Are the following two lines Parallel, Perpendicular, or Neither and WHY? Select the correct answer choice below.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Parallel, Perpendicular, or Neither = ?
Step 02:
We must analyze the lines to find the solution.
The lines intersect at a 90 degree angle.
Therefore, the lines are perpendicular.
The answer is:
Perpendicular, because the slopes are opposite and reciprocal.
Related Questions
Mary is preparing for hercollege entrance exams. In a practicetest, she answered 12 problems in30 minutes. At this rate, how manyquestions can she expect to answer in150 minutes?
Answers
Answer:
60 questions
Explanation:
If the rate of the number of problems per minute is constant, we can write the following equation:
[tex]\frac{12\text{ problems}}{30\text{ minutes}}=\frac{x}{150\text{ minutes}}[/tex]Where x is the number of questions that she can answer in 150 minutes.
So, solving for x, we get:
[tex]\begin{gathered} \frac{12}{30}=\frac{x}{150} \\ \frac{12}{30}\times150=\frac{x}{150}\times150 \\ 60=x \end{gathered}[/tex]Therefore, Mary can expect to answer 60 questions in 150 minutes.
what 10000 ÷ 400 x =55
Answers
We want to find the x value that makes the following equation true
[tex]\frac{10,000}{400}x=55[/tex]In order to solve the equation for x we want to "leave alone" the a on one side of the equation. In order to do that we just have to remember one simple rule: what we do on one side of the equal "=" is what we must do on the other side.
Step 1: taking 400 to the right side
[tex]\begin{gathered} \frac{10,000}{400}x=55 \\ \downarrow \\ 10,000x=55\cdot400 \end{gathered}[/tex]Step 2: taking 10,000 to the right side
[tex]\begin{gathered} 10,000x=55\cdot400 \\ \downarrow \\ x=\frac{55\cdot400}{10,000} \end{gathered}[/tex]For 8-10, given the recursive rule for an arithmetic sequence, write the explicit rule and complete the table of values. (All data in photo is all the information provided for that question).
Answers
SOLUTION:
Case: Arithmetic Sequence
Method:
a) The explicit rule
[tex]\begin{gathered} 8,8+7,8+7+7,... \\ a_n=8+7(n-1) \\ a_n=8+7n-7 \\ a_n=1+7n \end{gathered}[/tex]b) Completing the table
Paul is making turkey burgers that are 1/4 pound each. He has 2.93 pounds of turkey. Approximately how many burgers can he make? Explain your answer in sentences. Don't forget your math steps!
Answers
Answer:
12 burgers
Explanation:
Weight of each turkey burgers = 1/4 pound.
Since Paul has 2.93 pounds of turkey.
[tex]2.93\approx3\; \text{pounds}[/tex]Therefore, an approximate number of the burgers he can make will be:
[tex]\begin{gathered} =3\div\frac{1}{4} \\ =3\times4 \\ =12\text{ burgers} \end{gathered}[/tex]Paul can make approximately 12 burgers.
Answer: 12 burgers
Step-by-step explanation: I got it correct
50 pounds of pet food for 37.99What is the unit rate?
Answers
Since the exercise asks for the Unit rate, you know that you must find the price per pound of the pet food.
According to the information given in the exercise, the cost of 50 pounds of pet food is $37.99.
Let be "r" the unit rate or the price (in dollars) per pound of pet food.
In order to find its value, you need to divide $37.99 by 50 pounds. Then, you get that this is:
[tex]\begin{gathered} r=\frac{37.99}{50} \\ \\ r=0.7598\frac{dollars}{pound} \end{gathered}[/tex]The answer is: $0.7598 per pound.
write an equation in slope intercept form -17/12and(12,-8)
Answers
The slope-intercept form of a linear equation is given by:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
If the slope is -17/12, we have m = -17/12.
