Answers
The equation of the line that is perpendicular with y = 4 · x - 3 and passes through the point (- 12, 7) is y = - (1 / 4) · x + 4.
How to derive the equation of a line
In this problem we find the case of a line that is perpendicular to another line and that passes through a given point. The equation of the line in slope-intercept form is described below:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.In accordance with analytical geometry, the relationship between the two slopes of the lines are:
m · m' = - 1
Where:
m - Slope of the first line.m' - Slope of the perpendicular line.If we know that m = 4 and (x, y) = (- 12, 7), then the equation of the perpendicular line is:
m' = - 1 / 4
b = 7 - (- 1 / 4) · (- 12)
b = 7 + (1 / 4) · (- 12)
b = 7 - 3
b = 4
And the equation of the line is y = - (1 / 4) · x + 4.
To learn more on equations of the line: https://brainly.com/question/2564656
#SPJ1
Related Questions
the radius of a circle is 9 inches. what is the circumference?give the exact answer in simplest form.
Answers
Step 1
The circumference of a circle is given by;
[tex]2\pi r[/tex]where;
[tex]\begin{gathered} r=9in \\ \end{gathered}[/tex]Step 2
Find the circumference
[tex]\begin{gathered} C=2\times\pi\times9 \\ C=18\pi in\text{ches} \end{gathered}[/tex]Hence, in terms of π the circumference of the circle=18πinches
How do you know when an equation has infinite many solution?A. The coefficients are differentB. The coefficients are the same and the constants are differentC. The coefficients are the same and the constants are same
Answers
Solution:
An equation has infinitely many solutions when the coefficients are the same and the constants are the same.
This is illustrated as shown below:
[tex]\begin{gathered} 2a+5+a=\text{ 5+3a,} \\ thus,\text{ we have infinitely many solution} \end{gathered}[/tex]Hence, the correct option is C.
In the right trapezoid ABCD, BC is parallel to AD, and AD is contained in the line whose equation is y=−12x+10 y = − 1 2 x + 10 . What is the slope of the line containing BC? Explain how you got your answer
Answers
Garvin earned $ 948.35 in net pay for working 24 hours. He paid $ 348.26 in federal and state taxes, and $ 145.06 in FICA taxes. What is Garrett's hourly wage? Round your answer to two decimal places. If answer doesn't have two decimal places include zeros to make two decimal places. For the units, use a word not a symbol. Be sure to attach your work to this question in order to receive credit for your answer.Your Answer:units:
Answers
ANSWER:
18.96 dollars per hour
STEP-BY-STEP EXPLANATION:
The 24-hour salary is calculated with the earnings and we subtract the taxes, as follows:
[tex]\begin{gathered} s=948.35-348.26-145.06 \\ s=455.03 \end{gathered}[/tex]Now, we divide by 24 to find out Garvin's hourly wage:
[tex]\begin{gathered} h=\frac{455.03}{24} \\ h=18.96 \end{gathered}[/tex]Therefore, the hourly wage is $18.96.
7 ( 7x - 3y) - 6 Expand the expression
Answers
The expanded form of the expression is 49x - 21y - 6
Explanation:[tex]\text{Given: }7(7x\text{ - 3y) - 6}[/tex]To expand, we will multiply the terms outside by the terms inside the parentheiss:
[tex]\begin{gathered} U\sin g\text{ distributive property} \\ a(b\text{ + c) = a9b) + a(c)} \\ \\ 7(7x-3y)-6=\text{ }7(7x)\text{ -7(3y) - 6} \\ =\text{ 49x - 21y - 6} \end{gathered}[/tex]The expanded form of the expression is 49x - 21y - 6
What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
Answers
An example of situation involving quantitative comparison is:
The game-plan of an offensive coach for a NFL game.
What are quantitative variables?
Quantitative variables are variable that assume numbers as results, instead of labels such as yes/no or good/bad.
