We are asked to determine the equation of a line that passes through the point (-3, -1) and has a slope 2/5. To do that we will use the point-slope form of a line equation:
[tex]y-y_0=m(x-x_0)[/tex]Where:
[tex]\begin{gathered} (x_0,y_0)=\text{ point on the line} \\ m=\text{ slope} \end{gathered}[/tex]Now, we plug in the values:
[tex]y-(-1)=\frac{2}{5}(x-(-3))[/tex]Simplifying we get:
[tex]y+1=\frac{2}{5}(x+3)[/tex]Now, we apply the distributive law:
[tex]y+1=\frac{2}{5}x+\frac{6}{5}[/tex]Now, we subtract 1 from both sides:
[tex]\begin{gathered} y=\frac{2}{5}x+\frac{6}{5}-1 \\ \\ y=\frac{2}{5}x+\frac{1}{5} \end{gathered}[/tex]and thus we get the equation of the line.
15 POINT AND BRANLIEST
A 15-gallon gas tank. If you can drive 330 miles on a full tank of gas, what is the unit rate of miles per gallon he gets?
The unit rate he can drive in mile per gallon is 22 miles per gallon.
How to find unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1.
In other words, a unit rate describes the ratio of two different units for the quantity of one.
Therefore, the unit rate in miles per gallon can be calculated as follows:
Hence,
unit rate = number of miles / number of gallons
number of miles = 330 miles
number of gallons = 15 gallons
unit rate = 330 / 15
Therefore,
unit rate = 22 miles per gallon
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n
Find the value of x that makes m ||
(180 − x)°
m
An
to
W
Answer:
The value of x will be 90°
The vertices of triangle FGH are F(-5,1,) G(-2,4), and H(-1,2) the vertices of triangle F’G’H are F’(-5,-1) G(-2,-4) H (-1-2)Identify the transformation of triangle FGH to triangle F’G’H A. A translation across the x-axis B. A reflection across the x-axis C. A dilation D. A rotation
The transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.
What do we mean by reflection across the x-axis?The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).A graph will appear to be inverted or on the other side of an axis, such as the x-axis, when it is reflected along that axis.If you look closer, you'll notice that it's symmetrical, meaning that each point is equally spaced from the axis of reflection and the axis of its reflection.As a result, if you reflect a point (x, y) along the x-axis, its x abscissa will remain the same but its y ordinates will negate. So (x,y) becomes (x, -y)
So, the difference between the vertices of triangle FGH and F’G’H is the y-coordinates of the F’G’H triangle are inverse of the y-coordinates of the FGH triangle.
And as we know that in reflection across x-axis the x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse.Therefore, the transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.
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The height of a wave in California varies directlywith the seconds that pass by. At 4 seconds,the wave is 6 feet high. Find the constant ofvariation.Weight varies directly with arit
The constant variation of hight(y) to seconds(x) is 3y/2x.
What is the constant variation?The quantity that connects two variables that are directly or inversely proportional to one another is known as the constant of variation. By dividing the y-coordinate by the x-coordinate, we can find k when given any point because it is constant (the same for every point). For instance, the constant of variation is k = = 3 if y varies directly as x and y = 6 when x = 2.So, let the second be 'x' and the height is 'y'.
At 4 seconds the wavelength is 6 ft high.
Constant variation:
y/x = 6/4 = 3/23y/2xSo,
x = 4, x = 8, x = 12y = 6, y = 12, x = 18Therefore, the constant variation of hight(y) to seconds(x) is 3y/2x.
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Find the value of x
.............................
Show how you can make a ten to find the sum of 6+5
By rewritting the 6 as 5 + 1 we will get:
1 + 5 + 5 = 1 + (5 + 5) = 11
How to make a ten to simplify the sum?
One trick we do a lot when we do additions os making tens (or hundreds, thousands, etc... depending on the case).
This means that we play with the numbers in such a way that we can make tens, in this case we have the sum:
6 + 5
We can rewrite this as:
6 + 5 = 1 + 5 + 5
Using the associative property we rewrite:
1 + 5 + 5 = 1 + (5 + 5)
1 + (5 + 5) = 1 + 10 = 11
The sum is equal to 11.
