ANSWER
The choice is correct.
[tex]y = {(x -1)}^{2} + 2[/tex]
EXPLANATION
The equation of a parabola in vertex form is given by:
[tex]y = a {(x -h)}^{2} + k[/tex]
where (h,k) is vertex of the parabola and 'a' is the leading coefficient of the parabola.
From the given options, the leading coefficient must be a=1.
We also have the vertex of the parabola at (1,2). This implies that h=1 and k=2.
We substitute these values into the formula to get,
[tex]y = {(x -1)}^{2} + 2[/tex]
The second option is correct.
Does every line have a slope and a y-intercept? Explain
Answer:
the answer is yes because on a graph, even if it has a x intercept, it will eventually intercept the y intercept b/c the line will continue infinitely.
Step-by-step explanation:
Please mark brainliest and have a great day!
no
no becuase not every line acrosses along the whole graph and the y intercept gose up and down
Please help right now!!!!! Solve the system of equations below. x + y = 7 2x + 3y = 16
Answer:
[tex]x=5[/tex] and [tex]y=2[/tex].
Step-by-step explanation:
We have been given a system of equations. We are asked to solve our given system.
[tex]x+y=7...(1)[/tex]
[tex]2x+3y=16...(2)[/tex]
From equation (1), we will get:
[tex]x=7-y[/tex]
Upon substituting this value in equation (2), we will get:
[tex]2(7-y)+3y=16[/tex]
[tex]14-2y+3y=16[/tex]
[tex]14+y=16[/tex]
[tex]14-14+y=16-14[/tex]
[tex]y=2[/tex]
Now, we will substitute [tex]y=2[/tex] in equation (1).
[tex]x+2=7[/tex]
[tex]x+2-2=7-2[/tex]
[tex]x=5[/tex]
Therefore, the point [tex](5,2)[/tex] is solution for our given equation.
Answer:
The answer is (5,2)
Step-by-step explanation:
I took the test and got it correct.
A triangle has verticals at B(-3,0), C(2,-1), D(-1,2). Which transformation would produce an image with verticals B”(-2,1), C”(3,2), D”(0,-1)?
Answer:
The triangle is reflected across the x-axis and then translated 1 unite to the right , 1 unit up
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
then the new point = (x , -y)
- If point (x , y) reflected across the y-axis
then the new point = (-x , y)
- If the point (x , y) translated horizontally to the right by h units
then the new point = (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
then the new point = (x - h , y)
- If the point (x , y) translated vertically up by k units
then the new point = (x , y + k)
- If the point (x , y) translated vertically down by k units
then the new point = (x , y - k)
* Now lets solve the problem
- A triangle has three vertices
- The vertices are B (-3 , 0) , C(2 , -1) , D (-1 , 2)
- The images of the vertices are B" (-2 , 1) , C" (3 , 2) , D" (0 , -1)
after two steps of transformations
- After comparing the points with their images we find
# The x-coordinates of the points are added by 1
∴ There is translation to the right
# The y-coordinates of the points not add or subtracted by the same
number, that means there is a transformation before the translation
for the y-coordinates
# The sign of y-coordinates of the points are changed , that means
there is a reflection across the x-axis
∴ B' is (-3 , 0) , C' is (2 , 1) , D' is (-1 , -2)
- After comparing the 1st image with the 2nd images we find
# The x-coordinates of the points are added by 1 and the
y-coordinates are add by 1
∴ B" is (-2 , 1) , C" is (3 , 2) , D" is (0 , -1)
- From all above
* The triangle is reflected across the x-axis and then translated 1 unite
to the right , 1 unit up
Which parent function is represented by the table?
I need some help
Answer: C
Step-by-step explanation: The table represents absolute value
For this case we must find a function of the form:
[tex]y = f (x)[/tex]that complies with the relation of the table.
We note that for the first two values of x, the function yields the same value but with a positive sign.
So:
[tex]f (x) = | x |\\y = | -2 | = 2\\y = | -1 | = 1\\y = | 0 | = 0\\y = | 1 | = 1\\y = | 2 | = 2[/tex]
Answer:
Option C
Convert this decimal into its fractional
form, simplified completely.
