You are helping with some repairs at home. You drop a hammer and it hits the
floor at a speed of 8 feet per second. If the acceleration due to gravity (g) is
32 feet/second, how far above the ground (h) was the hammer when you
dropped it? Use the formula:
V = 2gh

Answer:

r = 7

Step-by-step explanation:

The common ratio r of a geometric sequence is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex], that is

r = [tex]\frac{21}{3}[/tex] = [tex]\frac{147}{21}[/tex] = 7

The common ratio of the sequence 3, 21, 147 is 7.

Start with the first and second terms:
21 ÷ 3

= 7

Confirm with the second and third terms:
147 ÷ 21

= 7

Thus, the common ratio (r) is 7.

Answer:

Point-slope equations:

y - 5 = 4/3 (x - 6)

or

y - 1 = 4/3 (x - 3)

Step-by-step explanation:

Given two coordinate points (6, 5) and (3, 1)

Slope = (5 - 1)/(6 - 3) = 4/3

Point-slope equations:

y - 5 = 4/3 (x - 6)

or

y - 1 = 4/3 (x - 3)

Two point-slope equations for the line passing through the points

(6, 5) and (3, 1) are,

Here, the line passes through the points (6,5) and (3,1).

Let,

[tex]$$(6,5)=\left(x_{1}, y_{1}\right)$$[/tex]

[tex]$(3,1)=\left(x_{2}, y_{2}\right)$[/tex]

Substitute

Slope(m) = [tex]\frac{1-5}{3-6}=\frac{-4}{-3}[/tex]

Slope(m) =[tex]\frac{4}{3}[/tex]

Point-slope equations of the line passing through [tex]$(6,5 \6})$[/tex] and [tex](3}, 1)$[/tex]

Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(6,5)$[/tex]into [tex]$y-b=m(x-a)$[/tex]

[tex]y-5=\frac{4}{3}(x-6)[/tex] (point-slope equation)

Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(3,1)$[/tex] into [tex]$y-b=m(x-a)$[/tex]

[tex]$y-1=\frac{4}{3}(x-3)$[/tex] (point-slope equation)

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Answer:

y = -5x + 39

Step-by-step explanation:

Plug either ordered pair into the Point-Slope Formula FIRST, y - y₁ = m(x - x₁), then convert to Slope-Intercept Form by moving whichever term is nearest to y, over to the right side of the equivalence symbol to get the above answer.

Answer:

Add 6 to both sides.

Step-by-step explanation:

You are trying to solve for x in this type of question. In this case, note that there is a equal sign, and that what you do to one side you do to the other. Also note that to isolate the x (your goal), you must do the opposite of PEMDAS. (Note that PEMDAS = Parenthesis, Exponent (& Roots), Multiplication, Division, Addition, Subtraction).

So your first step is to add 6 to both sides.

2/5x - 6 (+6) = -16 (+6)

Simplify. Solve:

2/5x + (-6 + 6) = -16 + 6

2/5x = -10

_________________________________________________________

Finish finding for x.

Multiply the recipricol of the fraction to both sides to isolate the x. Multiply 5/2 to both sides:

(5/2)(2/5)x = (-10)(5/2)

x = (-10)(5/2)

x = (-50)/2

x = -25

x = -25 is your answer.

~

Answer:

x + 3x + 5 = 101

Step-by-step explanation:

Consider your problem and think of an equation of each person. We know that Aylen has a certain amount of money, which will be x. Rich though has 5 more than 3 times Aylen.

Aylen: x amount of money

Rich: 5 more than 3 times the amount of money of Aylen.

