Answers
The straight line y = x -1 is shown figure
Sketching graph of a line:
To plot straight-line graphs we need to take values of x and y values to make a value table and to work out the graph.
Take x values as -1, 0, 1, etc. to make our work easy and clearer, and from that find the values of y.
After calculating the coordinates, use the resultant points to plot the line as a graph.
Here we have a line
y = x -1
To sketch the graph we need to make a value table as given below
First take x values as, -1, 0, 1 from that find the values of y
At x = -1 => y = -1 - 1 = -2
At x = 0 => y = 0 - 1 = -1
At x = 1 => y = 1 - 1 = 0
From the above calculations, the value table is
x -1 0 1
y -2 -1 0
Use the above value and Sketch the graph
[ the resultant graph is shown below ]
The straight line y = x -1 is shown figure
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Related Questions
What is the y-intercept of a line that has a slope of and passes through point (8, 3)?
000
3
5
11
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Answers
The y-intercept of a line that has a slope of and passes through points (8, 3) is (0,1).
what is the slope-intercept?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.
The slope-intercept form: y = mx + b
m - a slope
b - y-intercept
Here, we have
A slope m = 1/4.
Substitute: y = 1/4 x + b
We know that
the line passes through the point (8, 3) → x = 8, y = 3.
Put the values of x and y into the slope of the line:
1/4 · 8 + b = 3
2 + b = 3 |-2
b = 1
Hence, the y-intercept is (0, 1)
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If the area to the left of x in a normal distribution is 0.193, what is the area to the right of x?
Answers
The area to the right of x in the normal distribution is 0.807
What is the normal distribution?The normal distribution is the probability distribution that helps to find the probability for continuous variables.
For a probability x, for a normal distribution, we have that
P(X ≤ x) + P(X ≥ x) = 1
How to find the area to the right of x?Since the area to the left of x in a normal distribution is 0.193, we require the area to the right of x.
Since P(X ≤ x) + P(X ≥ x) = 1 where
P(X ≤ x) = area to the left of x P(X ≥ x) = area to the right of xMaking P(X ≥ x) subject of the formula, we have that
P(X ≥ x) = 1 - P(X ≤ x)
Given that P(X ≤ x) = 0.193
Substituting this into the equation, we have
P(X ≥ x) = 1 - P(X ≤ x)
P(X ≥ x) = 1 - 0.193
P(X ≥ x) = 0.807
So, the area to the right of x is 0.807
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Abe digs a hole at a steady rate of (meaning negative) 1.2 feet every hour.
Consider ground level to be 0.
What value represents the elevation of the hole relative to ground level after digging for 2.5 hours?
Enter your answer in the box.
Answers
The elevation of the hole relative to ground level after digging for 2.5 hours is -3.
2÷7756
Find the quotient.
77.56 divided by .2 = ?
Answers
By division, the following results are obtained
[tex]2 \div 7756\\[/tex] = 0.0025
[tex]77.56 \div 0.2 = 387.8[/tex]
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
The quotients of the two divisions are shown below-
[tex]2 \div 7756\\[/tex] = 0.0025
[tex]77.56 \div 0.2\\7756 \div 20 \\387.8[/tex]
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4.
The sum of two odd consecutive integers is 88. Find the integers.
Answers
Answer:
43 and 45
Step-by-step explanation:
→ State an expression for 2 odd consecutive numbers
2x + 1 and 2x + 3
→ Find the sum
4x + 4
→ Equate to 88
4x + 4 = 88
→ Minus 4 from both sides
4x = 84
→ Divide both sides by 4
x = 21
→ Substitute into original expressions
43 and 45
Please help :(
Solve each equation for x. Show all steps.
