Answer: y = (x-2)/3
This is equivalent to y = (1/3)x - 2/3
=================================================
To get this answer, we need to swap x and y in the original equation. Then solve for y to get the inverse.
y = 3x+2
x = 3y + 2 ... x and y swapped
x-2 = 3y
3y = x-2
y = (x-2)/3
y = x/3 - 2/3
y = (1/3)x - 2/3
This final equation has slope 1/3 and y intercept -2/3
if a number is tripled, it gives the same result as when 28 is added to it.find the number
Answer:
14
Step-by-step explanation:
let the number be y
if y is tripled we get 3y
3y = 28 + y
3y - y = 28
2y = 28
y = 14
Answer:
14
Step-by-step explanation:
Let the number be x.
Base on the given
↓ Equation ↓
3x=x+28
Solve:
3 x - x = 28
2 x = 28
x = 28/2
x = 14
Thus, The number is 14.
[RevyBreeze]
PLSS HELPP I DONT UNDERTANDD
Two numbers a and b are in the ratio 3 : 4. If the first number is decreased by 4 and the second is decreased by 2, they are in the ratio 2 : 3. Find a and b.
a =
b =
Please help me out, I need help.
Answer:
D (-1,-3)
Step-by-step explanation:
If h(x)=-3x-6, plug in for x
-3 =-3(-1)-6
-3=3-6
-3=-3
so two negatives cancel out and get you the positive three minus six, resulting in negative 3, which is also the h(x) value.
Answer:
D
Step-by-step explanation:
Plug it in
Y=3x-6
-3=-3(-1)-6
-3=-3
Sal was asked by his teacher to
compare the numbers 153.098 and
153.408. Which is the correct way to
compare these two numbers?
A. 153.098 > 153.408
B. 153.098 = 153.408
C. 153.408 < 153.098
D. 153.408 > 153.098
Answer:
153.098
153.408
When we look at these numbers, we want to see which one has the greatest digit.
Shown below, I'm going to compare both numbers and start from the hundreds place and gradually go further into the other digits until we've seen which number is the greatest.
153.098:
1
153.408:
1
153.098:
15
153.408:
15
153.098:
153
153.408
153
153.098:
153.0
153.408
153.4
Now, we can automatically know that 153.408 is the greatest because the 4 in the tenths place is bigger than 0 in the tenths place in the other number.
So 153.408 > 153.098, D is your answer.
50 POINTS AND BRAINLIEST
Which statement is true?
A.
The function is an even function because its graph is symmetric about the origin.
B.
The function is an odd function because .
C.
The function is an even function because .
D.
The function is an odd function because its graph is symmetric about the y-axis.
Answer:
B. The function f(x) = tan(x) is an odd function because f(-x) = -f(x)
Step-by-step explanation:
The function f(x) = tan(x) is odd as [tex]f(-x) = -f(x)[/tex] so we can conclude the statement B. The function f(x) = tan(x) is an odd function because [tex]f(-x) = -f(x)[/tex] is the true option.
What are functions?The function is a relation used to determine a value f(x) for a given x using an expression in x.
What are even functions?An even function is when f(x) = f(-x). It is symmetric along the y-axis.
What are odd functions?An odd function is when f(-x) = -f(x). It is symmetric along the x-axis.
How do we solve the given question?We are dealing with the function f(x) = tan(x).
We calculate f(-x) = tan(-x) = -tan(x) = -f(x).
∴ The function f(x) = tan(x) is an odd function, and odd functions are symmetric about the origin.
∴ The function f(x) = tan(x) is odd as [tex]f(-x) = -f(x)[/tex] so we can conclude the statement B. The function f(x) = tan(x) is an odd function because [tex]f(-x) = -f(x)[/tex] is the true option.
Learn more about odd functions and even functions at
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Part 3: Construct a prism from the above regular hexagon. The height of the hexagonal prism is 5 feet. Find the surface area and the volume of this prism.
The volume of the hexagonal prism is the amount of space in it.
