2(x+b)= ax + c
In the equation above, a, b, and c are constants. If
the equation has infinitely many solutions, which of
the following must be equal to c?
Α) α
B) 6
C) 2a
D) 26

Answer:

1 7/12

Step-by-step explanation:

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

14.1

Step-by-step explanation:

To find the height of the rectangular prism, use the formula for the length of a diagonal of a right rectangular prism.

d=l2+w2+h2−−−−−−−−−−√

Substitute 8 for l, 19 for w, and 25 for d

Then solve for h

25=82+192+h2−−−−√

Simplify.

25=64+361+h2−−−−√

Square both sides.

625=425+h2

Subtract 425 from both sides.

200=h2

Take the positive square root of both sides.

200−−−√=h

Round to the nearest tenth.

14.1≈h

Therefore, the height of the rectangular prism is about 14.1ft

The value of the expression is 1.766.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given the expression,

2\(e^{3x}\) = 400

divide by 2 into both sides

\(e^{3x}\) =  400/2

\(e^{3x}\) = 200

converting the expression in form of a log,

ln(\(e^{3x}\))= ln(200)

log(aⁿ) = n log(a)

3x ln(e) = ln(200)  [ln(e) = 1 and ln(200) = 5.2931]

3x = 5.2931

x = 1.766

Hence Option B is correct.

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so, Pat needs to save the minimum amount of $170.83 per month

Explanation

Step 1

Let

total = 14500

grandparents=3600

so, the total equals what the grandparents gave him plus what he can save

but, he will save the same amount of money every month

4 years= 48 months

let y represents the amount he saves per month ,so

x=48*y

now, replace

Step 2

solve the equation

so, Pat needs to save the minimum amount of 170.83 per month

I hope this helps you

Answer:

y = -8/3x + 8

Step-by-step explanation:

Step 1:  Identify which values we have and need to find in the slope-intercept form:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.

Step 2:  Find m, the slope of the line:

Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:

0 = m(3) + 8

0 = 3m + 8

-8 = 3m

-8/3 = m

Thus, the slope is -8/3.

Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.

Optional Step 3:  Check the validity of the answer:

Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:

Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:

0 = -8/3(3) + 8

0 = -24/3 + 8

0 = -8 = 8

0 = 0

Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;

8 = -8/3(0) + 8

8 = 0 + 8

8 = 8

Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.

The prime factorization of the given value is 2 × 2×2×√7

Prime factorization is the number of expressions written as a product of its prime factors.

Given the value 2√112

Prime numbers are numbers that can only be divisible by itself and 1.

2√112 = 2(√2×2×2×2×7)

2√112 = 2(√2⁴×7)

2√112 =  2(2²×√7)

2√112 =  2 × 2×2×√7

Hence the prime factorization of the given value is 2 × 2×2×√7

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For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

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Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

Answer:

D

Step-by-step explanation:

Since the weighing scale is balanced,

weight of the right side= weight on the left side

7(1)= 3x +1

7= 3x +1

Minus 1 on both sides:

3x= 7 -1

3x= 6

Divide both sides by 3:

x= 6 ÷3

x= 2

Thus, option D is correct.

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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The value of x is 50 for which line l is parallel to line m and the angles are equal by the properties of parallel lines that is vertically opposite angles are equal.

Two lines (in the same plane) are said to be parallel if they never collide, regardless matter how far they are extended on either side. Parallel lines travel parallel to each other, like train tracks. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.

Here,

Since l ⇵ m,

Vertically opposite angles are equal by the properties of parallel lines.

2x-5=95

2x=100

x=50

The value of x is 50, which means that line l is parallel to line m and the angles are equal according to the property of parallel lines, which states that vertically opposing angles are equal.

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The required value of x is 3 in the given equilateral triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The triangle given in the figure is an equilateral triangle.

We know that all sides are equal in the equilateral triangle.

As per the given figure,

side AB = side AC

6x - 3 = 3x + 6

6x - 3x = 6 + 3

Apply the arithmetic operation,

3x = 9

x = 9/3

x = 3

Therefore, the required value of x is 3 in the given equilateral triangle.

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Answer:

\(3 {x}^{2} - 15x - 18 = 0\)

\( {x}^{2} - 5x - 6 = 0\)

\((x + 1)(x - 6) = 0\)

x = -1 or x = 6

The coordinates of the zeroes are (-1, 0) and (6, 0).

Answer:

To find the constant proportionality, we can use the formula:

y = kx

where k is the constant of proportionality. To solve for k, we can use any of the given pairs of x and y values. Let's use the pair (2, 30):

30 = k(2)

k = 15

Therefore, the constant of proportionality is 15, and the equation can be written as:

y = 15x

a. The slope/rate is equal to the constant of proportionality, which is 15. So the formula can be written as:

y = 15x

b. One job or reason where you would need to know the rate of pieces of candy per box is in a candy store where you are responsible for restocking the shelves. By knowing the rate of pieces of candy per box, you can determine how many boxes of candy you need to order to maintain a certain level of inventory. For example, if you know that the store sells an average of 100 pieces of candy per day, and each box contains 15 pieces of candy, then you would need to order approximately 7 boxes of candy each day to keep up with the demand.

