Answer:
109 and 71Step-by-step explanation:
3x + 10 + 3x - 28 = 180
6x = 180 - 10 + 28
x = 198/6
x = 33
substitute the value of x = 33 back into the equation to solve for each angle
= 3x + 10
= 3(33) + 10
= 109
= 3x - 28
= 3(33) - 28
= 71
Help with solving this Functions problem
Answer:
See answers below
Step-by-step explanation:
Given the following functions:
r(x) = x - 6
s(x) = 2x²
r(s(x)) = r(2x²)
Replacing x with 2x² in r(x) will give;
r(2x²) = 2x² - 6
r(s(x)) = 2x² - 6
(r-s)(x) = r(x) - s(x)
(r-s)(x) = x - 6 - 2x²
Rearrange
(r-s)(x) = - 2x²+x-6
(r+s)(x) = r(x) + s(x)
(r-s)(x) = x - 6 + 2x²
Rearrange
(r-s)(x) = 2x²+x-6
Recall the scenario about Eric's weekly wages in the lesson practice section. Eric's boss have been very impressed with his work. He has given him a $2 raise and now Eric earns $12 an hour. His boss also has increased Eric's hours to 10 to 25 hours per week. The restrictions remain the same; he needs to work a full-hour in order to get the hourly wage working 1.5 hour does not pay him for 1.5 hours but for one hour. Tasks: Consider the scenario and restrictions and interpret the work hour and potential earning relation as a function. Express the relation in the following formats: 1. Function equation 2. Domain of the function in the set notation (Would domain (work hours) be infinite?(write the domain in the set notation) 3. Range of the function in the set notation (Would the range (weekly wage) be infinite(write the range in the set notation) 4. Sketch the function and plot the points for his earnings.
Answer:
\(1)\quad f(x)=\bigg\{\begin{array}{ll}12x&0\leq x <9\\18x-48&9\leq x \leq 24\end{array}\)
2) D: x = [0, 24]
3) R: y = [0, 384]
4) see graph
Step-by-step explanation:
Eric's regular wage is $12 per hour for all hours less than 9 hours.
The minimum number of hours Eric can work each day is 0.
f(x) = 12x for 0 ≤ x < 9
Eric's overtime wage is $18 per hour for 9 hours and greater.
The maximum number of hours Eric can work each day is 24 (because there are only 24 hours in a day).
f(x) = 18(x - 8) + 12(8)
= 18x - 144 + 96
= 18x - 48 for 9 ≤ x ≤ 24
The daily wage where x represents the number of hours worked can be displayed in function format as follows:
\(f(x)=\bigg\{\begin{array}{ll}12x&0\leq x <9\\18x-48&9\leq x \leq 24\end{array}\)
2) Domain represents the x-values (number of hours Eric can work).
The minimum hours he can work in one day is 0 and the maximum he can work in one day is 24.
D: 0 ≤ x ≤ 24 → D: x = [0, 24]
3) Range represents the y-values (wage Eric will earn).
Eric's wage depends on the number of hours he works. Use the Domain (given above) to find the wage.
The minimum hours he can work in one day is 0.
f(x) = 12x
f(0) = 12(0)
= 0
The maximum hours he can work in one day is 24 (although unlikely, it is theoretically possible).
f(x) = 18x - 48
f(24) = 18(24) - 48
= 432 - 48
= 384
D: 0 ≤ y ≤ 384 → D: x = [0, 384]
4) see graph.
Notice that there is an open dot at x = 9 for f(x) = 12x
and a closed dot at x = 9 for f(x) = 18x - 48
I'll mark whoever answers first!! Please help me
Answer:
Center ( -8, 1 )
Radius ( 13 )
What is a material called if it allows electricity to flow through it easily?
A. Conductor
B. Insulator
C. Porous
D. Transparent
Answer:
A
Step-by-step explanation:
it let's stuff thru like in electricity
Answer:
conductor
Step-by-step explanation:
What are the rules of multiplying decimals?
