The equation of the line perpendicular to the given equation is;
[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]Option C is the correct answer
Here, we want to select which of the equations in the option is perpendicular to the given equation
Firstly, we need to understand that for two equations to be perpendicular, then the product of their slopes must be equal to -1
Before we proceed to compare, we need to write the equation in the general form
The equation of the line written in the general form will be;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and the term b represents the y-intercept
Now, let us proceed to write the equation in the standard form;
We have this as;
[tex]\begin{gathered} 3y\text{ = -2x + 12} \\ \\ y\text{ = -}\frac{2}{3}x\text{ + 4} \end{gathered}[/tex]Compared with the general form, we can see that the slope of this line is -2/3
Now let us get the slope of the line that would be perpendicular to it;
[tex]\begin{gathered} \frac{-2}{3}\times\text{ m = -1} \\ \\ m\text{ = }\frac{3}{2} \end{gathered}[/tex]Now, the equation perpendicular to what was given will have a slope of 3/2
Fortunately, all the options in the question have been written in the general form
The one with a slope of 3/2 is option C
[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]Find the slope of the line with the equation 8x + 2y=12 m = -8 Om= 8 m = -4 m = 2
Simplify the equation 8x + 2y = 12 to obtain the equation in y = mx + b.
[tex]\begin{gathered} 8x+2y=12 \\ 2y=-8x+12 \\ y=-\frac{8}{2}x+\frac{12}{2} \\ y=-4x+6 \end{gathered}[/tex]In equation y = mx + b, slope is m and y-intercept is b.
So on compare the equation y = -4x + 6 with standard equation the slope is m - -4.
Answer: m = -4.
To the nearest tenth of pound Does has need to buy?
Answer: She needs approximately 142.5 pounds
Explanation:
From the information given,
A pound of fertilizer covers 39 square feet of lawn.
If the lawn measures 5557.4 square feet, then
the number of pounds of fertilizer that she needs to buy = 5557.4/39 = 142.4975
Rounding to the nearest tenth,
She needs approximately 142.5 pounds
solve using substitution or elimination
6x-12y=0
x-6y=4
Ava can run 4/5 of a mile in 4/3 of an hour. How far can she run in 1 hour? *
Answer:
She can run 3/5 miles in 1 hour
Explanation:
Given that Ava can run 4/5 of a mile in 4/3 of an hour, we want to find how far she can run in 1 hour.
Let x represent the number of miles she can run in one hour.
The statement can be represented in the pair of equations:
[tex]\begin{gathered} \frac{4}{5}miles=\frac{4}{3}\text{hours} \\ \\ x\text{ hour }=1\text{hour} \end{gathered}[/tex]Using these equations, we have:
[tex]\begin{gathered} \frac{4}{5}=\frac{4}{3}x \\ \\ x=\frac{\frac{4}{5}}{\frac{4}{3}} \\ \\ x=\frac{4}{5}\times\frac{3}{4} \\ \\ =\frac{3}{5} \end{gathered}[/tex]That is, she can run 3/5 miles in 1 hour
What is the probability of getting an even number on each one
Given:
Given that four far dice are thrown.
Required: Probability of getting an even number on each one.
Explanation:
The sample space is
[tex]S=\lbrace(x,y,z,w):\text{ x,y,z,w =1,2,3,4,5,6\textbraceright}[/tex]The number of elements in the sample space is
[tex]\begin{gathered} n(S)=6\times6\times6\times6 \\ =6^4 \end{gathered}[/tex]Let E be the event of getting even on each dice. Then
[tex]E=\lbrace(x,y,z,w);x,y,z,w=2,4,6\rbrace[/tex]The number of elements in E is
[tex]\begin{gathered} n(E)=3\times3\times3\times3 \\ =3^4 \end{gathered}[/tex]The probability of getting even on each dice is
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(S)} \\ =\frac{3^4}{6^4} \\ =\frac{3^4}{2^4\cdot3^4} \\ =\frac{1}{2^4} \\ =\frac{1}{16} \end{gathered}[/tex]The second option is correct.
Final Answer: The probability of getting even on each dice is 1/16.
HI there. I need some help with this question. I cannot figure out what the answer is.
From the question we were given the following:
Area of the square is 19 square units
Area of the circle is 30 square units
Area of intersection is 3 square units.
We are asked to find the area in square units of the entire coloured region.
