Answers
A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a reflection across the line x = -3 followed by a reflection across the line y = x.
What is the explanation of the above transformation?Given that both triangles are congruent, we can infer or deduce that there were no dilations or contractions. Hence, since we are moving in a clockwise direction, we can submit that this was not a rotation but a reflection.
Hence the first sequence of reflection was such that:
∆ABC reflects onto ∆A′B′C′ across the line x = -3; followed by
a reflection across the line y = x.
Note that in geometry, reflection refers to the mirror image of an image. The line through which an image reflects is called the line of reflection.
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Related Questions
The letter A B C D
represents the location of –1.5 on the number line.
Answers
Answer:
B
Step-by-step explanation:
q(x) = -x-2
r(x) = x² + 2
Find the following.
(r∙q)(-5) =
(q∙r)(-5) =
Answers
Answer: 5q-5r -5q+5r
Given mn, find the value of x.
(2x+6) (x+9)"
Answers
Answer:
(2x+6) = (x+9) ; x = 3
Step-by-step explanation:
-x both sides ; 2x-x = x and -6 both sides which is x = 3
ABC and △XYZ are similar. Find the missing side length. A B C X Y Z 4 8 ? 42 24 48 (The triangles are not drawn to scale.)
Answers
The missing side length of triangle XYZ is 7.
Given,
Triangle ABC and triangle XYZ are similar.
Triangle ABC;Length of AB = 4
Length of BC = 8
Length of AC = x
Triangle XYZ;Length of XY = 24
Length of YZ = 48
Length of XZ = 42
We have to find the missing length x.
Here,
Triangle ABC and triangle XYZ are similar.
So,
AB : XY = BC : YZ = AC : XZ
Then,
Take AB : XY = AC : XZ
= 4 : 24 = x : 42
= 4 × 42 = 24x
x = 4 × 42 / 24
x = 42/6
x = 7
That is,
The missing side length of triangle XYZ is 7.
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A model rocket is launched with an initial upward velocity of 235 feet the Rockets height H in feet after t seconds is given by the following
Answers
By assuming that the initial height of the rocket is the ground, we will get the height equation:
H(t) = -16*t^2 + 235*t
How to find the equation for the height?The height equation for any object near the surface of the heart that is not being subject to any other forces than the gravitational one is:
H(t) = -16*t^2 + v*t + h
Where:
t represents the time in seconds.
the first coefficient -16 is half of the gravitational acceleration in feet over squared seconds.
v is the initial velocity, which in this case is 235 ft/s
h is the initial height, in this case we assume is zero (the rocket is launched from the ground)
Replacing all that in the height equation, we will get:
H(t) = -16*t^2 + 235*t
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Thelma and Patrick went to a cafe
for lunch. One of them is a
vegetarian. Thelma ordered a
turkey sandwich with extra
mustard. Who is the vegetarian?
Answers
Patrick is vegetarian and Thelma is non vegetarian.
What are vegetarian?
The practice of not eating any meat is known as vegetarianism. It might also mean avoiding eating any leftovers from animal slaughter. There are several reasons to embrace a vegetarian diet. Due to their respect for sentient animal life, many people refrain from eating meat.
Main Body:
As Thelma ordered Turkey sandwich with extra mustard and turkey is an animal , which makes her non vegetarian so it is obvious that Patrick is a vegetarian and Thelma is non vegetarian.
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Find the equation of the line tangent to the curve defined by f(x) = x^2+1 / square root x at the point (1,2). Show all your work.
Answers
Answer:
[tex]y=x+1[/tex]
Step-by-step explanation:
I am assuming that, given the nature of the curve, you know what a derivative is, and you know how to compute the derivative of the ratio of two functions.
[tex]f'(x) = \frac1{(\sqrt x)^2}[(2x+0)\sqrt x-(x^2+1)(\frac1{2\sqrt x})][/tex]
Could be rewritten in a nicer form? Probably, do we care? No, let's just evaluate it for [tex]x=1[/tex]:
[tex]f'(1)=\frac11 [(2)(1)-(1+1)\frac12]=1[2-1]=1[/tex]
We're almost done. We got the point, we have the slope, we can rewrite the tangent line as
[tex]y-y_0=f'(x_0)(x-x_0)\\y-2=1(x-1) \rightarrow y=x+1[/tex]
Screenshot included in this work
Answers
The two blanks on the left side of the equation and the solution blank should be completed with the following ratios:
2050 kg/1 m³ × 2.2 lb/1 kg × 1 m³/35.3 ft³ = 127.76 lb/ft³.
