Explanation:
Given the equation:
[tex]y=\frac{1}{2}x+\frac{11}{6}[/tex]Comparing it with the slope-intercept form: y=mx+b
[tex]\text{Slope,m}=\frac{1}{2}[/tex]Definition: Two lines are perpendicular if the product of the slopes is -1.
Let the slope of the new line = n
[tex]\begin{gathered} \frac{1}{2}n=-1 \\ n=-2 \end{gathered}[/tex]Substitute the slope, -2 and point (4,-5) in the slope-point form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-2(x-4) \end{gathered}[/tex]We then express it in the slope-intercept form:
[tex]\begin{gathered} y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]The equation of the perpendicular line is y=-2x+3.
Answer:
[tex]y=-2x+3[/tex]how do I find AC if AE = x + 50 and CE = x + 32
ANSWER
AC = 18
EXPLANATION
Let us draw a diagram to represent the situation:
From the diagram, we see that:
AC + CE = AE (since they are colinear)
So, we have that:
AC + x + 32 = x + 50
=> AC = x + 50 - x - 32
AC = 18
That is the value of AC.
At the grocery store, 3 apples cost $0.65. What is the cost of 8 apples? 7th honors it is due today help
Answer:
$1.76 for 8 apples
Step-by-step explanation:
0.65 / 3 = 0.22
0.22 * 8 = 1.76
Hi, no explication/steps required I just need the final answer
SOLUTIONS
Graph the vertical and horizontal asymptote of the function below:
[tex]f(x)=\frac{4}{x-4}[/tex]The above graph represent the vertical and horizontal asymptote of the function, using desmos calculator.
The height of the object at 1 second is what amount of feet?
If t= 1s. Then let's replace t-value in the equation:
[tex]\begin{gathered} \text{ -16t}^2\text{ + 1130= } \\ \text{ -16 \lparen1\rparen + 1130= } \\ \text{ -16 + 1130= } \\ 1,114\text{ feet. } \end{gathered}[/tex]The height of the object at 1 second is 1,114 feet.
how much time will it take for a fire to reach this machine size
Given the equation:
[tex]y=4(1.8){}^t[/tex]You know that "y" represents the number of acres of land, and "t" represents the number of minutes the fire has raged.
In order to find the time (in minutes) it will take for a fire to reach 160 acres, you need to substitute this value of "y" into the equation:
[tex]y=160[/tex]And then solve for "t":
[tex]160=4(1.8){}^t[/tex]Follow these steps in order to solve for "t":
- Divide both sides of the equation by 4:
[tex]\begin{gathered} \frac{160}{4}=\frac{4(1.8){}^t}{4} \\ \\ 40=(1.8)^t \end{gathered}[/tex]- Take the logarithm from both sides:
[tex]\begin{gathered} log(40)=log(1.8)^t \\ \\ log(40)=t\cdot log(1.8) \end{gathered}[/tex]- Divide both sides by the logarithm on the right side of the equation:
[tex]\begin{gathered} \frac{log(40)}{log(1.8)})=\frac{t\cdot log(1.8)}{log(1.8)} \\ \\ t\approx6.28 \end{gathered}[/tex]Hence, the answer is:
[tex]6.28\text{ minutes \lparen approximately\rparen}[/tex]determine the value of d22, if possible. if the element indicated is not in the matrix, state “none”.
Answer:
[tex]5[/tex]Explanation:
Here, we want to determine the given element
From what we have, it is stated as d22
What this simply means is that we are looking at the element in row 2, column 2
The element here is:
[tex]5[/tex]Four a field trip 17 Students rode in cars and the rest filled ten buses. How many students were in each bus if 367 students were on the trip.
Hello there. To solve this question, we'll have to simply subtract and divide the numbers to find how many students were in each bus.
Knowing that for this field trip, 17 from 367 students went by cars, we know that 350 went by bus.
If there were 10 buses and we assume that all the buses transports the same amount of students, to find this amount, we just divide:
350/10 = 35
Therefore, 35 students were in each bus for this field trip.
6. For school uniforms, five shirts and three pairs of pants cost $113. 25. If a shirtcosts $3.75 less than a pair of pants, how much is a shirt and how much is a pairof pants?
