Answer:
[tex]y = \frac{2}{3} x + 2[/tex]
Step-by-step explanation:
Start by finding the slope of the given line.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of given line
[tex] = \frac{5 - ( - 1)}{ - 2 - 2} [/tex]
[tex] = \frac{5 + 1}{ - 4} [/tex]
[tex] = \frac{6}{ - 4} [/tex]
[tex] = - \frac{3}{2} [/tex]
A perpendicular bisector cuts through the line at its midpoint perpendicularly.
The product of the slopes of two perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
[tex] - \frac{3}{2} m = - 1[/tex]
[tex]m = - 1 \div ( - \frac{3}{2} )[/tex]
[tex]m = - 1 \times ( - \frac{2}{3} )[/tex]
[tex]m = \frac{2}{3} [/tex]
[tex]y = \frac{2}{3}x + c[/tex], where c is the y-intercept.
To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.
[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]
Midpoint of given line
[tex] = ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )[/tex]
[tex] =( \frac{0}{2} , \frac{4}{2} )[/tex]
= (0, 2)
[tex]y = \frac{2}{3} x + c[/tex]
When x= 0, y= 2,
2= ⅔(0) +c
2= 0 +c
c= 2
Thus, the equation of the perpendicular bisector is [tex]y = \frac{2}{3} x + 2[/tex].
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
Cassie wants to purchase a pair of binoculars that is on sale for $155.75. The sales tax rate in his county is 7%.
Calculate the amount of sales tax Cassie will pay on the purchase. Round to the nearest cent if necessary.
sales tax: $
Listen to the complete question
Part B
Fill in the blank question.
How much will Cassie pay in all for the pair of binoculars after sales tax is included? Round to the nearest cent if necessary.
total cost: $
Answer:
$10.12
Step-by-step explanation:
Step one:
given data
we are told that the cost of binoculars is $155.75
and also the sales tax is 7%
Step two:
We want to first solve for the sales tax which is 7% of $155.75
=7/100* 155.75
=0.070*155.75
=10.12
Cassie will pay a tax of $10.12
Also Cassie will pay a total amount of
= 155.75+10.12
=$165.87
A bakery asks 75 customers to vote for a new bagel flavor. Onion flavor receives 33 votes. Cheddar flavor receives 42 votes. Use this information to answer the questions below. What fraction shows the proportion of customers who voted for cheddar flavor? What percent of customers voted for cheddar flavor?
Using proportions, it is found that:
The fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]56% of customers voted for cheddar flavor.A proportion is the number of desired outcomes divided by the number of total outcomes.A percentage is the proportion multiplied by 100%.In this question, 42 out of 75 customers voted for the cheddar flavor, hence:
[tex]p = \frac{42}{75}[/tex]
That is, the fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]
The percentage is:
[tex]\frac{42}{75} \times 100\% = 56\%[/tex]
56% of customers voted for cheddar flavor.
To learn more about proportions, you can take a look at https://brainly.com/question/24372153
Solve |2x - 5| = 4.
a. {x | x = 0.5 or x = 4.5}
b. {x | 0.5 < x < 4.5}
c. {x | x = -4.5 or x = 4.5}
Sharon wants to buy a shirt that cost $60. The sales tax is 5%. How much is the sales tax. What is her total cost for the shirt?
A local rectangular shaped pool used by lap swimmers has dimensions 25 yd by 26 yd and is 5.1 feet deep. Find the cost for filling the pool if the city charges $1.50 per 1000 gallons. Use the conversion 1 gallon = 0.134 cubic ft.
Round your answer to two decimal places.
The cost for filling the pool if the city charges $1.50 per 1000 gallons is $333.97
Given:
Length = 25 yd
width = 26 yd
Height = 5.1 ft
convert yard to feet
25 yd = 75 ft
26 ft = 78 ft
Volume of the pool = length × width× height
= 75 × 78 × 5.1
= 29,835 cubic ft
1 gallon = 0.134 cubic ft.
222,649.3 gallon = 29,835 ft
charges per 1000 gallon = $1.50
Total charges = 222,649.3 gallon / 1000 gallon × $1.50
= 222.6493 × 1.50
= 333.97395
Approximately,
$333.97
Therefore, the cost for filling the pool if the city charges $1.50 per 1000 gallons is $333.97
Learn more about volume:
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Which function results in f(x)=13?
