Answer:
1st: One solution
2nd: Infinite many solutions
3rd: No solution
4th: No Solution
5th: One Solution
Step-by-step explanation:
1st:
The solution is (6,9)
x = 6 if a vertical line going though (6,0)
y = 9 is a horizontal line going through (0,9)
The two lines with intersect at (6,9)
2nd:
3y = 15x + 6 If you divide all the way through by 3, you get
y = 5x + 2
This is identical to the first equation given. Since it is the same line, the answer is infinite many solutions.
3rd:
3y = x + 2 Divide all the way through by 3
y = 1/3 x + 2/3
9y = 3x + 7 Divide all the way through by 9
y = 1/3 x + 7/9
Since the slopes are the same in both equations (1/3), these line are parallel and will never intersect.
4th:
Since the slopes are both the same (2), the lines are parallel and they will never intersect, so the answer is no solution.
5th:
2y = 3x Divide both sides by 2
y = 3/2
-5y = -10 Divide both sides by -5
y = 2x
These equations are proportional so they go through the origin. They both have a y intercept of zero, so they intersect at (0,0). The answer is one solution.
PLEASE HELP! select all true statement on the graph
In the given graph the correct statements are:
q ⊥ n
m ║ n
p ⊥ m
What are parallel lines and perpendicular lines ?Parallel lines are two straight lines that never intersect and are located in the same plane. They are equidistant lines that are always at the same distance from one another. Parallel lines are denoted by the apostrophe ||. AB || CD, for instance, denotes that line AB and line CD are parallel. Perpendicular lines, on the other hand, are when two lines cross at an angle of 90 degrees. The symbol stands for perpendicular lines. Line PQ is perpendicular to line RS, for instance, if PQ RS. Examine the following illustration and the characteristics of parallel and perpendicular lines to recognize and distinguish between them.
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15:45 in its simplest form
1:3
Step-by-step explanation:= 15:45
= 15/45
= 15/45 {can be divided by 15}
= 15/15 = 1 ; 45/15 = 3
Therefore, 15/45 is 1/3
15:45 is 1:3
If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
Answer:
65c
Step-by-step explanation:
Solve for x.
Please !!!
Step-by-step explanation:
6x-4+60=14x-8
6x+56=14x-8
8x=64
x=8
Question 9 of 10
Solve (x-3)² = 5.
A. x=-3+√√5
B. x=3+√5
C. x = 8 and x = -2
OD. x=5± √√3
Answer:
B (x = 3 + √5)
Explanation:
x² + 9 = 5
Take square root of both sides
x + 3 = ± √5
Add 3 to both sides
x = 3 + √5 or x = 3 - √5
Can anyone help me with this, I need an accurate answer also if possible. -thanks
The linear function of the table is a) g(x)=x-7
What is linear function?
If the largest power of the variables in a function is 1, then that function is linear. A line across these two points with a straightedge is needed to complete the graph because two points determine a line. When m and b are real numbers, the slope of a linear function has the form f(x)=mx+b. To find the x-intercept, set f(x)=0 and solve for x. Because y=f(x), we can use y and f(x) interchangeably.
Here let us take g(x) as y values. In given table take any two points ,
[tex](x_1,y_1)=(0,-7)\\(x_2,y_2)=(2,-5)[/tex]
Now using slope formula ,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = 2/2 = 1
Now using equation formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y+7=1(x-0)
=> y+7=x
=> y =x-7
Then y=g(x)
=> g(x) = x-7
Therefore the linear function of the given table is g(x)=x-7 .
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21 washing machines in a laundromat, and 4 broken down. what is the ratio of the broken to all washing machines?
Answer: 17:4
Step-by-step explanation:
21 washing machines
4 broken
21 - 4 = 17
17:4
Erik has 2 bags of bird seed. One bag has
10 pounds of seed, and the other bag has
8 pounds of seed. He fills
7 bird feeders
with 2 pounds each. Write and solve
an
equation to find how many
pounds of bird
seed are left.
