The vertices of the image triangle ABC, after reflecting across the line (y = -1), are A' (4, 5), B' (1, 6), and C' (2, 3).
To find the image of the triangle ABC after a reflection across the line (y = -1), you can use the formula for the reflection of a point across a line.
The formula for the reflection of a point (x, y) across the line (y = mx + b) is given by:
[tex]\[\left(\frac{{x - m(y - b)}}{{1 + m^2}}, \frac{{y - m(x - a)}}{{1 + m^2}}\right)\][/tex]
In this case, the line of reflection is (y = -1), so (m = 0) and (b = -1). Therefore, the formula simplifies to:
[tex]\[\left(x, \frac{{y + 2}}{{1}}\right)\][/tex]
Now, apply this formula to each vertex of triangle ABC.
1. For point A(4, 3):
[tex]\[A' = \left(4, \frac{{3 + 2}}{{1}}\right) = (4, 5)\][/tex]
2. For point B(1, 4):
[tex]\[B' = \left(1, \frac{{4 + 2}}{{1}}\right) = (1, 6)\][/tex]
3. For point C(2, 1):
[tex]\[C' = \left(2, \frac{{1 + 2}}{{1}}\right) = (2, 3)\][/tex]
So, the vertices of the image triangle after the reflection across the line (y = -1) are A'(4, 5), B'(1, 6), and C'(2, 3).
What do the factors (-7x-60)(x+4) in the factored form represent?
Answer:
Step-by-step explanation:
Each factor corresponds to a zero of the function.
If (x+4) is set = to 0, the corresponding root is x = -4.
If (-7x - 60) is set = to 0, the corresponding root is x = -60/7.
The factors (-7x-60)(x+4) represent the roots or solutions of the original quadratic equation in its expanded form, which are obtained by setting each factor equal to zero and solving for x.
Explanation:The factors (-7x-60)(x+4) in the factored form represents the roots of a quadratic equation. In a quadratic equation of the form ax² + bx + c = 0, the roots or solutions of the equation can be obtained by factoring the quadratic expression. In this case, the equation being factored must have been -7x² - 28x - 60x - 240 = 0. The roots are the values that make each factor equal to zero, so the roots of the original equation are obtained by solving -7x-60 = 0 and x+4 = 0, to get x = -60/(-7) = 8.57 and x=-4.
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.........help...........
Answer:
0.125
Step-by-step explanation:
solving the problem gives 0.125
For this case we must resolve the following expression:
[tex]\sqrt {(0.5) ^ 6}[/tex]
By definition of properties of roots and powers we have to:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So we have to:
[tex]\sqrt {(0.5) ^ 6} = 0.5 ^ {\frac {6} {2}} = (0.5) ^ 3 = 0.125[/tex]
So, we have to:
[tex]\sqrt {(0.5) ^ 6} = 0.125[/tex]
Answer:
0.125
Option B
The radius of a circle is 12 miles. What is the angle measure of an arc bounding a sector with area 10 square miles?
[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ A=10\\ r=12 \end{cases}\implies 10=\cfrac{\theta \pi 12^2}{360}\implies 10=\cfrac{2\pi \theta }{5} \\\\\\ 20=2\pi \theta \implies \cfrac{20}{2\pi }=\theta \implies \cfrac{10}{\pi }=\theta \implies 3.18\approx \theta[/tex]
A sequence of transformations maps triangle ABC to triangle A’B’C’. The sequence of transformations that maps triangle ABC to triangle A’B’C’ is a reflection across the
- y-axis
- x-axis
- line y=x
OR - line y=-x
...followed by a translation
- 4 units to the right and 10 units up
- 8 units to the right and 10 units up
- 10 units to the right and 2 units up
OR - 10 units to the right and 4 units up.
Answer:
Reflection across the line y=x followed by translation 10 units to the right and 4 units up.
Step-by-step explanation:
Triangle ABC has vertices at points A(-6,2), B(-2,6) and C(-4,2).
1. The reflection across the line y=x has the rule
(x,y)→(y,x).
Thus,
A(-6,2)→A''(2,-6);B(-2,6)→B''(6,-2);C(-4,2)→C''(2,-4).2. The translation 10 units to the right and 4 units up has the rule
(x,y)→(x+10,y+4).