5 more indicates addition, 3 times indicates multiplication

So then:

Rich: 5 + 3x     (where x is the amount of money of Aylen)

Now both of them have $101 together, in other words, if you add up their money they would have $101. So we add their equations:

x + 5 + 3x = 101

Because the operation is addition, we can switch their places and the result will not change so the answer would be:

x + 3x + 5 = 101

Answer:

The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]

Step-by-step explanation:

we have that

x ----> the time in years that she worked at a company

y ----> represent the hourly wage

[tex]-5x+4y=32[/tex] ----> linear equation that represent the situation

Solve for y

[tex]4y=5x+32[/tex]

[tex]y=(5/4)x+32/4[/tex]

[tex]y=1.25x+8[/tex]

The slope m of the linear equation is

[tex]m=1.25\$\ hour/year[/tex]

The rate of change in Erinn's hourly wage per year is equal to the slope of the linear equation

so

The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]

Answer:

Second option: y = 8x-3

Step-by-step explanation:

The equation tha satisfies the given values will be the required linear equation

So,

y = 8x + 45

For x=3 and y=21

21 = 8(3) +45

21 = 24+45

21≠69

As this equation is not satisfied by the values, it is not the correct option..

For y = 8x-3

x=3,y=21

21 = 8(3)-3

21 = 24-3

21=21

x=5, y=37

37 = 8(5)-3

37=40-3

37=37

x=7, y=53

53 = 8(7)-3

53 = 56-3

53 = 53

As the equation is true for all values of x and y. This is this correct option..

Answer:

the answer is C. Hope this helps

Answer:

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Solve the inequality  (20 + 0.5x) + 0.15(20 + 0.5x)   ≤ $62.10 for x:

20 + .5x + 3 + 0.75x ≤ 62.10

Combining the x terms, we get:

20 + 3 + 1.25x ≤ 62.10.

Combining the constants on the left:

23 + 1.75x ≤ 62.10

Combining the constants:

1.75x = 39.10

Solving for x:  39.10/1.75 = 22.34

Thus, the max number of whole pages she can have in her book is 22.

Answer:

22

Step-by-step explanation:

Answer:

Q1: 2nd row 2nd tile

Q2: 1st row 1st tile

Q3: 1st row 3rd tile

Q4: 2nd row 3rd tile

Step-by-step explanation:

When

[tex]y = a {(x + p)}^{2} + q[/tex]

Vertex is (-p, q)

Answer:

[tex](-1,-\frac{3}{7} )-->f(x)=\frac{1}{2}|x+1|-\frac{3}{7}\\(5,\frac{2}{3} )-->f(x)=\frac{3}{5}|x-5|+\frac{2}{3}\\(0,-\frac{4}{5} )-->f(x)=\frac{1}{2}|x|-\frac{4}{5}\\(\frac{2}{5},\frac{5}{3} )-->f(x)=\frac{3}{2}|x-\frac{2}{y5}|+\frac{5}{3}[/tex]

Step-by-step explanation:

We can solve all of them by writing the equations in a general form

[tex]f(x)=a|x+b|+c[/tex]

This is a function transformation of

[tex]f(x)=|x|[/tex]

where:

a=Factor of vertical stretch

b=Horizontal shift (- shifts right, + shifts left)

c=Vertical shift (+ shifts right, - shifts left)

The original function has its vertex in [tex](0,0)[/tex] so the horizontal shift will be the new x coordinate in the new vertex and the vertical shift will be the new y in the new vertex like this:

[tex]f(x)=\frac{1}{2}|x+1|-\frac{3}{7}\\b=1=HorizontalShiftof-1\\c=-\frac{3}{7}=VerticalShiftof-\frac{3}{7}\\(-1,-\frac{3}{7})\\f(x)=-\frac{3}{5}|x-5|+\frac{2}{3}\\b=-5=HorizontalShiftof5\\c=\frac{2}{3}=VerticalShiftof\frac{2}{3}\\(5,\frac{2}{3})\\f(x)=\frac{1}{2}|x|-\frac{4}{5}\\b=0=HorizontalShiftof0\\c=-\frac{4}{5}=VerticalShiftof\frac{4}{5}\\(0,-\frac{4}{5})\\f(x)=-\frac{3}{2}|x-\frac{2}{5}|+\frac{5}{3}\\b=-\frac{2}{5}=HorizontalShiftof\frac{2}{5}\\c=\frac{5}{3}=VerticalShiftof\frac{5}{3}\\(\frac{2}{5},\frac{5}{3})[/tex]

Answer:

y=3x+8, :m=3, b=8

Hope this helps!