1) log base4 (x^2 -12x+48) =2
2) 27^(4x-6) = (1/9)^(2x-7)
Answers
The values of x in the equations are as follows:
1. x = 8 or 4
2. x = 2
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, let's solve the equation as follows:
log₄ x² - 12x + 48 = 2
using law of logarithm
4² = x² - 12x + 48
16 = x² - 12x + 48
x² - 12x + 48 - 16 = 0
x² - 12x + 32 = 0
x² - 4x - 8x + 32 = 0
x(x - 4) - 8(x - 4) = 0
(x - 8)(x - 4) = 0
Therefore,
x = 8 or x = 4
[tex]27^{(4x-6)}=(\frac{1}{9})^{2x-7}[/tex]
[tex]27^{(4x-6)}=(3^{-2} )^{2x-7}[/tex]
[tex]3^{3(4x-6)}=3^{-4x+14}[/tex]
[tex]3^{12x-18} =3^{-4x+14}[/tex]
Cancel the base
Therefore,
12x - 18 = - 4x + 14
12x + 4x = 14 + 18
16x = 32
x = 32 / 16
x = 2
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if the selling price for a shirt is $39.98 and the tax rate is 4.5% what is the sales tax
Answers
Answer:
8.25 % I got this answer right.
If India works overtime, she receives an
hourly rate of 1-times her regular hourly 1/2
rate. What is her hourly overtime rate?
Answers
After solving, 50% is her hourly overtime rate.
In the given question,
India works overtime, she receives an hourly rate of 1-times her regular hourly 1/2 rate.
We have to find her hourly overtime rate.
India is working overtime so her regular hourly rate is 1/2.
Evaluating the expression
We find her hourly overtime rate in percentage.
She receive overtime rate for 1 time is 1/2 rate.
We can write 1/2 as 0.5.
To express it as percentage we multiply and divide by 100.
= 0.5 × 100/100
= 50%
Hence, 50% is her hourly overtime rate.
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Solve The Problem
All the students in grades 3, 4 and 5 are going on a field trip to Coney Island
Each grade has 125 students. The cafeteria needs to pack lunches. About how
many students are going on the trip? Represent the exact amount of student
in all three grades using an array, How many students are there altogether?
Answers
The number of Students going on the trip is 375.
In the question,
It is given that:
There are 125 students in Grade 3.
There are 125 students in Grade 4.
There are 125 students in Grade 5.
So, Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5
= 125 + 125 + 125 = 375.
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50. WATER HOSES A water hose can spray water at an
initial velocity of 40 feet per second. Use the formula
h(t) = vot – 16t², where h(t) is the height of the water
in feet, vo is the initial velocity in feet per second, and
t is the time in seconds.
-
a. How long will it take the water to hit the
nozzle on the way down?
b. Assuming the nozzle is 5 feet up, what is
the maximum height of the water?
Answers
It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.
a) Given equation
h(t) = v₀t - 16t^2
Substitute v₀ = 40, h(t) = 0 in the given equation
40t - 16t^2 = 0
Solve for t
⇒ 16t^2 = 40t
⇒ 16t = 40
⇒ t = 40/16
⇒ t = 2.5 seconds
Hence, water will take 2.5 seconds to hit the nozzle on the way down.
b) The function that represents the given condition
h(t) = -16t^2 + 40t + 5
The maximum value of the function is the y-coordinate of the vertex.
The x-coordinate of the vertex
= -40/2(-16) = 5/4
Find the y-coordinate of the vertex by substituting t = 5/4
⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5
⇒ h(5/4) = -25 + 50 + 5
⇒ h(5/4) = 30
Hence, the maximum height of the water is 30 ft.
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NEED HELP ASAPPPPPPPP
Answers
1) In figure 4, the area of the square os 16cubes. The shaded part is 7cubes, being one less than 4^2 or 4*4. The formula is n+n-1. This can be put in for 5 too. 5+5-1=9.
2) Using the formula, 50+50-1=99. Therefor, the shaded squares in the 50th figure would be 99.
Complete sentence:
1) The formula for the number of shaded squares in the Nth figure is n+n-1.