0.040
Hello There!
I Provided Steps In The Image Attached.
Have A Great Day!
Solve by using the given theorems of logarithms. log 5 + log 2 =
The expression log 5 + log 2 can be combined using the property that the logarithm of a product is equal to the sum of the logarithms, which simplifies to log 10. Since log 10 is equal to 1, the solution to the expression is 1.
To solve the expression log 5 + log 2 using the logarithmic theorems, we can apply one of the fundamental properties of logarithms. Specifically, the logarithm of a product of two numbers is equal to the sum of the logarithms of those two numbers (log xy = log x + log y). Applying this property to our expression, we can combine the two logarithms as follows:
log 5 + log 2 = log (5 x 2)
Now, we can easily calculate the combined term:
log (5 x 2) = log 10
Since the base of the logarithm is not specified, we can assume it is 10 (common logarithm). Therefore, we can simplify further:
log 10 = 1
Thus, the solution to the given expression is 1.
The letters that form the word ALGEBRA are
placed in a bowl. What is the probability, as a
percent, of choosing a letter other than A
and then choosing an A?
Answer:
Nearly 23.8%
Step-by-step explanation:
The word ALGEBRA consists of letters A, L, G, E, B, R and A (2 letters A and 5 letters other than A).
The probability that the first letter chosen will be other than A is
[tex]\dfrac{5}{7}[/tex]
Then 2 letters A and 4 letters other than A left (6 letters in total). The probabilty that the second letter chosen is A is
[tex]\dfrac{2}{6}=\dfrac{1}{3}[/tex]
Hence, the probability of choosing a letter other than A and then choosing an A is
[tex]\dfrac{5}{7}\cdot \dfrac{1}{3}=\dfrac{5}{21}\approx 23.8\%[/tex]
The probability of first drawing a letter other than 'A' and then drawing an 'A' from the word ALGEBRA is approximately 23.81%. This is determined by calculating the individual probabilities and then multiplying them together.
Explanation:The word ALGEBRA has 7 letters. The probability of choosing a letter other than 'A' means we are considering 5 valid letters out of the 7. Therefore, the probability is 5/7. Then, looking for an 'A' within the remaining 6 letters (after one letter is already taken), we see there are 2 'A' letters left, so the probability is 2/6 or simplified as 1/3.
Therefore, the combined probability of both these events happening is the product of their individual probabilities. We multiply the fractions: 5/7 * 1/3 = 5/21 = 0.238095. Translating that fraction into a percentage, we multiply by 100% to get approximately 23.81%.
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Which of the following is the quotient of the rational expressions shown below? 3x/2x+5 /2x/x+5
The quotient of the rational expressions given is obtained by converting the division to multiplication by the reciprocal leading to \((\frac{3x \times (x+5)}{2x \times (2x+5)})\). The final simplification depends on specific values of x.
Explanation:The question asks to find the quotient of the following rational expressions: \((\frac{3x}{2x+5}) \div (\frac{2x}{x+5})\). To solve this, we first recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, the problem becomes \((\frac{3x}{2x+5}) \times (\frac{x+5}{2x})\).
We simplify this further by multiplying the numerators together and the denominators together: \((\frac{3x \times (x+5)}{2x \times (2x+5)})\).
To solve the more difficult problem, as hinted, we might consider factoring or simplifying further. However, the key calculation here reveals that the certain factors in the numerator and denominator might not simplify directly in this expression, leading to a more nuanced understanding of rational expressions. As such, detailed simplification depends on the specific values of x and further factorization may not lead to a simpler form without more context.
The correct answer is: [tex]\text { B. } \frac{3 x+15}{4 x+10}[/tex].
To find the quotient of the given rational expressions, you divide the first rational expression by the second one.
[tex]\frac{\frac{3 x}{2 x+5}}{\frac{2 x}{x+5}}=\frac{3 x}{2 x+5} \cdot \frac{x+5}{2 x}[/tex]
Now, you can simplify this expression:
[tex]=\frac{3 x(x+5)}{2 x(2 x+5)}[/tex]
Cancel out x from both numerator and the denominator.
