Answers
If angle A is greater than angle C, then side BC is greater than side AB.
[tex]\begin{gathered} BC>AB \\ 8-x>4x+48 \end{gathered}[/tex]Then, we solve for x
[tex]\begin{gathered} -4x-x>48-8 \\ -5x>40 \\ x<-\frac{40}{5} \\ x<-8 \end{gathered}[/tex]Hence, the restriction of x is that its value must be less than -8.Related Questions
you started this year with $141 saved and you continue to save $27 per month. Write an equation to model this situation (use m for months and s for savings)
Answers
The money we would have at any time can be modeled as
M = 27k + 141
Why?
you started with $141, so that is the base amount,
every month you add 27 dollars,
in one month you add 27 dollars,
in two months you 27 again making 54 dollars,
so , in x months, you have added 27x dollars to the 141 dollars,
thus our equation is
M = 27k + 141
How do you evaluate the following polynomials for a domain value?P(x) = -3x² + 9x find P(-5)
Answers
The given polynomial is expressed as
P(x) = - 3x^2 + 9x
The domain values are the x values. To find P(-5), it means that we would substitute x = - 5 into the polynomial. It becomes
P(- 5) = - 3(- 5)^2 + 9(- 5)
P(- 5) = - 3 * 25 - 45
P(- 5) = - 75 - 45
P(- 5) = - 120
C. In which of the two functions is it possible to have negative output?
Answers
It is possible to have a negative output on:
[tex]y=a|x|[/tex]Since a can take possitive values and negative ones, and since it isn't inside the absolute value barrs.
7. f(x) = x² + 4 (a) f(-2) (b) f(3) f) f (c) f(2) (d) f(x + bx)
Answers
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 57 inches, and standard deviation of 7.3 inches.What is the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches? Do not round until you get your your final answer, and then round to 3 decimal places.
Answers
0.834
Explanations:The formula calculating the z-score is expressed as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Given the following parameters
• x1 = 49.55
,• x2 = 73.35
,• mean μ = 57inches
,• standard deviation σ = 7.3in
Convert the x-values to z-score
[tex]\begin{gathered} z_1=\frac{x_1-\mu}{\sigma} \\ z_1=\frac{49.55-57}{7.3} \\ z_1=-\frac{7.45}{7.3} \\ z_1=-1.02 \end{gathered}[/tex]For z2;
[tex]\begin{gathered} z_2=\frac{73.35-57}{7.3} \\ z_2=\frac{16.35}{7.3} \\ z_2=2.24 \end{gathered}[/tex]Determine the required probability
[tex]\begin{gathered} P(-1.02Hence the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches is 0.834Use the function below to find the indicated value:4x – 10,x21+12 <33
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Explain the given function
It can be seen from the function that there are three conditions which are defined below:
When x is less than 3, this states that we execute the first function for values of x less than 3
When x is between 3 and less than 7, this means that whenever x ranges from 3 to 6, we execute the second function.
When x is greater than or equals to 7, we execute the last function.
STEP 2: find f(7)
Since the value of x which is 7 is greater than or equal to 7, therefore we use the last function as seen below:
[tex]\begin{gathered} f(x)=f(7) \\ f(x)=\frac{x+1}{x-3} \\ Substitute\text{ 7 for x} \\ f(7)=\frac{7+1}{7-3}=\frac{8}{4}=2 \end{gathered}[/tex]Hence, the result is 2
The dimensions of a rectangular prism are shown below length 1 1over2 width 1 foot hight 2 1over2
Answers
Solution
Given the dimensions of a rectangular prism as
length: 1.5 ft
width: 1 ft
Height: 2.5 ft
Part A.
Volume of a rectangular prism =
[tex]\begin{gathered} V_{RP}=l\times w\times h \\ \\ l\text{ is the length} \\ \\ w\text{ is the width} \\ \\ h\text{ is the height} \end{gathered}[/tex][tex]V_{RP}=1.5\times1\times2.5=3.75\text{ ft}^3[/tex]Volume of small cubes
[tex]V_{SC}=0.5^3=0.125\text{ ft}^3[/tex]Number of small cubes that can be packed in a rectangular prism is 30
[tex]N=\frac{V_{RP}}{V_{SC}}=\frac{3.75}{0.125}=30[/tex]Hence, there are 30 small cubes that can be packed in the rectangular box.
