Answer:
The rate charged by first mechanic per hour= x =$85
The rat charged by second mechanic per hour =y = $70
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?
Solution
Let
x= hourly rate of the first mechanic
y= hourly rate of the second mechanic
Derive two equations to solve for the two unknowns
10x + 15y = 1900 (1)
x + y = 155 (2)
From (2)
x + y = 155
x=155-y
Substitute x=155-y into (1)
10x + 15y = 1900
10(155-y) + 15y =1900
1550 -10y + 15y =1900
5y =1900-1550
5y=350
Divide both sides by 5
y= 70
Substitute y=70 into (2)
x + y = 155
x + (70) =155
x=155 - 70
= 85
x= 85
The rate charged by first mechanic per hour= x =$85
The rat charged by second mechanic per hour =y = $70
For each of the following paralellogram calculate the unknown angles marked. x, y and z
Answer:
x = 50°, y = z = 40°
Step-by-step explanation:
x = 50° ( Alternate angle )
z = 180° - (110 + 30)° = 180° - 140° = 40° ( sum of angles in Δ )
y = z = 40° ( Alternate angles )
Find the graph of the inequality y<-1/5X+1.
Answer:
Please refer to attached image for the graph of inequality.
Step-by-step explanation:
Given the inequality:
[tex]y<-\dfrac{1}{5}x+1[/tex]
To graph this, first let us convert it to corresponding equality.
[tex]y=-\dfrac{1}{5}x+1[/tex]
As we can see that the above equation is a linear equation in two variables so it will be a straight line.
Now, let us find at least two points on the above equation so that we can plot them and then extend it to get the complete graph.
Two points that can be easily found, are:
1st put [tex]x = 0[/tex] , [tex]y=-\frac{1}{5}\times 0+1 =1[/tex]
So one point is (0, 1 )
Now, put y = 0,
[tex]0=-\frac{1}{5}\times x+1\\\Rightarrow 1=\frac{1}{5}\times x\\\Rightarrow x = 5[/tex]
Second point is (5, 0)
Let us plot the points on the graph and extend the straight line.
Now, we know that it is an inequality, the are will be shaded.
As there is no equal to sign in the inequality, so the line will be dashed.
Let us consider one point and check whether that satisfies the inequality or not.
If the point is satisfied in the inequality, we will shade that area towards the point.
Let us consider the point (0, 0).
0 < 0 +1
Point is satisfied.
Please refer to the attached image for the graph of given inequality.
i need help with this question
Answer:
1000ml
Step-by-step explanation:
4 days she drank ½ of the bottle
so she drank ⅛ l of juice everyday
so
1000ml is the answer
In ΔABC,if a=6cm,b=5cm and c=4cm.find the value of ∠A.PLZ solve it fast plz help me out of it it's urgent
Answer:
the value of angle A is 82.819°
PLEASE HELP!! Find the coordinates.
Answer:
Option (D)
Step-by-step explanation:
Coordinates of the points J, E and V are,
J → (-4, -5)
E → (-4, -3)
V → (-1, -1)
This triangle is translated by the rule [tex]T_{<2,4>}[/tex] given in the question.
Coordinates of the image will follow the rule,
(x, y) → [(x + 2), (y + 4)]
following this rule coordinates of the image triangle will be,
J(-4, 5) → J'(-2, -1)
E(-4, -3) → E'(-2, 1)
V(-1, -1) → V'(1, 3)
Therefore, points given in the option (D) will be the answer.
p^2/2+2/q^2)(p^2-2/q^2)
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]( \frac{p^{2} }{2} + \frac{2}{2_{q} }) ( p^{2} - \frac{2}{2_{q}})[/tex]
[tex]= \frac{\frac{1}{2}p^{4}q^{4} + p^{2} q^{2} - 4 }{q^{4}}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
ree
Step-by-step explanation:
Please answer this question now
Answer:
298.3 square centimeters
Step-by-step explanation:
We are given
Slant height (l)= 14cm
Radius (r)= 5cm
Since we are given the slant height ,
the formula for surface area of a cone =
πrl + πr²
πr(l + r)
π = 3.14
Hence,
3.14 × 5(14 + 5)
3.14 × 5(19)
= 298.3 square centimeters
A meter is a unit of length approximately equal to 39.37 inches. If someone is 1.64 meters tall, what is his or her approximate height in inches?
