Answer:
x - intercept = - 1
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 )
given
x - 2y = 7 ( subtract x from both sides )
- 2y = - x + 7 ( divide through by - 2 )
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{7}{2}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/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{1}{2} }[/tex] = - 2 , then
y = - 2x + c ← is the partial equation of the perpendicular line\to find c substitute (- 3, 4 ) into the partial equation
4 = 6 + c ⇒ c = 4 - 6 = - 2
y = - 2x - 2 ← equation of perpendicular line
to find the x- intercept let y = 0 into the equation and solve for x
- 2x - 2 = 0 ( add 2 to both sides )
- 2x = 2 ( divide both sides by - 2 )
x = - 1
the x- intercept of the perpendicular line is - 1 or (- 1, 0 )
You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 6? (b) What is the probability of getting a sum of 4? (c) What is the probability of getting a sum of 6 or 4? Are these outcomes mutually exclusive?
Based on the number of dice rolled, the probability of getting the sum of 6, and 4 and 6 or 4 can be found to be:
Probability of getting sum of 6 = 5 / 36Probability of getting sum of 4 = 1 / 12Probability of getting sum of 6 or 4 = 2 / 9How to find the probability?Probability of getting sum of 6:
(1 and 5) (2 and 4) (3 and 3) (4 and 2) ( 5 and 1)
= 5 / (6 x 6)
= 5 / 36
The number of sums of 4 are:
= (1 and 3), (2 and 2), (3 and 1)
= 3 / (6 x 6)
= 1 / 12
The probability of getting sums of 6 and 4 are:
= (5 + 3) / (6 x 6)
= 8 / 36
= 2 / 9
These events are mutually exclusive because they cannot roll a sum of 6 or 4.
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Given the system of equation 3x - 2y-9=0 X + 8y-3 = 0 Is (3, 0) a solution to the given system?
Yes (3,0) is the solution of the given equation.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given Data
Equation
3x - 2y-9=0
X + 8y-3 = 0
Solution(3, 0)
Finding the values of x,
x + 8y - 3=0
x = 3 + 8y...(1)
Substituting x in the equation
3x - 2y = 9
3(3+ 8y) -2y = 9
9 + 24y - 2y = 9
22y = 0
y = 0
Substituting the value in (1)
x = 3 + 8(0)
x = 3
Yes (3,0) is the solution of the given equation.
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Matt and Wei are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small boxes of fruit and large boxes of fruit. Matt sold 18 small boxes of fruit and 25 large boxes of fruit for a total of $529.50. Wei sold 18 small boxes of fruit and 10 large boxes of fruit for a total of $282.00. Find the cost of one small box of fruit and the cost of one large box of fruit.
Answer:
The small box price is 6.5 and The large box price is 16.5
Step-by-step explanation:
I did the question with a simultaneous equation
let's say the price of the small box = x and the price of the large box = y
Then, I just subtract downward;
18x+25y=529.50
- 18x+10y=282.00
_____________
0+15y=247.50
15y=247.50
— ————
15 15
I just canceled 15 by 15:
Then, y=247.50÷15=16.5
so I just find the value of Y which is 16.5, then I insert it into the second equation:
18x+10y=282
18x+10(16.5)=282
18x+165=282
18x=282-165
18x=117
— —
18 18
Cancel 18 by 18
finally x=6.5
Insert x and y into both equations, it works
A wheel on Amanda's bicycle is 0.3 m in diameter. Amanda races the bicycle for 35 m. How many times does the wheel turn as the bicycle travels this distance?
Use the value 3,14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answer:
37.2 rotations
Step-by-step explanation:
35 / (3.14 x .3) = 37.15499
Rounded = 37.2 rotations
(A.) Given the one-to-one function f(x)= 7x - 2, find it's inverse function.
Which is f ^ -1(x)= 1/7x - 2/7
(B.) The graphs of f and f^ -1 are symmetric with respect to the line defined by
y = _______
The inverse function of one-to-one function f(x)= 7x - 2 is [tex]f^{-1}=\frac{x}{7}+\frac{2}{7}[/tex].
The graphs of f and [tex]f^{-1}[/tex] are symmetric with respect to the line defined by y = x.