Part B.
The volume is given as
[tex]\sqrt[3]{30}=3.12[/tex]The bike you have been saving for is discounted 25%. You have $400 saved to purchase it. The original, non-discounted price of the bike is $450. There is a 5.44% sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax, how much money will you have left over? Round your answer to the nearest dollar.
Answers
1) Let's begin considering that our budget is $400.
Since the bike is discounted by 25%, we can get to know the price with this formula:
[tex]400\times(1-0.25)=\$300[/tex]2) Note that there is an increase in the price since there are taxes to pay. The original price is taken into consideration to charge the tax. So, let's find how much we have to pay:
[tex]450\times0.0544=\$24.48[/tex]So, let's add that to the discounted price:
[tex]\$300+\$24.48=\$324.48[/tex]3) Since I've got $400 let's find how much is left after that purchase:
[tex]\$400-\$324.48=\$75.52\approx\$76[/tex]Note that as requested we rounded off to the nearest dollar.
Thus, that's what's left after the purchase
decide whether circumference or area would be needed to calculate the total number of equally sized tiles on a circular floor and explain your reasoning
Answers
The total number of equally-sized tiles on a circular floor.
Here, we are covering the region or the total space occupied by all the tiles on the floor.
Hence, the area is calculated.
Calculate the determinant of this 2x2 matrix. Provide the numerical answer. 2 -14 - 5
Answers
In order to find the determinant we just multiply the diagonals
Then we substract the second result to the first:
[tex]\begin{gathered} \begin{bmatrix}{2} & {-1} & {} \\ {4} & {-5} & {} \\ & {} & {}\end{bmatrix}=2\cdot(-5)-4\cdot(-1) \\ =-10-\mleft(-4\mright)=-10+4 \\ =-6 \end{gathered}[/tex]Answer: the determinant of this 2x2 matrix is -6ea of the rectangle. 9 mm square millimeters х 30 mm
Answers
For this problem, we are given a rectangle and its dimensions. We need to use this information to determine the area of the rectangle.
The rectangle's area is given by the following expression:
[tex]A=(\text{width)}\cdot(\text{length)}[/tex]For this problem, we have:
[tex]A=9\cdot30=270\text{ square milimiters}[/tex]The rectangle's area is 270 square milimiters
Find the volume of a cube with a side length of 2.8 in, to the nearest tenth of a cubic inch (if necessary).
Answers
Given:
Length of side = 2.8 in
Let's find the volume of the cube.
To find the volume of a cube, apply the formula:
[tex]V=a^3[/tex]Where:
a is the side length = 2.8 in
Hence, to find the volume, we have:
[tex]\begin{gathered} V=2.8^3 \\ \\ V=2.8*2.8*2.8 \\ \\ V=21.952\approx22.0\text{ in}^3 \end{gathered}[/tex]Therefore, the volume of the cube is 22.0 cubic inch.
ANSWER:
22.0 in³
Help I’ll give extra points!10. Camilla is saving to purchase a new pair of bowling shoes that will cost at least $39. She hasalready saved $19. What is the least amount of money she needs to save for the shoes?11. Suppose you earn $20 per hour working part time at a tax office. You want to earn at least$1,800 this month, before taxes. How many hours must you work?For problem 12, translate the phrase intoalgebraic inequality.12. A tour bus can seat 55 passengers. A minimum of 15 people must register for the tour to bookthe bus.