Answer:
64.5668 inches tall
Step-by-step explanation:
If you set up a proportion, you would have to do 1.64 times 39.37, which would equal 64.5668 inches.
Just need the final answer
Answer:
[tex]\boxed{\sf a) \ 15.9}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trig functions to solve for x.
cos θ = adj/hyp
cos(51) = 10/x
x = 10/cos(51)
x = 15.89015729
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Answer:
a) 22:25 is the earliest time
b)15 min
Step-by-step explanation:
Since the time is in military time you must add the time it takes her to get to the bus stop to 12. then the rest is self explainitory....
10:10(standard) = 22:10 (military)
22:10 -> 15min-> 22:25
Answer:
a) 22:25 is the earliest time
b)15 min
Because
Since the time is in military time you must add the time it takes her to get to the bus stop to 12. then the rest is self explainitory....
Convert the radian measure to degree measure. Use the value of π found on a calculator, and round answers to two decimal places. nine pi divided by twelve
Answer:
135°
Step-by-step explanation:
π in radian = 180°
∴ 9π in radians = 9 X 180° = 1620°
Then 9π/12 = 1620°/12 = 135°
if the circumference of two circle are in the ratio 2:3, then their areas are in the ratio of
Answer:
4:9
Step-by-step explanation:
To take the scale factor from distance to area, we square it
2:3 distance
Square each term
2^2 : 3^2 area
4:9
3-2y-1+5x^2-7y+7+4x^2
Answer: Hi!
The only thing we can do to simplify the equation is combine like terms.
5x^2 + 4x^2 = 9x^2
-2y - 7y = -9y
3 - 1 + 7 = 9
Our equation now looks like this:
9x^2 - 9y + 9
We have nothing left to simplify, so we're done!
Hope this helps!
The sum of 2 numbers is 250. One of them is greater than 150. Which of these is definitely true about the other number? a) It is equal to 100. b) It has to be less than 100. c) It has to be greater than 100. d) It has to be a number between 150 and 250. Please answer fast and do explain how you got the answer...
Answer:
b
Step-by-step explanation:
Answer:
d) it has to be greater than 150 and 250
Step-by-step explanation:
It says in the question it is greater than 150. So the number will be between 150 and 250.
Mark it as Brainliest pls
Hope it helps!!!
3. A doctor treated 2,000 patients over a period of time. If he worked for
5 hours a day and spent 15 minutes pach patient, how many days
did the doctor spend to treat all the patients?
Answer:
100 days
Step-by-step explanation:
the doctor works 5 hrs per day, which means 20 patients per day, in 100 days he will be able to treat 2000 patients
Question 3 of 10
True or false? In a two-column proof, the right column states your reasons.
A. True
OB. False
SUBMIT
Answer:
A- True
Step-by-step explanation:
If you search a picture of the graph then you will see it as well!!! Hope this helps!!!!
A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand. Law of cosines: A triangle is created between a lifeguard stand and 2 floating docks. The distance from the lifeguard stand to one dock is 750 meters, and the distance to the second dock is 650 meters. The angle between the 2 sides is 60 degrees. Rounded to the nearest meter, what is the distance between the docks? Round to the nearest meter. 589 meters 705 meters 792 meters 861 meters
Answer:
705 meters
Step-by-step explanation:
[tex]cos~60=\frac{650^2+750^2-d^2}{2 \times 650 \times 750} \\2 \times 650 \times 750 \times \frac{1}{2}=50^2(13^2+15^2)-d^2 \\487500=2500(169+225)-d^2\\487500=2500(394)-d^2\\487500=985000-d^2\\487500-985000=-d^2\\d^2=497500\\d=\sqrt{497500}\\or~d\approx705.337 \approx 705~meters[/tex]
Answer:
7 0 5 M E T E R S !!!!!
