Answer:
x = 4/3
y = 1/3
Step-by-step explanation:
System of equations! This is set up really well to make the second equation equal x then substitute.
x - y = 1
x = 1 + y
and then our substitution:
2 (1+y) + y = 3
and solve:
2 + 2y + y = 3
3y + 2 = 3
3y = 1
y = 1/3
And now we can substitute that value into one of our equations:
x - (1/3) = 1
x = 4/3
Next we should check by substituting these values into both of our equations:
2 (4/3) + (1/3) = 3
9 / 3 does equal 3 !
(4/3) - (1/3) does equal 1 !
Therefore, x = 4/3 , and y = 1/3
∠DGC and ∠CGB are □ angles.Adjacent
Adjacent
Complementary
Supplementary
Vertical
Answer:
They are adjacent angles
Find all exact solutions of the equation on the interval [0, 2π).
cosxtanx=cosx
Answer:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\cos(x)\tan(x)=\cos(x)[/tex]
On the interval [0, 2π).
First, we can subtract cos(x) from both sides:
[tex]\cos(x)\tan(x)-\cos(x)=0[/tex]
Factor:
[tex]\cos(x)\left(\tan(x)-1\right)=0[/tex]
Zero Product Property:
[tex]\cos(x)=0\text{ or } \tan(x)-1=0[/tex]
Solve for each case:
[tex]\cos(x)=0\text{ or }\tan(x)=1[/tex]
Using the unit circle:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{\pi}{2}, \frac{5\pi}{4}, \frac{3\pi}{2}\right\}[/tex]
However, since tangent isn't defined for π/2 and 3π/2, we remove them from our solutions. Hence:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}[/tex]
Carl worked in the grocery store 24.25 hours last week. This week he worked 30.5 hours.
How many more hours did he work this week than last?
Answer:
6.25 hours
Step-by-step explanation:
30.5 - 24.25 = 6.25 hrs.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
Answer:
Y=2x+4
Step-by-step explanation:
Y=Mx+b is the slope intercept formula
subtract 2x so you get -y=-2x-4. Then divide everything by-1 .
Simplify 150 -(0.4 x 150)+15
For every 1000 videos it makes £2 from ad revenue.
How many videos are required to make £25
Step-by-step explanation:
If you divide 1,000 by 2 since there are £2, you get 500. Multiply 500 by 25 and you got it!
(the answer would be 12,500)
A billboard is 5.0 m by 2.5 m. A scale diagram of the billboard is 0.25 m by
0.125 m.
a.
1:
Calculate the scale.
b. Calculate the scale factor (k).
c.
Is this a reduction or enlargement? Justify your thinking.
Pls help
Answer:
A the answer is a because i was just working on that rn
Step-by-step explanation:
Describe the overall shape of this distribution. Explain your answer in complete sentences.
Answer: The histogram is skewered to the right (right-skewered)
Step-by-step explanation:
The peak veers to the left and the tail is towards the right.
The histogram given is right-skewed.
What is a histogram?
A histogram is a representation of the distribution of data with intervals.
We have,
Right-skewed and left-skewed are terms used to describe the shape of a data distribution.
A right-skewed (or positively skewed) distribution is one in which the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.
A left-skewed (or negatively skewed) distribution is the opposite of a right-skewed distribution.
In this case, the tail on the left-hand side of the graph is longer or fatter than the tail on the right-hand side.
Now,
We see that the histogram given is right-skewed because the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.
Thus,
The histogram given is right-skewed.
Learn more about histograms here:
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HELP PLEASE PICTURE ABOVE. NO LINKS JUST HOW TO SOLVE STEP BY STEP AND THE ANSWER PLEASE
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Answer:
4) -ln(2)/3
5) x = 9
6) x = 2
7) x = -6
Step-by-step explanation:
4) e^(-3x) = 2 . . . . given
-3x = ln(2) . . . . . take the natural log
x = -ln(2)/3 . . . . divide by the coefficient of x
__
5) ln(3x -5) = ln(11) +ln(2)
3x -5 = 11·2 . . . . . take antilogs
3x = 27 . . . . . . . . add 5
x = 9 . . . . . . . . . . divide by 3
__
6) log4(x -1) +log4(x +2) = 1
(x -1)(x +2) = 4 . . . . . take antilogs
x^2 +x -2 = 4 . . . . . . eliminate parentheses
x^2 +x +1/4 = 6 1/4 . . . add 2 1/4 to complete the square
(x +0.5)^2 = 6.25 . . . . write as a square
x +0.5 = ±2.5 . . . . . . . take the square root
x = -0.5 ± 2.5 = {-3, +2} . . . . . . x = -3 is an extraneous solution
x = 2
__
7) 8^x = 4^(x -3)
2^(3x) = 2^(2(x -3)) . . . . write using a common base of 2
3x = 2(x -3) . . . . . . . . . . take logarithms base 2
x = -6 . . . . . . . . . . . . . . .subtract 2x
Keiko bought 3 POUNDS of fruit salad. How many OUNCES of fruit salad did Keiko buy?
