Answer the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2
A linear equation can have the form
y = mx + b
The slope is m
The point-slope form is
(y- y1) = m(x -x1) (1)
the point (x1, y1) = (6, -3)
______________
Replacing in (1) the slope and the point (x1, y1)
(y- y1) = m(x -x1)
(y- (-3)) = 1/2(x -6)
y+3 = 1/2(x-6)
__________________
So, checking the options the correct answer is C
A.) y-6 = 1/2(x+3)
B.) y = 1/2x - 6
C.) y+3 = 1/2(x-6)
D.) y-2y = 12
126°r= 15 cmFind the arc length of the shaded sector.
To determine the arc length of the shaded area you have to use the following formula:
[tex]\text{arc.length}=2\pi r(\frac{\theta}{360º})[/tex]"θ" represents the measure of the central angle, in degrees
"r" represents the radius of the circle
We know that the arc measure is 126º, the central angle has the same measure as the intercepted arc, then its measure is also θ=126º
The radius of the circle is r=15cm
[tex]\begin{gathered} \text{arc.length}=2\pi\cdot15\cdot(\frac{126}{360}) \\ \text{arc.length}=30\pi\cdot\frac{7}{20} \\ \text{arc.length=}\frac{21}{2}\pi \\ \text{arclength}\approx32.98\approx33\operatorname{cm} \end{gathered}[/tex]Sketch a diagram showing VX intersectingUW at V so that VX is perpendicular toU and U, V, and W are collinear.
We have to do a diagram with the following characteristics.
• VX has to intersect UW at V.
,• VX is perpendicular to UW.
,• U, V, and W are collinear.
Based on the given information, we have the following diagram
The image above shows the answer.
Find the coordinates of the points of intersection of the graphs with coordinate axes: y= -1/4x+2
Answer:
Solutions below.
Step-by-step explanation:
This question is asking us to find the points of intersection, which means its asking to find the x-intercept abd y-intercept.
To find the x-intercept, we know that y = 0.
Therefore we can substitute y = 0 into the line equation:
[tex]0 = - \frac{1}{4} x + 2 \\ - \frac{1}{4} x = - 2 \\ x = - 2 \div - \frac{1}{4} \\ = 2 \times 4 \\ = 8[/tex]
Therefore the point of the x-intercept is (8,0).
Likewise to find the y-intercept, we know x = 0.
Therefore we can substitute x = 0 into the line equation:
[tex]y = - \frac{1}{4} (0) + 2 \\ = 0 + 2 \\ = 2[/tex]
Therefore the point of the y-intercept is (0,2).
Answer:
x-intercept: (8, 0)
y-intercept: (0, 2)
Step-by-step explanation:
Given equation:
[tex]y=-\dfrac{1}{4}x+2[/tex]
The graph intersects the y-axis when x = 0.
To find the graph's y-intercept, substitute x = 0 into the equation and solve for y:
[tex]\begin{aligned}x=0 \implies y&=-\dfrac{1}{4}(0)+2\\y&=0+2\\y&=2\end{aligned}[/tex]
Therefore, the coordinates of the point of intersection with the y-axis are:
(0, 2)The graph intersects the x-axis when y = 0.
To find the graph's x-intercept, substitute y = 0 into the equation and solve for x:
[tex]\begin{aligned}y=0\implies \-\dfrac{1}{4}x+2&=0\\-\dfrac{1}{4}x&=-2\\x&=8\end{aligned}[/tex]
Therefore, the coordinates of the point of intersection with the x-axis are:
(8, 0)Isabel will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.
(a) Option B, 30
At 180 miles, Option B costs $50, but Option A costs $80.(b) 60, Option A
The cost is the same when the graphs intersect.Before 60 miles, the graph for Option A is lower than the graph of Option B, meaning Option A will cost less money.Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, 2x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is nosolution, indicate "No Solution."cos(x) + cos(x) = 4cos(x) + 4
The solutions to the quadratic trigonometric equation are given as follows:
x = kπ, k = ± 1, ± 3, ± 5, ± 7.
How to solve the quadratic trigonometric equation?The quadratic trigonometric equation is defined as follows:
cos²(x) + cos(x) = 4cos(x) + 4.
Then the following transformation is applied to solve the equation:
y = cos(x).
Hence:
y² + y = 4y + 4
y² - 3y - 4 = 0
(y - 4)(y + 1) = 0.
