The reflection across the x-axis of Y(1.5, -2) is Y'(1.5, 2). Y(1.5,−2) →Y'(−1.5,−2) represents reflection across the y-axis.
What is an ordered pair?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.
The rule of reflection over the x -axis is A(x,y) → A'(x,-y)
The rule of reflection over the y -axis is A(x,y) → A'(-x,y).
A student finds that the reflection across the x-axis of Y(1.5,−2) is Y'(−1.5,−2).
Student follows the rule of reflection over the y -axis is A(x,y) → A'(-x,y).
Therefore students do mistake to consider a wrong formula.
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A line passes through the point (3,2) and has a slope of 4
The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Point (3,2)
Then Slope m = 4
Now Write the equation as;
y - 2 = 4(x - 3)
y = 4x - 10
Hence, The equation of the line is; y = 4x - 10
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which multiplication expression is equivalent to 5/8 divided by 1/16? A. 8/5 x 16/1 B. 5/8 x 16/1 C. 5/8 x 1/16 D. 8/5 x 1/16
Multiplication expression equivalent to 5/8 ÷ 1/16 is 5/8 × 16.
What do you mean by fractionol expression?
Fractions with a variable in the denominator are called fractional expressions. They frequently also include variables in the numerator. Since fractions can also be conceived of as ratios, these expressions are often called rational expressions. In algebra, we most frequently refer to fractional expressions as expressions that are the ratio of two polynomials.
Given expression:
5/8 divided by 1/16
⇒ 5/8 ÷ 1/16
= 5/8 × 16
= 10
Therefore, multiplication expression equivalent to 5/8 ÷ 1/16 is 5/8 × 16.
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the area of a triangle is half the area of a square. if the base of the triangle and a side of the square are equal, what is the ratio of the side of
As a result, the area of an equilateral triangle represented across one side of a square is equal to half the area (1/2)of something like the triangle described on one of its diagonals.
What is a square form?A square is a compact, two-dimensional object with four equal sides and four vertices. On either side, it has parallel sides. A rectangle with equal length and breadth is also comparable to a square.
Which four types of squares are there?a rectangle with two adjacent sides that is the same length. a quadrilateral with four equal sides and four straight angles. a parallelogram having one right angle and sides that are evenly spaced apart. a right-angled rhombus's form.
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Mr. Rooks' bank pays 4-% interest per year. He has $17,000 in the bank. How much interest would he receive in 3 years?
Mr. Rooks would receive $2,040 in interest in 3 years.
The interest rate is given as 4%, which means that for every $100 Mr. Rooks has in the bank, he will receive $4 in interest per year.
To find the total interest Mr. Rooks will receive in 3 years, we need to multiply the annual interest rate by the number of years, and then multiply that result by the amount of money Mr. Rooks has in the bank.
In this case, the calculation would be as follows:
Annual interest rate × number of years × amount in the bank = total interest
(4 / 100) × 3 × $17,000 = $2,040
Therefore, Mr. Rooks would receive $2,040 in interest in 3 years.
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Given 2x + 3 is the hypotenuse, use the Pythagorean
Theorem to find the length of the side labeled x.
Answer:
24
Step-by-step explanation:
Given right triangle sides x, 2x-3, and 2x+3, you want to know the length of the side labeled x.
Pythagorean theoremThe Pythagorean theorem tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.
(2x +3)² = (2x -3)² +x²
4x² +12x +9 = 4x² -12x +9 +x²
x² -24x = 0 . . . . . subtract 4x² +12x +9
x(x -24) = 0 ⇒ x = 0 or 24
The length of the side labeled x is 24 units.
__
Additional comment
The triangle is an 8-15-17 triangle scaled up by a factor of 3.
1/2 times 4/5 what’s the answer
Answer:
2/5.
Step-by-step explanation:
1/2 times 4/5 is equal to (1/2) * (4/5), which simplifies to 4/10. Since 4/10 can be simplified to 2/5, the answer is 2/5.
Answer:
the answer is 2/5 or as a decimal 0.4
Answer to this equation , simplified
If the value of a = 5 and c = √21 then the value of b = 2i, b = -2i.
