HELP FAST!!!!
A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?
A. -3x + 4y = 3
B. -1.5x − 3.5y = -31.5
C. 2x + y = 20
D. -2.25x + y = -9.75
Answers
Answer:
[tex]-1.5x - 3.5y =- 31.5[/tex]
Step-by-step explanation:
Given
AB: [tex]-7x + 3y = -21.5[/tex]
[tex]PQ(x_1,y_1) = (7,6)[/tex]
Required
Determine the equation of PQ
First, we calculate the slope of AB:
[tex]-7x + 3y = -21.5[/tex]
Make 3y the subject
[tex]3y = 7x - 21.5[/tex]
Make y the subject
[tex]y = \frac{7}{3}x - \frac{21.5}{3}[/tex]
An equation has the general form:
[tex]y = mx + b[/tex]
Where m = slope
So:
[tex]m = \frac{7}{3}[/tex] -- Slope of AB
From the attached diagram, we can see that PQ is perpendicular to AB.
This means that, the relationship between their slope is:
[tex]m_2 = -\frac{1}{m_1}[/tex]
Substitute 7/3 for m1
[tex]m_2 = -\frac{1}{7/3}[/tex]
[tex]m_2 = -\frac{3}{7}[/tex]
The equation of PQ is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = m_2 = -\frac{3}{7}[/tex]
and
[tex]PQ(x_1,y_1) = (7,6)[/tex]
So, we have:
[tex]y - 6 = -\frac{3}{7}(x - 7)[/tex]
Multiply both sides by 7
[tex]7(y - 6) = -\frac{3}{7}(x - 7)*7[/tex]
[tex]7y - 42 = -3(x-7)[/tex]
Open bracket
[tex]7y - 42 = -3x + 21[/tex]
Collect Like Terms
[tex]3x + 7y = 42 + 21[/tex]
[tex]3x + 7y = 63[/tex]
Divide through by -1/2
[tex]-\frac{1}{2}(3x + 7y) = -\frac{1}{2}*63[/tex]
[tex]-1.5x - 3.5y =- 31.5[/tex]
The equation of PQ is: [tex]-1.5x - 3.5y =- 31.5[/tex]
Answer:
B. -1.5x − 3.5y = -31.5
Step-by-step explanation:
Got it right on the test. ; )
Related Questions
write a word problem that can be modeled by the equation x + 5 = 12
Answers
Answer:
x=7
Step-by-step explanation:
x+5=12
-5 -5
x=7
Help please someone
Answers
Answer:
60°
Step-by-step explanation:
the relationship between angle RST and its arc TR is:
2m∠(RST)=m(arcTR);
using this formula m∠(RST)=0.5*m(arcTR);
m∠(RST)=60°
Answer:
<S = 60
Step-by-step explanation:
The arc TR and the central angle (T to the center then to R ) are equal.
So the Central angle is 120o
S anywhere on the minor arc is 1/2 the central angle.
<S = 1/2 120
<S = 60
On a separate sheet of paper practice drawing a 10ft. Vertical line at three different scales using American system:
1) 1/2” = 1’;
2) 1/2” = 1’;
3)1/8” = 1’;
Draw also 12m. Vertical line at three different scales using the Metric System
4) 1/50 CM;
5) 1/100 CM;
6) 1/200 CM;
A street on a block plan is drawn at a scale of 1”=50’. When the drawing is measured with a ruler, the street is 1/2” wide. How wide is the actual street? Explain
Answer:
A street on a block plan is drawn at a scale of 1”=10’. When the drawing is measured with a ruler, the street is 5” wide. How wide is the actual street? Explain
Answer:
In your own words describe the three types of scale answer here:
En una Homs de paper separada, practique el dibujo de una linea vertical de 10 pies a tres escalate diferentes untilizando Sistema Americano:
1/2 “=1’;
1/2 “=1’;
1/8 “=1’;
Dibuja tamben una linea vertical de 12m. A tres escalas diferentes untilizando el Sistema Metrico:
4) 1/50 CM;
5) 1/100 CM;
6) 1/200 CM;
Una Calle en un plano de bloque se dibuja a una escala de 1 “=50 cuando el dibujo se mide con una regal, la calle tiene 1/2 “de ancho qué anchura real tiene la Calle? Explique
Una Calle en un Plano de bloque se dibuja a una escala de 1 “= 10 cuando el dibujo de mide con una regal, la Calle tiene 5 “ de ancho qué anchura real tiene la Calle? Explique
En sus palabras descibe las tres tipos de escala.