So,
Are of Square = 19 square units
Are of Circle = 30 square units
Area of Intersection = 3 square units
Area of coloured region = Area of Square + Area of Circle - Area of Intersection
Therefore, Area of coloured region = 19 + 30 - 3
= 46 saqure units.
Help with this special right triangle
Answer:
6 ft
Step-by-step explanation:
You want the length of the short side of a 30°-60°-90° triangle, given the longest side is 12 ft.
Special triangleA 30°-60°-90° triangle has side lengths in the ratios ...
1 : √3 : 2
Here, the longest side is given as 12 ft, so we can multiply this set of ratios by 6 ft to find the lengths of all of the sides:
1 : √3 : 2 = (6 ft) : (6√3 ft) : (12 ft)
The shortest side has length ...
k = 6 ft
__
Additional comment
You can also use trig functions to find the length k:
k/(12 ft) = cos(60°) = 1/2, or
k/(12 ft) = sin(30°) = 1/2
k = (1/2)(12 ft) = 6 ft
Round to the answer to the nearest tenth.18. A 24-foot ladder leaning against a building forms an 18° angle with the side of the building,How far is the base of the ladder from the base of the building?
In order to solve this problem, first let's draw the corresponding image to the problem:
Then, to calculate the distance x, we can use the sine relation of the angle of 18°.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (18\degree)=\frac{x}{24} \\ \text{0}.309=\frac{x}{24} \\ x=24\cdot0.309 \\ x=7.42 \end{gathered}[/tex]So the distance wanted is 7.42 ft.
Order √70,-8.2.25,-8
47
from least to greatest.
Arrange them in Ascending order :
-8(4/7) < -8.2 < 25/3 < √70
What is Ascending order?
When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.
Given numbers,
√70 ,-8.2, 25/3, -8(4/7)
We have to Arrange these in ascending order
First lets get these terms to its simplest form
Value of √70 = 8.36
value of 25/3 = 8.33
Value of -8(4/7) = -8.57
Now we have the simplest value of all the following numbers
That is:
8.36, -8.22, 8.33, -8.57
The smallest of all is -8.57
Then -8.57 will be at first
-8.57, 8.36, -8.22, 8.33
now the second will be -8.22
-8.57, -8.22, 8.36, 8.33
Now the third would be 8.33
So the last would be 8.36 that is the greatest
-8.57, -8.22, 8.33, 8.36
Now, for the original value it would be:
-8(4/7) < -8.2 < 25/3 < √70
Hence, The ascending order of the number is -8(4/7) < -8.2 < 25/3 < √70
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Hey! what would the answer be, I am a little lost!
All of the triangles are an isosceles triangle, which means that they have two congruent side, and two congruent angles.
The first triangle has ∠B as 56°, AB ≅ BC.
The angle opposite to AB and BC are therefore, congruent, which means that
∠A + ∠B +∠C = 180°
∠A + 56° + ∠A= 180° (∠A and ∠C are congruent)
2∠A = 180° - 56°
2∠A = 124
∠A = 62°
The second triangle has ∠C equal to 62°. Since ∠A and ∠Care the angle opposite to the congruent side, they are also congruent which means ∠A = 62°.
The fourth triangle which has an exterior angle of ∠C equal to 118° forms a linear pair, and are thus supplementary
∠C = 62°, and both ∠C and ∠A are the corresponding angles to the congruent sides, it follows that they are also congruent.
∠A = 62°.
Conclusion
The following triangles have m∠A = 62°, first, second, and fourth triangle.
The record high temperature on January 15 is 41.5 Fahrenheit the record low temperature on that day is -16.8 Fahrenheit what is the difference in the record temperatures in degrees Fahrenheit
The difference in the record temperatures is 58.3° Fahrenheit.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol - , or, denotes subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.
Given Data
The record high temperature on January 15 is 41.5 Fahrenheit the record low temperature on that day is -16.8.
Difference = High temperature - Low temperature
Difference = 41.5 -(-16.8)
Difference = 41.5 + 16.8
Difference = 58.3
The difference in the record temperatures is 58.3° Fahrenheit.
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Find the missing endpoint if S is the midpoint RT. R(-9, 4) and S(2, -1); Find T.
