Answer:
y = - 3x + 12
Step-by-step explanation:
Slope intercept form of line
y = mx + b where m = slope, b = y-intercept
==> y = -3x + b is the equatin
To find b, plug in values for point x = 9, y =-15 and solve for b
-15 = -3(9) + b
-15 = -27 + b
Add 27 both sides
-15 + 27 = b
12 = b
b = 12
Equation is
y = - 3x + 12
Y² = 64 ? What is the solution of this equation it could possibly be more that one answer
Answer: Y = -8 or Y = 8
Step-by-step explanation:
Y² = 64
Y = -8 or Y = 8 ==> yes there is more than one answer
The real solutions to the equation 3x5 + 25x4 + 26x3 – 82x2 + 76x = 48 are shown on the graph. What are the nonreal solutions? StartFraction 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus i StartRoot 5 EndRoot Over 3 EndFraction. StartFraction negative 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus i StartRoot 5 EndRoot Over 3 EndFraction. StartFraction negative 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus StartRoot 5 EndRoot Over 3 EndFraction. StartFraction 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
Using the Factor Theorem, the non-real solutions are given as follows:
[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
For this problem, the function is:
f(x) = 3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48.
The function can be written as:
f(x) = g(x)h(x).
In which:
g(x) is the polynomial with the real solutions.h(x) is the polynomial with the non-real solutions.Using a calculator, as the graph is not given, the real solutions are given as follows:
[tex]x_1 = -6, x_2 = -4, x_3 = 1[/tex]
Hence:
g(x) = (x + 6)(x + 4)(x - 1)
g(x) = (x² + 10x + 24)(x - 1)
g(x) = x³ + 9x² + 14x - 24.
f(x) is of degree 5, g(x) of degree 3, hence h(x) is of degree 2 and:
f(x) = g(x)h(x)
3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48 = (x³ + 9x² + 14x - 24)(ax² + bx + c)
Hence:
ax^5 = 3^5 -> a = 3.-24c = -48 -> c = 2.-24bx + 14cx = 76x
-24b + 28 = 76
-24b = 48
b = -2.
Then the equation with the non-real solutions is:
h(x) = 3x² - 2x + 2.
Which is a quadratic equation with coefficients a = 3, b = -2 and c = 2, thus:
[tex]\Delta = b^2 - 4ac = (-2)^2 - 4(3)(2) = -20[/tex][tex]x_1 = \frac{2 + \sqrt{-20}}{6} = \frac{2 + 2\sqrt{5}i}{6} = \frac{1 + \sqrt{5}i}{3}[/tex][tex]x_2 = \frac{2 - \sqrt{-20}}{6} = \frac{2 - 2\sqrt{5}i}{6} = \frac{1 - \sqrt{5}i}{3}[/tex]Hence the non-real solutions are:
[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]
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branlyueer099799893
3 minutes ago
Mathematics
College
ANSWER RIGHT AWAY PLEASE!
question one: simply the exponents. (show your work)
- 21^0 = ?
- (2/3)^-2 = ?
question two: Solve the problem. (leave your answer as a base number with an exponent and show your work)
- 4^6 / 4^2 = ?
question three: Convert the number into numerical form. (show your work)
- 8.723 x 10^-10 = ?
question four: Solve the problem. (leave your answer in scientific notion and show your work)
- 5.1 x 10^8 - 2.3 x 10^3 = ?
- 6 x 10^5 x 1.1 x 10^7 = ?
PLEASE ANSWER I WILL GIVE 50 POINTS TO ANYONE WHO ANSWERS AND MARK BRAINLIEST AT LEAST ANSWER THE ONES YOU KNOW
The capacities at which U.S. nuclear power plants are working are shown in table for various years.
Year Percent
1975 56
1980 59
1985 58
1990 70
1995 76
2000 88
2004 89
Let
f
(
t
)
be the capacity (in percent) at which U.S. nuclear power plants are working at t years since 1970. A model of the situation is
f
(
t
)
=
0.027
t
2
+
0.216
t
+
53.296
.
Use a graphing calculator to draw the graph of the model and, in the same viewing window, the scattergram of the data. Does the model fit the data well?
The function is not a good model for the data
The function is a good model for the data.
