The coordinates of the image of the point (-7, 5) are (7, -5).
We are given point P. The coordinates of the point P are (-7, 5). We perform a transformation on the given point. We rotate the given point about the origin counter-clockwise. The angle of rotation is 180°. We need to find the coordinates of the image of the point after rotation.
Let the new coordinates of the image of the point after rotation be denoted by (X, Y). If the coordinates of the original point are (x, y), then the relations between the coordinates of the point and the image are given below.
X = x*cosθ - y*sinθ
X = (-7)*cos(180°) - (5)*sin(180°)
X = (-7)*(-1) - (5)*(0)
X = 7
Y = x*sinθ + y*cosθ
Y = (-7)*sin(180°) + (5)*cos(180°)
Y = (-7)*(0) + (5)*(-1)
Y = -5
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Can write the equation to this problem?
The equation, in vertex form, of the graph in the diagram is determined as: y = 1|x - 3| + 5.
What is the Equation of a Graph that Represents an Absolute Value Function?The formula that represents the equation in vertex form of an absolute value function is y = a|x - h| + k, where:
Vertex = (h, k).
Therefore, we will need to determine what the values of a, h, and k is using the information derived from the graph.
Thus:
(h, k) = (3, 5)
a = 1 (this is because the graph opens upward)
To write the equation of the graph, substitute a = 1, h = 3, and k = 5 into:
y = 1|x - 3| + 5
The equation is, y = 1|x - 3| + 5.
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Which number should be on the bottom left stamp?
Explain what the answer is and how you got it!
The number that should be on the bottom left stamp is 1. It was gotten by dividing 2 by 2.
What will the number be?From the first picture, we have 82 and the number below it is 4. This was gotten as:
= 8 ÷ 2
= 4
The second picture has 93 and the number below it is 3. This was calculated as:
= 9 ÷ 3
= 3
The third picture has 61 and the number below it is 6. This was calculated as:
= 6 ÷ 1
= 6
The fourth picture will be:
= 2 ÷ 2
= 1
Therefore the value is 1.
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determine if l=these points have a right angle
2,3 6,3 2,7
The points (2, 3) (6, 3), and (2, 7) sides corresponds to length of 4 : 4 : 5 and do not form Pythagorean triple hence they do not form a right angle
How to determine if the points (2, 3) (6, 3), and (2, 7) form a right angleThe distance between the points is calculated and Pythagoras theorem is used to determine if the triple forms a right angle
let the points be
A (2, 3) B (6, 3), and C (2, 7)
using the equation
d = √{(x₁ - x₂)² + (y₁ - y₂)²}
AB = √{(2 - 6)² + (3 - 3)²} = 4
BC = √{(6 - 2)² + (3 - 7)²} = 5
CA = √{(2 - 2)² + (3 - 7)²} = 4
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Directions: Write an equation passing through the point and PARALLEL to the given line.
1. (4, 7); y = 3x+6
Answer: y=3x-5
Step-by-step explanation:
This was the answer i got after solving
Hope that helped :)
Screenshot is the proof of the answer btw :)
(car sales) of the cars sold during the month of july, 90 had air conditioning, 102 had automatic transmission, and 72 had power steering. 7 cars had all three of these extras. 22 cars had none of these extras. 25 cars had only air conditioning, 61 cars had only automatic transmissions, and 33 cars had only power steering. 11 cars had both automatic transmission and power steering. how many cars had exactly two of the given options?
There were 58 cars sold with exactly two of the given options.
1. There were 90 cars sold with air conditioning.
2. There were 102 cars sold with automatic transmission.
3. There were 72 cars sold with power steering.
4. There were 7 cars sold with all three options.
5. There were 22 cars sold with none of the options.
6. There were 25 cars sold with only air conditioning.
7. There were 61 cars sold with only automatic transmission.
8. There were 33 cars sold with only power steering.
9. There were 11 cars sold with both automatic transmission and power steering.
Let's just count the number of cars that have exactly two of the given options:
Air Conditioning & Automatic Transmission: 25
Air Conditioning & Power Steering: 22
Automatic Transmission & Power Steering: 11
So there are 25 + 22 + 11 = 58 cars that have exactly two of the given options.
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Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral.
The dimension of the rectangle of the largest area in an equilateral triangle is √3/4L.
Here we have to find the dimension of the rectangle of the largest area.
Let the distance from the tip of the base of the triangle to the point that the top of the rectangle meets the triangle be x.
The width of the rectangle is √3/2 x.
By this, we can find the area of the rectangle
Area = √3/2x ( L -x) = √3/2 xL - √3/2x²
To find the maximum area we have:
dA/ dx = 0
dA / dx = √3/2L - √3x = 0
From we have to find the value of x,
√3 x = √3/2L
x = L/2
The dimension of rectangle is √3/2x = √3/2(L/2)
= √3/4 L
Therefore the dimension of the rectangle is √3/4 L.