Answers
the least amount of money she needs to save is 20
the number of hours you must work is at least 90hours
Explanation:
10) The pair of shoes cost at least $39
at least $39 means: the cost is ≥ 39
≥ means greater than or equal to
Amount saved = $19
Let the least amount of money = x
x + 19 ≥ 39
x ≥ 39-19
x ≥ 20
This means the least amount of money she needs to save is 20
11) Let the number of hours worked = x
Amount earned per hour = $20
Amount to be earned this month is at least $1,800
This means amount to be earned this month ≥ 1800
[tex]\begin{gathered} 20\times x\text{ }\ge\text{ 1800} \\ 20x\text{ }\ge\text{ 1800} \\ \text{Divide through by 20} \\ x\text{ }\ge\text{ }\frac{1800}{20} \\ x\text{ }\ge\text{ 90} \end{gathered}[/tex]This means the number of hours you must work is at least 90hours
I need help with my math assignment thank you :)
Answers
Okay, here we have this:
Considering the provided information, we are going to match the situations to their corresponding functions, so we obtain the following:
1: The total pages a person reads in x days, if the person reads 6 pages a day: f(x)=6x.
2: The cost of x boxes of mangoes, if 1 box cost $6 and the shipping charge is $6 per order: f(x)=6x+6 -> f(x)=6(x+1)
3: The total cost of x notebooks, if one notebook cost $6 and students receive a discount of $1 off their bill: f(x)=6x-1
4: The total cost of x novels and a pocket dictionary if you buy a novels each at $6 and get a pocket dictionary at $1: f(x)=6x+1
jeslie ann has a 48 month installment loan of 82.91. the amount she borrowed was 3600
Answers
Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome of credit.
Step 1
Loan Amount(p)= 3600
Number of Payments per year(n)= 12
Time in Years (t)=4
Installment Payment (m)=83.81
Total amount paid in 48 installments= 4022.88
Amount Paid - Amount Financed = 4022.88 - 3500 = 522.88 in finance charges.
To determine the annual percentage rate. Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome.
Finance Charge/ Amount financed × 100= 522.88/ 3600× 100= 14.5
To use Table , look for 48 in the far left-hand column under the heading Number of Payments. Then move across to the right until you find the value closest to 14.5. In this case, 14.5 is in the table. The value 7 is at the top of this column. The yearly percentage rate is therefore around 7. Monthly payments are 83.81. After 12 payments have been made, 30 payments remain. Therefore, P = 83.81 and n = 30. Use the APR table to calculate V . In the Number of Payments column, find the number of remaining payments, 30, and then look to the right until you reach the column headed by 7%, the APR. intersect at 9.30. Thus, V = 9.30.
:[tex]u=nPV/100+V\\u=30*83.81*9.30/100+9.30=213[/tex]
Total due amount = Total remaining payment including interest- saving on interest + 12th monthly payment= 2514.3- 213.934+ 83.81= 2384.17
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Consider the following functions.S(x) = x2 - 4x + 4 and g(x) = x - 2Step 1 of 2: Find• ()a). simplify your answer.AnswerKeybo(*)(x) =Subn
Answers
Answer:
[tex]x-2[/tex]Explanation:
Here, we want to simplfy the given expression
From what we have:
[tex](\frac{f}{g})(x)\text{ = }\frac{f(x)}{g(x)}[/tex]Substituting the values, we have it that:
[tex]\frac{x^2-4x+4}{x-2}\text{ = }\frac{(x-2)(x-2)}{x-2}\text{ =x-2}[/tex]The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 6". Find P(A). Outcome Probability 1 0.394 - 2. 0.152 3 0.001 4 0.09 5 0.112 6 0.047 7 0.053 8 0.151
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Problem-Solving in Probability.
Prob( A ) = Prob( Outcome divisible by 6 ):
only outcome 6 is divisible by 6, and it has a probability of 0.047
Hence,
[tex]\text{Prob(A) =Prob(outcome 6) = 0.047}[/tex]Hence, the correct answer is 0.047
A store charges $140 for every 10 bags of fertilizer a farmer buys. a. Complete the table. Graph the values. 30 40 Fertilizer (bags) 10 Cost ($) 140 280 840 b. How much would a farmer pay for 50 bags of fertilizer? Explain. a. Complete the table. 30 40 Fertilizer (bags) 10 Cost ($) 140 280 840
Answers
Question:
Solution
a) If for every 10 bags the store charges $140 then
1. for 10x2 = 20 bags the store charges 2x$140 = 280.