Answer:
48 ounces.
Step-by-step explanation:
:) have a good rest of your day.
HELP!! 5) Which number is IRRATIONAL?
A) V9
B) V27
C) V36
D) V81
URGENT PLZ HELP
use the graph to write an equation of the line
Answer the question.
11. Sarah's mom buys a basket that contains 8 bottles of lotion. Half of
the bottles each contain 150 milliliters of lotion. The other bottles
each contain 175 milliliters of lotion.
How many liters of lotion does Sarah's mom buy?
Answer:
1.3 liters
Step-by-step explanation:
4 x 150 is 600
4 x 175 is 700
700 + 600 = 1300 milliliters
1300 milliliters = 1.3 liters
Answer:
1.3 liters
Step-by-step explanation:
So first off, lets find the amount of milileters of lotion there is.
To do this, take 8, and divide it in half:
8/2 = 4. So we know that 4 bottles of lotion each contain 150 militers of lotion.
We know that the other 4 bottles each contain 175 milileters of lotion.
Next, lets multiply the 150 and 175 by the four bottles:
150x4
=
600
175x4
=
700
Now lets add these two values together, to find the total amount of lotion:
700+600
=
1300
Remember, this problem asked for liters of lotion, not milileters. Lets recall that 1000 milileters are equivelent to 1 liter:
1300/1000
=
1.3
This is your answer!
Hope this helps! :)
ava goes to lunch with 3 of her friends. The cost of their meals are $8, $4, $7, and $5. if they split the bill evenly. how much should each person pay? ANSWER NOW
Answer:
Each person should pay $6.00
Step-by-step explanation:
First, add everyone's cost
8 + 4 + 7 + 5 = 24
Then, divide by 4
24 ÷ 4 = 6
Lastly, have a great day! :)
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 9 kg, the acceleration of the object is 5 m/s². When the same force acts upon another object, its acceleration Is 3 m/s? What is the mass of this
object?
Answer:
Constant Force F= ?
A= 5m/s²
M=9kg
According to the Question
A
[tex] \alpha [/tex]
1/m
A=F/m
So F=ma
F=5×9
F=45N
we look for m using the formula A=F/m
m=F/A
where A=3
F=45
M=?
So M=45/3
M=15kg
A rectangular prism has a volume of 192 cubic inches the prism is 4 inches wide.....
Answer:
6 inches
Step-by-step explanation:
the formula for the volume of a rectangular prism is width*length*height.
Here we are asked to find the height when given a volume. The resultant equation is:
volume = w * l * h
192 cu.in. = 4in*8in*h(inches), simplify the equation by dividing each side by 32 (which is 4*8) to yield:
192 cu.in./32 sq.in.= h inches
6 inches = height
Compound Interest: You deposit $100 in an account that earns 3% annual interest compounded continuously. How long does it take the balance to reach the following amounts? (A = Pe^(rt). NO LINKS
a. $110
b. $150
c. $200
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Answer:
a) 3.18 years
b) 13.52 years
c) 23.10 years
Step-by-step explanation:
Solving for t, we find ...
A = Pe^(rt)
A/P = e^(rt)
ln(A/P) = rt
t = ln(A/P)/r
For P=100 and r=.03, the times are ...
a. $110: t = ln(110/100)/.03 ≈ 3.18 years
b. $150: t = ln(150/100)/.03 ≈ 13.52 years
c. $200: t = ln(200/100)/.03 ≈ 23.10 years
solve system of equations
y= 8x + 1
y = 6x + 3
(2,4)
(0,1)
(1,9)
or (4,14)
What is the location of the point on the number line that is 3/5 of the way from
A = 2 to B = 17?