Now, to find the value of b, let's use the ordered pair (12, -8) in the equation:
[tex]\begin{gathered} y=-\frac{17}{12}x+b \\ (12,-8)\colon \\ -8=-\frac{17}{12}\cdot12+b \\ -8=-17+b \\ b=-8+17 \\ b=9 \end{gathered}[/tex]So our equation is:
[tex]y=-\frac{17}{12}x+9[/tex]Solve. Remember to check for extraneous solutions. Use a comma to separateanswers14 – 2y + 5 = 9Please explain!!
Answers
Answer:
The solutions are:
[tex]y=4[/tex]and
[tex]y=0[/tex]Explanation:
Given the equation:
[tex]|4-2y|+5=9[/tex]To solve for y:
Subract 5 from both sides
[tex]\begin{gathered} |4-2y|+5-5=9-5 \\ |4-2y|=4 \end{gathered}[/tex]Next, the absolute value always has two solutions:
[tex]4-2y=4[/tex]and
[tex]4-2y=-4[/tex]We need to solve each of these equations.
1.
[tex]\begin{gathered} 4-2y=4 \\ \text{Subtract 4 from both sides} \\ 4-2y-4=4-4 \\ -2y=0 \\ y=\frac{0}{-2}=0 \end{gathered}[/tex]2.
[tex]\begin{gathered} 4-2y=-4 \\ \text{Subtract 4 from both sides} \\ 4-2y-4=-4-4 \\ -2y=-8 \\ \text{Divide both sides by -2} \\ y=\frac{-8}{-2}=4 \end{gathered}[/tex]Represent the following sentence as an algebraic expression, where “a number” is the letter x1 is subtracted from a number
Answers
Let:
x = Unknown number
We need to subtract 1 from the unknown number, therefore:
[tex]x-1[/tex]Answer:
x - 1
the square below is dilated by a scale factor of 2. Find the perimeter and area of the square below, as well as the perimeter and area of the dilated square. Figure are not necessarily drawn to scale. Help me please♀️♀️
Answers
Given:
Side Length of the original square, a = 11
Scale factor = 2
Let's find the perimeter and area of each square.
To find the area apply the formula:
[tex]\text{Area}=a^2[/tex]To find the perimeter of the square, apply the formula:
[tex]Perimeter=4a[/tex]Area of the smaller square:
[tex]\text{Area}=11^2=11\ast11=121\text{ }[/tex]Perimeter of the smaller square:
[tex]\text{Perimeter}=4(11)=44[/tex]To find the side length of the dilated square given a scale factor of 2, we have:
a = 2 x 11 = 22
The side length of each side of the dilated square is 22.
We have:
Area of the dilated square:
[tex]\text{Area}=22^2=22\ast22=484[/tex]Perimeter of the dilated square:
[tex]\text{Perimeter = 4(22)=4}\ast22=88[/tex]ANSWER:
Area of square = 121 square units
Perimeter of square = 44 units
Area of dilated square = 484 square units
Perimeter of dilated square = 88 units
algebra 2 what is x+4-12
Answers
Given the expression
[tex]x+4-12[/tex]We are asked to simplify the expression. This can be seen below;
[tex]x+4-12=x-8[/tex]Answer: x-8
Referring to the figure, find the unknown measure of angle ABC.
Answers
We know that for any inscribed angle on a cricle we have that:
[tex]m\angle ABC=\frac{1}{2}m\hat{AC}[/tex]Then in this case we have:
[tex]m\angle ABC=\frac{1}{2}(200)=100[/tex]Therefore the angle ABC is 100°
Ronald is taking a road trip. After 2 hours he has covered 90 miles and after 5 hours he has covered 225 miles. a. Write a linear model and b. use this model to predict the number of miles covered after 10 hours.
Answers
Ronald is taking a road trip. After 2 hours he has covered 90 miles and after 5 hours he has covered 225 miles. a. Write a linear model and b. use this model to predict the number of miles covered after 10 hours.