Estimate at what capacity U. S. nuclear power plants were working in 2014.
% Round to the nearest whole percent.
Predict when U. S. nuclear power plants will be working at full (100%) capacity.
Enter the year this occurs.
The function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.
Given that the table which shows the capacities at which U.S. nuclear power plants are working and a model of the situation is f(t)=0.027t²+0.216t+53.296.
The Scatter plot for our function and points is shown in attached image and the point are highly related to the curve .
So the function is good model.
The year 2014 means t=2014-1970=44
So to get the population,put t=44 in equation
f(t)=0.027(44)²+0.216(44)+53.296
f(t)=0.027(1936)+0.216(44)+53.296
f(t)=52.272+9.504+53.296
f(t)=115.072
And on rounding it we get 115%.
Now, to find year at which capacity is 100% ,put f(t)=100 and solve for t
f(t)=0.027t²+0.216t+53.296=100
0.027t²+0.216t+53.296=100
0.027t²+0.216t+53.296-100=0
0.027t²+0.216t-46.704=0
Now, we will solve this using quadratic formula for f(x) =ax²+bx+c=0
[tex]\begin{aligned}x&=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end[/tex]
for our function a= 0.027 , b=0.216 ,c=-46.704 substitute this value and we get
[tex]\begin{aligned}t&=\frac{-0.216\pm \sqrt{(0.216)^2-4\times 0.027\times (-46.704)}}{2\times 0.027}\\ &=\frac{-0.216\pm \sqrt{0.046656+5.044032}}{0.054}\\ &=\frac{-0.216\pm \sqrt{5.090688}}{0.054}\\ &=\frac{-0.216\pm 2.256}{0.54}\\ &=37.78, -45.78\end[/tex]
As we all know time cannot be negative so t=-45.78 will be rejected.
So, t=37.78=38
Now, we will find the corresponding year
1970+38=2008
Hence, from the given table the function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.
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7 divide 161 step by step
this is what you need?if yes than look and write
Factor x^4y^2+x^3y^3
Answer: x^3y^2(x+y)
Step-by-step explanation:
x^4y^2+x^3y^3=
x*(x^3y^2)+(x^3y^2)*y=x^3y^2(x+y)
5. Kerry McCarthy is a news traffic reporter with an annual gross
pay of $44,500. He is single and is paid on a monthly basis.
How much is withheld monthly for state taxes?
$3,708.33 is withheld monthly for state taxes.
Some states have a graduated income tax that involves a different tax rate for each of several levels of income. The tax rate increases as income increases.
Tax Withheld per Pay Period = Annual Tax Withheld/ Number of Pay Periods per Year
Here, we are given that Kerry McCarthy is a news traffic reporter with an annual gross pay of $44,500.
Thus, the Annual Tax Withheld = $44,500.
He is paid on a monthly basis ⇒ Number of Pay Periods per Year = 12
Hence, we get-
Tax Withheld per Pay Period = 44,500/ 12
= 3,708.33
Thus $3,708.33 is withheld monthly for state taxes.
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Determine whether the given situation is best described by a linear model or an exponential model. What function models the situation?
The population of rabbits in a forest is tripling every month.
At 0 months (the starting point) there was only one rabbit.
The model that best described the statement is an exponential model and the function that models the situation is A(t) = 4^t
How to determine whether the given situation is best described by a linear model or an exponential model.The statement is given as:
The population of rabbits in a forest is tripling every month.At 0 months (the starting point) there was only one rabbit.The above statement is a population function
Population functions are best represented by an exponential function
Hence, the model that best described the statement is an exponential model.
What function models the situation?Here, we have
Initial value, a = 1
Rate, r = 3
The function is represented as
A(t) = A * (1 + r)^t
So, we have
A(t) = 1 * (1+3)^t
Evaluate
A(t) = 4^t
Hence, the function that models the situation is A(t) = 4^t
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Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms
The correct option is b. -30x + 32 = 182.
After combining the like terms, the equation that represents -8x + 23 - 22x + 9 = 182 is -30x + 32 = 182, where x = -5.
What is defined as equation?In its most basic form, an equation is a statement that demonstrates that 2 mathematical expressions have been equal.