Given that:-
f(x)= 7x - 2
Let f(x) = y
Hence,
[tex]f^{-1}(y)=x[/tex]
Hence, we can write,
y = 7x - 2
y + 2 = 7x
x = y/7 + 2/7
[tex]f^{-1}(y) = y/7 + 2/7[/tex]
Replacing y by x, we get,
[tex]f^{-1}(x) = x/7 + 2/7[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = x/7 + 2/7[/tex].
The graph of inverse is always the mirror image of the function's graph in the line y = x. It is because they're basically 100% similar but in reverse just like you in a mirror.
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Graph the function. Label the vertex and axis of symmetry. Hint: Recall when in Standard form use x value=-b/2a. ( SHOW WORK)
The features of the graphs are
Graph 1: Vertex = (4, 3); Axis of symmetry: x = 4Graph 2: Vertex = (-0.4, -1.8); Axis of symmetry: x = -0.4How to graph the functions?Function 1
The equation of the function is given as
f(x) = 3(x - 4)^2 + 3
A quadratic equation can be represented as
f(x) = a(x - h)^2 + k
Where, the vertex is
Vertex = (h, k)
And the axis of symmetry is
x = h
By comparing the equations, we have
Vertex = (4, 3)
Axis of symmetry: x = 4
See attachment 1 for the graph of the function
Function 2
The equation of the function is given as
f(x) = 5x^2 + 4x - 1
Differentiate the function
f'(x) = 10x + 4
Set to 0
10x + 4 = 0
This gives
x = -0.4
Substitute x = -0.4 in f(x) = 5x^2 + 4x - 1
f(-0.4) = 5(-0.4)^2 + 4(-0.4) - 1
Evaluate
f(-0.4) = -1.8
This means that
Vertex = (-0.4, -1.8)
Axis of symmetry: x = -0.4
See attachment 2 for the graph of the function
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Riders for the Kiddie Koaster at the State Fair must be no more than 48 inches tall. Which inequality best expresses the height of the riders?
Answer:Note that at least means greater than or equal to (≥) . It was stated that you must be at least 48 inches tall to ride the roller coaster. Hence, the inequality is h≥48 h ≥ 48
Step-by-step explanation: poopity poop UWU UWU UWU oodfijdisfioahgioahiodfhipodioajhierfia MUSIC MUSIC MUSIC MUSIC MUSIC MUSIC HACKER HACKER HAKER HACKER HACKER OMG UWU UWU UWU YOUR 13 LOL YOUR FATHERLESS GT DELETED TRASH KID
A company uses two factories to manufacture three different sizes of boats. Each boat takes a different amount of time to perform each task. For example, the small boat requires 1 hour of cutting, 0.5 hours of assembly, and 0.2 hours of packaging. The medium boat requires 1.6 hours of cutting, 1 hour of assembly, and 0.2 hours of packaging. Finally, the large boat requires 2.5 hours of cutting, 2 hours of assembly, and 1.4 hours of packaging time. The factory pays each department at each factory differently, according to this pay scale: Factory A pays out $15 per hour for cutting, $12 for packaging, and $11 for assembly. Factory B pays out $13 for cutting, $11 for assembly, and $10 for packaging. How much will each factory have to pay in wages to construct each type of boat?
Using proportions, the costs for the boats are given as follows:
Factory A:
Small: $22.9.Medium: $37.4.Large: $76.3.Factory B:
Small: $20.5.Medium: $33.8.Large: $68.5.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using the standard operations such as addition, subtraction, multiplication and division with the unit rates to find the equivalent amounts.
Considering the costs per hour and the number of hours needed, the cost of a small boat at Factory A is given by:
15 x 1 + 11 x 0.5 + 12 x 0.2 = $22.9.
For example, 15 x 1 is because it requires one hour of cutting, and each hour of cutting pays of $15.
The cost of a medium boat at Factory A is given by:
15 x 1.6 + 11 x 1 + 12 x 0.2 = $37.4.
The cost of a large boat at Factory A is given by:
15 x 2.5 + 11 x 2 + 12 x 1.4 = $76.3.
