The linear equation that passes through the two given points is:
7 = (-3/2)*x + 31/2.
What is the equation of the line?A general linear equation is 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) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
Here the line passes through (5, 8) and (9, 2), then the slope is:
m = (2 - 8)/(9 - 5) = -6/4 = -3/2
So we have:
y = (-3/2)*x + b
To find the value of b, we can replace the values of one of the points in the equation, I will use (5, 8)
8 = (-3/2)*5 + b
8 = -15/2 + b
8 + 15/2 = b
31/2 = b
The line is: y = (-3/2)*x + 31/2
Jack has an old scooter. He wants to sell it for 60% off the current price. The
market price is $130. What should his asking price be? Explain your reasoning.
On Monday, Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch. Let r represent the cost of a burger and y represent the cost of an order of fries. What linear equation would model this?
Let:
r = Cost of a burger
y = Cost of an order of fries
Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch, therefore:
[tex]3r+4y=20[/tex]Convert the measurement as indicated 83 qt = Gal Qt
20 gallons 3 quarts
Explanation:Note that:
1 quart = 0.25 gallons
83 quarts can be written as
80 quarts + 3 quarts
80 quarts = 80 x 0.25 gallons
80 quarts = 20 gallons
Therefore:
83 quarts = 20 gallons 3 quarts
Yusuf is going to the amusement park, where he has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money Yusuf will spend is given by the equation y=4x+20y=4x+20, where yy represents the total amount of money, in dollars and cents, and xx represents the number of rides Yusuf goes on. What could the number 20 represent in the equation?A.The total amount of money Yusuf will spend if he goes on 1 ride.B.How much it cost for a ticket to go on one of the rides.C.The total amount of money Yusuf will spend if he goes on 0 rides.DThe total amount of money Yusuf will spend if he goes on 100 rides.
Given the equation:
[tex]y=4x+20[/tex]If x = 0, then:
[tex]\begin{gathered} y=4\cdot0+20 \\ \Rightarrow y=20 \end{gathered}[/tex]Answer: C
What is the value of x?2445°X=(Simplify your answer. Type an exact answer, using radicals as needed.)
Given the figure of a right-angle triangle
As shown, the given triangle is a 45-45-90 triangle
The relation between the hypotenuse (h) and the length of one leg (l) is as follows:
[tex]h=(\sqrt{2})l[/tex]As shown, h = 24, and l = x
[tex]\begin{gathered} 24=\sqrt{2}*x \\ \\ x=\frac{24}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{24\sqrt{2}}{2}=12\sqrt{2} \end{gathered}[/tex]So, the answer will be:
[tex]x=12\sqrt{2}[/tex]Translate the following word phrase to an algebraic expression and simplify: “8 times the difference of 6 times a number and 3”
Given the word phrase
8 times the difference of 6 times a number and 3
Let the number = x
6 times the number = 6x
The difference of 6 times the number and 3 = 6x - 3
8 times the difference of 6 times a number and 3 will be:
[tex]8(6x-3)[/tex]A company is going to make a storage container with sheet steel walls. The container will be in the shape of a rectangular prism, as shown below. If the sheet steel costs $30 for each square meter, how much will the sheet steel cost in total?
ANSWER
$3060
EXPLANATION
Each steel sheet used for the prism costs $30 per square meter.
To find the total cost of the sheet, we have to find the surface area of the rectangular prism. Then we multiply the surface area by the cost per square meter.
The surface area of a rectangular prism is:
[tex]\begin{gathered} A\text{ = 2(}wh\text{ + wl + hl)} \\ \text{where h = height} \\ w\text{ = width} \\ l\text{ = length} \end{gathered}[/tex]From the diagram:
l = 7 m ; w = 3 m ; height = 3 m
Therefore, the surface area of the prism is:
[tex]\begin{gathered} A\text{ = 2\lbrack(3 }\cdot\text{ 3) + (3 }\cdot\text{ 7) + (3 }\cdot\text{ 7)\rbrack} \\ A\text{ = 2(9 + 21 + 21)} \\ A\text{ = 2(51)} \\ A\text{ = 102 square meters} \end{gathered}[/tex]Now, we multiply by the cost per square meter:
[tex]\begin{gathered} C\text{ = 102 }\cdot\text{ 30} \\ C\text{ = \$3060} \end{gathered}[/tex]That is the total cost of the steel sheet.
