The graph of the function g(x) = -x is shown on the grid below.
Graph the function h(x) = -x +2+3 in the interactive graph.
←++
-9-8-7-6-5-4-3-2
888610321
9
Y
7+
6+
5+
4+
3.
2.
-2-
-3+
-4+
-5+
-6+
$7
-8+
69
-9.
2 3 4 5 6 7 8 9
y= g(x)
→x
Answers
The graph is shown in the attached image.
The final graph of y = -|x + 2| + 3 is a V-shaped curve that opens downwards and is shifted upwards by 3 units.
This curve intersects the x-axis at x = -4 and x = -0 and passes through the point (-2, 1).
The graph is given below.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The graph of y = -x is a straight line that passes through the origin and has a slope of -1.
It extends infinitely in both directions and has a negative slope, which means that as x increases, y decreases.
The graph of y = |x + 2| - 3 is a bit more complex.
The absolute value function |x + 2| means that the value of x + 2 is taken, and then the absolute value of that value is calculated.
The absolute value function always returns a positive value, so the graph of y = |x + 2| is a V-shaped curve that opens upwards and passes through the point (-2, 0).
The minus sign outside the absolute value function means that the entire curve is reflected about the x-axis, so the graph of y = -|x + 2| is also a V-shaped curve, but this time it opens downwards.
Finally, the +3 at the end of the equation means that the entire graph of
y = -|x + 2| is shifted upwards by 3 units.
Thus,
The final graph of y = -|x + 2| + 3 is a V-shaped curve that opens downwards and is shifted upwards by 3 units.
This curve intersects the x-axis at x = -4 and x = -0 and passes through the point (-2, 1).
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Related Questions
One positive integer is 2 times another positive integer and their product is 50. what are the positive integers?
Answers
The first integer is 5.
The second integer is 10.
What is Positive integer ?If an integer is higher than zero, it is positive; if it is lower than zero, it is negative. Zero can be either positive or negative. Since a b and c d, then a + c b + d, the ordering of integers is consistent with algebraic operations.
According to the information:One integer is twice the other
so,
If one integer is x then
The other will be 2x.
Their product :
2x * x = 50
2x² = 50
x² = 50/2
x² = 25
x = √25
x = 5
the first integer is 5.
the second integer is 2x = 2 x 5
= 10.
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What is the value of the expression when n = 3?
StartFraction 6 (n squared plus 2) Over n EndFraction
16
22
30
66
Answers
Answer:
B) 22
Step-by-step explanation:
The expression is:
[tex]\cfrac{6(n^2+2)}{n}[/tex]Find its value when n = 3, substitute n with 3 in the expression:
[tex]\cfrac{6(3^2+2)}{3} =\cfrac{6(9+2)}{3} =\cfrac{6(11)}{3}=2(11) = 22[/tex]The matching answer choice is B.
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 634" by 412" on the drawing, how large is the bedroom?
Answers
For a bedroom measuring 6 3/4" by 4 1/2" on the drawing, the dimensions of the bedroom are 18 ft. by 27 ft.
Option (C) is correct.
In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.
According to the question,
The scale of an architectural sketch is 1/4" = 1'. If, according to the drawing, a bedroom has the dimensions 6 3/4 by 4 1/2 inches.
Then, the dimensions of the bedroom in feets are calculated as follows:
As 1/4" = 1'
6 3/4" = 27'= 27 ft.
Similarly,
4 1/2" = 18' =18 ft.
Thus, the dimensions of the bedroom are: 18 ft. by 27 ft.
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Hurry A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annual interest is $510?
Answers
Answer:
Step-by-step explanation:
We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:
[tex]5x+10x=510[/tex]
Solve for x
[tex]15x=510\\x=34[/tex]
Now multiply x by the corresponding percentages to find how much was invested into each percentage.
[tex]34*5=170[/tex]
[tex]34*10=340[/tex]
Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.
We can of course check our answer by adding 170+340 which equals our original investment of 510.
$1800 is invested at 5% and the remainder, $4200, is invested at 10%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let us consider the amount invested at 5% x.