Let x be the cost of 1 pair of pants, and y be the cost of one shirt, then since five shirts and three pairs of pants cost $113. 25 we can set the following equation:
[tex]5y+3x=113.25,[/tex]also, a shirt costs $3.75 less than a pair of pants, then:
[tex]y=x-3.75.[/tex]Substituting the second equation in the first one we get:
[tex]5(x-3.75)+3x=113.25.[/tex]Solving for x we get:
[tex]\begin{gathered} 5x-18.75+3x=113.25, \\ 8x=113.25+18.75, \\ x=\frac{33}{2}=16.5. \end{gathered}[/tex]Now, substituting x=16.5 in the second equation we get:
[tex]y=16.5-3.75=12.75.[/tex]Answer:
A shirt costs $12.75, and a pair of pants cost $16.5.
The quadratic equation y = - 16t² +40t+2 represents the height of aprojectile, y, in feet, at a particular time, t, in seconds.For what interval or intervals of time will the projectile be above 18 feet?
The given equation is:
[tex]y=-16t^2+40t+2[/tex]It is required to find which interval or intervals of time will the projectile be above 18 feet.
To do this, solve the inequality:
[tex]\begin{gathered} y>18 \\ \Rightarrow-16t^2+40t+2>18 \end{gathered}[/tex]First, find the critical points of the inequality by solving the equation:
[tex]\begin{gathered} −16t^2+40t+2=18 \\ \text{ Subtract 18 from both sides:} \\ \Rightarrow-16t^2+40t+2-18=18-18 \\ \Rightarrow−16t^2+40t-16=0 \\ \text{ Factor the left-hand side of the equation:} \\ \Rightarrow−8\left(2t−1\right)\left(t−2\right)=0 \\ \text{ Equate the factors to 0 to find the t-values:} \\ \Rightarrow(2t-1)=0\text{ or }(t-2)=0 \\ \Rightarrow2t=1\text{ or }t=2 \\ \Rightarrow t=\frac{1}{2}=0.5\text{ or }t=2 \end{gathered}[/tex]The possible interval of solutions are:
[tex]t<0.5,\;0.52[/tex]Use test values in the intervals to check which interval whose set of values satisfies the given inequality.
The only interval that satisfies it is 0.5.
Hence, the answer is between 0.5 second and 2 seconds.
The answer is option (c).this year Benny is 12 years old and his mom is 48 years old in two years what percent of his age will Benny's mom's age be at the time
Now
Benny = 12
Mom = 48
In 2 years
Benny = 14
Mom = 50
50 years ------------------------ 100
14 years ------------------------- x
x = (14 x 100) / 50
x = 1400/50
x = 28%
Benny's age will be 28% of his mom's age.
Jackie cut 3-yards of ribbon into 6 equal lengths of ribbon. What is the length of each ribbon in yards? A. C. 1 2 B. 18 1 colo D.2 ОА OB Ос OD (
The ribbon is 3 yards. He cuts the ribbon into 6 equal length. The length of each ribbon can be calculated below
total length of the ribbon = 3 yards
[tex]\begin{gathered} \text{each length of the cut ribbon=}\frac{3}{6} \\ \text{each length of the cut ribbon}=\frac{1}{2}\text{ yards} \end{gathered}[/tex]There are 150 people at an International Medical Conference. 40 are Africans, 70 are women and 110 are doctors. 12 of the women are Africans, 46 of the doctors are women and 31 of the Africans are doctors. If 5 of the African men are not doctors: a how many of the African women are doctors b how many of the men are neither African nor doctors?
Draw a Venn Diagram to visualize the situation:
Notice that the numbers in purple correspond to the total amount of people in the regions P and O, P and Q, P and S, respectively.
Numbers in red correspond to the number of people in each region.
Then, we should find the correct numbers for the regions O, P, Q and S, as well as M, N, R and T so that the total number of people in each group matches the labels.
Let x represent the amount of people in the region P.
Since the total amount of people in regions O and P must be 31, then the amount of people in O must be 31-x.
Similarly, the amount of people in region Q must be 12-x.
Since the amount of people in the region N (African men who are not doctors) is 5 and the total amount of African people is 40, then, we can write down an equation for x, where the sum of the amount of people in regions N, O, P and Q is 40:
[tex]5+(31-x)+x+(12-x)=40[/tex]Solve for x:
[tex]\begin{gathered} \Rightarrow5+31-x+x+12-x=40 \\ \Rightarrow48-x=40 \\ \therefore x=8 \end{gathered}[/tex]Notice that the number of people in region P, which is 8, corresponds to amount of African women who are doctors. Therefore, the answer for part a) is: 8.
