A quadratic function has an "a" value of (2) and a vertex at (5,-18) How many solution does the function have, and what are they?
The function bas solution (s), which is x=__ and x=___ (Write NA tar the second box at there is only one solution)
Answers
The function has 2 solutions which is x = 2 and x = 8.
What is a quadratic function?
A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Solution:
Given :
a = 2 , vertex = (5, -18)
f(x) = a(x-h)² + K
f(x) = 2(x - 5)² - 18
f(x) = 2(x² -10x + 25) -18
f(x) = 2x² - 20x +50 - 18
f(x) = x² - 10x +16
∴ x² -10x + 16 = 0
x² - 8x - 2x + 16 = 0
x(x-8) -2(x-8) = 0
(x-2) = 0 and (x-8) = 0
∴ x = 2 and x = 8
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The quadratic function has 2 solutions which is x = 2 and x = 8.
What is a quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. A polynomial of degree two in one or more variables in mathematics is known as a quadratic polynomial. Any polynomial function that is defined by a quadratic polynomial is said to be quadratic.
The terms "quadratic polynomial" and "quadratic function" were almost interchangeable before the 20th century because it was difficult to tell a polynomial from its corresponding polynomial function. This is still true in many elementary courses where "quadratic" is frequently used to refer to both terms.
Solution:
Given :
a = 2 , vertex = (5, -18)
f(x) = a(x-h)² + K
f(x) = 2(x - 5)² - 18
f(x) = 2(x² -10x + 25) -18
f(x) = 2x² - 20x +50 - 18
f(x) = x² - 10x +16
∴ x² -10x + 16 = 0
x² - 8x - 2x + 16 = 0
x(x-8) -2(x-8) = 0
(x-2) = 0 and (x-8) = 0
∴ x = 2 and x = 8
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Related Questions
At a certain zoo, the average mass of one blue whale is measured to be 190000 kilograms. Use scientific notation to express the mass of 125 blue whales.
PLEASE ONLY ANSWER IF YOU KNOW THE ANSWER, PLEASE DON'T JUST USE IT TO GET THE POINTS!!!!!!!!!!!!!
Answers
The weight of the 125 blue whales in the scientific notation will be 23.75 × 10⁶ kilograms.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
At a specific zoo, the typical mass of one blue whale is estimated to be 190000 kilograms. Utilize logical documentation to communicate the mass of 125 blue whales.
⇒ 190,000 × 125
Simplify the expression in the scientific notation, then we have
⇒ 190,000 × 125
⇒ 23,750,000
⇒ 23.75 × 10⁶ kilograms
The weight of the 125 blue whales in the scientific notation will be 23.75 × 10⁶ kilograms.
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Find the equation of a line parallel to y=−7+4x that passes through the point (-2,-1)
Answers
To find the equation of a line that is parallel to y=−7+4x and passes through the point (-2,-1), we can use the point-slope form of the equation of a line. The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Since the given line y=−7+4x is in slope-intercept form, we can find the slope by taking the coefficient of x, which is 4. This means that the slope of the line is 4.
We can then use the point-slope form to find the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1). Plugging in the values for the slope and the point, we get:
y - (-1) = 4(x - (-2))
Simplifying this expression gives us:
y + 1 = 4(x + 2)
Which simplifies to:
y = 4x + 5
So the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1) is y = 4x + 5.
The discount d is 50% of the list price L
Answers
The expression for the discount will be written as d = 0.5L.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the discount d is 50% of the list price L. The expression for the discount will be written as below,
Discount = 50% of the list price
d = ( 50 / 100) x L
d = 0.5L
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Gina puts $ 4500 into an account earning 7.5% interest compounded continuously. How long will it take for the amount in the account to grow to $ 5150?
Time in years =
Answers
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5150\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years \end{cases}[/tex]
[tex]5150=4500e^{0.075\cdot t} \implies \cfrac{5150}{4500}=e^{0.075t}\implies \cfrac{103}{90}=e^{0.075t} \\\\\\ \log_e\left( \cfrac{103}{90} \right)=\log_e(e^{0.075t})\implies \log_e\left( \cfrac{103}{90} \right)=0.075t \\\\\\ \ln\left( \cfrac{103}{90} \right)=0.075t\implies \cfrac{\ln\left( \frac{103}{90} \right)}{0.075}=t\implies\stackrel{\textit{about 1 year and 291 days}}{ 1.8\approx t}[/tex]
Select all the correct locations on the table.
Classify each situation as an exponential growth, exponential decay, or linear relationship.