What is meant by simplest radical form?Simply said, simplifying a radical eliminates the need for further square, cube, fourth, etc. roots to be found. This is known as expressing in the simplest radical form. In the denominator of a fraction, it also means eliminating any radicals. The top and bottom of a fraction are said to be in its simplest form if they only share the number one. For the top and bottom to remain whole numbers, you cannot divide them further. Additionally, lowest terms, or simple form, may be used. Take the fraction, as an example.The formula goes a² + b² = c², where a and b are legs of the triangle (the non hypotenuse sides), and c is the hypotenuse (the side opposite to the right angle).In this problem, we have one leg and the hypotenuse.
Let the equation be a² + b² = c²
substitute the values in the above equation, we get
5² +b² = (√21)²
25+b²=21
Move 25 to the right side
b² = -4
For x² = f(a) the solutions are [tex]$x=\sqrt{f(a)},-\sqrt{f(a)}$[/tex]
[tex]$$b=\sqrt{-4}, b=-\sqrt{-4}$$[/tex]
simplifying the above equation, we get
[tex]& \sqrt{-4}=2 i \\[/tex]
[tex]& -\sqrt{-4}=-2 i \\[/tex]
b = 2i, b = -2i
Therefore, the value of b = 2i, b = -2i.
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Answer!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
if a person is not a hockey player, they are not a prof athlete
if a person is a hockey player, they are a prof athlete
if a person is not a prof athlete, then they r not a hockey player
1 · 3.2 = d
i need the answer now
Answer:
d = 3.2
Step-by-step explanation:
1 * 3.2 = 3.2
Hence,
d = 3.2
What is the slope of the line that passes through the points (2, 3) and (0,11)?
Can you please help me
Answer:
The Answer is B/2/middle option
Step-by-step explanation: im great at math
Find the product of -1.5x and -0.25x.
O 0.375x²
O-1.75x²
O 0.375x
O -1.75x
Step-by-step explanation:
(-1.5)x × -0.25x = 0.375x²
remember, -×- = +
What is the value of the expression
4(2+y)
______
2y-x
when x = 2 and y = 47
Answer:
Step-by-step explanation:
I got 196/90
I got this by plugging in 47 for y so I got 4(2+47) and got 196 when I solved it. The bottom one I did 2(47-2) and got 90...( I don't know if it's right though, if wrong I'm sorry)
Two bells P and Q ring at intervals of 3hours and 4hours respectively. After how many hours will the two bells first ring simultaneously (at the same time)
Answer:
12 hours
Step-by-step explanation:
4 / 2
2/2
1
4 = 2²
2² x 3 = 4 x 3 = 12
Ahmad will spend at most $34 on gifts. So far, he has spent $21 . What are the possible additional amounts he will spend?
Use c for the additional amount (in dollars) Ahmad will spend.
Write your answer as an inequality solved for c .
The additional amount Ahmad will spend if Ahmad will spend at most $34 on gifts. So far, he has spent $21 is c = 13.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
Ahmad will spend at most $34 on gifts,
He spent = $21,
c = additional amount
The total amount he can spend now = total amount - he spent
c = 34 - 21
c = 13
Therefore, the additional amount Ahmad will spend, if Ahmad will spend at most $34 on gifts. So far, he has spent $21 is c = 13.
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NO LINKS!! Please help me with the Domain and Range and Functions Part 2bb
Domain - the set of possible x-coordinates of a function.
Range - the set of possible y-coordinates of a function.
Question 25
Domain is:
x ∈ (- 6, 6), both ends excluded as open circles.Range is:
y ∈ [-5, 3), the lowest point is included as part of graph, the highest value is excluded as open circle..This is a function as it passes the vertical line test.
Question 26Domain is:
x ∈ [- 3, 7], both ends included as part of the graph.Range is:
y ∈ [-1, 5], both ends included as part of the graph.This is not a function as it fails the vertical line test.