Let
x ------> number of hours
y -----> number of miles
we have
the ordered pairs
(2,90) and (5, 225)
step 1
Find the slope m
m=(225-90)/(5-2)
m=135/3
step 2
Find the linear equation in slope intercept form
y=mx+b
we have
m=45
point (2,90)
substitute
90=45(2)+b
solve for b
b=90-90
b=0
y=45xstep 3
For x=10 hours
substitute in the linear model
y=45(10)
y=450 milesWhich expression could be used to calculate Mary’s age in relation to Jacob, j? Select all that apply.
Answers
Answer:
The expressions that could represent Mary's age are;
[tex]\begin{gathered} j+5 \\ or \\ 5+j \end{gathered}[/tex]Explanation:
Given that Mary is 5 years older than her little brother Jacob.
if j represents Jacob's age.
Mary's age will be j plus 5;
[tex]\begin{gathered} j+5 \\ or \\ 5+j \end{gathered}[/tex]Therefore, the expressions that could represent Mary's age are;
[tex]\begin{gathered} j+5 \\ or \\ 5+j \end{gathered}[/tex]Translate: The product of a number and 5
Answers
Answer:
5x
Explanation:
Let the number be = x
Product means multiplication
Therefore, the product x and 5
[tex]\begin{gathered} =5\times x \\ =5x \end{gathered}[/tex]Where x represents any number
Find the sum of the infinite geometric series. You may state your answer as a fraction or a decimal. Round your answer to four decimal places if necessary. If the sum does not exist, write "none" in the answer box. a1 = 4, r = 23
Answers
Take into account that a geometric series is given by:
[tex]undefined[/tex]For which equation would x = 4 be a solution?2 x + 7 = 222 x + 8 = 48 - 3 x = 206 x ÷ 8 = 3
Answers
Remember that
If a value of x is a solution to an equation, the value of x must satisfy the equation
For x=4
substitute in the equation
[tex]\begin{gathered} \frac{6x}{8}=3 \\ \\ \frac{6(4)}{8}=3 \\ \\ \frac{24}{8}=3 \\ 3=3\text{ ----> is ok} \end{gathered}[/tex]The answer is the option N 4If θ is a first quadrant angle in standard position with P(u,v) = (3,4) evaluate tan2θ1) 24/72) -8/73) -24/7
Answers
Given:
The required angle is in the first quadrant with position P(u,v) = (3,4)
Let us begin by showing the position of the angle using the given position:
Using trigonometric ratios, we can solve for theta as shown:
[tex]\begin{gathered} \tan \text{ }\theta\text{ = }\frac{Opposite}{Adjacent} \\ \text{Substituting the given sides} \\ \tan \theta\text{ =}\frac{4}{3} \\ \theta\text{ = }\tan ^{-1}\frac{4}{3} \\ \theta=53.13^0 \end{gathered}[/tex]Solving for the required angle:
[tex]\begin{gathered} \tan (2\theta)\text{ =tan(2}\times53.13) \\ =tan106.26^0 \\ =\text{ -3.429} \end{gathered}[/tex]The result is equivalent to -24/7.
Answer: -24/7 (Option 3)
Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. X: 0 1 2 3P(x): 0.085 0.336 0.421 0.158
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xpThe data is given as
X: 0 1 2 3
P(x): 0.085 0.336 0.421 0.158
To find the standard deviation , first find the mean of the variable.
The mean is calculated as
[tex]\mu=\Sigma xP(x)=0+0.336+0.842+0.474=1.652[/tex]Now another table,
Now the formula for standard deviation is determined as
[tex]\sigma=\sqrt[]{\Sigma(x^2P(x))-\mu^2}[/tex][tex]\sigma=\sqrt[]{3.442-1.652^2}=\sqrt[]{3.442-2.729104}=\sqrt[]{0.712896}[/tex][tex]\sigma=0.8443[/tex]Thus the standard deviation is 0.8443.