A catering company purchased a delivery van
for $25,000. After 2 years, the value of the van
was $17,500. After 4 years, the value of the van
was $12,250.
At the beginning of the day, a laptop had 100%
battery life. After 3 hours, the laptop had 60%
battery life. After 6 hours, it had 20% battery life.
A tiger reserve had an initial population of
20 tigers. After 5 years, the population was
30 tigers. After 10 years, the population was
45 tigers.
exponential growth
exponential decay
linear
Answers
The required answer choices are (i)exponential decay (ii) linear and (iii) exponential growth
What are exponential growth and exponential decay?
Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously.
From question,
1) The first question is like, initially delivery van price is $25,000 after 2 years, the value of the van becomes $17,500
This means it is decaying. The difference between the initial price and after 2 years price is $7500.
To be linear, further after 2 years, or from start after 6 years, the price should be $10000. But it is given to be $12250.
Thus exponential decay.
2) In the second, Initially, a laptop had 100% battery life. After 3 hours, the laptop has 60% battery life. Thus the loss in 3 hours is (100 - 60) = 40%.
After 4 hours, the loss is (60 -20) = 40%
As the loss is the same in equal intervals of time, the decay is linear.
3) In the third one, A tiger reserve had an initial population of 20 tigers.
After 5 years the population was 30 tigers, thus the growth is (30-20) =10.
After 10 years, the population was 45 tigers. Thus the growth is (45-30) = 15.
Thus the increase is non-linear, and so is exponential growth.
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Sum of -5a + 6 and 3a + 2
Answers
Answer:
:)
Step-by-step explanation:
-5a + 6 + 3a + 2
Combine like terms:
-5a + 3a + 6 + 2
2a + 8 is your answer, you can't simplify it further
----------------------------------------------------------------------------------------------------------
If you want to solve for the a value:
-5a + 6 = 3a + 2
Subtract 2 from both sides
-5a + 6 = 3a + 2
- 2 - 2
-5a + 4 = 3a
(The +2 and -2 cancel each other out, it makes 0)
Add +5a to both sides
-5a + 4 = 3a
+5a +5a
(The -5a and +5a cancel each other out, it makes 0)
4 = 8a
Divide by 8 on both sides
4/8 (OR 1/2 OR 0.5) = a
Thanks for reading my ted talk lol pls mark as brainliest and give lots of points i need them lol help a girl out!!
-5a + 3a = 2a
6+2 = 8
make equation
2a + 8
John Morse corporation buys a van for $16,000. The estimated life of the van is four years. The residual value of the van is $4,000. After two years, the van is sold for $8,000. What was the difference between the book value and the amount received from selling the van if John used the straight-line method of depreciation?
A.$4,000
B. $12,000
C. $8,000
D. $2,000
Answers
The difference between book value and the amount received is $2000
What was the difference between the book value and the amount received ?
van cost = $16000
Estimated life= 4 years
Residual value= $4000
using straight line method of depreciation
Depreciation per year= 16000-4000/4= 3000
Therefore book value after two years = $16000- 2*3000= $10000
Selling price of book after 2 years= $8000
hence the difference between book value and the amount received
10000-8000= $2000
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Select the correct answer. Solve for x. x2 + 4x - 21 = 0 A. -3, -7 B. -3, 7 C. 3, -7 D. 3, 7
Answers
Answer:
Answer: the correct option is(C) 3, -7.
Step-by-step explanation:
Cailen needs at least $150 to buy an X-box. She earns $15 for each lawn she mows and has $30 in savings. Write an inequality to determine how many lawns Cailen must mow to buy an x-box. How many lawns must she mow to buy the x-box?
Answers
total = 15x + 30
EDIT: She has to mow 8 lawns. I didn't read the question
there you go its that simple
Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15
Answers
After solving the given equation, we know that the value of c is -11.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
Let's learn more about math equations in this tutorial.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
Sc, we have the equation:
3c + 7 = c - 15
Now, calculate this equation for c as follows:
3c + 7 = c - 15
3c - c = -15 - 7
2c = -22
c = -22/2
c = -11
Therefore, after solving the given equation, we know that the value of c is -11.
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Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15. What is c in this situation?
Which of the following statements is correct based on the number line below?
-8
-6
A
B
C
D
-4 -2
P
200
808
Q
0 2 4
6
√68 is to the right of Point Q because it is less than 8.
√68 is between points P and Q because it is less than 0 and greater than 8.
√68 is between points P and Q because it is greater than 0 and less than 8.
68 is to the right of Point Q because it is greater than 8.