What is a conversion factor?In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.
Conversion:
2050 kg/1 m³ × 2.2 lb/1 kg = 4,510 lb/1 m³
4,510 lb/1 m³ × 1 m³/35.3 ft³ = 4,510 lb/35.3 ft³
4,510 lb/35.3 ft³ = 127.76 lb/ft³.
Additionally, take note of the following units of conversion:
kg = kilograms.m³ = cubic meter.lb = pounds.ft³ = cubic foot.In conclusion, we can logically deduce that the crate's density is equal to 127.76 pounds per cubic foot.
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Pls help 3z2-6z for z=5
Answers
Answer:
0
Step-by-step explanation:
to me you use the exponent first and then add the variable after, 30-30=0 and if you do the variable first 225-30=195. But my answer would be 0.
Answer: 78
Step-by-step explanation:
3z2-6z for z=5
Barbara borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is
Answers
The actual end-of-year payment or present value of this ordinary annuity is equal to $1,482.
How to calculate the actual end-of-year payment?For the rate of interest, we have:
Rate of interest, r = APR/12
Rate of interest, r = 0.12/12
Rate of interest, r = 0.01
Next, we would calculate the present value of this ordinary annuity by using this formula:
Present value, PV = [P ÷ [1 - (1 + r)^{-n}]/r]
Where:
r is the interest rate.P is the principal.n is the number of times compounded.Substituting the given parameters into the formula, we have;
Present value, PV = 4,500 ÷ ((1 - (1 + 0.12)^(-4))/(0.12))
Present value, PV = 4,500 ÷ ((1 - (1.12)^(-4))/(0.12))
Present value, PV = 4,500 ÷ ((1 - 0.635518078)/(0.12))
Present value, PV = 4,500 ÷ ((0.364481922)/(0.12))
Present value, PV = 4,500/3.0373
Present value, PV = $1,481.58 ≈ $1,482.
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(HELP ASAP) ABC Is Isosceles m
Answers
Answer:
m∠A = 55°-----------------------------
A and C are congruent angles opposite to congruent sides of the isosceles triangle.
m∠A = m∠C3x + 40 = x + 503x - x = 50 - 402x = 10x = 5Find the measure of ∠A
m∠A = 3×5 + 40 = 15 + 40 = 55Answer:
The angle A is 55°.
Step-by-step explanation:
We know that,
→ <A = <C
Now the value of x will be,
→ 3x + 40 = x + 50
→ 3x - x = 50 - 40
→ 2x = 10
→ x = 10/2
→ [ x = 5 ]
Then the value of m<A is,
→ A = 3x + 40
→ A = 3(5) + 40
→ A = 15 + 40
→ [ A = 55° ]
Hence, the answer is 55°.
round this number to the hundredth 3.6432
Answers
Because the 3 in the thousandths place is not 5 or greater, the 4 in the hundredths place does not round up to 5
Ryan is going to spin the spinner 80 times.
(b)
Work out an estimate for the number of times he should expect the spinner to land on 2
Answers
The estimate for the number of times Ryan should expect the spinner to land on 2 is 13.
How to calculate the number of times?From the information, the spanner has numbers labeled 1 - 6 and Ryan is going to spin the spinner 80 times.
It should be noted that the fraction for getting a 2 is 1 out of 6. This will be 1/6.
Therefore, when it's spinned 80 times, the expected number will be:
= 1/6 × 80
= 13
The number of times is 13.
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Complete question
A spanner has numbers labeled 1 - 6. Ryan is going to spin the spinner 80 times. Work out an estimate for the number of times he should expect the spinner to land on 2
Can someone awnser all three questions please.
Answers
Answer:
Step-by-step explanation:
87
99
128
The figure below is made up of a square with height, h units, and
a right triangle with height, h units, and base length, b units.
h
b
The area of this figure is 80 square units.
Write an equation that solves for the height, h, in terms of b.