The amount invested at 10% is then the remainder, which is:
$6000 - x
Now we can set up an equation for the total interest earned:
0.05x + 0.10($6000 - x) = $510
Simplifying and solving for x:
0.05x + $600 - 0.10x = $510
-0.05x + $600 = $510
-0.05x = -$90
Divide both sides by 0.05
x = $1800
Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.
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If p(x,3) Q(7,1) and pQ(15) unit find the possible value of x
Answers
Answer:
Step-by-step explanation: P(x 3), Q(7, -1) and PQ= 5 .
To Find :
The possible value of x.
Solution :
We know, distance between two points in coordinate plane is given by :
Therefore, the possible value of x are 10 and 4.
The value of x from the set {1, 3, 5, 7} that holds true for the equation is?
Answers
The value of x from the given set of values is 5
Area and perimeter of a rectangleA rectangle is a 2 dimensional shape with 4 sides and angle. The formula for calculating the area and perimeter is given as:
Area = length * width
Perimeter = 2(length + width)
If the length of a rectangle is 2 inches more than its width and the perimeter of the rectangle is 24 inches, the resulting equation will be:
2x + 2(x + 2) = 24,
Expand and determine the value of "x"
2x+ 2x + 4 = 24
4x + 4 = 24
Subtract 4 from both sides
4x = 24 - 4
4x = 20
Divide both sides by 4
4x/4 = 20/4
x = 5
Hence the value of x from the given set of values is 5
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Complete question
The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x is the width in inches, represents this situation. The value of x from the set {1, 3, 5, 7} that holds true for the equation is . So, the width of the rectangle is inches and its length is inches.
HELP ASAP!!! 40 POINTS
Identify each x-value at which the slope of the tangent line to the function f(x) = 0.2x2 + 5x − 12 belongs to the interval (-1, 1).
Answers
Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:
(-15,-10).
What is the slope of the tangent line to a function f(x) at point x = x0?It is given by the derivative at x = x0, that is:
[tex]m = f^{\prime}(x_0)[/tex].
In this problem, the function is:
[tex]f(x) = 0.2x^2 + 5x - 12[/tex]
Hence the derivative is:
[tex]f^{\prime}(x) = 0.4x + 5[/tex]
For a slope of -1, we have that:
0.4x + 5 = -1
0.4x = -6
x = -15.
For a slope of 1, we have that:
0.4x + 5 = 1.
0.4x = -4
x = -10
Hence the interval is:
(-15,-10).
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What must be true in order to find a sum for an infinite geometric series?
Answers
Answer:
0 < r < 1
Step-by-step explanation:
That every sequence gets multiplied by a number less than 1 but more than 0
The law is
Common ratio or r must lies in between 0 and 1
It means
r is in (0,1)
r is greater than 0 but less than 1The formula is
[tex]\boxed{\sf S_{\infty}=\dfrac{a}{1-r}}[/tex]
Find the terms through degree four of the maclaurin series for f(x) = sin(x) 1−x.
Answers
The terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].
In this question,
The function is f(x) = [tex]\frac{sin(x)}{1-x}[/tex]
The general form of Maclaurin series is
[tex]\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......[/tex]
To find the Maclaurin series, let us split the terms as
[tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] ------- (1)
Now, consider f(x) = sin(x)
Then, the derivatives of f(x) with respect to x, we get
f'(x) = cos(x), f'(0) = 1
f''(x) = -sin(x), f'(0) = 0
f'''(x) = -cos(x), f'(0) = -1
[tex]f^{iv}(x)[/tex] = cos(x), f'(0) = 0
Maclaurin series for sin(x) becomes,
[tex]f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....[/tex]
⇒ [tex]f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....[/tex]
Now, consider [tex]f(x) = (1-x)^{-1}[/tex]
Then, the derivatives of f(x) with respect to x, we get
[tex]f'(x) = (1-x)^{-2}, f'(0) = 1[/tex]
[tex]f''(x) = 2(1-x)^{-3}, f''(0) = 2[/tex]
[tex]f'''(x) = 6(1-x)^{-4}, f'''(0) = 6[/tex]
[tex]f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24[/tex]
Maclaurin series for (1-x)^-1 becomes,
[tex]f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....[/tex]
⇒ [tex]f(x)=1+x+x^{2} +x^{3} +......[/tex]
Thus the Maclaurin series for [tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] is
⇒ [tex]f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)[/tex]
⇒ [tex]f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....[/tex]
⇒ [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex]
Hence we can conclude that the terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].
