Draw a line representing the “rise” and a line representing the “run” of the line. State the slope of the line in simplest form.
Answers
The slope of the line in its simplest form is 3.
The slope of a line is [tex]Slope=\frac{Rise}{Run}[/tex].
We need to find the slope of the line in its simplest form.
What is the slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope is often denoted by the letter m; there is no clear answer to the question of why the letter m is used for slope.
Select any two points on the line like A and B.
From the below figure it is clear that
Rise = Change in y = -2-(-5) = 3
Run = Change in x = 9-0 = 9
Now, [tex]\frac{9}{3} =3[/tex]
Therefore, the slope of the line in simplest form is 3.
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Related Questions
find x if 2+x = -2/3
Answers
First you want to isolate x by subtracting 2 from -2/3. To do this make sure there is a common denominator of 3 so our equation is now x=-6/3 -2/3 which with regular subtraction is -8/3.
Hope this helps:)
Will a stand that hold up to 40 pounds support a 21-kilograms television? Explain used 2.2 Lb = kg
Answers
Answer: No, the stand will not support the TV. It is too heavy.
Work Shown:
1 kg = 2.2 lbs approximately
21*1 kg = 21*2.2 lbs
21 kg = 46.2 lbs
A 21 kilogram tv is roughly equivalent to 46.2 pounds.
This exceeds the 40 pound weight limit, so this stand will not support it.
Answer: No
Step-by-step explanation:
Weight limit = 40 Lb
Weight given = 21 kg
Conversion factor
2.2 Lb = 1 kg
2.2 x 21 = 46.2
46.2 Lb = 21 kg
46.2 > 40, the stand cannot support the TV
a hyperbola centered at the origin has vertices PLEASE HELP QUICK
Answers
The equation of the hyperbola with a given origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at (±[tex]\sqrt{98}[/tex], 0) is [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].
Given, that a hyperbola centred at the origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at (±[tex]\sqrt{98}[/tex], 0)
What is hyperbola?In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The formula for a hyperbola centred at the origin is [tex]\frac{x^2}{a^2} -\frac{y^2}{b^2 } =1[/tex]
The vertices are located at (±a, 0), so we have that the value of a is [tex]\sqrt{61}[/tex].
The foci are located at (±c, 0), where [tex]c^2 = a^2 + b^2[/tex].
So if we have that [tex]c = \sqrt{98}[/tex], we can find the value of b:
[tex]98 = 61 + b^2[/tex]
⇒ [tex]b^2 = 37[/tex]
⇒ [tex]b = \sqrt{37}[/tex]
So, the formula for this hyperbola is [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].
Therefore, the equation of the hyperbola with a given origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at (±[tex]\sqrt{98}[/tex], 0) is [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].
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The pipe has a length 29cm, internal diameter 6.5cm and thickness 0.5cm. What is the Volume
Answers
Answer:
Length of pipe = 21 cm
Internal diameter = 4 cm
Internal radius = \frac{4}{2} = 2 cm24=2cm
Thickness = 0.5 cm
Outer radius = 2+0.5=2.5 cm
Volume of pipe =\pi R^2 h - \pi r^2 hπR2h−πr2h
Volume of pipe =\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3
=\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3722(2.5)2(21)−722(2)2(21)=148.5cm3
Hence The volume is 148.5 cubic cm.
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The thickness of a metal pipe is 1.5cm. The inner diameter is 21cm. What is the volume of metal required for a pipe of length 7cm
The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score? A) 20 B) 24 C) 32 D) 36
Answers
The highest score is 32.
What is mean?The mean refers to the average of a set of values.
Total players = 8
Mean= 14.5
Now, total score of 8 players,
= 14.5*8
=116
and, Total score for the remaining 7 players
= 12 * 7
= 84
Hence, the highest score is 116-84 =32
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Complete the steps to factor the polynomial by grouping. p(x) = x3 5x2 – x – 5 p(x) = x2 (x ) – (x 5) p(x) = (x2 – )(x 5) p(x) = (x – )(x 1)(x )
Answers
The polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
The given polynomial to us is p(x) = x³ + 5x² - x - 5.
We are asked to factor the polynomial by grouping.
We can do this by following these steps:
p(x) = x³ + 5x² - x - 5.We group the first two terms and the next two terms to get p(x) = (x³ + 5x²) + (-x -5).Now, we take x² common from the first group and -1 common from the second group to get p(x) = x²(x + 5) -1(x + 5)Now, we take (x + 5) common from both the terms to get, p(x) = (x + 5)(x² - 1).Now, we right (x² - 1) as (x + 1)(x - 1). to get the polynomial as, p(x) = (x + 5)(x + 1)(x - 1).Therefore, the polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
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Jean had $25.86 in her pocket. If shoes cost $7.50 a pair plus 10% of tax. How many pairs can she buy?