Find the range of the function for the given domain. {-5, -1, 0, 2, 10}
[tex]g(x)=x^{2}+2[/tex]
A. 2
B. -23
C. 3
D. 1
E. 102
F. 27
G. 6
The range of the function g(x) = x² + 2 for the given domain is found to be {27,3,25,6,102}.
What is the difference between domain and range in function?The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value.
How do you find domain and range in the absence of numbers?To determine the domain of a function, f(x), determine which values of x cause f(x) to be undefined/not real. The usual procedure for determining range is to find x in terms of f(x) and then locate values of f(x) for which x is not defined.
Given:
g(x) = x² + 2
Domain of the function: {-5, -1, 0, 2, 10}
We need to find the range.
Let us substitute x = -5 in g(x)
g(-5) = (-5)² + 2
= 27
g(-1) = (-1)² + 2
= 3
g(0) = (0)² +(-5)²
= 25
g(2) = (2)² + 2
=6
g(10) = (10)² + 2
= 102
Therefore, the range of the given function g(x) = x² + 2 for a given domain is found to be {27,3,25,6,102}.
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Jeremy says this dilation can be represented by (X+3\4,Y+3\4)Julie says this dilation can be represented by (3\4X, 3\4Y)whoo is correct and why
The scale factor for dilation is 3/4. Therefore, the dilation can be represented below
[tex](\frac{3}{4}x,\frac{3}{4}y)[/tex]This means Julie is correct.
At a certain hospital 39080 patients had their falls reported in the winter of 2004, thisrose to 42045 patients in the winter of 2014 (Lifespan, 2019). How would you calculatethe percentage rise in patients from 2004 to 2014?In a several sentences, how would you apply this to your life or job? If you had to teachsomeone who did not know how to this, what would be the steps from beginning to endthat you would use to teach them so that they would eventually do it accurately as youwould?Professor,I would calculate the percentage rise in patients from 2004 to 2014 by
Percentage rise in patients from 2004 to 2014 = 7.59%
Explanation:The number of patients in 2004 = 39080
The number of patients in 2014 = 42045
Increase in the number of patients = (The number of patients in 2014) - (The number of patients in 2004)
Rise in the number of patients = 42045 - 39080
Rise in the number of patients = 2965
[tex]\begin{gathered} \text{Percentage rise in patients = }\frac{\text{Rise in the number of patients}}{\text{Number of patients in 2004}}\times100 \\ Percentage\text{ rise in patients = }\frac{2965}{39080}\times100 \\ \text{Percentage rise in patients = }7.59\text{ \%} \end{gathered}[/tex]Percentage rise in patients from 2004 to 2014 = 7.59%
What is the slope of the line that passes through the points (10,8) and (7,14)?
Answer:
Step-by-step explanation:
-0.5
In the items below a physical property is identified along with two objects/figures. For each item identity whether the property applies to one, both, or neither of the objects/figures listed and explain why it does or does not.1) Property: MassCylinder Square
Background
• Mass: ,is the quantity of matter in a physical body.
,• Cylinder: ,a three-dimensional solid.
,• Square: ,a one-dimensional figure (flat shape).
As a square is just a one-dimensional figure, it cannot have mass, then...
Answer: the property applies only to the Cylinder.
