step explanation:

1. Find m∠1

m∠1 and m∠2 are supplementary, since they are on the same line.

That means m∠1 + m∠2 = 180.

Plug in: 4x + 2x - 6 = 180

Simplify + subtract: 6x = 186

Divide: x = 31

Plug in: m∠1 = 4(31) --> m∠1 = 124°

2. Since ∠1 and ∠4 are vertical, they are congruent. Since ∠4 and ∠8 are corresponding on parallel lines, they are also congruent. Therefore, ∠1 and ∠8 are congruent, which means m∠1 = m∠8

Plug in: m∠8 = 124°

Answer:

2=9

4=17

Step-by-step explanation:

4(2)+1

8+1=9

4(4)+1

16+1=17

The ratio of 20:1 means for every 20 inches the car is in real life, the drawing will be 1 inch.

To find the length of the drawing, divide the length of the real car by 20.

193.2 / 20 = 9.66 inches.

Answer:

Complementary angles are two angles which add up to 90° or forms a right angle. First, we find the value of A and B.

A = arccosine (0.83) = 34°

B = 90 - 34 = 56°

Thus, sin A = 0.56 and sin B = 0.83.

Step-by-step explanation:

Answer:

A^2+B^2=C^2

-/(A^2+B^2)=C

Step-by-step explanation:

-/ means squareroot whats in the parenthese

Answer:

sin(50°) = 3/c

Step-by-step explanation:

Answer:

C. Children who weigh more spend more time on studying for achievement test .

Step-by-step explanation:

Correlation is a measure of relationship , mutual co-interdependence (fluctuation) between two quantitative variables .

Direct / Positive (+) correlation means the variables are directly related - one increase , other increase & one increase , other decrease .                                         Inverse / Negative (-) correlation means the variables are inversely related - one increase , other decrease & one decrease, other increase .                       It lies between -1 to +1 . Correlation more than + 0.5 implies Strong correlation, less than that implies Weak correlation.

The correlation between above variables - weight and achievement test score is 0.9734 i.e there is Strong Positive relationship . So , increase in one strongly leads to increasing trend in other

Answer:

B) As age increases, so do body weight and achievement test scores.

Step-by-step explanation:

Answer:

14/23

Step-by-step explanation:

The total number of marbles is 6 + 8 + 9 = 23.

The probability of yellow or red is:

P(yellow or red) = P(yellow) + P(red)

P(yellow or red) = 8/23 + 6/23

P(yellow or red) = 14/23

Answer:

8 in 23 chance of picking a yellow marble

6 in 23 chance of picking a red marble

Explanation:

Firstly, we must determine the total number of marbles. To do this, we add all the marbles together:

6+8+9 = 23

Since the question says we have 8 yellow marbles, that means 8/23 marbles are yellow. Therefor, you would have a 8 in 23 chance (8/23) of picking a yellow marble. Similarly, the question states that we have 6 red marbles. Meaning 6/23 marbles are red. So, one would have a 6 in 23 or 6/23 chance of picking a red marble.

Answer:

B. -1.75 and 4

Step-by-step explanation:

f(x)=g(x)

Input the equations

x²-2x-8 = 1/4x-1

add 1 to both sides

and subtract 1/4x from both sides

x²-2 1/4x - 7 = 0  

factor

a + b = -2 1/4

a * b = -7

1.75 + -4 = -2 1/4

1.75 * -4 = -7

reverse their symbols

1.75 becomes -1.75 and -4 becomes 4.

Answer:

[tex]\boxed{\text{B. x = 4 and x = -1.75}}[/tex]

Step-by-step explanation:

ƒ(x) = x² - 2x – 8; g(x) = ¼x -1

If ƒ(x) = g(x), then

x² - 2x – 8 = ¼x -1

One way to solve this problem is by completing the square.

Step 1. Subtract ¼ x from each side

[tex]x^{2} - \dfrac{9}{4}x - 8 = -1[/tex]

Step 2. Move the constant term to the other side of the equation

[tex]x^{2} - \dfrac{9}{4}x = 7[/tex]

Step 3. Complete the square on the left-hand side

Take half the coefficient of x, square it, and add it to each side of the equation.