Answers
Answer:
3 pairs
Step-by-step explanation:
10% of 7.50 is 0.75. So one pair will cost $8.25. Now, 25.86/8.25 and you get 3 pairs
Answer:
[tex]\fbox {3 pairs}[/tex]
Step-by-step explanation:
Cost of 3 pairs with tax :
⇒ 7.50 × 3
⇒ 22.50
* Adding tax *
⇒ 22.50 + 22.5 (0.1)
⇒ 22.50 + 2.25
⇒ 24.75
∴ Since 24.75 is less than 25.86, Jean can buy 3 pairs of shoes.
The table below shows the results of a survey that asked 1052 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at
random. Complete parts (a) through (c).
(a) Find the probability that the person opposed the tax or is female.
P(opposed the tax or is female) =
(Round to the nearest thousandth as needed.)
(b) Find the probability that the person supports the tax or is male.
P(supports the tax or is male) =
(Round to the nearest thousandth as needed.)
(c) Find the probability that the person is not unsure or is female.
P(is not unsure or is female)=
(Round to the nearest thousandth as needed.)
Answers
The complete options are P(opposed the tax or is female) = 0.28, b. P(supports the tax or is male) = 0.15, c. P(is not unsure or is female) 0.025.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
(a) The probability that the person opposed the tax or is female.
P(opposed the tax or is female) = 298 / 1052 = 0.28
(b) The probability that the person supports the tax or is male.
P(supports the tax or is male) = 168/1052 = 0.15
(c) The probability that the person is not unsure or is female.
P(is not unsure or is female) = 27 / 1052 = 0.025
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PLEASE HELP ASAP!!!!
The polar equation r=7sin(2θ) graphs as a rose.
What is the length of the petals of this rose?
Enter your answer in the box.
Answers
============================================================
Explanation:
r = distance from the origin (0,0) to a point on the polar curve
To find the length of the flower petal, we need to max out r (i.e. get it as large as possible).
Recall that sin(x) maxes out at 1, so that also applies to sin(2θ) as well.
Therefore, r = 7*sin(2θ) maxes out at r = 7*1 = 7 and this is the length of each petal. Basically it's the number out front of the sine term.
The graph is shown below. To type the symbol θ into desmos, you need to type "theta" without quotes.
Pls help and explain tyyy
Answers
Answer:
11) 195312
13) 5461
Step-by-step explanation:
11)
15÷(-3) = -5
(-75)÷15 = -5
375÷(-75) = -5
It’s clear that the common ratio of this geometric sequence is -5
Then using the sum formula for geometric sequences :
[tex]S_{11}=\left( -3\right) \times \frac{1-\left(-5 \right)^{8} }{1-(-5)} =-\frac{1}{2}\times(1-(-5)^8)=195312[/tex]
……………………………………………………
13)
[tex]S_{13}=1\times \frac{1-4^{7}}{1-4} =-\frac{1}{3} \times(1-4^{7})=5461[/tex]
For a given interest rate, simple interest varies jointly as principal and time. If $2000 left in an account for 4 yr earned interest of $280, how much interest would be earned in 6 yr?
Answers
$280 / 4 = $70
$70 * 6 = $420
one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?
Answers
After 3 months memberships will cost the same.
We have,
Cost of Membership of 1st gym = $ 10 per month
And, the Cost of the sign-up fee for 1st gym = $ 45
And,
Cost of Membership of 2nd gym = $ 25 per month
And, the Cost of the sign-up fee of the 2nd gym = $ 0
Now,
Let the number of months = m
So,
According to the question;
45 + 10m = 25m
⇒
25m - 10m = 45
15m = 45
m=3
So, After 3 months memberships will cost the same.
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Solve the following system to find the point(s) of intersection.
y = x² - 2x - 3
y = 2x - 3
Answers
x=4 y=5
if we put two pharases together
the answer is as follows pic :
x=4 y=5
The fences will be aligned with the exterior angles 1 and 2. what are some other relationships you can see between 1,2,a, and b? (2 points)
please help
1.8.4
Answers
The relationships between angles 1, a, b, and 2 can be defined using the angles between parallel lines.
In the diagram, we can see the fences, making angles 1 and 2 with the parallel lines X and Y respectively.