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Ventana High School has found that some offerings on the lunch menu aremuch more popular than others. The following table displays students'favorite lunch choices:1875923PizzaTacosSubSandwichesChineseComboPlate98What is the estimated population proportion of students who prefer tacos?A. 0.12B. 0.32C. 0.16D. 0.06
Answer:
C. 0.16
Explanation:
In the table there are 59 students that prefer tacos and there are 367 students in total because
187 + 59 + 23 + 98 = 367
Then, the estimated population proportion of students that prefer tacos is calculated as
P = 59/367 = 0.16
Therefore, the answer is
C. 0.16
When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones. Explain why you regroup before the next step
When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones, it's important to regroup in order to correctly multiply the values.
How to illustrate the information?Using partial products or multiplying in parts is how the conventional method does multiplication. A word that also signifies multiplication is "product," so keep that in mind. Any two numbers, regardless of how tiny or how large, can be multiplied using this standard technique.
The top number is multiplied by the bottom number, one digit at a time, working your way from right to left, using this procedure.
In this case, it should be noted that the value of 5,917 × 29 is 171593.
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Each of the four shapes represents a positive whole number. The sum of the shapes in
each row and column is displayed at the end of each row and column. Using this
information, determine the numerical value of each shape.
The numerical value of each of the four given shapes filled in the rows and columns are;
pentagon shape = 8star shapes = 6spiral shapes = 3rectangle shape = 5How to find numerical value of each shape.let
pentagon shape = AStar shape = BSpiral shape = Crectangle shape = DRow 1: There are 2 stars, one pentagon and one spiral shape.
A + 2B + C = 23 .....(equation 1)
Row 2: There are 2 spiral shapes and 2 rectangle shape.
2C + 2D = 16 ......( equation 2)
Row 3: There are 1 star, one pentagon and 2 rectangle shape.
A + B + 2D = 24 ....(equation 3)
Row 4: There are 3 spiral shapes and one star shape.
B + 3C = 15 ....(equation 4)
Column 1:
2C + A + D = 19 ....(equation 5)
Column 2:
2B + C + D = 20 .....(equation 6)
From equation 4;
B = 15 - 3C
From equation 2:
D = 8 - C
Substitute B = 15 - 3C into equation 1;A + 2B + C = 23
A + 2(15 - 3C) + C = 23
A + 30 - 6C + C = 23
A = 5C - 7
Substituting D = 8 - C and A = 5C - 7 into equation 5;2C + A + D = 19
2C + (5C - 7) + 8 - C = 19
6C + 1 = 19
6C = 18
C = 3
Substitute 3 for C inA = 5C - 7
A = 5(3) - 7
A = 8
Substitute 3 for C inB = 15 - 3C
B = 15 - 3(3)
B = 6
Substitute 3 for C inD = 8 - C
D = 8 - 3
D = 5
Therefore, there are 8 pentagon shape, 6 star shapes, 3 spiral shapes and 5 rectangle shape.
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(x^3y^5)^3 × -x^6y^5
To simplify the expression you can first use this property of exponents
[tex](a\cdot b)^m=a^mb^m[/tex]Then you have
[tex]\begin{gathered} (x^3y^5)^3=(x^3)^3(y^5)^3 \\ (x^3y^5)^3=x^{3\cdot3}y^{5\cdot3} \\ (x^3y^5)^3=x^9y^{15} \end{gathered}[/tex]Now apply this property of exponents
[tex]a^b\cdot a^c=a^{b+c}[/tex]Therefore, you have
[tex]\begin{gathered} (x^3y^5)^3\cdot-x^6y^5=x^9y^{15}\cdot-x^6y^5 \\ (x^3y^5)^3\cdot-x^6y^5=x^9\cdot-x^6\cdot y^{15}\cdot y^5 \\ (x^3y^5)^3\cdot-x^6y^5=-x^{9+6}\cdot y^{15+5} \\ (x^3y^5)^3\cdot-x^6y^5=-x^{15}\cdot y^{20} \\ (x^3y^5)^3\cdot-x^6y^5=-x^{15}y^{20} \end{gathered}[/tex]Please help, Pre-Algebra super easy math question
Answer:
-16
Step-by-step explanation:
b) -x²; x = -4
-(-4)²
-(16)
-16
I hope this helps!
Answer: -16
Step-by-step explanation:
a 20$ bill, two $10 three $5 and four $1 are placed in a bag, if a bill is chosen at random what is the expected value for the amount choses
The expected value for the amount chosen from the bag is $5.90
How to get the expected value?