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A circle is circumscribed around a rectangle with sides lengths 6 and 8 what is the area of the circle?
A. 16[tex]\pi[/tex]
B. 20[tex]\pi[/tex]
C. 24[tex]\pi[/tex]
D. 25[tex]\pi[/tex]
E. 30[tex]\pi[/tex]
Answers
Answer:
D. 25pi
Step-by-step explanation:
"circumscribed" means the rectangle is inside the circle and just the corners (vertices) of the rectangle are touching the circle. This means the diagonal of the rectangle is the diameter of the circle. See image. If the sides of the rectangle are 6 and 8 then the third side that makes the triangle(half the rectangle) is 10. You can find this using Pythagorean Theorem or Pythagorean triples (shortcut)
6^2 + 8^2 = d^2
36 + 64 = d^2
100 = d^2
d = 10
This is the diameter of the circle. The radius would then be 5.
Area of a circle is:
A = pi•r^2
= pi•5^2
= 25pi
How is a circumference related to an arc
Answers
Answer:
An arc of a circumference or of a circle mostly is a portion of the circumference. The length of an arc for all intents and purposes is simply the length of this portion of the circumference in a definitely major way. The circumference itself can particularly be considered an arc that goes around the circle in a fairly major way.
Given that log 2 = 0.3010 and log 3 = 0.4771 , how can we find log 6 ?
Answers
Step-by-step explanation:
log 6 = log (2×3) = log 2 + log 3 = 0.3010+0.4771
=0.7781
Answer:
[tex]\sf \log_{10}6=0.7781[/tex]
Step-by-step explanation:
Given:
[tex]\sf \log_{10} 2 = 0.3010[/tex]
[tex]\sf \log_{10} 3 = 0.4771[/tex]
To find log₁₀ 6, first rewrite 6 as 3 · 2:
[tex]\sf \implies \log_{10}6=\log_{10}(3 \cdot 2)[/tex]
[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \sf \log_{10}(3 \cdot 2)=\log_{10}3+\log_{10}2[/tex]
Substituting the given values for log₁₀ 3 and log₁₀ 2:
[tex]\begin{aligned} \sf \implies \log_{10}3+\log_{10}2 & = \sf 0.4771+0.3010\\ & = \sf 0.7781 \end{aligned}[/tex]
Therefore:
[tex]\sf \log_{10}6=0.7781[/tex]
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Factorise 10xy-12+15x-8y
Answers
Answer: 10xy-12+15x-8y=(5x-4)*(2y+3).
Step-by-step explanation:
[tex]10xy-12+15x-8y=(10xy-8y)+(15x-12)=\\=2y*(5x-4)+3*(5x-4)=(5x-4)*(2y+3).[/tex]
OA=
Please help asap!! Thanks so much :))
Answers
In the given diagram, the value of the dashed side of rhombus OABC is 5
Distance between two pointsFrom the question, we are to determine the length of the dashed line (OA), in rhombus OABC
In the diagram, we can observe that the length of OA is the distance between point A and the origin (O).
Using the formula for calculating distance between two points,
d =√[(x₂-x₁)² + (y₂-y₁)²]
In the diagram,
The coordinate of the origin is (0, 0)
The coordinate of point A is (3, 4)
Thus,
x₁ = 0
x₂ = 3
y₁ = 0
y₂ = 4
Putting the parameters into the formula, we get
OA =√[(3-0)² + (4-0)²]
OA =√(3² + 4²)
OA =√(9+16)
∴ OA =√25
OA = 5
Hence, in the given diagram, the value of the dashed side of rhombus OABC is 5
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A polynomlal function has x-Intercepts at -2, ;, and 2 and a relative maximum at x=-1. graph Which graph matches the description of this function?
Answers
The graph that matches the polynomial function that has x-Intercepts at -2, ;, and 2 and a relative maximum at x = -1 is: graph A.