Answer:
The answer is B
Step-by-step explanation:
plug 2 into x to see
A.
x^2 + 8
2^2 + 8
4 + 8 = 12
B.
3x^2 + 1
3(2)^2 + 1
3(4) + 1
12 + 1 = 13
C.
2x^3 + 5
2(2)^3 + 5
2(8) + 5
16 + 5 = 21
D.
x^2 + x
2^2 + 2
4 + 2 = 6
what is linear independent vector
Help, please
Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made.
−5x − 25 = 78
Step 1: −5x − 25 − 25 = 78 − 25
Step 2: −5x = 53
Step 3:negative five times x over negative five = fifty-three over negative five
Step 4: x = negative fifty-three over five
Answer:
The first step.
Step-by-step explanation:
expand and simplify 3(5x+1)+5(5x-4)
Answer:
40x-17
Step-by-step explanation:
SOMEBODY PLZ CHECK IF MY ANSWER ARE CORRECT NO LINKS PLZ AND THANK YOU
Answer:
the first one's right i think
Help me with my math please
Step-by-step explanation:
1 _21:00_ , _22:10_, 1:10
2. 1:20
3. 18:00
4. 21:35
1. 21:00, 22:10, 1 hr and 10 minutes
2. 20 minutes
3. 18:40
4. 21:35
Helppp it’s due today
Answer:
128
Step-by-step explanation:
Please help with this question please and thank you
Answer:
I need help with this too!!!
Step-by-step explanation:
Answer:
what does it mean?
Step-by-step explanation:
I do not understand.
PLS HELP!!!!!! (again! XP)
Express each of these numbers, as a product of two fractions 2/25
The base of a triangle is 4 ft more than the height. If the area is 30ft2, find the base and the height.
Answer:
Base = 10 ft. and the height = 6.
Step-by-step explanation:
Area of triangle = 1/2bh
base is 4 + h ⇔ base = 4 + h
height = h
Using the formula for the area of triangle substitute into the formula the given facts.
A = 1/2bh
30 = 1/2(4 + h) (h)
30 = 1/2(4h + h²) Multiply both sides by 2
60 = 4h + h²
-60 = -60 Add -60 to both sides
0 = h²+ 4h -60
(h + 10)(h - 6) = 0 Factor
h + 10 = 0 h - 6 =0
h = -10 h = 6
reject any negative number and use the positive answer for h.
So h = 6 and the base = 4 + 6 ; base = 10
Customers at Musicland can buy 4 DVDs for $15. How many DVDs can April buy at Musicland with $75?
Answer:
20 I believe because 15 divided by 4 is 3.75 so I then divided 75 by 3.75 giving me 20:)
One angle in a complementary pair of angles measures 3 times the other angle.
What is the measure, in degrees, of the
smaller angle?
Answer:
22.5 degrees
Step-by-step explanation:
Complementary angles add up to be 90 degrees. You can model the simple equation [tex]x+3x=90[/tex] where is x is the small angle and 3x is the large angle.
[tex]4x=90\\x=22.5[/tex]
the smaller angle is 22.5 degrees
Which statement is generally true about retirement?
A. Your income will increase, while your expense will stay the same.
B. Your income will decrease, while your expenses will increase.
C. Your income will increase, while your expenses will decrease.
D. Your income will decrease, while your expenses will stay the same.
The general statement that is true about retirement is B. your income will decrease, while your expenses will increase.
Retirement is the leaving of one's of occupation. This means you cease to be involved in active service in a job or occupation especially when one is considered old and of retirement age.
During retirement, retirement benefits and pension are usually made available to retirees. However, one's income will come to a decline which makes most people scared of retirement. Keeping up with the standard of living they are used to becomes difficult as income to sustain such may not be available.
Therefore, the general statement that is true about retirement is B. your income will decrease, while your expenses will increase.
Learn more about retirement on:
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Answer:
It's B
Step-by-step explanation:
Just took it
Melissa has 120 kilograms of rice. Her mother sold 105 kilograms. What percent of the rice was sold? with solution :D please
Answer:
225
Step-by-step explanation:
po ang answer ko
please comment if I'm wrong
Which expression is equivalent to 53p + (16p + 7p)
Answer:
u777766665655566667777777777777
76p is the equivalent expression of 53p + (16p + 7p)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 53p + (16p + 7p)
Fifty three times of p plus sixteen p plus seven p.
In the given expression p is the variable and plus is the operator.