Answers
It’s greater than 8 so it would be to the right of Q
Use the formula A=P\left(1+r/n)^nt to solve the compound interest problem.
Find how long it takes a 1700$ investment to earn 500$ interest if it is invested at 2% interest compounded quarterly.
500$ interest will be earned in approximately years. (Round to the nearest tenth.)
Answers
It will take 12.91 years to earn $ 500 in interest
What is Compound interest:
Compound interest refers to the interest added to a loan or deposit. It is the concept that we employ every day on a regular basis. Amounts are based on both the principal amount and Rate of interest when calculating compound interest.
The formula used for
Amount, A = P(1+r/n)^ntP = Principal amount
r = Rate of interest
n = Number of compounds in a year
t = Time period in years
And the formula for
Compound Interest, C.I = A - P
Here we have
Principal amount = 1700,
Rate of interest = 2% = 2/100 = 0.02 on decimals
Given that compound interest gained = $ 500
Number of compounds = 4 times
Let a be the time period
By the given formula,
Amount, A = 1700(1+0.02/4)^4t
= 1700(1+0.005)^4t
= 1700 (1.005)^4t
Compound interest = 1700 (1.005)^4t - 1700
From the given data,
Compound interest = $ 500
=> 1700 (1.005)^4t - 1700 = 500
=> 1700 (1.005)^4t = 2200
=> (1.005)^4t = 1.294
Take logs on both sides
=> log (1.005)^4t = log 1.294
=> 4t log (1.005) = log (1.294)
=> 4t = log(1.294)/log(1.005)
=> 4t = 0.111934276/ 0.00216606176
[ Use calculator for log(1.294) and log(1.005) ]
=> 4t = 51.6764012
=> t = 12.9191003
=> t = 12.91
Therefore,
It will take 12.91 years to earn $ 500 in interest
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From the graph, estimate what numbers should go into the empty cells in the first two columns. Do not complete the columns on the right of the dividing line.
Answers
The first two columns of the table, considering logarithms, are completed as follows:
2 - 10^0.3.5 - 10^0.7.9 - 10^(0.95).4 - 10^(0.6).2.51 - 10^(0.4).How to complete the table?The table is completed in this problem applying the logarithms.
This is because on the first column we had that:
10^(0.3) = 2, which means that log10(2) = 0.3.
(log10(x) represents the logarithm of base 10 of x).
For the second row, the decimal approximation is found applying the power of 10^0.7, hence:
10^0.7 = 5.
For the third and fourth rows, to obtain the power of 10 expression, we need to calculate the logarithms of these numbers, as follows:
log10(9) = 0.95.log10(4) = 0.6.Hence the power of 10 expressions are given as follows:
9 = 10^(0.95).4 = 10^(0.6).For the fifth row, we just need to calculate the exponential expression, hence:
10^(0.4) = 2.51.
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50 POINTS URGENT!
Choose the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power end quantity all raised to the negative third power.
Group of answer choices
−76
1 divided by 7 raised to the third power
negative 1 divided by 7 raised to the sixth power
718
Answers
Answer:
1 divided by 7 raised to the third power
Step-by-step explanation:
To find the equivalent expression, we can start by applying the rule for multiplying powers with the same base:
(7^(-2)) * (7^3) = 7^(-2+3) = 7^1 = 7
Then, we can apply the rule for raising a power to a power:
7^1 = (7^1)^(-3) = 7^(-3)
Finally, we can apply the rule for raising a number to a negative power:
7^(-3) = 1 / (7^3) = 1 / 343 = 1/7^3
Therefore, the equivalent expression is 1 divided by 7 raised to the third power.
3. Diana uses 30 grams of coffee beans to
make 48 fluid ounces of coffee. When
company comes she makes 96 fluid ounces of coffee. How many grams of coffee
beans does Diana use when company comes?
A. 160
B. 60
C. 98.2
D. 14.4
Answers
Answer:
Step-by-step explanation:
The grams of coffee beans Diana uses when the company comes is:
62.5 grams
Evaluate the following:
Logc1 = ?
Answers
The given logarithmic expression can be evaluated as Logc1 = 0.
What is Logarithm?Logarithm function is defined as the inverse of the exponential function.
If a^(b) = c, then b = log(c) at the base of a.
Logarithm of any number is always positive.
For negative numbers, the logarithm are complex numbers.
The given expression is Logc1.
It implies that it is the logarithm of 1 with c as a base.
Sine, the logarithm of 1 to any base is equal to zero, the given expression can be evaluated as follows,
Logc1 = 0
Hence, the value of the given expression is 0.