[tex]\dfrac{1}{2} \times \dfrac{9}{4} = \dfrac{9}{8};\qquad \left(\dfrac{9}{8}\right)^{2} = \dfrac{81}{64}\\\\x^{2} - \dfrac{9}{4}x + \dfrac{81}{64} = 7\dfrac{81}{64} = \dfrac{529}{64}[/tex]

Step 4. Write the left-hand side as a perfect square

[tex]\dfrac{1}{2} \times \dfrac{9}{4} = \dfrac{9}{8};\qquad \left(\dfrac{9}{8}\right)^{2} = \dfrac{81}{64}\\\\x^{2} - \dfrac{9}{4}x + \dfrac{81}{64} = 7\dfrac{81}{64} = \dfrac{529}{64}[/tex]

Step 5. Take the square root of each side

[tex]x - \dfrac{9}{8} = \pm\sqrt{\dfrac{529}{64}} = \pm\dfrac{23}{8}[/tex]

Step 6. Solve for x

[tex]\begin{array}{rlcrl}x - \dfrac{9}{8} & =\dfrac{23}{8}& \qquad & x - \dfrac{9}{8} & = -\dfrac{23}{8} \\\\x & =\dfrac{23}{8} + \dfrac{9}{8}&\qquad & x & = -\dfrac{23}{8} + \dfrac{9}{8} \\\\x& =\dfrac{32}{8} &\qquad & x & \ -\dfrac{14}{8} \\\\x& =4 & \qquad & x & -1.75 \\\end{array}\\\\\text{f(x) = g(x) when \boxed{\textbf{x = 4 or x = -1.75}}}[/tex]

Check:

[tex]\begin{array}{rlcrl}4^{2} - 2(4) - 8 & = \dfrac{1}{4}(4) -1&\qquad & (-1.75)^{2} - 2(-1.75) - 8 & = \dfrac{1}{4}(-1.75) - 1\\\\16 - 8 -8& = 1 - 1&\qquad & 3.0625 +3.5 - 8 & = -0.4375 - 1 \\\\0& =0&\qquad & -1.4375 & = -1.4375 \\\\\end{array}[/tex]

The diagram below shows that the graph of g(x) intersects that of the parabola ƒ(x) at x = -1.7 and x = 4.

[tex]\bf \begin{cases} y=x^2-7x+12\\ y=-x+7 \end{cases}\implies \stackrel{y}{x^2-7x+12}=\stackrel{y}{-x+7} \\\\\\ x^2-6x+12=7\implies x^2-6x+5=0 \\\\\\ (x-5)(x-1)=0 \implies \blacktriangleright x= \begin{cases} 5\\ 1 \end{cases} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf y=-x+7\implies \stackrel{x=5}{y=-(5)+7}\implies \blacktriangleright y=2\blacktriangleleft \\\\\\ y=-x+7\implies \stackrel{x=1}{y=-(1)+7}\implies \blacktriangleright y=6 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,2)\qquad (1,6)~\hfill[/tex]

Answer:

[tex](5, 2)[/tex], [tex](1, 6)[/tex]

Step-by-step explanation:

We have a system composed of two equations

The first is a quadratic equation and the second is a linear equation.

[tex]y=x^2-7x+12[/tex]

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

To solve the system, equate both equations and solve for x

[tex]x^2-7x+12 = -x+7\\\\x^2 -6x +5=0[/tex]

To solve the quadratic equation we must factor it.

You should look for two numbers a and c that when multiplying them obtain as result 5 and when adding both numbers obtain as result -6.

This is:

[tex]a * c = 5\\a + c = -6[/tex]

The numbers searched are -5 and -1

So

[tex]x^2 -6x +5 = (x-5)(x-1) = 0[/tex]

Finally the solutions to the system of equations are:

[tex]x= 5[/tex], [tex]x=1[/tex]

Answer:

3/5 kg of nickel, 4/5 kg of zinc and 13/5 kg of copper

Step-by-step explanation:

we know that

An alloy is composed of nickel, zinc, and copper in a ratio of 3:4:13

so

(3+4+13)=20 kg

That means

For 20 kg of alloy is needed 3 kg of nickel, 4 kg of zinc and 13 kg of copper

so

using proportion

Find the kilograms of nickel needed for 4 kg of alloy

20/3=4/x

x=3*4/20

x=12/20

x=3/5 kg of nickel

Find the kilograms of zinc needed for 4 kg of alloy

20/4=4/x

x=4*4/20

x=16/20

x=4/5 kg of zinc

Find the kilograms of copper needed for 4 kg of alloy

20/13=4/x

x=13*4/20

x=52/20

x=13/5 kg of copper

To create 4 kg of an alloy with nickel, zinc, and copper in a 3:4:13 ratio, you will need 0.6 kg of nickel, 0.8 kg of zinc, and 2.6 kg of copper.

