The greatest common factor of 60 and z, some unknown positive integer, is 10. There are two possible values for z between 35 and 55. What is the difference between these two values?

Answer:log_3 (3) + log_3(x)

=log_3(36)

Step-by-step explanation:log_3 (3) + log_3(x)

=log_3(36)log_3 (3) + log_3(x)

=log_3(36)

Answer:

For two functions to be equal, the arguments of each must be equal.

x=12

Step-by-step explanation:

the answer should be 6, 12, 18. 24

The correct option is option: rotation 90°counterclockwise about the origin.

What is transformation?

A transformation is generally the shifting of the picture for manipulating the shape or position of a point, a line, or a geometric figure.

Transformation is a process by which the orientation or size of a given picture is changed without any effect on the shape.

A rotation is one kind of transformation in which the object rotates about a fixed point or line. The direction of rotation is clockwise or anticlockwise.

It is clear from the figure that

the triangle ∆ABC is mapped over triangle ∆A'B'C' by rotating every point 90° from 2nd quadrant to 3rd quadrant by the rotation of  90° counterclockwise about the origin.

Therefore triangle is rotated 90°counterclockwise about the origin.

Answer:

Step-by-step explanation:

Answer:

$8.75

Step-by-step explanation:

$4.50 × 2.5 = $11.25

$20.00 - $11.25 = $8.75 change

He defined quality as a speedy procedure and document security through the use of a web interface, and the data was safely backed up to Amazon S3.

Houston determined that his potential customers, who would be his target demographic, were already technically savvy, but that because of the product's simplicity and the advent of the internet, it could fast increase.

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The value of M is 20.

What is Line segment?

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

M is the midpoint of line PQ.

The value of P = 14

The value of Q = 26

Now,

Since, M is the midpoint of overline PQ.

So, By the definition of midpoint, we can formulate;

M = 14 + 26 / 2

M = 40 / 2

M = 20

Therefore, The value of M is 20.

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The location of the eagle's nest at 1,284 feet and the diving speed of the eagle of 88 feet/seconds gives;

First part;

The function that gives the height of the eagle after a seconds is presented as follows;

h(a) = 1,284 - 88•a

Second part;

After 7 seconds, the eagles height is; 668 feet

A function maps an input element to one output element or value

First part;

The given parameters are;

Initial height of the eagle = 1,284 feet

Speed at which the eagle can dive, v = 88 feet/second

Required; The eagles height after 7 seconds of diving

Solution;

Height reached, h, which is the same as distance traveled, is given by the equation;

Distance = Speed, v × Time, a

The height reached by the eagle is given by the difference between the initial height and the distance traveled.

Distance traveled by the eagle = 88 × a

Eagles height = Initial height - 88 × a

Therefore, the eagles height, h, after t seconds is given by the equation;

Second part;

The eagle's height reached after 7 seconds

Solution;

The height reached after 7 seconds is found by plugging in a = 7 in the function for the height as follows;

h(7) = 1,284 - 88×7 = 668

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Answer: -6

Step-by-step explanation:

Given: y = 100 - 2x

New: y = 100 - 2(x + 3)

          = 100 - 2x - 6

          = 94 - 2x

The original equation had a y-intercept of 100.  The new equation has a y-intercept of 94.  The y-value changes by -6 units.

Answer:

7+w

Step-by-step explanation:

I think this is the answer hope it helped

A sequence of transformations that would not return a shape to its original position is: 'Translate 3 unit left, then 3 units down.'

1. Reflect over line x, and over x again.

These transformations are direct opposite and will cancel out one another. Hence, the shape will return to its initial position.

2. Translate 1 unit up, then 4 units down, then 3 units up.

This transformation will return a shape to its original position.

3. Rotate 270° counterclockwise around center C, then rotate 90° counterclockwise around C again.

This means, rotate object by 360° counterclockwise around C.

And this sequence of  transformations will return a shape to its original position.

4. Translate 3 unit left, then 3 units down.

These sequence of transformations would not make a shape go back to its original position.

Therefore, a sequence of transformations that would not return a shape to its original position is: 'Translate 3 unit left, then 3 units down.'

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Answer:

Step-by-step explanation:

To find the lowest price per ounce, we must find the unit rate (how much does it cost to buy 1 unit of something).