The surface area is 369.9 square feetThe volume is 831.4 cubic feetHow to determine the surface area?From the complete question, we have:
Length (l) = 8
Height (h) = 5
The surface area of the hexagonal prism is:
[tex]A=6lh+3l^2\sqrt 3[/tex]
So, we have:
[tex]A=6*8*5+3*5^2\sqrt 3[/tex]
Evaluate
[tex]A = 369.9[/tex]
Hence, the surface area is 369.9 square feet
How to determine the volume?The volume of the hexagonal prism is:
[tex]V = \frac{3\sqrt 3}{2} * l^2h[/tex]
So, we have:
[tex]V = \frac{3\sqrt 3}{2} * 8^2 * 5[/tex]
Evaluate
[tex]V = 831.4[/tex]
Hence, the volume is 831.4 cubic feet
Read more about surface area and volume at:
https://brainly.com/question/13175744
Ollie has installed security lights on the side of his house that are activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m and the distance from B to C is 6 m. Angle AĈB is 15°.
Answer:
20.19°
Step-by-step explanation:
Find the diagram to the question attached. We are to look for <CAB
Applying sine rule on ΔABC:
[tex]\frac{4.5}{sin15^0} = \frac{6}{sin<CAB}[/tex]
cross multiply
[tex]4.5 * sin<CAB =6 sin15^0\\\\sin<CAB = \frac{6sin15^0}{4.5}\\ \\sin<CAB = \frac{6*0.2588}{4.5}\\ \\sin<CAB = \frac{1.5529}{4.5}\\\\sin<CAB = 0.3451\\\\<CAB = sin^{-1}0.3451\\[/tex]
[tex]<CAB = 20.19^0\\[/tex]
Hence the angle <CAB is 20.19°
The angle ∠CAB is 20.19° and the distance (d) Ollie is from the entrance to his house when he first activates the sensor is 5.77 m.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Ollie has installed security lights on the side of his house that is activated by a sensor.
The sensor is located at point C directly above point D.
The area covered by the sensor is shown by the shaded region enclosed by triangle ABC.
The distance from A to B is 4.5 m and the distance from B to C is 6 m.
The angle ACB is 15°.
The ∠CAB is ∠A.
We know that the sine rule
[tex]\dfrac{a}{\sin A} =\dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]
We have
[tex]\dfrac{AB}{\sin C} \ \ = \dfrac{BC}{\sin A} = \dfrac{AC}{\sin B}\\\\\\\dfrac{4.5}{\sin 15^o} = \dfrac{6}{\sin A} = \dfrac{b}{\sin B}[/tex]
From the first two, we have
[tex]\dfrac{4.5}{\sin 15^o} = \dfrac{6}{\sin A} \\\\\sin A = \dfrac{6}{4.5} \times \sin 15^o\\\\A \ \ \ \ = 20.19^o[/tex]
We know that the sum of the angle is 180 degrees. Then we have
∠A + ∠B + ∠C = 180°
20.19° + ∠B + 15° = 180°
∠B = 144.81°
Then the value of b will be
[tex]\dfrac{4.5}{\sin 15^o} = \dfrac{b}{\sin 144.81^o}\\\\\\b \ \ \ = 10.02[/tex]
Then the distance (d) Ollie is from the entrance to his house when he first activates the sensor will be
d = b × sin 144.81°
d = 10.02 × sin 144.81°
d = 5.77 m
More about the trigonometry link is given below.
https://brainly.com/question/22698523
Marshall works at an animal shelter. He makes sure all the cats are vaccinated. In July, 56 of the cats entering the shelter had already been vaccinated. Based on this result, he predicts that if 100 cats entered the shelter, 80 of the cats would have already been vaccinated. How many cats entered the animal shelter in July?
Answer: 70 animals
Step-by-step explanation:
Since Marshall predicted that if 100 cats entered the shelter, 80 of the cats would have already been vaccinated . This means that 80/100 = 4/5 of the animals that enter the shelter are vaccinated.