Find the missing endpoint if S is the midpoint RT. R(-9, 4) and S(2, -1); Find T.
we know that
The formula to calculate the midpoint between two points is equal to
[tex]s(\frac{x1+x2}{2},\frac{y1+y2}{2}_{})[/tex]we have
S(2,-1)
(x1,y1)=R(-9,4)
(x2,y2)=T
substitute the given values in the formula
[tex]s(2,-1)=(\frac{-9+x2}{2},\frac{4+y2}{2}_{})[/tex]Find the x2 coordinate
2=(-9+x2)/2
-9+x2=4
x2=4+9=13
Find the y2 coordinate
-1=(4+y2)/2
4+y2=-2
y2=-2-4
y2=-6
therefore
the coordinates of point T(13,-6)Find the midpoint of the segment with the following endpoints.
(4, 2) and (7, 6)
The midpoint of the segment with the following endpoints, (4, 2) and
(7, 6) is (5.5, 4).
How to determine the midpoint of a given segment?
The center point of a straight line can be located using the midpoint formula. We can use this midpoint formula to determine the coordinates of the supplied line's midpoint in order to discover its location on a graph. Assuming that the line's endpoints are (x₁, y₁) and (x₂, y₂), the midpoint (a, b) is determined using the following formula:
(a , b) ≡ (((x₁ + x₂)/2), ((y₁ + y₂)/2))
Let the line segment be AB having endpoints as A(4, 2) and B(7, 6);
also let the co-ordinates of midpoint be C = (a, b)
Using the given formula in the available literature,
(a, b) = ((4 + 7)/2, (2 + 6)/2)
Equating parts of the previous equation, we get,
a = (4 + 7)/2 = 11/2 = 5.5
b = (2 + 6)/2 = 4
Thus, the midpoint of the segment is (5.5, 4).
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A set of data has a mean of 9.6 and a standard deviation of 0.8. What number in the data set would have a z-score of -1.5?
A set of data has a mean of 9.6 and a standard deviation of 0.8. The number in the data set that would have a z-score of -1.5 is
x =8.4
This is further explained below.
What is the z-score?The number of normal deviations within which the value of a raw score is either above or below the average value of what is observed or measured is the number that is referred to as the standard score in the field of statistics.
Raw scores that are greater than the mean are assigned positive standard scores, and raw scores that are equal to or lower than the mean are assigned negative standard scores.
Generally, the parameters of the solutionare
[tex]\mu &=9.6 \quad \sigma=0.8 \quad z=-1.5 \\\\z &=\frac{x-\mu}{\sigma} \\\\-1.5 &=\frac{x-9.6}{0.8} \\[/tex]
Where
z=distribution
x=mean
[tex]\sigma[/tex]=standard deviation
u=population mean
Hence, solve for x
x =-1.2+9.6
x =8.4
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if a student scored a 52 on his first test ,make a prediction for his score on the second test .Assume the regression equation is appropriate for the prediction. Round the answer to 2 decimal places.
Solution
We have the following info given:
x: 75,76, 91, 65,48,75,85,62,51,80,94,43
y: 69, 88, 101, 63, 59, 82, 86, 67, 56, 84, 105, 44
After apply OLS (Ordinary LEast Squares) we got the following regression line:
y= 1.0607x + 0.6442
We want to find the best prediction for a student who scored 52 in the first test so we have this:
y= 1.0607* 52 + 0.6442 = 55.80
Then the best prediction for this case is 55.80
If the sum of 5 consecutive analysis numbers is 170, what is the analysis number?
Answer:
The five consecutive integers whose sum is 170 are 32, 33, 34, 35, and 36
Step-by-step explanation:
hope it help
have a nice day
Bell WorkDIRECTIONSSolve the equation for the variable x.-2(x-3) = 26*Hint: Make sure to use distribution arrows and identifylike terms.
You have the following equation:
-2(x - 3) = 26
in order to solve the previous equation, proceed as follow:
-2(x - 3) = 26 use distribution property
-2(x) - 2(-3) = 26
-2x + 6 = 26 subtract 6 both sides
-2x = 26 - 6 simlify like terms right side
-2x = 20 divide by -2 both sides
x = 20/(-2)
x = -10
Hence, the solution to the given equation is x = -10
Starting at sea level, a submarine descended at a constant rate to a depth of −34 mile relative to sea level in 5 minutes.
What was the submarine's depth relative to sea level after the first minute?
Enter your answer as a fraction in simplest form.
