Answer:
<QRT = 130°
X = 135
<QRS = 180°
Step-by-step explanation:
1. A straight line is 180°.
180° - 50° = 130°
<QRT = 130°
2. x - 5 = 130°
130° + 5° = 135°
3. As stated before, a straight line is 180°.
Bobby drives his truck at a rate of 50 to 60 miles per hour.
a. Approximately how far can Bobby drive in 2, 3, 4, and 5 hours?
b. Bobby plans to take an 8-hour trip, which will include a 1-hour stop for
lunch. What is a reasonable distance for Bobby to drive?
a. 2 hours = 100 to 120m
3 hrs = 150 to 180m
4 hrs = 200 to 240m
5 hrs = 250 to 300m
b. 400 to 480 miles
Bobby can drive between 50 times the number of hours and 60 times the number of hours depending on the drive duration. For an 8-hour trip with a 1-hour lunch stop, he drives for 7 hours, covering between 350 and 420 miles.
Explanation:a) Bobby's driving speed varies between 50 to 60 miles per hour. Therefore:
If he drives for 2 hours, at the minimum speed he can cover 50*2=100 miles, and at the maximum speed, he can cover 60*2=120 miles.If he drives for 3 hours, the range is between 50*3=150 miles and 60*3=180 miles.If he drives for 4 hours, the range is between 50*4=200 miles and 60*4=240 miles.And if he drives for 5 hours, the range is between 50*5=250 miles and 60*5=300 miles.b) For an 8-hour trip with a 1-hour stop for lunch, Bobby will effectively be driving for 7 hours. So, the minimum distance he could cover is 50*7=350 miles and the maximum distance is 60*7=420 miles.
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25% of the students attended the school dance. if 32 attended the dance, how many students are there in all?
Answer:
128 students in total
Step-by-step explanation:
25/100 = 1/4
1/4 = 32/ x
1 x 32
Answer:
your answer is A
Step-by-step explanation:
32 *4=128
4*25=100%
Determine and state an equation of the line perpendicular to 5x-4y=10nand passing through point (5,12).
Answer:
4x + 5y = 80
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 5x - 4y = 10 into this form
Subtract 5x from both sides
- 4y = - 5x + 10 ( divide all terms by - 4 )
y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{5}{2}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{5}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex], thus
y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation
To find c substitute (5, 12) into the partial equation
12 = - 4 + c ⇒ c = 12 + 4 = 16
y = - [tex]\frac{4}{5}[/tex] x + 16 ← in slope- intercept form
Multiply through by 5
5y = - 4x + 80 ( add 4x to both sides )
4x + 5y = 80 ← in standard form
The equation of line perpendicular to [tex]5x-4y=10[/tex] and passing through the point (5,12) is [tex]y=-\frac{4}{5}+16[/tex]
The line given in the problem is in Standard Form. The standard form of a linear equation is: [tex]Ax+By=C[/tex]
Where, if at all possible, A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.
[tex]5x-4y=10[/tex]
The slope of an equation in standard form is: [tex]m=-\frac{A}{B}[/tex]. Substituting the values from the equation in the problem gives:
[tex]m=-\frac{5}{(-4)} =\frac{5}{4}[/tex]
Let's call the slope of the line perpendicular to this line [tex]m_{p}[/tex] . The slope of a perpendicular line is:
[tex]m_{p} =-\frac{1}{m} =-\frac{4}{5}[/tex]
We can now use the point-slope formula to find the equation of the line. The point-slope formula states: [tex](y-y_{1})=m(x-x_{1})[/tex]
[tex]y-12=-\frac{4}{5} (x-5)[/tex]
[tex]5(y-12)=-4(x-5)\\5y-60=-4x+20\\5y=-4x+80\\y=-\frac{4}{5}x+16[/tex]
Therefore, the equation of line perpendicular to [tex]5x-4y=10[/tex] and passing through the point (5,12) is [tex]y=-\frac{4}{5}+16[/tex]
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Mai spends 7 3/5 hours in school each day. Her lunch period is 30 minutes long, and she spends a total of 42 minutes switching rooms between classes. The rest of her day is spent in 6 classes that are all the same length. How long is each class?
The each class is 64 minutes or 1 hour 4 minutes long.
Step-by-step explanation:
1 hour = 60 minutes.