When an NFL offensive coordinator is game-planning, he has to consider numeric stats of the opponent defense, such as these ones:
Average passing yards allowed per play.Average rushing yards allowed per play.These stats are also compared to the NFL average to verify if the weak point of the opponent defense is the run or the pass, hence the game-plan is adjusted accordingly as follows:
Bad run defense: the coordinator should call more running plays.Bad pass defense: the coordinator should call more passing plays.A similar problem, also about quantitative variables, is given at https://brainly.com/question/15212082
#SPJ1
Question HelpMultiple Representations A vehicle ses 7 gallons of gasoline to travel 147 miles. The vehicle uses gasoline at a steady rate. Use pencil and paper to draw a picture that models the situation Write a table of equivalent ratiosThen use the table to find the number of gallons of gasoline the vehicle uses to travel 63 milesComplete the tableGallons Miles1231411421
Answers
We know a vehicle uses 7 gallons of gasoline to travel 147 miles.
This gives us a ratio: 147/7 = 21
The vehicle travels 21 miles per gallon of gasoline
The situation can be modeled as a line with a constant slope of 21 miles/gallon
If we use the horizontal axis for the number of gallons and the vertical axis for the miles traveled, we can draw an approximate graph
Let's give the gallons (g) some values to fill up the table:
For g=1, miles = 21
For g=2, miles = 42
For g=3, miles = 63
For g=7, miles = 147
For g=14, miles = 294
For g=21, miles = 441
The graph is shown below
Suzy has $2000 to invest and needs $2400 in 12 years. What annualrate of return will she need to get in order to accomplish her goal, if theinterest is compounded continuously? (Round your answer to twodecimal places) A = Pert
Answers
Given data:
Principal Amount=$2000.
Final Amount=$2400
Time period(t)=12 years
Let the rate of return be r.
As per formula of continous compunding:
[tex]\begin{gathered} \text{Final amount=Principal}(e^{rt}) \\ 2400=2000(e^{12r}) \\ e^{12r}=\frac{2400}{2000} \\ e^{12r}=1.2 \\ 12r=\ln (1.2) \\ 12r=0.1823 \\ r=0.01519 \end{gathered}[/tex]Thus, the rate of interest required is 1.519%.
Based on a recent study, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.38 and standard deviation of 0.14. Find the percentageof preterm infants who have the following arterial cord pH levels.a. pH levels between 7.00 and 7.50.b. pH levels over 7.46A.The percentage of arterial cord pH levels that are between 7.00 and 7.50 is ____%.(Round to two decimal places as needed.)B.The percentage of arterial cord pH levels that are over 7.46 is ___%.(Round to two decimal places as needed.)
Answers
We have the pH level as a random normal variable with mean 7.38 and standard deviation of 0.14.
A) We have to calculate the percentage of infants that are expected to have pH levels between 7.00 and 7.50.
We can approximate this as the probability of selecting a random infant and it has a pH level within this interval.
Then, to calculate the percentage we will use the z-scores for each boundary of the interval:
[tex]z_1=\frac{X_1-\mu}{\sigma}=\frac{7-7.38}{0.14}=\frac{-0.38}{0.14}\approx-2.7143[/tex][tex]z_2=\frac{X_2-\mu}{\sigma}=\frac{7.5-7.38}{0.14}=\frac{0.12}{0.14}\approx0.8571[/tex]Then, we can use the standard normal distribution to look for the probabilities for each z-score and calculate the probability as:
[tex]\begin{gathered} P(7.00Given that the probability is 0.80099, we can express the percentage as:[tex]P=0.80099\cdot100\%=80.01\%[/tex]B) We now have to calculate the percentage that is above 7.46.
We start by calculating the z-score as:
[tex]z=\frac{X-\mu}{\sigma}=\frac{7.46-7.38}{0.14}=\frac{0.08}{0.14}\approx0.571428[/tex]Then, we can calculate the probability as:
[tex]P(X>7.46)=P(z>0.571428)\approx0.28385[/tex]This correspond to a percentage of 28.39%.
