Answer:
y = [tex]-\frac{2}{3} x[/tex] - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The line (l1) passes through (-2, 1) and is perpendicular to the line whose equation is;
3x - 2y = 5
Converting this equation to slope intercept form gives;
2y = 3x - 5
y = 1.5x - 2.5
Let the slope of the perpendicular line (l2) be m(PERP).
The product of slopes of two perpendicular lines is -1
The slope of our first line (l1) = 1.5
So 1.5 × m(PERP) = -1
m(PERP) = -1 ÷ 1.5 = [tex]-\frac{2}{3}[/tex]
Taking another point (x,y) on line (l2);
[tex]\frac{y - 1}{x + 2} = -\frac{2}{3}[/tex]
Cross multiplying this gives;
y = [tex]-\frac{2}{3} x[/tex] - [tex]\frac{1}{3}[/tex]
which is the equation of our second line (l2).
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the origin. On a coordinate plane, square S has points (0, 0), (5, 0), (5, negative 5), (0, negative 5). Square S prime has points (0, 1), (0, 3), (2, 3), (2, 1). a dilation by a scale factor of Two-fifths and then a translation of 3 units up a dilation by a scale factor of Two-fifths and then a reflection across the x-axis a dilation by a scale factor of Five-halves and then a translation of 3 units up a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Answer:
The correct option is;
A dilation by a scale factor of Two-fifths and then a translation of 3 units up
Step-by-step explanation:
Given that the coordinates of the vertices of square S are
(0, 0), (5, 0), (5, -5), (0, -5)
Given that the coordinates of the vertices of square S' are
(0, 1), (0, 3), (2, 3), (2, 1)
We have;
Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)
Where;
(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices
When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;
s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5
For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)
Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2
Therefore;
The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5
The after the dilation (about the origin), the coordinates of S becomes;
(0, 0) transformed to (remains at) (0, 0) ....center of dilation
(5, 0) transformed to (5×2/5, 0) = (2, 0)
(5, -5) transformed to (2, -2)
(0, -5) transformed to (0, -2)
Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;
For (0, 0), (2, 0), (2, -2), (0, -2) we have;
(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)
(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)
For (0, 1), (0, 3), (2, 3), (2, 1) we have;
(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)
(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)
Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)
That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up
The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.
Answer:
a
Step-by-step explanation:
In a right triangle the lengths of the legs are a and b. Find the length of a
hypotenuse, if:
a =5, b =6.
PLEASE ANSWER ASAP
Answer:
7.8
Step-by-step explanation:
because if you square 5 and 6 you get 25 and 36. Add them together and you get 61. Square 61 to get 7.8102... which you can round to 7.8
The equation to find the hypotenuse of a right triangle is a^2+b^2=c^2
ABCD is a square. Square A B C D is shown. A diagonal is drawn from point A to point C. The measure of angle B A C is question mark. What is the measure of angle BAC? 30° 45° 60° 90
Answer:
45°
Step-by-step explanation:
Since the diagonal cuts the square into two triangles, the angles b, a, and , c all add up to 180°. Because the shape is a square we know that one of the angles is right/90° meaning the two remaining angles are 45°. Angles a, and c had the diagonal drawn through so those two angles are each 45° and b is 90°, and since they are asking for bac we know that they want the middle angle, i.e angle A.
Since ABCD is a square, and AC is the diagonal of the square, therefore, the measure of angle BAC would be: B. 45°.
What is a Square?A square is a quadrilateral that has four interior angles of 90 degrees each, and also has four equal sides.The diagonal of a square bisects each vertex of the square into equal halves.Thus, since ABCD is a square, and AC is the diagonal of the square, therefore, the measure of angle BAC would be: B. 45°.
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Expand And Simplify
2(3a - 2b) + b
Answer:
the expansion is 6a-4b+b
the simplification is 6a-3b
Answer:Hey there...
Step-by-step explanation: 2(3a - 2b) + b
Apply Distributive property
(2*3a - 2*2b) + b
( 6a - 4b) + b
2b + b
= 3b
Hope this helps :)
Cómo representa un diagrama de barras en una tabla de frecuencias
Answer:
Es lo mismo, la unica diferencia es que se ve differente. La tabla de frecuencia tiene dos lados igual a la de la tabla de barras.
multiply: 4x ^3sqrt 4x^2 (2 ^3sqrt 32x^2 * x ^3sqrt 2x)
Answer:B on edge 2020 :)
Step-by-step explanation:
its b
Step-by-step explanation:
edge 2022
Simplify the expression 11+2/3(15-21a)
Answer:
21-14a
Step-by-step explanation:
You have to distribute the (2/3) into the (15-21a) then add it to the 11. So after distributing the (2/3) into the (15-21a) is (10-14a). Then add that to the 11
Answer:
-14a + 21
Step-by-step explanation:
11 + 2/3(15 - 21a)
Expand brackets.