How to Determine the Graph of a Polynomial Function?We are given that the polynomial function has the following characteristics:
Relative maximum at x = -1, this implies that the peak point of the graph has an x-value that is equal to -1. In order words, the "mountain" is at x = -1.
Graph A has a "mountain" that is at x = -1.
We are given the x-intercepts of the polynomial function as:
-2, 1/2, and 2. This means that the graph intercepts the x-axis at -2, 1/2, and 2.
Graph A in the image attached has x-intercepts of -2, 1/2, and 2.
Therefore, we can conclude that the graph that matches the polynomial function that has x-Intercepts at -2, ;, and 2 and a relative maximum at x = -1 is: graph A.
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Li Juan solves the equation below by first squaring both sides of the equation. [tex]\sqrt{3-2w}=w+6[/tex]
What extraneous solution does Li Juan obtain?
Answers
Answer:
w = -11
Step-by-step explanation:
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex](\sqrt{3 - 2w})^2 = (w + 6)^2[/tex]
[tex] 3 - 2w = w^2 + 12w + 36 [/tex]
[tex] w^2 + 14w + 33 = 0 [/tex]
[tex] (w + 11)(w + 3) = 0 [/tex]
[tex] w + 11 = 0 [/tex] or [tex] w + 3 = 0 [/tex]
[tex] w = -11 [/tex] or [tex] w = -3 [/tex]
When you square both sides of an equation, you must check all solutions for extraneous solutions.
Check w = -11.
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex] \sqrt{3 - 2(-11)} = -11 + 6 [/tex]
[tex] \sqrt{3 + 22} = -5 [/tex]
[tex] \sqrt{25} = -5 [/tex]
[tex] 5 = -5 [/tex]
This is a false statement, so the solution w = -11 is extraneous since it does not satisfy the original equation.
Check w = -3.
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex] \sqrt{3 - 2(-3)} = -3 + 6 [/tex]
[tex] \sqrt{3 + 6} = 3 [/tex]
[tex] \sqrt{9} = 3 [/tex]
[tex] 3 = 3 [/tex]
This is a true statement, so the solution w = -3 is valid.
Answer: w = -11
Please explain to me how to do this
Answers
Answer:
see explanation
Step-by-step explanation:
basically Gauss' method simplifies to
Sum = (number of terms) ÷ 2 × (1st term + last term)
43
S₂₀₀ = 200 ÷ 2 × (1 + 200) = 100 × 201 = 20,100
44
S₄₀₀ = 400 ÷ 2 × (1 + 400) = 200 × 401 = 80,200
45
S₈₀₀ = 800 ÷ 2 × (1 + 800 ) = 400 × 801 = 320,400
46
S₂₀₀₀ = 2000 ÷ 2 × (1 + 2000) = 1000 × 2001 = 2,001,000
Answer:
Sum = (number of terms) = 2 x (1st term + last term) 43
43. S200 = 200 = 2 × (1+200) = 100 201 = X 20,100
44 400 400 = 2 × (1+400) = 200 × 401 = 80,200
45 S800 = 800 = 2 × (1+800) = 400 × 801 = 320,400
46 S2000 = 2000 2 × (1+ 2000) = 1000 × 2001 = 2,001,000
Which equation could represent a linear combination of the system?
Answers
The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2/3x + 5/2y = 15
4x + 15y = 12
Multiply the first equation by 6, to eliminate the fractions.
6 * (2/3x + 5/2y = 15)
This gives
4x + 15y = 90
Subtract the equation 4x + 15y = 90 from 4x + 15y = 12
4x - 4x + 15y - 15y = 12 - 90
Evaluate the difference
0 + 0 = -78
Evaluate the sum
0 = -78
The above equation is the same equation as option (b) 0 = 26
This is so because they both represent that the system of equations have no solution
Hence, the equation that could represent a linear combination of the system is 0 = 26
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Complete question
The system of equations below has no solution.
2/3x + 5/2y = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?
Question 5(Multiple Choice Worth 2 points)
(07.01 MC)
What is the range of the function f(x) = x - 3?
