Given:
A trapezoid has a height of 16 miles.
The lengths of the bases are 20 miles and 35 miles.
To find:
The area of the trapezoid.
Explanation:
Using the area formula of the trapezoid,
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]On substitution we get,
[tex]\begin{gathered} A=\frac{1}{2}(20+35)\times16 \\ =\frac{1}{2}\times55\times16 \\ =440\text{ square miles} \end{gathered}[/tex]Therefore the area of the trapezoid is 440 square miles.
Final answer:
The area of the trapezoid is 440 square miles.
This is very hard for me I need to know how to do it
The zeros of a function are the values of x that make the function be equal to zero.
When graphing a quadratic equation, the graph is a parabola, and the zeros of the function are the x-intercepts of the graph, which are the points where the graph intersects the x-axis.
So, if the zeros of this function are x = -8 and x = 2, that means the parabola crosses the x-axis at x = -8 and x = 2.
Therefore the correct option is the first one.
the ratio of men to woman working for a company is 5 to 4. if there is 225 employees total how many women work for the company
Given:
The ratio of men to women = 5: 4
Total number of employees = 225
The total ratio is:
[tex]\begin{gathered} =\text{ 5 + 4} \\ =\text{ 9} \end{gathered}[/tex]The number of women is the ratio of women to the total ratio times the number of employees
[tex]\begin{gathered} =\frac{4}{9}\times225 \\ =\text{ 100} \end{gathered}[/tex]Answer:
100 women
Write an addition equation and a subtraction equation
to represent the problem using? for the unknown. Then solve.
There are 30 actors in a school play. There are 10 actors from second grade. The rest are from third grade. How many actors are from third grade?
a. Equations:
b. Solve:
The Equation is 10 + x= 30 and 20 actors are from third grade.
What is Equation?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.
Given:
There are 30 actors in a school play.
There are 10 actors from second grade.
The rest are from third grade.
let the actors in third grade is x.
Equation is:
Actors from second grade + Actors from third grade = Total actors
10 + x= 30
Now, solving
Subtract 10 from both side
10 +x - 10 = 30 - 10
x = 20
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Mr. Garcia gave his students a biology test last week.Here are the test scores for each of the fifteen students.Test scores938398899791838692908884858291(b) Construct a histogram for the data.(a) Complete the grouped frequency distribution forthe data. (Note that the class width is 5.)FrequencyTest scores7-6+79 to 835+84 to 88Frequency0.0043+89 to 932+1194 to 980-79 1083941 98844 to 58 89 to 93Test scoresx5?
Test scores: 93 83 98 89 97 91 83 86 92 90 88 84 85 82 91
organizing the data: 82,83,83,84,85,86,88,89,90,91,91,92,93,97,98
(a) Complete the grouped frequency distribution for the data.
79 to 83 -> 3
84 to 88 -> 4
89 to 93 -> 6
94 to 98 -> 2
(b) Construct a histogram for the data.
the histogram can be constructed using the information obtained in point (a)
1. The sliders for y = ax + b have been set to create the following graph. What are possible values for a and b?
The slope of the line is m = 2 and the y-intercept b = 2
Therefore, the equation for the graph is
[tex]y=-2|x|+2[/tex]meaning a = -2 and b = 2.
(The negative sign in front of the absolute value drags the graph below the y = 0 )
Leila wrote an equation to represent the revenue of a parking lot for one day. She let x represent the number of cars that paid to park and y represent the number of trucks that paid to park. If a car costs $8 per day, a truck costs $10 per day, and the total revenue for the day was $830, which equation could Leila use to represent the number of cars and trucks that paid to park that day?
8 x + 10 y = 1,660
10 x + 8 y = 1,660
8 x + 10 y = 830
The equation that Leila can use to represent the number of cars and trucks that paid to park that day is C. 8 x + 10 y = 830
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let x represent the number of cars that paid to park.
Let y represent the number of trucks that paid to park.
Therefore, the equation will be:
= (8 × x) + (10 × y) = 830
8x + 10y = 830
In conclusion, the correct option is C.