Total time spent in school = 7 hours+3/5 hour = 7(60) + (3/5)(60) minutes.Total time = 420+36 = 456 minutes.Lunch period = 30 minutes.Time for switching classrooms = 42 minutes.Time spent in 6 classes :
Time spent in 6 classes = Total time - (lunch period + switching classes)
⇒ 456 - (30+42)
⇒ 456 - 72
⇒ 384 minutes.
The Time for each of 6 classes :
Time for each class = Time spent for all 6 classes / 6
⇒ 384/6
⇒ 64 minutes.
⇒ 1 hour 4 minutes.
The histogram shows the time Mr. Lopez’s students spent studying for the final exam.Which statement is correct about the time Mr.Lopez's students spent studying for the final exam
Answer:
Most students spent an hour or less studying for the exam.
Step-by-step explanation:
Answer:
C on edge 2020
Most students spent an hour or less studying for the exam.
Step-by-step explanation:
I just took the assignment. Hope this helps!
The lines kx + 2y = -7 and y = 2x - 5 are perpendicular to each other. Find the value of k.
Answer:
k=1
Step-by-step explanation:
1. find the negative reciprocal of the slope of y=2x-5 because that is the slope perpendicular to it.
m=2 ; negative reciprocal is 1/-2
2. isolate y in the first equation
y= kx/-2 + 7/-2
3. the only value for k that would make their slopes the same would be 1
Use the system of equations to answer the questions.
2x + 3y = 3
y = 8 - 3r
The value of y from the second equation is substituted back into the first equation. What is the resulting equation?
What is the value of x?
What is the value of y?
Answer:
the value of x and y is 3 and -1 respectively.
Step-by-step explanation:
from the question
let
2x + 3y = 3........................ equation 1
y = 8 - 3x.............................. equation 2
put y = 8 - 3x in equation 1
2x + 3y = 3........................ equation 1
2x + 3 ( 8 - 3x) = 3
2x + 24 - 9x = 3
24 - 7x = 3
24 = 3 + 7x
24 -3 = 7x
21 = 7x
divide both sides by 7
x = 3
put x = 3 in equation 2
y = 8 - 3x.............................. equation 2
y = 8 - 3 ( 3)
y = 8 -9
y = -1
therefore the value of x and y is 3 and -1 respectively.
what is the answer to 8x27383922
Answer:
219071376
Step-by-step explanation:
Answer:
219071376. Hope this helps :)
The measure of an angle is 32°. What is the measure of its supplementary angle?
The mass of an empty container is 3/10kg. When the container is half filled with water, the mass becomes 1 1/10kg. What is the mass of the container when it is completely filled with water
Answer:
1.9 kg
Step-by-step explanation:
Empty container: 3/10 kg = 0.3 kg
Container half filled: 1 1/10 kg = 1.1 kg
Mass of water that fills it halfway: 1.1 kg - 0.3 kg = 0.8 kg
Mass of water that fills it completely: 2 * 0.8 kg = 1.6 kg
Mass of container completely filled with water: 0.3 kg + 1.6 kg = 1.9 kg
plz help me asap will give brainliest and 100 points.
3. A new ice cream shop is opening up and the owners are making a large ice cream cone for display (see
picture below). What is the volume of the ice cream cone? Round your answer to the nearest hundredth of a
cubic inch. Use 3.14 to approximate pi. Show your work and explain your steps.
Answer:
167.47 cubic metres
Step-by-step explanation:
Volume of a cone is given by [tex]\frac {\pi r^{2}h}{3}[/tex] where r is radius and h is the height of the cone. Assuming a radius of 4m and height of 10 m then the volume, using 3.14 for [tex]\pi[/tex] will be
V=[tex]\frac {3.14\times 4^{2}\times 10}{3}\approx 167.47 m^{3}[/tex]
The product of four and a number
Answer:
1+4x
Step-by-step explanation:
what is the answer to 6 more than the product of five and a number decreased by one
Melinda has a scrap piece of fabric with one angle
measuring 52°. If she needs to find a complementary
angle, what angle measure does she need to cut the
next piece?
Melinda should cut the piece of fabric at an angle of______
Answer:
38
Step-by-step explanation:
Answer:
38
A right angle. A line comes out of the angle to split the angle into 52 degrees and blank.
Melinda has a scrap piece of fabric with one angle measuring 52°. If she needs to find a complementary angle, what angle measure does she need to cut the next piece?
Melinda should cut the piece of fabric at an angle of
38
°.
Step-by-step explanation:
The solution set for -18 < 5x - 3 is _____.
