Answer:
$950
Step-by-step explanation:
(500*6*15)/100 = 450 (applying the formula of simple interest)
450 + 500 ( adding the interest to the initial investment or princlple)
= 950 (bank balance after 15 years)
Hope this helps! :)
Find the equation of the line through (2,9)(1,6)(-7,-6)
Answer:
y=(3/2)x+6
If your equation is in a different form, let me know.
Step-by-step explanation:
So the slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
Parallel lines have the same slope, m (different y-intercept (b) though).
So we need to find the slope going through (1,6) and (-7,-6).
To do this you could use [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Or, what I like to do is line the points up vertically and subtract vertically then put 2nd difference over first difference. Like so:
( 1 , 6)
-( -7, -6)
---------------
8 12
So the slope of our line is 12/8.
Let's reduce it! Both numerator and denominator are divisible by 4 so divide top and bottom by 4 giving 3/2.
Again parallel lines have the same slope.
So we know the line we are looking for is in the form y=(3/2)x+b where we don't know the y-intercept (b) yet.
But we do know a point (x,y)=(2,9) that should be on our line.
So let's plug it in to find b.
y=(3/2)x+b with (x,y)=(2,9)
9=(3/2)2+b
9=3 +b
Subtract 3 on both sides:
9-3=b
6=b
So the equation in slope intercept form is y=(3/2)x+6
PLEASE HURRY
In the diagram of circle O, what is the measure of ∠ABC?
I WILL GIVE BRAINLIEST
Answer:
The measure of angle ABC is 34°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
so
∠ABC=(1/2)[major arc AC-minor arc AC]
∠ABC=(1/2)[major arc AC-146°]
Find the measure of major arc AC
major arc AC=360°-146°=214°
substitute
∠ABC=(1/2)[214°-146°]=34°
18 is what percent of 24?
The number 18 expressed as a percentage of 24 is; 75%
To determine what percentage of 24 is 18;
We must evaluate the percentage as follows;
(18/24) × 100%= 0.75 × 100%= 75%Read more;
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Evaluate the function rule for the given value. y = 4 • 2^x for x = –6
Answer:
y = 1/16
Step-by-step explanation:
y = 4 • 2^x
Let x = -6
y = 4 • 2^(-6)
The negative exponent puts it in the denominator
y = 4 • 1/ 2^6
y = 4 * 1/64
y = 4/64
y = 1/16
What is the vertex of the graph of f(x) = |x + 5| – 6? (–6, –5) (–6, 5) (–5, –6) (5, –6)
Answer:
(-5, -6)
Step-by-step explanation:
The general form of absolute function is, and
its vertex form is given by:
.....[1]
where, (h, k) is the vertex
As per the statement:
we have to find the vertex of the graph of f(x).
On comparing given equation with [1] we have;
we have;
h =-5 and k = -6
⇒Vertex = (-5, -6)
Therefore, the vertex of the graph of f(x) = |x + 5| – 6 is, (-5, -6)
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Answer:
The answer is (-5, -6)
Point W is located on QR so that QW/QR = 3/4. What are the coordinates of point W?
Answer:
(9,9)
Step-by-step explanation:
I like to use similar triangles.
To take some confusion out of of this let's translate the line down 3 units and left 3 units.
Alright from the drawing we get:
a/8 = b/8 and a/8 = 3k/4k (or b/8=3k/4k )
We don't need the k's, they cancel.
a/8 = b/8 and a/8=3/4
So the first equation means a=b.
Now let's see what a and b are by solving a/8 = 3/4.
Cross multiply:
[tex]\frac{a}{8}=\frac{3}{4}[/tex]
[tex]a(4)=8(3)[/tex]
[tex]4a=24[/tex]
a=6
So if a=b and a=6, then b=6.
The ordered pair is (6,6).
Now let's move the line back.
We have to move it up 3 units and right 3 units which gives us the point (9,9).
what would N be in this problem 9=8n
Answer:
9/8 = n
Step-by-step explanation:
9=8n
Divide each side by 8
9/8 = 8n/8
9/8 = n
Find the coordinates when the parallel lines AB and PQ are reflected over the x-axis. The points are A(1, 1), B(1,4), and
P(3, 1). Q(3, 4).