Answer:
25) Domain: (-6, 6)
Range: [-5, 3)
26) Domain: [-3, 7]
Range: [-1, 5]
Step-by-step explanation:
Definitions
An open circle indicates the value is not included in the interval.A closed circle indicates the value is included in the interval.An arrow shows that the function continues indefinitely in that direction.Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 25From inspection of the graph, the endpoints of the continuous curve are:
(-6, -3) and (6, 3)As the endpoints are open circles, the values are excluded from the domain and range.
Therefore, the domain in interval notation is:
Domain: (-6, 6)The smallest y-value is y = -5 and the greatest y-value is y = 3.
Therefore, the range in interval notation is:
Range: [-5, 3)Question 26The graph is a conic section (ellipse) and therefore it is not a function.
The smallest x-value is x = -3 and the greatest x-value is x = 7.
The smallest y-value is y = -1 and the greatest y-value is y = 5.
Therefore, the domain and range in interval notation are:
Domain: [-3, 7]Range: [-1, 5]What are the possible rational zeros of f(x) = x^4+2x^3-3x^2-4x-12
The solution of the function f(x) = (x - 2)(x + 6)(x² + x + 2) will be 2, -3, - 1/2 + (√7/2)i, and - 1/2 - (√7/2)i.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The function is given below.
f(x) = (x⁴ + 2x³ - 3x² - 4x - 12)
Factorize the expression, then we have
f(x) = (x⁴ + 2x³ - 3x² - 4x - 12)
f(x) = x⁴ - 2x³ + 4x³ - 8x² + 5x² - 10x + 6x - 12
f(x) = x³(x - 2) + 4x²(x - 2) + 5x(x - 2) + 6(x - 2)
f(x) = (x - 2)(x³ + 4x² + 5x + 6)
f(x) = (x - 2) (x³ + 3x² + x² + 3x + 2x + 6)
f(x) = (x - 2)[x²(x + 3) + x(x + 3) + 2(x + 3)]
f(x) = (x - 2)(x + 6)(x² + x + 2)
The zeroes of the function are given as,
f(x) = 0
(x - 2)(x + 3)(x² + x + 2) = 0
x = 2, -3, - 1/2 + (√7/2)i, - 1/2 - (√7/2)i
The solution of the function f(x) = (x - 2)(x + 6)(x² + x + 2) will be 2, -3, - 1/2 + (√7/2)i, and - 1/2 - (√7/2)i.
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Forty-five year old Jim Wiseman just got a new job earning $60,000 per year. He will save 10% of his income each year for his retirement at age 55. He must decide whether to invest his savings in Big Sky Bank which offers 20% compounded semi-annually or Valley Bank which offers 8% compounded quarterly. What compounded amount would he earn he chooses to invest his savings in Big Sky Bank? What compounded amount would he earn if he chooses to invest his savings in Valley Bank?
The compounded amount earned in Big Sky Bank is $40,365.00.
The compounded amount earned in Valley Bank is $13,248.24.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = 10% of 60,000
P = 6000
t = 10 years
Big sky Bank:
r = 20%
n = 2 (semiannually)
A = 6000 [tex](1 + 0.1)^{20}[/tex]
A = 6000 x [tex]1.01^{20}[/tex]
A = $40,365.00
Valley Bank:
r = 8%
n = 4 (quarterly)
A = 6000 [tex](1 + 0.02)^{40}[/tex]
A = 6000 x [tex]1.02^{40}[/tex]
A = $13,248.24
Thus,
Big Sky Bank compounded amount is $40,365.00.
Valley Bank compounded amount is $13,248.24.
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The figure below is reflected over x-axis. What are the coordinates of the image of point Y after this transformation?
The coordinates of point y after the transformation is (-6,5).