Escribe Aqui:
Help me
Answers
Answer:
Step-by-step explanation:ok
Please help fast!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x² + 2x - 6
Step-by-step explanation:
= f(x) + g(x)
= (2x + 1) + (x² - 7)
= 2x + 1 + x² - 7
= 2x - 6 + x²
= x² + 2x - 6
good luck, i hope this helps :)
There were 140 geese living in Larson Lake last year. It is overpopulated. A scientist has suggested a program to decrease the population of geese by 15% after 5 years. How many geese does the scientist hope will be in the lake in 5 years? Show your work.
Answers
Answer:
119
Step-by-step explanation:
Find 10% by dividing by 10, then halve it to get 5%. The answers are 14 and 7 accordingly.
Add them together to get 15%, which is now 21.
Take 21 off of 140 to get the answer, which is 119.
ALTERNATIVE METHOD - CALCULATOR
To solve the question using a calculator and with only one equation, multiply the number by 0.85 to find 85% of the number, and there's your answer.
Of the flowers in Bella’s garden, 5/8 are tulips. What percent of the flowers in the garden are tulips?
Answers
I hope this helps!!
Answer:
62.5
Step-by-step explanation:
the ratio of the base to the leg of an isosceles triangle is 2:7. if the perimeter of the triangle is 304 feet, find the length of the base
Answers
Step-by-step explanation:
I hit a expected tomorrow:No for completion of a
The required base of the isosceles triangle is given as 38 feet.
What is the isosceles triangle?A triangle with two sides and two congruent angles is called an isosceles triangle.
here,
For a given isosceles triangle,
side/base = 2 / 7
side = 2/7 base = 7 /2 sides
According to the question,
The perimeter of the triangle is 304 feet,
2 side + base = 304
2 [7/2 base] + base = 304
8 base = 304
base= 304 / 8
base = 38 feet
Thus, the required base of the isosceles triangle is given as 38 feet.
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find the values of x and y
Answers
Answer:
x = 79 y = 22
Step-by-step explanation:
x would be the same as the other side so 79 * 2 would be 158. A whole triangle is 180. 180 - 158 = 22
Christine has her own dog-walking business. She charges her customers $20 per day to walk their dog.
Make a table to show how much she earns for walking 1 to 8 dogs.
Please help me !
Answers
Answer:
Number of dogs (x) | Amount charged to walk a dog (y)
1 | 20
2 | 40
3 | 60
4 | 80
5 | 100
6 | 120
7 | 140
8 | 160
Step-by-step explanation:
Charge for walking a dog = $20 per dog
Number of dogs = x
Amount charged to walk a dog in a day = y
Unit rate = 20
Equation to represent this is: y = 20x
Let's use this to form a table for walking 1 to 8 dogs:
For 1 dog (x):
y = 20(1) = $20
For 2 dogs (x):
y = 20(2) = $40
For 3 dogs(x):
y = 20(3) = $60
For 4 dogs:
y = 20(4) = $80
And so on till we get to tl8 dogs.
This, we should have the following table:
Number of dogs (x) | Amount charged to walk a dog (y)
1 | 20
2 | 40
3 | 60
4 | 80
5 | 100
6 | 120
7 | 140
8 | 160
The doctor prescribes Sam a 140 ml bottle of medicine with the instructions to take 5 ml twice a day. How long does the medicine last? Show your solution
Answers
Answer:
14 days
Step-by-step explanation:
14
If a man walks at the rate of 3 feet per second, how many minutes will it take him to walk 5760 feet?