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what is (3z+1)+(1+7z)
Answers
Answer:
10z + 2
Step-by-step explanation:
combine the like terms
3z + 7z = 10z
1 + 1 = 2
10z + 2
1. Without solving, explain why the two linear systems below have the same solution. 4x + 2y = 26 x+y=8 4x + 2y = 26 -2x - 2y = -16
Answers
Answer
The first equation is the same (4x+2y=26), so we only need to compare the second equation. Just by looking at the second equation, you can see that x+y=8 and -2x - 2y = -16 are the same equation because -2 is multiplied to both sides of the equation x+y=8.
help meeeeeeeeeee pleaseee
Answers
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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The expected return on HiLo stock is 13.69 percent while the expected return on the
market is 11.5 percent. The beta of HiLo is 1.3. What is the market risk premium?
Answers
The risk-free rate of return on Hilo stock is 1.58%
What is the market risk premium?
Expected return on the stock=risk free rate beta x (expected market return-risk free rate)
14.08%=risk free rate+1.26 x (11.5%-risk free rate)
14.08%=risk free rate+14.49%-1.26 x risk free rate
0.41=0.26 x risk-free rate
risk-free rate=[tex]\frac{0.41}{0.26} %=1.58%[/tex]%=1.58%
The hazard-free price is the price of going back offered by means of funding that carries 0 risks. each investment asset incorporates a few degrees of threat, however small, So the risk-free price is something of a theoretical concept. In practice, it is taken into consideration to be the hobby price paid on short-time period government debt. the risk-free rate threat-unfastened price of going back no longer genuinely exists, as each investment carries at least a small quantity of hazard.To calculate the actual chance-unfastened charge, subtract the inflation rate from the yield of the Treasury bond matching your funding duration. Crucial banks control the threat-loose fee – nicely understood as the yield on short-term authorities’ payments.That is a risk-free rate fact of financial life but not one that we frequently think about. The capital asset pricing model and present-day portfolio idea take the danger-loose price as “given” instead of as “determined”.To learn more about risk-free rates visit here:
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i have no idea how to do this can anyone help
Answers
The long term behavior of the rational function f(x) = (x² - 3) / (x³ + 2) is 0, for the rational function g(x) = (x³ - 3) / (x³ + 2) is 1 and for the rational function h(x) = (x⁴ - 3) / (x³ + 2) does not exist.
How to determine the long run behavior of a rational function
In this case we find three rational functions, that is, functions of the form:
m(x) = p(x) / q(x)
Where:
p(x) - Function numerator.q(x) - Function denominator.Please notice that both numerator and denominator are polynomic functions, the long run behavior of the function depends on the grades of numerator and denominator according to these rules:
If the grade of the numerator is greater than the grade of the denominator, then long run behavior is divergent as x → ± ∞.If the grade of the numerator and the grade of the denominator are the same, then the function tends to a / b as x → ± ∞, where a and b are the lead coefficients of the numerator and the denominator, respectively.If the grade of the numerator is less than the grade of the denominator, the function tends to be 0 as x → ± ∞.Now we proceed to analyze the long run behavior of each rational function:
Case 1: f(x) = (x² - 3) / (x³ + 2)
Grade of numerator: 2, grade of denominator: 3
Result: 0
Case 2: g(x) = (x³ - 3) / (x³ + 2)
Grade of numerator: 3, grade of denominator: 3
Result: 1
Case 3: h(x) = (x⁴ - 3) / (x³ + 2)
Grade of numerator: 4, grade of denominator: 3
Result: N / A
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WILL MARK BRAINLIEST PLEASE HELP ME ‼️‼️‼️‼️‼️‼️
NEED #13 AND #14 ‼️‼️
PLEASE HELP ME I NEED THIS FINISHED ASAP IM DOING OVERDUE ASSIGNMENTS FOR MATH I NEED THIS PELASE
Answers
Answer:
Step-by-step explanation: Q13 Find the perimeter of the shape
42x *2=84x
72x*2=72x
Perimeter=84x+72x=156x
Q14 Find the perimeter of the shape just add up 3x +(4x+8)+3(x-2)
=3x+4x+8+3*x+3 *-2
=3x+4x+8+3x-6
=3x+4x+3x+8-6......add together like terms and number terms
=10x+2
Answer:
13.) 156x
14.) 10x + 2 or 2( 5x + 1)
Step-by-step explanation:
13.)perimeter of a parallelogram is
p = 2(a + b)
P = 2( 36x + 42x)
P = 2( 78x )
P = 156x
14.) perimeter of a scalene triangle
P = a + b + c
P = 3x + 3(x – 2) + 4x + 8
P = 3x + 3x –6 + 4x +8
P = 6x + 4x –6 + 8
P = 10x + 2
in factorise form
P = 2(5x + 1)
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If you sold 30% of a business for 500 dollars how much is the bussnis worth
Answers
it would be 1600 i hope this helps
26034 i hope this help man pls pls
What is an equation of the line that passes through the points (-4, 8)(−4,8) and (6, 3)(6,3)
Answers
Answer:
y=-1/2x+6
Step-by-step explanation:
slope: -5/10 = -1/2
y=mx+b
y=-1/2x+b
substitute points to find b: 8=-1/2(-4)+b
8=2+b
6=b
Solve the equation -3.98=x-11.24
Answers
x = 7.26
Step-by-step explanation:How to solve your problem:1. Add 11.24 to both sides
-3.98 = x - 11.24
-3.98 + 11.24 = x - 11.24 + 11.24
2. Simplify
Add the numbers:
-3.98 + 11.24 = x - 11.24 + 11.24
7.26 = x - 11.24 + 11.24
Add the numbers:
7.26 = x - 11.24 + 11.24
7.26 = x
Move the variable to the left:
7.26 = x
x = 7.26
Solution:
x = 7.26
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Answer:
x = 7.26
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.