What is coordinates of point ?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). a group of variables that accurately depict a stance. The first number on a graph represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is located 12 units down and 5 units up.Firstly , we need to get the coordinates of the point y before the transformation
The coordinates are
(-6,-5)
By reflecting over the y-axis, we have the following change;
(x,y) becomes (-x,y)
So we have;
(6,-5)
Then we are to rotate at an angle of 180 degrees counterclockwise
The operation here will be;
(x,y) to (-x,-y)
So we have;
(6,-5) to (-6,5)
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The China Health and Nutrition Survey aims to examine the effects of the health, nutrition, and family planning policies and programs implemented by national and local governments.48 It, for example, collects information on number of hours Chinese parents spend taking care of their children under age 6. The side-by-side box plots below show the distribution of this variable by educational attainment of the parent. Also provided below is the ANOVA output for comparing average hours across educational attainment categories. (a) Write the hypotheses for testing for a difference between the average number of hours spent on child care across educational attainment levels. (b) What is the conclusion of the hypothesis test?
(a). The alternative to the null hypothesis, H₀ = μ₁= μ₂ = μ₃=μ₄= μ₅ is Hₐ: At least two 1s are unequal. (b). Refuse H₀ If p-value is less than 0.05, the 5% presumed threshold of significance is exceeded.
What is a typical value?In mathematics, the middle value—which is determined by dividing the sum of each of the values by the total number of values—is the approximate amount in a collection of numbers. To determine the median of a collection of data, add all of the values and divide the result by the total number of values.
Briefing:a). The study's goal is to determine if there is discernible variation in the typical quantity of time spent on childcare services across levels of educational achievement.
Null hypothesis, H₀ = μ₁= μ₂ = μ₃=μ₄= μ₅
(The average quantity of time spent on child rearing across educational levels does not change much.)
Alternative hypothesis, Hₐ : At least two μ₁s are unequal.
(The mean number of hours on child care varies significantly depending on the degree of education).
b). Let the level of significance be, ∝ = 0.05
Decision rule: Reject H₀ if p-value ≤ 0.05
The result statistic F has a value of 1.26 and a p-value of 0.2846 based on the provided ANOVA table. Keep in mind that the p-value exceeds the 5% expected level of significance. Therefore, don't reject H₀.
There is insufficient data to draw the conclusion that the average quantity of time spent with child care throughout education level differs significantly.
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4. Alex gets $5.00 every week she does cvs
her chores. She did chores 3 weeks.
Now, she wants to buy a video
game for $36.00. How much more
money does she need?
The amount of money that she needs to buy a video game will be $21.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Alex gets $5.00 consistently she does CVS her tasks. She tackled errands for a long time. Presently, she needs to purchase a computer game for $36.00.
The amount of money is given as,
⇒ $36 - $5 x 3
⇒ $36 - $15
⇒ $21
The amount of money that she needs to buy a video game will be $21.
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Solve the inequality and graph the solution.
k/2 – 20 ≥ –18
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
The graph of the inequality is attached below.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
K/2 - 20 ≥ -18
Add 20 on both sides,
K/2 - 20 + 20 ≥ -18 + 20
K/2 ≥ 2
Multiply both sides by 2,
K/2 x 2 ≥ 2 x 2
K ≥ 4
Now to graph the inequality.
The graph of the inequality is attached below.
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10. The perimeter of the table shown is 16 feet. Write an equation in
the form px + q=r to solve for x.
the value of x is 5 feets and p = 2, q = 6 and r = 16.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,
Area of rectangle is A = a*b
Perimeter = 2(a+b)
given in the question that the perimeter is 16 feet.
p= 2(3+x)
p = 6+2x
p = 2
q = 6
r = 16
2x = 10
x =5 feet.
Hence, the value of x is 5 feets.
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50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!!
Quadrilateral RUST has a vertex at T (5, 2).
An image displaying a quadrilateral RUST.The vertex of R is R of 1 comma 5.
What are the coordinates of T' after the translation (x, y) → (x – 1, y + 2), followed by a dilation by a scale factor of 2, centered at the origin?
A.
(8, 8)
B.
(6, 2)
C.
(4, 4)
D.
(10, 4)
Answer:
A) (8, 8)-------------------------------
Apply the rules to point T.
Translation:
T(5, 2) → T'(5 - 1, 2 + 2) = T'(4, 4)Dilation:
T'(4, 4) → T''(4*2, 4*2) = T''(8, 8)The matching choice is A.