Answer:
(10 + 8) - (7 * 2) = x, 4 pounds of birdseed left
Step-by-step explanation:
For the first part of our equation, we will find the total amount of pounds of seeds among the bags (addition).
For the next part, we will find out how much of the bird seed is used (subtraction).
Then, it will equal whatever is left.
(10 + 8) - (7 * 2) = x, x = pounds of bird seed left
Now, we will solve.
(10 + 8) - (7 * 2) = x
(18) - (14) = x
x = 4 pounds of birdseed left
On Saturday, Bianca has $50 on her debit card when she goes out with some friends. She uses her debit card to spend $14.50 on lunch. She and her friends would like to go to see a movie, but some of her friends are out of money.
If the movie tickets cost $6.50 each, write an inequality to represent the number of tickets Bianca can buy without overdrawing on her debit card.
The inequality to represent the number of tickets Bianca can buy without over drawing on her debit card is 14.50 + 6.50x ≤ 50 .
In the question ,
it is given that
amount of money present in Bianca's Debit card = $50
amount of money spend on lunch = $14.50
cost of 1 movie ticket = $6.50
le the number of ticket = "x"
according to the question ,
the inequality is
14.50 + 6.50x ≤ 50
6.50x ≤ 50 - 14.50
6.50x ≤ 35.5
x ≤ 35.5/6.50
x ≤ 5.46
≈ 5
Therefore , The inequality to represent the situation is 14.50 + 6.50x ≤ 50
, and the number of tickets she can buy is 5 .
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Question content area top
Part 1
Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Perpendicular to the line y=
1
2x−2; containing the point (−3,6)
The equation of the line in slope-intercept form is y = -x/12 + 23/4
How to find the equation of the line?Given that: the line is perpendicular to the line y= 12x−2 and it contains the (−3,6).
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system
The slope-intercept form of a straight line is:
y = mx + c,
where m is the slope and c is the y-intercept
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ x m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the given line be m₁ and the slope of the unknown line be m₂
Line1(given):
y = 12x−2 and m₁ x m₂ = 12
m₁ x m₂ = -1
12 x m₂ = -1
m₂= -1/12
Line 2(unknown) with the point (−3,6):
y = mx + c
6 = -1/12 (-3) + c
6 = 1/4 + c
c = 6 -1/4 = 23/4
y = -x/12 + 23/4
Therefore, the slope-intercept form of the equation of the line is y = -x/12 + 23/4
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Determine the slope-intercept form of the equation of the line parallel to y = -4/3x + 11 that passes through the point (–6, 2). y = x +
The equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
According to the question,
We have the following information:
The line is parallel to y = -4/3x + 11 and passes through the point (–6, 2).
Now, we know that the following formula is used to find the equation of the line:
y-y' = m(x-x')
In this case, m is the slope of the line.
m = -4/3
We have the following values:
x' = -6 and y' = 2
Now, we have the following expression:
(y-2) = -4/3(x+6)
y-2 = -4x/3-8
Adding 2 to both sides of the equation:
y = -4x/3-8+2
y = -4x/3-6
Hence, the equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
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This season, the probability that the Yankees will win a game is 0.45 and the probability that the Yankees will score 5 or more runs in a game is 0.6. The probability that the Yankees win and score 5 or more runs is 0.34. What is the probability that the Yankees will win when they score fewer than 5 runs? Round your answer to the nearest thousandth.