In this problem, we are being asked to make 4 kilograms of an alloy for which the mixture ratio of nickel, zinc, and copper is given as 3:4:13 respectively.

To find the quantity of each metal needed, we first need to understand that the ratio represents parts of the whole. In this case, the whole is the total weight of the alloy, which is 4 kilograms. Therefore, the sum of the ratio numbers (3+4+13=20) represents this total weight. Each part of the ratio represents a fraction of this total weight, so for any individual metal, the weight in kilograms will be  (its ratio number / the total ratio number) * the total alloy weight.

For nickel, it would be (3/20)*4 = 0.6 kg. For zinc, the calculation is (4/20)*4 = 0.8 kg. And for copper, it will be (13/20)*4 = 2.6 kg.

So, to make 4 kg of this alloy, 0.6 kg of nickel, 0.8 kg of zinc, and 2.6 kg of copper are required.

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Answer:

x = 8

Step-by-step explanation:

Given

6x + 4(3x - 7) = 116 ← distribute the parenthesis on the left side

6x + 12x - 28 = 116 ← collect like terms on left side

18x - 28 = 116 ( add 28 to both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Answer:

Step-by-step explanation:

First, let's simplify the equation:

y = √(-4x - 36)

y = √(4(-x - 9))

y = 2√(-x - 9)

The 2 coefficient in front means the function is stretched by a factor of 2.

The - sign in front of the x means the function is reflected over the y axis.

The -9 constant means the function is shifted 9 units to the right.

The third one is the correct answer.

Answer:

D:  Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Step-by-step explanation:

I actually just did this and used the answer above and got it wrong, so the answer I put down is the correct answer according to edg... Good Luck!!!

Answer:

Step-by-step explanation:

2nd one

Answer:

a = 23, b = - 14

Step-by-step explanation:

If the polynomial is divisible by (x - 1) then f(1) = 0

f(x) = x³ - 10x² + ax + b

f(1) = 1³ - 10(1)² + a + b = 0, that is

1 - 10 + a + b = 0, hence

a + b = 9 → (1)

Similarly if (x - 2) is a factor then f(2) = 0

f(2) = 2³ - 10(2)² + 2a + b = 0, that is

8 - 40 + 2a + b = 0, hence

2a + b = 32 → (2)

Subtract (1) from (2)

a = 23

Substitute a = 23 into (1)

23 + b = 9 ⇒ b = 9 - 23 = - 14

Answer:

a) The sold games of Jezebel had the greatest spread.

b) The middle 50% of the games sold by Colin has the least spread.

c) Jezebel sold more games than colin.

Step-by-step explanation:

Range is sued to calculate the spread of the given data.

Range is given by:

Range=Max Value-Min Value

So,

Part a)

For Collin:

Range=21-3=18

For Jezebel:

Range=26-5=21

Part b)

Middle 50% of the values will be the values between 1st quartile and 3rd quartile

So, to find quartiles:

For Colin:

=3,9,9,14,15,16,17,20,21

The median is 15.

The lower half is 3,9,9,14

Q1 = (9+9)/2= 18/2 = 9

The upper half is 16,17,20,21

Q3 = (17+20)/2= 37/2= 18.5

The middle 50% is first quartile subtracted from third quartile

So, the spread is:

18.5-9=9.5

For Jezebel:

4,5,8,10,11,14,20,20,26

The median is 11.

The lower half is 4,5,8,10

Q1 = (5+8)/2=13/2=6.5

The upper half is 14,20,20,26

Q3 = (20+20)/2=40/2=20

The middle 50% values' spread is:

20-6.5=13.5

Part c) The answer to part a tells us that Jezebels sold games have more spread than Colin's sold games. Similarly the answer of part b tells us that the spread of middle 50% values of Jezebel's sold games was more than the spread of middle 50% values of Colin's sold games ..