Using the angles among parallel lines, we can state the relationships between angles 1, a, b, and 2 as follows:
Angle 1 and Angle a are adjacent angles, thus their sum is 180°, that is m∠ 1 + m∠ a = 180°.Angle 2 and Angle b are adjacent angles, thus their sum is 180°, that is m∠ 2 + m∠ b = 180°.Angle 1 and Angle b are corresponding angles, thus they are equal, that is m∠1 = m∠ b.Angle 2 and Angle a are corresponding angles, thus they are equal, that is m∠2 = m∠ aAngle 1 and angle 2 are co-exterior angles, thus their sum is 180°, that is, m∠ 1 + m∠ 2 = 180°.Angle a and angle b are co-interior angles, thus their sum is 180°, that is, m∠ a + m∠ b = 180°.These were the relations among angles 1, a, b, and 2, using the parallel lines X and Y.
Refer to the diagram for a better understanding.
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Absolute value of (0, -4/5)
Answers
To answer this question, we need to know what absolute value is in the first place. ANSWERS ARE AT THE BOTTOM.
Absolute value represents how far something is from 0 in a number line.
For example, lets take 4.
4 is 4 units away from 0 on the number line, so the absolute value of 4 is 4.
Now lets look at another example, -4. -4 is also 4 units away from 0, just in the other direction. However, when calculating absolute value, we do not care about the direction. Therfore, the absolute value of -4 is also 4.
Now let's look at your problem.
You want the absolute value of 0 and -4/5
Following the same principle above about the distance from 0, here are your answers:
Absolute value of 0: 0
Absolute value of -4/5: 4/5
A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
(Answer is not 10 cents) Tried it
Answers
you could also use the equation x + (x + 1) = 1.10 where x is the cost if the ball and x + 1 is the cost of the bat. x + x + 1 is the same as 2x + 1 = 1.10, and when solved x = 0.05.
Given: AC and BD are parallel. BX and CY are parallel. AX = DY.
Prove: AYC is congruent to DXB
Answers
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Using the ASA congruency the triangles are congruent.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
For the two of the given triangles ΔACY and ΔDXB,
∠A = ∠D {Alternate Interior Angles}∠DXB = ∠ACY {Alternate Interior Angles}AY = YD ⇒ (AX + XY) = (DY + XY) {Given AX=DY}Since the measure of the two angles and one side of the two triangles are equal, therefore, using the ASA congruency the triangles are congruent.
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What are the exact solutions of x2 − 3x − 5 = 0? (1 point) a x = the quantity of negative 3 plus or minus the square root of 29 all over 2 b x = the quantity of 3 plus or minus the square root of 29 all over 2 c x = the quantity of 3 plus or minus the square root of 11 all over 2 d x = the quantity of negative 3 plus or minus the square root of 11 all over 2
Answers
x = the quantity of 3 plus or minus the square root of 29 all over 2. Then the correct option is B.
What is the solution of the quadratic equation by formula method?The quadratic equation is given as ax² + bx + c = 0.
Then the solution is given as
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic equation is given below.
x² – 3x – 5 = 0
Then the solution of the equation will be
[tex]\rm x = \dfrac{-(-3)\pm \sqrt{(-3)^2 - 4 *1*(-5)}}{2*1}\\x = \dfrac{3 \pm \sqrt{29}}{2}[/tex]
Then the correct option is B.
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A randomly generated list of integers from 1 to 5 is being used to simulate an event, with the numbers 1 and 2 representing a success. What is the estimated probability of a success?
A.50%
B.30%
C.40%
D.20%
Answers
Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| + 1 > 7/2
Answers
The graph is shown below:
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Rearrange unknown terms to the left side of the equation:
|x| > 7/2-1
Now,
|x| > (7-2)/ 2
Calculate the sum or difference:
|x| > 5/ 2
Convert the absolute inequality to standard inequality:
x> 5/2 or x< -5/2
Solve the inequality:
x> 5/2
Solve the inequality:
x< -5/2
Graph on number line is attached
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Y W P 8 cm E R WERP is a square. Find.
1. m2WER=
2. measure of PE =_______
3. measure of WA =
4. Value of y=
Answers
1) All interior angles of a square are right angles, so angle WER measures 90°
2) All squares are parallelograms, and diagonals of a parallelogram bisect each other, meaning PA=AE=8 cm. Thus, PE=16 cm
3) All squares are rectangles, and diagonals of a rectangle are congruent, meaning WR=16 cm. Then, using the fact that the diagonals bisect each other, we get that WA=8 cm
4) If we consider right triangle WPR, we know it is isoceles because all sides of a square are congruent. So, the length of WP is:
[tex] \frac{16}{ \sqrt{2} } = 8 \sqrt{2} [/tex]
a toolbox has 10 screwdrivers and 6 wrenches. bella put 8 more wrenches in the toolbox. how many more wrenches are in the toolbox than screwdrivers
Answers
Answer:
4 more wrenches than screwdrivers
Step-by-step explanation:
6+8=14
14-10=4
therefore there are 4 more wrenches than screwdrivers.