The probability that the Yankees will win when they score fewer than 5 runs is; 0.567
How to solve conditional probability?We are given;
Event A which is when Yankees win has a probability of; P(A) = -.45
Thus, Event that the Yankees don't win which is when they lose is;
P(A') = 1 - 0.45 = 0.55
Event B which is the event that the Yankees score 5 or more runs has a probability of; P(B) = 0.6
Event that the Yankees score 4 or less run is given by the probability;
P(B') = 1 - 0.6 = 0.4
The probability that the Yankees win and score 5 or more runs is;
P(A' ∩ B') = 0.34
Thus, the probability that the Yankees will win when they score fewer than 5 runs wanted is given by the chain rule in conditional probability of the formula;
P(A' | B') = P(A' ∩ B')/P(B') = 0.34/0.6
P(A' | B') = 0.567
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Helpi really need this
Answer:
The height of the flagpole is about 25.6 feet.
Step-by-step explanation:
The figure is omitted--please sketch it.
Put your calculator in degree mode.
Let h be the height of the flagpole.
[tex] \tan(52) = \frac{h}{20} [/tex]
[tex]h = 20 \tan(52) = 25.6[/tex]
A quarterback threw a football from a height of 6 feet with an initial velocity of 20 feet per second. The height, h, of the ball at time t seconds can be represented by
the equation h (t)=-16t² + 20t+6.
True or False?
The ball was in the air for 1.5 seconds before hitting the ground.
The ball was in the air for 1.5 seconds. The answer is true.
What is a quadratic equation?The equation of the form ax² + bx +c is known as a quadratic equation.
The given equation is h(t) = -16t² + 20t + 6.
To find the time for which the ball was in the air, substitute h(t) =0.
0 = -16t² + 20t + 6
Use the quadratic formula to solve the equation:
[tex]t= \frac{- 20 \pm\sqrt{20^2 - 4(-16)(6)}}{2(-16)}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{784}}{-32}\\\\t= \frac{- 20 \pm28}{-32}[/tex]
t = (-20 + 28)/(-32) or t = (-20-28)/(-32)
t = -0.25 or t = 1.5
Since time cannot be negative, discard the negative value.
Hence, the ball was in the air for 1.5 seconds. The answer is true.
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For this discussion post do the following:
Write two expressions with positive and negative numbers to be evaluated with a given variable value.
Evaluate one of them correctly and in the other one make an error. For both, clearly explain the steps you used.
Do not tell which problem has the error as your classmates will be determining that later.
The two expressions to be evaluated are
y = 2x - 5y = 4x - 3How to evaluate the expressionsThe problem asks for two expressions with positive and negative numbers
the positive numbers in the expressions are 2x and 4x
the negative numbers in the expressions are -5 and -3
At x = 5.
evaluating the first expression gives
y = 2x - 5
y = 2 * 5 - 5
y = 10 - 5
y = 5
evaluating the second expression gives
y = 4x - 3
y = 4 * 5 - 3
y = 4 * 2
y = 8
One of the expressions evaluated has error and on is error free
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In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1
Answer:cap
Step-by-step explanation:C A P
find the x-intercept of the line y=5/12x+1/6
Answer:
(-2/5,0)
Step-by-step explanation:
if y=0,
5/12 x + 1/6 = 0
5x + 2 = 0
x = -2/5
or, multiply by 6 to get the intercept form:
6y = 5/2 x + 1
-5/2 x + 6y = 1
x/(-2/5) + y/(1/6) = 1
Solve. 4x+2=(1/8)x-2
_______
Pls help i need the answer!:(
Answer:
12*(1/4+1/3)(1/4+1/3)+2/3= 12*(1/16+1/12+1/12+1/9)+2/3=12*(9/144+12/144+12/144+16/144)+2/3= 12*(49/144)+2/3=12*49/144+2/3= 49/12+2/3=49/12+8/12=57/12= 4*9/12=4* 3/4
Step-by-step explanation:
How many numbers are there from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4?
For example 15 and 51, where 5 – 1 = 4.
