Answers
Answer:
Both the relations are functions, the correct answer is a.
Step-by-step explanation:
In order to solve this problem we will first find the inverse relation as shown below:
[tex]y = 3x^2 + 5\\x = 3y^2 + 5\\3y^2 = x - 5\\y^2 = \frac{x - 5}{3}\\y = \sqrt{\frac{x - 5}{3}} = \frac{\sqrt{x - 5}}{\sqrt{3}}\\y = \frac{\sqrt{x - 5}\sqrt{3}}{\sqrt{3}\sqrt{3}} = \frac{\sqrt{3x - 15}}{3}[/tex]
Functions are relations between two groups of numbers, for which the input must generate only one output. Using this definition we can classify both the relation and its inverse as a function, therefore the correct answer is a.
Related Questions
10.
Find the length of the arc on a circle of radius r intercepted by a central angle 0.
r=20 cm,
e
1/4 radian
Answers
Answer:
Length of arc = 5 cm (Approx)
Step-by-step explanation:
Given:
Radius of circle = 20 cm
Angle = 1/4 radian
Find:
Length of arc
Computation:
Angle in degree = 1/4 radian × 180°π
Angle in degree = 1/4 × 180° / 22/7
Angle in degree = 14.31° Approx
Length of arc = (Ф / 360)2πr
Length of arc = (14.31 /360)2(22/7)(20)
Length of arc = 4.997 cm
Length of arc = 5 cm (Approx)
Please help meeee I need help finding x y and z :)
Answers
Answer:
Hey there!
We see that z is equal to 40, because angles in a triangle add to 180 degrees.
We see that x is equal to 70, because an isosceles triangle has two angles that are congruent to each other, and can be represented using the equation 2x+y=180.
We see that y is equal to 110, because x+y needs to equal 180.
Hope this helps :)
Answer:
∠x = 70º, ∠y = 110º, ∠z = 40º
Step-by-step explanation:
to find ∠z: 180 - (71 + 69) = 40º = ∠z
the smaller triangle is an isosceles triangle, therefore ∠x is equal to the angle on its left.
so 180 - ∠z = 2 x ∠x
180 - 40 = 140 / 2 = 70º = ∠x
the angle to the left of ∠x forms 180º with ∠y.
as that angle is 70º, ∠y = 180 - 70 = 110º
Please factorise the equations in the doc bellow ASAP. please show full working
Answers
Answer:
b. x² + 8x + 12 =
1. use the factoring X (see attachment)
2. 6 x 2 = 12; 6 + 2 = 12
3. (x + 6)(x + 2) = 0
4. x = -6, -2
c. x² + 13x + 12 =
1. 12 x 1 = 12; 12 + 1 = 13
2. (x + 12)(x + 1) = 0
3. x = -12, -1
c. x² + x - 12 =
1. 4 · (-3) = -12; 4 - 3 = 1
2. (x +4)(x - 3) = 0
3. x = -4, 3
f. x² + 15x + 36 =
1. 12 x 3 = 36; 12 + 3 = 15
2. (x + 12)(x + 3) = 0
3. x = -12, -3
hope this helps :)
Answer:
b) - (x + 2)(x + 6)
c) - (x + 12)(x + 1)
c) - (x - 3)(x + 4)
f) - (x + 12)(x + 3)
Step-by-step explanation:
Well to factor the given info we need to find the factors.
b)
[tex]x^2 + 8x + 12[/tex]
So 6*2 = 12
6x + 2x = 8x
x*x = x^2
Factored - (x + 2)(x + 6)
c)
[tex]x^2 + 13x + 12[/tex]
Well x*x = x^2
and 12*1 = 12
12x + x = 13x
Factored - (x + 12)(x + 1)
The second c)
[tex]x^2 + x - 12[/tex]
Well x*x = x^2
-3*4 = -12
-3x + 4x = x
Factored - (x - 3)(x + 4)
f)
[tex]x^2 + 15x + 36[/tex]
So x*x = x^2
12*3 = 36
12x + 3x = 15x
Factored - (x + 12)(x + 3)
Thus,
everything factored is (x + 2)(x + 6) , (x + 12)(x + 1) , (x - 3)(x + 4) ,
(x + 12)(x + 3).
Hope this helps :)
Robert buys $3 shirts at $16.90 each, and a pair of jeans for $20.50. The shop has a sale on, and so he receives a $7.12 discount.