Graphing LinearWhich of the following graphs represents the solution(s) of the following system-y = -24y-8 = X半 半 半 半平DONE
Answers
Step by step explanation:
We must graph the two functions, so:
The first one corresponds to:
[tex]\begin{gathered} x^2-y=-2 \\ -y=-x^2-2 \\ y=x^2+2 \end{gathered}[/tex]A parabola with vertex at (0,2).
And the second one corresponds to:
[tex]\begin{gathered} 4y-8=x \\ 4y=x+8 \\ y=\frac{x}{4}+2 \end{gathered}[/tex]A line with y-intercept at (0,2) and 1/4 slope.
Answer:
Option D.
The Sugar Sweet company needs to transport sugar to marlet .The graph bellow shows the transporting costs (in dollars) versus the weight of the sugar being tranported (in tons)
Answers
Given
To find:
1) How much does the cost increase for each ton of sugar being transported?
Explanation:
It is given that,
That implies,
The point (0,500) and (1,2000) lies on the line.
Therefore, the equation of the line is,
[tex]\begin{gathered} \frac{y-500}{2000-500}=\frac{x-0}{1-0} \\ \frac{y-500}{1500}=x \\ y=1500x+500\text{ \_\_\_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]Hence,
1) For each ton, the increase in the cost of transporting sugar is $500.
2) And, the slope of the line 1500.
the 5th graders at Bronx 2 Middle School used a identical airplanes with 90 seats on a chair plate for a trip to the Bahamas in order to maintain Social Justice League the bus take over one-third of the seats on each episode on 1/3 of the students and adults chaperones used the following steps to board the airplane:first they filled every available seat on 1/4 of the airplanes.what do you want next they sell 2/3 of the available seats on 1/3 of the remaining airplanes.last they filled in 25 seats on each photos of the remaining airplanes.if 1/10 of all the passengers on the airplane were adults how many adults were on the trip to the Bahamas ?
Answers
N= number of airplanes
1/4N of airplanes were filled
3/4N are remaining airplanes
2/3x1/3N= (2/9)•N are remaining airplanes chairs filled
1/10 of passengers were adults
There are 90 chairs for plane
1/4•90= 90/4= 22.5 passengers
2/3•1/3•90= 180/9= 20 passengers
last were 25 passengers
Then
Total passengers= 22+20+25= 67
10% of 67 = 6 passenger
Then answer is 6 adults were for an airplane
Use the drawing tools to form the correct answer on the graph. Graph the System of Inequalities and then draw a point on it.
Answers
Given the System of Inequalities:
[tex]\begin{cases}y>1.5^x+4{} \\ y<{\frac{2}{3}x+6}\end{cases}[/tex]• You can identify that the boundary curve of the first inequality is:
[tex]y=1.5^x+4[/tex]Notice that it is an Exponential Function with this base:
[tex]b=1.5[/tex]Since it is greater than 1, it shows an Exponential Growth.
Find three points on the curve in order to graph it by substituting these values of "x" into the equation and evaluating:
[tex]\begin{gathered} x=-10 \\ x=0 \\ x=6 \end{gathered}[/tex]You get:
[tex]y=1.5^{(-10)}+4\approx4.017[/tex][tex]y=1.5^{(0)}+4=1+4=5[/tex][tex]y=1.5^{(6)}+4\approx15.391[/tex]Since the symbol of the inequality is:
[tex]>[/tex]The shaded region is above the curve and the curve is dotted.
Notice that the boundary line of the second inequality is:
[tex]y=\frac{2}{3}x+6[/tex]It is written in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case:
[tex]b=6[/tex]By definition, the value of "y" is zero when the line intersects the x-axis. Then, in order to find the x-intercept, substitute this value into the equation and solve for "x":
[tex]y=0[/tex]You get:
[tex]0=\frac{2}{3}x+6[/tex][tex]\begin{gathered} (-6)(\frac{3}{2})=x \\ \\ x=-\frac{18}{2} \\ \\ x=-9 \end{gathered}[/tex]Since the inequality symbol of the second inequality is:
[tex]<[/tex]The shaded region is above the line and this is dotted.