The way to do this is divide the price by the quantity.

Option 1) [tex]\frac{1.65}{26/5} = 1.65 * 5/26 = 8.25/26 = 33/104[/tex]

For the first option, every ounce costs $33/104.

Option 2) [tex]\frac{10.4}{26} = 0.4 = \frac{4}{10}[/tex]

For the second option, every ounce costs $4/10.

Since we know that 33/104 is less than 4/10, option 1 is more worth it as every ounce costs less than option 2.

The correct answer is the first option.

We can show that the 2 triangles are congruent by using vertical angles, to prove that m∠DCA = m∠TCS

Then by Alternating Interior Triangles, m∠A = m∠T and m∠D = m∠S

And finally, the sides AC and CS are equal, and DC = CT

Then we have 3 pairs of congruent corresponding sides and 3 pairs of congruent corresponding angles, which is the first option.

If jenny and penny play on the same basketball team last season a combined total of 485 points. Jenny scored 192 of points then the points penny scored is 293.

Jenny and penny play on the same basketball team last season a combined total of 485 points.

Individually Jenny scored 192 of points.

Let the score of penny on the same basketball team last season be x

Then the equation which represents the combined score of Jenny and Penny is

x + 192 = 485

x = 485 - 192

x = 293

The score of penny on the same basketball team last season is 293 points.

Therefore, if  jenny and penny play on the same basketball team last season a combined total of 485 points. Jenny scored 192 of points then the points penny scored is 293.

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Hey, this question lacks the statement, answer choices, and pictures...etc

I can't answer unless you give more details.

Answer:

A) 25% or 1/4

B) 5% or 1/20

Step-by-step explanation:

Part A)

Divide the down payment by the total purchase price to find the percent:

[tex]60,000/240,000=1/4=0.25[/tex]

Part B)

Divide the new down payment by the total purchase price to find the percent:

[tex]12,000/240,000=1/20=0.05[/tex]

Answer: negative

Step-by-step explanation:

When graphing the points on a coordinate plane, the line falls as it moves from left to right. This means that the line has a negative slope.

Answer:

negative

Step-by-step explanation:

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.

A % is a number without dimensions and without a standard measurement.

How many students were on the honor roll overall as a percentage increase?

In response: The circumstances we are aware of, boys: 144 * 1+25% =144 * 1.25=180 girls: 75 * 1+16% =75 * 1.16=87 144+75. There were 75 females and 144 guys on the honor list at a particular high school last year. In comparison to last year, there were 25% more males and 16% more girls on the honor roll this year.

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Ok, so

First of all, remember that a line can be described by two forms:

1. y = mx+b, where m is the slope and b is the y - intercept-

2. We would have the general equation for a line, which is:

Ax + By + C = 0

Where m(slope) is -A/B and the intercept (b) is -C/B.

Now, let's find the slope and y - intercept for each line here below.

a. y = 5 - 6x

Here we have a line which has the first form (1). So, if we rewrite:

y = - 6x + 5.

So, If we compare with the first equation, we notice that m = -6 and b = 5

or, m = -6 and b = (0,5)

b. y = (5/6)x + 1

Here we have a line which has the first form (1).

So, if we compare, we notice that m = 5/6 and b = 1, or, m = 5/6 and b = (0,1)

c. 5x - 6y = 6

If we rewrite the equation:

5x - 6y - 6 = 0

Here we have a line which has the second form (2).

We know that

A = 5

B = -6

C = -6

If we replace, m = -A/B, which is -(5) / (-6) , and this is 5/6.

And, y intercept will occurs at y = -C/B, which is -(-6) / -6, which is 6/-6, or -1.

So, the slope will be 5/6 and y-intercept (0,-1).

m = 5/6 and b = (0,-1)

d. 5x + 6y = 6

If we rewrite the equation:

5x + 6y - 6 = 0

Here we have a line which has the second form (2).

We know that:

A = 5

B = 6

C = -6

If we replace, m = -A/B, which is -(5) / 6, so, m = -5/6

And, y intercept will occurs at y = -C/B, which is -(-6) / 6, so, b = 1

Finally, m = -5/6, and b = (0,1)

Answer:

Technically, there is a proportionality because there will always be more road bikes than mountain bikes rented, but the proportionality is not completely constant as the ratio is 300/425 which is 0.75 compared to 575/680 which is 0.84.