Applying the Factor Theorem, the solutions are given as follows:
y - 4 = 0 -> y = 4.y + 1 = 0 -> y = -1.However, we want the solutions for x, hence they are obtained as follows:
cos(x) = 4.
x = arccos(4), which has no solution, as there are no angles with a cosine of four.
cos(x) = -1.
x = arccos(-1)
x = kπ, k = ± 1, ± 3, ± 5, ± 7
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An agent lists a sellers house for 6% commission. The final agreed sales price is $205,000. How much commission did the seller pay?
Out of $205000, the total commission earned by the agent will be $12300.
What is Commission?
A commission is a fee paid to a salesperson in exchange for services in facilitating or completing a sale transaction. Mathematically -
Commission [C] = Sales revenue [R] x commission rate [rc]
Given is an agent who lists a sellers house for 6% commission. The final agreed sales price is $205,000.
The total sales price = [P] = $205000
The commission on house = [C] = 6%
Now, the money agent gets as a commission will be = [M] -
[M] = 6% of 205000
[M] = (6/100) x 205000
[M] = 6 x 2050
[M] = 12300
Therefore, out of $205000, the total commission of the agent will be $12300.
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2 × 4/3, but the answer as a fraction
The given expression is : 2 × 4/3
[tex]\begin{gathered} 2\times\frac{4}{3}=\frac{2\times4}{3} \\ 2\times\frac{4}{3}=\frac{8}{3} \end{gathered}[/tex]Answer :
[tex]2\times\frac{4}{3}=\frac{8}{3}[/tex]
in January 2008, the temperature in parts of Minnesota fell from 41 degrees to -13 degrees over a 24 hour period. what was the average temperature change per hour?
We need to find the average termperature change per hour during January 2008.
We have the information that Minnesota fell from 41 degrees to -13 degrees over 24 hours.
Then, 41 degrees to -13 degrees, there is a difference of 41+13 = 54 degrees over 24 hours.
If the difference is over 24 hours, then:
54 degrees / 24 hours =2.25 F is the rate of change.
However, the termperature is decreasing, so the rate of change must be negative.
Hence, the rate of change = -2.25 F.
The correct answer is the third option.
Dialate about the origin using a scale factor of 1/3
To determine the post image coordinates after a dilation centered about the origin, we will simply multiply each of the coordinates by the given scale factor of 1/3.
Let's start with Point A.
[tex](-12\times\frac{1}{3},24\times\frac{1}{3})\Rightarrow(-4,8)[/tex]The post image coordinate of A is at (-4, 8).
Moving on to Point B.
[tex](-30\times\frac{1}{3},0\times\frac{1}{3})\Rightarrow(-10,0)[/tex]The post image coordinate of B is at (-10, 0).
Lastly to Point C.
[tex](-36\times\frac{1}{3},36\times\frac{1}{3})\Rightarrow(-12,12)[/tex]The post image coordinate of C is at (-12, 12).
The pentagons ABCDE and PQRST are similar.
Find the length x of TP.
Yo bro, I'm just doing this for the rewards for my homework. please don't read this or take it serious
A building floor plan is shaped like a trapezoid, with two right angle corners. If the third corner is a 40° angle, what is the measure of the fourth angle?
Recall that the interior angles of a regular quadrilateral add up to 360 degrees, and a right angle has a measure of 90 degrees.
Let x° be the measure of the fourth angle, then we can set the following equation:
[tex]40^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}.[/tex]Adding like terms we get:
[tex]220^{\circ}+x^{\circ}=360^{\circ}.[/tex]Subtracting 220 degrees from the above result we get:
[tex]\begin{gathered} 220^{\circ}+x^{\circ}-220^{\circ}=360^{\circ}-220^{\circ}, \\ x^\circ=140^\circ. \end{gathered}[/tex]Answer:
[tex]140^{\circ}.[/tex]I need help solving for x and y
[tex]\cos \theta=\frac{x}{16} \implies x=16 \cos \theta \\ \\ \sin \theta=\frac{y}{16} \implies y=16 \sin \theta[/tex]
Given the scatter plot on the graph below. What is the slope of the line of fit
Hello there. To solve this question, we'll have to remember some properties about scatter plots and slope of a line.
Given the scatter plot of the data information, we have to determine the slope of the line.