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two functions are given below: f(x) and h(x) state the axis of symmetry for each function and explain how to find it f(x)=3(x+4)^2+1
The axis of symmetry for each function are x = -4 and x =1
How to determine the axis of symmetry for each function?The functions are given as
f(x) and h(x)
As a general rule of functions;
The axis of symmetry for a function is the x-coordinate of the vertex of the function
In f(x), we have
f(x)=3(x+4)² + 1
The vertex of this function is
(x, y) = (-4, 1)
So, the axis is x = -4
For function h(x), we have
The vertex of this function is
(x, y) = (1, -3)
So, the axis is x = 1
Hence, the axis of symmetry are x = -4 and x =1
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Find the volume of a cone with a height of 10cm and diameter of 6cm. Round to the nearest tenth. Use 3.14 for .
We can find the volume of a cone using the formula
[tex]V=\frac{\pi r^2h}{3}[/tex]Where
h = height
r = radius
Remember that
[tex]d=2r\Rightarrow r=\frac{d}{2}[/tex]Therefore, let's find out the radius first, the problem says that the diameter is 6cm, then
[tex]r=\frac{6}{2}=3\text{ cm}[/tex]The radius is 3cm and the height is 10cm, let's use it in our formula:
[tex]\begin{gathered} V=\frac{\pi\cdot(3)^2\cdot10}{3} \\ \\ V=30\pi \end{gathered}[/tex]The problem also say to use = 3.14, then the volume is
[tex]\begin{gathered} V=30\cdot3.14 \\ V=94.2 \end{gathered}[/tex]Therefore, the volume is
[tex]V=94.2\text{ cm}^3[/tex]
will send image. select the expression. that is not equivalent to 10 + 10p
We have that
[tex]\begin{gathered} 5(10\text{ + p +p) = 5(10 + 2p)} \\ =\text{ 50 + 10p }\ne\text{ 10 + 10 p} \end{gathered}[/tex]So the answer is the first one.
What does 10 represent in 10/6
10/6
This is a fraction, in a fraction the bottom number represents the denominator and the top number represents the numerator.
So, in this case, 10 represents the numerator.
18. The table below gives the population of a town (in thousands) from the year 2000 to the year 2008. Year '00 '01 '02 03 04 '05 06 '07 '08 Population 87 84 83 80 77 76 78 81 85 (thousands) What was the average rate of change of population: a. between 2002 and 2004? b. between 2002 and 2006?
a . Average rate of change between 2002 and 2004 can be calculated below
[tex]\begin{gathered} average\text{ rate of change=}\frac{chang\text{e in y}}{\text{change in x}} \\ average\text{ rate of change = }\frac{77-83}{2004-2002} \\ average\text{ rate of change}=\frac{-6}{2}=-3(thousand) \end{gathered}[/tex]b. Average rate of change between 2002 and 2006 is
[tex]\begin{gathered} \text{average rate of change = }\frac{78-83}{2006-2002} \\ average\text{ rate of change}=\frac{-5}{4}=-\frac{5}{4}(thousand) \end{gathered}[/tex]Task 2: Interest in Finance
Interest is a concept familiar to most people: every credit card in existence has a term called annual percentage rate (APR), which is an interest rate. Suppose you charged $1,000 to a credit card that has a minimum payment each month equal to the interest owed. Can you figure out how much the interest rate is based on this amount?
The formula for simple interest is where I is the amount you will pay in interest, r is the rate at which interest will accrue, P is the principal (amount borrowed), and m is the number of times the interest is applied.
2
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To solve for the interest rate of your credit card, you need to understand which variables in the above formula you have. If your minimum monthly payment is $22 on the $1,000 credit card bill, which variables do you know the values of?
Type your response here: rate= interest/$1000
Manipulate the formula so it will calculate the interest rate you are paying instead of the amount of money you are paying.
Type your response here:
Now that you have a formula that will give you the interest rate, plug in the values for the problem and solve for that interest rate. Interest rates are usually represented for a time period: over what time period does this rate apply? What would the interest rate be if it were a yearly rate?