Answers
Answer:
32 minutes
Step-by-step explanation:
There are 60 seconds in a minute
That means we will need to know how many feet he walks in a minute
So we would do 3 x 60 which equals 180 so he walks 180 ft per miute
Now we need to figure out how many minutes it took for him to walk 5760 ft.
So we would do 5760 ÷ 180 which equals 32
So the aswer is 32 minutes for him to walk 5760 ft.
Hope this helps
What's two numbers that total 26 and have a difference of 6
Answers
Answer:
3?
Step-by-step explanation:
i will give brainliest and also 10$
Answers
add 90 because the right angle and 45 which then equals 135
180-135
45
i may be wrong but i think so
33.85 or 32.75 sorry if I am wrong
Step-by-step explanation:
for this one you have you multiply 17 by itself like this 17x17=289 but you also have to do it with the 28 to like this 28x28=784, now what you do it add up the 289+784=1,073 then you square root 1,073 which gives you 32.75 round it to the nearest tenth of needed so your will be between 33.85 or 32.75
AUVW - APOR
W
63
U
V
77
P
66
R
?
2
Q
SOMEONE PLS HELP.
Answers
Answer:
x = 54
Step-by-step explanation:
Since both triangles are similar, therefore,
[tex] \frac{UV}{PQ} = \frac{VW}{QR} [/tex]
[tex] \frac{77}{66} = \frac{63}{x} [/tex]
[tex] \frac{7}{6} = \frac{63}{x} [/tex]
Cross multiply
[tex] 7*x = 63*6 [/tex]
[tex] 7x = 378 [/tex]
Divide both sides by 7
x = 54
Please help thank you
Answers
Answer:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
How to convert 2 years 4 months to years
Answers
Answer:
2 1/3 years
Step-by-step explanation:
4 months = 1/3 years
2 + 1/3 = 2 1/3 years
Answer:
2.25 years
Step-by-step explanation:
Please help this question finding a side on a triangle
Answers
Answer:
The side of the hypotenuse is 12.233 centimeters.
Step-by-step explanation:
The triangle presented in the figure represents a right triangle, we know an angle and a leg adjacent to such angle and we need to determine the length of the hypotenuse, which is found by this trigonometric relation:
[tex]\cos 56^{\circ} = \frac{7.4\,cm}{x}[/tex] (1)
Where [tex]x[/tex] is the length of the hypotenuse, measured in centimeters.
Then, we clear the variable within (1):
[tex]x = \frac{7.4\,cm}{\cos 56^{\circ}}[/tex]
[tex]x = 13.233\,cm[/tex]
The side of the hypotenuse is 12.233 centimeters.
Describe, in words, how the figure at the right was translated.
Answers
Answer:
8 up, 6 left
Step-by-step explanation:
Locate any point from triangle A and go up 8 steps to get on the same level as triangle A'. Then, move to the left 6 steps.
The graph translated 6 unit left and 8 unit upward.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, A figure "A" that translated at different position in cartesian plane.
Since, A translation is when a geometric figure slides up, down, left or right on the coordinate plane. The figure moves its location, but doesn't change its orientation. It also doesn't change its size or shape.
Thus, we can observe only one point on the figure and calculate the movement of the figure.
Lets focus on the left bottom corner of the figure.
It moves from the coordinates (1, -5) to the coordinates ( -5, 3)
Since Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis
So, we can say it translated to the lefty by 6 unit.
Same it goes with vertical translation.
Therefore, The graph translated 6 unit left and 8 unit upward.
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PLSSS HELP ASAPPPP I BEG
MARKI BRAINLIST AND GIVING POINTS
Answers
Answer:
b = 34
m = 5
f(t) = 5x+34
Step-by-step explanation:
f(0) = 34, so that is its y intercept.
f(t) contains (0,34) and (8,74), which can be used to find the slope:
[tex]\frac{74-34}{8-0}=\frac{40}{8}=5[/tex]
Please solve if you know no trolls please im desparate
Please if you can answer any question or if all if you can.