To find how many of the men are neither African or doctors, find first the correct amount of people in regions R and T. This can be done by taking into account the total amount of people who are doctors and the total amount of people who are women.
The number of people in regions O, P, R and S must be equal to 110. For that to happen, the number of people in region R must be 41.
The amount of people in region T can be found similarly, and it is equal to 20.
Once the total amount of people in regions N, O, P, Q, R, S and T is known, we can deduce the number of people that must be in region M taking into account that the total amount of people in the conference is 150.
Substract the total amount of people in regions N to S (which is 139) from 150, in order to find the total amount of people in region M:
[tex]150-139=11[/tex]The region M corresponds to men who are neither African or doctors. Therefore, the answer to part b) is 11.
At what point will the lines x= -21 - 2y and x = -39 - 4y intersect? (i need the answer)
ANSWER
The lines intersect at (-3, -9)
EXPLANATION
The point where the lines intersect is the solution to the system of equations
[tex]\begin{cases}x=-21-2y \\ x=-39-4y\end{cases}[/tex]We can solve it using the elimination method, which consists in subtracting one equation from the other in order to eliminate one of the variables and obtain only one equation with only one variable:
[tex]\begin{gathered} x=-21-2y \\ - \\ x=-39-4y \\ \text{ ------------------------------} \\ (x-x)=(-21-2y)-(-39-4y) \end{gathered}[/tex]Solving for y:
[tex]\begin{gathered} 0=-21+39-2y+4y \\ 0=18+2y \\ 2y=-18 \\ y=-9 \end{gathered}[/tex]Now we have to replace y = -9 into one of the equations and solve for x:
[tex]\begin{gathered} x=-21-2y \\ x=-21-2(-9) \\ x=-21+18 \\ x=-3 \end{gathered}[/tex]The lines intersect at (-3, -9)
Harry wants to buy a motorbike that costs £600.He saves 30% of his wages each month.Each month Harry earns £400.Calculate how many months it will take Harry to save enough money?
First, let's calculate how much money he saves each month, by calculating 30% of £400:
[tex]\frac{30}{100}\cdot400=30\cdot4=120[/tex]He saves £120 each month.
So, to reach the value of £600, the number of months needed is:
[tex]\frac{600}{120}=5[/tex]Therefore it will take 5 months to save enough money.
What is the volume of the following shape?
the multiple answers are A) 62,000 B) 32,000 C) 56,000 D) 52,000
I get 50,000.
I appreciate any help you can provide.
The volume of the shape is 59000.
Given that,
There is a picture in that we have a diagram.
We have to find the volume of the shape.
The shape we can divide into 2 parts.
Such as,
Cube and rectangular cube
That is by the measurements we can see
30 is the side of the cube then the length is 50+30 =80 and the width is 50-30=20.
The volume of the shape is Volume of the cube + Volume of rectangular cube.
The volume of the shape= a³+l×w×h
Here,
a is side of the cube that is 30
l is length of the rectangular cube is 80
w is width of the rectangular cube is 20
h is height of the rectangular cube is 20
The volume of the shape=30³+80×20×20
The volume of the shape=27000+32000
The volume of the shape=59000
Therefore, The volume of the shape is 59000.
To learn more about volume visit: https://brainly.com/question/1578538
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Aidan walked 440 feet in one minute. Find his average rate in miles per hour.
Take into account the following equivalences as conversion factors:
1 mi = 5280 ft
1 h = 60 min
Then, you have:
[tex]440\frac{ft}{\min}\cdot\frac{1mi}{5280ft}\cdot\frac{60\min }{1h}=5mph[/tex]Hence, the average rate is 5 miles per hour
Find the equation of the line
Use exact numbers
Answer:
y = (1)x +(-5)
Step-by-step explanation:
You want the slope-intercept equation of the line graphed with y-intercept -5 and x-intercept +5.
Intercept formThe intercept form of the equation for a line with x-intercept 'a' and y-intercept 'b' is ...
x/a +y/b = 1
Using the given intercept values, a=5, b=-5, the equation is ...
x/5 +y/(-5) = 1
Slope-intercept formThe desired form of the equation can be found by solving for y:
-x +y = -5 . . . . . . multiply by -5
y = x -5 . . . . . . . . add x
The numbers that go in the boxes are 1 and -5.