Answer:
A) 80.01%
B) 28.39%
Graph the line that has an x-intercept of (-1,0) and a y-intercept of (0,5). What is the slope of this line?
Answers
Answer:
The slope is 5.
Step-by-step explanation:
To solve this, you could have plotted the two points, drew a line between them, and then calculated the slope by counting on the graph the line's rise/run.
To slove this by finding the slope with the points:
(5 - 0) / (0 - - 1) = 5 / 1 = 5
The slope is 5
can you please help me? I'm having trouble with algebra 2 doing online school
Answers
Brianna, this is the solutiuon:
Part 2: Recalling that the perfect square trinomial has the form:
ax² + bx + c
(x - 1)² = (x - 1) * (x - 1)
x² - x - x + 1
x² - 2x + 1
Thus, b = -2. The correct answer is A.
Part 3: Recalling that the perfect square trinomial has the form:
ax² + bx + c
(x + 25)² = (x + 25) * (x + 25)
x² + 25x + 25x + 625
x² + 50x + 625
Therefore, c = 625. The correct answer is D.
This is not from a test or graded assessment. The Question is included in the picture.
Answers
Given:
[tex]\begin{gathered} g(x)=-x^5-4x^3+6x \\ \\ h(x)=x^4+2x^3-2x^2+x-7 \\ \\ j(x)=3x^4+7x^2 \end{gathered}[/tex]It's required to determine if the functions are odd, even, or neither.
An even function satisfies the property:
f(-x) = f(x).
And an odd function satisfies the property:
f(-x) = -f(x)
We substitute x by -x on each function as follows:
[tex]\begin{gathered} g(-x)=-(-x)^5-4(-x)^3+6(-x) \\ \\ g(-x)=x^5+4x-6x \end{gathered}[/tex]Note the function g(-x) is the inverse (negative) of g(x), thus,
g(x) is odd
Now test h(x):
[tex]\begin{gathered} h(-x)=(-x)^4+2(-x)^3-2(-x)^2+(-x)-7 \\ \\ h(-x)=x^4-2x^3-2x^2-x-7 \end{gathered}[/tex]Comparing h(-x) and h(x) we can see none of the properties are satisfied, thus:
h(x) is neither odd nor even
Let's now test j(x):
[tex]\begin{gathered} j(-x)=3(-x)^4+7(-x)^2 \\ \\ j(-x)=3x^4+7x^2 \end{gathered}[/tex]Since j(-x) and j(x) are equal,
j(x) is even
According to the theory of the color yellow + red = orange. If Luisa has x liters of yellow paint and/ 4 liters of red paint. How many liters of orange paint will he get Louise? And if I had 4 liters of yellow paint, could I get exact 5 liters of paint orange?
Answers
Yellow + red = Orange
Yellow paint , x liters
Red paint , 4 liters
a) Because addition applies , adding x liters of Yellow + 4 liters of red and the result is x + 4 liters of orange
b) for second question apply equation
4 • yellow + Red •N = 5
then find N
its possible to obtain 5 liters of paint orange with
2 liters of yellow, 2 liters of red, and adding
0.5 liters of yellow, 0.5 liters of red.
The two-way table represents the number of clubs that two hundred high school studentswere involved in.One Club Two clubsBoys 17Girls 28Total 45256893Three or more clubs Total50126292108200What is the probability that a student will be in two clubs only and a girl?
Answers
Given:
The two-way table represents the number of clubs that two hundred high school students
We will find the probability that a student will be in two clubs only and a girl
From the table, we will select the number that represents the number of girls that will be in the two clubs
so, the number = 68
the total number of students = 200
So, the probability will be =
[tex]\frac{68}{200}*100=34\%[/tex]So, the answer will be 34%
16 - 2t = 5t +9 Can you help me solve this?