[tex]=\frac{3 (x+5)}{2 (2 x+5)}[/tex]
[tex]=\frac{3x+15}{4x+10}[/tex]
This value matches with the option B. Thus, B is the correct answer.
Complete Question:
Which of the following is the quotient of the rational expressions shown below?
[tex]\frac{3 x}{2 x+5} \div \frac{2 x}{x+5}[/tex]
[tex]\text { A. } \frac{4 x^2+10 x}{3 x^2+15 x}[/tex]
[tex]\text { B. } \frac{3 x+15}{4 x+10}[/tex]
[tex]\text { C. } \frac{6 x^2}{2 x^2+15 x+25}[/tex]
[tex]\text { D. } \frac{3}{4}[/tex]
The distance between the points (3, 3) and (7, 3) is 4 √13 6
Answer:
4 units
Step-by-step explanation:
We have to calculate the distance between two points first to check the correct answer.
so,
The formula for distance is:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\Here\\(x_{1},y_{1})=(3,3)\\(x_{2},y_{2})=(7,3)\\Putting\ Values\\d=\sqrt{(7-3)^{2}+(3-3)^{2}}\\d=\sqrt{(4)^{2}+(0)^{2}}\\d=\sqrt{16+0} \\d=\sqrt{16} \\Taking\ Square\ Root\ will\ give\ us:\\d=4 units\\So\ the\ distance\ between\ two\ points\ is\ 4\ units ..[/tex]
Person 1 can do a certain job in 21 minutes, and person 2 can do the same job in 28 minuets. When completing the job together, which expression would be used to represent the amount of work done by person 1. 21,1/21,x/21,21x
Answer:
1/21.
Step-by-step explanation:
To solve the problem 'How long would they take to do the job working together?' you would work in fractions of the job done / minute:
1/21 + 1/28 = 1/x.
So for person 1 the expression is 1/21.
15 points?Im just being lazy Lol
Answer:
38
Step-by-step explanation:
The 38-deg angle and <6 are vertical angles, so they are congruent.
m<6 = 38 deg
Answer:
38 degrees. Congruent inside angles. <3
Step-by-step explanation:
Could you Solve. 21r<7
Yes, I can solve that inequality.
Any value of ' r ' that's less than 1/3 is a solution.
Answer:
r < 1/3
Step-by-step explanation:
21r<7
Divide each side by 21
21r/21<7/21
r < 1/3
Solve the equation for x.
5x - ( 4x - 1) = 2 help please
Answer:
x = 1
Step-by-step explanation:
Given
5x - (4x - 1) = 2 ← distribute the parenthesis by - 1
5x - 4x + 1 = 2
x + 1 = 2 ( subtract 1 from both sides )
x = 1
If f(x)= -15x-5, then f^-1(x)=
Answer:
(x+5) /-15 = f^-1(x)
Step-by-step explanation:
f(x)= -15x-5
y = -15x-5
Exchange x and y
x = -15y -5
Solve for y
Add 5 to each side
x+5 = -15y -5+5
x+5 = -15y
Divide by -15
(x+5)/-15 = -15y/-15
(x+5) /-15 = y
(x+5) /-15 = f^-1(x)
Please Answer I’m desperate
Answer:
B
Step-by-step explanation:
Given
f = c / λ ( multiply both sides by λ )
fλ = c
You simply have to multiply both sides by lambda:
[tex]f = \dfrac{C}{\lambda} \iff f\cdot \lambda = \dfrac{C}{\lambda}\cdot \lambda \iff C = f\lambda[/tex]
Determine the number of solutions for the equation shown below.
X = X-9
A. O
B. Infinitely many
c. 1
D. 2
Answer:
A. 0
Step-by-step explanation:
Nothing can be equal to itself if you subtract 9 from it.
Final answer:
The equation X = X - 9 yields a contradiction upon simplification (0 = -9), indicating that there are no solutions.