2) There would be 99 shaded squares in the 50th figure.
explanation: Knowing that the area of a square is length*width, in this case because the figures are squares, the length and the width are both the same number. From this, we can tell that for figure 45, the length is 45 and so this the width. The one square in the corner is both the length and the width so this is why we take 1 away or -1.
I dont understand, please help
Answers
The slope is 5 and the y-intercept is -2000.
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.
(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.
What is meant by slope intercept form?In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b). y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.
(a) Consider two points
(x₁, y₁) = (400, 0)
(x₂, y₂) = (500, 500)
The slope is given as
m = (y₂ - y₁)/ (x₂ - x₁)
= (500-0)/(500-400)
= 500/100
= 5
To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)
0 = 5(400)+b
0 = 2000 + b
b= - 2000
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) Let the number of customers per week = x
And the profit per week = y
Then, the situation can be modeled using slope-intercept form as
y = 5x -200
(d) Put x= 2500 in y = 5x -200
y = 5(2500)-2000
= 12,500-2000
= 10,500
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Find the average rate of change.
Answers
The average rate of change = 1.59 ≈ 2
The average rate of change can be calculated by
1) The first one = [tex]\frac{3 + 0}{2}[/tex] = 1.5
2 ) the second can also be solved by ; 8 + 2/ 2 = 5
3 ) the third one will be 20 + 6 / 2 = 13
4) 8.5
5) 12.5
To calculate the average rate of change
we will first add all the distance
Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51
The total time = 2 + 6 + 9 +15 = 32
Thus the average rate of change = 51 / 32 = 1.59
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Alisha used her bank card to buy a bus pass 3 times. Each time she bough
a pass it cost her $13.75. She then deposited $30 into her bank account. Write
an expression to find the change in Alisha's bank account in dollars as a result
these transactions. Also, evaluate the expression to find the change in the
account balance.
Answers
The answer will be A-3*13.75+30 using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Alisha used her bank card to buy a bus pass 3 times.
Each time she bought a pass it cost her $13.75,
She then deposited $30 into her bank account.
So the expression A-3*13.75+30
A is the initial value.
Hence this will be the expression A-3*13.75+30
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A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
How much langer is the pygmy rabbit than the
wase?
Answers
Pygmy rabbit is 22.61-10 meters longer than the wasp.
Given:
A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
Pygmy rabbit longer than the wasp = size of pygmy rabbit - size of wasp.
= (24 - 1.39)-10meters
= 22.61-10 meters.
Therefore pygmy rabbit is 22.61-10 meters longer than the wasp.
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HELP FOR BRIANLEST
Answers
The function will be;
⇒ y = 3x - 1
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The domain and the range is shown in table.
Two points on the line are (2, 5) and (7, 20).
Now,
Since, The equation of line passes through the points (2, 5) and (7, 20).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (20 - 5) / (7 - 2)
m = 15 / 5
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - 5 = 3 (x - 2)
⇒ y - 5 = 3x - 6
⇒ y = 3x - 6 + 5
⇒ y = 3x - 1
Therefore, The function will be;
⇒ y = 3x - 1
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The statement 4 less than a number is given w
Answers
The equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following statement - "4 less than a number is given w".
Assume the number to be [x].
We can write the equation representing the statement -
"4 less than a number is given w" as a mathematical expression as -
[w] = x where x ∈ (- ∞, 4)
Therefore, the equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
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The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given
by the function D(h) = 111.7√/h. Find the height that would allow a person to see 40 kilometers.
h=km
(Round to two decimal places as needed.)
...