Answer:
To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Step-by-step explanation:
21x² - 2x + 1/2 =0
find the following quadratic equation by factorization method
PLESE SOMEONE HELP
Step-by-step explanation:
21x²-2x +1/2 = 0
x² - 2x ×21 + 1/2× 21 = 0
Can anyone help me? If f (x) = -2x +5, what is f (-3x) equal to?
Answer:
B
Step-by-step explanation:
Use the given functions to set up and simplify f(-3x)
substitute x with -3x
-2 (-3x) =6x remember a - x - = +
6x +5
1
Select the correct answer.
Which graph shows a quadratic equation with complex roots?
Answer:
C (the bottom one)
Step-by-step explanation:
B (the top one) has roots/solutions — as in, it crosses the x-axis.
C doesn't have roots, and therefore doesn't have normal solutions, instead it has "complex" roots which require the use of imaginary numbers: \(i\)
Find the equation of the line that satisfies the conditions given in each of the following: 1. Through (3, 2) and (5, 7) 2. Through (-3, 4), m = 2 3. m = -3, b = 5 4. x-intercept = 3, y-intercept
The equation of each line that satisfies the given conditions are:
1. y - 2 = 5/2(x - 3)
2. y - 4 = m(x + 3)
3. y = -3x + 5
What is the Equation of a Line?If we know the slope (m) and the y-intercept (b) of a line, we can write the equation of the line as y = mx + b in slope-intercept form.If we know the point (a, b) and the slope (m) of the line, we can write the equation of the line in point-slope form as y - b = m(x - a).1. Given the points, (3, 2) and (5, 7), find the slope (m):
Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)
m = 5/2
Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):
y - 2 = 5/2(x - 3)
2. Given:
A point = (-3, 4)
Slope (m) = 2
Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):
y - 4 = m(x + 3) [equation of the line]
3. Given:
Slope (m) = -3
Y-intercept (b) = 5
Substitute m = -3 and b = 5 into the equation y = mx + b:
y = -3x + 5
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Dividing by a Monomial
What is (9x^3-6x^2+15x) ÷ 3x^2?
Answer:
\(3x-2+\frac{5}{x}\)
Step-by-step explanation:
To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:
(9x^3 - 6x^2 + 15x) ÷ (3x^2)
To simplify the division, we divide each term of the polynomial by 3x^2:
(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)
To divide monomials with the same base, we subtract the exponents. So:
9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x
(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2
15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x
Putting it all together, we have:
(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x
Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.
Which problem can be solved using this equation: 9x + 14 = 100
Answer:
James has 9x cookies he needs 100 he buys 14 more what’s the value of x?
Step-by-step explanation:
Anyone I need this please
What is the playing surface called where the college basketball semi-finals are played?
Answer:
The answer is "floor".
Step-by-step explanation:
The playground on which the semi-finals of basketball was performed is called the Floor. It also has a double-dimensional or three-dimensional ground throughout the form of a square or a rectangle. It may be a Cube, or Cuboid, which would be a Pyramid whenever a surface becomes three-dimensional elevated beyond Earth's level.
If cos of Ф = 2/5, find sin Ф/2 and cos Ф/2. Assume the angles are in the 1st quartile
The exact values of the sine and the cosine of the half angle are √(3 / 10) and √(7 / 10), respectively.
What are the exact values of two trigonometric functions?
Herein we know the exact value of the cosine of an angle set in the first quadrant. Then, the half angle is also in the first quadrant, whose sine and cosine are, respectively:
cos 0.5Ф > 0, sin 0.5Ф > 0
sin 0.5Ф = √[(1 - cos 0.5Ф) / 2]
cos 0.5Ф = √[(1 + cos 0.5Ф) / 2]
First, replace the values of the cosine of the half angle:
sin 0.5Ф = √[(1 - 2 / 5) / 2]
cos 0.5Ф = √[(1 + 2 / 5) / 2]
Second, simplify the resulting expression:
sin 0.5Ф = √[(1 - 2 / 5) / 2]
sin 0.5Ф = √[(3 / 5) / 2]
sin 0.5Ф = √(3 / 10)
cos 0.5Ф = √[(1 + 2 / 5) / 2]
cos 0.5Ф = √[(7 / 5) / 2]
cos 0.5Ф = √(7 / 10)
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which is pattern 12,24,36,48
Answer:
multiples of 12
Step-by-step explanation: when looking at the GCF, the answer is 12
Without writing the equation x^2 + y^2 + 24x – 26y+ 277 = 0 in the standard form, state whether the graph of this equation is a
parabola, circle, ellipse, or hyperbola.