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Find the measures of each numbered angle:
What is a,b,c and day
[tex]a=-5(-3)-2=13\\\\b=-5(-1)-2=3\\\\c=-5(1)-2=-7\\\\d=-5(2)-2=-12[/tex]
Answer:
A = 13 B = 3 C = -7 D = -12
Step-by-step explanation:
Just insert the x values for a, b, c, and d. for example if we were to find a.
The x value for a is -3 so we would put -3 in place of x in the equation.
-5(-3) - 2
Remember: Two negative numbers multiplied with each other equal a positive.
15 - 2 = 13
Write the coordinates of the vertices after a translation 3 units right and 12 units down
Step-by-step explanation:
3 units right = x + 3
12 units down = y - 12
E = (-5, 4) -> E' (-2, -8)
F = (-5, 9) -> F' (-2, -3)
G = (1, 9) -> G' (4, -3)
H = (1, 4) -> G' (4, -8)
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6?
write each choice into the boxes to correctly complete the table. *picture below *
Step-by-step explanation:
in order to be able to decide each case we need the slopes of all involved lines.
and that means we need to bring all of the equating into a "y = ..." form, because then the slope is always the factor of x.
parallel lines have the same slope.
the slopes of perpendicular lines (intercept at a right angle) have the y/x ratio turned upside-down and a flipped sign : -x/y.
"neither" is everything else.
our reference line
x + 2y = 6
2y = -x + 6
y = -1/2 x + 3
so, the reference slope is -1/2.
y = -1/2 x - 5 is parallel (same slope).
-2x + y = -4
y = 2x - 4 perpendicular (2/1 vs. -1/2)
-x + 2y = 2
2y = x + 2
y = 1/2 x + 1 neither
x + 2y = -2 parallel (as the structure except for the constant part is the same as our reference line).
2y = -x - 2
y = -1/2 x - 1
Can someone help me with this aleks question
For the given triangles ΔTRS and ΔQRP , the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
As given in the question,
Two triangles ΔTRS and ΔQRP,
It is given that :
Line segment SR ≅ Line segment PR
Line segment SP bisects Line segment TQ
⇒ line segment TR ≅ line segment RQ
∠TRS ≅ ∠PRQ ( by vertically opposite angle )
By Side angle side theorem we have ,
ΔTRS ≅ ΔPRQ
Therefore, for the given triangles ΔTRS and ΔQRP ,the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
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determine if line AB and line CD are parallel, perpendicular or neither
Answer:
Line 1 is considered perpendicular
Line 2 is considered parallel
Line 3 is also parallel
Step-by-step explanation:
This should be right if this is the rest to your problem:
1. Line AB formed by A(-1,3) and B(1,5); Line CD formed by C(2,3) and D(-2,7)
2. Line AB formed by A(3,8) and B(-6,5); Line CD formed by C(-6,7) and D(-3,8)
3. Line AB formed by A(2,-7) and B(2,3); Line CD formed by C(-4,0) and D(-4,-5)
Decide whether each equation is true for all, one, or no values of x.
Answer:
For the first equation, it is "True for one value of x."
For the second equation, it is "True for no value of x."
For the third equation, it is "True for all values of x."
Step-by-step explanation:
Just solve the equation and check the numbers:
If both numbers are the same, it is "true for all values of x"
If there is a variable and a number, it is "true for one value of x"
If there are two numbers and they are different, it is "true for no values of x"
Hope this helps!
Please give brainliest
We need to check whether the given equations are true for all values of [tex]x[/tex] , one value of [tex]x[/tex] , or no values of [tex]x[/tex] .
The equations are ,
[tex]3x +9 = -4.5x +20[/tex]solve this equation for x ,
[tex]\longrightarrow 3x +9=-4.5x+20\\[/tex]
[tex]\longrightarrow 3x+4.5x =20-9\\[/tex]
[tex]\longrightarrow 7.5x =11\\[/tex]
[tex]\longrightarrow \underline{\underline{x =\dfrac{11}{7.5}}}[/tex]
Hence the equation is true for one value of x .
[tex] 9(x+3)=9x+12[/tex]solve out for x ,
[tex]\longrightarrow 9x +27=9x-12\\ [/tex]
[tex]\longrightarrow 9x -9x =-27-12\\ [/tex]
[tex]\longrightarrow 0 = -39[/tex]
This can never to true , so the equation is true for no values of x .
[tex]4(2x+3)=12+8x[/tex]solve out for x ,
[tex]\longrightarrow 8x+12=12+8x \\[/tex]
[tex]\longrightarrow 12-12=8x-8x\\[/tex]
[tex]\longrightarrow 0=0 [/tex]
Hence this equation is true for all values of x .
And we are done!