Step-by-step explanation:

1) The four points are:

(x₁, y₁) = (-2, -1)

(x₂, y₂) = (3, 13)

(x₃, y₃) = (15, 5)

(x₄, y₄) = (13, -11)

Using the distanced formula the four side lengths are:

d₁₂ = √((13−-1)² + (3−-2)²) = √221

d₂₃ = √((5−13)² + (15−3)²) = √208

d₃₄ = √((-11−5)² + (13−15)²) = √260

d₄₁ = √((-1−-11)² + (-2−13)²) = √325

None of the lengths are equal, so we know this isn't a rhombus, parallelogram, or kite.  Is it a trapezoid?  To find out, let's find the slopes between the two lines that look like they might be parallel.

m₂₃ = (5 - 13) / (15 - 3) = -2/3

m₄₁ = (-1−-11) / (-2−13) = -2/3

They are indeed parallel.  So this is a trapezoid.

2) Given:

PS ≅ QR

m∠P + m∠Q = 180

m∠R + m∠S = 180

∠P ≅ ∠S

By converse of Alternate Interior Angles Theorem, since ∠P and ∠Q are supplementary, line PS and QR must be parallel.

If a quadrilateral has one pair of opposite sides that are both parallel and congruent, then it is a parallelogram.

Adjacent angles of a parallelogram are supplementary, so m∠P + m∠S = 180.

Since ∠P ≅ ∠S, then by definition of congruent angles, m∠P = m∠S.

Substitution:

m∠P + m∠P = 180

m∠P = 90

Substitution:

m∠S = 90

Opposite angles of a parallelogram are congruent, so m∠Q = m∠S = 90 and m∠R = m∠P = 90.

A parallelogram with four right angles is a rectangle.

[tex]

(2x^2+2x+3)-(x^2+2x+1) \\

2x^2+2x+3-x^2-2x-1 \\

\boxed{x^2+2}

[/tex]

The answer is your mom. Nah it’s B)10

For this case we have that the perimeter of the figure is given by the sum of its sides, they tell us that the perimeter is 62 feet.

So:

Let "x" be the variable that represents the length of the unlabeled wall, so the perimeter is:

[tex]x + 8 + 5 + 13 + 18 + 8 = 62[/tex]

We find the value of "x":

[tex]x = 62-8-5-13-18-8\\x = 10[/tex]

Thus, the length of the unlabeled wall is 10 feet.

Answer:

Option B

ANSWER

D) (a + 1, b + m)

EXPLANATION

The given line passes through (a,b) and has slope m.

The equation is:

[tex]y - b = m(x - a)[/tex]

When x=a+1, we obtain

[tex]y - b = m(a + 1 - a)[/tex]

This

[tex]y = m( 1 ) + b[/tex]

[tex]y = m + b[/tex]

Therefore,(a + 1, b + m) must also lie on this line.

The correct answer is D.

Answer:

d

Step-by-step explanation:

I got it correct

Answer:

8+4n=height of tree in 4 years

Step-by-step explanation:

start of with 8

then every year add N feet

4 years times n feet + what we started with(8)

and you get 8+4n

The height of the tree, in feet, 4 years from now can be calculated as 8 + 4n, where n is the number of feet the tree grows each year.

The subject of this question is a mathematical problem involving height growth over time, specifically about a tree that grows at a constant rate each year. In this case, the height of a tree in the future can be represented by a simple equation which considers the current height of the tree (8 feet), the rate of growth each year (n feet per year), and the number of years in the future we want to calculate for (4 years). The formula to calculate the height of the tree 4 years from now is:

Future Height = Current Height + Growth Rate * Time

Plug in the values we know:

Future Height = 8 feet + n feet/year * 4 years

So, the height of the tree, in feet, 4 years from now is 8 + 4n.

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Given the expression y^3 + x, upon substituting y = 1 and x = 6 into the equation, the resultant value of the expression is 7.

The question requires finding the value of the expression y3 + x when x = 6 and y=1. Since y is equal to 1, y3 (1 cubed) is also 1. So the expression becomes 1 + 6, which equals 7. Therefore, the value of the expression y3 + x for y = 1 and x = 6 is 7.

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Final answer:

The value of the expression  [tex]y^3 + x[/tex] for x = 6 and y = 1 is 7, which is found by substituting the values into the expression and performing the arithmetic operations.

Explanation:

To find the value of the expression [tex]y^3 + x[/tex]for x = 6 and y = 1, you simply substitute the given values into the expression and perform the arithmetic operations.