There are 9 numbers from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4
How to determine the count of the numbers?The difference can be represented as
Largest - Smallest = 4
Also, we have two instances to be
15 and 51
And the range is given as
Range = 10 to 99
In a range of 10, there is only one number whose difference between the digits is 4
There are 9 ranges of 10 from 10 to 99
So, the count of the range is
Count = 9 range * one number
Rewrite as
Count = 9 * 1
Evaluate
Count = 9
Hence, there are 9 of such numbers from 10 to 99
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1. Write and solve an equation for the following statement: Eight less than one-third of a number,
Answer: (1/3)x - 8
Step-by-step explanation:
one - third means 1/3
one - third of a number means (1/3)x
( x being the number )
Eight less means -8
Eight less than 1/3 of an number is (1/3)x - 8
Given that logb(7)≈1.946, logb(9)≈2.197, and logb(16)≈2.773, find the logarithm of logb(1/63)
b is base b
The logarithmic expression given as logₙ(1/63) has its value to be -4.143
How to determine the logarithmic expression?From the question, the given parameters are
logₙ(7) = 1.946
logₙ(9) = 2.197
logₙ(16) = 2.773
The logarithmic expression to calculate is given as
logₙ(1/63)
Express 1/63 as 1/7 * 1/9
So, we have the following representation
logₙ(1/63) = logₙ(1/7 * 1/9)
Apply the product of logarithm
This gives
logₙ(1/63) = logₙ(1/7) + logₙ(1/9)
Apply the exponent of logarithm
This gives
logₙ(1/63) = -logₙ(7) - logₙ(9)
Substitute logₙ(7) = 1.946 and logₙ(9) = 2.197 in logₙ(1/63) = -logₙ(7) - logₙ(9)
logₙ(1/63) = -1.946 - 2.197
Evaluate
logₙ(1/63) = -4.143
Hence, the value of the logarithmic expression is -4.143
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Five students were looking at a large poster of the periodic table. They noticed the elements were arranged in rows and columns. They also noticed the elements were nged in order from 1-118. They had different ideas about the arrangement of the elements on the periodic table. This is what they said:
Damon: I think the elements are arranged by increasing mass.
Flo: I think the elements are arranged according to their properties.
Sienna: I think the elements are arranged by when they were discovered.
Kyle: I think the elements are arranged according to how common they are.
Glenda: I don't agree with any of you. I think there must be a different reason for the arrangement.
WHO DO YOU AGREE WITH?
The person that I agree with is Glenda I don't agree with any of you. I think there must be a different reason for the arrangement.
What is a periodic table?The periodic table, commonly known as the periodic table of (chemical) elements, is a table that displays the chemical elements in a tabular format.
The chemical elements are ordered from left to right and top to bottom by increasing atomic number, or the number of protons in an atom's nucleus, which generally corresponds to increasing atomic mass.
The elements in the periodic table are organized into rows, called periods, in ascending atomic number order. Vertical columns, referred to as groups, in which the elements have similar qualities.
I agree with Glenda because they're arranged in atomic number.
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there are 4 consecutive even integers that sum to 276
The required consecutive even integers are 66, 68, 70, and 72.
We have four integers. The integers are consecutive, that means the integers are one after the other. The integers are even, which means they are all divisible by two. The sum of these four even integers is 276.
Let the first even integer be represented by the variable "n". The next three consecutive integers are (n + 2), (n + 4), and (n + 6). Let the sum be denoted by "S".
S = n + (n + 2) + (n + 4) + (n + 6)
276 = 4n + 12
4n = 264
n = 66
Hence, the required integers are 66, 68, 70, and 72.
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Mike Meier purchased a lawnmower for $328.61, a lawn sprinkler for $13.27, and a hose reel for $27.96. He must pay the state tax of 5.5 percent, the county tax of 1.5 percent, and the city tax of 2 percent. What is the total purchase price?
Answer: $402
Step-by-step explanation: I believe this answer is correct i did all the math
A metal strip is being installed around a rectangular workbench that is 11 feet long and 4 feet wide. If the stripping costs
$5 per foot, find the total cost of the stripping.
total cost =$?