Write and solve a numerical expression for how much he spends in total.
Answers
Answer:
64.08
Step-by-step explanation:
3^16.90+1*20.50-7.12
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that
costs $3.25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30
before tax. The restaurant only sells pancakes in stacks of 4 pancakes for $5.50.
Let S represent the number of stacks of pancakes that Benjamin buys.
1) Which inequality describes this scenario?
Answers
Answer:
[tex]\bold {3.25+5.50S \le 30}[/tex] is the correct answer.
Step-by-step explanation:
Given that
Chocolate milk already ordered for the cost of $3.25.
Maximum bill that Benjamin wants = $30
Cost of a stack pancake = $5.50
Number of stacks of pancakes bought = S
It is given that all the money available is to be spent on 1 chocolate milk and S number of stacks of pancakes.
Cost of 1 pancake = $5.50
Cost of S number of stacks of pancakes = [tex]\text{Number of stacks of pancakes} \times \text{Cost of each pancake}[/tex]
i.e. [tex]S \times 5.50 = 5.50S[/tex]
So, total money spent = $3.25+5.50S
Now, this money should be lesser than or equal to $30 because maximum bill that Benjamin wants is $30.
So, the inequality can be written as:
[tex]\bold{3.25+5.50S \le 30}[/tex]
three people are watching a hot air balloon travel over their town. at a certain point in time, one person stands directly below the balloon, and the others look at it at certain angles. in the following image, a,b, and c are people, and d is the balloon. person c is 384m directly below the balloon, person b is 200m away from person c, and the angle between person a, the balloon, and person b is 33 degrees. how far is person a from the hot air balloon
Answers
Answer:
Distance between balloon and a is = 383.67 m
Step-by-step explanation:
The given situation can be represented as the given diagram as attached in the answer area.
cd = 384 m
cb = 200 m
[tex]\angle adb = 33^\circ[/tex]
To find:
Distance between balloon and a i.e. side ad = ?
Solution:
First of all, let us consider the right angled [tex]\triangle bcd[/tex].
We know the trigonometric identity that:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan\angle cbd =\dfrac{cd}{cb}\\\Rightarrowtan\angle cbd =\dfrac{384}{200}\\\Rightarrowtan\angle cbd =1.92\\\Rightarrow \angle cbd = tan^{-1}(1.92) = 62.49^\circ[/tex]
Now, using the external angle property for the external [tex]\angle cbd[/tex] for the [tex]\triangle abd[/tex]:
(External angle is equal to the sum of two opposite angles of the triangle.)
[tex]\angle cbd = \angle adb+\angle a[/tex]
[tex]\Rightarow \angle a =62.49-33 =29.49^\circ[/tex]
Now, let us consider the right angled [tex]\triangle acd[/tex].
We have the value of [tex]\angle a[/tex] and perpendicular dc.
We have to find the hypotenuse ad.
Let us use the sine identity:
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\angle a =\dfrac{cd}{ad}\\\Rightarrow sin(29.49^\circ) =\dfrac{384}{ad}\\\Rightarrow ad = \dfrac{384}{0.49}\\\Rightarrow \bold{ad = 783.67\ m}[/tex]
So, the answer is:
Distance between balloon and [tex]\bold{a}[/tex] is = 383.67 m
students enter school in the morning through doors on opposite sides of cafeteria. At Ms. Logrieco's door,35 students enter in the first 10 minutes. At Mr. Riley's door,22 students enter in the first 8 mins. If students continue to arrive at school at the same rate,how many students do you expect to be in the cafeteria after 24 minutes?
Answers
Ms. Logrieco's door: 35 students per 10 minutes
Mr. Riley's door: 22 students per 8 minutes
Time Frame: 24 minutes
35 x 2 = 70
35 x 2/5 = 14
70 + 14 = 84
22 x 3 = 66
84 + 66 = 150
Thus, we can expect for 150 students to be in the cafeteria after 24 minutes.
The volume of a triangular prism is increased by a factor of 8.
By what factor is the surface area of the figure increased?