Type your response here:
Now consider a different situation. Payday loans are a type of loan where you can get money for a future paycheck, typically two weeks in advance. A typical payday loan service might charge $15 for a loan against a paycheck you will receive in two weeks. The interest rate is 10% of the paycheck over that two-week period. Given this information, which variables in the interest formula are known? Develop a formula that will solve for the unknown variable.
Type your response here:
Solve for the value of the unknown variable.
Type your response here:
1. One cannot figure out how much the interest rate is based on the amount charged to the credit card unless other variables are supplied.
2. We know the values of the following variables now:
The interest amountThe principal amount.3. The interest rate is 2.2% per month.
4. The period that this interest rate applies is monthly, called the MPR.
5. The annual interest rate (APR) is 26.4%.
6. The known variables about this payday loan are the interest amount, the interest rate, and the period.
7. A formula to solve for the unknown variable, principal/credit amount, is P = I / (RT), where I = interest, R = rate, and T = time period.
8. The solution for the value of the unknown variable, Principal, is $3,900.
Minimum monthly payment = interest amount = $22
Credit card bill = $1,000
Rate = interest/$1,000
Rate = $22/$1,000 = 0.022
= 2.2%
MPR = 2.2%
APR = 26.4% (2.2% x 12)
Payday Loans:The service charge for a 2-week loan = $15
Interest rate = 10%
Principal/Payloan = $3,900 ($15 / (10% x 2/52)
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need help with math
The y intercept is when x = 0.Therefore,
[tex]\begin{gathered} \text{when} \\ x=0 \\ y=0 \end{gathered}[/tex]The vertex can be found below
a rectangle width is 3 1/2 inches and the lenght is 4 3/4 inches. What is the area of the rectangle?
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The length of the rectangle = [tex]4 \frac{3}{4}[/tex] inches
= 19 / 4 inches
The width of the rectangle = [tex]3 \frac{1}{2}[/tex] inches
= 7 / 2 inches.
Since, We know that;
The area of the rectangle = Length x Width
Substitute all the values , we get;
The area of the rectangle = Length x Width
The area of the rectangle = 19 / 4 x 7 / 2
= 133 / 8 inches²
= [tex]16 \frac{5}{8}[/tex] inches²
Therefore,
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
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What is the area of the shaded region if the radius of the circle is 6 in.
Then, the area of 1/4 of the circle is:
[tex]\begin{gathered} A=\text{ }\frac{\theta}{360}\text{ x }\pi r^2 \\ A=\text{ }\frac{90}{360}\text{ x }\pi r^2 \\ A\text{ = }\frac{1}{4}\pi\text{ 6}^2 \\ A=\text{ 9}\pi \\ \\ \end{gathered}[/tex]The area of the triangle is:
[tex]\begin{gathered} A=\text{ }\frac{b\text{ x h }}{2} \\ A\text{ = }\frac{6\text{ x 6}}{2} \\ A=\text{ 18in}^2 \end{gathered}[/tex]The area of the shaded region is the area of 1/4 of the circle minus the area of the triangle:
[tex]\begin{gathered} A\text{ = 9}\pi\text{ - 18 in}^2 \\ A=\text{ 28.27in}^2\text{ - 18in}^2 \\ A=\text{ 10.27in}^2 \end{gathered}[/tex]A cab company charges a flat rate of $2 plus an additional $0.50 for every mile traveled. Use this information for Items 12 and 13. 12. a. Write an expression that can be used to determine the total cab fare for a distance of m miles. b. When Sara arrived at your destination, her cab fare was $7.50. Write an equation to represent this situation. How many miles did Sara travel?