Thus,
A''(2,-6)→A'(12,-2);B''(6,-2)→B'(16,2);C''(2,-4)→C'(12,0).Points A'B'C' are exactly the vertices of the triangle A'B'C'.
The sequence of transformations that maps triangle ABC to triangle A’B’C’ is a reflection across the y-axis, followed by a translation 8 units to the right and 10 units up.
Explanation:The sequence of transformations that maps triangle ABC to triangle A’B’C’ is a reflection across the y-axis, followed by a translation 8 units to the right and 10 units up.
First, the reflection across the y-axis changes the x-coordinate to its opposite. So, the new coordinates of point A are (-2, 5), the new coordinates of point B are (-3, 2), and the new coordinates of point C are (-5, -1).
Next, the translation moves the triangle 8 units to the right and 10 units up. So, the new coordinates of point A are (6, 15), the new coordinates of point B are (5, 12), and the new coordinates of point C are (3, 9).
Write an algebraic expression with the constant 7 and the variable and Y
answer
y/7
step by step explanation
Help me what is the answer ?
Answer:
Correct choce is (a). 30.
Step-by-step explanation:
Given equation is [tex]f(x)=x^2-x[/tex].
Now we need to find the value of (fof)(3). Then select correct matching choice from the given choices. Where given choices are:
(a). 30
(a). 33
(a). 6
(a). -6
Now let's find [tex](fof)(3)[/tex]
[tex](fof)(3)=f(f(3))[/tex]
[tex](fof)(3)=f(3^2-3)[/tex]
[tex](fof)(3)=f(9-3)[/tex]
[tex](fof)(3)=f(6)[/tex]
[tex](fof)(3)=6^2-6[/tex]
[tex](fof)(3)=36-6[/tex]
[tex](fof)(3)=30[/tex]
Hence correct choce is (a). 30.
Answer:
The correct answer is option A. 30
Step-by-step explanation:
It is given that
f(x) = x² - x
To find f o f(3)
F(x) = x² - x
f(3) = 3² - 3
= 9 - 3 6
f o f(3) = f(6)
f(6) = 6² - 6
= 36 - 6 = 30
Therefore the correct answer is f o f(3) = 30
The correct option is Option a. 30
What equation represents the relationship between p and q shown in the table
q = 10p because all of them are multiplied by ten
write the equation of the line that is parallelto the graph of y=2/3x+7 and passes through the point (-1 -2)
Answer:
[tex]y + 2 = \frac{2}{3}(x+1)[/tex]
Step-by-step explanation:
Parallel lines are parallel because they never intersect. As such, they have the same slope. The slope of the line y = 2/3x + 7 is 2/3. Substitute m = 2.3 and the point (-1,-2) into the point slope form of a line.
[tex]y -y_1 = m(x-x_1)\\y --2 = \frac{2}{3}(x --1)\\y + 2 = \frac{2}{3}(x+1)\\[/tex]
Hillary works for a company that offers 75% matching on all of her retirement contributions. For the last 35 years, Hillary has been depositing $200 into her 401(k) savings account that pays 4.99% interest annually. After 35 years, how much money has been deposited into the 401(k) by both Hillary and her employer?
Answer: The total is $12,250.
Step-by-step explanation: First, we will calculate the amount that Hillary has deposited over the past 35 years. She has deposited $200 for each of the past 35 years. The total that she has deposited is 200 x 35 = $7,000.
Her employer also deposits into her account 75% of what she has deposited. In order to calculate their contribution you need to multiply $7,000 x .75 = $5,250.
The total that has been deposited into the account is $7,000 + $5,250 = $12,250.
Hillary's total contribution over the 35 years was $84,000. The employer matched 75% of Hillary's contribution, totaling $63,000. The combined contribution of Hillary and her employer for 35 years is $147,000.
Explanation:Hillary has been depositing $200 into her 401(k) per month for the past 35 years. For 35 years, there are a total of 35 times 12 months which equals 420 months. Given this, Hillary has contributed $200 times 420 months which is $84,000.
Her employer has a 75% match on all her contributions. This means they are adding another 0.75 times the $84,000, which equals $63,000.