3 > x
-3 > x
3 < x
-3 < x
Answer:
-3 < x
Step-by-step explanation:
add the negative 3 to the other side
you get: -15 < 5x
divide by 5 on both sides
you get: -3 < x
that's the answer
write an equation of the circle with center 6.-9) and radius 10!
The equation of the given circle is [tex](x-6)^{2}+(y+9)^{2}=100.[/tex]
Step-by-step explanation:
Step 1:
The equation of a circle with its center at (h, k) and a radius of r is given by
[tex](x-h)^{2}+(y-k)^{2}=r^{2}.[/tex]
The h value is the x coordinate and the k value is the y coordinates, so (h, k) is (6, -9).
The radius is given as 10 so [tex]r =10[/tex] and [tex]r^{2} = 100.[/tex]
Step 2:
By substituting the values we know, we get
[tex](x-h)^{2}+(y-k)^{2}=r^{2} = (x-6)^{2}+(y-(-9))^{2}=10^{2}.[/tex]
So the equation of the given circle is
[tex](x-6)^{2}+(y+9)^{2}=100.[/tex]
Factor the quadratic expression completely.
-7x^2-24x-9=
Answer:
[tex] - 7 {x}^{2} - 24 - 9 \\ - 7 {x}^{2} - 21x - 3x - 9 \\ - 7x(x + 3) - 3(x + 3) \\ ( - 7x - 3)(x + 3)[/tex]
What is a proportional equation
Answer:
it is when the x and y intercept coordinates are changed by the same factor.
Step-by-step explanation:
Solve for all solutions x2=29
Answer:
x=14.5
PLEASE MARK BRAINLIST!!
Step-by-step explanation:
2x=29
Divide by 2 on both sides:
x=14.5
Answer: it should be x=14.5
Which of the following describes a pattern in the table
Im not sure it depends on the pattern? lol
The pattern described in the table is the value of b is 5 times the value of a.
What is a pattern?A pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object. A pattern has a rule that tells us which objects belong to the pattern and which objects do not belong to the pattern.
Given is a table,
a - 0 1 2 3 4
b - 0 5 10 15 20,
We can see, that the values in the b row are 5, 10, 15, 20 they are the multiple of 5
And values in row a, are 1, 2, 3, 4, we can see they are the numbers which are related to row b, in a way that, values in b are 5 times the value of a,
1 × 5 = 5
2 × 5 = 10
3 × 5 = 15
4 × 5 = 20
5 × 5 = 25
Therefore, we can say that the numbers in b are 5 times the corresponding value of the a,
Hence, the pattern described in the table is the value of b is 5 times the value of a.
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The complete question is :
Which rule describes the pattern in the table?
a 0 1 2 3 4
b 0 5 10 15 20
The value of b is 5 times the value of a.
The value of b is 5 less than the value of a.
The value of b is 5 more than the value of a.
The value of a is 5 times the value of b.
How do you put y+2x=5 into slope-intercept form?
Answer: y=-2x+5
Step-by-step explanation:
Y+2x=5
y-2x=5-2x
y=-2x+5
then graph
Answer:
y=-2 x +5
Step-by-step explanation:
Write in slope-intercept form, y=m x+b
Which expressions are equivalent to 5 x-15? Select three options.
5 (x + 15)
5 (x-3)
4 x + 3 y-15- 3 y + x
-7 y-6 x- 8 y + x
-20 - 3 x + 5 + 8 x
PLSSS help my teacher already thinks i'm going crazy!
Answer:
[tex]b) 5 (x-3)\\c) 4 x + 3 y-15- 3 y + x\\e) -20 - 3 x + 5 + 8 x[/tex]
Step-by-step explanation:
We are given the following expression in the question:
[tex]5x-15[/tex]
a)
[tex]5 (x + 15)\\=5(x) + 5(15)\\=5x + 75[/tex]
which is not equivalent to the given expression.
b)
[tex]5 (x-3)\\=5(x)-3(5)\\=5x-15[/tex]
which is equivalent to the given expression
c)
[tex]4 x + 3 y-15- 3 y + x\\=4x+x+3y-3y-15\\=5x-15\\=5(x-3)[/tex]
which is equivalent to the given expression.
d)
[tex]-7 y-6 x- 8 y + x\\=-7y-8y-6x+x\\=-15y-5x\\=-5(x+3y)[/tex]
which is not equivalent to the given expression.
e)
[tex]-20 - 3 x + 5 + 8 x\\=-3x+8x-20+5\\=5x-15[/tex]
which is equivalent to the given expression.