The cost for each travel on this cab company can be expressed as a sum of the fixed fee and the price per mile multiplied by the distance in miles of the travel. Therefore:
[tex]c(m)=2+0.5\cdot m[/tex]If Sarah paid $7.5 for her cab, then c(m)=7.5 and we can use this value on the expression above to solve for "m". We have:
[tex]\begin{gathered} 7.5=2+0.5\cdot m \\ 0.5\cdot m=7.5-2 \\ 0.5\cdot m=5.5 \\ m=\frac{5.5}{0.5}=11 \end{gathered}[/tex]She traveled 11 miles.
Simplify 6+ √-80.
06+16√5i
06+4√5
06+16/ √5
06+4√ √5i
Answer:
6 + 4[tex]\sqrt{5}[/tex]i
Step-by-step explanation:
The prime factorization of 80 is 2x2x2x2x5
6 + [tex]\sqrt{-2x2x2x2x5}[/tex] We can take out 2 pairs of 2 which would be 4 and [tex]\sqrt{-1}[/tex] is i
6 + 4[tex]\sqrt{5}[/tex] i
Find the measure of the indicated angle to the nearest degreeQuestion 15
Question 15.
Given:
Length of side opposite the indicated angle = 12 units
Length of side adjacent the hypotenuse = 24 units
Let's find the measure of the indicated angle.
Here, we have a right triangle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for sine:
[tex]sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]Where:
θ is the indicated angle.
Thus, we have:
[tex]\begin{gathered} sin\theta=\frac{12}{24} \\ \\ sin\theta=\frac{1}{2} \end{gathered}[/tex]Take the sine inverse of both sides:
[tex]\begin{gathered} \theta=sin^{-1}(\frac{1}{2}) \\ \\ \theta=30^o \end{gathered}[/tex]Therefore, the measure of the indicated angle us 30 degrees.
• ANSWER:
30°
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Problem
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Solution
For this case we can find the real price with this operation:
95+265= 360
And the rate of discount can be founded as:
(95/265)*100= 35.85%
Rounded to the nearest percent would be 36%
13. slove for x so the [tex]f(x) = 5[/tex]
Solution
We have the following function given:
f(x) = -3x+5
And we need to do the following:
5= -3x+5
And if we subtract 5 in both sides we got:
0 =-3x
Dividing both sides by -3 we got:
[tex]\frac{0}{-3}=\frac{-3x}{-3}[/tex]And finally we got:
x= 0
Problem 17
17) f(-2)= 3
18) f(0)= 3
19) f(1)= 0
20) f(-1)= 5.2
which number is 5 more than 8009998
A number which is 5 more than 8009998 is 8010003
In this question we need to find a number which is 5 more than 8009998.
Let x be a number which is 5 more than 8009998.
We get the required number by adding 5 to 8009998.
so, we write it down as:
x = 8009998 + 5
x = 8010003
Therefore, a number which is 5 more than 8009998 is 8010003
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Which decimal represents 8 X 1,000 + 4 X 100 + 7 X7 16 +31,0001,0A 8,004.073C 8,400.703B 8,040.073D 8,400.730
The given expression:
[tex]8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}[/tex]Simplify the expression:
[tex]\begin{gathered} 8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}=8000+400+0.7+0.003 \\ 8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}=8400.703 \end{gathered}[/tex]Answer : c) 8400.703
Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
A) f(x) = (x − 8)2
B) f(x) = (x − 4)2 − 13
C) f(x) = (x − 4)2 + 3
D) f(x) = (x − 4)2 + 16
By using the completing the square method, f(x) = x² − 8x + 3 in vertex form is: B. f(x) = (x − 4)² − 13.
The vertex form of a quadratic equation.In this exercise, you're required to rewrite the given function in vertex form by using the completing the square method. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
f(x) = x² − 8x + 3
f(x) = x² − 8x + (8/2)² - 13
f(x) = x² − 8x + (4)² - 13
f(x) = x² − 8x + 16 - 13
f(x) = (x² − 8x + 16) - 13
f(x) = (x − 4)² − 13
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Suppose A is true, B is true, and C is true. Find the truth values of the indicated statement.