Which of these square numbers also happens to be the sum of two smaller square numbers? Select one:a. 16b. 25c. 36d. 49
Notice that:
[tex]25=9+16.[/tex]Recall that:
[tex]\begin{gathered} 3^2=9, \\ 4^2=16. \end{gathered}[/tex]Answer: Option b.
Simplify. In the form of a paragraph, explain in complete sentences the steps necessary to simplify the expression andinclude the final answer in your explanation. Complete your work in the space provided or upload a file that can displaymath symbols if your work requires it.
1. When dividing with exponents, the exponent of a variable in the denominator is subtracted from the exponent in the numerator for the same variable. Then, first step to simplify is subtract the exponents of x and y in the fraction in parentheses:
[tex]\begin{gathered} =(x^{3-1}y^{1-2})^{-2} \\ =(x^2y^{-1})^{-2} \end{gathered}[/tex]2. To remove the parentheses you multiply each exponent in the parentheses by the exponent out of the parentheses:
[tex]\begin{gathered} =x^{2\cdot(-2)}y^{(-1)\cdot(-2)} \\ \\ =x^{-4}y^2 \end{gathered}[/tex]3. When you have a negative exponent (as the x powered to -4) you divide 1 in to the term with negative exponent (after you divide the exponent turns into a positive exponent):
[tex]=\frac{1}{x^4}\cdot y^2[/tex]4. Then, the given expression simplified is:
[tex](\frac{x^3y}{xy^2})^{-2}=\frac{y^2}{x^4}[/tex]Simplify 9y - 11 + 4y - 16y
The given expression is
9y - 11 + 4y - 16y
In order to simplify the expression, we would collect like terms. The like terms in this situation are
1) the terms containing y
2) the terms that don't contain y.
By collecting the like term, we would bring them together. It becomes
9y + 4y - 16y - 11
13y - 16y - 11
- 3y - 11
Which of the following has a graph that is an ellipse centered at (−2, 3)
Solution:
The vertex equation of an ellipse is;
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Thus, given the center;
[tex](h,k)=(-2,3)[/tex]Then, the equation whose graph is an ellipse centered at (-2,3) is;
[tex]\frac{(x+2)^2}{12}+\frac{(y-3)^2}{18}=1[/tex]
Find the measure Z BCD in thefollowing parallelogram.ADх2x2xХСBmZBCD = [ ? 10
Ok, so
We got the following parallelogram:
We want to find the value of the angle BCD.
For this, remember that the sum of the internal angles of a parallelogram must be always equal to 360°.
So, we could write:
[tex]\begin{gathered} 2x+2x+x+x=360 \\ 6x=360 \\ x=\frac{360}{6} \\ x=60 \end{gathered}[/tex]The value of x is equal to 60°. Now, the angle BCD is an angle that measures 2x degrees.
So, BCD measures 2*60, which is 120°.
What is the surface area of 1 Katie's chests? What is the surface area of all four chests Katie needs to paint?
We have to add the areas from A to F.
We then can write:
[tex]S=A+B+C+D+E+F[/tex]As each area is a rectangle, the area is the product of the sides.
We can also simplify and see that:
[tex]A=E=16\cdot13=208[/tex][tex]B+C+D+F=25\cdot(13+16+13+16)=25\cdot58=1450[/tex]Then:
[tex]\begin{gathered} S=A+(B+C+D+F)+E \\ S=208+1450+208 \\ S=1866in^2 \end{gathered}[/tex]The surface of one chest is 1866 square inches.
The four chests will represent:
[tex]4\cdot1866=7464in^2[/tex]If each can paints 933 square inches, she will need:
[tex]\frac{7464}{933}=8\text{ cans}[/tex]Answer:
Each chest has a surface of 1866 sq. in.
The four chest represent 7464 sq. in. of surface area.
She needs 8 cans of paint to paint all 4 chests.