We have
one $20 bill.two $10 bills.three $5 billsfour $1 bills.So in total, we have 1 + 2 + 3 +4 = 10 bills.
The expected value will be then given by the sum of the products between the value of each bill and the number of bills of that type, divided by the total number of bills.
EV = (1*$20 + 2*$10 + 3*$5 + 4*$1)/10 = $5.9
The expected value is $5.9
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Solve the quadratic equation using the method indicated. See attached photo. Thanks in advance!
The quadratic formula is given by th following formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are the coefficients of the quadratic equation. In this case, you have:
a = 6
b = 9
c = -22
replace the previous values into the quadratic formula and simplify:
[tex]\begin{gathered} x=\frac{-9\pm\sqrt[]{(9)^2-4(6)(-22)}}{2(6)} \\ x=\frac{-9\pm\sqrt[]{609}}{12} \\ x_1\approx1.31 \\ x_2\approx-2.81 \end{gathered}[/tex]Hence, the solutions for the given equation are 1.31 and -2.81
Given P(A) = 0.2, P(B) = 0.31 and P(AB) = 0.152, find the value of
P(AUB), rounding to the nearest thousandth, if necessary.
Probability - The value of P(AUB) = 0.557
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
P(A) = 0.2,
P(B) = 0.31 and
P(A/B) = 0.152,
Since, we know that
P(A⋃B) = P(A)+P(B)-P(A⋂B)
So, we have to find P(A⋂B)
We know that,
P(A/B) = P(A⋂B)/P(B)
Putting the values we get,
0.152 = P(A⋂B) / 0.31
P(A⋂B) = 0.152 x 0.31
P(A⋂B) = 0.047
Now, lets find the value of P(A⋃B)
P(A⋃B) = P(A)+P(B)-P(A⋂B)
Putting the values we get,
P(A⋃B) = 0.2 + 0.31 + 0.047
P(A⋃B) = 0.557
Hence the value of P(A⋃B) = 0.557
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A high school band raises $6, 764 to buy instruments
and uniforms for its members. Half the money is spent
on new instruments. They buy 38 new uniforms with
the remaining money.
Answer:
$89 dollars per uniform
Step-by-step explanation:
Total amount of money raised= $6,764.
Money spent on new instruments= $6,764÷1/2 = $3382
The number of new uniforms bought with the remaining money= 38.
How much was spent on one= $3,382÷38 = $89
3. a) Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. The actual
was 4.1 ft. What is John's percent decrease on his measurement?
measurement
Jack's percentage decrease on his measurement of painting by 18%.
What is meant by percentage change?
Measures of percent change include percent increase and percent decease, which indicate how much an element of a variable changes in terms of intensity, size, extent, or value.
Given that,
Jack's measurement for his room = 5 ft (taking this as old value)
Actual measurement for Jack's room = 4.1 ft (taking this as new value)
Using formula for Percent change = [tex]\frac{new - old}{old}[/tex] × 100% = [tex]\frac{4.1 - 5}{5}[/tex] × 100%
= [tex]\frac{-0.9}{5}[/tex] × 100% = -0.18 × 100%
= -18%
Here, minus sign represents the decrease in percentage.
Hence, Jack's percentage decrease on his measurement of painting by 18%.
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Correct question will be :
Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. But the actual measured painting is 4.1 ft. What is Jack's percent decrease on his measurement of the painting?
solve for x if the equation is[tex]3 \sqrt{x + a - z = b} [/tex]
EXPLANATION
Given the expression:
[tex]b=\sqrt[3]{x+a-z}[/tex]Applying the cubic power to both sides:
[tex]b^3=(\sqrt[3]{x+a-z})^3[/tex]Simplifying the cubic root with the cubic power:
[tex]b^3=x+a-z[/tex]Subtracting -a to both sides:
[tex]b^3-a=x+a-a-z_{}[/tex]Adding z to both sides:
[tex]b^3-a\text{ +z = x + a - a -z + z}[/tex]Simplifying terms:
[tex]b^3-a+z=x[/tex]Switching sides:
[tex]x=b^3-a+z[/tex]Assume that when you take a bath, you fill a tub to the haltway point. The tub measures 5 feet by 2 feet by 2.7 feet. When you take a shower, you
use a shower head with
flow rate of 2.03 gallons per minute, and you typically spend 9 minutes in the shower. There are 7.5 gallons in one cubic
foot. Complete parts (a) through (c) below.
a. Do you use more water taking a shower or taking a bath? Select the correct choice below
and fill in the answer box to complete your choice.