2
4
16
24
Answers
In a recent year 5 out of 6 movies cost between $50 and $99 million to make. At this rate, how many movies in a year with 687 new releases would you predict to cost between $50 and $99 million to make
Answers
Answer:
573 movies
Step-by-step explanation:
Here, we have 5 out of 6 movies having that cost
Therefore the rate we will be working with is 5/6
Now there are 687 new releases, the value that cost the given price range will be; 5/6 * 687 = 572.5 which is approximately 573
1. Which financial statement reports the amount of cash paid for acquisitions of property, plant, and equipment? In which section (operating, investing, or financing) of this statement is the information reported? 2. Indicate the amount of cash paid for acquisitions of property and equipment in the year ended September 30, 2017.
Answers
Answer:
1. Cash flow statements; the investing section
Step-by-step explanation:
The cash flow statements is a useful document that shows where the company receives funds and uses it. Thus, it shows both incoming and outgoing cash flow.
The investment section of the cash flow statement is where all the amount of cash paid for acquisitions of property and equipment is imputed. Usually the transactions are written as capital expenditure.
what is an equation of the line passes through the points (8,-8) and (-5,-8)
Answers
Answer:
The answer is
y = - 8Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the line we must first find the slope
That's
Slope of the line using points
(8,-8) and (-5,-8) is
[tex]m = \frac{ - 8 + 8}{ - 5 - 8} = \frac{0}{ - 13} = 0[/tex]
So the equation of the line using point (8,-8) is
y + 8 = 0(x - 8)
y + 8 = 0
We have the final answer as
y = - 8Hope this helps you
03.07A LC)Which of the following describes a situation in which a basketball player ends up 0 m from his starting point? The player runs 9 meters forward, and then runs 0 meters in the opposite direction. The player runs 5 meters forward, and then runs 6 meters in the opposite direction. The player runs 6 meters forward, and then runs 5 meters in the opposite direction. The player runs 4 meters forward, and then runs 4 meters in the opposite direction.
Answers
Answer:
The correct option is;
The player runs 4 meters forward, and then runs 4 meters in the opposite direction
Step-by-step explanation:
From the question relates to the displacement of a body, compared to the distance covered by the body
In the question instance, the situation in which the player displacement will be zero is one where both the players forward and backward displacement are equal such that they cancel each other
We have the instance where the forward and opposite displacement are equal is given by the situation where the player runs 4 meters forward, and then runs 4 meters in the opposite direction.
Answer:
d would be the answer if your so needy
Step-by-step explanation:
PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. find the probability that a randomly selected light bulb will last between 900 and 975 hours.
Answers
Answer:
P = 0.0215 = 2.15%
Step-by-step explanation:
First we need to convert the values of 900 and 975 to standard scores using the equation:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Where z is the standard value, x is the original value, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation. So we have that:
standard value of 900: [tex]z = \frac{900 - 750}{75} = 2[/tex]
standard value of 975: [tex]z = \frac{975 - 750}{75} = 3[/tex]
Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:
z = 2 -> p_2 = 0.9772
z = 3 -> p_3 = 0.9987
We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:
P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215
So the probability is 0.0215 = 2.15%
Answer:
2.35 babyyyyyyyyyyy
Step-by-step explanation:
Acellus sux
A right triangle has legs of 5 ft and 6 ft. What is the length of the hypotenuse? _____ ft. A. 7.8 B. 3.3 C. 11.0 D. 1.0
Answers
Answer:
7.8Option A is the correct option.
Step-by-step explanation:
Base (b) = 5 ft
Perpendicular (P) = 6 ft
Hypotenuse (h) = ?
Now,
Using Pythagoras theorem,
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {h}^{2} = {(6)}^{2} + {(5)}^{2} [/tex]
[tex] {h}^{2} = 36 + 25[/tex]
[tex] {h}^{2} = 61[/tex]
[tex]h = \sqrt{61} [/tex]
[tex]h = 7.8 \: ft[/tex]
Hope this helps...