Hope this helps! I'm sorry if it doesn't. (Sorry for the late answer) If you need more help, ask me! :]

The probability of rolling a sum from 2 to 12 on 2 dices is 100%

Given the data,

The two dice should be rolled.

Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).

The resultant 36 results are as follows:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6

2-1, 2-2, 2-3, 2-4, 2-5, 2-6

3-1, 3-2, 3-3, 3-4, 3-5, 3-6

4-1, 4-2, 4-3, 4-4, 4-5, 4-6

5-1, 5-2, 5-3, 5-4, 5-5, 5-6

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

When using two dice, there are a total of 36 possibilities that might occur.

As a result, the results' total ranges from 2 to 12.

Hence , the probability is 100 %

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Answer:

D-y=-3x+5

Step-by-step explanation:

Slope is -3x and y intercept is positive 5

Answer:

Step-by-step explanation:

y - 2 = -3(x - 1)

y - 2 = -3x + 3

y = -3x + 5

answer is D

Amount = P ( 1 + R ) ^n

= 37,500 ( 1 + 4.3% ) ^6

= 37, 500 ( 1. 043 ) ^6

= $ 48, 276. 65

On a number line, the value C that represents the square root of 24 would be located between 6 and 7, although it would be closer to 6. Option C is correct

A horizontal line with number increments that are uniformly spaced apart is called a number line.

The answers to the number on the line will be determined by the numbers that are already on the line.

The inquiry that follows the number explains how it will be used, such as by charting a spot in the data.

Number lines are extremely versatile manipulatives that can be used for a wide variety of mathematical operations, including finding numbers, comparing numbers, working with fractions and mixed numbers, decimals, integers, absolute value, addition, subtraction, inequalities, multiples, and common denominators, and much more.

Find the point on the number line that corresponds to the value -37 by doing the following:

As is well knowledge, the value of 37 is 6.082.

If we round the number up to the next whole number, we get 6.

Therefore, the answer is somewhere between 6 and 7, although probably closer to 6.

On a number line, the value C that represents the square root of twenty-four would be located between 6 and 7, although it would be closer to the number 6.

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Ingat rumus determinan fungsi kuadrat yaitu :

\(\longmapsto\boxed{\sf{D = b^2 - 4ac}}\)

Maka, Kita kembali jawab soalnya.

⏩Nomor (1) :

»8x² + 7x + 10 = 0

Didapatkan nilai² a, b, dan c yaitu :

Maka, nilai determinannya adalah

\(\:\)

⏩Nomor (2) ;

»2x² + 10x + 10 = 5

»2x² + 10x + 10 - 5 = 0

»2x² + 10x + 5 = 0

Didapatkan nilai² a, b, dan c yaitu :

Maka, nilai determinannya adalah

\(\\ \rm\hookrightarrow 8x^2+7x+10=0\)

Determinant be D

\(\\ \rm\hookrightarrow D=b^2-4ac\)

\(\\ \rm\hookrightarrow D=7^2-320\)

\(\\ \rm\hookrightarrow D=49-320\)

\(\\ \rm\hookrightarrow D=-271\)

#2

\(\\ \rm\hookrightarrow 2x^2+10x+10=5\)

\(\\ \rm\hookrightarrow 2x^2+10x+5=0\)

\(\\ \rm\hookrightarrow D=10^2-40\)

\(\\ \rm\hookrightarrow D=100-40\)

\(\\ \rm\hookrightarrow D=60\)

The equation of the line is y = x + 6

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

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The linear equation on the graph can be written as:

y = (3/2)*x + 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁), then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we can see the points (0, 6)  (so the y-intercept is b = 6)  and (4, 10)

Then the slope will be:

a = (10 - 6)/(4 - 0) = 6/4 = 3/2

Then the linaer equation is:

y = (3/2)*x + 6

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Given that for every hundred pages a thickness of 1/4 inch is added to the book, then the equation is:  y = 1/2 + 1/4*x

Considering that the book's front and back covers each have a thickness of 1/4 inch, adding them together results in a thickness of 1/2 inch for the book, regardless of how many pages it has.

Given that a book's thickness increases by a quarter of an inch for every hundred pages, the equation is:

y = 1/2 + 1/4*x

where y denotes the book's width and x is the number of bond paper pages printed every 100 pages. Y has a length of inches.

Equations that have the same roots or solutions are said to be equivalent.

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Answer:

B. f(x) = | x + 61 |

Step-by-step explanation:

An absolute value function is known by single vertical parenthesis demarcating the equation on both sides.

The only option with this indication is option B.

B. f(x) = | x + 61 |

This equation can be solved in two ways;

first; f(x) = - (x + 61)

second; f(x) = x + 61

Answer:

Triangles in Geometry

Step-by-step explanation:

Answer:

Step-by-step explanation:

A solution to the inequality x < 24 is a value of x that makes the inequality true when it is substituted into the expression. In other words, when x is a solution to the inequality x < 24, it must be less than 24.

For example, some solutions to the inequality x < 24 include -5, 0, 23.5, and any other value that is less than 24. However, the numbers like 24 and greater than 24 are not solutions to the inequality x < 24.

Answer:

12.6

Step-by-step explanation:

10.08/.8 = 12.6, dividing the amount of time by the amount of time to make a skirt to get the number of skirts she can make