11 + 2/3(15) + 2/3(-21a)
11 + 30/3 + -42/3a
Evaluate.
11 + 10 + - 14a
21 + - 14a
Which best explains why the orthocenter of an obtuse triangle is outside the triangle?
Answer: All three of the altitudes lie entirely outside the triangle.
Step-by-step explanation:
The orthocenter is the center of the triangle formed by creating all the altitudes of each side.
The altitude of a triangle is formed by creating a line from each vertex that is perpendicular to the opposite side.
In acute traingle , the orthocenter lies inside it.
In right angled triangle, the orthocenter lies on the triangle.
In obtuse triangle , the orthocenter lies outside the triangle because all the three altitudes meet outside .
So, the best explains why the orthocenter of an obtuse triangle is outside the triangle : All three of the altitudes lie entirely outside the triangle.
Answer: It’s A on edge
Given that (1,-8) is on the graph of f(x), find the corresponding point for the function 1/2 f(x)
Answer: 1 (-4)
Step-by-step explanation: f(x) is a function of x giving you a y value. 1/2 f(x) means you're halving every y value that plugging in x gives you.
Hi, I don't know how to do these, if you could help me answer them, that would be great
Answer:
137°Step-by-step explanation:
From the diagram, mAD lies on the line BDF. Sum of angle on a straight line is 180°. According to the line BDF; mAB + mAD = 180°
From the diagram, mAB = 43°. Substituting this value into the above equation;
mAB + mAD = 180°
43° + mAD = 180°
mAD = 180°-43°
mAD = 137°
Hence, the measure of angle mAD is 137°
An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid has base lengths of x and 2 x, and a height of x. The distance between the 2 trapezoid bases is 20. The vertical height of the prism is 10. Which expression represents the volume of the prism? 10x3 cubic units 15x2 cubic units 20x3 cubic units 30x2 cubic units
Answer:
volume of trapezoidal prism = 15x^2 cubic units
Step-by-step explanation:
First, area of the trapezoidal bases.
Parallel sides measure x and 2x, for an average of 1.5x.
Height = x
Area of trapezoidal base = 1.5x*x = 1.5x^2
Volume of prism = area base * height
(length does not matter, height does)
= 1.5x^2 * 10 = 15x^2
The volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
An oblique prism has trapezoidal bases and a vertical height of 10 units.
As we know, the area of the trapezoidal bases:
From the figure:
Height = x
Area of trapezoidal base = (1.5x)(x) = 1.5x²
The volume of prism = area base×height
= 1.5x²×10 = 15x² cubic units
Thus, the volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
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Suppose ACT Reading scores are normally distributed with a mean of 21 and a standard deviation of 6.2. A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission
Answer:
24.25
Step-by-step explanation:
The minimum admission score is at the 70th percentile of the normal distribution which, according to a z-score table, corresponds to a z-score of 0.524.
The z-score, for any given value X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
If the mean score is 21 and the standard distribution is 6.2, the minimum required score for admission is:
[tex]0.524=\frac{X-21}{6.2}\\X=24.25[/tex]
The minimum score required for admission is 24.25.
Given: Quadrilateral PQRS is isosceles trapezoid
If S=120, Q=?
30
60
120
Answer:
60
Step-by-step explanation:
60. answer degree 60120+60=180degreeThe measurement of the angle Q will be equal to 60°.
What is a isosceles trapezoid?An isosceles trapezoid is a convex quadrilateral with one pair of opposite sides bisected by a line of symmetry. It is a subset of the trapezoid. It can also be defined as a trapezoid with equal lengths for both legs and base angles.
Given that the angle S= 120. The measure of the angle Q will be calculated as:-
∠Q = ∠R = 120°
The pair of the two angles with the two parallel lines are supplementary.
∠R + ∠Q = 180
120 + ∠Q = 180
∠Q = 180 - 120 = 60
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Starting at sea level, a submarine descended at a constant rate to a depth of −5/6 mile relative to sea level in 4 minutes. What was the submarine's depth relative to sea level after the first minute? Answer with a fraction :3
Answer:
-5/24 miles
Step-by-step explanation:
The submarine descends at a rate of -5/6 miles every 4 minutes.
To find the depth of the submarine relative to sea level after the first minute, we have to multiply the rate of descent by he time spent (1 minute). That is:
[tex]\frac{\frac{-5}{6} }{4} * 1[/tex]
=> D = -5 / (6 * 4) = -5/24 miles
Therefore, the submarine's depth is -5/24 miles.