Good luck on your assignment
Answer:
a. 7.8
Step-by-step explanation:
Please answer this in two minutes
Answers
Answer:
4.5cm
Step-by-step explanation:
Using Sine Rule:
a/sinA = b/sinB = c/sinC
step:
7/sin90 = TU/sin40
TU = 7/sin90 X sin40
TU = 4.4995
TU = 4.5cm
MAKE ME AS THE BRAINLIEST
how do i wright this as a expression? seven and the quotient of z and eight
Answers
8÷7=z and z is the answer you got when you divided,that's how I understand the question
Mrs johnson grows herbs in square plots Her basil plot measures. 5. 9 yd on each side. A. Find the total area of the basil plot. B. Mrs. Johnson puts a fence around the basil. If the fence was 2 ft from the edge of the garden on each side, whats the perimeter
Answers
Answer:
Area = 34. 81 yd^2
Perimeter = 86.6 feets
Step-by-step explanation:
Given the following :
Shape of Mrs. Johnson's plot = square
All sides of a square are of equal length
Measure of each side = 5.9 yd
A.) Area of plot
Area of plot = Area of a square
Area of a square(A) = a^2
Where a = side length
A = 5.9^2
A = 34.81 yd^2
B) Perimeter of Basil plot = Perimeter of a square
Converting yard to feet
1 yard = 3feets
Therefore,
5.9 yards = (3 * 5.9) = 17.7 feets
Fence is 2ft from the garden on each side,
Length of fence on each side = (2 + 17.7 + 2) Feets = 21.7 Feets
Perimeter of a square (P) = 4a
Where a = side length
P = 4 × 21.7
P = 86.6 feets
Answer:
86.6 feet
Step-by-step explanation:
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
The third option is correct.
The domain of the function is given by
[tex]Domain = 0 \leq t \leq 40[/tex]
The range of the function is given by
[tex]Range = 0 \leq V(t) \leq 200[/tex]
Step-by-step explanation:
Sara bought a cell phone for $200 and its value has decreased at rate of $5 per month.
V(t) is the value of the phone and t is the number of months.
The domain of the function is the possible values of the number of months t.
The domain of the function is given by
[tex]Domain = 0 \leq t \leq 40[/tex]
The range of the function is the values of V(t) that we get after substituting the possible values of the number of months t.
The range of the function is given by
[tex]Range = 0 \leq V(t) \leq 200[/tex]
When the number of months is t = 0 then the value of the function is maximum V(t) = 200
When the number of months is t = 40 then the value of the function is minimum V(t) = 0
Therefore, the third option is correct.
HELPPP
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answers
Answer:
[tex] slope (m) = -\frac{3}{2} [/tex]
Step-by-step explanation:
We can find the slope (m) by using coordinate pairs of any 2 points located along the slope of the line that we have on the graph.
This, let's use the coordinate pairs at:
x = -4, y = 2 (-4, 2) => (x2, y2)
x = 0, y = -4 (0, -4) => (x1, y1)
[tex] slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] slope (m) = \frac{2 -(-4)}{-4 - 0} [/tex]
[tex] slope (m) = \frac{2 + 4}{-4 - 0} [/tex]
[tex] slope (m) = \frac{6}{-4} [/tex]
[tex] slope (m) = \frac{3}{-2} [/tex]
[tex] slope (m) = -\frac{3}{2} [/tex]
Write the function in standard form.
Y=(3x-2)(3x+6)
Answers
Answer:
y = 9x^2 + 12x - 12.
Step-by-step explanation:
y = (3x - 2)(3x + 6)
y = 9x^2 - 6x + 18x - 12
y = 9x^2 + 12x - 12.
Hope this helps!
PLEASE HELP! I WILL GIVE BRAINIEST! Look at the figure below: A triangle ABC is drawn. D is a point on BC such that BD is equal to DC. A straight line joins points A and D. This line extend Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? a Triangle ABD and triangle ECD b Triangle ABC and triangle ECD c Triangle ABD and triangle ADC d Triangle ADC and triangle ABC
Answers
Answer:
ADB and ADC
Step-by-step explanation:
SAS is side angle side. so, which 2 triangles have same side, then angle, then side. We have to have it in that specific order.
Answer:
ABD and ECD
Step-by-step explanation:
EDC and ADB are vertical angles, so that is the angle we need for the SAS postulate. The markings on each of the corresponding sides is the same, which means we have 2 congruent sides, as well as an angle.
the sum of the first term of an ap is 240 and the sum of the next 4 term is 220 find the first term of the ap
Answers
Answer:
The common difference is -5/4
T(n) = T(0) - 5n/4,
where T(0) can be any number. d = -5/4
Assuming T(0) = 0, then first term
T(1) = 0 -5/4 = -5/4
Step-by-step explanation:
T(n) = T(0) + n*d
Let
S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240
S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220
S2 - S1
= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)
= (5+6+7+8 - 1 -2-3-4)d
= 4(4)d
= 16d
Since S2=220, S1 = 240
220-240 = 16d
d = -20/16 = -5/4
Since T(0) has not been defined, it could be any number.