Explanation:
To determine the number of solutions for the given equation, we start by inspecting it closely:
X = X - 9
If we attempt to solve for X, we will subtract X from both sides of the equation:
0 = -9
This is a contradiction since 0 does not equal -9. Therefore, the given equation has no solution. Other examples of equations can have one solution, such as X = 1, or have two solutions, such as quadratic equations like x = 4.133 or 9.435. But in this case, the equation does not balance and therefore has no solutions.
The correct answer is:
A. 0
Find the value of k such that the quadratic polynomials x2-(k+6)x+2(2k+1) as sum of the zeroes as the half of their product
Answer:
k = 5
Step-by-step explanation:
The sum of the zeros is the opposite of the coefficient of x, so is (k+6).
The product of zeros is the constant term, 2(2k+1), so half their product is (2k+1).
The problem statement asks us to find k so that these values are the same:
k +6 = 2k +1
5 = k . . . . . . . . subtract k+1
The value of k is 5.
_____
The zeros are 5.5±√8.25. Their sum is 11; their product is 22.
simplify each of the following
a) 3a×9ac
b) 7de×3de²
Answer:
3a x 9ac
=(3a×9a)(c)
27a2 ×c
7de×3de2
=(7×3)(de ×de2)
= 21de3
ZE and ZF are vertical angles with mZE= 9x + 12 and mZF= 3x + 24.
What is the value of x?
Answer:
x=2
Step-by-step explanation:
Vertical angles are equal
m ZE = m ZF
9x+12 = 3x+24
Subtract 3x from each side
9x -3x +12 = 3x-3x+24
6x+12 = 24
Subtract 12 from each side
6x+12 -12 = 24-12
6x = 12
Divide each side by 6
6x/6 =12/6
x = 2
f(x) = x + 8 and g(x) = -4x - 3, find (f-g)(x)
Answer:
5x + 11
Step-by-step explanation:
We are subtracting function g(x) from function f(x).
Write f(x) as is: f(x) = x + 8.
Then change all of the signs of g(x): -g(x) = 4x + 3.
Now combine like terms for the sum (f - g)(x) = x + 8 + 4x + 3. We get
(f - g)(x) = 5x + 11
How is the graph of y=2x^2+3 different from the graph of y=x^2-9x+20 shown below?
Answer:
○ The graph of y = -2x² + 3 opens downward and is shifted up.
Step-by-step explanation:
According to the Quadratic Equation, y = Ax² + Bx + C, C acts like a y-intercept, and in this case, since both graphs shift up [because both are positive values], we do not pay attention to those. Now, we come over to our A, which makes a BIG difference because both graphs open in opposite directions [one negative, one positive]. With this being stated, we have our answer.
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** Extended information on Parabolas
Opens down → -A
Opens up → A
Please help me with this
Answer:
B, D
Step-by-step explanation:
Angles 1 and 2 combined form a right angle, so the sum of their measures is 90°. Therefore, they are complementary angles.
Since they share a common side and vertex and don't overlap, they are also adjacent angles.
Find the equation for a parabola that has a vertex at (0, 4) and passes through the point (–1, 6).
Answer:
[tex]\large\boxed{y=2x^2+4}[/tex]
Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (0, 4) → h = 0 and k = 4.
Substitute:
[tex]y=a(x-0)^2+4=ax^2+4[/tex]
The point (-1, 6) is on the parabola. Put the coordinates of the point to the equation:
[tex]6=a(-1)^2+4[/tex] subtract 4 from both sides
[tex]2=a\to a=2[/tex]
Finally:
[tex]y=2x^2+4[/tex]
Solve for y.
1. y= -1/4
2. 1/4.
3. y=41/4.
4.41/25
What is the correct answer?
Answer:
1. y= -1/4
Step-by-step explanation:
y/5 + 3/10 = (y+2)/7
Get a common denominator for the left hand side
2y/10 + 3/10 = (y+2)/7
(2y+3)/10 = (y+2)/7
Using cross products
(2y+3) *7 = 10*(y+2)
Distribute
14y+21 = 10y+20
Subtract 10y from each side
14y-10y +21 = 10y-10y+20
4y+21 =20
Subtract 21 from each side
4y+21-21 = 20-21
4y = -1
Divide by 4
4y/4 = -1/4
y = -1/4
Jim makes $10.35 per hour. Write an equation that Jim can use to calculate his pay.
