Answer:
option A.) y-3 = 1/16 (x-2)^2
Step-by-step explanation:
we know that
If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola
The equation of a vertical parabola is equal to
[tex]4p(y-k)=(x-h)^{2}[/tex]
where
(h,k) is the vertex
In this problem we have
(h,k)=(2,3)
p=4
substitute
[tex]4(4)(y-3)=4(4)(x-2)^{2}[/tex]
[tex]16(y-3)=(x-2)^{2}[/tex]
[tex](y-3)=(1/16)(x-2)^{2}[/tex]
Answer:
option A.) y-3 = 1/16 (x-2)^2
Step-by-step explanation:
A bell tower is 17 meters tall. It casts a long shadow on the ground below. The tip of the shadow of the bell tower is 51 meters from the base of the bell tower. At the same time, a tall elm tree casts a shadow that is 63 meters long. If the right triangle formed by the tower and its shadow is similar to the right triangle formed by the elm and its shadow, how tall is the elm to the nearest tenth?
Check the picture below.
The elm is 21 m tall.
How to find the height is the elm to the nearest tenth?Both the triangles are the same.
To find the height, by similarity we get
17 / h = 51 / 63
h = 63 * 17 / 51 = 21
The answer is 21 m.
If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar. Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
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Evaluate the function g(x) = 2x2 + 3x – 5 for the input values -2, 0, and 3.
g(-2) = -2(-2)2 + 3(-2)-5
g(-2) = -2(4) – 6-5
g(-2) =
g(0) =
-
9(3) =
Evaluate the function
g(x) = 2x2 + 3x – 5 for the input values -2, 0, and 3.
This is tedious math work but necessary to sharpen your skills.
Let x = -2
g(-2) = 2(-2)^2 + 3(-2) – 5
g(-2) = 2(4) - 6 - 5
g(-2) = 8 - 11
g(-2) = -3
Now let x = 0 and repeat the process.
g(0) = 2(0)^2 + 3(0) - 5
g(0) = 0 + 0 - 5
g(0) = -5
Lastly, let x = 3.
g(3) = 2(3)^2 + 3(3) - 5
g(3) = 2(9) + 9 - 5
g(3) = 18 + 9 - 5
g(3) = 27 - 5
g(3) = 22
Did you follow through each step?
Answer:
-19
-5
-14
Step-by-step explanation:
Jack plays cards with friend each afternoon here are his scores from the last 5 games 8,-6,-3,4,7 which is the least of his scores
Answer:
-6
Step-by-step explanation:
8,-6,-3,4,7 rearranged in ascending order produces -6, -3, 4, 7, 8.
-6 is the least of these scores (i. e., -6 is the lowest score).
Final answer:
Jack's least score from his last 5 card games is -6, as it is the smallest number in the set of his scores.
Explanation:
The question involves identifying the least score from a set of given numbers. To find the least score, Jack's scores from the last 5 card games are considered: 8, -6, -3, 4, 7.
Upon reviewing these numbers, it can be determined that -6 is the least because it is the smallest number and also it has a negative value, which makes it less than all the positive scores or any potential zero scores. Thus, the least of Jack’s scores is -6.
What is the surface area of this rectangular prism
Answer:
C. [tex]490 \textrm{ units}^{2}[/tex]
Step-by-step explanation:
The formula for surface area is
LA + 2B
LA indicated Lateral Area and can be found multiplying perimeter of base by the height.
7 + 7 + 14 + 14 = 42 * 7 = 294
Multiply the LA from above with the area of base times 2.
98 * 2 = 196
294 + 196 = 490, so the surface area of the rectangular prism is 490 units.
To find the surface area of a rectangular prism, add up the areas of all six faces by multiplying length by width.
Explanation:To find the surface area of a rectangular prism, you need to add up the areas of all six faces. Each face is a rectangle, so to find the area, you multiply the length by the width. Then, you add up the areas of all the faces to get the total surface area.
For example, if the length of one side is 4 units, the width is 2 units, and the height is 3 units, the surface area would be:
Face 1: 4 units x 2 units = 8 square units
Face 2: 4 units x 2 units = 8 square units
Face 3: 4 units x 3 units = 12 square units
Face 4: 4 units x 3 units = 12 square units
Face 5: 2 units x 3 units = 6 square units
Face 6: 2 units x 3 units = 6 square units
Total surface area: 8 + 8 + 12 + 12 + 6 + 6 = 52 square units.