a. parabola
c. hyperbola
b. ellipse
d. circle
Answer:
circle
Step-by-step explanation:
You can see there is a x^2 and y^2 and 24 x and 26 y meaning if you do complete the square you can write it as a circle in standard form
Given the following data, find the weight that represents the 53rd percentile.
Weights of Newborn Babies9.4 7.5 5.4 7.5 7.1
6.0 8.1 5.7 7.1 6.6
9.4 5.8 8.7 5.7 9.3
Answer:
Step-by-step explanation:
Rearranging the weights in ascending order, it becomes
5.4, 5.7, 5.7, 5.8, 6.0, 6.6, 7.1, 7.1, 7.5, 7.5, 8.1, 8.7, 9.3, 9.4, 9.4
The formula for determining the percentile is expressed as
n = (P/100)N
Where
n represents the value of the given percentile
P represents the given percentile
N represents the number of items(weights)
From the information given, the number of items, n is 15
P = 53
Therefore,
n = (53/100) × 15
n = 7.95
n = 8
Therefore, the weight that represents the 53rd percentile is the 8th value. It becomes 7.1
53rd percentile is 7.1
Write in index form
3x * 3x * 3x * 3x
Parallelogram ABCD has the coordinates:
Find the coordinates of point D.
A)
(4,0)
B)
(4, -1)
C)
(3,-1)
D)
(5,-2)
Find the midpoint of the line segment with endpoints: Midpoint = (-5/2, -1) to (5/2,8) Give your answer as a point, using integers or reduced fractions for coordinates.
Answer:
(0,3.5)
Step-by-step explanation:
midpoint formula :)
One of the families plans to bring 9 bundles of flowers to decorate the picnic tables. If you plan to set up 12 tables, what fraction of a bundle will be on each picnic table?
The fraction of flower bundle on each table will be 3/4.
We will find the fraction of bundle of flowers required for each table by performing division. Relating the two entities as per given information.
Fraction of bundle on each table = total number of tables ÷ available number of bundles
Keep the values in above mentioned relation to find the fraction of bundle that will be on each picnic table.
Fraction of bundle on each table = 9 ÷ 12
Performing division of both numerator and denominator by 3
Fraction of bundle on each table = 3/4
Therefore, the fraction of flower bundle on each table will be 3/4.
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Simplify: 7/6 x −3/28 Also, find the reciprocal of the answer.
Answer:
Simplify = 7x/6 - 3/28
Reciprocal = 6x/7 - 28/3
Step-by-step explanation:
Add x to the top of the first fraction to combine them.
To find the reciprocal you flip the numbers. So the numerator is the bottom and the dominator is the top.
For the hypothesis H0: mu = 25 and Ha: mu ≠ 25, if the p-value = 0.08 and alpha = 0.05, which, if any, type of error could be made?
a.) Both a Type 1 Error and a Type 2 Error
b.) Not enough information
c.) Type 1 Error
d.) Type II Error
We have that the type of error could be made is
Type II Error
From the Question we are told that
\(H0: mu = 25\\\\ Ha: mu ≠ 25\\\\p-value = 0.08\\\\alpha = 0.05\)
it is important to note that
p-value>alpha
Hence we fail to reject the null hypothesis
Now,Type II Error gives null hypothesis H_0 a chance to be false
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Which statements about opposites are true?
Select each correct answer.
The opposite of a negative number is always a positive number.
A number and its opposite are located the same distance from zero on a number line.
The product of a number and its opposite is always 1.
The opposite of zero is zero.
Answer:
your selections would be:
..the opposite of a negative number is always a positive number
.. a number and it's opposites are located same distance from zero on the number line
..the opposite of zero is zero
Luis includes sit ups and push ups as part of his training for the race. This graph shows his plan for increasing the number of sit ups and push ups he does each week. Write an equation that can be used to find the number of sit ups, y, luis will do during week x.