Triangle ABC, with vertices A(-2, 4), B(0, -5), and C(-3, -8) was dilated to form triangleA'B'C' with vertices A(-1.8, 3.6), B(0, -4.5), and C(-2.7, -7.2). What rule represents thedilation applied?(x, y) = (2/3x, 2/3y)(x, y) - (0.9x, 0.9y)(x, y) - (-X, -Y)(x, y) - (1.2x, 1.25y)
A = (-2,4)
B= (0,-5)
C = (-3,-8)
A'= (-1.8, 3.6 )
B'= (0, -4.5 )
C' = (-2.7, -7.2)
Try each option:
(x, y) = (2/3x, 2/3y)
A = (-2,4) = (2/3*-2 , 2/3*4) = (-4/3, 8/3) NOt equal to A'
(x, y) - (0.9x, 0.9y) =
A = (-2,4) = (0.9*-2, 0.9*4) = (-1.8, 3.6) = A' YES
B = (0,-5) = (0.9*0, 0.9*-5) = (0, -4.5) = B'
C= (-3,-8) = (0.9*-3, 0.9*-8) = ( -2.7, -7.2)= C'
Correct option : (x, y) - (0.9x, 0.9y)
can you tell me if I did the equation right
Answer: The equation is correct
Write a system of equations and solve using elimination The sum of two numbers is 18. The difference between the two numbers is 2. What are the two numbers?
Assume that the 2 numbers are x and y, then
Since their sum is 18
That means add x and y, equate the sum by 18
[tex]x+y=18(1)[/tex]Since their difference is 2
That means subtract x and y, equate the difference by 2
[tex]x-y=2(2)[/tex]Add (1) and (2) to eliminate y
[tex]\begin{gathered} (x+x)+(y-y)=(18+2) \\ 2x+0=20 \\ 2x=20 \end{gathered}[/tex]Divide both sides by 2 to find x
[tex]\begin{gathered} \frac{2x}{2}=\frac{20}{2} \\ x=10 \end{gathered}[/tex]Substitute the value of x in (1) to find y
[tex]10+y=18[/tex]Subtract 10 from both sides
[tex]\begin{gathered} 10-10+y=18-10 \\ y=8 \end{gathered}[/tex]The 2 numbers are 10 and 8
Hi, can you help me answer this question please, thank you
From the given z-value z=1.841, we can find the corresponding P-value by means of a z-table:
Then, by rounding to 4 decimal places, the p-value is 0.9672
determine whether the following graphs are functions using the vertical line test. what is the vertical line test?
The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of the relation, and then observe the points of intersection.
The vertical line test supports the definition of a function. That is, every x-value of a function must be paired to a single yy-value. If we think of a vertical line as an infinite set of x-values, then intersecting the graph of a relation at exactly one point by a vertical line implies that a single x-value is only paired to a unique value of y.
If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
If a vertical line intersects the graph in some places at more than one point, then the relation is NOT a function.
With the above illustration,
Graph 3 is not a function using vertical test because it has infinitely many solutions
Graph 4 is not a function because the vertical cuts the graph and intersect at a points
Graph 5 is a constant function because it has a repeated value of x and a constant y value
Graph 6 is not a function because the x-values which is the domain is repeated for different values of y
Graph 7 is not a function because the vertical line cuts the graph at two-point
Graph 8 is a function because it has one point intersection and each value of x have a corresponding value of y
A prism is completely filled with 72 cubes that have edge lengths of 1/2 in.What is the volume of the prism?Enter your answer in the box. in³
Given:
A prism is completely filled with 72 cubes that have edge lengths of 1/2 in.
Required:
To find the volume of the prism.
Explanation:
The volume of the each cube is
[tex]\begin{gathered} =(\frac{1}{2})^3 \\ \\ =\frac{1}{8}in^3 \end{gathered}[/tex]So the volume of the complete prism is
[tex]\begin{gathered} =72\times\frac{1}{8} \\ \\ =9in^3 \end{gathered}[/tex]Final Answer:
The volume of the prism is
[tex]9in^3[/tex]Look at the figure which now shows the value of x for DS. Write the similarity ratio as a fraction in simplest form
Since both figures are similar, we have the following proportions:
[tex]\frac{HP}{GD}=\frac{PT}{DS}[/tex]in this case, we have that HP=4, GD=8, PT=6 and DS=12, then we have:
[tex]\frac{4}{8}=\frac{6}{12}[/tex]the ratio in its simplest form is 1/2, since:
[tex]\frac{6}{12}=\frac{4}{8}=\frac{1}{2}[/tex]