Answer:
-1 1/5
Step-by-step explanation:
I took the test and this was the correct answer :D
2. The diagram shows a playground which is a combination
of three different shapes. TSVU is a square, SRQV is a
trapezium and PQVU is a parallelogram. Calculate the
total area of the playground.
Answer:
The diagram shows a playground which is a combination
of three different shapes. TSVU is a square, SRQV is a
trapezium and PQVU is a parallelogram. Calculate the
total area of the playground
a man buys a dozen cameras for $1800.He sells them at a profit of $36 each.Express his profit as a percentage of his selling price.
Step-by-step explanation:
The solution is the document i sent please check through.
The number of vertices a triangle has
3
6
4
5
When a biased coin is tossed, heads is three times as likely to come up as tails. Rearrange the following procedure in the correct order to find the probability that should be assigned to the outcome of heads and tails?
1. p(T) = 1/4 and p(H) = 3/4
2. since heads and tails are the only two outcomes p(H) + p(T) = 1.
3. p(H) = 3p(T)
4. 3p(T) + p(T) = 1
5. 4p(T) = 1
Answer: 1
Step-by-step explanation:
If heads is 3 more likely to come up than tails, then there are 3 heads for every tails.
Hope it helps <3
help me with this I'm stuck I will give you branliest
Answer:
d = 9
Step-by-step explanation:
Use the slope formula to calculate m and equate to m = 3
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(d, 21)
m = [tex]\frac{21-6}{d-4}[/tex] = [tex]\frac{15}{d-4}[/tex] = 3 ( multiply both sides by d - 4 )
3(d - 4) = 15 ( divide both sides by 3 )
d - 4 = 5 ( add 4 to both sides )
d = 9
help me please I dont remember how to do this
Answer:
A
Step-by-step explanation:
Expand brackets.
-4y - 28 = -4y - 18 - 10
Both sides have -4y, the equation has no solutions.
-4y + 4y = - 18 - 10 + 28
0 = 0
There are no solutions.
Ben and his three sisters are competing to see who gets home first from their grandmother's
house. There are four different routes from her house back to their home in Garland. Ben
chooses Route 1. What are the possible outcomes of the routes taken by the family if Ben
chooses first? Label that set S.
Answer: {Route2, Route3, Route4} (Total 3 outcomes)
Step-by-step explanation:
Given: There are 4 different routes from Ben's house back to their home in Garland.
Let Sample space for all outcomes: {Route1, Route2, Route3, Route4 }
Ben chooses Route 1.
The possible outcomes of the routes taken by the family if Ben chooses first:
{Route2, Route3, Route4}
Hence, the possible outcomes of the routes taken by the family if Ben chooses first: {Route2, Route3, Route4} (Total 3 choices)
Sarah’s room is in the shape of a rectangle that is 15 feet long and 11 feet wide. Which expression can she use to find the total amount of carpeting (in square feet) that she needs to cover the floor? A.15-11 B. 11x15 C.15+11 D. 2(15+11)
Answer:
The answer is choice B , 11 x 15
Step-by-step explanation:
To find area, you multiply one side by the adjacent side
11 and 15 are both adjacent, so you multiply to find the area of Sarah's room
Hope this helps !!!! Brainliest would be appreciated
Answer:
11x15
Step-by-step explanation:
it is the answer above because the dimensions of the room are 11 by 15 so written in an expression it is the answer above
Solve : √x+5 + √x = 15÷√x+5
Ans : 4
Answer:
x = 4
Step-by-step explanation:
The equation given is a radical equation, we will solve using the steps below:
√x+5 + √x = 15÷√x+5
√x+5 + √x = [tex]\frac{15}{\sqrt{x+5} }[/tex]
Multiply both-side of the equation by [tex]\sqrt{x+5}[/tex]
[tex]\sqrt{x+5}[/tex](√x+5 + √x) = [tex]\frac{15}{\sqrt{x+5} }[/tex] × [tex]\sqrt{x+5}[/tex] ----------------------------------(2)
Note
[tex]\sqrt{x+5}[/tex] × [tex]\sqrt{x+5}[/tex] = x +5
Also at the right-hand side of the equation [tex]\sqrt{x+5}[/tex] cancel-out [tex]\sqrt{x+5}[/tex] leaving us with just 15
so equation(2) becomes
x+5 +√x [tex]\sqrt{x+5}[/tex] = 15
subtract 5 from both-side of the equation
x+5-5 +√x [tex]\sqrt{x+5}[/tex] = 15-5
x +√x [tex]\sqrt{x+5}[/tex] = 10
subtract x from both-side of the equation
x-x +√x [tex]\sqrt{x+5}[/tex] = 10-x
√x [tex]\sqrt{x+5}[/tex] = 10-x
square both-side of the equation
(√x [tex]\sqrt{x+5}[/tex]) ² = ( 10-x)²
x (x+ 5) = ( 10-x)(10-x)
open the bracket
x² + 5x = 100 - 20x + x²
subtract x² from both-side of the equation
x² - x² + 5x = 100 - 20x + x² - x²
5x = 100 - 20x
collect like term
5x + 20x = 100
25x = 100
divide both-side of the equation by 25
25x/25 = 100 /25
x = 4
What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Greetings from Brasil...