The ages (in years) of the 5 doctors at a local clinic are the following30, 40, 39, 36, 30Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places
Solution
For this case we have the following data:
30, 40, 39, 36, 30
Representing the ages (in years) of the 5 doctors at a local clinic
these values represent an entire population, and we want to find the standard deviation of the population
1) First we need to calculate the mean
[tex]\mu=\frac{30+40+39+36+30}{5}=35[/tex]2) Now we can find the population variance like this:
[tex]\sigma^2=\frac{(30-35)^2+(40-35)^2+(39-35)^2+(36-35)^2+(30-35)^2}{5}=\frac{92}{5}=18.4[/tex]3) Calculate the population standard deviation
[tex]\sigma=\sqrt[]{18.4}=4.29[/tex]then the answer would be:
4.29
For each value of v, determine whether it is a solution to v - 42 = 11
Given equation:
[tex]v\text{ - 42 = 11}[/tex]The first step is to solve the equation i.e. find the value of v
[tex]\begin{gathered} Collect\text{ like terms} \\ v\text{ = 11 + 42} \\ v\text{ = 53} \end{gathered}[/tex]The given options
how do I solve an angle in right triangles. what is angle B?AB=7BC=3
To find the value of the b angle.
First, label the sides of the right angle
The biggest side is always the hypotenuse
The side between the right angle and angle A is the adjacent side.
and the other side it's my opposite side.
Let's use the trigonometric function to find the value of b
I have the value of the hypotenuse
h = 7
and the value of my opposite side
opp = 3
So we need a trigonometric function that involves my hypotenuse and the opp
sin = opp/ hyp
Replace the values
sin b = 3/7
Solve the equation for b
b = arcsin (3/7)
b = 25.376
Rounded to hundredths
b = 25.37
Rewrite 9/11 and 6/7 so that they have a common denominator.Then use <, =, or > to order 9/11 and 6/7
Answer:
• 9/11=63/77
,• 6/7=66/77
,• 9/11<6/7
Explanation:
Given the fractions: 9/11 and 6/7
First determine the lowest common multiple of the denominators: 11 and 7
L.C.M of 11 and 7 = 77
Next, make this the common denominator as follows:
[tex]\begin{gathered} \frac{9}{11}=\frac{9}{11}\times\frac{7}{7}=\frac{63}{77} \\ \frac{6}{7}=\frac{6}{7}\times\frac{11}{11}=\frac{66}{77} \end{gathered}[/tex]Comparing the numerators, since 63<66:
[tex]\implies\frac{9}{11}<\frac{6}{7}[/tex]When 9 and 2/3 is written in simplest radical form, which value remains under the radical?36927
Given
[tex]9^{\frac{2}{3}}[/tex]To write it in the simplest form and to find which value remains under the radical.
Explanation:
It is given that,
[tex]9^{\frac{2}{3}}[/tex]It is known that,
[tex]x^{\frac{m}{n}}=\sqrt[n]{x^m}[/tex]That implies,
[tex]\begin{gathered} 9^{\frac{2}{3}}=\sqrt[3]{9^2} \\ =\sqrt[3]{3\times3\times3\times3} \\ =3\sqrt[3]{3} \end{gathered}[/tex]Therefore, the simplest form of the expression is,
[tex]3\sqrt[3]{3}[/tex]and the value that remains under the radical is 3.
marh questions i need to solve and i have problems with it
7.
Given the side ratio as:
[tex]5:13[/tex]The area ratio is the second power of the above, which is:
[tex]\begin{gathered} 5^2:13^2 \\ =25:169 \end{gathered}[/tex]Given the area ratio of:
[tex]36:49[/tex]The perimeter ratio is:
[tex]\begin{gathered} \sqrt{36}:\sqrt{49} \\ \\ =6:7 \end{gathered}[/tex]Part A Estimate 10/12 - 3/8 using benchmark values. Your equation must show the estimate for each fraction and the final estimate for the expression.Part BSolve 10/12 - 3/8Part Ccalculate the difference between your stimate in Part A and the actual value calculated in Part B.Show the solution as an equation Based on the results was your estimate in Part A reasonable?