Answers
Answer:
0.13 km
Step-by-step explanation:
Rearrange the formula to solve for [tex]h[/tex]:
[tex]D(h)=111.7\sqrt{h}[/tex]
[tex]\frac{D(h)}{111.7}=\sqrt{h}[/tex]
[tex](\frac{D(h)}{111.7})^2=(\sqrt{h})^2[/tex]
[tex](\frac{D(h)}{111.7})^2=h[/tex]
Then, substitute the distance of 40 km:
[tex](\frac{40}{111.7})^2=h[/tex]
[tex]0.13\approx{h}[/tex]
Use the literal symbols listed at the end of the problem to translate the given statement into an algebraic formula.
In a given weight, the number of grams equals 454 times the number of pounds. (g. p)
Choose the correct formula below.
A. g=454 +p
C. p=454g
E. g=454-p
G. g= 454
——
p
B. p=454 +g
D. p=454-g
F. g=454p
H. g= p
—
454
Answers
Pounds = p
Number(g) = 454 x p
Which means;
g = 454p
A rectangular patio has a length of 9 2/5 feet and an area of 81 3/8 square feet. What is the width of the patio?
Answers
Step-by-step explanation:
81 3/8 ÷ 9 2/5
81*8+3 = 651
651/8
9 2/5 = 9*5+2=47
47/5
651/8 ÷ 47/5 =
651/8 * 5/47 = 3255/376 =
8.65691489362
Suppose 57% of the doctors in a hospital are surgeons.
If a sample of 465 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 6%? Round your answer to four decimal places.
Answers
The probability that the proportion of surgeons will differ from the population proportion by greater than 6%-22.22%
How to solve for the probabilityP of 6%
= P (p > 0.06)
we would have to use the formula that is given below
[tex]P[z > \frac{p-P}{\sqrt{} \frac{PQ}{n} }[/tex]
where we have n = 465
p = 6%
P = 0.57
Q = 1 - 0.57 = 0.43
We would have to put the values into the equation that we have here as:
0.06 - 0.057 = -0.51
0.57 x 0.43 / 465 = 0.000527
√0.000527 = 0.022956
The probability = -0.51 / 0.022956
= -22.22%
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a.) find the test statistic
b.) what is the p-value
c.)what is the conclusion about the null hypothesis
d.) what is the final conclusion?
Answers
a) The test statistic is: t = -7.44.
b) The p-value is: < 0.0001.
c) The conclusion is that the null hypothesis is rejected.
d) The final conclusion is that there is sufficient evidence to conclude that the mean prediction error is different of zero.
What are the features of the test and how does it relates to the hypothesis?From the pop-up shown at the complete problem given by the image at the end of the answer, the test statistic and the p-value are given as follows:
Test statistic: t = -7.44.P-value: < 0.0001.The conclusion regarding the null hypothesis is to reject the null hypothesis, as the test statistic has an absolute value less than the critical value, as we are using a two-tailed test, comparing if the mean is different of zero.
Considering that the null hypothesis is rejected, and also that the p-value is less than the significance level of 0.05, there is sufficient evidence to conclude that the mean prediction error is different of zero.
Missing InformationThe pop-ups with the information of the test are given by the image at the end of the answer.
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Find m/1 and m/2
1
95°
2
m<1 =
m<2=
Answers
Answer: 85
Step-by-step explanation:
How can the narrator's parents be described in chapters 1-4 of Frankenstein?
A. Poor farmers
B. Distinguished counsellors
C. Military officers
D. Migrant workers
Answers
Answer: B)
Step-by-step explanation:
The graph below shows the relationship between the number of ounces and the number of calories in steak.
Which equation best represents this relationship?
Responses
Answers
Answer:
??
Step-by-step explanation:
where are the equations ?
Answer:
Step-by-step explanation:
Jose hopes to earn $600 in interest in 4.8 years time from $30,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.
Answer
Answers
The annual rate of interest have to be 3.87%.