Answers
1=t
add 2t to the second side, so that it is going to be 16=7t+9
now, subtract 9 from the right side: 16-9=7t
7t=7
t=1
A gumball machine contains orange, yellow, and purple gum balls. The probability of getting an orange gumball is 3/4. The probability of getting a yellow gumball is 1/6. If there are 36 gumballs in the machine, how many are there of each color number of purple marbles _______ number of yellow marbles_____ number of orange marbles______
Answers
Given:
Probability of getting orange gumball is, p(o) = 3/4.
Probability of getting yellow gumball is, p(y) = 1/6.
The objective is to find the number of each colored gumballs.
Since, the sum of the events of probability is always 1.
Then, the probability of purple ball p(p) can be calculated as,
[tex]\begin{gathered} \frac{3}{4}+\frac{1}{6}+p(p)=1 \\ p(p)=1-\frac{3}{4}-\frac{1}{6} \\ p(p)=\frac{12-3(3)-1(2)}{12} \\ p(p)=\frac{1}{12} \end{gathered}[/tex]Since, it is given that the total number of gumball is N = 36.
Then, the number of orange ball can be calculated as,
[tex]\begin{gathered} p(o)=\frac{n(o)}{N} \\ \frac{3}{4}=\frac{n(o)}{36} \\ n(o)=36\cdot\frac{3}{4} \\ n(o)=27\text{ balls.} \end{gathered}[/tex]Similarly, the number of yellow ball can be calculated as,
[tex]\begin{gathered} p(y)=\frac{n(y)}{N} \\ \frac{1}{6}=\frac{n(y)}{36} \\ n(y)=\frac{36}{6} \\ n(y)=6 \end{gathered}[/tex]And the number of purple ball can be calculated as,
[tex]\begin{gathered} p(p)=\frac{n(p)_{}}{N} \\ \frac{1}{12}=\frac{n(p)}{36} \\ n(p)=\frac{36}{12} \\ n(p)=3 \end{gathered}[/tex]Hence, the number of orange ball is 27, number yellow ball is 6 and number of purple ball is 3.
Suppose that the 99% confidence interval for the true average number of canteen operating hours is [6, 9]. Which conclusion is correct if the average number of operating hours for canteens in the region is 8 hours? a. The average number of canteen operating hours in this city is not significantly different from that of the region since 8 is not contained in the interval. b. The average number canteen operating hours in this city is not significantly different from that of the region since 8 is contained in the interval. c. The average number of canteen operating hours in this city is significantly different from that of the region since 8 is contained in the interval. d. The average number of canteen operating hours in this city is significantly different from that of the region since 8 is not contained in the interval.
Answers
Given: Suppose that the 99% confidence interval for the true average number of canteen operating hours is [6, 9].
To Determine: Which conclusion is correct if the average number of operating hours for canteens in the region is 8 hours
Solution
Given the confidence interval of [6,9]. This means that
A confidence interval indicates where the population parameter is likely to reside. For example, a 99% confidence interval of the mean [6 9] suggests you can be 99% confident that the population mean is between 6 and 9
If the average number of operating hours for canteens in the region is 8 hours, then we can conclude that
The average number canteen operating hours in this city is not significantly different from that of the region since 8 is contained in the interval, OPTION B
How can you use transformations to verify that the triangles are similar?
Answers
We need to know about congruency to solve the problem. Two pairs of congruent angles prove that the triangles are similar.
We can define similarity of two geometrical objects on a plane as possibility to transform one into another using dilation optionally combined with congruent transformations of parallel shift, rotation and symmetry. We need to use transformation to verify whether the triangles in the diagram are similar. The two triangles have a common angle D and angles ABD and ECD are equal. Thus we can say that we have two pairs of congruent angles in the two triangles, so the two triangles are similar.
Therefore the triangles are similar since they have two pair of congruent angles.
Learn more about congruency here:
https://brainly.com/question/6032353
#SPJ1
andrew went to the store to buy some walnuts. the price pee walnut is $4 per pound and he has a coupon for $1 off the final amount. with the coupon, how much would andrew have to pay to buy 4 pounds of walnuts? what is the expression for the cost to buy p pounds of walnuts , assuming at least one pound is purchased.