Here's the step-by-step calculation:

Replace y with 1: (1)3 + 6.

Calculate 1 cubed, which is 13 = 1.

Add the result to x, where x is 6: 1 + 6.

The final answer is 7.

This means that the value of the expression [tex]y^3 + x[/tex]when x = 6 and y = 1 is 7.

Answer:

(1,1), (-3,4)

Step-by-step explanation:

Given  x + 2y ≥ 3

Rewrite the inequality as;

x + 2y = 3

Form a table for values of x and y

x        y

3        0

1         1

-3        3

Plot the points on a Cartesian plane

From the graph, the points are; (1,1), (-3,4)

For this case we have the following inequality:

[tex]x + 2y \geq3[/tex]

We substitute each of the points and see which one is fulfilled:

Point A: (1,1)

[tex]1 + 2 (1) \geq3\\1 + 2 \geq3\\3 \geq3[/tex]

Is fulfilled!

Point B: (-3,4)

[tex]-3 + 2 (4) \geq3\\-3 + 8 \geq3\\5 \geq3[/tex]

Is fulfilled!

Point C: (-2,2)

[tex]-2 + 2 (2) \geq3\\-2 + 4 \geq3\\2 \geq3[/tex]

It is not fulfilled!

Point D: (5, -2)

[tex]5 + 2 (-2) \geq3\\5-4 \geq3\\1 \geq3[/tex]

It is not fulfilled!

Answer:

Option A and B

Answer:

What is your question?

Is " n " to the left or the right?

How many units are on the number line?

It may be the number 3.

The values of n is a distance of 3 units from 1 1/2 on a number line are 4.5 units and -1.5units

The number line consists of positive values to the right of zero and negative values to the left.

Given the value 1 1/2 units, it is 1.5 units to the right of zero.

If the value of n is a distance of 3 units from 1 1/2 on a number line, the value of n can be 3 units to the right or to the left.

Valuee to the right  = 3 + 1.5 = 4.5units

Value to the left = 1.5 - 3 = -1.5 units

Hence the values of n is a distance of 3 units from 1 1/2 on a number line are 4.5 units and -1.5units

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Answer:

B

Step-by-step explanation:

rsu is equal to vst, so you can solve 5x+17=9x-11, which yields x=7.

So vst=52 and wsv=90-52=38.

4. The value f issue is the quantity  of shares multiplied by the price of each share.

25,000 shares x $9.20 = $230,000.

The answer is b.$230,000

5. Total selling expense would be the commission plus all the fees.

Multiply the value of issue by the commission percentage and then add the other costs.

230,000 x 0.065 = 14,950

14,950 + 1,985 = $16,935

The answer is a. $16,935

6. Divide the total selling expense by the number of shares:

750,000 / 900,000 = 0.83

The answer is d. $0.83

Answer:

Simple interest = $1,000(.10)(3) = $300

Compound interest =

$1,000(1.05)² - $1,000 = $102.50

Answer:

The slope is 2

Step-by-step explanation:

The slope is equal to

m = (y2-y1)/(x2-x1)

   = (-2-2)/(-1-1)

   = -4/-2

   = 2

Answer:

$1.38 per pound

Solution:

1 ton = 2,000 pounds

2,000 * 3 = 6,000 pounds

8,280 / 6,000 = $1.38 per pound.

Hope This Helps ;)

Answer: 8,280 divided by 6,000   is 1.3,

Step-by-step explanation: there are 2,000 pounds in one ton so 3 tons would be 6,000 pound so divivde the pounds from the price

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - [tex]\frac{4}{7}[/tex] and (a, b) = (- 6, - 6), hence

y - (- 6) = - [tex]\frac{4}{7}[/tex] (x - (- 6) ), that is

y + 6 = - [tex]\frac{4}{7}[/tex](x + 6) ← c or d

Answer:

y + 6 = -4/7(x + 6)

Step-by-step explanation:

The point-slope form of an equation for a line that passes through a point

( a, b )with a slope m is given as;

[tex]y-a=m(x-b)[/tex]

we substitute the given values into the given equation above and simplify. Our point is given as (–6, –6) while the slope is -4/7;

[tex]y-(-6)=-\frac{4}{7}(x-(-6))\\\\y+6=-\frac{4}{7}(x+6)[/tex]