We need to find the equivalent expression.
Equivalent expressions are expressions that work the same even though they look different.
53p + (16p + 7p)
76p
Hence, 76p is the equivalent expression of 53p + (16p + 7p)
To learn more on Expressions click:
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#SPJ6
Help Meh I need it SOON
Step-by-step explanation:
the option you chose (<C~=<Y) is absolutely correct.
Solve the inequality below for z.
8z+3>3z-17
A.z>-4
B.z<-14/5
C.z<-4
D.z>-14/5
Therefore, the solved inequality is z > -4.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
need help with solving this please
Answer:
3/2
Step-by-step explanation:
Since the shape is an equilateral triangle, all the angles are equal measure, 60° and all the sides are also of equal measure that was given, root3. So half of the triangle has length (root3)/2. The perpendicular drawn in the interior is also an angle bisector. The triangles created are 30°-60°-90° triangles. The sides of this special right triangle are in the ratio
s : 2s : sroot3
The longest side of the 30-60-90 triangle is given. The shortest side is half the length of the longest side. The length of the long leg is the short leg × root3
In this diagram the short leg is (root3)/2 .
(root3)/2 × root3 = 3/2
See image.
Let F(x)=∫
t−3
t
2+7
for − ∞ < x < ∞
x
0
(a) Find the value of x where F attains its minimum value.
(b) Find intervals over which F is only increasing or only decreasing.
(c) Find open intervals over which F is only concave up or only concave down.
(a) It looks like you're saying
[tex]\displaystyle F(x) = \int_0^x (t - 3t^2 + 7) \, dt[/tex]
Find the critical points of F(x). By the fundamental theorem of calculus,
F'(x) = x - 3x² + 7
The critical points are where the derivative vanishes. Using the quadratic formula,
x - 3x² + 7 = 0 ⇒ x = (1 ± √85)/6
Compute the second derivative of F :
F''(x) = 1 - 6x
Check the sign of the second derivative at each critical point.
• x = (1 + √85)/6 ≈ 1.703 ⇒ F''(x) < 0
• x = (1 - √85)/6 ≈ -1.370 ⇒ F''(x) > 0
This tells us F attains a minimum of
[tex]F\left(\dfrac{1-\sqrt{85}}6\right) \approx \boxed{-6.080}[/tex]
(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.
• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0
• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0
• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0
This tells us that
• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)
• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)
(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :
F''(x) = 1 - 6x = 0 ⇒ 6x = 1 ⇒ x = 1/6
Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.
• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0
• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0
This tells us that
• F(x) is concave up over (-∞, 1/6)
• F(x) is concave down over (1/6, ∞)
please help with this!!!!
Answer:
6311000
Step-by-step explanation:
The first thing we do is calculate the total amount of people in both states. 6.89 x10 raised to the 6th power is equal to 6890000. Then we multiply 5.79 by 10 to the fifth power, which equals to 579000. Then we subtract the numbers, and get 6311000. They want you to answer in standard notation, which is the regular way of writing numbers such as 10, instead of 10^1.
The difference in population
[tex] = (6.89 \times {10}^{6} ) - (5.79 \times {10}^{5} ) \\ = (6.89 \times 10 \times {10}^{5} ) - (5.79 \times {10}^{5} ) \\ = (68.9 \times {10}^{5} ) - (5.79 \times {10}^{5} ) \\ = (68.9 - 5.79) \times {10}^{5} \\ = 63.11 \times {10}^{5} [/tex]
Answer:
[tex]63.11 \times {10}^{5} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Simplify fully
x2 - 9
3x2 + 8x - 3
+
X-3
x+2
(-3x³+2x²+4x+24) (x-2)
---------------------------------
8x
For her phone service, Kala pays a monthly fee of $24, and she pays an additional $0.07 per minute of use. The least she has been charged in a month is $118.64.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Answer:
m=1352
Step-by-step explanation:
(118.64-24)/0.07=m
I don’t understand, please help
Answer:
cosA=root8/3 is the answer
The store is 7⁄8 of a mile away from your house. You walked 1⁄5 of a mile towards the store before getting on the bus. If the bus went directly to the store, how many miles long was the bus ride?
LAST ATTEMPT MARKING AS BRAINLIEST!! ( graph the image of the figure using the dilation given )
Step-by-step explanation:
follow the steps in the picture. I've started it for you all you need to do is finish