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The circumference of a circle is 60π cm. What is the length of an arc of 140°?
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=60\pi \end{cases}\implies 60\pi =2\pi r\implies \cfrac{\stackrel{30}{~~\begin{matrix} 60\pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} }{~~\begin{matrix} 2\pi\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }=r\implies 30=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=30\\ \theta =140 \end{cases}\implies s=\cfrac{\pi (140)(30)}{180}\implies s=\cfrac{70\pi }{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 73.30~\hfill[/tex]
A group of 8 friends (5 girls and 3boys ) plan to watch a movie, but they have only 5 tickets. How many different combinations of 5 friends could possibly receive the tickets ?
Given one zero of the polynomial function, find the other zeros.
f(x)=x^3+3x^2-34x+48; 3
f(x)=x^3+2x^2-20x+24; -6
f(x)=2x^3+3x^2-3x-2; -2
f(x)=3x^3-16x^2+3x+10; 5
Answer:
Step-by-step explanation:
You need to use synthetic division to do all of these. The thing to remember with these is that when you start off with a certain degree polyomial, what you get on the bottom line after the division is called the depressed polynomial (NOT because it has to math all summer!) because it is a degree lesser than what you started.
a. 3I 1 3 -34 48
I'm going to do this one in its entirety so you get the idea of how to do it, then you'll be able to do it on your own.
First step is to bring down the first number after the bold line, 1.
3I 1 3 -34 48
_____________
1
then multiply it by the 3 and put it up under the 3. Add those together:
3I 1 3 -34 48
3
----------------------------
1 6
Now I'm going to multiply the 6 by the 3 after the bold line and add:
3I 1 3 -34 48
3 18
_________________
1 6 -16
Same process, I'm going to multiply the -16 by the 3 after the bold line and add:
3I 1 3 -34 48
3 18 -48
___________________
1 6 -16 0
That last zero tells me that x-3 is a factor of that polynomial, AND that the depressed polynomial is one degree lesser and those numbers there under that line represent the leading coefficients of the depressed polynomial:
[tex]x^2+6x-16=0[/tex]
Factoring that depressed polynomial will give you the remaining zeros. Because this was originally a third degree polynomial, there are 3 zeros as solutions. Factoring that depressed polynomial gives you the remaining zeros of x = -8 and x = 2
I am assuming that since you are doing synthetic division that you have already learned the quadratic formula. You could use that or just "regular" factoring would do the trick on all of them.
Do the remaining problems like that one; all of them come out to a 0 as the last "number" under the line.
You got this!
The length of a rectangular garden ABCD is 9 feet more than its width. It is surrounded by a brick walkway 4 feet wide as shown below. Suppose the total area of the walkway is 400 square feet. 25. What are the dimensions of the garden?
Answer:
16.5 ft by 25.5 ft
Step-by-step explanation:
Let w represent the width of the garden in feet. Then w+9 is the garden's length, and w(w+9) represents its area.
The surrounding walkway adds 8 feet to each dimension, so the total area of the garden with the walkway is ...
(w+8)(w+9+8) = w^2 +25w +136
If we subtract the area of the garden itself, then the remaining area is that of the walkway:
(w^2 +25w +136) - (w(w+9)) = 400
16w + 136 = 400 . . .simplify
16w = 264 . . . . . . . . subtract 136
264/16 = w = 16.5 . . . . . width of the garden in feet
w+9 = 25.5 . . . . . . . . . . .length of the garden in feet
In a basketball drill, two players start at the same spot on the court. One player runs 6 feet
down the court and the other player runs 4.5 feet across the court (in a direction perpendicular
to the first player). What is the distance that one player must pass the ball for it to reach the
other?
Answer:
7.5 ft
Step-by-step explanation:
The distance can be found using the Pythagorean theorem. The given distances form the legs of a right triangle, and the ending distance (d) between the players is its hypotenuse. The Pythagorean theorem tells you ...
d² = (6 ft)² +(4.5 ft)² = 36 ft² +20.25 ft²
d² = 56.25 ft² = (7.5 ft)² . . simplifying and rewriting as a square
d = 7.5 ft . . . . . . . . . . . . . . . taking the positive square root
The ball must be passed a distance of 7.5 ft for it to reach between players.