For this, we could determine it numerically using the least squares method, if we knew the data (the coordinates of the points we're plotting the best fit).
In this case, we simply need to find, by inspection, two points contained in the line and use the slope formula.
Given two points (x0, y0) and (x1, y1) that a line L passes through, then the slope m of this line is given by:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]By inspection, we can easily spot the points (16, 12) and (28, 20).
Plugging these coordinates in the formula, we get:
[tex]m=\frac{20-12}{28-16}[/tex]Add the numbers and simplify the fraction
[tex]m=\frac{8}{12}\overset{:4}{=}\frac{2}{3}[/tex]This is the slope of this line.
The values of x and y
The values of x and y are 26° and 54° respectively.
Consider the triangle with x is triangle 1
Triangle with y is triangle 2
In triangle 1
Since it is a right angled triangle one angle is already known
Another angle is 64°
We know the sum of interior angles of a triangle is equal to 180
Hence 90 + 64 +x = 180°
154 + x = 180°
x= 180 - 154
x = 26°
From triangle 2 it is evident that x and y are complementary angles which means they sum up to 90°
Hence x + y = 90°
26 + y = 90
y = 90 - 26
y = 54°
Hence the value of x and y are 26° and 54° respectively
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The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a
followed by a
A 90 degree counterclockwise rotation about point A, a reflection across the y-axis, and a translation 20 units down may be used on quadrilateral ABCD to demonstrate that it is congruent to quadrilateral GHIJ.
A quadrilateral in geometry is a four-sided polygon with four edges and four corners. A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English term quadrilateral. A four-sided polygon with four angles is known as a quadrilateral. Parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid are the seven different forms of quadrilaterals.
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Can you please help me out with a question
Note:
For similar shapes, the ratio of their areas is equal to the square of the ratio of sides.
That is:
[tex]\text{ ratio of areas of similar shapes = (ratio of sides )}^2[/tex][tex]\begin{gathered} \frac{846}{376}\text{ = (}\frac{X}{24})^2 \\ \frac{846}{376}\text{ = }\frac{x^2}{576} \\ \text{cross multiply} \\ 376X^2=\text{ 576 x 846} \\ 376X^2=487296 \\ X^2=\frac{487296}{376} \\ X^2=1296 \\ X=\sqrt[]{1296}\text{ = 36} \end{gathered}[/tex]The value of X is 36
College Algebra
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 5 hours, while the outlet pipe can empty it in 8 hours. How long will it take to fill the vat if both pipes are left open?
It will take__ hours.
(Simplify your answer. Do not round.)
Answer:
3 1/13
Step-by-step explanation:
rate(time) of one pipe + rate(time) of the other pipe = 1 job
The rate would be the the number of jobs over the time
The rate of the first pipe is 1/5 and the rate of the second pipe is 1/8.
Together:
1/5t + 1/8t = I job
t(1/5 + 1/8) = 1
t(8/40 + 5/40) = 1
t(13/40) = 1 multiply each side by 40/13
t(40/13)(13/40) = 1(40/13)
t = 40/13
t = 3 1/13
8y=5x-15;y=10 which is the answer
Since we have that y = 10, then:
[tex]8\cdot(10)=5x-15[/tex][tex]80=5x-15\Rightarrow80+15=5x-15+15\Rightarrow95=5x+0[/tex]Then
[tex]5x=95\Rightarrow\frac{5}{5}x=\frac{95}{5}\Rightarrow x=19[/tex]In the first part, we need to sum 15 to both sides of the equation.
In the second part, we divide both sides by 5.
Then, x = 19.
At preseident Obama's inauguration in 2013 the newspaper head lines stated there were about 800.000 people in attendance if the newspaper rounded to the nearest hundred thousand what is the largest number and smallest number of people who could have been there
The smallest whole number is 750,000, while the largest whole number is 849,999.
Consider the facts offered.
We must determine the smallest whole integer that, when rounded to the nearest hundred thousands, equals 800,000
Rounding a numerical rule
If the number on the right side of the rounding digit is 0, 1, 2, 3, 4, there is no need to modify the rounding digit and replace the remainder of the digit on the right with 0.
If the number on the right side of the rounding digit is 5, 6, 7, 8, 9, the rounding digit rounds up by one number and replaces the remainder of the digit on the right with 0.
