In the figure below, A ABC has an area of
20 square units. What is the height, h,
of the triangle?
A
A
h
2½ units
B 4 units
C
C 4 units
D 5 units
E 10 units
8
B

A Histogram from the menu should be used.

A histogram is a bar graph-like representation of data that buckets a range of outcomes into columns along the x-axis. The y-axis represents the number count or percentage of occurrences in the data for each column and can be used to visualize data distributions.

Given data is $25,745; $26,512; $27,322; $27.750; $29,820; $32,500; $35,448; $52,020; $63,485: $87,167

We know that Histograms are graphs that are preferred to determine any probability distribution of data. So, the Median, maximum value, and lowest value can be easily demonstrated in "Histogram graphs"

Thus, Histograms should be used.

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The area of the shape as shown in the diagram  is 50.24 squared unit.

Area can be defined as the region bounded by a plane shape.

To calculate the area of the shape, we use the formula below.

Formula:

Where:

From the question,

GIVEN:

Substitute these values into equation 1

Hence, the area is 50.24 squared unit.

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The quotient is 33x-8 and the remainder is 44.

What is quotient?

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

The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

The result of dividing 23-2-11x-8 by x+1 using synthetic division is:

23 | -2  -11x -8

x+1 | 23  21  11x

          44  33x-8

I conclusion, synthetic division is also an arithmetic method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.

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Answer:

✓2^5

Step-by-step explanation:

use the concept of indixes.

so;

By the power rule;

= (2^1/2)^2 *(2^3/4)^2

=2*(2^3/2)

2^(1+3/2)

2^5/2

✓2^5.

The value of solution of the expression is,

⇒ [tex]\sqrt{2^{5} }[/tex]

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ [tex](2^{1/2} * 2^{3/4} )^{2}[/tex]

Now, We can simplify as;

⇒ [tex](2^{1/2} * 2^{3/4} )^{2}[/tex]

⇒ [tex](2^{(5/4) } )^{2}[/tex]

⇒ [tex](2^{5/2} )[/tex]

⇒ [tex]\sqrt{2^{5} }[/tex]

Thus, The value of solution of the expression is,

⇒ [tex]\sqrt{2^{5} }[/tex]

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The fraction that is equivalent to a terminating decimal between 0.25 and 0.50 is given as follows:

C. 7/20.

A fraction is represented by the division of a term x by a term y, such as in the equation presented as follows:

Fraction = x/y.

The terms that represent x and y are listed as follows:

Hence the conversion from fraction to decimal for each item in this problem is given as follows:

This means that the correct option is given by option C.

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The equation of line j in the form of slope intercept is " y = -2/3x - 24".

The definition of a line's slope commonly referred to as its gradient is the degree of steepness or the direction of a line in a coordinate plane. Given the equation of a line or the coordinates of points along the line, there are various ways to determine slope.

Given, line h passes through the point (3,3) and this is perpendicular to the graph of a y=3/2x-4 line

the slope of the line which is perpendicular to another line = -1/m

thus the equation of the line h is y = -2/3x + c

Since this line goes through Coordinate (3,3) this will satisfy the equation

Substituting the values in the equation, c = 15

thus the equation of line h is y = -2/3x +15

also given, line j is parallel to line h and passes through the point (-6,-3)

the slope of the line which is parallel to another line = m

thus the equation of the line j is y = -2/3x + c

Since this line goes through Coordinate (-6,-3) this will satisfy the equation

Substituting the values in the equation, c = -24

thus the equation of line h is y = -2/3x -24

Therefore, "Y = -2/3x - 44" is the slope-intercept version of the equation for line j.

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The car will cover a distance of 180 miles in three hours.

We know that,

                      s = d/ t

           or       d = s* t

Where, s = speed

            d = distance

             t = time

According to the question,

               speed of the car (s) = 60 miles/ hour

                 Time taken (t)         = 3 hours

                 Distance travelled (d) = s * t

                                                      = 60miles/ hour * 3 hours

                                                      = 180 miles

Hence, the distance traveled by car in 3 hours is 180 miles.