First, add 11.24 to both sides of the equation:
-3.98 = x - 11.24
-3.98 (+11.24) = x - 11.24 (+11.24)
Next, simplify.
11.24 - 3.98 = x
x = 7.26
x = 7.26 is your answer.
~
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Find a rectangular equation for the plane curve defined by the parametric equations.
X = t + 4, y = t^2 ; - ∞ < t < ∞
Answers
Answer:
[tex]y=x^2-8x+16[/tex]
Step-by-step explanation:
[tex]x=t+4 \implies t=x-4 \\ \\ y=(x-4)^2=x^2-8x+16[/tex]
Insert a monomial such that each expression can be rewritten as the square of a sum or the square of a difference.
0.01 b²+.....+100 c²
0.01 b²+____+100 c²
Answers
The monomial that completes the expression 0.01 b²+.....+100 c² is 2bc
How to determine the monomial that completes the expression?From the question, we have the following parameters that can be used in our computation:
0.01 b²+.....+100 c²
Complete the expression with a variable
So, we have
0.01 b² + x + 100 c²
The given terms of the expression are factors/multiples of 10
By trial and error, we make use the following representation
0.01 b² + x + 100 c² = (0.1b + 10c)²
Expand the expression
0.01 b² + x + 100 c² = 0.01 b² + 2bc + 100 c²
Evaluate the like terms
x = 2bc
Hence, the monomial is 2bc
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olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%.If she has a 92 test average and 100% HW average, what must her quiz average be? Let x = the average of the
Answers
Olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%. The quiz average is 82%.
What do you mean by Average?It is forming the outcome of multiplying the total of multiple quantities by their sum and then dividing this result by the number of quantities
Given,
She has test count = 55%,
quizzes count = 30%,
homework counts = 15%
If she had
test count = 92%
Homework counts = 100%
quizzes count = ?
Let x be the test count
x = (90 - (0.55(92) + 0.15(100)))/0.30x
= 82
Olivia must have an 82 average on quizzes in order to have a 90 average in algebra.
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The expression (4k + 8)/4 simplifies to an expression of the form ak+b where a and b are integers. find a/b.
Answers
If the expression (4k + 8)/4 simplifies to an expression of the form ak + b, then the value of a/b is 1/2
The expression is (4k + 8) / 4
The expression is the mathematical statement that consist of the different variables, numbers and the mathematical operator. The mathematical operators are addition, subtraction, division and multiplication.
The given expression is (4k + 8)/ 4
Solve the expression
(4k + 8) / 4 = 4k/4 + 8/4
Divide the terms
=k + 2
The result is in the form of ak + b
The value of a = 1
The value of b = 2
The value of a/b = 1/2
Therefore, the value of the expression a/b is 1/2
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"Question 60
Find the probabilities below using a standard 52 card deck.
Answers
By using the concept of probability, it can be calculated that-
1) P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]
5) P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
1) Number of ace card = 4
Number of '5' card = 4
P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]
= [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)
Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]
P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) Number of black coloured even numbered card = 10
Number of even numbered card = 20
Number of card of black colour = 26
P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]
= [tex]\frac{36}{52}[/tex]
5) Number of face cards of diamond = 3
P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
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