The line y - 5 = 3(x + 1) in the form of slope intercept is y = 3x + 8 and slope of the line is 3, y-intercept is 8.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a line:

y - 5 = 3(x + 1)

In slope intercept form:

y = 3x + 3 + 5

y = 3x + 8

Thus, the line y - 5 = 3(x + 1) in the form of slope intercept is y = 3x + 8 and slope of the line is 3, y-intercept is 8.

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Answer:

30 minutes

Step-by-step explanation:

3 pipes takes 60 minutes, so one pipe must take 3*60 minutes as it would be 3 times slower. This equates to 180 minutes.

1 pipe takes 180 minutes so 6 pipes would take 1/6 of the time or 6 times faster.

The equation becomes 180/6

= 30 minutes.

Equation is; 3*60/6 = 30 minutes

This is inverse proportion.

The answer is 30 minutes

If it takes 3 pipes 60 minutes to water the field

The amount of time it will take one pipe can be calculated as follows

t= constant(k) × number of pipes

60= k/3

cross multiply

k = 60×3

= 180

Since it takes one pipe 180 minutes to water the field, then the amount of time it will take 6 pipes can be calculated as follows

= 180/6

=  30

Hence it will take 6 pipes 30 minutes to water the field

It is an inverse proportion because an increase in one quantity leads to a decrease in the other.

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Answer:

The missing information is attached in the picture below.

The company made $292.5 dollars in profit.

Step-by-step explanation:

Using the information provided by the table, we can calculate how much money was spent

1. gravel

12 and a half cubic yards * $15  = $187.5

2. tar/sealant

$0.15 per square foot * (75*20 ft^2) = $225

3. labor

$10 per hour * 25 hours = $250

4. insurance

fixed $45

We add all the expenses together

$(187.5 + 225 + 250 + 45)  = $707.5

The profit will be equal to

$1000 - $707.5 = $292.5

Step-by-step explanation:

For this case we have by definition, that the equation of a line in the point-slope form is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

m: It's the slope

[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes.

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

We have as data two points, replacing:

[tex]m = \frac {1-6} {0 - (- 5)}\\m = \frac {1-6} {0 + 5}\\m = \frac {-5} {5}\\m = -1[/tex]

We substitute a point, then the equation is:

[tex](y-1) = - 1 (x-0)\\(y-1) = - x[/tex]

Answer:

[tex](y-1) = - x[/tex]

Answer: [tex]y-6=-(x+5)[/tex]

Step-by-step explanation:

The Point-slope form of the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope of the line and [tex](x_1,y_1)[/tex] is a point on the line.

We know that this line passing through the points (-5,6) and (0,1), then we can find the slope with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting, we get:

 [tex]m=\frac{1-6}{0-(-5)}=-1[/tex]

Finally, we can substitute the point (-5,6) and the slope into  [tex]y-y_1=m(x-x_1)[/tex], then:

[tex]y-6=-(x-(-5))[/tex]

[tex]y-6=-(x+5)[/tex]

Answer:

a) Equation: 9x+9 = 72

b) x =7

Step-by-step explanation:

The total cost of 9 bracelets = $72

Shipping charge = $9

a) Define your variable and write an equation that models the cost of each bracelet.

Let x be the cost of one bracelet, the equation will be

9x + 9 = 72

As 9 bracelets were there and the shipping cost was 9 and total cost was 72.

b) Use the equation you have written above determine the cost for each bracelet. Show the algebraic steps that it takes to find the answer.

Now solving the equation to find the value of x that represent cost of each bracelet

9x + 9 = 72

Adding -9 on both sides

9x +9 -9 = 72 -9

9x = 63

Dividing both sides by 9

9x/9 = 63/9

x = 7

The value of x=7 so, the cost of each bracelet is $7

c) Provide your conclusion.

So, each bracelet was of cost $7 and $9 was the shipping charge. so, the total cost is $72.