Therefore, the total contribution by both Hillary and her employer over the 35 years is both amounts added together: "$84,000 (Hillary’s contribution) + $63,000 (Employer match) = $147,000".
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O A. Vertical angles are congruent.
O B If two lines are parallel, then alternate exterior angles are congruent.
O C. If two lines are parallel, then alternate interior angles are congruent.
O D Corresponding angles theorem.
The answer to this question is A
Vertical angles are congruent. Option A
How to describe the statementVertical angles are pairs of angles formed by the intersection of two lines or line segments, where the angles are opposite each other and share a common vertex but do not share any sides.
Vertical angles are always congruent, meaning they have equal measures.
For instance, in an "X" shape formed by two intersecting lines, the angles opposite each other at the intersection are vertical angles.
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Which expression will have the same sum as 3/8+ 1/4
The sum of 3/8 and 1/4 is 5/8. Therefore, any expression that sums up to 5/8 will have the same sum as 3/8 + 1/4.
Explanation:To find the expression that has the same sum as 3/8 + 1/4, we need to first compute the sum of the given fractions. When summing fractions, we need the denominators to be the same. In this case, 8 and 4 could both be divisible by 2, so we need to convert the second fraction to have the denominator of 8:
3/8 + 2/8 = 5/8
Therefore, the expression that will have the same sum as 3/8 + 1/4 is any other expression that also amounts to 5/8. Examples could be 2/8 + 3/8 or even 5/8 + 0.
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To find an expression with the same sum as 3/8 + 1/4, we need to find a common denominator and add the fractions. The expression with the same sum is 5/8.
Explanation:To find an expression with the same sum as 3/8 + 1/4, we need to find a common denominator.
The least common multiple of 8 and 4 is 8, so we can rewrite 3/8 as 3/8 × 1 = 3/8 × 2/2 = 6/16.
Now we can add 6/16 + 1/4, which equals (6 + 4)/16 = 10/16.
Simplifying this fraction gives us 5/8. Therefore, the expression with the same sum as 3/8 + 1/4 is 5/8.
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Find the value of each variable. Answer in simplest radical form.
Answer:
x = 5√3; y = 5
Step-by-step explanation:
Finding y: The sine function links the 30° angle, the 10 unit hypotenuse and the side opposite the angle, y:
sin 30° = 1/2 = y/10
Solve the equation of ratios
1 y
-- = ----- using cross-multiplication first: 2y = 10 → y = 5
2 10
We can now find x either by using a similar approach and the cosine function or by using the Pythagorean Theorem:
x² + y² = 10² = 100 → x² = 100 - y² = 100 - 5² = 75
If x² = 75, then x = ±√75 = ± (√25)·(√3) → ±5√3
Since lengths are always positive, take x = 5√3 as the answer.
Can you help, please.?
Answer:
No 1 inch cubes will fit
28 one-half inch cubes will fit
Step-by-step explanation:
No cubes with a side length of 1 inch will fit because one dimension of the prism is only 1/2 inches, so we can't fit a 1 inch cube in anywhere.
Since one dimension is 1/2 inch, we can line up 1/2 inch cubes along the other 2 dimensions. Let's say that the 1/2 inch dimension is the base, the 2 inch dimension is the height, and the 7/2 inch dimension is the length.
We can stack the cubes 4 high, (2 inches of height with 1/2 inch being the cube height, there are 4 halves in 2).
We can place 7 cubes along the length (7/2 inches = 3.5 inches. There are 7 halves in 3.5).
So we can have 4(7) = 28 one half inch cubes can fit in to the prism
Matt’s friend, Franny, found that the volume of a rectangular prism was 96 in sqaured. She remembered that the area of the base was 16 in squared. What was the height of the box? Show your work.