2. for 10x3 = 30 bags the store charges 3x$140 = 420.
3. for 10x4 = 40 bags the store charges 4x$140 = 560
4. for 10x6 = 60 bags the store charges 6x$140 = 840
b) According to the previous item, we can conclude that for 10x5 = 50 bags the store charges 5x$140 = 700 then, the farmer must pay $700 for 50 bags.
c)
According to the previous item, we can conclude that for 10x5 = 50 bags the store charges 5x$140 = 700 then, the farmer must pay $700 for 50 bags.
I apologize about the quality the shaded region is the trapezoid part not the square in the middle
Answers
First, find the area of the trapezoid.
Area of a trapezoid = 0.5 ( sum of bases ) x height
bases = 15in, 8in
height = 8in
A 1 = 0.5 (15 + 8 ) x 8 = 92 in 2
Then, subtract the area of the rectangle:
Area of a rectangle = lenght x width
L = 5
W= 3
A2 = 5 x 3 = 15 in 2
Area of the shaded region = A1 - A2 = 92 - 15 = 77 in2
I need help on this please! Assignment is called “Periods and Amplitudes” not sure if that helps lol
Answers
Solution:
The sine function is generally expressed as
[tex]\begin{gathered} y=A\sin(B(x+C))+D\text{ ---- equation 1} \\ where \\ A\Rightarrow amplitude \\ C\Rightarrow phase\text{ shift} \\ D\Rightarrow vertical\text{ shift} \\ \end{gathered}[/tex]The period of the function is expressed as
[tex]period=\frac{2\pi}{B}[/tex]Given the function:
[tex]y=\sin((\frac{7\pi}{4}x))\text{ ---- equation 2}[/tex]Comparing equations 1 and 2, we see that
[tex]B=\frac{7\pi}{4}[/tex]Thus, by substituting the value of B into the period formula, we have
[tex]\begin{gathered} period=\frac{2\pi}{\frac{7\pi}{4}} \\ =2\pi\times\frac{4}{7\pi} \\ =\frac{2\times\text{4}}{7} \\ =\frac{8}{7} \end{gathered}[/tex]Hence, the period of the function is
[tex]\frac{8}{7}[/tex]ok so I understand the first 2 steps of solving this but I dont entirely get it........
Answers
You have the following equation:
2x² - 12x + 16 = 0
in order to solve the previous equation, first divide by 2 both sides:
x² - 6x + 8 = 0
next, consider that the factors of the previous expression has the form:
(x - )(x - ) = 0
consider the first number inside the first factor is the result of the sum of two numbers, and the number of the second factor is the product of the same numbers. Such numbers are:
(2)·(4) = 8
2 + 4 = 6
hence, the factorized expression is:
(x - 8)(x - 2) = 0
the solutions of the equations are:
x = 8
x = 2
Write the product using exponents. I need help I’m not sure how to do this
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Given:
The given expression is,
[tex]\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}[/tex]Required:
Write the product using exponent.
Answer:
Let us compute the product using exponents.
[tex]\begin{gathered} \frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5} \\ =(\frac{1}{5})^5 \\ =\frac{\left(1\right)^5}{\left(5\right)^5} \\ =\frac{1}{3125} \end{gathered}[/tex]Final Answer:
The product using exponents is given by,
[tex]\frac{1}{3125}[/tex]
Find the cosine of angle R. Reduce the answer to the lowest terms.
Answers
Cosine formula
[tex]\cos (angle)=\frac{\text{ adjacent side}}{\text{ hypotenuse}}[/tex]Considering angle R, the adjacent side has a length of 9 units, and the hypotenuse of the triangle has a length of 15 units. Substituting this information into the above formula:
[tex]\cos (m\angle R)=\frac{9}{15}=\frac{\frac{9}{3}}{\frac{15}{3}}=\frac{3}{5}[/tex]Find the percent markdown. Cost of a pants $36.95, selling price $24.02
Answers
Answer:
35%
Explanation:
Given cost of a pant = $36.95 and selling price = $24.02.