O A. 12
O B. 10
C. 9
O D. 11
The location of the point on the number line that is 3/5 of the way from A = 2 to B = 17 is 11
How to determine the location of the point?The points are given as:
A = 2
B = 17
Point = 3/5
The location of the point is then calculated as:
Point = A + 3/5(B - A)
So, we have:
Point = 2 + 3/5(17 - 2)
Evaluate the product
Point = 2 + 9
Evaluate the sum
Point = 11
Hence, the location of the point on the number line that is 3/5 of the way from A = 2 to B = 17 is 11
Read more about number lines at:
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The point-slope equation of a line is
A. y + x - Xoyo = m
B. y= m(x - Yo)
O C. y+ mx - mxoyo
D. y-yo = m(x- xo)
Answer:
[tex]y - y_1 = m(x - x_1)[/tex]
Step-by-step explanation:
Given
A to D
Required
Which is the point slope equation
The point slope form of a coordinate pair is:
[tex]y - y_1 = m(x - x_1)[/tex]
Hence, (d) is correct
Henry is looking for the best deal on a tablet that regularly costs $829. Help him compare the price of the tablet at a stre
with the price on the store's website by completing the following.
(a)
The store's website is offering the tablet at a 80% discount off the regular price. Ignoring tax and shipping, how
much would he pay for the tablet on the store's website?
(b)
The store is having a sale, offering a 70% discount off the regular price of the tablet. Henry also has an
in-store-only coupon for an additional 10% off the sale price. Ignoring tax, how much would he pay for the tablet at
the store?
(c)
Select the true statement.
Henry would pay less for the tablet on the website.
Henry would pay less for the tablet at the store.
O Henry would pay the same amount at the store and on the website.
X
$
Answer:
$165.8 ;
$223.83 ;
Henry would pay less for the tablet on the website.
Step-by-step explanation:
Given :
Regular price = $829
On website :
80% discount off the regular price :
(100 - 80)% * regular price
20% * 829
0.2 * $829 = $165.8
At store :
70% off regular price :
(100 - 70)% * 829
0.3 * 829
= $248.7
10% off sale price :
(100 - 10)% * $248.7
0.9 * 248.7
= $223.83
Henry would pay less for the tablet on the website.
Evaluate g(2) given. Help
Answer:
[tex]g(2) = 3[/tex]
Step-by-step explanation:
Given
See attachment
Required
[tex]g(2)[/tex]
To solve this, we make use of:
[tex]g(x) = |7 - x^2|[/tex]
Because [tex]x \le 2[/tex]
i.e. [tex]2 \le 2[/tex]
So, we have:
[tex]g(2) = |7 - 2^2|[/tex]
[tex]g(2) = |7 - 4|[/tex]
[tex]g(2) = |3|[/tex]
Remove absolute brackets
[tex]g(2) = 3[/tex]
The A-frame cabin shown below is 35 feet wide. The roof of
the cabin makes a 60° angle with the cabin's base. Find the
length of one side of the roof from its ground level to the
peak. Round to the nearest tenth of a foot.
Answer:
25
Step-by-step explanation:
Please helpppp i will mark brainlisttt
Carlos, Brad, and Rick earned $221.88 raking leaves and cleaning yards last week. If they split their earnings equally, how much will each of them get?
Answer:
Step-by-step explanation:
Chanclas
Answer:
$110.94
Step-by-step explanation:
221.88 divided by 2 is 110.94
What is the equation of the graph below? y=1/2sinx y=1/2cosx y=1/2sin2x
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Answer:
(d) y = 1/2sin(2x)
Step-by-step explanation:
The sin(x) function will have a maximum value of 1 and a period of 360°. The function plotted is a sine function with a maximum value of 1/2 and a period of 180°.
For a function g(x) = a·f(b·x), the vertical scale factor is 'a', and the horizontal compression factor is 'b'. Our sine function has a vertical scale factor of 1/2, and a horizontal compression of 360/180 = 2, so the transformed function is ...
y = 1/2sin(2x)
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer: 4.12 km
Step-by-step explanation:
Use the Pythagorean theorem. Name the hypotenuse (longest side) c and the bottom side b. Then, simplify and solve for a.
a^2 + b^2 = c^2
a^2 + 8^2 = 9^2
a^2 + 64 = 81
a^2 = 17
a = square root of 17 or approx. 4.12
Please give brainliest!
Which choice is equivalent to the expression below?
(-4)-5
When you sunbathe nine feet from the swimming pool, your distance to a point of
tangency with the pool is twelve feet. Find the radius of the pool.
Answer:
[tex]9.5 \sqrt{?} [/tex]
(HElP) which answers describe the shape below?
I think it would be A, B, D and E.