8) Tayna made a mistake in her work. Identify the mistake and explain how she could fix the mistake. *
How many degrees are there in the "Department Store" angle? *
How many degrees are there in the "Gas Station" angle? *
Answers
Answer:
Department Store:
7(18.75)+8= 139.25
Gas Station:
18.75+22= 40.75
Step-by-step explanation:
The mistake is 7x+8+x+22 should not equal 90. It should equal 180 degrees because the two angles are supplementary angles. (It forms a straight line)
Correct equation and how to solve for X:
7x+8+x+22=180
8x+30= 180
8x= 150
x=18.75
Department Store:
7(18.75)+8= 139.25
Gas Station:
18.75+22= 40.75
F(x)=(x-7)^2-64
Please help
Answers
Answer:
x-intercepts/ roots= (-1,0), (15,0)
f(0)= -15 (y-intercept)
Axis of symmetry: x = 7
Vertex: (7, -64)
Domain: All real numbers
Range: [-64, infty)
A principal of $7000 is invested in an account paying an annual rate of 7%. Find the amount in the account after 5 years if the account is compounded semiannually, quarterly, and monthly. (a) The amount in the account after 5 years if the account is compounded semiannually is? (Round to the nearest cent.)
Answers
Answer:
$2,874.19
Step-by-step explanation:
Hope this helps
Which graph represents the solution to this inequality? 16x-80x<37+27
Answers
Answer:
The answer for this would be B.
in the figure below explain why line p is or isn't parallel to line q
Answers
Answer:
Step-by-step explanation:
If the lines were parallel the angle measruing 72 and the angle measuring 109 would add up to 180 degrees(corrosponding and theroum ,sum of angles on line)
1/3 of 5/8 as a fraction
Answers
Answer: how are you doing this tho
Step-by-step explanation:
The 1/3 of 5/8 as a fraction is 5/24 after applying the arithmetic operation the answer is 5/24.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
1/3 of 5/8 as a fraction
Let x be the fraction:
x = 1/3 of 5/8
Or
x = (1/3)(5/8)
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
After multiplication:
x = 5/24
Thus, the 1/3 of 5/8 as a fraction is 5/24 after applying the arithmetic operation the answer is 5/24.
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Divide. Enter your answer as a fraction in simplest form.
1/5 divided by 11/15
Answers
A srtuv
B srvut
C vrust
D rsvut
Answers
Answer:
B. srvut
Step-by-step explanation:
To name a polygon, or any shape, remember that you must name it so that each angle is in order. Basically, do not go from angle s to angle u, and instead go to angle stu or srvu.
Hope this helps :)
1:the range
2:positive interval
3:increasing interval
4:maximum point
5:domain
6:decreasing intveral
7: negative interval
Answers
Step-by-step explanation:
1:the range
2:positive interval
3:increasing interval
4:maximum point
5:domain
6:decreasing intveral
7: negative interval
Answer:
As per the graph we have:
1: the range
[-4, +∞)2: positive interval
(-∞, 1) ∪ (5, +∞)3: increasing interval
(3, +∞)4: maximum point
Undefined5: domain
x = (-∞, +∞)6: decreasing interval
(-∞, 3)7: negative interval
(1, 5)17
Select the correct answer from the drop-down menu.
A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as
x+2x+6 < 50, where x represents the smaller number.
From the set {13, 14, 15, 16, 17), the values of x for which the inequality holds true are
Reset
Next
Answers
Answer:
13 and 14
Step-by-step explanation:
From the inequality
x + 2 x + 6 < 50
we work out the answer for x isolating it on one side of the inequality as shown below
3 x + 6 < 50
3 x < 50 - 6
3 x < 44
x < 44/3 ≅ 14.6666...
Therefore, select from the set the numbers: 13 and 14.
Tom saves 50% of his paycheck. If his
pay is $148, how much will he save?
Answers
Answer:
triangllllllllllllllllllllllllllllllllllllleeeee
Step-by-step explanation:
Answer:
$74
Step-by-step explanation:
50% means he saves half of his paycheck
148 ÷ 2 = 74
Thus, he saves $74 from his paycheck