Solution:
If A is true, B is true, and C is true, then:
[tex]A\lor(B\wedge C)=\text{ T }\lor(T\wedge T)\text{ = T}\lor(T)\text{ = T }\lor\text{ T = T}[/tex]we can conclude that the correct answer is:
TRUE
Look at triangles A through F shown in the rectangles below.Which triangles are acute triangles?
The acute triangles are those whose all 3 angles have a measure less than 90 degrees.
We need to follow the next image:
Let us check each triangle.
Triangle A:
It has a right angle, hence, it can not be an acute triangle.
Triangle B:
All three sides are less than 90 degrees. Hence, it is an acute triangle
Triangle C:
It has an angle with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle D
All three sides are less than 90 degrees. Hence, it is an acute triangle.
Triangle E
It has a side with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle F
It has a right angle, hence, it can not be an acute triangle.
Hence, the correct answer is H. B and D
White the inequality shows by the shaded region in the graph with the boundary line y=x/3-5
From the given figure
Since the line is a dashed line, then
The sign of inequality does not have equal (< OR > )
Since the shading area is down the line, then
The sign of inequality should be smaller than (<)
Then the inequality is
[tex]y<\frac{x}{3}-5[/tex]Hello hope all is well can you tell me what am doing wrong for number 6
We have the next data
70,89,75,36,80
First we will calculate the mean
(70+89+75+36+80)/5=70
mean=70
Then we will calculate the Median
36,70,75,80,89
median =75
Then we will calculate the mode because any value is repeated all the values given are the mode
mode:70,89,75,36,80
Range
89-36=53
Range =53
Solve the system of equations. If the system has no solution say that it's inconsistent. [tex]\begin{gathered}x + 5y = 2 \\ 3x + 15y = 6\end{gathered}[/tex]
Answer:
Explanation: Given the system of equations:
[tex]\begin{gathered} x+5y=2 \\ 3x+15y=6 \end{gathered}[/tex]The bar graph below shows the number of students at Lindsay's school who were born in various states.Oregon?ColoradoStateUtah -Arizona -New Mexico04812 16 20 24 28 32Number of StudentsThe number of students who were born in Oregon is the same as the number of students from Utah and NewMexico combined.Umantudante at Lindsay's school were born in Oregon?We
Since the number of students who were born in Oregon is the same as the number of students from Utah and New Mexico, add the amount of students from Utah and New Mexico to find the number of students who were born in Oregon.
18 students were born in Utah, and 12 students were born in New Mexico.
Since 18+12=30, then, 30 students were born in Utah and New Mexico combined.
Therefore, the amount of students who were born in Oregon, is:
[tex]30[/tex]0 Rick has been losing weight at a constant rate since he began his new fitness plan. The table below shows Rick's weight for the first four weeks, 2 3 I 220.2 218.6 221.8 223.4 Weight (lbs) a) Write an equation to represent this sequence. b) Find Rick's weight after 16 weeks. ter your answer(s) here
To make the equation lets us find the rate of change of the weight
The form of the equation is y = m x + b
where:
m is the rate of change (slope)
b is the y-intercept (value y when x = 0)
To find m use two-point from the table
(1, 223.4) , (2, 221.8)
[tex]m=\frac{221.8-223.4}{2-1}=-\frac{8}{5}=-1.6[/tex]Substitute it in the form of the equation
[tex]y=-1.6x+b[/tex]To find b use any point in the table
(1, 223.4)
x = 1 , y = 223.4
[tex]\begin{gathered} 223.4=-1.6(1)+b \\ 223.4=-1.6+b \end{gathered}[/tex]Add 1.6 for both sides to find b
[tex]\begin{gathered} 223.4+1.6=-1.6+1.6+b \\ 225=b \end{gathered}[/tex]Substitute value b in the equation
[tex]y=-1.6x+225[/tex]The equation of the sequence is y = -1.6 x + 225
to find his weight after 16 weeks substitute x by 16
[tex]\begin{gathered} y=-1.6(16)+225 \\ y=-25.6+225 \\ y=199.4 \end{gathered}[/tex]His weight after 16 weeks is 199.4 Ibs