The cost of a small boat at Factory B is given by:
13 x 1 + 11 x 0.5 + 10 x 0.2 = $20.5.
The cost of a medium boat at Factory B is given by:
13 x 1.6 + 11 x 1 + 10 x 0.2 = $33.8.
The cost of a large boat at Factory B is given by:
13 x 2.5 + 11 x 2 + 10 x 1.4 = $68.5.
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HELPPPP PLEASEEE!!!
(MATH AND CHEMISTRY RELATED)
2(x+4)-3(2x-5)=-3
What is the answer
Answer: x= 13/2 or 6 1/2
Step-by-step explanation:
2(x+4)-3(2x-5)=-3
Simplify the equation,
2x+8-6x+15 = -3
-4x+23= -3
-4x = -26
Cancel the minus sign, now we get
2x = 13
i.e., x= 13/2
Assuming the population has an approximate normal distribution,
if a sample size n = 12 has a sample mean
= 36 with a sample standard deviations = 9, find the margin of error at a 98% confidence level. Round
the answer to two decimal places.
E = 38.33 the margin of error at a 98% confidence level by standard deviation mean.
What does standard deviation mean ?
The term "standard deviation" (or "") refers to a measurement of the data's divergence from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.The average degree of variability in your dataset is represented by the standard deviation. It reveals the average error of each statistic from the mean.Given that,
bar x = 36
s = 9
n = 12
Degrees of freedom = df = n - 1 =12 - 1 = 11
At 98% confidence level the t is ,
∝ = 1 - 98% = 1 - 0.98 ⇒ 0.02
∝/2 = 0.02/2 = 0.01
t∝/2 df = t0.01 ,11 = 1.231
Margin of error = E = t∝/2, df * ( s/n/sqrtn)
E = 1.231 * ( 9 /0.01/sqrt12)
E = 38.33
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Is a tutor availible
So if i have a bag of rice of 3.5 pounds, that means that it weighs:
[tex]3.5\text{ pounds = 56 ounces}[/tex]since
[tex]3.5\text{ x 16 = 56}[/tex]that means that you will have enough rice for the recipe
4. (01.02 LC) Brandi earned $78 in interest after one and one half years on an account that paid 7.5% simple interest annually. Use the formula I = Prt to find Brandi's principal balance. Round to the nearest hundredth. (1 point) $69.33 $87.75 $693.33 $768.00
The principal amount is $693.33.
What is Simple Interest?Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount.
The formula is
Simple Interest = P x R x T/100
Given:
Interest = 78
Rate= 7.5%
Time= 1 and half year = 1.5 year
Now, Simple Interest= P x R x T / 100
78 = P x 7.5 x 1.5 / 100
7800= P x 11.25
P = 7800/11.25
P = 693.33
Hence, the principal amount is $693.33.
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HURRY Find all solutions to the equation x3 + 100x + 8x2 = –800.
–10, –8, 10
–10, 8, 10
8, –10i, 10i
–8, –10i, 10i
Answer:
-8, -10i, 10i
Step-by-step explanation:
x^3 + 8x^2 + 11x = -800
I just plugged it into my calculator
Enter a range of values for x.85°5x - 1025Sk[ ? ]
°
the two triangles have a bisetor that makes the adjacent side equal, so based on this 25 = 5x- 10
25+ 10 = 5x
meaning your x = 7
but on the equation 5x-10 =0
we get that x = 10/5
x >2
so the range would be 2
Solving a value mixture problem using a system of linear....
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $20 and same-day tickets cost $35. For one performance,
there were 60 tickets sold in all, and the total amount paid for them was $1500. How many tickets of each type were sold?
Number of advance tickets sold:
Number of same-day tickets sold:
The linear equation 20x + 35(60-x) = 1500 can be solved to find the number of tickets.
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its related terms in various languages may have somewhat different definitions; for example, in French, an equation is described as including one or more elements, but in English, an equation is any well-formed formula that includes two expressions linked by an equals sign.