How to determine the annual rate of interest?Mathematically, compound interest can be calculated by using this formula:
A = P(1 + r/n)^{nt}
Where:
A represents the future value.P represents the principal.r represents the interest rate.n represents the number of times compounded.T represents the time measured in years.Making the interest rate (r) the subject of formula, we have:
r = n[(A/P)^{1/nt} - 1]
Note: A = SI + P = 600 + 30,000 = $36,000
Substituting the given parameters into the formula, we have;
Interest rate, r = 1[(36,000/30,000)^{1/1 × 4.8} - 1]
Interest rate, r = [(1.2)^{0.20833333333} - 1]
Interest rate, r = [1.0387 - 1]
Interest rate, r = 0.0387
Interest rate, r = 3.87%.
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Can someone please help me solve this, I’m so stressed
Answers
Answer:
3a. $8493.42
3b. 139.0 months
4a. 10
4b. 10.2 years
Step-by-step explanation:
Given exponential equations, you want values for specific times, and you want times for specific values.
In part (a), the value is found by substituting an appropriate value for t and doing the arithmetic.
In part (b), logarithms will be involved in solving for t.
3. Investment(a) Use t=12, the number of months in one year. You want the value of ...
S = 8000·1.005^12 ≈ 8493.42
The amount after 1 year is $8493.42.
(b) The time it takes to double the investment is the value of t such that ...
16000 = 8000·1.005^t
2 = 1.005^t . . . . . . divide by 8000
log(2) = t·log(1.005) . . . . . take logarithms
t = log(2)/log(1.005) ≈ 138.976
The investment will double in about 139.0 months.
4. Otters(a) Use t=0 and evaluate.
y = 2500 -2490e^(-0.1·0) = 2500 -2490 = 10
The population of otters was 10 when they were reintroduced.
(b) The time it takes for the population to reach 1600 is the value of t such that ...
1600 = 2500 -2490e^(-0.1t) . . . . use 1600 for y
-900 = -2490e^(-0.1t) . . . . . . . . . subtract 2500
900/2490 = e^(-0.1t) . . . . . . . . . divide by -2490
ln(900/2490) = -0.1t . . . . . . . . . take natural logs
t = ln(900/2490)/-0.1 . . . . . . . . divide by the coefficient of t
t ≈ 10.176 ≈ 10.2
It will be 10.2 years before the otter population reaches 1600.
write 10 forms for 1 over 8 as you can think of, be creative and use positive and negative powers or other forms of number.
Answers
Answer:
No entendí porfavor puedes ponerlo en Español
In the fall of 2017, there were 48 thousand more female undergraduate students enrolled at a college than male
undergraduate students. If the total undergraduate enrollment was 414 thousand that fall, find the numbers of female
undergraduate students and male undergraduate students who were enrolled.
The number of female undergraduate students was
thousand.
Answers
Answer: 231 thousand
Step-by-step explanation:
given,
total number of undergraduate students enrolled = 414000
let us take number of total number of male students as, X
then, total number of female students will be X + 48000
now we get,
total number of male students + total number of female students = total number of students enrolled.
X + (X + 48000) = 414000
X + X + 48000 = 414000
2X = 414000 - 48000
X = 366000/2
X = 183000
total number of male students is 183000
total number of female students is
X + 48000
183000 + 48000 = 231000
Raise the powers of all variables and numbers indicated, and then turn the following expressions in radical form into exponential expressions in rational form. You do not need to evaluate or solve any of the expressions, just put them in simplest exponential form. [All sets of similar base variables and numbers are meant to be under the same radical sign]
Answers
The radical expression [tex]\sqrt[5]{x^3}^8.x^4[/tex] simplifies to [tex]x^\frac{44}{5}[/tex].
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, [tex]\sqrt[5]{x^3}^8.x^4[/tex].
= [tex]x^3(^\frac{8}{5}).x^4[/tex].
= [tex]x^\frac{24}{5}.x^4[/tex].
= [tex]x^\frac{24}{5}^{+4}[/tex].
= [tex]x^\frac{24 + 20}{5}[/tex].
= [tex]x^\frac{44}{5}[/tex].
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