Step-by-step explanation:
a rectangle is 12 in wide and 18 in tall.if it is reduce to a height of 3 inches, then how wide will it be?
Answer:
2 in
Step-by-step explanation:
18/3=6 , 6 is the scale factor
12/6=2
Answer:
width= 2
Step-by-step explanation:
18 inches is the original height and we are now reducing that to 3 inches.
In order to do that, we have to divide 18 by 3 which equals 6.
Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which equals 2.
Your final answers should be: width= 2
Given [tex]f(x)=-x^{2} +6x-11[/tex], find [tex]f(x-3)[/tex]
Answer:
See below.
Step-by-step explanation:
[tex]f(x)=-x^2+6x-11\\f(x-3)=-(x-3)^2+6(x-3)-11\\f(x-3)=-(x^2-6x+9)+6x-18-11\\f(x-3)=-x^2+6x-9+6x-29\\f(x-3)=-x^2+12x-38[/tex]
What is a "real number"
Answer: are numbers which include all the rational numbers, such as -3 which is an integer and the fractions such as 5/4, and all the irrational numbers, such as √7, and π
Find all of the missing angles of sides of the triangle below. Note that side lengths are in centimeters. Show and/or explain your work thoroughly and round answers to the nearest hundredth if needed.
Answer:
c=19.21
<C=90
<B=38.66°
<A=51.34
Step-by-step explanation:
12²+15²=c²
144+225=c²
c=19.21
<C=90
For angle B, the sinB=Opposite over Hypotenuse
sinB=12/19.21
sinB=0.62467
B=sin^-1(0.62467)
<B=38.66°
To find A, 180-90-38.66
<A=51.34
how to do this question plz answer me step by step plzz plz plz plz plz I really struggling
Answer: 48
There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.
========================================================
1 min = 60 sec
30 min = 1800 sec (multiply both sides by 30)
1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")
The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.
There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.
--------------------
Extra info:
If you're curious about finding the more accurate value, then you could follow these steps
1 prize = 2014 seconds
x prizes = 86400 seconds (number of seconds in a full day)
1/x = 2014/86400
1*86400 = x*2014
86400 = 2014x
2014x = 86400
x = 86400/2014
x = 42.8997020854021
Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.
SOS...Complete the following proof. 25 POINTS!!!
Answer:
See below
Step-by-step explanation:
Given:
AC ≅ CE
To Prove:
ΔABC ≅ ΔEDC
Proof:
Statements | Reasons
ΔABC ⇔ ΔEDC |
AC ≅ CE | Given
∠ACB ≅ ∠ECD | Vertical Angles are congruent
∠BAE ≅ ∠DAE | Alternate Interior Angles are Congruent
ΔABC ≅ ΔEDC | S. A . A Postulate
[Hence Proved]
Line m and point P are shown below. Part A: Using a compass and straightedge, construct line n parallel to line m and passing through point P. Leave all construction marks. Part B: Explain the process that you used to construct line n.
Answer:
see the attached
Step-by-step explanation:
In the attachment, we will refer to the circles, bottom-to-top, as circles 1, 2 and 3. The black points of intersection, bottom-to-top, will be referred to by the letters A, B, C, D. The transversal line through the white point (W) and pink point (P) will be line q.
Step 1. Draw line q through point P so it intersects line m at some convenient point. Label that point W.
Step 2. Choose an arbitrary radius for your compass. Here, we have chosen it to be the length WB. It happens to be less than half the length of WP, but that is not a requirement.
Step 3. Draw an arc of the chosen radius centered at W and intersecting line q and line m. Label the intersection points A (on line m) and B (on line q). These intersection points are on circle 1.