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Hence
A(1, 1 ) →A'(1, - 1 )
B(1, 4 ) → B'(1, - 4 )
P(3, 1 ) → P'(3, - 1 )
Q(3, 4 ) → Q'(3, - 4 )
Identify the number that is NOT the same as the others when rounded to the nearest tenth.
a. 34.62 c. 34.49 b. 34.59 d. 34.56
Please select the best answer from the choices provided
A
B
C
D
Answer:
c. 34.49
Step-by-step explanation:
Note that the nearest tenth place value is directly next to the decimal point (located on the right). Round each number to the nearest tenth. Look at the number in the hundredth place value. If it is 5 or greater round up, if 4 and less, round down.
a. 34.62 rounded to the nearest tenth is 34.6
c. 34.49 rounded to the nearest tenth is 34.5
b. 34.59 rounded to the nearest tenth is 34.6
d. 34.56 rounded to the nearest tenth is 34.6
This makes it so that C. 34.49 is your answer.
~
If h(x) is the inverse of f(x), what is the value of h(f(x))?
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0 1
ООО
o f(x)
Answer:
x.
Step-by-step explanation:
If h(x) is the inverse of f(x) them h(f(x)) = x.
If h(x) is the inverse of f(x) then the the value of h(f(x)) is x.
What is a function?A relation is a function if it has only One y-value for each x-value.
The inverse function of a function f is a function that undoes the operation of f.
If h(x) is the inverse of f(x), then by definition we have:
h(f(x)) = x
This is because the composition of h and f is the identity function, which means that applying h to f(x) gives us back x.
Therefore, the value of h(f(x)) is x.
Hence, If h(x) is the inverse of f(x) then the the value of h(f(x)) is x.
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Find the GCF of 52 and 84.
Answer:
4
Step-by-step explanation:
The GCF of 52 and 84 is 4.
52 = 2 × 2 × 13
84 = 2 × 2 × 3 × 7
Therefore, GCF = 2 × 2
GCF = 4
The GCF of 52 and 84 is found by finding the prime factors of each number and identifying the common factors. The GCF is 4.
Explanation:The GCF (Greatest Common Factor) of two numbers is the largest number that can evenly divide both numbers. To find the GCF of 52 and 84, we need to find the prime factors of each number and then find the highest common factor of these sets of prime factors.
Prime factors of 52: 2 x 2 x 13 Prime factors of 84: 2 x 2 x 3 x 7
The common factors are 2 and 2, so the GCF of 52 and 84 is 2 x 2, which equals 4.
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A rectangle has a base length of 14 inches and an unknown height, h. The area of the rectangle is less than 56 square inches.
Which inequality represents the possible values of h, the height of the rectangle?
on-14> 56
14-h <56
14h> 56
14h <56
Answer:
14h <56
Step-by-step explanation:
The area of a rectangle is given by
A =bh
We know the area is less the 56
bh <56
The base length is 14
14h <56
Answer:
D
Step-by-step explanation:
i got this question right on edgeinuity
Find the zeros of y = x + 6x- 4 by completing the square.
Answer:
[tex]\large\boxed{x=-3\pm\sqrt{13}}[/tex]
Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+6x-4=0\qquad\text{add 4 to both sides}\\\\x^2+2(x)(3)=4\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=4+9\\\\(x+3)^2=13\Rightarrow x+3=\pm\sqrt{13}\qquad\text{subtract 3 from both sides}\\\\x=-3\pm\sqrt{13}[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10). Match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral JKLM.
Answer:
1. W(5,1),X(1,7),Y(9,9) and Z(11,7).
2.A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).
3. E(5,6) ,F(1,12),G(9,14) and H(11,12).
4.O(10,1),P(6,7),Q(14,9) and R(16,7).
Step-by-step explanation:
We are given that a quadrilateral JKLM with vertices J(8,4),K(4,10),L(12,12) and M(14,10)
We have to match a quadrilateral with its correct transformation of given quadrilateral JKLM
1.a transformation 3 units down and 3 units left
By using transformation rule [tex](x,y)\rightarrow (x-3,y-3)[/tex]
The new vertices of quadrilateral is (5,1), (1,7),(9,9) and (11,7).