Let the number of advance tickets sold = x
And then, the number of same-day tickets sold = 60 - x
Then, the equation formed is
20x + 35(60-x) = 1500
=> 20x + 2100 - 35x = 1500
=> -15x = 1500 - 2100
=> x = -600/ -15 = 40
Hence, the number of advance tickets sold = 40
And the number of same-day tickets sold = 60 - 40 = 20
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The lengths of the side of a triangle are 6, 8, 10. Can the triangle be a right triangle?
Yes, the triangle is a right-angle triangle.
Right angle triangle is a triangle in which one of the angles as 90 degree.
For the triangle to be right angle triangle
perpendicular² + base² = hypotenuse²
The three sides of a triangle are 6, 8 and 10
So,
6² + 8² = 10²
36 + 64 = 100
100 = 100
Therefore the triangle is a right-angle triangle.
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Find the midpoint of the line segment joining the points (-2,-3) and (-4,10)
THE MIDPOINT FORMULAR IS GIVEN BY
[tex]( \frac{x1 + x2}{2} . \frac{y1 + y2}{2} ) \\ \\ = (\frac{ - 2 + ( - 4)}{2} . \frac{ - 3 + 10}{2} ) \\ = ( \frac{ - 6}{2} . \frac{7}{2} ) \\ = ( - 3. \frac{7}{2} )[/tex]
ATTACHED IS THE SOLUTION
Shureka Washburn has scores of 86, 84, 83, and 49 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 76 or higher, given that the final exam counts as two tests.
b. Explain the meaning of the answer to part (a).
The most appropriate choice for average will be given by-
Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.
What is average?
In a data set, there are many numbers. Average is the single number which acts as a representative of all the numbers in the data set.
Average is calculated by sum of all observations divided by total number of observations.
Here,
Let the score of Shureka Washburn in her last test be x
Score of Shurek Washburn on first test = 86
Score of Shurek Washburn on second test = 84
Score of Shurek Washburn on third test = 83
Score of Shurek Washburn on fourth test = 49
Total sum of all her scores = 86 + 84 + 83 + 49 + x
= 302 + x
Average = [tex]\frac{302 + x }{5}[/tex]
By the problem,
[tex]\frac{302 + x}{5} \geq 76[/tex]
[tex]302 + x \geq 76[/tex] [tex]\times 5[/tex]
[tex]302 + x \geq 380[/tex]
[tex]x \geq 380 - 302[/tex]
[tex]x \geq 78[/tex]
Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.
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What is the distance between points A(2,9) and B(-2,6)? Round to the nearest whole number.
The distance between the two points is 5.
The formula to find the distance between two points (x1, y1) and (x2, y2)
distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]
Substituting points A(2,9) and B(-2,6), we get
distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]
=[tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
= [tex]\sqrt{16 + 9}[/tex]
=[tex]\sqrt{25}[/tex]
= 5
Therefore the distance between the two points is 5.
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Recall that the sum of the measures of the angles of a triangle is 180°. In the triangle below, angle Chas the same measure as angle B, and angle measures 42° less than angle B.
Find the measure of each angle.
Answer:
180=x+42
collect like terms
x=180-42
x=138
Solve the inequality.
C - 12 > -1
Answer:
c>11
Step-by-step explanation:
you +12 on both sides then u now have 11 rather than -1 which leaves u with c>11
Together, Luke and James have never eaten more than 16 pieces of pizza at one time.Which equation describes y, the total number of pieces that Luke has eaten at one time givenx, the number of pieces that James has eaten?a. y <_16-x b. y>_16-x c. y=16-x d. not here
y ≤ 16 - x (option A)
Explanation:let the total number of pieces Luke ate at a time = y
Let the total number of pieces James ate at a time = x
They have never eaten more than 16 pices of pizza
This is written as:
maximum 16 : ≤ 16
number of pieces Luke ate at a time + total number of pieces James ate at a time ≤ 16
y + x ≤ 16
rewritting to make y subject of formula:
y ≤ 16 - x (option A)
Zach and Ginny are building model cars. Ginny's car is 2 more than 3 times the length of Zach's car. The sum of the lengths of both cars is 30 inches. Write an equation to determine the lengths of Zach's and Ginny's cars.
3x + 2 = 30
x + 2 + 3x = 30
2x + 3 = 30
x + 2x + 3 = 30
A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $35 and then an additional 6 cents per minute of use.