Step 4. Draw an arc of the same radius centered at P. It should be a long enough arc that it would intersect the proposed line parallel to m. Label the intersection point on line q with label C. This intersection point is on circle 3.
Step 5. Adjust the compass width (radius) to the distance from A to B. This is the radius of circle 2.
Step 6. Draw an arc centered at C so that it intersects the arc of Step 4. This is circle 2, and you want it to intersect circle 3. Label that point of intersection D.
Step 7. Draw line PD parallel to m.
_____
The point of the construction is to create congruent alternate interior angles AWB and CPD, so that lines AW and PD are parallel.
The table shows the annual profits (in thousands of dollars) of a county fair from 2013 to 2016. What must the 2017 profit be (in hundreds of dollars) to break even over the five-year period?
Answer:
8 hundred dollars
Step-by-step explanation:
The break even value means zero profit or loss over the five years period. So if 2017 profit is x, then we get:
2.5 + 1.4 - 3.3 - 1.4 + x = 0x - 0.8 = 0x = 0.8 thousands of dollars x= 800 dollarshow many are 7 raised to 2 ???
Answer:
[tex]\huge \boxed{49}[/tex]
Step-by-step explanation:
7 raised to 2 means the base 7 is to the power of 2.
[tex]7^2[/tex]
7 is squared or multiplied by itself.
[tex]7^2 =7 \times 7=49[/tex]
type the correct answer in the box. use numerals instead of words. what value of x makes this equation true? x/6 - 7 = -4
[tex]\dfrac{x}{6}-7=-4\\\dfrac{x}{6}=3\\x=18[/tex]
Answer:
x = 18
Step-by-step explanation:
x/6 - 7 = -4
Add 7 to each side
x/6 - 7+7 = -4+7
x/6 = 3
Multiply each side by 6
x/6 *6 = 3*6
x = 18
Julio is paid 1.3 times his normal hourly rate for each hour he works over 31 hours in a week. Last week he worked 42 hours and earned $548.13. Enter and solve an equation to find Julio's normal hourly rate, r. Complete the explanation how you know that your answer is reasonable.
Step-by-step explanation:
Answer:
$12.10 / hour
Step-by-step explanation:
42 - 31 =
1.3(11)r + 31r = 548.13
14.3r + 31r = 548.13
45.3r = 548.13
r = 12.1 / hour
if S( 1, 2, 3, 4, 5,6 ) find the probability that a number chosen is more than 4
[tex]|\Omega|=6\\|A|=2\\\\P(A)=\dfrac{2}{6}=\dfrac{1}{3}[/tex]
Answer:
1/3
Step-by-step explanation:
The list of sample space's elements: {1, 2, 3, 4, 5, 6}
The number of elements in sample space: 6
The list of elements belonged to the event "choosing the number larger than 4": {5, 6}
The number of elements in the event: 2
Hence, the probability of event "choosing a number larger than 4":
P = number of event's elements/number of sample space's elements
= 2/6
= 1/3
What is the maximum number of pages the report can have so that it can be completely stored on a USB drive that holds 4 \cdot 10^6 \text{ KB}4⋅10 6 KB4, dot, 10, start superscript, 6, end superscript, start text, space, K, B, end text?
Answer:
2,300,000pages report.
Step-by-step explanation:
Given a USB drive with memory of 4.6*10⁶KB, in order to know the maximum number of pages a report can have so that it can be completely stored on the drive, the conversion factor must be used.
We must first understand that 1 page of a document uses up approximately 2kB of the storage.
Since 2kB = 1page
4.6*10⁶KB = x page
Cross multiply
2kB * x = 4.6*10⁶KB * 1
2x = 4.6*10⁶
x = 4.6*10⁶/2
x = 2.3*10⁶
x = 2,300,000
Hence the maximum number of pages that the report can have so that it can be completely stored on a USB drive that holds 4.6*10⁶KB is approximately 2,300,000pages report.