3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are 2 expressions separated by a 'equal' sign.An equation is a formula in mathematics that conveys the equality of two expressions by linking them with the equal sign =.Now, as per the given question;
The stated equation in the question is is,
-8x + 23 – 22x + 9 = 182
Considering like terms together;
-8x – 22x + 23 + 9 = 182
Further simplifying;
– 30x + 32 = 182
Subtracting 32 from the both sides.
– 30x + 32 - 32 = 182 - 32
On solving;
– 30x = 150
⇒ x = -5
Therefore, the expression which defined the equation after taking alike terms is -30x + 32 = 182 for which the value of 'x' comes to be -5.
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The complete question is;
Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms?
-8x + 23 – 22x + 9 = 182
a. 14x + 32 = 182
b. -30x + 32 = 182
c. 14x + 14 = 182
d. -30x + 14 = 182
Solve.
2x+y+z=−4
3x+2y−z=6
x+2y−3z=2
Enter your answer, in the form (x, y, z), in the boxes in simplest terms.
Solution of 2x+y+z=−4, 3x+2y−z=6, x+2y−3z=2 value of
(x , y, z) =(10,-16,-8) in the simplest terms.
As given,
2x+y+z=−4 __(1)
3x+2y−z=6 __(2)
x+2y−3z=2 __(3)
Add (1) and (2)
2x+y+z=−4
3x+2y−z=6
5x + 3y=2 __(4)
Multiply 3 to (1) add it to (3)
6x+3y+3z=-12
x+2y−3z=2
7x + 5y = -10 __(5)
Now [5× (4)] subtract [3×(5)] from it
25x + 15y=10
21x+15y=-30
4x= 40
⇒x=10
Substitute in (4)
y=[2-5(10)]/3
=-16
Substitute value of x and y in (1)
z=-4 -2(10)-(-16)
=-8
Therefore, solution of 2x+y+z=−4, 3x+2y−z=6, x+2y−3z=2 value of
(x , y, z)=(10,-16,-8) in the simplest terms.
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Solve the equation below for p:
14p-3=25
Answer:
p=2
Step-by-step explanation:
One hall can accommodate 65 people. How many halls are required to accommodate 520 people?
8 halls would be required to accommodate 520 people in the hall.
As we know that a hall can accommodate 65 people.
To determine the number of hall required for 520 people,
first we need to find that how many halls would be required for one person,
So, we will divide the 1 by 6 to find :
The number of one person accommodate = 1/65 Hall
Then, 520 people required to accommodate = 1/65 × 520
= 8 Halls.
[Accommodate: to have enough space for somebody/something, especially for a certain number of people]
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7x 1 3/5
simplest formm
Answer:
56/5 or 11 1/5
Step-by-step explanation:
Convert 1 3/5 to an improper fraction
1 3/5 = (1 x 5 + 3)/5 = (5 + 3)/5 = 8/5
7 x 1 3/5 = 7 x 8/5 = 56/5
In mixed fraction, 56/5 = 11 1/5
22647 inches to miles, please show work
Answer: 0.3574 miles
Step-by-step explanation:
22647 inches = 0.3574 miles
A coffee company surveyed 40 potential customers to see where they would like the company's new organic coffee sold. Respondents were given the following four locations and asked to choose as many as they liked: grocery stores, drugstores, health food stores, and big box stores. The results are summarized in the bar graph below, with the number of times each location was chosen noted above the corresponding bar.
As per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.
As given,
Total number of potential customers =40
Number of respondents from bar graph
At grocery stores= 40
At drugstores respondents =32
At health food stores =8
At big box stores =20
Average number=(40 +32+8+20)/40
= 100 /40
=2.5
Therefore, as per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.
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How can you find the reciprocal of 0.375? Select all the correct methods.
A Solve the equation 0.375x=1
B. Solve the equation 0.375+X=1,
C. Divide 1 by 0.375.
D. Solve the equation 0.375x=-1.
OE. Divide 0.375 by (1-0.375)
The reciprocal of 0.375 is gotten by Dividing 1 by 0.375 and Solving the equation 0.375x = 1
What is reciprocal?The reciprocal of a number is the multiplicative inverse of that number. For a number x, the reciprocal is x⁻¹
Hence, the reciprocal of 0.375 is:
a) Dividing 1 by 0.375
b) Solving the equation 0.375x = 1
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mars has a maximum temperature of "-7°c" at the equator and a minimum temperature of "-133" °c at the winter pole. write an inequality that describes the possible temperatures on mars.