For what amounts of monthly phone use will Plan A cost less than Plan B?
Use m for the number of minutes of phone use, and solve your inequality for m
Answer: Less than 470 minutes
Step-by-step explanation:
This equation represents this problem.
0.04x + 44.4 = 0.06x + 35
Solve,
0.02x = 9.4
1 / .02 = 50
x = 470
At 470 minutes they're equal and we are looking for when Plan A is cheaper then Plan B, so x < 470
Use m instead of x in this problem, sorry didn't read the last line.
Emily works at a factory that makes computer parts. The machine that produces internal hard drives results in a certain number of defects during the day. The table below represents the probability density function for the random variable X, the number of defects per day. Find the standard deviation of X. Round the final answer to two decimal places.
The standard deviation of the discrete distribution of the number of defects in a day is of 0.75 defects.
What are the mean and the standard deviation of a discrete distribution?The mean of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.The standard deviation of a discrete distribution is given by the square root of the sum of the difference squared between each outcome and the mean, multiplied by it's respective probability.From the distribution at the end of the answer, the mean is:
E(X) = 0.1667 x 4 + 0.3333 x 5 + 0.5 x 6 = 5.3333.
Hence the standard deviation is of:
S(X) = sqrt(0.1667 x (4-5.3333)² + 0.3333 x (5 - 5.3333)² + 0.5 x (6 - 5.3333)²) = 0.75 defects.
What is the missing information?The distribution is missing, and is given as follows:
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Use a law of exponents to write (-3mn^5)^4 as a product of powers
The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]
Here we have to determine the sign for exponential or radical expression
(-3m[tex]n^{5}[/tex])^4
Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]
Similarly
(-3m[tex]n^{5}[/tex])^4
= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]
Now using the exponent power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get
= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]
Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].
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(X^3- 5x+ 3) ÷ (x- 2)
Over the last three evenings, James received a total of 90 phone calls at the call center. The second evening, he received 2 times as many calls as the third evening. The first evening, he received 6 more calls than the third evening. How many phone calls did she receive each evening?
Answer:
first evening = 27 calls
second evening = 42 calls
third evening = 21 calls
Step-by-step explanation:
Total of 90 calls
f = first evening
s = second evening
t = third evening
Solve:
f=t+6
s = 2t
t=t
f+s+t=90
t+6 + 2t + t
(2t+t+t)+6 = 90
4t+6 = 90
4t=84
t=21
ANSWER:f=t+6=21+6
= 27
s = 2t
= 42
t = t
= 21
7.
Write and solve the system of equations needed to model this situation: You have thirty coins
a total value of $3.40, which are made up of nickels, dimes, and quarters. There are twice as many
nickels than quarters. How many of each type of coin do you have?
The system of equations for the given conditions in question includes equation: 3.40 = 0.05x + 0.1y + 0.25z, and 2x = z. and we have 2 nickels, 23 dimes, and 4 quarters.
What is system of equations?
A system of equations is a collection of some equations with one or more numbers of variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.
Let the quantities of nickels, dimes, and quarters are x, y, and z respectively.
We know that, 1 nickel = $0.05, 1 dime = $0.1, and 1 quarter = $0.25
So, the values of nickels, dimes, and quarters would be value of one times total quantity.
Nickels = 0.05x, dimes = 0.1y, and quarters = 0.25z
As given in the question, the total value is 3.40
So, we get equation:
3.40 = 0.05x + 0.1y + 0.25z
Also it is given that there are twice as many nickels than quarters.
2x = z
Combining above two equations
3.40 = 0.05x + 0.1y + 0.25(2x)
3.40 = 0.05x + 0.1y + 0.5x
3.40 = 0.55x + 0.1y
Lets put 2 in place of x, we get y
(3.40 - 1.1)0.1 = y
y = 23.
Now, putting values of x, y in equation to get value of z
3.40 = 0.05(2) + 0.1(23) + 0.25z
3.40 = 0.1 + 2.3 + 0.25z
(3.40 - 2.4)/0.25 = z
z = 4
Therefore, we have 2 nickels, 23 dimes, and 4 quarters.
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