Consider the number 800,000 for a moment.
Because we want the smallest number possible, the number at the hundred thousand place should be 7.
As a result, the smallest whole number is 750,000.
We now want the largest whole number that rounds to 800,000
Similarly, the biggest whole number must be bigger than 800,000 We don't want to raise the number at the hundred thousand place, hence the best ten thousand place option is 4. Put 9 at the rest locations to get the highest number.
As a result, the biggest whole number is 849,999.
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At an animal shelter, 3/8 of the animals are dogs. Of the
dogs, 2/5 have spots. What portion of the animals at the
shelter are dogs that have spots?
At an animal shelter, 3/8 of the animals are dogs, of the dogs, 2/5 have spots, 3/20 portion of the animals at shelter are dogs that have spots. A fraction, which derives from Latin word fractus, which means "broken," is a portion of whole or, more broadly, any number of equal pieces.
What is a fraction?A fraction, which derives from Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator that is displayed below (or after) line on which the numerator is shown. Compound fractions, complicated fractions, and mixed numeral fractions are the examples of uncommon fractions that use numerators and denominators.
The numerator and the denominator of positive common fractions are both natural integers. The denominator shows how many of numerator's equal parts make up a unit or whole, and the numerator reflects the number of equal parts. Since there can never be zero components in a whole, denominator cannot be zero. For instance, numerator 3 in the fraction 3/4 denotes that the fraction is made up of 3 equal parts, while denominator 4 denotes that the fraction is made up of 4 parts altogether.
Let, [tex]\frac{3}{8} x[/tex] animals are dogs,
[tex]\frac{2}{5} * \frac{3}{8}x = \frac{3}{20}x[/tex]
Therefore, [tex]\frac{3}{20}[/tex] of the animals at shelter are dogs that have spots.
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What is the area of this figure?
5 mm
19 mm
36 mm
7 mm
8 mm
7 mm
13 mm
9 mm
Write your answer using decimals, if necessary.
9 mm
11 mm
A stand at the farmers market sells different types of apples, as shown in the table.
Apple A Apple B Apple C
Cost ($)4.90 1.00 0.45
Weight 4 lb 10 oz 1/2 lb
Which type of apple costs the least per pound?
The apple that costs the least per pound is Apple B.
What is the least cost?The cost per pound for each apple will be calculated as:
= Cost / Weight
Apple A:
= Cost / Weight
= 4.90 / 4
= $1.25 per pound
Apple B:
= Cost / Weight
= $1 / 10
= $0.1 per pound
Apple C:
Cost / Weight
= $0.45 / 0.5
= $0.9 per pound
Therefore, apple B is the cheapest
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{2x + 3y = 5}{ y= 5 x -4}
Solve the system using substitutions:
[tex]\begin{gathered} 2x+3y=5 \\ 2x+3(5x-4)=5 \\ 2x+15x-12=5 \\ 17x=5+12 \\ 17x=17 \\ x=\frac{17}{17} \\ x=1 \end{gathered}[/tex]x has a value of 1. Use this value to find the value of y.
[tex]\begin{gathered} y=5x-4 \\ y=5\cdot1-4 \\ y=5-4 \\ y=1 \end{gathered}[/tex]y has a value of 1.
x=1
y=1
Consider the two expressions (6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)/(2x + 3 - 7x - 11) and 4x^2 - 7 + 1/(2x + 3 - 7x - 11)
a) Show that the two expressions represent equal numbers when x = 10
b) Explain why these two expressions do not represent equal numbers when x = -3/2
c) Show that these two expressions represent equal numbers for all x other than -3/2.
Step-by-step explanation:
a)
(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)(2x + 3 - 7x - 11)
[tex] \sf \frac{(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)}{(2x + 3 - 7x - 11)}[/tex]
[tex] \sf = \frac{(6(10)^3 + 9(10)^2 + 4(10) + 7 - 17(10)^2 - 8(10) + 8)}{(2(10) + 3 - 7(10) - 11)}[/tex]
[tex] = \frac{ - 5175}{58}[/tex]
4x^2 - 7 + 1/(2x + 3 - 7x - 11)
[tex] \sf{ 4x^2 - 7 + \frac{1}{(2x + 3 - 7x - 11)}}[/tex]
[tex] \sf{ 4(10)^2 - 7 + \frac{1}{(2(10) + 3 - 7(10) - 11)}}[/tex]
[tex] = \sf \frac{22793}{58}[/tex]
I can’t seem to understand this. I need 2 solutions and the work. If you could explain the work so I can do it in the future that would be great!!