(Round to one decimal place as needed.)
O A. Shower; you use
more cubic feet of water than taking a bath.
• B. Bath; you use
more cubic feet of water than you do taking a shower.
The person is therefore using more water for bathing than for showering, according to the conclusion.
Half of the tub's total water is consumed while taking a bath.
Water used divided by volume equals
[tex]\frac{volume}{2}[/tex]
= [tex]\frac{(5)(3)(2.8)}{2}[/tex]
=[tex]\frac{42}{2}[/tex]
=21 cubic feet.
The following will provide the total amount of water utilized while having a shower:
Total water Equals rate ×time
= 1.52 × 12
= 18.24 gallons.
So, if there are 7.5 gallons in a cubic foot, the amount of water in cubic feet will be amount
=[tex]\frac{18.24}{7.5}[/tex]
=2.432 cubic feet.
The person is therefore using more water for bathing than for showering, according to the conclusion.
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Answer to exercise 1 please
Using an exponential function and a differential equation, the constant k for the situation is given by:
k = 0.03.
What is an exponential function?An increasing exponential function is modeled according to the following rule:
[tex]A(t) = A(0)e^{kt}[/tex]
In which:
A(0) is the initial amount of the function.k is the exponential growth rate of the function, as a decimal.This exponential function is the solution to the following differential equation:
A'(t) = kA(t)
One example of application of these functions is for continuous compounding, in which the value of an investment of P(0) after t years is given by:
[tex]P(t) = P(0)e^{kt}[/tex]
For the continuous compounding situation in this problem, the interest rate is of 3%, hence k = 0.03, which is the desired parameter.
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simplify (-2)(-3)(6) 20 points plus brainliest if right
Answer:
36
Step-by-step explanation:
-2(-3)(6)
6(6)
36
Answer:
-8/2 / 6/-3 -8/2 x -3/6 24/12= 2
Step-by-step explanation:
Simplify
Y exponent -5/ y exponent -4
Answer:
"Simplify" is an instruction to rewrite the expression with as few symbols as possible. 5y-4 and 5/y4 have the same number of symbols.
A possible alternative direction might have been to rewrite without the negative exponent.
Answer:
[tex]\frac{1}{y}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
[tex]\frac{y^{-5} }{y^{-4} }[/tex]
= [tex]y^{(-5-(-4))}[/tex]
= [tex]y^{(-5+4)}[/tex]
= [tex]y^{-1}[/tex]
= [tex]\frac{1}{y}[/tex]
You purchase 5 tickets to a football game from TicketMaster. In addition to the cost per ticket, the agency charges a convenience charge of $2.50 per ticket. You also choose to pay for rush delivery, which costs $15. The total cost of your order is $352.50. What is the price per ticket before the convenience charge?
The price per ticket, excluding the convenience charge, is $65.
How to solve for the privce per ticketthe rush delivery is given as $15.
The total cost of the tickets is said to be put at $352.50
Then the value that we would have for the the 5 tickets wpould be 352.50 - 15 = $337.50.
There is the convenience charge of $2.50 per ticket. This charge is excluded from the convenience charge that is to be paid.
Hence you would have to make the payment of
337.50 - 5*2.50
= 325.
Next we are to solve for the price of the ticket whioch is independent of the convenience charge
= 325 / 5
= $65
Hence the price per ticket is given as 65 dollars
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A company borrows $68,000 for 8 years at a simple interest rate of 15.5%. Find the interest paid on the loan and the total amount paid.
The interest paid on the loan and the total amount paid are $84,320 and $152,320 respectively.
It is given in the question that:-
Money borrowed by the company (Principal) = $68,000
Time period for which the money is borrowed = 8 years
Simple Interest rate = 15.5 %
We have to find the interest paid on the loan and the total amount paid.
We know that,
Simple interest = (Principal * Interest * Rate)/100
Hence, we can write,
Simple interest = (68000 * 15.5 * 8)/100 = $84,320
Also, we know that,
Amount = Principal + Interest
Hence, we can write
Amount = 68,000 + 84,320 = $152,320
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Based on this data what is the probability that the next car will not be white why
The probability of the next car not being a white car is 0.92
What is probability?The probability of an event is the chance or the likelihood that the event would occur.