Answers
Answer:
(-∞, ∞)
Step-by-step explanation:
Unless there are restrictions on the domain, the range of any odd-degree polynomial function is "all real numbers."
Linear functionThe given function is a linear function, degree 1. This is an odd degree, so the range of the function is "all real numbers."
-∞ < f(x) < ∞
(-∞, ∞) . . . . . in interval notation
Find the absolute maximum and minimum values of the function, subject to the given constraints. k(x,y)=−x2−y2 4x 4y; 0≤x≤3, y≥0, and x y≤6
Answers
For function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
For given question,
We have been given a function k(x, y) = -x² - y² + 4x + 4y
We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
First we find the partial derivative of function k(x, y) with respect to x.
⇒ [tex]k_x=-2x+4[/tex]
Now, we find the partial derivative of function k(x, y) with respect to y.
[tex]\Rightarrow k_y=-2y+4[/tex]
To find the critical point:
consider [tex]k_x=0[/tex] and [tex]k_y=0[/tex]
⇒ -2x + 4 = 0 and -2y + 4 = 0
⇒ x = 2 and y = 2
This means, the critical point of function is (2, 2)
We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
Consider k(0, 0)
⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)
⇒ k(0, 0) = 0
Consider k(3, 3)
⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)
⇒ k(3, 3) = -9 - 9 + 12 + 12
⇒ k(3, 3) = -18 + 24
⇒ k(3, 3) = 6
Therefore, for function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
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If ₹405 is to be divided among three persons A, B, C in the ratio of 3:5:7, how much money does each one get? Express them in percentages.
I will mark the first answerer as Brainliest.
Answers
Answer:
A = 20%
B = 33.33%
C = 46.67%
Step-by-step explanation:
Ok we need to add up 3, 5, and 7
3+5+7 = 15
405/15 = 27.
27*3 = A
27*5 = B
27*7 = C
A = 81 / 20%
B = 135 / 33.33%
C = 189 / 46.67%
How many ways are there to get from (0, 0) to (7, 7) in the coordinate plane
with movements of only one unit right or one unit up? How many ways are there to do so that do not go above the line y = x?
Answers
The number of ways there are to move from (0, 0) to (7, 7) in the coordinate plane with movements of only one unit right or one unit up accordingly is; 49 while that such that y =x is; 7.
How many ways are there to get from (0, 0) to (7, 7) in the coordinate plane with pmovements of only one unit right or one unit up?It follows from the task content that the movement intended on the coordinate plane is; from (0, 0) to (7, 7).
The number of ways to move such that movements of only one unit right or one unit up is; 7 × 7 = 49.
The number of ways for which y= x is therefore is; 7 as the movement is diagonal.
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Build Your Math Skills 2A, Round decimals to the nearest hundredth (0.01): 42.988
Answers
Answer: 42.99
Step-by-step explanation:
42.988. Since 8 is close to ten and is in the hundredth we round it hence 42.99.
PLLLLLEASE I NEEED HELP
Answers
Answer:
-3/(b-6) = 3/(-b+6) = 3/(6-b)
Step-by-step explanation:
7/(b-6) + 10/(6-b)
= 7/(b-6) + 10/(-b+6)
= 7-10/(b-6)
= -3/(b-6) = 3/(-b+6) = 3/(6-b)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{6 - b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{ - (b - 6)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{7}{b - 6} - \cfrac{10}{ b - 6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ - 3}{ b - 6}\:\:\: or \:\:\: \dfrac{3}{6-b} [/tex]
What is the las digit of the product of all the numbers between 11 and 29?
Answers
The last digit of the product of all the numbers between 11 and 29 is 0.
A product is something that has undergone one or more multiplications.
Here, we're looking for the final digit of the product of all whole numbers greater than 11 and less than 29.
Next, we have the product as: 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28
Now take note of the 20 that is present.
Any number multiplied by 20 will result in a zero, so:
Product = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)
Using only that, we can infer that 0 represents the final digit in the product of all the numbers between 11 and 29.