Knowing the above, you get this graph:
• The intersection region is the solution to the System of Inequalities. Therefore, you can conclude any point inside that region is a solution. For example:
[tex](0,5.5)[/tex]Then, you can plot it on the Coordinate Plane.
Hence, the answer is:
The sum of two consecutive integers is less than 55. The pair of integers with the greatest sum are 26 and 27A.TrueB.False
Answers
Answer
Option A is correct.
True.
Explanation
Let the smaller one of the two consecutive numbers be x.
Since they are consecutive numbers, the other number will be (x + 1)
The sum of the two numbers is said to be less than 55.
x + x + 1 < 55
2x + 1 < 55
2x < 55 - 1
2x < 54
Divide both sides by 2
(2x/2) < (54/2)
x < 27
So, we are told that x has to be less than 27.
Hence, the highest value that x can take on is 26.
x + 1 = 27
So, the greatest pair of integers whose sum can only be less than 55 are 26 and 27.
Hope this Helps!!!
Jenna bought some rope for a craft project. The rope cost $3.50 per meter. She bought 432 centimeters of rope. How much did Jenna pay for the rope?
Answers
The rope cost $3.50 per mete
Cost of one meter = $3.50
She bought 432 centimeters of rope.
Cost of 432 cm meter of rope = 432 x 3.50
Cost of 432 cm meter of rope = $1512
Alba is constructing an angle that is congruent to angle A. She is almost finished. What is the final step in her construction? B А X Х Y А. Place the compass point at X and draw an arc between X and Y. B Use a straightedge to draw a ray from X through any point on hie arc. C. Without changing the setting of the compass, place the compass point at A and draw an arc between A and B. Label the point Z where the two arcs intersect. Use a straightedge to draw AZ O Without changing the setting of the compass, place the compass point at Y and draw an arc Label the point Z where the two arcs intersect Use a straightedge to draw XZ.
Answers
After drawing the same arc on your transfer angle, you have to place the compass point at X and draw and arc between X and Y.
A rectangle has a length=-7 and width=(3x-5)What is the AREA?
Answers
Answer
The area of the rectangle with the given length and width is
(-21x + 35) square units.
Explanation
The question wants us to calculate the AREA of a rectangle with
Length = -7
Width = (3x - 5)
The Area of a rectangle is given as
Area of Rectangle = Length × Width
Length = -7
Width = (3x - 5)
Area of this rectangle = -7 × (3x - 5)
= (-7 × 3x) + (-7 × -5)
= (-21x + 35) square units.
Hope this Helps!!!
A side of the triangle below has been extended to form an exterior angle of 77º. Findthe value of x
Answers
The exterior angle (the one with a measure of 77°) and angle x are supplementary angles since the first is next to angle x and are located on the same line, supplementary angles add up to 180°, then we can calculate the measure of x by means of the following formula:
x + 77° = 180°
x + 77° - 77° = 180° - 77°
x + 0 = 103°
x = 103°
Then, x equals 103°
I’m confused with how to start this off. It’s function graphs, (square root) algebra 2
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Looking at the red graph, we can see that the square root function was translated 3 units down and 3 units left, so we can write the following equation:
[tex]f(x)=\sqrt[]{x+3}-3[/tex]Then, for the green graph, we have a translation of 3 units up and 3 units right, so the equation is:
[tex]g(x)=\sqrt[]{x-3}+3[/tex]what's twelve minus y ?
Answers
We are required to solve:
[tex]=12\text{ -y}[/tex]Since 12 and y do not have a common term, we subtract y from 12 hence, the solution to this problem is:
[tex]=\text{ 12 - y}[/tex]Answer:
12 - y
Find the length of R and T using the special right triangle below.Answer ChoicesA. r=12, t= 12 square root 2B. r=24, t= 24 square root 3C. r=24, t= 12 square root 3D. r=12 square root 3, t=24
Answers
sum of all three angles in triangle=180
30+90+x=180
x=180-120
x=60