Hence, the quadrilateral WXYZ with vertices W(5,1),X(1,7),Y(9,9) and Z(11,7).
2.A sequence of reflection across x- axis and y-axis in order
Reflection across x- axis
The transformation rule [tex](x,y)\rightarrow (x,-y)[/tex]
By using this rule
The vertices of quadrilateral are (8,-4),(4,-10),(12,-12) and (14,-10).
After the reflection across y- axis
The transformations rule
[tex](x,y)\rightarrow (-x,y)[/tex]
By using this rule
We get the new vertices of quadrilateral are (-8,-4),(-4,-10),(-12,-12) and (-14,-10).
Hence, the quadrilateral ABCD with vertices A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).
3.a translation 3 unit left and 2 units up
The transformation rule [tex](x,y)\rightarrow (x-3,y+2)[/tex]
By using this rule
The new vertices are (5,6),(1,12),(9,14) and (11,12).
Hence, the quadrilateral EFGH with vertices E(5,6) ,F(1,12),G(9,14) and H(11,12).
4.a translation 2 units right and 3 units down
The transformation rule
[tex](x,y)\rightarrow (x+2,y-3)[/tex]
By using this rule
The new vertices are (10,1),(6,7),(14,9) and (16,7)
Hence, the quadrilateral OPQR with vertices O(10,1),P(6,7),Q(14,9) and R(16,7).
The point slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y-1=1/4(x-12) what is the standard formula equation for this line?
Answer:
x - 4y = 8Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
============================================
We have the points (-4, -3) and (12, 1).
Substitute:
[tex]m=d\frac{1-(-3)}{12-(-4)}=\dfrac{4}{16}=\dfrac{1}{4}[/tex]
Put the volume of a slope and the coordinates of the point (12, 1) to the equation of a line:
[tex]y-1=\dfrac{1}{4}(x-12)[/tex]
The standard formula of an equation of a line:
[tex]Ax+By=C[/tex]
Convert:
[tex]y-1=\dfrac{1}{4}(x-12)[/tex] multiply both sides by 4
[tex]4y-4=x-12[/tex] add 4 to both sides
[tex]4y=x-8[/tex] subtract x from both sides
[tex]-x+4y=-8[/tex] change the signs
[tex]x-4y=8[/tex]
Examine the first two steps used to solve the equation.
3 4 (20y − 8) + 5 = 1 2 y + 1 4 (20y + 8)
15y − 6 + 5 = 1 2 y + 5y + 2
15y − 1 = 11 2 y + 2
Which would be a good third step to solve the equation?
A. Combine like terms 11/2 and 2
B. Distribute 15 to each term on the left side.
C. Subtract 11/2y from each side of the equation.
D. Divide each side of the equation by 2.
Answer:
C.
Step-by-step explanation:
Your fractions are missing there fraction bars:
3/4 (20y − 8) + 5 = 1/2 y + 1/4 (20y + 8)
15y − 6 + 5 = 1/2 y + 5y + 2
15y − 1 = 11/2 y + 2
A. 11/2y and 2 aren't like terms because one contains the variable y and the other contains no variable
B. The distribute property can't be used there because you don't have 15(y-1) you have 15y-1
C. Subtracting 11/2y sounds like a good step because there is a y term on the opposing side.
15y-1=11/2y+2
Subtracing 11/2y on both sides
9.5y-1=2
That looks pretty good because then you would add 1 on both sides giving:
9.5y =3
Last step would get the y by itself which is dividing both sides by 9.5 giving you 6/19.
D. You could actually do this but it doesn't help you get x by itself. The equation would look like this: 15/2 y-1/2=11/4 y+1
Answer:
C. Subtract 11/2y from each side of the equation.
Step-by-step explanation:
Evaluate the expression, given functions f,g, and h:
Answer:
-1
Step-by-step explanation:
So you are asked to find 3f(1)-4g(-2).
In order to find this you must first find f(1) and g(-2).