We would check whether our equation is satisfied.

9x+ 9 = 72

9(7) + 9 = 72

63 + 9 = 72

72 = 72

The equation is satisfied.

Answer:

The cost of each bracelet is: $7

Step-by-step explanation:

Let's call x the cost of each bracelet.

Then the cost of the 9 bracelets is:

9x

If we know that the cost of the bracelets plus the shipping was $ 72 and the cost of shipping is $ 9.

So

The total cost was:

[tex]9x + 9 = 72[/tex]

Now we solve the equation for the variable x.

[tex]9x + 9 = 72[/tex]

Subtract 9 on both sides of equality

[tex]9x + 9-9 = 72-9[/tex]

[tex]9x = 72-9[/tex]

[tex]9x = 63[/tex]

Divide by 9 on both sides of equality

[tex]\frac{9}{9}x = \frac{63}{9}[/tex]

[tex]x = \frac{63}{9}[/tex]

[tex]x = \$7[/tex]

Answer:

[tex]\sqrt{98}[/tex]

Step-by-step explanation:

Using the distance formula

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, - 5)

d = [tex]\sqrt{(3+4)^2+(-5-2)^2}[/tex]

  = [tex]\sqrt{7^2+(-7)^2}[/tex]

  = [tex]\sqrt{49+49}[/tex]

  = [tex]\sqrt{98}[/tex]

C= [tex]\sqrt{98}[/tex]

We could say that the square root or the square cancel each other out. They are a inverse of each other. If we have the number written with the index two ( squared) then taking the square root simply means that we leave out the two ( this only applies on the positive numbers ).

Using the distance formula

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, - 5)

[tex]d= \sqrt{(3+4)^{2} +(-5-2)^{2}} \\\\= \sqrt{7^{2} + (-7)^{2}} \\\\= \sqrt{49+49} \\\\=\sqrt{98}[/tex]

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Answer:

D. 9/4 ÷ 3/4

Step-by-step explanation:

In the question, the number line represents 9/4 divided into 3 equal units.

The size of each unit is 3/4 as shown.

Showing that 3/4 divides 9/4 into 3 divisions:

9/4 ÷ 3/4

= 9/4 x 4/3

= 9/3 x 4/4

= 9/3 x 1

= 3 x 1

= 3

Hence, the number line represents three divisions given by 9/4 ÷ 3/4.

Answer:

P = 2x + 2y + 14

Step-by-step explanation:

Length (L) = x + 8 units

Width (W) = y - 1 units

Perimeter (P) = 2L + 2W

P = 2(x + 8) + 2(y - 1)

P = 2x + 16 + 2y - 2

P = 2x + 2y + 16 - 2

P = 2x +2y + 14

Answer:

P = 2x + 2y + 14

Step-by-step explanation:

For this case we must simplify the following expression:

[tex]\sqrt [5] {\frac {10x} {3x ^ 3}}[/tex]

We rewrite the expression as:

[tex]\sqrt [5] {\frac {10x} {x * 3x ^ 2}} =[/tex]

We eliminate common factors:

[tex]\sqrt [5] {\frac {10} {3x ^ 2}} =\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}}[/tex]

We multiply the numerator and denominator:

[tex](\sqrt [5] {3x ^ 2}) ^ 4:\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}} * \frac {(\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 4} =[/tex]

\frac {\ sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {\sqrt [5] {3x ^ 2} * (\sqrt [5] {3x ^ 2} ) ^ 4} =

[tex]\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 5} =\\\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {3x ^ 2} =[/tex]

[tex]\frac {\sqrt [5] {10} * \sqrt [5] {(3x ^ 2) ^ 4}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 8}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 5 * x ^ 3}} {3x ^ 2} =[/tex]

[tex]\frac {\sqrt [5] {10} * x \sqrt [5] {81x ^ 3}} {3x ^ 2} =\\\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]

Answer:

[tex]\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]

[tex]\frac {\sqrt [5] {810x ^ 3}} {3x}[/tex]

Answer:

The simplified form is [tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Step-by-step explanation:

we need to simplify the value of x in given expression:

[tex]\sqrt[5]{\frac{10x}{3x^{3}}}[/tex]

Re- write the above as,

[tex]\sqrt[5]{\frac{10}{3x^{2}}}[/tex]

[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}}[/tex]

Multiply numerator and denominator by [tex](\sqrt[5]{3x^{2}})^{4}[/tex]

[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}} \times \frac{(\sqrt[5]{3x^{2}})^{4}}{(\sqrt[5]{3x^{2}})^{4}}[/tex]

[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{(3x^{2}}})^4}{{3x^{2}}}[/tex]

[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{81x^{8}}}}{{3x^{2}}}[/tex]

[tex]\frac{x \sqrt[5]{810 x^{3}}}{3x^{2}}[/tex]

[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Hence, the simplified form is

[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Answer:

what are the graphs?

Step-by-step explanation:

Answer:

(0,6)

Step-by-step explanation:

The parenthesis tell you which equation to do first.

P arenthesis

E xponents

M ultiplication

D ivision

A ddition

S ubtraction

Shown below

To solve this problem, we need to analyze the leading coefficient and the roots of the polynomial function:

[tex]f(x)=x^3-6x^2+11x-6[/tex]

Recall that a polynomial function can be represented by:

[tex]f(x)=a_{n}(x)+ \ldots +a_{1}x+a_{0}[/tex]

So the leading coefficient is [tex]a_{n}[/tex]. In our problem, this coefficient is [tex]a_{n}=1[/tex]

Since [tex]n[/tex] is odd and the leading coefficient [tex]a_{n}>0[/tex], then the graph must falls to the left and rise to the right. Also, the roots are [tex]x_{1}=1 \ x_{2}=2 \ and \ x_{3}=3[/tex]. So the only graph that matches this is the fourth one as indicated below.

Answer:

w

Step-by-step explanation:

for Plato

Answer:

х – 9 = +9

Step-by-step explanation:

The equation results from taking the square root of both sides of

(x- 9)² = 81 is x -9 = ±9.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have Equation,

(x- 9)² = 81

Now, simplifying for x we get

Take square root on both side

x-9 = √81

x -9 = ±9.

Then, the equation results from taking the square root of both sides is

x -9 = ±9.

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Answer:

Choice B

Step-by-step explanation:

Formula for slope:

[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]y_2 = 1\\y_1 = -10\frac{2}{3} \\\\x_2 = -3\\x_1 = 4[/tex]

[tex]1 - (-10\frac{2}{3}) = 11\frac{2}{3} \\-3 - 4 = -7[/tex]

[tex]\frac{-11\frac{2}{3} }{-7} = \frac{5}{3} = 1\frac{2}{3}[/tex]

Answer: y=-2x+2/4

Step-by-step explanation:

Answer:

y + 4 =1/2 (x + 4)

Step-by-step explanation:

Your welcome uwu

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (t^9)^{-8}\implies t^{-8\cdot 9}\implies t^{-72}\implies \cfrac{1}{t^{72}}[/tex]

Answer:

1/3

Step-by-step explanation:

Slope intercept form: y=mx+b

m=rise/run (slope)

b= y-intercept

b=1/3

Answer:

D

Step-by-step explanation:

g(x)=f(5x)

this means plugging in 5x for x in f(x):

g(x)=f(5x)=(5x)^2

which can be further simplified:

5^2x^2=25x^2

Since the coefficient of x being larger means a vertical stretch, the answer is D

example:

g(2)=f(5*2)=f(10)=f(10^2)=100

so for g(x), it has the coordinates (2,100), which is most definitely not C

The graph of g(x) = f(5x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5, with the vertex remaining the same.

The graph of g(x) = f(5x) can be obtained by substituting 5x for x in the function f(x) = x^2. So, g(x) = f(5x) = (5x)^2 = 25x^2. This means that the graph of g(x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5. The vertex of the parabola remains the same, but the x-values and the y-values are scaled.

Answer:

Step-by-step explanation:

4 square root 5