:)
Answer:
14
Step-by-step explanation:
solution
Screwdrivers- 10
wrenches- 6
if bella adds 8 more wrenches.
= 6 + 8
=14
Now, there are 14 wrenches in the box
PLEASE HELP!!!!! ASAP
Answers
[tex]\text{Let's factor this quadratic.}\\\text{ We can start by thinking of two numbers such that,}\\\text{ if they are multiplied together, the product is 9}\\\text{if they're added together, the sum is -10, the middle term.}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{These numbers are -9 and -1.}\\\text{Checkup::}\\\text{-9*(-1)=9 and -9+(-1)=-10. The answer is good}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now, write these numbers as factors::}\\\text{(x-9)(x-1)=0 (make sure that the equation is \textbf{set to zero})}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now we can solve these mini equations in terms of x::}\\\text{x-9=0; \, x=9}\\\text{x-1=0; x=1}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Our factors are:: \textsl{9 and 1}}[/tex]
Answer:
x=1
Step-by-step explanation:
Which of the following is needed to construct a hexagon?
OA. Six obtuse triangles
OB. Six isosceles triangles
OC. Six right triangles
OD. Six equilateral triangles
Answers
The answer choice which represents the what is needed to construct a hexagon is Choice B; Six isosceles triangles.
What is needed to construct a hexagon?
By definition, an hexagon is a closed figure with six equal sides and six congruent interior angles.
On this note, upon assembly of six isosceles triangle s in which cases, the excluded side of the isosceles triangles form the sides of the hexagon and the congruent sides represents lines joining each vertex to the center of the hexagon, an hexagon is formed.
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Answer:
The correct answer is six equilateral triangles.
Step-by-step explanation:
The angle at the center of the hexagon is 360°, which is being divided into 6 equal parts. The value of each angle at the center is equal to 60°. All three angles of the 6 triangles formed in the given hexagon are equal to 60°. This proves that there are 6 equilateral triangles.
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks. If at year’s end an auditor
checks your accounting records and randomly selects one week to check the company’s payroll, what is the probability that the auditor will select a week in which you paid overtime wages and hired
temporary help?
Answers
The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.
What is probablitity?
Probability, can be define as the ratio of favorable outcomes to the n number of total events.
Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
p(b) = temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
= 0.81 + 0.46 -1
= 0.28
The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
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Subtract the equations. Two-Variable Systems: Elimination
(screenshot of the question below)
Answers
Answer:
4x = 14
Step-by-step explanation:
7x + 2y = 17
– (3x + 2y = 3)
- - -
4x = 14
So, the correct option is A. 4x = 14
Hope it helps!
Lewis has a net spendable income of $2,000 per month. He sets up the following transportation budget for himself.
3. Transportation (15% - 20%) 400
a. Car payments 210
b. Gas/Oil 120
c. Insurance 60
d. License/Registration 8
e. Taxes 2
f. Maintenance/Repair
What has Lewis done wrong?
Answers
What Lewis did wrong was that; He budgeted more than the maximum recommended amount of money for transportation.
How to budget effectively?
We are given;
Net spendable income = $2,000 per month
Now, we see how much he has budgeted for other items such as Car payments, Gas/Oil, Insurance, License/Registration, Taxes, Maintenance/Repair.
Now, from the recommended transportation budget of between 15% - 20% of the net spendable income, we can see that he would likely spend more than that if we add the cost of maintenance and repair.
Thus, what Lewis did wrong was that he budgeted more than the maximum recommended amount of money for transportation.
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Answer:
Step-by-step explanation:
Answer:
A. He budgeted more than the maximum recommended amount of money for transportation. PLATO (Im 100% sure
if the unit rate is 30 miles per hour , then how much miles is traveled in 9 hours
Answers
Answer:
270 miles
Step-by-step explanation:
Since the unit rate is 30 miles per hour, the miles on 9 hours will be:
= 30 × 9
= 270 miles.
Express 10cm as percentage of 50cm
Answers
Answer:
10 cm is 20% of 50 cm.
Step-by-step explanation:
1) Put the "question" into fraction form: 10/50
2) Divide the numerator by the denominator (essentially changing the fraction into the decimal form): 10 ÷ 50 = 0.2
3) Multiply the quotient by 100: 0.2 × 100 = 20
4) Slap a "%" on the end and you're good to go!! : 20%
I need help!!!!
True OR False
------------------------
m - 63 = 37, m = 100?
Answers
Answer:
The answer is true!!!
Step-by-step explanation:
If m=100, 100-63=37 which is true.
Detailed Solution:
m - 63 = 37
m = 63 + 37
=> m = 100
Therefore, m = 100 so this Statement is True.