Let the markdown percent be y.
To determine the markdown percent, we'll use the below formula;
Sale Price = Original Price x (1 - Markdown% in decimal)
So let's go ahead and substitute the given values into the equation;
[tex]\begin{gathered} 24.02=36.95\ast(1-y) \\ 24.02=36.95-36.95y \\ -12.93=-36.95y \\ y=\frac{-12.93}{-36.95} \\ y=0.35 \\ \therefore y=35percent \end{gathered}[/tex]So the markdown percent is 35%
Question 1
Is the sequence arithmetic: 78, 785, 7855, 78555, ...
O No
5 pts
Yes
Next >
Answers
The sequence is not arithmetic
What is a sequence?
A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the series is defined as the number of items (which might be infinite). Unlike a set, the same components can occur numerous times in a sequence at various points, and the order does important. Formally, a sequence may be defined as a function from natural numbers (the sequence's places) to the items at each point. The concept of a sequence may be extended to include an indexed family, which is defined as a function from an arbitrary index set.
The given sequence 78, 785, 7855, 78555, ... is not arithmetic.
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I need help with this please it’s revisiting proportional relationships
Answers
In order to calculate the cost of 7.5 lbs of walnuts, we can use the following rule of three, knowing that 3/4 lbs have a cost of $3.45:
[tex]\begin{gathered} \text{weight}\to\text{ cost} \\ \frac{3}{4}\text{ lbs}\to3.45 \\ 7.5\text{ lbs}\to x \end{gathered}[/tex]Now, we can write the following proportion and solve for x:
[tex]\begin{gathered} \frac{\frac{3}{4}}{7.5}=\frac{3.45}{x} \\ x\cdot\frac{3}{4}=7.5\cdot3.45 \\ x=\frac{7.5\cdot3.45\cdot4}{3} \\ x=34.5 \end{gathered}[/tex]Therefore the cost is $34.50.
A number decreased
by the sum of the number and three
Answers
Answer:
-3
Step-by-step explanation:
x - (x+3)
x - x -3
-3
12*pi=pi*12Name the property that the following statement illustratesA. Identify property of multiplicationB. Associative property of multiplication C. Commutative property of additionD. Commutative property of multiplication E. Identity property of additionF. Associative property of addition
Answers
The commutative law says that we can swap the position of numbers when we add or multiply and still get the same result
The commutative property of multiplication can be expressed as
ab = ba
The commutative property of addition can be expressed as
a + b = b + a
Looking at the given expression,
12 and pi were swapped and the sign involved is multiplication. Thus, the correct option is
D. Commutative property of multiplication
Solve the inequality: -1 <= x - 3 > 7
Answers
-1 ≤x-3>7
So:
-1≤x-3
x-3>7
Solve each
-1≤x-3
Add 3 to both sides:
-1+3≤x-3+3
2≤x
x-3>7
add 3 to both sides:
x-3+3>7+3
x>10
Solution:
2≤x or >10
What is the height of a parallelogram with an area of 50 square meters
and a base length of 5 meters?
Answers
The height of a parallelogram with an area of 50 square meters and a base length of 5 meters is 10 meters
What is a parallelogram?The word "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bounded by parallel lines." As a result, a quadrilateral that is bound by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides. Square, rectangle, and rhombus are the three primary varieties of parallelograms, and each one has distinct characteristics. If a quadrilateral's opposite sides are parallel and congruent, it will be a parallelogram. So a quadrilateral with both pairs of opposite sides being parallel and equal is known as a parallelogram.
Various forms of parallelograms can be distinguished from one another based on their unique characteristics. It can be broadly classified into three distinct types:
RectangleSquareRhombusArea = 50
Base = 5
Area of ║gm = base (height)
50 = 5(X)
x = 10
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