This is hard for me, can someone please help? Loren solved the equation 10 = StartFraction 19 Over 9 EndFraction (149) + b for b as part of her work to find the equation of a trend line that passes through the points (1, 130) and (10, 149). What error did Loren make? She should have solved 10 = StartFraction 9 Over 19 EndFraction (149) + b for b. She should have solved 1 = StartFraction 19 Over 9 EndFraction (130) + b for b. She should have solved 149 = StartFraction 19 Over 9 EndFraction (10) + b for b. She should have solved 130 = StartFraction 9 Over 19 EndFraction (1) + b for b.
Answers
Answer:
149=19/9 (10) +b
130=19/9(1)+b
Step-by-step explanation:
for Loren to find a line passes through two points:(1,130), (10.149)
1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9
m=19/9
to find b in the equation y=mx+b for point (1,130)
y=130, x=1, m=19/9
130=19/9(1)+b
for point (10,149)
149=19/9 (10) +b
you have two options
The solution is, the equations of line passes through two points:(1,130), (10.149) is:
149=19/9 (10) +b
130=19/9(1)+b
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
for Loren to find a line passes through two points:(1,130), (10.149)
1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9
m=19/9
to find b in the equation y=mx+b for point (1,130)
y=130, x=1, m=19/9
130=19/9(1)+b
for point (10,149)
149=19/9 (10) +b
you have two options
Hence, The solution is, the equations of line passes through two points:(1,130), (10.149) is:
149=19/9 (10) +b
130=19/9(1)+b
To learn more on Equation 0f Straight-Line click:
brainly.com/question/11116168
#SPJ6
How can 2182 be written as the sum of four consecutive whole numbers?
Answers
Answer:
544 + 545 + 546 + 547
explanation: if the numbers are consecutive whole numbers then it would be near the ¼ of the given number
Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes?Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes? A. 6 cups B. 7 cups C. 8 cups D. 9 cups
Answers
Answer:
hi:) If chen needed 3 1/5 and 3 2/3, the answer should be 7. 7 cups. i hope this is right but feel free to correct me if im wrong.
B. 7 cups
The best estimate of the number of cups of flour that Chen needs to bake both recipes is 7cups.
What is the fraction?A fraction is a number which has numerator and denominator.Number of cups used to make muffins = 3 1/5
Estimation = 3 cups
Number of cups used to make banana bread = 3 2/3
Estimation = 4 cups
Number of cups of flour needs to bake both recipes = Estimated number of cups used to make muffins + Estimated number of cups used to make banana bread
= 3 + 4 cups
= 7 cups.
The best estimate of the number of cups of flour that Chen needs to bake both recipes is 7cups.
Learn more about fraction here:
https://brainly.com/question/78672
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Assume that adults have it scores that are normally distributed with a mean of 100 standard deviation of 15 find probability that randomly selected adult has an Iq between 89 and 111
Answers
Answer:
0.5346
Step-by-step explanation:
Find the z-scores.
z = (x − μ) / σ
z₁ = (89 − 100) / 15
z₁ = -0.73
z₂ = (111 − 100) / 15
z₂ = 0.73
Find the probability.
P(-0.73 < Z < 0.73)
= P(Z < 0.73) − P(Z < -0.73)
= 0.7673 − 0.2327
= 0.5346
21.(03.02)
If f(x) = 7x – 1, what does f(12) represent?
Answers
Answer:
83
Step-by-step explanation:
f(x) = 7x - 1
Put x as 12.
f(12) = 7(12) - 1
f(12) = 84 - 1
f(12) = 83
Jessica calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it?
E
F
G
H
Answers
Answer:
G
Step-by-step explanation:
We can find a missing length of a triangle using a Pythagorean theorem if and only the triangle is a right angled triangle.
The side of the missing length is:
a^+b^=c^
2^+4^=c^
4+16=c^
20=c^
[tex] \sqrt{20} = c ^{2} \\ 4 \sqrt{5} = c[/tex]
Name an inscribed angle
Answers
Answer:
BHF
Step-by-step explanation:
Definition of inscribed
100 points timed Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles? 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side 5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answers
Answer: A
Step-by-step explanation:
The answer is A. It accurately describes the equation shown. Negative values are represented by negative tiles and positive values are represented by positive tiles.
Hope it helps <3