Answers
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts= 4p - 1
Explanation:
Amount per pound of walnut = $4
Amount of coupon = $1
The cost of 4 pounds of walnuts:
[tex]\text{Cost = 4 }\times5=\text{ \$20}[/tex]The amount Andrew have to pay to buy 4 pounds of walnuts:
Amount = cost - coupon
Amount = $20 - $1
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts:
let number of pounds = p
Cost for p pounds of walnut = Amount per walnut * number of walnut
Cost for p pounds of walnut = $4 * p
= $4p
The expression for the cost to buy p pounds of walnuts= cost for p - coupon
= 4p - 1
What is the solution set of x over 4 less than or equal to 9 over x?
Answers
we have
[tex]\frac{x}{4}\leq\text{ }\frac{9}{x}[/tex]Multiply in cross
[tex]x^2\leq36[/tex]square root both sides
[tex](\pm)x\leq6[/tex]see the attached figure to better understand the problem
the solution is the interval {-6,6}
the solution in the number line is the shaded area at right of x=-6 (close circle) and the shaded area at left of x=6 (close circle)
write a word problem in which you divide two fractions into mixed numbers or a mixed number and a fraction solve your word problem and show how you found the answer
Answers
Jade share 4 1/3 cups of chocolate by 1/3 among his friends
The mixed fraction = 4 1/3
Fraction = 1/3
[tex]\begin{gathered} \text{Firstly, we n}eed\text{ to convert the mixed fraction into an improper fraction} \\ 4\frac{1}{3}\text{ = }\frac{(3\text{ x 4) + 1}}{3} \\ 4\frac{1}{3}\text{ = }\frac{12\text{ + 1}}{3} \\ 4\frac{1}{3}\text{ = }\frac{13}{3} \\ \text{Divide }\frac{13}{3}\text{ by 1/3} \\ =\text{ }\frac{13}{3}\text{ / }\frac{1}{3} \\ \text{ According to mathematics, once the numerator and denominator of the LHS is interchanged then the order of operator changes from division to multiplication} \\ =\text{ }\frac{13}{3}\text{ x }\frac{3}{1} \\ =\text{ }\frac{13\text{ x 3}}{3} \\ \text{= }\frac{39}{3} \\ =\text{ 13} \end{gathered}[/tex]Therefore, the answer is 13
Real world compositions: A manufacturer sells a lawn mower to a store at $75 over the manufacturing cost. The store then sells the lawn mower for 140% of the price paid to the manufacturer. Determine the function of the price of a lawn mower in terms of the cost to manufacture the mower. What price will a customer pay for this mower if the manufacturer's cost was $230? Solve using composite functions
Answers
From the information provided, the lawn mower is sold at a price which is $75 over the cost of manufacture.
If the cost of manufacture is x, then we would have;
[tex]f(x)=x+75[/tex]Also, the store now sells the lawn mower for 140% of the price paid to the manufacturer. Therefore, we would have;
[tex]g(x)=f(x)1.4[/tex]Hence, if the manufacturer's cost is $230, the customer would be paying g(x). When the cost x is now given as 230, we wou;d have;
[tex]\begin{gathered} f(230)=230+75 \\ f(230)=305 \\ \text{Hence;} \\ g(x)=f(x)1.4 \\ g(x)=305\times1.4 \\ g(x)=427 \end{gathered}[/tex]ANSWER:
The function of the price is;
[tex]f(x)=x+75[/tex]The price a customer pays when the cost of manufacturing is $230 would now be $427
The graph of a function is shown below. find the following, g(10), g(-3)
Answers
According to the graph, the value of the function g(-3) is 4 and g(10) is out of view
What are graphs?Graphs are graphical representations of equations, ordered pairs, tables of a relation
How to evaluate the function?From the question, the function is represented by the attached graph
Also from the question, the function to calculate is given as g(10) and g(-3)
This means that we calculate the values of the function, when x = 10 and -3
i.e.