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The function that best shows the relationship between n and f(n) is;

f(n) = 24(0.5)ⁿ⁻¹

The function table below that shows the amount of chlorine is;

n    1        2      3     5

f(n)  24     12      6    3

Where f(n) is the amount in ounces, that was left in the pool after n weeks:

We can see that the value of f(n) is decreasing as n increases from the table.

Due to the fact that f(n) does not have common difference. Let us attempt tp see if it has a common ratio;

12/24 = 0.5

6/12 = 0.5

3/6 = 0.5

Using the formula for the nth term of a geometric progression is;

aₙ = arⁿ⁻¹

Where;

a represents the first term = 24

r represents the common ratio = 0.5

Thus, the equation of the function is;

f(n) = 24(0.5)ⁿ⁻¹

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Answer:

13 problems

Step-by-step explanation:

20% is 1 part of 5; 1/5

1/5 times 65 is the same as 65 ÷ 5

65÷5=13

Answer:

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

Step-by-step explanation:

The midpoint can be thought of as drawing a line between two points and then going half-way along that line, wherever that point is, is the midpoint. The vertical and distance will be cut in half.

I attached a diagram which I will be referring to in this explanation.

The main takeaway, is we have a formula, or at least somewhat of a formula:

[tex]\text{midpoint} = (x_1 + \frac{\text{horizontal distance}}{2}, y_1 + \frac{\text{vertical distance}}{2})[/tex]

But if you look at the graph, you'll notice, the vertical and horizontal distance are simply the difference in x and y values.

[tex]\text{horizontal distance} = x_2 - x_1\\\text{vertical distance} = y_2 - y_1[/tex]

This means we can substitute something into the equation.

[tex]\text{midpoint} = (x_1 + \frac{x_2-x_1}{2}, y_1 + \frac{y_2-y_1}{2})[/tex]

Now we could directly use this equation, but we can also simplify a bit, which we can do by rewriting the following: [tex]x_1\to \frac{2x_1}{2}, y_1 \to \frac{2y_1}{2}[/tex]

[tex]\text{midpoint} = (\frac{2x_1+x_2-x_1}{2},\frac{2y_1+y_2-y_1}{2})[/tex]

combining like values, you get:

[tex]\text{midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}})[/tex]

And now we have a convenient formula we can use for this problem, which is the midpoint formula.

Now all that's left to do, is plug in x and y values, and since we're adding values, the order does not matter.

[tex]\text{midpoint} = (\frac{2+2}{2},\frac{3+9}{2})\to (2, 6)[/tex]

so the answer is: [tex](2, 6)[/tex]

The inequality that can be used to find out what grade Melissa needs in the third trimester is x ≥ 90. She needs at least 90.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Let the grade be represented by x. This will be:

= (72 + 93 + x) / 3 ≥ 85

165 + x / 3 ≥ 85

165 + x ≥ 255

Collect the like terms

x ≥ 255 - 165

x ≥ 90

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The width of the rectangle if The Area of the rectangle is 5/6 decimal 96 m, and the length is 16 m, is 1 / 2 decimal 6 m.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given;

The Area of a rectangle is 5/6 decimal 96 m,

the length and 16 m,

Area = 5 / 6 + 96

Area = 0.83 + 96

Area = 96.83

Area = 16 × width

96.83 = 16 × width

width = 96.83 / 16

width = 6.05

Thus, the width of the rectangle is 6.05 m or 6 and 1 / 2 m.

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The measure of the ∠ RST if, In Δ QRS, QS is extended through point S to point T, a measure of the ∠ QRS = (x + 8)°, m ∠ RST = (4x + 11)°, and m ∠ SQR = (x + 13)°, is 31°.

One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices, known as a triangle.