The inequality that describes the possible temperatures on Mars is
-133°c ≤T≤ -7°c .
What is inequality ?Inequality compares two values by if they are less than or greater than each other.
According to the given question Mars has a maximum temperature of -7°c at the equator and a minimum temperature of -133°c at the winter pole.
We have to write an inequality that describes the possible temperatures on Mars.
Let us denote all the possible range of temperatures by T,
∴ T is less or equal to the maximum temperature and T is greater than or equal to the minimum temperature.
So, -133°c ≤T≤ -7°c .
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Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below.
f(-2) = ? f(2) = ?
The domain is ___. (use interval notation)
From the graph of the function, we have that:
a) The domain is all real values.
b) The range is y ≤ 4.
c) The x-intercepts are x = -4 and x = 1.
d) The y-intercept is y = 3.
e) f(-2) = 3, f(2) = -5.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, the domain is composed by the values of x.The range of a function is the set that contains all the values of the output. In a graph, the domain is composed by the values of y.Hence, for this problem:
a) The domain is all real values.
b) The range is y ≤ 4.
What are the intercepts of a function?The x-intercepts of a function are the values of x when f(x) = 0, that is, the values of x for which the function crosses the x-axis.The y-intercept of a function is the values of f(x) when x = 0, that is, the value of y for which the function crosses the y-axis.Hence:
c) The x-intercepts are x = -4 and x = 1.
d) The y-intercept is y = 3.
What are the numeric values?For the graph, when x = -2 y = 3 and when x = 2 y = -5, hence:
f(-2) = 3, f(2) = -5.
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Candace bought a laptop for x dollars. She decided to sell it, after adding an $875 markup amount to the original price. If the markup rate used was 20%, then how much did she originally purchase the laptop for? Round your answer to the nearest dollar.
The original amount for the laptop that Candace bought when the markup rate is 20% will be $4375.
How to calculate the value?It should be noted that she added 875 markup amount to the original price and the markup rate used was 20%,
Therefore, 20% of x = 865
0.2x = 875
Divide
x = 875 / 0.2
x = 4375
Therefore, the original amount for the laptop is $4375.
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For a single randomly selected steel rod, find the probability that the length is between 213.3-cm and 213.7-cm.
Answer: probably like 1.8%
Step-by-step explanation:
The value of the 7 in 7.8 is. then the 7 in 23.97. 10 times greater 100 times greater 10 times last 100 times less
7 in 7.8 is 100 times greater than 7 in 23.97.
What is place value ?As the name suggests place value is where the digit is being placed in decimal number system.
We can multiply both these numbers by 100 in that way we'll get rid of the decimal and it doesn't effect our answer.
Now 7.8 and 23.97 multiplied by 100 becomes 780 and 2397.
We can observe that 7 in 780 is in hundreds place and 7 in 2397 is in ones place.
∴ If we divide (100/1) = 100.
So, it is 100 times greater.
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Taylor and Alex are looking for a daycare for their child. They want to make sure the daycare is midway between their jobs. Taylor works at the Rogers Middle School located at (4, -5), and Alex works at St. Philip's located at (2, 5). Where should the daycare be located?
Step-by-step explanation:
(5 ,_4) it the location this is the answer
Find each sum 5/7+1/2
Answer: 17/14 or 1 3/14 simplified
Step-by-step explanation:
14 is the least common multiple of denominators 7 and 2. Use it to convert to equivalent fractions with this common denominator.
PLEASE HELP!! 50 points
I’m confused on how to solve this for gross pay :(
Ted worked 40 hours last week and earned $1200. 40% of his pay is from commission. How much did Ted earn in commission? What is his hourly wage?
a cheetah that is running 90 feet per second is running 120 feet behind an antelope that is running 60 feet per second. How long does it take for the cheetah to run up to the antelope? PLS FINISH ASAP
Answer: 4 seconds
Step-by-step explanation:
c=cheetah. a=antelope
a=c+120
c/90=a/60
c/90=(c+120)/60
60*c/90=60*(c+120)/60
6*c/9=c+120
2c/3=c+120
(2c/3=c+120)*3 ==> multiply the equation by 3 to get rid of fractions
2c=3c+360
2c-3c=3c-3c+360
-c=360
c=-360 feet==> position of cheetah before catching up to the antelope. This means that the cheetah needs to travel 360 feet before reaching 0 ft when it catches the antelope.