We need to use the Cosine Law in Any Triangle, so we can use Heron's formula.
AC² = AB² + BC² - 2.AB.BC.COS B
AC² = 11² + 9² - 2.11.9.COS 63
AC ≈ 10,63
Heron's Formula:
Area = √[P.(P - AB).(P - BC).(P - AC)]
where P = (AB + BC + AC)/2
P = (11 + 9 + 10,63)/2 ⇒ P ≈ 15,31
Area = √[15,31.(15,31 - 11).(15,31 - 9).(15,31 - 10,63)]
Area ≈ 44,21 u.a.What is the equation of a circle with center (0, 5) and radius 8
Answer:
See below.
Step-by-step explanation:
Recall that the equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
We know the center is (0,5) and the radius is 8. Plug in the numbers:
[tex](x-(0))^2+(y-(5))^2=(8)^2[/tex]
We can remove the parentheses on the left. Therefore, the equation will be:
[tex]x^2+(y-5)^2=64[/tex]
Answer:
( x) ^2 + ( y-5) ^2 = 64
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x-0) ^2 + ( y-5) ^2 = 8^2
( x) ^2 + ( y-5) ^2 = 64
Can somebody please help? i need to graph the piecewise function. i won't forget to give brainliest.
Answer: see graph (attached)
Step-by-step explanation:
Plot coordinates for each line. You MUST include the boundary points.
y = 3x - 5 x ≤ 1
Choose x = -2, then y = 3(-2) - 5 = -11
Must include x = -1, then y = 3(-1) - 5 = -8
Draw a line starting at (-1, -8) and passing through (-2, -11)
y = -2x + 3 -1 < x < 4
Must include x = -1, then y = -2(-1) + 3 = 5
Must include x = 4, then y = -2(4) + 3 = -5
Draw a line segment starting at (-1, 5) and ending at (4, -5).
Note that both are strictly less than so must have open dots.
y = 2 x ≥ 4
Must include x = 4, then y = 2
Choose x = 5, then y = 2
Draw a line starting at (4, 2) and passing through (5, 2)
Please help I’ll mark brainliest
Answer:
A is the correct answer
Hope this helps :)
Answer:
A is the answerStep-by-step explanation:
This is because you have to substitute numbers.
So,
f(x) = 4 * 2^x
f(1) = 4 * 2^1 = 8
f(2) = 4 * 2^2 = 16
f(3) = 4 * 2^3 = 32
This shows exponential growth. Hope this helped!
Hope this helps,
Kavitha
Determine if the event shows uniform probability or not. You have a spinner with 8 equal spaces on it. Each space is numbered with a different integer between 1 and 8.
Answer:
it does show uniform probability.
Step-by-step explanation:
because the spaces are all equal, so there is an equal chance of every integer being picked.
Given that ACAB - ACED, lind the value of y to 1 dermal place
Answer:
y = 15
Step-by-step explanation:
The triangles CAB and CED are similar (Using the case AA), so we can write the following relations:
[tex]\frac{12}{28} =\frac{15}{x}=\frac{y}{35}[/tex]
Using the first two fractions, we can find the value of x:
[tex]\frac{12}{28} =\frac{15}{x}[/tex]
[tex]12x = 28*15[/tex]
[tex]12x = 504[/tex]
[tex]x = 504/12 = 42[/tex]
Using the first and last fractions, we can find the value of y:
[tex]\frac{12}{28} =\frac{y}{35}[/tex]
[tex]28y = 12*35[/tex]
[tex]28y = 420[/tex]
[tex]y = 420/28 = 15[/tex]
If f(x) = 4x - 20, what is f(4)?
O A. -4
оо
O B. -12
O c. 4
O D. 16
Answer:
A. - 4
Step-by-step explanation:
f(4) = 4(4) - 20 = 16 - 20 = - 4