1. Vanessa works as an event planner during the summer. She makes $50 for every birthday
party she plans and $100 for every wedding she plans. Her goal every summer is to make
$1000 to put towards college. Write an equation that represents the number of parties (x) and
the number of weddings (y) that Vanessa could plan during the summer in order to meet her
$1000 goal:
The required equation for the given condition is 50x + 100y = 1000.
What is an algebraic expression?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).
Given, the charge for every birthday party =$50
number of birthday parties = x
So, the total charge for birthday parties = 50x
the charge for every wedding = $100
the number of weddings = y
So, the total charge for the wedding = 100y
Then,
Total amount achieve = $1000
or, 50x + 100y = 1000
Hence, the required equation is 50x + 100y = 1000.
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survey of 397 children given at a local elementary school showed that 175 like chocolate ice cream 225 like pistachio ice cream, and 97 do not like chocolate or pistachio ice cream. how many children like at most one kind of ice cream mentioned in the survey?
297 children like at most one kind of ice cream.
Total number of children = 397
Let C and P be the number of children like chocolate and pistachio ice cream respectively.
n(C) = 175
n(P) = 225
The number of student do not like chocolate or pistachio ice cream is,
n(P' and C') = 97
n(P or C)' = 97, by De Moivre's theorem
n(P or C) = 397-97 = 300
n(P) + n(C) - n(P and C) = 300
175 + 225 - n(P and C) = 300
400 - n(P and C) = 300
n(P and C) = 100
So the required number of children like at most one kind of ice cream = 397-n(P and C) = 397-100 = 297
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Ken can walk 40 dogs in 8 hours. How many dogs can Ken walk in 1 hours?
Answer:
5
Step-by-step explanation:
divide.
45 point reward if you help !! Find the volume of each shape and then compare do not reduce your fractions.
Answer:
150/512 < 64/125
Step-by-step explanation:
5/8 * 6/8 * 5/8 = 150/512 = 0.295
4/5 *4/5 * 4/5 = 64/125 = 0.512
Therefore: 0.295 < 0.512 or 150/512 < 64/125
Find x
80°
x+51
X =
OK
60°
ALGEBRA
For the given triangle and the measures of the given angle the value of x is equal to -11° .
As given in the question,
For the given triangle,
Let us consider the triangle name ABC,
Where, m ∠A = x + 51° ,
m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)
m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)
To get the value of x we have,
Sum of all the interior angles of a triangle is equal to 180°
m ∠A + m ∠B + m ∠C = 180°
⇒ x + 51° + 80° + 60° = 180°
⇒ x + 191° = 180°
⇒ x = 180° - 191°
⇒ x = - 11°
Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .
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what is the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet? the total surface area is about square feet.
Using the concepts of equilateral triangle, we got that 107 square feet is the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet.
We have :
Base (b) = 6 feet
Slant height (l) = 10 feet
The lateral surface area is calculated using:
L = (3/2)× Length × Breadth
So, we have:
L = (3/2) ×6 × 10
=>L=(3×3×10)
=>L=90 square feet.
The total surface area is calculated using:
T=Lateral surface area of the wall + area of equilateral triangle
=>T=L+ (√3/4)b²
So, we have:
T = 90 + (√3/4)×(6×6)
=>T=90+(3×3×√3)
=>T=90+9√3
=>T=107 square feet (approx)
Hence, the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet is 107 square feet.
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Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, , what is the predicted fuel efficiency for a speed of 30 mph?
17. 67 mpg
26. 50 mpg
30. 00 mpg
37. 74 mpg
The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.
What is the least-squares regression line?If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.
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Solve for y
q• (a + y) = 67y + 93
Answer: y = 160/q -a
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
In the image below, the measure of angle 3 is equal to the sum of the measures of angle 6 and what other angle?
For the given figure, angle 3 will be equal to angle 2.
According to the question,
We have the following information:
We have a figure where some angles are marked in form of numbers and the measure of angle 3 is equal to the sum of the measures of angle 6.
Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.
(More to know: the sum of three angles of a triangle is equal to 180°.)
Hence, for the given figure, angle 3 will be equal to angle 2.
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Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
-4, (-2 , 1)
0, (-1, 21)
The equation of straight line having
(a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7
(b) gradient 0 and coordinates (-1,21) is y = 21 .
In the question ,
the gradient and coordinates of the point on the line is given .
we have to find the equation of the straight line .
Part(a)
the gradient of the line [tex]=[/tex] -4 ,
the coordinates of a point on the line = (-2,1)
So , the equation of the line is
(y - 1) = (-4)*(x -(-2))
y - 1 = -4(x + 2)
y - 1 = -4x - 8
4x + y = -8 + 1
4x + y = -7
the equation is 4x + y = -7 .