Step-by-step explanation:
that is the same as calculating the perimeter of the rectangle (the way 1 time around the rectangle).
the perimeter of a rectangle is
2×length + 2×width
in our case that is
2×11 + 2×4 = 22 + 8 = 30 ft
the stripping costs $5 per foot, and we have 30 ft.
so, the total costs are
5 × 30 = $150
Simplify completely. 3x+18 divided 18
solution
3x+18/18
ans4
The radius of the circle below is 27 mm.
Calculate the area of the circle.
Give your answer in mm² to 1 d.p.
27 m
84.78 mm² is area of circle .
What is a circle ?
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the center.Having no sides or edges, a circle is a figure with a round shape. A closed, two-dimensional curved form is what is meant by the term "circular" in geometry.radius of the circle = 27 mm
area of the circle = πr²
= 3.14 * 27
= 84.78 mm²
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assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypothesis?
The null and alternative hypothesis regarding the test on whether the mean error is of zero is given by the following option:
D. H0: μ = 0 minutes, H1: μ ≠ 0 minutes.
How to identify the null and the alternative hypothesis in this test?The first step in identifying the hypothesis is to identify the claim tested, given as follows:
The mean prediction error is equals to zero.
At the null hypothesis, it is tested if there is not enough evidence to go against the claim, hence we suppose that the mean is of zero minutes, as follows:
H0: μ = 0 minutes.
At the alternative hypothesis, it is tested if there is enough evidence to reject the null hypothesis, that is, if there is enough evidence to conclude that the mean prediction error is different of zero minutes, hence it is given as follows:
H1: μ ≠ 0 minutes.
Thus option D gives the correct null and alternative hypothesis in the context of this problem.
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Write and solve a system of equations that represents the scenario below. Be sure to define your variables, and
answer the question.
Ricky Bobby and Betty Sue are super hungry after doing all of these problems, so they ask their uncle Billy Joe Bob to
take them to "Burgers and Dogs" for some tasty mini burgers and mini hot dogs. Ricky Bobby orders 3 mini burgers
and 2 mini dogs for $8. Betty Sue orders 2 mini dogs and 1 mini burger for $6. How much would Uncle Billy Joe Bob spend if he ordered 3 mini dogs and 4 mini burgers?
Can someone help me!
Answer: $11.50
==================================================
Explanation:
x = cost of one burger
y = cost of one hot dog
3 burgers = 3x dollars
2 hot dogs = 2y dollars
3 burgers + 2 hot dogs = 3x+2y = 8 dollars
The first equation to set up is 3x+2y = 8 which is based on the info of what Ricky purchased.
Through similar logic, the other equation is x+2y = 6 based on what Betty ordered.
This is the system of equations
[tex]\begin{cases}3x+2y = 8\\x+2y = 6\end{cases}[/tex]
There are a few approaches we could take. I'll use substitution.
Let's isolate x in the 2nd equation.
x+2y = 6
x = -2y+6
Then plug this into the 1st equation. Solve for x.
3x + 2y = 8
3(-2y+6) + 2y = 8
-6y+18+2y = 8
-4y+18 = 8
-4y = 8-18
-4y = -10
y = -10/(-4)
y = 2.50 dollars is the cost of one hot dog
Then,
x = -2y+6
x = -2*2.50+6
x = -5+6
x = 1 dollar is the cost of one burger
-----------------------
Check:
Ricky: 3x+2y = 3*1+2*2.50 = 3 + 5 = 8 dollars spentBetty: x+2y = 1+2*2.50 = 1+5 = 6 dollars spentThe x and y values are confirmed correct.
------------------------
The last thing to find out is how much is spent if Billy bought 4 burgers and 3 hot dogs
4x+3y = 4*1 + 3*2.50 = 4 + 7.50 = 11.50 dollars is the final answer
This assumes that Billy is paying for himself and the other people pay for themselves as well. If Billy is paying for everyone, then the total comes to 11.50+8+6 = 25.50 dollars.