Answer: x=3

Step-by-step explanation:

[tex]g(x)=x^3-3\\\\g(x)=24\\\\Hence,\\\\x^3-3=24\\\\x^3-3+3=24+3\\\\x^3=27\\\\x^3=3^3\\\\Thus,\\\\x=3[/tex]

We have to blend two brands of dressing with different proportions of vinegar. We want to obtain a mix of 230 cubic milimiters with a proportion of 11% of vinegar.

We can call A to the amount of dressing with 8% vinegar and B the amount of dressing with 13% vinegar.

Then, if the volume of the mix is 230 mm³, we can write:

We can obtain another equation by looking at the amount of vinegar in the mix.

The amount will be the volume of the mix (230 mm³) times the proportion of vinegar (11% or 0.11 in decimal).

This amount of vinegar will be contributed by the vinegar of each brand. The first brand will contribute with a volume of A times 0.08 and the second brand will contribute with B times 0.13.

We can write this as a equation like this:

We now have a system of linear equations (two equations and two unknowns).

We can replace B from the second equation by using the first equation:

Knowing A = 92 mm³, we can find B as:

Answer:

First brand: 92 mm³

Second brand: 138 mm³

The range of values of T is the domain and the range of values of W is the domain, then the,

Domain : Number of minutes water has been added ( 0 , 60 )

Range : Amount of water in the pond (in liters) ( 0 , 2800 )

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.

Consider the relation {(0,7),(0,8),(1,7),(1,8),(1,9),(2,10)} . Here, the relation is given as a set of ordered pairs. The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} .

The range of values of T is the domain is,

T = ( 0 , 60 )

The range of values of W is the domain is,

W = ( 0 , 35T+700 )

0 ≤ 35T+700

Then,

We can substitute T value,

0 ≤ 35T+700 ≤ 35*60 + 700

0 ≤ 35T+700 ≤  2800

Therefore,

Domain : Number of minutes water has been added ( 0 , 60 )

Range : Amount of water in the pond (in liters) ( 0 , 2800 )

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Three combination of gift card you have purchased is 1 gift card for $10 and 14 gift card for $15 ; 4 gift card for $10 and 12 gift card for $15; 16 gift card for $10 and 4 gift card for $15

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

10 + 210 = 220

40 + 180 = 220

160 + 60 = 220

Three combination of gift card you have purchased is 1 gift card for $10 and 14 gift card for $15 ; 4 gift card for $10 and 12 gift card for $15; 16 gift card for $10 and 4 gift card for $15

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The simplification of the given expression is [tex]2^{\frac{1}{12} }[/tex].

Given expression:

[tex]\frac{8^{\frac{1}{4} }*4^{\frac{1}{6} }}{2^{\frac{1}{6} }}[/tex]

Exponents

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 8 is multiplied by itself 3 times, i.e. 8 × 8 × 8. This can be written as [tex]8^3[/tex]. Here, 3 is the exponent and 8 is the base. This can be read as 8 is raised to power 3.

We know that,

8 is the cube of 2 and 4 is the square of 2, hence, we can write,

[tex]\frac{(2^3)^{\frac{1}{4} }*(2^2)^{\frac{1}{6} }}{2^{\frac{1}{6} }}[/tex]

Using the properties of exponents, we can write,

[tex]\frac{(2)^{\frac{3}{4} }*(2)^{\frac{2}{6} }}{2^{\frac{1}{6} }}[/tex]

Simplifying this further, we can write,

[tex]\frac{2^{(\frac{3}{4}*\frac{2}{6}) }}{2^{\frac{1}{6} }} = \frac{2^{\frac{1}{4} }}{2^{\frac{1}{6} }} = 2^{\frac{1}{4}-\frac{1}{6} }=2^{\frac{3-2}{12} }=2^{\frac{1}{12}}[/tex]

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At x=1 in the domain f(x)=0.

The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

Keep in mind that a fraction's denominator (bottom) cannot be zero when determining the domain.

A square root must have a positive number under it.

At the points where the function's graph and the x-axis connect, f(x)=0.