:)):))):)/):)::!:&’s
The congruent reason for 5 is (c) ASA
How to determine the congruent reason for 5?From the question, we have the following parameters that can be used in our computation:
Triangles = VWX and ZYX
The ASA similarity theorem implies that the corresponding angles of the triangles in question are similar and the sides between these angles are congruent
From the question, we can see that the following corresponding angles on the triangles:
Angles W and Y
Angles X and X
This implies that these angles are congruent angles
For the triangle to be congruent by ASA, the following sides must also be congruent
WX must be congruent to YX
This is indicated in the table of values at (3)
Hence, the additional information on the similarity of the triangles is (d) ASA
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following quadratic equation, find the
5 x²+60 x+187=7
(x + 6) is the solution for the quadratic equation 5x² + 60x + 187 = 7
Given,
The quadratic equation;
5x² + 60x + 187 = 7
Arrange this in standard form;
5x² + 60x + 187 - 7 = 0
5x² + 60x + 180 = 0
We have to find the solution for this quadratic equation;
Quadratic formula ;
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = 5
b = 60
c = 180
Now,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex] = [tex]\frac{-60(+-)\sqrt{60^{2}-4*5*180 } }{2*5}[/tex] = [tex]\frac{-60(+-)\sqrt{3600-3600} }{10}[/tex] = -60±0 / 10 = -60/10 = -6 = (x + 6)
That is,
The solution for the quadratic equation 5x² + 60x + 187 = 7 is (x + 6)
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Pslspslspslsp someone help snd pls right answer it’s a test
What is the slope?
simplify your answer and write it as a proper fraction, improper fraction or integer
Answer:
2
Step-by-step explanation:
Slope is Rise/Run
Pick two points and count the number of units up (rise) and sideways (run) between them
Answer: Slope = 2
Step-by-step explanation: The equation for slope is y2 - y1 / x2 - x1
so using points (2,2) and (3,4)
4-2 / 3-2 = 2/1 = 2
compute the integral
integral 2x+11/x^2-x-2 dx
The Integral value of (2x+11)/(x²-x-2) is[tex]2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex]
What is Integration?An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.
The given integral is [tex]\int\dx \frac{2x+11}{x^{2} -x-2} dx[/tex]
By partial fractions we divide the integral
Apply the sum rule:
∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx
[tex]=\int\dx \frac{2x}{x^{2} -x-2} dx+\int\dx \frac{11}{x^{2} -x-2} dx[/tex]
Let us calculate the first integral part
[tex]=\int\dx \frac{2x}{x^{2} -x-2} dx[/tex]
Let us use the partial fraction of [tex]\frac{x}{x^{2} -x-2} dx:\frac{1}{3(x+1)} +\frac{2}{3(x-2)}[/tex]
[tex]\int\dx \frac{2x}{x^{2} -x-2} dx=2\int\dx \frac{1}{3(x+1)} dx+ \frac{2}{3(x-2)} dx[/tex]
[tex]\int\dx \frac{2x}{x^{2} -x-2} dx=2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)[/tex]
Now let us integrate second term.
[tex]\int\dx \frac{11}{x^{2} -x-2} dx=11\int\dx \frac{1}{x^{2} -x-2} dx[/tex]
We can write denominator as x²-x-2= (x-1/2)²-9/4
[tex]=11\int\dx \frac{1}{(x-\frac{1}{2}) ^{2} -\frac{9}{4}} dx[/tex]
We apply u substitution method
[tex]\int\dx \frac{11}{x^{2} -x-2} dx=-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)[/tex]
[tex]=2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex]
Hence, [tex]2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex] is the integral value of of (2x+11)/(x²-x-2).
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Teena bought a bicyhcle for $528 after getting a discount of 12% taken off its normal price. Find the normal price of the bicycle.
Answer:
Originally $600.
Step-by-step explanation:
[tex]\frac{528}{88} =\frac{y}{100}[/tex]
88 · y = 528 · 100
88y = 52800
y = 600
Originally $600.