Answer:
y = 10x
Step-by-step explanation:
y = number of sit-ups
x = number of weeks
Equation of that can be used to find the number of sit-ups can be generated using the graph in the slope-intercept form, y = mx + b. Where, slope = m, and y-intercept is b.
Let's find slope using two points on the blue line, (0, 0) and (3, 30):
Slope (m) = change in y/change in x
m = (30 - 0)/(3 - 0)
m = 30/3
m = 10
b = 0 (the point where the line intercepts the y-axis)
✔️To write the equation, substitute m = 10 and b = 0, into y = mx + b
y = 10x + 0
y = 10x
Eric is randomly drawing cards from a deck of 52. He first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. What is the probability of drawing a red card, placing it back in the deck, and drawing another red card
Half the deck is red so you have. 1/2 chance of picking red each time.
Picking red both times would be 1/2 x 1/2 = 1/4
The answer is 1/4
The probability of drawing a red card, placing it back in the deck, and drawing another red card is 0.25 or \(\bold{\frac{1}{4}}\).
Given to us:
Eric is randomly drawing cards from a deck of 52.
Also, Eric first draws a red card, places it back in the deck, meaning this is case of probability with replacement (outcomes are returned back to the sample space again).
So, the both the events are independent of each other, therefore the probability for second event will be same as the first, as the sample size and the desired outcome are same.
Probability for first event
\(=\dfrac{Desired\ outcome}{Total\ number\ of\ samples}\\\\=\dfrac{26}{52} \\\\=\dfrac{1}{2} = 0.5\)
The probability of drawing a red card, placing it back in the deck, and drawing another red card
= Probability for first event x Probability for second event
= 0.5 x 0.5
= 0.25
Hence, the probability of drawing a red card, placing it back in the deck, and drawing another red card is 0.25 or \(\bold{\frac{1}{4}}\).
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Pablo deposited $600 in an account earning 2% interest compounded annually.To the nearest cent, how much interest will he earn in 3 years?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
The given information is:
- The initial amount is $600
- The interest rate is 2% (compounded annually)
The given formula is:
\(B=p(1+r)^t\)Where B is the balance (final amount), p is the principal (starting amount), r is the interest rate as a decimal, and t is the time in years.
By replacing the known values we obtain the balance after 3 years:
\(\begin{gathered} B=600*(1+0.02)^3 \\ B=600(1.02)^3 \\ B=600*1.06 \\ B=636.72 \end{gathered}\)The answer is $636.72
what is the square root of 35000
Answer:
187 is closer so the square root of 35000 would be 187.082... or just
√35000
Step-by-step explanation:
187 x 187 = 34960
188 x 188 = 35344
Now find which is closer
35344-35000=31844
35000-34960=40
Hope this helps :)
Answer:
\(50\sqrt{14}\)
Step-by-step explanation:
\(\sqrt{35000 }\\ \\\mathrm{Prime\:factorization\:of\:}35000:\quad 2^3\times\:5^4\times\:7\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^b\times\:a^c\\\\2^3\times\:5^4\times\:7=2^2\times\:2\times\:5^4\times\:7\\\\=\sqrt{2^2\times\:5^4\times\:2\times\:7}\\\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{ab}=\sqrt{a}\sqrt{b}\\\\\sqrt{2^2\times\:5^4\times\:2\times\:7}=\sqrt{2^2}\sqrt{5^4}\sqrt{2\times\:7}\\\\\sqrt{2^2}=2\\\\=2\sqrt{5^4}\sqrt{2\times\:7}\\\\\sqrt{5^4}=25\)
\(=2\times\:25\sqrt{2\times\:7}\\\\2\times\:25\sqrt{2\times\:7}=50\sqrt{14}\)
What's the volume of 2 inches 1 inch and 4 inches
Answer:
1=1
2=8
4=64
Step-by-step explanation:
If it's cubic inches then
ax a x a
So if it's 1 then it's 1
If it's 2 it's 8
If it's 4 it's 64