Answers
Answer: $4x4x
Step-by-step explanation:
-1/3v = -7 how do i solve this equation?
Answers
Answer: v=2.33333333333333.........
Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
Answers
The area of left over wrapping paper is 380 square inches
How to determine the amount left?The given dimensions are:
Box = 8 inches by 9 inches by 10 inchesWrapping paper = 2 feet by 3 feet.The surface area of the box is calculated as
Surface area = 2(lw + lh + wh)
This gives
Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches
The surface area of the wrapping paper is calculated as
Wrapper = lw
This gives
Wrapper = 2 * 3 = 6 square feet
Express the area in square inches
Wrapper = 864 square inches
The area left is the difference between the areas calculated above
i.e. Amount left = Wrapper - Box
So, we have
Amount left = 864 square inches - 484 square inches
= 380 square inches
Hence, the amount left is 380 square inches
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Solve the inequality4x + 13 ≥ 27
Answers
Work Shown:
4x + 13 ≥ 27
4x + 13-13 ≥ 27-13
4x ≥ 14
4x/4 ≥ 14/4
x ≥ 7/2
The inequality sign stays the same for each step. The inequality sign only flips if we were to multiply both sides by a negative number (or divide both sides by a negative number).
Note: 7/2 = 3.5
2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?
A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds
Answers
The weight of Luna is 82 pounds , the correct option is (d) .
In the question ,
it is given that
Kira has three dogs Luna , Cooper and Daisy .
let the weight of cooper be c .
given Cooper weighs 25 pounds less than Daisy
which is c = daisy - 25
So , daisy = c + 25
and Luna weighs 20 pounds less than three times Cooper ,
which is Luna = 3c - 20
Given the combined weight is = 175 pounds
Cooper + Daisy + Luna = 175
c + c + 25 + 3c - 20 = 175
5c + 5 = 175
5c = 175 - 5
5c = 170
c = 170/5
c = 34
So, Luna = 3c - 20 = 102 - 20 = 82 pounds .
Therefore , The weight of Luna is 82 pounds .
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What is the image of (-9,12)(−9,12) after a dilation by a scale factor of \frac{1}{3} 3 1 centered at the origin?
Answers
The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
In the given question,
We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.
Since we have to find the image after a dilation.
So we learn about it now,
Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.
So the given point is (-9,12).
Scale factor is 1/3.
So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as
=(-9×1/3,12×1/3)
Simplifying
=(-3,4)
Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
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Gabriel has a stack of nickels that is 2 inches tall. The thickness of a nickel is
0.08 inch. How many nickels does Gabriel have?
Show your work.
Answer: Gabriel has
nickels.
Answers
Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.
As given in the question,
Gabriel has 2 inches tall stack of nickel
Thickness of each nickel = 0.08inch.
Let 'n' be the number of nickels Gabriel has .
Required equation to get the number of nickel is equal to :
0.08 × n = 2
⇒ n = 2 / 0.08
⇒ n = 200/ 8
⇒ n = 25
Therefore, Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.
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Answer 0.04
Step-by-step explanation:
because 0.08 divided by two is 0.04
I need help with math please help me..!!!
I need help with math please help me..!!!
I need help with math please help me..!!!
Answers
Step-by-step explanation:
please remember you middle school and high school classes, homework and exams.
here on college level this is just meant as a quick reminder.
so, what exactly don't you understand, please, so that I can provide specific guidance ?
6
the vertex : the turn-around point, where the parabola curve changes its tendency : (-3, 0.5)
axis of symmetry : since the parabola opens downwards, the axis of symmetry (it is like a mirror for one half of the curve to the other half) is a vertical line going right through the vertex : x = -3
y-intercept is the y-value when x = 0 : (0, -4)
x-intercepts are the x-values when y = 0 :
(-4, 0) and (-2, 0)
max or min : there is only one identifiable extreme value, it is at the vertex, of course, and is clearly a maximum :
at x = -3 the max value of the function is 0.5
the optimal value is the y-coordinate of the vertex (the function value between the 2 x-intercepts) : 0.5
4
y = 0.5x + 6 is linear. why ? because the highest exponent of x is 1. that creates a proportional relationship between x and y meaning y only increases with x in a constant manner.
y = 2x² + 5 is quadratic. why ? because the highest exponent of x is 2. this squares things, in other words, it makes them quadratic.
the graph as third item in the list is neither. the functional value gets exponentially bigger, the closer x gets to 0.
this looks like y = -1/x = x^(-1)
the graph as forth item in the list is a parabola again, and as such it is quadratic.