Part(b)
the gradient of the line = 0 ,
the coordinates of a point on the line = (-1 , 21)
So , the equation of the line is
(y - 21) = 0(x-(-1))
y - 21 = 0
y = 21
the equation of the line is y = 21 .
Therefore , The equation of straight line having (a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7 and (b) gradient 0 and coordinates (-1,21) is y = 21 .
The given question is incomplete , the complete question is
Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
(a) -4, (-2 , 1)
(b) 0, (-1, 21)
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4x−1=3y+5 khan academy
The slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Given is a equation of a straight line as -
4x - 1 = 3y + 5
We have the equation as follows -
4x - 1 = 3y + 5
Rearranging the equation -
3y = 4x - 1 - 5
3y = 4x - 6
y = (4/3)x - 2
Refer to the graph attached.
The slope of the line is [m] = 4/3
The [y] intercept is at [c] = -2
Therefore, the slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2
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A merchant offers a large group of items at 18% off. later, the merchant takes 10% off these price sales and claims that the final price of these items is 86 off the original price. what is the total percent discount?
26.2% is the total percent of discount offered by the merchant.
Let us assume that each item is $100.
As it is given that 18% is off, we have an amount after off is:
Amount after 18% off = 100 × (100 - 18)/ 100
= 100 × 0.82
= 82
Next, there is 10% off
So the amount become = 82 ×( 100 - 10) / 100
= 82 ×0.9
= 73.8
So the final price of an item is $73.8
The discount = (100 - 73.8) / 100
= 26.2%
Therefore the total percent of discount is 26.2%.
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Alonso went to the store to buy some almonds. The price per pound of
the almonds is $7.25 per pound and he has a coupon for $3.50 off the
final amount. With the coupon, how much would Alonso have to pay to
buy 5 pounds of almonds? Also, write an expression for the cost to buy
p pounds of almonds, assuming at least one pound is purchased.
The required price of almond and expression are $32.75 and c= $7.25P - $3.5 respectively.
What is pound?Pound is unit used to measure weight of quantity. It is used by the English speaking peoples.It equal to the 16 ounces and 0.454 kilogram.
According to given information:Alonso has a coupon of $3.5, let us consider P pound of almond. And price per pound of almond is $7.25
So, equation for the cost,
Cost(c) = $7.25P - $3.5
Then, the price of 5 pound of almond = $7.25×5 - $3.5
⇒ $36.25 - $3.5 = $32.75
Thus, the price of 5 pounds of almond is $32.75.
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Find the solution to the following equation: 2(2x - 7) = 14
x = 14
x = 7
x = 1
x = 0
Answer:
x=7
Step-by-step explanation:
2(2x - 7) = 14
Solve for x
Divide each side by 2
2/2(2x - 7) = 14/2
2x-7 = 7
Add 7 to each side
2x-7+7 = 7+7
2x = 14
Divide each side by 2
2x/2 = 14/2
x = 7
Answer:
b) x = 7
Step-by-step explanation:
Given equation,
→ 2(2x - 7) = 14
Now the value of x will be,
→ 2(2x - 7) = 14
→ 4x - 14 = 14
→ 4x = 14 + 14
→ x = 28/4
→ [ x = 7 ]
Hence, the value of x is 7.
eight times the quotient of x and 2
Answer:
4x
Step-by-step explanation:
the quotient of x and 2 is [tex]\frac{x}{2}[/tex] , then
8 × [tex]\frac{x}{2}[/tex] ( cancel 8 and 2 by 2 )
= 4 × x
= 4x
Dina pours 16-ounce containers of juice into a dispenser with a capacity of 960 ounces. The function y = 16x models this situation. What is the range of the function?
The range of the function is [0, 960]
How to determine the range of the function?From the question, we have the equation of the function to be
f(x) = 16x
Where
The size of the container is 16 ouncesThe capacity of the dispenser is 960 ouncesWhen the dispenser is empty, it means that f(x) = 0
When the dispenser is full, it means that f(x) = 960
When these values are combined, they represent the range
In other words, the range is 0 to 960
This can be rewritten as [0, 960]
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Answer:
big black men
Step-by-step explanation:
(i have your search history)
Write a linear function f with the values f(0) =10 and f(6) =34.
Answer:
f(x) = 4x + 10
Step-by-step explanation:
The given information is in the form f(x) = y.
f(0) = 10 means if x is 0, y is 10. This is the point (0,10)
Likewise, f(6) = 34
means when x is 6, y is 34. That is the point (6,34).
Slope is y-y / x-x
34-10 / 6-0
is 24/6.
The slope is 4.
The y-intercept is where x is 0, that is 10.
y=mx+b is slope-intercept form. Fill in the slope, 4 for m and the y-intercept, 10, for b.
y = 4x + 10
but they also asked to call it f, so for function notation, use f(x) instead of y.
f(x) = 4x + 10