Given:
Ethan is 23 years older than Evan
So, let Ethan is (x) years old
And Evan is (y) years old
So, the difference between them is 23 years old
so, x - y = 23
And the sum of Ethan and Evan's age is 43
so, x + y = 43
So, we have the following system of equations:
[tex]\begin{gathered} x-y=23 \\ x+y=43 \end{gathered}[/tex]add the equations to eliminate (y):
[tex]\begin{gathered} (x-y)+(x+y)=23+43 \\ 2x=66 \\ x=\frac{66}{2}=33 \end{gathered}[/tex]Now, substitute with (x) into the second equation to find (y):
[tex]\begin{gathered} 33+y=43 \\ y=43-33=10 \end{gathered}[/tex]So, the answer will be:
Ethan's age = x = 33
Evan's age = y = 10
A bicycle has a listed price of 803.98 before tax. If the sales tax is 9.5%, fins the total cost of the bicycle with sales tax included. Round to the nearest cent its necessary.
The total cost with taxes included is given by
[tex]803.98+803.98\times\frac{9.5}{100}[/tex]which is equal to
[tex]803.98(1+\frac{9.5}{100})[/tex]which gives
[tex]\begin{gathered} 803.98(1+0.095) \\ 803.98(1.095) \end{gathered}[/tex]then, we have $880.3581. By rounding to the nearest cent, the answer is $880.36
Joe is taking an amortized loan for 85,000 to open a small business, and it's deciding between the offers if two lenders. He wants to know which one would be the better deal over the life of the small business loan, and by how much. a) His credit union had offered him a 9- year small business loan at an annual interest rate of 14.4% find the monthly payment $_b) a bank has offered him a 10-year small business loan at an annual interest rate of 12.8% find the monthly payment c) suppose Joe pays the monthly payment each month for the full term. which lender small business loan would have the lowest total amount to pay off, and how much? Credit UnionThe total amount paid would be $ less than the bank. BankThe total amount paid would be $ less than the credit union.
solve the equations and verify the answer
The value of m is -6/5.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Given:
2m -3 = 3/10 (5m - 12)
Now, cross multiplying
10( 2m -3)= 3( 5m -12)
20m -30 = 15m - 36
20m- 15m= -36 + 30
5m = -6
Divide both side by 5
m= -6/5
Verification:
LHS = 2m-3
=2(-6/5)-3
=-12/5-3
=-27/5
and, RHS
= 3/10( 5m -12)
=3/10(5 x (-6/5) -12)
=3/10 (-6 - 12)
=3/10 x -18
= -54/10
= -27/5
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. Lisa, Bret, and Gary harvested apples.
Lisa filled 3 carts with apples. Bret also
filled 3 carts with apples. Gary filled
another 3 carts with apples. Write a
multiplication equation and a division
equation for this story.
Multiplication:
Lisa, Bret, and Gary harvested apples. If they each harvested 3 carts of apples, how many carts did they harvest in total?
--> 3 * 3 = 9 carts in total
Division:
Lisa, Bret, and Gary harvested apples. If all three of them harvested 9 carts of apples in total, how many carts did each person harvest.
--> 9 / 3 = 3 carts per person
evaluate the expression, given the functions f and h: f(x)=3x-1, h(x)=-2x^2+3x-9. f(7/3)-h(-2)
The value of the function f(7/3)-h(-2) is 30
What are functions?Functions are simply defined as theorems, laws, equation or rules that holds true for the relationship between two variables in a given expression.
The variables are known as;
Independent variableDependent variableGiven the functions as;
f(x)=3x-1 h(x)=-2x^2+3x-9To determine f(73), substitute the value as x in the function, we have;
f(7/3) = 3(7/3) - 1
expand the bracket
f(7/3) = 7 -1
f(7/3) = 6
For h(-2), substitute the value as x in the function, we have;
h(-2) = -2(-2)² + 3(-2) - 9
expand the bracket
h(-2) = -8 -6 - 9
Subtract the values
h(-2) = -23
Now, f(7/3)-h(-2) = 7 --23
f(7/3)-h(-2) = 30
Hence, the value is 30
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