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be kilograms.
Answers
According to the scatter plot provided, the weight for someone who is 1.5 meters tall is predicted to be 45.45 kilograms.
What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical and analytical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the weight (in kilogram) would be plotted on the y-axis of the scatter plot while the height (M) would be plotted on the x-axis of the scatter plot.
From the scatter plot (see attachment) which models the relationship between data points in the table, a linear function for the line of best fit is given by:
Weight, kg = -114.3 + 106.5M
When M = 1.5 meters, we have:
Weight, kg = -114.3 + 106.5(1.5)
Weight, kg = -114.3 + 159.75
Weight, kg = 45.45 kg.
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Complete Question:
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be ____ kilograms.
Find the value of the expression:
3x^0 for x=2.6
Answers
Answer:
1
Step-by-step explanation:
We don't even need to calculate 3 x 2.6 considering any number raised to the power of zero equals 1.
5. Simplify the complex fraction. a.-2/7
1 1/3
Answers
The simplification of the complex fraction is found as 11/14.
Define complex fraction/mixed fraction?A mixed fraction is a fraction that is created by fusing a fraction with a whole number. An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that. Step 1: Multiply the mixed fraction's denominator by the whole number component.Step 2: Increase the product from Step 1 by the numerator.Step 3: In the numerator/denominator form, write the improper fraction using the total from Step 2.For the given question, the expression is-
-2/7 + 1 1/3
To convert mixed fraction 1 1/3 i improper fraction, multiply 3 with 1 and add 1.
1 1/3 = 1 x 3 + 1 /3
1 1/3 = 4/3 Put in main equation.
-2/7 + 4/3
Simplify the expression.
= -2 x 3 + 4 x 7/ (7 x 4)
= -6 + 28 / 28
= 22/28
Divide both with 2
= 11/14
Thus, the simplification of the complex fraction is found as 11/14.
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The correct question is
Simplify the complex fraction.
-2/7 + 1 1/3
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2y - 3x = 6
Answers
Equation of the line is y = 3/2x + 3.
Define slope intercept form.Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The "slope-intercept" form is one of the most popular methods. It is so named because it makes the slope and y-intercept of the equations in the equation more clear. The number that is placed before the x is the slope.
Given,
Slope intercept form:
Formula:
y = mx + b
Where m = slope
2y - 3x = 6
2y = 6 + 3x
Equation:
y = 3 + 3/2x
y = 3/2x + 3
Equation of the line is y = 3/2x + 3.
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Evaluate the power.
0.5² =
(Type a whole number or a decimal.)
Answers
Find the value of k such that the system of linear equations is inconsistent.
6x-12y = -7
2x + ky = 14
Answers
For the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.
As given in the question,
Given system of linear equations are as follow:
6x-12y = -7 ____(1)
2x + ky = 14 _____(2)
Form equation (1) we have,
6x -12y = -7
⇒3 ( 2x -4y) = -7
⇒ 2x - 4y = -7 /3 ____(3)
From equation (2) and (3) we have,
2x + ky = 14
2x - 4y = - 7/3
Value of k so that the given system of equations are inconsistent is given by:
k = -4
For inconsistent there is no solution.
Therefore, for the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.
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Need asap! Write the expression as a power and evaluate it. The expression as a power is __. The value is__.
8•2^7 and 16•32
Answers
The expression as power is written as 2¹⁰ and 2^9
The values are
2¹⁰= 1024 2^9 = 512How to write expression as a powerpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.
8• 2^7
= 2 * 2 * 2 * 2^7
= 2^10
= 1024
16•32
2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2^9
= 512
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If the random variable Zhas a standard normal distribution, then P(1.17 S ZS 2.26) is
Answers
The value of P(1.17 <= Z <= 2.26 ) is 0.1091
From the question, we have
Z value for 1.17 is 0.8790
Z value for 2.26 is 0.9881
P(1.17 <= Z <= 2.26 ) = 0.9881 - 0.8790 = 0.1091
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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