Let the animals that enter in July be y. This will be:
4/5 × y = 56
0.8y = 56
y = 56/0.8
y = 70
70 animals entered in July
Write an equation with a slope of -5 and a y-intercept of O
Answer:
[tex]y=-5x+0[/tex]
Step-by-step explanation:
We know that slope intercept form is:
[tex]y=mx+b[/tex]
And our slope is -5, and the variable we use for slope is m:
[tex]m=-5[/tex]
Our new equation becomes:
[tex]y=-5x+???[/tex]
And our y-intercept is 0, and the letter we use to express our y-intercept is b:
[tex]b=0[/tex]
Our new equation is:
[tex]y=-5x+0[/tex]
Hence, the correct answer is [tex]y=-5x+0[/tex]
The scatter plot shows the time spend watching TV,x, and the time spend doing homework,y, by each 24 students last week
Answer:
Equation of the best fit line is given as y = - 0.76x + 26.04 Now we need to find the decrease in time spent in doing homework for increase in one hour in time spent in watching TV.
Step-by-step explanation:
hope this helps
have an awesome day -TJ
Find the distance between the two points in simplest radical form (3, 8) and (5, - 1)
Answer:
[tex]d = \sqrt{85}[/tex]
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in the 2 coordinates into the distance formula to find distance d:
[tex]d = \sqrt{(5-3)^2+(-1-8)^2}[/tex]
[tex]d = \sqrt{(2)^2+(-9)^2}[/tex]
[tex]d = \sqrt{4+81}[/tex]
[tex]d = \sqrt{85}[/tex]
A triangular prism has a base that is 10 cm. It’s height is 8 cm. What is its volume
Answer:
C.
Step-by-step explanation:
Do 10 to the 2nd power (which is 100) the multiply it by the 8 then you get 800!
Two squares have sides of 3 & 6. what is the ratio of their perimeter
Answer:
Step-by-step explanation:
Square with side (s) = 3
P = 4s
s = 3
P = 4*3
P = 12
Square with side (s) = 6
P = 4s
s = 6
P = 4 * 6
P = 24
Answer
It is asking for the ratio of P(with side = 3)/ to P(with side = 6)
P(3) /P(6) = 12/24 = 1/2s(3) / s(6) = 3/6 = 1/2So the perimeter ratio is 1/2
The side ratio is 1/2
They are the same.
Two angles are supplementary. The measure of the larger angle is 12 less than 3 times the measure of the smaller angle.Find the measure of each angle
Answer:
48 , 132
Step-by-step explanation:
Let smaller angle = x
Larger angle = 3x - 12
x & (3x - 12) are supplementary
So, x + 3x - 12 = 180°
4x - 12 = 180
4x = 180 +12
4x = 192
x = 192/4
x = 48°
Larger angle = 3*48 - 12 = 144 - 12 = 132
Answer: The measure of the smaller angle is 48,and the larger angle is 132.
Step-by-step explanation:
(8r^2-12r+4)-(3r^2+5r-1) in standard form
Answer:
[tex]=5r^2-17r+5[/tex]
Step-by-step explanation:
[tex]\mathrm{Apply\:rule}:\quad \left(a\right)=a[/tex]
[tex]\left(8r^2-12r+4\right)=8r^2-12r+4[/tex]
[tex]=8r^2-12r+4-\left(3r^2+5r-1\right)[/tex]
[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]
[tex]-\left(3r^2+5r-1\right)=-3r^2-5r+1[/tex]
[tex]=8r^2-12r+4-3r^2-5r+1[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=8r^2-3r^2-12r-5r+4+1[/tex]
[tex]\mathrm{Add\:the\:numbers:}\:4+1=5[/tex]
[tex]=8r^2-3r^2-12r-5r+5[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:8r^2-3r^2=5r^2[/tex]
[tex]=5r^2-12r-5r+5[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:-12r-5r=-17r[/tex]
[tex]=5r^2-17r+5[/tex]
2. Find the surface area of the following figure.
8 km
-3+3.5)
8 km
tis)
7 km
8 km
8 km
Answer:
344
Step-by-step explanation:
First we are going to find the area of the top and bottom
8x8=64. Since the top and bottom are the same, we can do 64x2=128.