Answer:
Step-by-step explanation:
Pay = 10.35 * h where h is the number of hours that he works. The other 2 questions should have been included with this one. I'll answer the second one here.
Distance = 65 * h
distance = 65 * h miles.
the product of 3/4 and a number is 16
Answer:
21 1/3
Step-by-step explanation:
Write this as an expression
3/4 x = 16
Now it is a one step equation
divide 3/4 from its self and 16
3/4 divided by 16 = 21 1/3
x= 21 1/3
Answer:
[tex]21\frac{1}{3}[/tex] or 21.3
Step-by-step explanation:
We are given that the product of [tex] \frac { 3 } { 4 } [/tex] and a number is [tex] 1 6 [/tex].
Assuming that number to be [tex] x [/tex], we can write it as:
[tex] \frac { 3 } { 4 } \times x = 1 6 [/tex]
Taking the denominator to the other side of equation and multiplying it to get:
[tex] 3 x = 1 6 \times 4 [/tex]
[tex] 3 x = 6 4 [/tex]
Isolating the variable to get:
[tex] x = \frac { 6 4 } { 3 } [/tex]
[tex] x = 21\frac{1}{3}[/tex] or [tex] x = 21.3[/tex]
When 3 is subtracted from one third of a number less than 6. Which inequality and solution represents this sitution?
Answer:
1/3(n) - 3 < 6; n < 27
Step-by-step explanation:
" 3 subtracted from one third of a number"
= 1/3(n) - 3
given that this is less than 6:
1/3(n) - 3 < 6
1/3(n) < 6 +3
1/3(n) < 9
n < 27
Inequality and solution is 1/3(n) - 3 < 6 and n < 27.
The correct option is (A).
what is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given statement is : " 3 subtracted from one third of a number less than 6"
or, 1/3(n) - 3 < 6
or, 1/3(n) < 6 +3
or, 1/3(n) < 9
or, n < 27
Hence, Inequality and solution is 1/3(n) - 3 < 6 and n < 27.
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WILL GIVE BRAINLIEST b. Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
Answer:
When x <= 8000
The cost remains constant at 0.35 when x increases from 0 to 8000
The slope of cost function over this part is 0
When 8000 < x <= 20000
The cost remains constant at 0.75 when x increases from 8000 to 20000
The slope of cost function over this part is 0
When 20000 < x <= 42000
The cost decreases when x increases from 20000 to 42000
The slope of cost function
[tex]m = \frac{y2 - y1}{x2 - x1} \\ = \frac{(0.83 - \frac{40000}{200000}) - (0.83 - \frac{20000}{200000})}{40000 - 20000} [/tex]
m= -5 × 10^-6
the average height range if a golden retriever is 20-24 inches. Write the average height range as an absolute value inequality
Answer:
|x-22| < 2
The < has an underline below it
The absolute value inequality that represents the average height range of a golden retriever (20-24 inches) is |h - 22| <= 2, where h represents any height within the range. This means that the difference between any height in the range and the midpoint (22 inches) is at most 2 inches.
Explanation:To write the average height range of a golden retriever as an absolute value inequality, we need to first find the midpoint of the range and then use that to express the distance from any height in the range to that midpoint. In this case, the average height range for a golden retriever is 20-24 inches. The midpoint of the range is (20 + 24) / 2 = 22 inches. So, any height h in the range satisfies |h - 22| <= 2. This is because the maximum difference between any height in the range and the midpoint is 2 inches (24 - 22 or 22 - 20).
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The table represents a function. Which value is an output of the function? (A) –6 (b)–2(c) 4(d) 7
Answer:
Option B
Step-by-step explanation:
. If a function is given in the form of f(x) = ax² + bx + c, then value of x is "input" and the value ... Now from the given table output values of the function are 8, 3, -5, -2 and 12. ... Therefore Option B