Note that the chance or the likelihood is represented as a numerical value
How to determine the probability?The complete question is added as an attachment
From the attached question, we have the following parameters
P(White Vehicle) = 0.25
P(Car) = 0.36
P(White Car) = 0.08
Using the complement rule of probability, we have the following equation
P(White Car) + P(Not White Car) = 1
Substitute the known values in the above equation
So, we have the following equation
0.08 + P(Not White Car) = 1
Subtract 0.08 from both sides of the equation
So, we have
P(Not White Car) = 1 - 0.08
Evaluate the difference
P(Not White Car) = 0.92
Hence, the probability that the next car will not be a white car is 0.92
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The Life time in hours of a certain aircraft has the normal distribution with mean 80, Standard devation 16. What is the probability that the aircraft Will last 100 hours
1.25 is the probability that the aircraft Will last 100 hours.
What is probability?The area of mathematics described as probability concerns with numerical representations of the likelihood that an event will occur or that an assertion is correct. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.
Given Data
Mean = 80
Standard deviation = 16
P( x < 100)
P( x < 100) = P( Z< [tex]\frac{x- mean}{standard deviation}[/tex])
P(x<100 ) = P( Z < [tex]\frac{100-80}{16}[/tex])
P(x< 100) = P(Z< [tex]\frac{20}{16}[/tex])
P(x < 100) = 1.25
1.25 is the probability that the aircraft Will last 100 hours.
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1/16x+1/320y-29=0 rewrite the equation as a function of x
The equation as a function of x is y = 9280 -20x
What is equation ?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" sign in the statement. It shall be taken into account as an expression.
The equation is =[tex]\frac{1}{16}x + \frac{1}{320}y - 29= 0[/tex]
Now rearranging the function we write
[tex]\frac{y}{320}= 29 -\frac{x}{16}[/tex]
y = 9280 -20x
The equation as a function of x is y = 9280 -20x
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As long as you follow through with a plan to save $2000 a year, at the end of each year, in your account that earns 4% interest how much would you have after 25 years future value?
We have to use the simple interest formula.
[tex]A=P(1+rt)[/tex]Where P = 2,000, r = 0.04, t = 25. Let's solve for A
[tex]\begin{gathered} A=2,000(1+0.04\cdot25)=2\cdot2,000 \\ A=4,000 \end{gathered}[/tex]Therefore, you will have $4,000 in 25 years.a₁ = 4; a = (a)²-3 (n ≥2) list the first five terms
The first five terms of the given sequence are 4, 1, 6, 13, 22
We can solve this problem by following a few steps.
The formula to find the next four terms is, a = (n)²- 3, (n ≥2) as per the question.
Where n is the sequence of the number ( n = 2, 3, 4, 5, 6, etc. )
So, for the 2nd term A₂ = 2² - 3 = 4 - 3 = 1 [As n = 2 for the second term ]
Similarly, for the 3rd term A₃ = 3² - 3 = 9 - 3 = 6 [ As n = 3 for the third term ] ,
for the 4th term A₄ = 4² - 3 = 16 - 3 = 13 [ As n = 4 for the second term ] ,
for the 5th term A₂ = 5² - 3 = 25 - 3 = 22 [As n = 5 for the second term ]
Now, we can conclude that the first five terms of the given sequence are 4, 1, 6, 13, 22
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The correct question is :
a₁ = 4; a = (n)²-3 (n ≥2) list the first five terms
Graph the linear function p(x) = 4x
The graph is attached below.
We are given a linear function.The function p(x) equals 4x.We have to graph the function.In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.Let "y" denote p(x).y = 4xNow, we can get several pairs of coordinates that satisfy the above linear function.We plot the points on the graph and join them.We can see that the given function is an equation of a straight line that passes through the origin and has a positive slope of magnitude 4.To learn more about functions, visit :
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what is an equation
We have to write the equation of the line that pass through (4,-5) and (2,0).
We can calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-5)}{2-4}=\frac{5}{-2}=-2.5[/tex]We can then write the slope-point form of the equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-0=-2.5(x-2) \\ y=-2.5x+5 \end{gathered}[/tex]Answer: y=-2.5x+5