Based on the fact that the submarine's depth was descended to at a constant rate, the submarine's depth relative to sea level with the passing of the first minute was -6⁴/₅ miles
How to find the submarine depth?The submarine descended at a constant rate to the current depth of -34 miles in 5 minutes. This means that the rate can be found by the formula:
= Current depth / Time
= -34 / 5
= -6.8 miles per minute
After the first minute, the depth is:
= -6.8 x 1
= -6.8 miles
This number in fractions is:
= -6 + 8/10
= -6 + 4 / 5
= -6⁴/₅ miles
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Please show your but an short explanation, i inserted a picture of the question
With the given information we can make the following equation:
[tex]x+2x+3x=30[/tex][tex]6x=30[/tex][tex]x\text{ = 5}[/tex]Then David will have:
[tex]2\times5=10\text{ years}[/tex]Answer: 10 years.
Help Please!
A.
[tex] \frac{3}{4} [/tex]
B.
[tex] \frac{5}{4} [/tex]
C.
[tex] \frac{3}{5} [/tex]
D.
[tex] \frac{4}{5} [/tex]
Answer:
Step-by-step explanation:
Soh Cah Toa
S stand for sine, C stand for Cosine and the T stand for Tangent
'o' is the opposite, 'a' stand for adjacent (next to) and h stand for hypotenuse (the longest length of the triangle)
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
We care about angle A and we want sine. So we will use the first equation.
The opposite from A is 3 and the hypotenuse is 5.
[tex]sin(A)=\frac{3}{5}[/tex]
Write a system of equations that represent the graph .
To write an equation for the lines of the graph, we have to find the slope and the y-intercept of each line.
The y-intercept can be find as the value of y when the line intersects the y-axis.
For company L, that intersects at (0,10), the y-intersect is y(0)=10.
For company K, that intersects at (0,5). the y-intersect is y(0)=5.
The slope can be find using two points of the line.
For Company L we will use points (0,10) and (20,15). Then, we calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{15-10}{20-0}=\frac{5}{20}=0.25[/tex]For Company K, the points will be (0,5) and (20,15), and the slope will be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{15-5}{20-0}=\frac{10}{20}=0.5[/tex]With the slope and y-intercept we can write the equation of each line in slope-intercept form.
For Company L, with slope m=0.25 and y-intercept b=10 we will have:
[tex]\begin{gathered} y=mx+b \\ y=0.25x+10 \end{gathered}[/tex]For Company K, with slope m=0.5 and y-intercept b=5, we will have:
[tex]y=0.5x+5[/tex]Answer:
The system of equations will be:
Company L: y=0.25x+10
Company K: y=0.5x+5
4) The measure of one of two supplementary angles is 8 degrees more than three times the other. Find the measure of the larger of the two angles.
Supplementary angles add 180 degrees.
One of the two angles is 8 degrees more than 3 times the other.
If one of the angles is A and the other is B, then:
[tex]A=8+3B[/tex]As they are supplementary, they add 180 degrees:
[tex]A+B=180[/tex]We replace the information of the second equation in the first one and solve:
[tex]\begin{gathered} A=180-B \\ A=8+3B=180-B \\ 8+3B=180-B \\ 4B+B=180-8 \\ 5B=172 \\ B=\frac{172}{5} \\ B=34.4 \end{gathered}[/tex]Now we can solve for the other angle:
[tex]A=8+3B=8+3(34.4)=8+103.2=111.2[/tex]The measure of the angles is 34.4 degrees and 111.2 degrees.
a number increased by 6
Answer:
x + 6.
Step-by-step explanation:
a number which is x and increased by 6 is adding 6
Given H(t)=10-2t^2 , find h^-1 (t), is h (t) one to one ? What does this imply about h^-1(t)
We have the function:
[tex]H(t)=10-5t^2[/tex]And we have to find the inverse function.
We can write this as:
[tex]H(H^{-1}(t))=t[/tex]We can solve this as:
[tex]\begin{gathered} H(H^{-1}(t))=10-2(H^{-1})^3=t \\ 10-2(H^{-1})^3=t \\ 2(H^{-1})^3=10-t \\ (H^{-1})^3=\frac{10-t}{2} \\ H^{-1}=\sqrt[3]{\frac{10-t}{2}}^{} \end{gathered}[/tex]The inverse function is:
[tex]H^{-1}=\sqrt[3]{\frac{10-t}{2}}^{}[/tex]The domain of H is all the real numbers, as the domain of H^-1.
Which expression below represents the average wages the company pays per employee each week?