So f(1) means what is the value of the expression 3x-2 for when x=1.
f(1)=3(1)-2
f(1)=3-2
f(1)=1
And g(-2) mean what is the value of the expression 5-x^2 for when x=-2.
g(-2)=5-(-2)^2
g(-2)=5-(4)
g(-2)=5-4
g(-2)=1
So both of those function values were 1.
Our problem of 3f(1)-4g(-2) becomes 3(1)-4(1)=3-4=-1.
Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?
Step-by-step explanation:
[tex]4x^3+x^2-8x-2\qquad\text{distributive}\\\\=x^2(4x+1)-2(4x+1)\\\\=(4x+1)(x^2-2)[/tex]
To pass science, a student must earn at least a grade of 70. How many students failed this science class?
Answer:
7 students.
Step-by-step explanation:
To pass science, a student requires at least 70 grades so students who scored below 70 will be failed.
From the given bar chart we can calculate the number of students who scored below 70 grades
Students who earned 50 - 59 = 2
Students who earned 60 - 69 = 5
Therefore, number of students who failed were
2 + 5 = 7 students.
Answer:7 students
Step-by-step explanation:
When figures (including points) are rotated 270° counterclockwise about the origin, it is also the same rotating figures clockwise by what other degree amount? Please help!
Answer: 90 degrees.
Step-by-step explanation: since 360 degrees is a whole circle, subtract 360 from 270 to get 90 degrees.
The formula for the circumference of a circle is C = 2tr,
where r is the radius and C is the circumference. The
equation solved for r is r= .
The correct formula to calculate the circumference of a circle is C = 2πr. To solve for r, the radius, we can rearrange the equation to r = C/(2π), which can be used to find the radius when the circumference is known.
Explanation:The formula for the circumference of a circle is given by C = 2πr, where 'C' represents the circumference and 'r' is the radius of the circle. The formula has been provided in an errorneous format, it should be 2πr not 2tr.
If we want to solve this equation for 'r', which represents the radius, we would need to isolate 'r' on one side of the equation. We can do this by dividing both sides of the equation by 2π. The resulting equation solved for r would be r = C/(2*π).
This equation can be utilized to find the radius if the circumference is known.
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What is the vertex form of y=x^2-6x+6
[tex]y=x^2-6x+6\\y=x^2-6x+9-3\\y=(x-3)^2-3[/tex]
The vertex form of the quadratic equation is y = (x-3)^2 + 3.
Explanation:The vertex form of a quadratic function is given by y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex. To convert the quadratic equation y = x^2-6x+6 into vertex form, we need to complete the square.
First, let's group the terms with x together: y = (x^2-6x) + 6.To complete the square, take half the coefficient of x (-6), square it (-6/2)^2 = 9, and add it inside the parentheses: y = (x^2-6x+9) - 9 + 6.Simplify the equation: y = (x-3)^2 + 3. This gives us the vertex form of the quadratic equation.Learn more about Vertex form of quadratic equation here:https://brainly.com/question/31546205
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Misaka solved the radical equation x – 3 = square root of 4x-7 but did not check her solutions. (x – 3)2 = square root of 4x-7^2 x2 – 6x + 9 = 4x – 7 x2 – 10x + 16 = 0 (x – 2)(x – 8) = 0 x = 2 and x = 8 Which shows the true solution(s) to the radical equation x – 3 = square root of 4x-7 x = 2 x = 8 x = 2 and x = 8 There are no true solutions to the equation.
Answer:
x=8 is a true solution of the radical equation
Step-by-step explanation:
we have
[tex]x-3=\sqrt{4x-7}[/tex]
Solve for x
squared both sides
[tex](x-3)^{2}=4x-7\\\\x^{2}-6x+9=4x-7\\\\ x^{2}-10x+16=0[/tex]
Convert to factored form
[tex]x^{2}-10x+16=(x-2)(x-8)[/tex]
The solutions are x=2 and x=8
Verify the solutions
For x=2
Substitute in the original equation
[tex]2-3=\sqrt{4(2)-7}[/tex]
[tex]-1=1[/tex] ----> is not true
therefore
x=2 is not a true solution of the radical equation
For x=8
Substitute in the original equation
[tex]8-3=\sqrt{4(8)-7}[/tex]
[tex]5=5[/tex] ----> is true
therefore
x=8 is a true solution of the radical equation
The true solution to the radical equation is x = 8, after checking the potential solutions by substituting them back into the original equation.