_____
If you recognize the given numbers as having the ratio 3:4, then you may realize they are the legs of a 3-4-5 right triangle with a scale factor of 1.5. The distance between players will be 1.5×5 = 7.5 feet.
Answer:
[tex]\boxed{\text{7.5 ft}}[/tex]
Step-by-step explanation:
If the players are running perpendicular to each other, we have a right triangle, as in the diagram below.
We can apply Pythagoras' Theorem.
[tex]\begin{array}{rcl}a^{2} & = & b^{2} + c^{2}\\& = & 4.5^{2} + 6^{2}\\& = & 20.25 +36\\& = & 56.25\\a & = & \sqrt{56.25}\\& = & \mathbf{7.5}\\\end{array}\\\text{The distance between the two players will be } \boxed{\textbf{7.5 ft}}[/tex]
If log(a) = 1.2 and log(b)= 5.6, what is log(a/b)?
a. 4.4
b. 6.8
c. not enough information
d. -4.4
Answer:
d. -4.4
Step-by-step explanation:
We know that log (a/b) = log a - log b
Since log a = 1.2 and log b = 5.6 , we can substitute these values into the equation.
log (a/b) = 1.2 - 5.6
= -4.4
Which one of the following is an example of deductive reasoning?
A) The first term of a sequence of numbers is 1, the second term is 3, and the third term is 5. Thus, the nth term is 2n-1.
B) The sum of the angles in Which one of the following is an example of deduct and in Which one of the following is an example of deduct is 180 degrees. Therefore, the sum of the angles in any trianlge is 180 degrees.
C) All rectangles have four right angles. Since ABCD is a rectangle, it must have four right angles.
D) Line l1 has a slope of 5 and line l2 has a slope of 4. Line l1 is closer to the appearance of a vertical line than l2. Thus, the larger the slope of a line, the more vertical the line will appear.
Answer:
I want to say that the answer is C.
Hope this helps!
Use the Binomial Theorem and Pascal’s Triangle to write each binomial expansion.
(x-5)^3
NEED HELP ASAP!!
Answer
x^3-15x^2+75x-125
Question 19 of 24
1 Point
Which value of x makes the quotient of (6x +90X2 - 135x)=(x+5) undefined?
Answer:
D. -5
Step-by-step explanation:
The denominator of the quotient is x+5. When the denominator is zero, the quotient is undefined. The denominator will be zero when x=-5.
How many solutions does the nonlinear system of equations graphed below have?
Answer:
its one
Step-by-step explanation:
ape x legends
The area of triangle ABC is ____
square units.
Answer:
A = (1/2)(7 units)(5 units) = (35/2) units^2.
Step-by-step explanation:
Call AB "the base" and recognize that its length is 7 units. Call BC "the height" and recognize that its length is 5 units.
Then apply the area-of-a-triangle formula A = (1/2)(base)(height):
A = (1/2)(7 units)(5 units) = (35/2) units^2.
The area of triangle ABC is A = (1/2)(7 units)(5 units) = (35/2) units^2.
What is area of triangle?Triangle's area is equal to 1/2 (b* h) square units.
where the triangle's base and height, respectively, are denoted by b and h.
Given
Call AB "the base" and recognize that its length is 7 units. Call BC "the height" and recognize that its length is 5 units.
Then apply the area-of-a-triangle formula A = (1/2)(base)(height):
A = (1/2)(7 units)(5 units) = (35/2) units²
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Find an equation for the nth term of the arithmetic sequence.
a14 = -33, a15 = 9
HELP ASAP!! THANK YOU!
Answer:
The equation of the nth term is an = -621 + 42n
Step-by-step explanation:
* Lets revise the arithmetic sequence
- There is a constant difference between each two consecutive numbers
- Ex:
# 2 , 5 , 8 , 11 , ……………………….
# 5 , 10 , 15 , 20 , …………………………
# 12 , 10 , 8 , 6 , ……………………………
* General term (nth term) of an Arithmetic sequence:
- U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
- Un = a + (n – 1)d, where a is the first term , d is the difference
between each two consecutive terms
, n is the position of the term
* Lets solve the problem
∵ an = a + (n - 1)d
∴ a14 = a + (14 - 1)d
∴ a14 = a + 13d
∵ a14 = -33
∴ a + 13d = -33 ⇒ (1)
- Similar we can find another equation from a15
∵ a15 = a + (15 - 1)d
∴ a15 = a + 14d
∵ a15 = 9
∴ a + 14d = 9 ⇒ (2)
- We will solve equations (1) and (2) to find a and d
* Lets subtract equation (2) from equation (1)
∴ (a - a) + (13 - 14)d = (-33 - 9)
∴ -d = -42 ⇒ × both sides by -1
∴ d = 42
- Substitute this value of d in equation (1) or (2)
∵ a + 13d = -33
∵ d = 42
∴ a + 13(42) = -33
∴ a + 546 = -33 ⇒ subtract 546 from both sides
∴ a = -579
* Now lets write the equation of the nth term
∵ an = a + (n - 1)d
∵ a = -579 and d = 42
∴ an = -579 + (n - 1) 42 ⇒ open the bracket
∴ an = -579 + 42n - 42
∴ an = -621 + 42n
* The equation of the nth term is an = -621 + 42n
The interior angle of the regular octagon below measures 135º, and the
octagon has rotational symmetry. Which of the following is the measure of an
interior angle after a 90° rotation around the point of symmetry?
Answer:
D
Step-by-step explanation:
Since the shape won't change, it won't deform, nothing will happen to the interior angle.
This figure is symmetric and not deformed, so the measure of the interior angle won't change no matter how many times you rotate it.
So the interior angle would still be 135º.
Correct answer D
Answer:
the answer is D on e2020
Step-by-step explanation:
What do you know to be true about values of p and q?
Answer:
p = q
Step-by-step explanation:
There are 180 degrees in a triangle. If you subtract 50 and 60 from 180, you get 70. If you subtract 30 an 80 from 180, you get 70. therefore p = q.
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
-3
-2
-1
0
1
2
Answer:
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
-3
-1
1
Select all numbers that are in the range.
-2
0
2
Have great day :)
Step-by-step explanation:
The -3, -1, and 1 are in the domain if the domain of the function as follows R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have domain of a function:
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
From the above relation, we can see:
-3 is in the domain.
-1 is in the domain.
1 is in the domain.
Thus, the -3, -1, and 1 are in the domain if the domain of the function as follows R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
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CAN SOMEONE PLEASE HELP ME WITH FINDING X
x = 30°.
The triangle drawn inside the circle is an equilateral and equiangular triangle which means that its three sides and its internal angles (that measure 60°) are equal.
To find x°:
First, we can see from the image that the tangent line to circle with arrows is formed a right angle, the angle of one side of the equilateral triangle, and the angle formed with the other side of the equilateral triangle, this three angles has to form 180° respect to the tangent line:
90° + 60° + y° = 180°
y° = 180° + 150°
y° = 30°
Second, the line in the right side of the equilateral triangle form an angle of 180°, so:
60° + z° = 180°
z° = 180° - 60°
z° = 120°
Finally, the triangle formed by this lines its internal angles are x°, y°, and z° and its sum is 180°, then:
x° + y° + z° = 180°
x° + 30° + 120° = 180°
x° + 150° = 180°
x° = 180° - 150°
x° = 30°
Will vote brainliest.
Answer:
The last choice availablle
Step-by-step explanation:
The way you can tell the points the function has in common with the x-axis (also known as the solutions, roots, or zeros of the functiion) you have to factor it to solve for x. When you throw this into the quadratic formula you get that there is a negative under the square root sign, which is indicative of imaginary solutions. Imaginary solutions do NOT cross the x-axis. So the answer to your problem is the last choice.
Answer:
21 jk
Step-by-step explanation:
PLS HELP SHOW ALL YOUR WORKING OUT
THANK YOU IN ADVANCE :D
Answer:
[tex]AB =3 \sqrt{5} = 6.708203932...[/tex]
Step-by-step explanation:
[tex]A( - 1,6) \:,\: B(5,3)\\ AB = \sqrt{{(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ AB = \sqrt{ {( - 1 - 5)}^{2} + {(6 - 3)}^{2} } \\ AB = \sqrt{ {( - 6)}^{2} + {(3)}^{2} } \\ AB = \sqrt{36 + 9} \\ AB = \sqrt{45} = 3 \sqrt{5} = 6.708203932...[/tex]
The distance between A and B to 3 significant figure is 6.71
The formula for calculating the distance between two points is expressed as:
[tex]D =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given the coordinate points (-1, 6) and (5, 3)
Substitute the given coordinates into the formula;
[tex]D =\sqrt{5+1)^2+(3-6)^2}\\D =\sqrt{(6^2+(-3)^2}\\D=\sqrt{36+9}\\D=\sqrt{45}\\D= 6.71\\[/tex]
Hence the distance between A and B to 3 significant figure is 6.71
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In a week, a light bulb factory produces 12,500 light bulbs. The ratio of light emitting diodes (LED bulbs) to compact fluorescent lamps (CFL bulbs) is 2:3. Of the LED bulbs produced, 3% were defective. How many LED bulbs were not defective?