Now we are going to find the area of the left and right sides.
8x7=54. Since the right and left are the same, we can do 54x2=108.
Now we are going to find the area of the front side and the back side.
8x7=54. Since the front and back are the same, we can do 54x2=108.
Now we add our answers up. 128+108+108=344
if 2 is the same as 4 how
Answer:
2 is not the same as 4.
[tex]2^2[/tex] is the same as 4, since 2*2 = 4.
2 is not the same as 4 but 2x2 is the same as 4
Name a pair of corresponding angles
Answer: ∠2, ∠6 is your answer. If that's not the answer than ∠7, ∠5 might be your answer.
hope it helps
Help me please.......
Answer:
50+25n=$125 and 3 hours
Step-by-step explanation:
3y +2x - 1, when y = 4 and x = 5
Answer: 21
3(4) + 2(5) - 1 = 21
What is y=56x+9 written in standard form
the sum of two numbers is 840. one of the numbers is 357. what is the other number?
Answer:
483
Step-by-step explanation:
840 minus 357 is 483
what is the exponent on 10 when you write 41200 in scientific notation
Answer:
41200 in scientific notation = 4,1 . 10⁴
Answer:
The exponent is 4
[tex]4.12[/tex] × [tex]10^{4}[/tex]
Step-by-step explanation:
Hope this helps
Your doctor prescribes you to take 400 milligrams of medicine every 8 hours. How many ounces of medicine do you take in a day?
Answer:
0.04233 ounces of medicine in a day
Step-by-step explanation:
Bob is doing a quality test on machine bots , he tested 24 bolts that he randomly found that 5 were defective. Based on bob’s results what is the expected number of bolts that will be defective if he tests 840 bolts? A.139 B. 145 C. 175 D. 211
The expected number of defective bolts are obtained as 175. The correct option is (C).
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The total number of bolts tested are 24.
And, the number of defective bolts are 5.
Then, the probability of defective bolts is given as,
P(defective bolts) = 5/24
Now, the expected number of bolts can be found as,
Expected number = P(defective bolts) × Total number of bolts tested
⇒ 5/24 × 850 = 175
Hence, the expected number of bolts that will be defective is given as 175.
To know more about probability click on,
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Is -51/5 rational or irrational
Answer:
irrational
Step-by-step explanation:
Help asap
what is the measure of angle dgv?
enter your answer in the box
The measure of angle MBT as shown in the diagram is 28 degrees.
What is an angle?An angle is formed from the intersection of two or more lines. Types of angles are obtuse, acute and right angled.
From the diagram:
∠MBN = ∠MBT
17x - 6 = 5x + 18
x = 2
∠MBT = 5(2) + 18 = 28 degrees
The measure of angle MBT as shown in the diagram is 28 degrees.
Find out more on angle at: https://brainly.com/question/25770607
Given that x = 7.6 m and θ = 47°, work out BC rounded to 3 SF.
7.09 meters
Step-by-step explanation:
first start by using sin of 47 to find the hypotenus.
Then after finding the hypotenus you just have to use cos of 47 to find BC
Answer:
7.09 m
Step-by-step explanation:
3:45 a.m. to 12:00 p.m.
Answer:
8 Hours 15 Minutes
Step-by-step explanation:
12:00 p.m - 3:45 a.m = 8 Hours 15 Minutes
Marina babysits her neighbors' kids once a week and earns $40 each night. She loves coffee so she treats herself three times a week by buying a $5 latte at her favorite coffee shop. Marina wants to buy a new laptop for herself which will cost $800 and has already saved $200. If she continues her spending habits, how many months will it take Marina to save enough money to buy the laptop?
Answer:
24weeks
Step-by-step explanation:
So if she spends 5$ three times a week she spends 15$ a week
She babysits once a week for 40$
That means that she saves 25$ from babystitting each week
As she already has saved 200$, she only lacks 600$ for the purchase
600$ / (25$/week) = 24 weeks
If she stops buying coffee it will instead only take her 15 weeks to buy a new laptop