According to the given data we have the following:
19 employees that earn $360
18 employees that earn $400
8 employyes that earn $480
5 employees that earn $600
The total employees would be=19+18+8+5=50
Therefore, to find the average we have to put at the numerator the amount of wages times of what correspond to each employee, and at the denominator the total of employees which are 50. Therefore, the expression that represents the average wages the company pays per employee each week would be 2.
Maya attended her town's annual Worm Charming Competition. Contestants are assigned to a square foot of land, where they have 30 minutes to "charm" worms to the surface of the dirt. Maya observed contestants' charming techniques and kept track of how many worms surfaced. The probability that a contestant tried tapping the ground is 0.22, the probability that a contestant charmed 5-10 worms is 0.71, and the probability that a contestant tried tapping the ground and charmed 5-10 worms is 0.16. What is the probability that a randomly chosen contestant tried tapping the ground or charmed 5-10 worms?
Using Venn probabilities, there is a 0.77 = 77% probability that a randomly chosen contestant tried tapping the ground or charmed 5-10 worms.
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given according to the following rule:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In the context of this problem, the events are given as follows:
Event A: Contestant tried tapping the ground.Event B: Contestant charmed 5-10 worms.From the text, the probabilities of the events are given as follows:
P(A) = 0.22, P(B) = 0.71, P(A and B) = 0.16.
Hence the or probability is given replacing the values as follows:
P(A or B) = P(A) + P(B) - P(A and B) = 0.22 + 0.71 - 0.16 = 0.77.
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Find the savings plan balance after 2 years with an APR of 7% and monthly payments of $.300
the savings plan balance after 2 years with an APR of 7% and monthly payments of $.300 will be A = $209314.286 or A = $209314.3 .
The formula to calculate amount,
[tex]A= \frac{P[(1+\frac{APR}{100n})^{n*N}-1 ]}{(\frac{APR}{100n}) }[/tex]
where, we are given,
N = 2 years
APR = 7%
P = 300
n = 12
subsituting these values in the equation above we get,
[tex]A=\frac{300[1+\frac{7}{100*1} ]^{12*2} -1}{\frac{7}{100*12} }[/tex]
[tex]A=\frac{300*100*12}{7}} * [\frac{107}{100}^{24} -1][/tex]
[tex]A=\frac{ 360000}{7}[5.07-1][/tex]
[tex]A=\frac{360000}{7}[4.07][/tex]
A=51428.57 * 4.07
A = $209314.286
or
A = $209314.3
What is APR?
An annual percentage rate is a calculation that includes all fees and costs associated with borrowing in addition to the interest rate.
APR is a number provided for all mortgages, loans, and credit cards, and there is a precise formula the bank must use in order to calculate the number in accordance with the Financial Service Authority's guidelines. It is simple to compare the APR between various accounts. All of the additional fees and expenditures you must pay on top of the basic interest rate are factored into the APR calculation.
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Tareq pays $22.10 for 2.6 pound of salmon. What is the price per pound of salmon?
Answer:
22.1$ = 2.6 pound
x = 1 pound
so when we criss cross
22.1$ X 1 pound = 2.6x pound
22.1 = 2.6x
22.1/2.6 2.6x/2.6
X=22.1/2.6
x=8.5
so it costs 8.5$ per pound
Use the graph of the inequality to answer the question.Randy wants to make a mixture of raisins and nuts. Theraisins cost $3.00 a box, and the nuts cost $6.00 a tin. Canhe make a mixture consisting of 3 boxes of raisins and 1 tinof nuts if he wants to spend no more than $12.00?
The raisins cost $3.00 a box while the nuts cost $6.00 a tin.
The graph in the picture provide to us, in the shaded region, the relation between the number of boxes of raisins and the tins of nuts that can be buyed without spend more than $12.00.
We can check in the graph that the point representing a mixture consisting of 3 boxes of raisins and 1 tin of nuts is out of the shaded region.
Therefore, Randy can't make this mixture without spend no more than $12.00
Rafael bought a bag of candy that contains 50 pieces. 30 of those pieces are chocolate and 5 are caramel. Write a ratio that compares the number of chocolate pieces to the number of pieces that are not either chocolate or caramel.
Answer:
so 50:30
=50-30=20
chocolate and 5are caramel
20:5
5can go into 20 =4
20:5
=4:1
Step-by-step explanation:
bag of candy is 50pieces 30piecesare chocolate and 5arecaramel
step 2 . you will subtract 50from30=20
step 3. 5can go into 20=4times
20:5 is equal to 4:1