You can see from the diagram that the function's graph crosses the x-axis three times:

1)between -3 and -2

2)between -1 and 0;

3)at x=1.

Since x=1 is the value of x from the domain, then correct choice is option C.

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The most appropriate choice for mean, median and mode will be given by-

Value of m = 20

What is mean, median and mode?

Mean of a data set gives the average value of the data set

Mean is calculated by the dividing sum of all observations by the number of observations.

Median is the middle value of the data set when the data set is arranged in ascending or descending order

Mode is the value of the data set which has the highest frequency

Here,

Let the number of integers be n

mean = 22

Sum = 22 x n

       = 22n

Now m is replaced by m + 10

New sum = 22n + 10

New mean = 24

New sum = 24n

By the problem,

22n + 10 = 24n

24n - 22n = 10

2n = 10

n = [tex]\frac{10}{2}[/tex]

n = 5

Now mode of 5 numbers = 32

Smallest number = 10

Data set = {10, x, m, 32, 32}

Now , if m is replaced by m - 8, the new median is m - 4

Since 5 is odd, m - 4 is a member of this data set

So x = m-4 (As m- 8 < m - 4, so on replacing m by m-8 will shift m - 8 to second place and x to third place as the data set is arranged in ascending order)

Data set  = {10, m-4, m, 32, 32}

Mean = [tex]\frac{10+(m-4)+m+32+32}{5}[/tex]

[tex]22 = \frac{70 + 2m}{5}\\70 + 2m = 22 \times 5\\70 + 2m = 110\\2m = 110 - 70\\2m = 40\\m = \frac{40}{2}\\m = 20[/tex]

Value of m = 20

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Complete Question

A list of integers has mode 32 and mean 22. The smallest number in the list is 10. The median m of the list is a member of the list. If the list member m were replaced by m+10, the mean and median of the new list would be 24 and m+10, respectively. If were m instead replaced by m-8, the median of the new list would be m-4. What is m?

(A)16 (B) 17 (C) 18 (D) 19 (E) 20

The equation of the line is: y = 9.

To write the equation of a line in point-slope form, where (a, b) is a point on the line, and m is the slope, the equation can be expressed as:

y - b = m(x - a).

Given:

Two ponts on a line, (-4, 9) and (-1, 9)

Find the slope (m):

Slope of the line, m = change in y / change in x = (9 - 9)/(-4 -(-1))

Slope (m) = 0/-3 = 0

Substitute m = 0, and (a, b) = (-1, 9) into y - b = m(x - a):

y - 9 = 0(x - (-1))

y - 9 = 0(x + 1)

y - 9 = 0

y = 9

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{2\implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2}}}[/tex]

so we're really looking for the equation of a line with a slope of -1/2 and that it passes through (4 , 6)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y-6=- \cfrac{1}{2}x+2\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x+8 \end{array}}[/tex]

x^2+4x-5>0 is the required quadratic inequality which is represented in the graph

Quadratic inequality: A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Examples of quadratic inequalities are: x2 – 6x – 16 ≤ 0, 2x2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc. Solving a quadratic inequality in Algebra is similar to solving a quadratic equation

as per the shaded region we can consider a number line from (-5,0) to(,1,0)

where x lies between the two points as per the given question

-5<x<1

which gives x>-5 and x<1

in the shaded region f(x)>0

so we can directly write that ,

(x+5)(x-1)>0

x^2-x+5x-5>0

x^2+4x-5>0

x^2+4x-5>0 is the required quadratic inequality which is represented in the graph

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If Lamont withdraws $2,750 monthly, he will be 66 years old (after 134.326 months) when the money runs out.

We can calculate the number of monthly withdrawals using an online finance calculator.

It determines the number of periods it will take for the investment to be exhausted, given an interest rate of 3.8%.

I/Y (Interest per year) = 3.8%

PV (Present Value) = $300,500

PMT (Periodic Payment) = $-2750

FV (Future Value) = $0

Results:

N = 134.326 months

Years = 11 years (134.326/12)

Age at FV = $0 is 66 years (55 + 11)

Sum of all periodic payments = $-369,397.09 (134.326 x $-2,750)

Total Interest = $68,897.09

Thus, making a monthly withdrawal of $2,750 will exhaust the investment when Lamont turns 66.

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