What is the answer to this question
Answer:
[tex]\large\boxed{\dfrac{18}{2x-6}=\dfrac{9}{x-3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{18}{2x-6}=\dfrac{18\!\!\!\!\diagup^9}{2\!\!\!\!\diagup_1(x-3)}=\dfrac{9}{x-3}[/tex]
The wholesale price of a TV is 65% less than the retail price therefore the wholesale price is ? times the retail price
Answer:
The wholesale price of TV is 0.35 times the retail price of this TV
x = 0.35y
Step-by-step explanation:
Let say x = wholesale price of a TV
Let say y = retail price price of a TV
We can write an equation that represents what is mention in the question
Equation
x = y - 65%y
x = y - 65/100y
x = y - 0.65y
x = 0.35y
Hence, the wholesale price is 0.35 times the retail price
the coefficients corresponding to k = 0, 1, 2, ..., 4 in the expansion of (x+y)^4 are what
Answer:
The coefficients in increasing order of k are;
1, 4, 6, 4, 1
Step-by-step explanation:
The expansion of (x+y)^4 falls under the category of binomial expansions in which the coefficients are computed using combinations;
For k = 0, the coefficient is;
4 combination 0 = 1
For k = 1, the coefficient is;
4 combination 1 = 4
For k = 2, the coefficient is;
4 combination 2 = 6
For k = 3, the coefficient is;
4 combination 3 = 4
For k = 4, the coefficient is;
4 combination 4 = 1
These values can also be obtained from the Pascal's triangle;
The coefficients always exhibit some degree of symmetry
Answer:
1, 4, 6, 4, 1
Step-by-step explanation:
apex
Is this is the right answer, I divided 17/20?
Answer:
17 x 5 = 85. It is the right answer, my way of solving it was different but still correct.
Step-by-step explanation:
4 / 20 = 5
5 x 17 = 85.
In a basketball game, Marlene made 16 field goals. Each field goals was worth either 2 points or 3 points, and Marlene scored a total of 39 points from field goals. Let x represents the number of two-point field goals and y to model the situation. How many three-point field goals did Marlene make in the game?
Answer:
The number of three-point field goals was [tex]7[/tex]
Step-by-step explanation:
Let
x-----> the number of two-point field goals
y-----> the number of three-point field goals
we know that
[tex]x+y=16[/tex]
[tex]x=16-y[/tex] -----> equation A
[tex]2x+3y=39[/tex] ----> equation B
substitute equation A in equation B and solve for y
[tex]2(16-y)+3y=39[/tex]
[tex]32-2y+3y=39[/tex]
[tex]y=39-32=7[/tex]
Using a system of equations, it is found that Marlene made 7 three-point field goals in the game.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of two-point field goals made.Variable y: Number of three-point field goals made.Marlene made 16 field goals, hence:
x + y = 16 -> x = 16 - y
She scored a total of 39 points from field goals, hence:
2x + 3y = 39
2(16 - y) + 3y = 39
32 - 2y + 3y = 39
y = 7
Marlene made 7 three-point field goals in the game.
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when g(x) is divided by x^2+x-6 the remainder is 7x+13 . what is the remainder when g(x) is divided by x+3
Answer: (x - 2)(7x + 13) which is equivalent to 7x² - x - 26
Step-by-step explanation:
[tex].\qquad \dfrac{g(x)}{x^2+x-6}=7x+13\\\\\\\implies g(x)=(x^2+x-6)(7x+13)\\\\.\qquad \qquad =(x+3)(x-2)(7x+13)\\\\\\\text{What is g(x) divided by x+3?}\\\\\dfrac{g(x)}{3}=\dfrac{(x+3)(x-2)(7x+13)}{x+3}\\\\\\.\qquad =(x-2)(7x+13)\\\\\\.\qquad =7x^2+13x-14x-26\\\\\\.\qquad =\large \boxed{7x^2-x-26}[/tex]
3,982 to the nearest ten.
Answer:3980
Step-by-step explanation:
Answer:
Step-by-step explanation:
3980
Can y’all plss help me people with all of those math problems
Answer: # is 1.15 miles
2/5 of a mile is the same as 4 tenths of a mile. 3/4 of a mile is the same as .75. So ---- .75 plus .4
Step-by-step explanation:
find the least common denominator of 3/8 and 11/2
Answer:
8
Step-by-step explanation:
Note that 2 divides into 8 evenly, yielding the quotient 4. 8 is the LCD. To combine 3/8 and 11/2, we would rewrite 11/2 as
4·11
------ = 44/8
4·2
and then combine 44/8 with 3/8. The sum would be 47/8.