A) 150
B) 2,425
C) 4,850
D) 7,275
Answer:
C) 4,850
Step-by-step explanation:
No. of
LED bulbs : CFL bulbs : Total
2 : 3 : 5
5000 : 7500 : 12 500
Percentage of non-defective LED bulbs = 100% - 3% = 97%
No. of non-defective LED bulbs = 97% x 5000 = 4850
What is the inverse of the function f(x) = x + 2?
h(x) = 18x – 2
h(x) = 9x – 18
h(x) = 9x + 18
h(x) = 18x + 2
The inverse of the function f(x) = x + 2 is found by swapping the variables and solving for y, resulting in f^-1(x) = x - 2.
Explanation:The function f(x) = x + 2 is a simple linear function in Mathematics. The inverse of any function can be found by swapping the x and the y, and then solving for y. In this case, step-by-step, it would work like this:
Swap x and y to get x = y + 2.Solve for y by subtracting 2 from both sides to get y = x - 2.So the inverse of the function f(x) = x + 2 is f^-1(x) = x - 2.
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The inverse of the function f(x) = x + 2 is found by switching the roles of x and y and solving for y, resulting in the inverse function h(x) = x - 2. None of the provided options is correct.
Explanation:To determine the inverse of the function f(x) = x + 2, you need to first replace f(x) with y, resulting in the equation y = x + 2. Next, swap x and y to get x = y + 2. Solve for y to find the inverse function: y = x - 2. Therefore, none of the options provided is the correct inverse of the function f(x) = x + 2. The correct inverse is h(x) = x - 2.
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The highest elevation in California is 14,494 feet at Mt. Whitney and the lowest elevation is –282 feet at Death Valley. What is the total difference in elevation between these two places
14,776
/////////////////////////////////////////////////////////////
equation: 14494 + 282 = 14,776
(you convert the negative 282 to positive)
Add the highest elevation with the lowest elevation, to find the total difference. 14494 + 282 = 14,776. You convert the negative 282 to positive. The total difference in elevation between these two places is 14,776.
Please help 10points
Answer:
x = 9
Step-by-step explanation:
Those are chords of a circle, and the theorem to find x is, in this context:
6(3) = 2(x) so
18 = 2x and
x = 9
Use the graph of each polynomial function to find the factored form of the related polynomial. Assume the polynomial has no constant factor.
What are the zeros of this function? (2 points) _______, _______
What is the factorization of the polynomial? (2 points)
Answer:
zeros: x = -2; x = +4factorization: y = (x +2)(x -4)Step-by-step explanation:
The zeros are where the graph crosses the x-axis (y=0). They are x=-2 and x=4.
The factors are the binomials that are zero when x has the value of a zero:
y = (x +2)(x -4)
Bag a contains 3 white marveled and 2 marbles bag b contains 6 white marbles and 3 red marbles a person draws one marbles from each bag find the probability that both marbles are white
[tex]|\Omega|=5\cdot9=45\\|A|=3\cdot6=18\\\\P(A)=\dfrac{18}{45}=\dfrac{2}{5}[/tex]
Write the quadratic equation in standard form and then choose the value of “b” (2x - 1)(x + 5) =0
We want to write the given function in the form ax^2 + bx + c = 0.
We foil the left side.
(2x - 1)(x + 5) =0
2x^2 + 10x - x - 5 = 0
2x^2 + 9x - 5 = 0
Can you see the value of "b"?
The b-value is the coefficient of x.
So, b = 9.
Done!
Please help me with this question, I'm actually sick of people who keep answering dumb things just to get the points. I really need help with this.
Answer:
see below
Step-by-step explanation:
Events are independent when the probability of one of them does not depend on the other one. That is, P(A|B) = P(A) and P(B|A) = P(B).
They are not independent if the above condition is not met.
A quick assessment of the given table shows ratios of one row to the next are different between columns, and vice versa. Hence the events are not indpendent.