Given:

In Δ QRS, QS is extended through point S to point T, a measure of the ∠ QRS = (x + 8)°, m ∠ RST = (4x + 11)°, and m ∠ SQR = (x + 13)°,

Calculate the value of x as shown below,

∠ RST = ∠ SQR + ∠ QRS   (Using exterior angle theorem)

4x + 11 = x + 13 + x + 8

4x - x - x = 13 + 8 - 11

2x = 10

x = 5

Calculate the measure of ∠ RST as shown below,

∠ RST = 4 × 5 + 11

∠ RST = 20 + 11

∠ RST = 31°

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Answer:

C. Jamila is correct because glucose is a product, not a reactant, of photosynthesis.

Step-by-step explanation:

Photosynthesis is a process that occurs in plants and some other organisms in which energy from sunlight is used to convert carbon dioxide and water into glucose (a sugar) and oxygen. In this process, carbon dioxide and water are the reactants, and glucose and oxygen are the products. Therefore, Anton is incorrect and Jamila is correct because glucose is a product of photosynthesis, not a reactant.

Michelle worked for at least 11 hours.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. On the number line, size comparisons between two numbers are typically conducted.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are universal.

given,

tips per day = $15

hourly rate=$9

total earnings =#110

h is the number of hours work

The equation is 9h+15[tex]\geq[/tex]110

To find the hours worked:

9h+15[tex]\geq[/tex]110

9h[tex]\geq[/tex]110 - 15

9h[tex]\geq[/tex]95

h[tex]\geq[/tex]10.55

Therefore h must at least be 11

since  Michelle worked for at least 11 hours.

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Answer:

Step-by-step explanation:

x² + 81= x² + 20x + 100 · Polynomial.

The equation is x^2-x+71=0

A. The remainder theorem states that the value of f(a) is equal to the remainder for any polynomial f(x) when divided by the binomial x-a. The factor theorem states that (x-a) is a factor of f(x) and vice versa if a is a zero of a polynomial f(x).

B. Using long division method the quotient is x^2+2x-35.

C. The polynomial x^2+2x-35 has degree 2.

D. The x-intercepts of x^3-x^2-41x+105 are (-7,0), (3,0), and (5,0).

What are polynomials?

The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases." There is no limit to the number of terms that can exist in a polynomial.

A. According to the Remainder Theorem, long polynomial division yields some polynomial q(x) when the polynomial p(x) is divided by some linear factor x-a. It can be stated as follows-

p(x)/x-a=q(x)+r(x)

A polynomial can be factored and its roots can be discovered using the factor theorem. The polynomial remainder theorem is a special instance of this one.

The factor theorem states that if f(x) is a polynomial of degree n>=1 and f(a)=0, then (x-a) is a factor of f(x). If f(x) is a polynomial and f(a)=0, where an is the root, then (x-a) is a factor of f(x).

B. Using the long division method the quotient obtained after dividing x^3-x^2-41x+105 by x-3 is x^2+2x-35.

C. The solution obtained is also a polynomial of degree 2. This is known as the highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial. The degree denotes the polynomial's highest exponential power.

D. The x-intercept(s), if they exist, are of the form (a,0) where x=a is a real solution to f(x)=0.

Plot the graph for the polynomial - x^3-x^2-41x+105.

Therefore,  x-intercepts are found to be (-7,0), (3,0), and (5,0).

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August surveys may not adequately represent Christmas buyers' intentions. Surveying customers on a weekday between 10 AM and 4 PM may not capture the spending intentions of all demographic groups, resulting in a skewed sample.

It's also vital to consider economic situations, customer preferences, and promotional bargains when predicting consumer spending.

Generally, It is possible that the survey results do not accurately predict the actual spending during the Christmas season. Surveying shoppers in August, several months before the Christmas season, may not accurately reflect the shopping plans of consumers closer to the holiday. Additionally, surveying shoppers during a weekday and between the hours of 10 AM and 4 PM may not capture the spending plans of all demographic groups, potentially leading to a biased sample.

Another reason why the survey estimate of $250 is so far below the previous $400 figure could be due to the fact that the survey only asked 5 questions. This may not have been enough to gather enough information about the spending habits and intentions of the shoppers surveyed.

It's also worth noting that there are many different factors that can influence consumer spending, such as economic conditions, changes in consumer preferences, and the availability of promotional deals, so it's important to consider these other factors as well when trying to predict future spending.

In conclusion, the survey results do not provide a reliable indication of the sales for the upcoming Christmas. Without more information about the survey methodology and the results, it's difficult to determine the reasons for the discrepancy between the survey estimate and the actual spending from the previous Christmas season.