We calculate g(x), when x = -3
We calculate g(x), when x = 10
So, we look at the graph for this function value
From the graph of values, we have
When x = -3, g(x) = 4
When x = 10, g(x) = not visible
This means that
g(-3) = 4
g(10) = out of view
Hence, the function g(-3) has a value of 4 and g(10) is out of view
Read more about functions at
brainly.com/question/28532394
#SPJ1
I haven’t got a clue about what it is or what to do
Answers
EXPLANATION
Rotating the shape , give us the third shape form.
Use the positions of the numbers on the number line to compare them.Select the two true inequalities.A. 3/4 < 4/5B. 0.85 > 4/5C. 3/4 > 4/5D. 0.85 < 4/5
Answers
Answer:
Explanation:
Given:
0.85,4/5, 3/4
To easily compare the given numbers, we simplify each number first and plot them on the number line:
Therefore, the two true inequalities are:
[tex]\frac{3}{4}<\frac{4}{5}[/tex]and
[tex]0.85>\frac{4}{5}[/tex]need help with a question
Answers
From the image, we have the equation:
3x - 6 = -2x + 4
Let's solve for x:
3x - 6 = -2x + 4
Add 2x to both sides of the equation:
3x - 6 + 2x = -2x + 2x + 4
3x + 2x - 6 = 4
5x - 6 = 4
Add 6 to both sides:
5x - 6 + 6 = 4 + 6
5x = 10
Divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{10}{5} \\ \\ x\text{ = 2} \end{gathered}[/tex]ANSWER:
x = 2
determine the area of the shaded regionA. 6 square unitsB. 19 square unitsC.20 square unitsD. 25 square units
Answers
area of the square:
[tex]\begin{gathered} a=l\times l \\ a=5\times5 \\ a=25 \end{gathered}[/tex]area of the rectangle
[tex]\begin{gathered} a=b\times h \\ a=3\times2 \\ a=6 \end{gathered}[/tex]area of the shaded region:
area of the square - area of the rectangle = area of the shaded region
[tex]25-6=19[/tex]answer: B 19 saquare units
I'll send a pic of it
Answers
Solution:
Since the slope of the given function represents the rate at which the temperature changes, the answer is the slope of the equation, that is, the correct solution would be:
[tex]0.7[/tex]
what is quotient of 0.5?
A.25÷5
B.2.5÷5
C.25÷0.5
D.25÷0.05
Answers
Answer:
B
Step-by-step explanation:
2.5/5=0.5
Answer: the answer is b
Step-by-step explanation:
because 2.5 goes into 5 0.5 times also written as 1/2 and said as one half i hope this helps have a great day (brainly pls)
A Census Burcau report on the income of Americans says that with 95% confidence themedian income of all U.S. households is $49,841 to $50,625. The point estimate and margin oferror for this interval are: *Point estimate = $49,841; Margin of error = $784Point estimate = $50,233; Margin of error = $784oPoint estimate = $50,233; Margin of error = $392Point estimate = $50,625; Margin of error = $392
Answers
Let the point estimate be x and the margin of error be e.
Then, we must have
[tex]\begin{gathered} x+e=50625----------------------(1) \\ x-e=49841----------------------(2_{}) \end{gathered}[/tex]Add the equation (1) and equation(2) to eliminate the variable e, we have
[tex]\begin{gathered} 2x=100466 \\ \text{ thus} \\ x=\frac{100466}{2}=\text{ \$}50233 \end{gathered}[/tex]Subtracting equation (2) from equation(1) to eliminate the variable x, we have
[tex]\begin{gathered} 2e=784 \\ \text{ thus} \\ e=\frac{784}{2}=392 \end{gathered}[/tex]Hence, the point estimate is $50233 and the margin of error is $392, The Third option