Simplify the expression -23 + 6
Answer:
−23+6
=−23+6
=−17
Step-by-step explanation: Mark brainliest please!
-4 1/4 divided by 1/2
Answer:
-8.5, or -8 1/2
Step-by-step explanation:
Put it into an improper fraction: -17/4
Multiply: -17/4 * 2/1 (To divide, multiply by reciprocal)
= -34/4
Simplify: -17/2, or -8 1/2
Answer:
-34/4 or -8 1/2
Step-by-step explanation:
First we want to put -4 1/4 so its all a fraction we do this by multiplying 4 to 4 and adding it to the 1 already in the fraction (We can ignore the sign and just add it to the fraction because the entire fraction is negative not just the 4). So we have -17/4
To divide fractions we use keep change flip it is an easier way to divide fractions with out making decimals. We keep the first fraction change the division into multiplication and flip the last fraction, in this case 1/2 becomes 2/1. Now we have
-17/4 * 2/1
Our next step is to multiply the numerators together and the denominators together and then put it back in fraction form.
-17 * 2 = -34
4 * 1 = 4
Our final result is
-34/4
Or if you need it as a mixed number you just divide the 34 into 4 as many times as you can and make that the whole number. 34 doesn't completely fit into 4 but 32 does so we have
-8 2/4 or simplified further
-8 1/2
Two number cubes are rolled for two separate events:
Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Complete the conditional-probability formula for event B given that event A occurs first by writing A and B in the blanks:
Answer:
11/30
Step-by-step explanation:
P(B/A) = P(B^A)/P(A)
P(A) = 30/36 = 5/6
P(B^A) = (2+5+4)/36 = 11/36
11/36 ÷ 30/36
11/30 or 0.3667
what is the y-intercept of y=3x - 8
Answer:
(0, -8)
Step-by-step explanation:
y is defined as x=0,
therefore y = 3*0 - 8= -8
Answer:
-8 or (0, -8)
Step-by-step explanation:
The point slope form: y = mx + b
m is the slope
b is the y-int
Step 1: Identify the y-int
y = 3x - 8
-8 is the y-int
(0, -8)
Answer: -8 or (0, -8)
1/10(x+50)=-3x-13+4x
The question is about solving the linear equation 1/10(x+50)=-3x-13+4x. This process involves simplifying the equation, combining like terms, and isolating x to find the solution.
Explanation:This question involves algebra, specifically the solving of linear equations. To start, your equation is
1/10(x+50)=-3x-13+4x
. First step is to simplify the equation: both sides of the equation need to be simplified and rearranged. After simplifying, we can combine the x terms and constants together. You will then isolate x on one side of the equation by adding or subtracting terms as needed. This will give you the solution to the equation. It's important to remember that the solution to the equation is the value of x that makes both sides of the equation equal. Note that one might end up with no solution if the equation is not consistent after simplifying.
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If 3x + 8 = -4, then
evaluate x3 + 5
Answer:
-59
Step-by-step explanation:
x3 is meaningless; I assume you meant x^3.
If that's the case, then:
3x + 8 = -4 is equivalent to 3x = -12, so that x = -4.
Then (-4)^3 + 5 = -64 + 5 = -59
Answer:
-59
Step-by-step explanation:
the question can be solved by some simple mathematical steps.
If 3x + 8 = -4
then, x3 + 5 =?
from 3x + 8 = -4
collect the like terms
3x = -4 - 8
3x = -12
divide both sides by 3
3x/3 = -12/3
x = -4
if x = -4 then to find x3 + 5 will imply that we will insert the value of x = -4 into the x3 + 5
-4 ³ + 5
-64 + 5
= -59
therefore the value of x3 + 5 is solved to be -59
Find the surface area of number 1. Will give Brainliest
Answer:
142 in^2
Step-by-step explanation:
Base: 7 × 3 = 21 (×2 = 42)
Small faces: 5 × 3 = 15 (×2 = 30)
Larger faces: 5 × 7 = 35 (×2 = 70)
Add: 21 + 30 + 70 = 142
what is the product of (2X+ Y) (5x-4+3)
Product is 10x² - 2x - y + 5xy
Step-by-step explanation:
Step 1: Find the product. Use distributive property.(2x + y)(5x - 4 + 3) = 10x² - 8x + 6x + 5xy - 4y + 3y
= 10x² - 2x - y + 5xy
Hope this will help u..✌✌