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What are the solutions to the system of equations? {−x+y=4y+12=x2+x
Answers
Answer: (-4, 0) and (4, 8)
Step-by-step explanation:
Looking at the graph, we can see where the line passes the parabola and can tell the solutions are (-4, 0) and (4, 8)
H=(,),()
F=(),()
Help please asap
Thanks so much
Answers
From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).
According to the statement
we have given that the a rectangle on the graph with the two given points and we have to find the another points of the graph.
So, to find the points of the rectangle
firstly the given points are:
E(2,3) And G(-2,-2) and we have to find the point H and F.
So, The point H :
For the point H the lines of rectangle meet with each other at the 3 from origin on the x axis to the negative side and at the 3 from origin on the y axis.
So, the point H become H(-3,3)
And for point F:
For the point F the lines of rectangle meet with each other at the 2 from origin on the x axis to the positive side and at the 2 from origin on the y axis on the negative side.
So, the Point F become F(2,-2).
So, From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).
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Russell has $38 and is saving $2 per day. cornelius has $64 and is spending $2 per day. after how many days will russell have more money than cornelius?
Answers
The equation be 38 + 2x - (64 - 2x) = 0 then the value of x = 6.5.
How to find the value of x?To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Let the day be x
38 + 2x - (64 - 2x) = 0
Subtract 38 from both sides
38 + 2x - (64 - 2x) - 38 = 0 - 38
Simplifying the above equation, we get
2x - (64 - 2 x) = -38
Expanding the above equation, 2x - (64 - 2x) = 4x - 64
4x - 64 = -38
Add 64 to both sides
4x - 64 + 64 = -38 + 64
Simplify
4x = 26
Divide both sides by 4
[tex]$\frac{4 x}{4}=\frac{26}{4}[/tex]
Simplifying the equation
[tex]$x=\frac{13}{2}[/tex]
The value of x = 6.5.
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A three-digit number has one more ten than it has hundreds, and it also has one more than twice as many units as tens. The sum of the number and that number reversed is 31 less than 10 cubed. Find the reverse number.
15 pts
Answers
The reverse number of the three-digit number is 732
How to determine the reverse of the number?Let the three-digit number be xyz.
So, the reverse is zyx
This means that
Number = 100x + 10y + z
Reverse = 100z + 10y + x
From the question, we have the following parameters:
y = x + 1
z = 1 + 2y
The sum is represented as:
100x + 10y + z + 100z + 10y + x = 10^3 - 31
100x + 10y + z + 100z + 10y + x = 969
Evaluate the like terms
101x + 101z + 20y = 969
Substitute y = x + 1
101x + 101z + 20(x + 1) = 969
101x + 101z + 20x + 20 = 969
Evaluate the like terms
101x + 101z + 20x = 949
121x + 101z = 949
Substitute y = x + 1 in z = 1 + 2y
z = 1 + 2(x + 1)
This gives
z = 2x + 3
So, we have:
121x + 101z = 949
121x + 101* (2x + 3) = 949
This gives
121x + 202x + 303 = 949
Evaluate the sum
323x = 646
Divide by 323
x = 2
Substitute x = 2 in z = 2x + 3 and y = x + 1
z = 2*2 + 3 = 7
y = 2 + 1 = 3
So, we have
x = 2
y = 3
z = 7
Recall that
Reverse = 100z + 10y + x
This gives
Reverse = 100*7 + 10*3 + 2
Evaluate
Reverse = 732
Hence, the reverse number of the three-digit number is 732
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What number has to fill in the blank to make this a perfect square trinomial: 9x^2 + ___+ 144
Answers
The number that has to fill the blank to make the trinomial a perfect square is 72x
Perfect square trinomialFrom the question, we are to determine the number that makes the given trinomial a perfect square
The given trinomial is
9x² + ___+ 144
For any given trinomial ax² + bx + c, the trinomial is a perfect square if
b² = 4ac
In given trinomial,
a = 9, c = 144, b = ?
Now, we will determine the value of b
Putting the values into the equation,
b² = 4ac
b² = 4×9×144
b² = 5184
b = √5184
b = 72
Thus,
The trinomial will become 9x² + 72x+ 144
Hence, the number that has to fill the blank to make the trinomial a perfect square is 72x
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