Explanation:The student is asked to find the true solution(s) to the radical equation x – 3 = square root of 4x-7. The student has solved the equation, but it is essential to check the solutions by substituting them back into the original equation to ensure they are not extraneous. The student got x = 2 and x = 8 as potential solutions. We must substitute these values back into the original equation to determine their validity:
For x = 2: 2 – 3 does not equal the square root of (4(2) – 7), so x = 2 is not a solution.For x = 8: 8 – 3 does equal the square root of (4(8) – 7), so x = 8 is a solution.Hence, the only true solution to the radical equation x – 3 = square root of 4x-7 is x = 8.
What are the zeros of the function f(x)=x^2+x-6 divides by x^2-x-6?
Answer:
It is B.
Step-by-step explanation:
x^2+x-6 / x^2-x-6 = 0
The numerator equates to zero:
x^2 + x - 6 = 0
(x + 3)(x - 2) = 0
the zeroes are {-3, 2).
The zeroes of the function f(x) = (x² + x - 6)/(x² - x - 6) are -3, 2.
Hence, option B. is the right choice.
What are functions?A function (say f(x)) is defined over x, when an expression in x, gives only one value f(x) for all the x in its domain.
What are zeroes of function?A zero of a function (say f(x)) is the value x, where f(x) = 0.
How do we solve the given question?We are asked to find the zeroes of the function
f(x) = (x² + x - 6)/(x² - x - 6).
To find the zeroes, we put the value of f(x) = 0, in the above equation to get:
(x² + x - 6)/(x² - x - 6) = 0
or, (x² + 3x - 2x - 6)/(x² + 2x - 3x - 6) = 0
or, {x(x + 3) -2(x + 3)}/{x(x + 2) -3(x + 2)} = 0
or, {(x - 2)(x + 3)}/{(x - 3)(x + 2)} = 0
Zeroes are where the numerator = 0, as the denominator can not be 0.
∴ (x + 3)(x - 2) = 0
∴ Zeroes of the function x + 3 = 0 ⇒ x = -3, and x - 2 =0 ⇒ x = 2, that is
-3, 2. Hence, option B. is the right choice.
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I Need The Answer Plz Geometry Is Hard!!!
Answer:
∠F = 106°
Step-by-step explanation:
The opposite angles of a parallelogram are congruent, hence
∠F = ∠J = 106°
which graph represents a function with direct variatio?
Answer:
In short, you are looking a diagonal line passing through the origin. And yes diagonal line is a straight-edged line that is running diagonally.
Step-by-step explanation:
If you want a better answer you can post the graphs.
I will tell you the trick, direct variations is another words for the relation is proportional.
The graph will have equation y=kx where k (k can't be zero) is the slope and your y-intercept is 0. The graph should be a diagonal line.
In short, you are looking a diagonal line passing through the origin. And yes diagonal line is a straight-edged line that is running diagonally.
A(n)_______ (rational /irrational) number answer is desired.
Answer: rational number answer is desired
Step-by-step explanation:
Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 3, -2 is the only other zero, leading coefficient is 2.
f(x)=?
Can some help?
Answer:
[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]
Step-by-step explanation:
we know that
2 is a zero of multiplicity 3 of the polynomial
so
we have that
x=2 is a solution of the polynomial
A factor of the polynomial is
[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3
and the other solution is x=-2
since the polynomial is fifth degree, x=-2 must have a multiplicity 2
so
the other factor of the polynomial is
[tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2
therefore
The polynomial is equal to multiply the factors by the leading coefficient
so
[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]
Find the equationOf the line who slope is -3 and Y intercept is five
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
It tells us that the slope (m) is -3 and the y-intercept (b) is 5. Plug this into the formula given above:
y = -3x + 5
Hope this helped!
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What is the conjugated expression?