360 feet * 1 second/90 feet=
360*1/90=
360/90=4 seconds
(4x+2)+(x-2) can someone tell me its procedure
[tex] \green\star\:{\underline{\underline{\sf{\orange{Answer:}}}}}[/tex]
¡Hello :D!
To solve the similar terms we must eliminate the parentheses and then put the parentheses back but this time it would be like this: (4 x + x) + ( 2 - 2)
Once we have done that we must restore the ones on the right side which gives us the result of 1 then as we see that there is + in the Parenthesis and another + outside the Parenthesis we do not care + since we are using the law of signs .
We proceed to solve:
[tex]\: \: \: \: \: \: \bold \: \bold \: \bold \: ( \bf4x+2)+(x-2)[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \bf \bold4x + 2 + x - 2[/tex]
[tex] \: \: \: \: \: \: \: \: \bf\tt( \bf4x + x) + (2 - 2)[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf5x[/tex]
So the result is 5x
I hope I've helped XD
() Listen
Which expressions of the division of integers will result in a rational number?
Select all that apply.
-5/7
0/6
4/0
-2/0
Reason:
A rational number is a fraction of any two integers, as long as the denominator is nonzero. This applies to the first two answer choices.
Choices C and D are undefined because of the 0 in the denominator. You cannot divide by zero. This rules out the last two choices.
[(10-9+8)-7] + [6-((5+4] ÷ 3)] ² - 1
Answer:
10
Step-by-step explanation:
1 Simplify 10-910−9 to 11.
1+8-7+{(6-(5+4)\div 3)}^{2}-1
1+8−7+(6−(5+4)÷3)
2
−1
2 Simplify 5+45+4 to 99.
1+8-7+{(6-9\div 3)}^{2}-1
1+8−7+(6−9÷3)
2
−1
3 Simplify 9\div 39÷3 to 33.
1+8-7+{(6-3)}^{2}-1
1+8−7+(6−3)
2
−1
4 Simplify 6-36−3 to 33.
1+8-7+{3}^{2}-1
1+8−7+3
2
−1
5 Simplify {3}^{2}3
2
to 99.
1+8-7+9-1
1+8−7+9−1
6 Simplify 1+81+8 to 99.
9-7+9-1
9−7+9−1
7 Simplify 9-79−7 to 22.
2+9-1
2+9−1
8 Simplify 2+92+9 to 1111.
11-1
11−1
9 Simplify.
10
simplify (7-1 over 4 square root of 16) ^2 +2-5^2 and REALLY ANSWER IT YOU WILL GET BRAINLEST
Answer:
13
Step-by-step explanation:
Simplify the following:
(7 - (sqrt(16))/4)^2 + 2 - 5^2
sqrt(16) = sqrt(2^4) = 2^2:
(7 - (2^2)/4)^2 + 2 - 5^2
2^2 = 4:
(7 - 4/4)^2 + 2 - 5^2
(-4)/4 = 4/4×-1 = -1:
(-1 + 7)^2 + 2 - 5^2
7 - 1 = 6:
6^2 + 2 - 5^2
5^2 = 25:
6^2 + 2 - 25
6^2 = 36:
36 + 2 - 25
36 + 2 - 25 = 13:
Answer: 13
6x + 4y = 36 when x = 3 and y = 4
Answer:
No solution.
Explanation:
Given expression:
6x + 4y = 36when x = 3, y = 4
Substitute these values inside expression:
6(3) + 4(4) = 36
18 + 16 = 36
34 = 36
As the statement "34 = 36" not true. The solution is false or no solution.
Answer:
The given values are wrong.
Step-by-step explanation:
Given information,
→ x = 3
→ y = 4
Solving the given equation,
→ 6x + 4y = 36
→ (6 × 3) + (4 × 4) = 36
→ 18 + 16 = 36
→ 34 ≠ 36
Hence, there is no solution.