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Answer:

-34p-63q

Step-by-step explanation:

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The line segment AB in the square pyramid is parallel to the base side

A square pyramid is a three-dimensional shape with a square base and four triangular faces that meet at an apex. It is a type of polyhedron with five faces, a square base, and four triangular faces that meet at the top.

In this problem, the line segment AB is only parallel to the base side.

The base side of a square pyramid is the length of one side of the square base of the pyramid in which they are all equal to one another.

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Answer:

The ratio for the first print job is 150/30 = 5 pages per second.

The ratio for the second print job is 130/20 = 6.5 pages per second.

Since the ratios are different, the data do not represent a proportional relationship. In a proportional relationship, the ratio between two variables remains constant.

Step-by-step explanation:

By using the distributive property, we can rewrite the expression as:

24 + 8k = 8*(3 + k)

The distributive property can be written as:

C*(A + B) = C*A + C*B

Now we have the expression:

24 + 8k

And we want to rewrite it by using the distributive property, to do so we need to identify the common factor.

We can rewrite the expression as:

24 + 8k

8*3 + 8k

Then we can take 8 as a common factor, then:

8*3 + 8k = 8*(3 + k)

That is the expression rewritten.

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A compound inequality for the given statement "a number is less than 24 or greater than 35" include the following:

x < 24.

x > 35.

In Mathematics, there are four major rules that are used for writing and interpreting an inequality or compound inequality that are plotted on a graph and these include the following:

Assuming the unknown number is represented by the variable x, the required compound inequality would be written as follows;

Number less than 24 ⇒ x < 24.

Number greater than 35 ⇒ x > 35.

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Answer:

Step-by-step explanation:

Statement 1 : The graph has a domain of [tex]{x|0 < x < ∞o}[/tex]and approaches 0 as x decreases.

Statement 2 : The graph has a range of [tex]{yl-co < y < ∞o}[/tex] and decreases as x approaches 0.

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

The common logarithm, abbreviated log x, is the base-10 logarithm. The natural logarithm, abbreviated ln x, is the logarithm with base e. Positive real numbers (0, ) make up the domain of logarithmic functions with definitions of the form f(x)=logb x, whereas all real numbers (0,∞ ) make up the range (-∞, ∞).

Therefore, all positive real numbers are the domain of logx, or x ∈ (0,∞) when expressed symbolically.

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By using the table for the function f(x), we will see that:

f(4) = 74

f(6) = 40

Here we have a table for the function f(x), first we want to find f(4).

So we need to find x = 4 on the table (the first row of the table) and the value right below will be the value of f(4), there we can see that the value is:

f(4) = 74

Now we want to find:

f(x) = 40

So we want to find the value of x such that when we evaluate f(x) on it, it is equal to 40.

So we need to find 40 on the second row, and the value that is above it will be the value of x.

We can see that for x = 6:

f(6) = 40

Then here the answer is x = 6.

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Answer:

Step-by-step explanation:

y=1/3x-13/3

Okay so we have the points (1,-4) and (-5,-6).

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

Slope = -2/-6

Slope = 1/3

y=mx+b

m=1/3

Now let's take a point from the equation, and use the slope to determine b.

-4=1/3(1)+b

b=-4 1/3

Now let's combine our elements.

y=1/3x-13/3

The solution is Option B.

The percentage increment in the preference for  Enterprise Content Management is given by the equation A = 366 %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the percentage increment be represented as A

Now , the equation will be

The number of 41+ year olds having a preference for Enterprise Content Management = 3,215

The number of 18-25 year olds having a preference for Enterprise Content Management = 690

So , the difference in number of preference = 3,215 - 690

On simplifying the equation , we get

The difference in number of preference = 2,525

And , the percentage increase A = ( difference in number of preference / number of 18-25 year olds having a preference for Enterprise Content Management ) x 100

Substituting the values in the equation , we get

The percentage increase A = ( 2525/690 ) x 100

The percentage increase A = 3.659 x 100

The percentage increase A = 366 %

Therefore , the value of A is 366 %

Hence , the percentage increment is 366 %

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Answer:

The summation of 5+5+6+7 is 23.

Answer:

Step-by-step explanation:

around 24 meters