Answer:
[tex]\begin{gathered} A\text{. 1/2} \\ B\text{. 11/24} \\ C\text{. }\frac{1}{24} \\ \end{gathered}[/tex]Yes, the calculations in A were reasonable because the difference is pretty close to 0.
Step-by-step explanation:
For part A,
-estimate the fraction 10/12 using 1/2 as our benchmark
The lower range is 1/2 and the upper range is 1
The halfway point is:
[tex]\begin{gathered} \frac{1}{2}\cdot\frac{(1+2)}{2} \\ \frac{1}{2}\cdot\frac{3}{2}=\frac{3}{4} \end{gathered}[/tex]Therefore, our range is 1/2 < 3/4 < 1
10/12 ≥ 3/4, we round up to 1
-estimate the fraction 3/8 using the 1/2 as our benchmark:
The lower range is 0 and the upper range is 1/2
The halfway point is:
[tex]\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Therefore, our range is 0 < 1/4 < 1/2
3/8 ≥ 1/4, we round up to 1/2
[tex]\frac{2}{2}-\frac{1}{2}=\frac{1}{2}[/tex]For part B, the denominators are 12 and 8, so the LCM would be;
[tex]\text{LCM}=24[/tex]Then, we make a common denominator and subtract the numerators
[tex]\begin{gathered} \frac{10}{12}-\frac{3}{8}=\frac{20}{24}-\frac{9}{24} \\ \frac{10}{12}-\frac{3}{8}=\frac{11}{24} \end{gathered}[/tex]For part C, compute the difference between the two results from parts A and B:
[tex]\frac{1}{2}-\frac{11}{24}=\frac{1}{24}[/tex]Yes, the calculations in A were reasonable because the difference is pretty close to 0.
Solve this equation:-36q = 18
Given:
[tex]36q=18[/tex]Required:
To solve the given equation.
Explanation:
Consider
[tex]36q=18[/tex]Divide 36 on both side, we get
[tex]\begin{gathered} \frac{36q}{36}=\frac{18}{36} \\ \\ q=\frac{18}{36} \\ \\ q=\frac{1}{2} \end{gathered}[/tex]Final Answer:
[tex]q=\frac{1}{2}[/tex]13. What transformations take place by graphing the function below in respect to its parents go
function? Check all that apply.
Up 7 units
Down 7 units
Left 7 units
Right 7 units
3
f(x)=(x+7)² +2
Up 2 units
Down 2 units
Left 2 units
Right 2 units
Theis)
Textes
Vertical Stretch
Vertical Compression
Reflection in x-axis
Reflection in y-axis
81
The graph is being transformed Right 7 units and Down 2 units.
The function is given as:
f (x) = (x + 7)² + 2
This can also be written as:
y = (x + 7)² + 2
y - 2 = (x + 7)²
Now, we can see the following transformations:
The graph is translated 7 units to the right.
Also, it is being translated 2 units to the down.
So, the option will be
Right 7 units and Down 2 units
Therefore, we get that, the graph is being transformed Right 7 units and Down 2 units.
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Hello can you assist me with number 11Find the midpoint
Answer:
(-3, 2.5)
Explanation:
The midpoint of two points of coordinates (x1, y1) and (x2, y2) has the following coordinates
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}_{})[/tex]Then, the midpoint can be calculated replacing (x1, y1) = (3, 3) and (x2, y2) = (-9, 2), so
[tex](\frac{3+(-9)}{2},\frac{3+2}{2})=(\frac{-6}{2},\frac{5}{2})=(-3,2.5)[/tex]Therefore, the midpoint is (-3, 2.5)
6ft 3ft 8ft 16ft area of irregular figures
Solution.