In summary, the LCD of 3/8 and 11/2 is 8; 3/8 stays as is and 11/2 is rewritten by mult. numerator and denominator by 4 each.
find the area of this figure
Answer:
79.25 square inches
Step-by-step explanation:
To find the area of the figure, split it into two shapes - a rectangle and a semi-circle.
The area of a rectangle is A = b*h. Substitute b = 10 and h = 4.
A = 4*10 = 40.
The area of a semi-circle is A =1/2 πr². Substitute r = 5 since the diameter is 10.
A =1/2 π5² = 12.5π = 39.25.
Add the two areas together.
39.25 + 40 = 79.25
Plzzzzzzz hellppppp really fasttttttttttttt plzzz someone be my savior !!!!!!
Surface area of original prism: 113.5 cm
Surface area of enlarged prism: 1816
its pretty simple to find the ratio so you can probably figure that out on your own :) Good luck!
Consider the function given below.
Step-by-step explanation:
[tex]f(x)=x^3+2x^2-x-2=x^2(x+2)-1(x+2)=(x+2)(x^2-1)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\f(x)=(x+2)(x-1)(x+1)\\\\\text{The zeros (x-intercepts):}\\\\f(x)=0\iff(x+2)(x-1)(x+1)=0\iff \\x+2=0\ \vee\ x-1=0\ \vee\ x+1=0\\\\x=-2\ \vee\ x=1\ \vee\ x=-1\\\\\text{y-intercept}:\\\text{Put x = 0:}\\\\f(0)=0^3+2(0^2)-0+2=2\to(0,\ 2)[/tex]
What is the value of y?
According to the diagram, which of the following statements about area and perimeter of pentagon ABCDE is true?
A) Area = 25 Perimeter = 20
B) Area = 30 Perimeter = 22.31
C) Area = 33 Perimeter = 12.5
D) Area = 35 Perimeter = 18
Answer:
Area = 30 , Perimeter = 22.31 ⇒ Answer (B)
Step-by-step explanation:
* Lets study the figure
- The length of AE = 5
- The length of DC = 3
- The length of BC = 4
- Tho find the length of DE and AB we must use Pythagoras Theorem
∵ The vertical distance of ED = 3 and the horizontal distance = 2
∴ ED = √(3² + 2²) = √13
- Similar we will find AB
∵ The vertical distance of AB = 6 and the horizontal distance = 3
∴ AB = √(6² + 3²) = √45
* Now we can find its perimeter
- The perimeter = 5 + 4 + 3 + √13 + √45 = 22.31
* to find the area we will divided it into 2 trapezium
- The first one contains E , D , C with point of intersection
between the vertical axis with side CB
- The lengths of its 2 parallel bases are 3 , 6 and height 2
- The second one contains E , A , B with point of intersection
between the vertical axis with side BC
- The lengths of its 2 parallel bases are 2 , 5 and height 6
∵ Area trapezium = (1/2)(b1 + b2) × h
- The area of 1st one = (1/2)(3 + 6) × 2 = 9 units²
- The area of 2nd one = (1/2)(2 + 5) × 6 = 21 units²
∴ The area of the figure = 9 + 21 = 30 units²
* Area = 30 , Perimeter = 22.31
does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria. IQ score 50-69,70-89, 90-109, 110-129, 130-149 frequency 24, 228, 490, 232, 26
No, the distribution does not appear to be normal.
Yes, all the requirements are met.
No, the frequencies do not decrease from the maximum frequency to a low frequency.
No, the frequencies do not decrease from the maximum frequency to a low frequency
Answer:
Yes, all the requirements are met.
Step-by-step explanation:
Frequency Distribution is a graph or table which shows the frequency of different outcome.
Normal Distribution has bell like-shape.
Since here the value of frequency is less for score 50-69 then it increases from 70- 109 then the frequency is again decreasing from score 110-149. So the curve of frequency distribution when plotted appears like bell-shaped. Hence, It appears like a normal distribution.
riddle time if there was 2 motheres 2 daughters 1 grandma and 1 grandaughter how much people are in the family will mark as brainlist worth alot
Answer:
3 people
Step-by-step explanation:
The grandma is a mother to her daughter and her daughter is the mother to the granddaughter.