From the figure given we will have to find the
(Area of A) + (The Area of B)
STEP 1 :
For figure B
b = 3
h = 6
[tex]\begin{gathered} \text{Area of A = }\frac{1}{2}\times b\times h \\ \text{ = }\frac{1}{2}\times3\times6 \\ \text{ = }\frac{18}{2}\text{ = 9} \end{gathered}[/tex]Step 2:
For Figure A
L = 16
b = 8ft
Area of B = L x B
= 16 x 8
= 128
STEP 3
Area of A + Area of B
128 + 9 = 137 square feet
Diego's goal is to walk more than 70,000 steps this week. The mean number of steps that Diego walked during the first 4 days of the week is 8,019.If the mean number of steps Diego walks during the last 3 days of the week is 12, 642, will Diego reach his goal of walking more than 70,000 steps this week? Explain your reasoning.
Solution
Diego goal was walk more than 70000 steoes
And in average in the first 4 days he walks 8019 steps
The expected mean number of steps for the next 3 days is 12642 then we can do this:
8019*4 + 12642*3= 32076 +37926 = 70002
then since 70002 > 70000
We can conclude that Diego can reach the goal for this case
write a multiplication equation for the area of the square with side lengths of 1 meter
Area of a square is expressed using the formula;
A = L^2
L is the side length of the square
From the question, we are given;
L = 1 meter
The multiplication equation for the area of the square will be;
A = 1 meter * 1 meter
A = 1m^2
can someone help me set it up im very confused.
let h be the height of the television set
4: 3 = 46 : h
[tex]\frac{4}{3}=\frac{46}{h}[/tex]cross multiply
4h = 138
Divide both-side of the equation by 4
h = 34.8 inches
Geometric Probability: I don’t know how to do this please help quickly
Solution
From the question,
If buses arrive every 19 mins and each waited 3 mins before departing
Then we can say that each bus departed (19 + 3) = 22 mins.
if you arrived at the moment the bus left, you would need to wait for the next bus
The probability is
[tex]\frac{9}{22}=0.409[/tex]What is the first quartile of the data displayed in this box-and-whisker plot?O 49O 41O 37O 353436403844424648T54 56525058
1) In any box and whiskers plot we can tell the following about how to read it:
3) So, reading that box and whiskers plot, we can tell the first quartile is:
[tex]Q_1=37[/tex]60 is what % of 150? Can you help?
Given:
There are given that the final number is 150.
Explanation:
According to the question:
We need to find the percentage number.
Then,
Suppose the percentage number is x.
Then,
The equation will be:
[tex]150\times x\%=60[/tex]Now,
We need to solve the above equation for the value of x.
Then,
Divide by 150 on both sides of the equation:
[tex]\frac{150}{150}\times x\operatorname{\%}=\frac{60}{150}[/tex]Then,
[tex]\begin{gathered} x\%=\frac{60}{150} \\ x\operatorname{\%}=\frac{6}{15} \\ x\operatorname{\%}=0.4 \\ x=0.4\times100 \\ x=40 \end{gathered}[/tex]Final answer:
Hence, the percentage is 40%.
Listed below are amounts (in millions of dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service company's employees?The coefficient of variation for the amount collected by the security service company is __%.The coefficient of variation for the amount collected by other companies is __%.
The coefficient of variation of a dataset is given by the ratio between the standard deviation to the mean.
[tex]CV=\frac{\sigma}{\mu}[/tex]The mean and the standard deviation of a dataset with N elements are given by the following formulas:
[tex]\begin{gathered} \mu=\frac{\sum_i^Nx_i}{N} \\ \\ \sigma=\sqrt{\frac{1}{N-1}\sum_{n\mathop{=}0}^{\infty}(x_i-\mu)^2} \end{gathered}[/tex]Then, using those formula for the security service company, we have the following coefficient of variation:
[tex]\begin{gathered} \mu=1.53 \\ \sigma=0.15670212364724... \\ CV=0.102419689...\approx10.2\% \end{gathered}[/tex]Then, using those formula for the other companies, we have the following coefficient of variation:
[tex]\begin{gathered} \mu=1.72 \\ \sigma=0.11352924243951... \\ CV=0.0660053735...\approx6.6\% \end{gathered}[/tex]