Answer:
See below.
Step-by-step explanation:
So we know that:
[tex]f(x)=4x+8\text{ and } g(x)=2x-12[/tex]
First, know that:
[tex](f-g)(x)[/tex]
Is the same as:
[tex]=f(x)-g(x)[/tex]
Substitute:
[tex]=(4x+8)-(2x-12)[/tex]
Distribute:
[tex]=4x+8-2x+12[/tex]
Combine like terms;
[tex]=2x+20[/tex]
Thus:
[tex]f(g(x))=2x+20[/tex]
This is simply a linear equation.
Thus, the domain is all real numbers.
In interval notation, this is:
[tex](-\infty, \infty)[/tex]
The line $x = 4$ is an axis of symmetry of the graph of $y = ax^2 + bx + c.$ Find $\frac{b}{a}$.
Answer: b/a = -8
Step-by-step explanation:
When we have a quadratic equation:
y = a*x^2 + b*x + c.
The vertex of this function (and the axis of symetry) is located at:
x = -b/2a
Now, we know that the axis of symmetry is at x = 4.
then we have:
4 = -b/2a
And we want to find b/a.
Then we start with:
-b/2a = 4.
first we multiply by 2 in each side:
2*(-b/2a) = -b/a = 2*4 = 8.
now we multiply by -1 in each side:
-1*(-b/a) = b/a = -1*8.
Then we have: b/a = -8
If the marked price of an article is Rs. x, discount amount is
Rs. y and the VAT amount is Rs. 2, Calculate the selling
price of the article including VAT.
Answer:
Rs. (x - y + 2)
Step-by-step explanation:
The marked price is the price that a product is to be sold. The product can be sold at a discount which is below the marked price of the product.
The marked price of the article is Rs. X. The discount is Rs. y, therefore the article price = marked price - discount = x - y.
But since the article is sold with a VAT of Rs. 2, the VAT is added to the price, therefore the selling price of the article including VAT is Rs. (x - y + 2)
The San Andreas fault separates the pacific plates from the North America plate. The pacific plate moved northward relative to the North American plate at a rate of 5.7 cm/year. Currently LA and San Francisco are about 470km away from each other, how long will it take for LA and SF to be next to each other? Answer in years
Answer:
8.2 million years
Step-by-step explanation:
The time can be found from ...
time = distance/speed
time = (47.0×10^4 m)/(5.7×10^-2 m/yr) = 8.2×10^6 yr
It will take about 8.2 million years for LA to have the same latitude as SF.
__
The given numbers each have 2 significant digits, so the answer is appropriately rounded to 2 significant digits.
Point P is located at (−2, 7), and point R is located at (1, 0). Find the y value for the point Q that is located two over three the distance from point P to point R
Answer:
7/3
Step-by-step explanation:
The distances have the ratio ...
(Q -P) = (2/3)(R -P)
Q = P +(2/3)R -(2/3)P = (2R +P)/3
Qy = (2Ry +Py)/3 = (2·0 +7)/3 = 7/3
I'm really confused about this. Can I get some help?
If you had 6 million dollar and you divided that by 1 billion what would you get. Then once you find that multiply your answer by 10. What do you get.
Answer: You get 0.06 which is 6 cents in terms of money.
Step-by-step explanation:
6 millions could be written as 6,000,000 and 1 billion could also be written as 1,000,000,000 so using this set up a fraction to divide it.
[tex]\frac{6000000}{1,000,000,000}[/tex] = 0.006
0.006 * 10 = 0.06
45% of the pizzas in the freezer in the store are cheese pizzas. There are 120 pizzas in the
freezer. How many of them are cheese pizzas?
Answer:
54 cheese pizzas
Step-by-step explanation:
We know that there are 120 pizzas in the freezer, and 45% of them are cheese pizzas.
We want to find out how many cheese pizzas are in the freezer, so we should multiply 45% and 120.
45% * 120
Convert 45 % to a decimal. Divide 45 by 100 or move the decimal place 2 spots to the left.
45/100= 0.45 or 45.0 --> 4.5 ---> 0.45
0.45 * 120
Multiply 0.45 and 120
54
54 cheese pizzas are in the freezer.
si la economía produce actualmente dos unidades de armas y cuatro unidades de mantequilla cuál es el costo de oportunidad de aumentar la producción de mantequilla de 4 unidades 11 unidades
Answer:
0.36 %
Step-by-step explanation:
seria el 36 por ciento de aumento por que las dos cantidades divididas te daría a cero punto treinta y seis porciento más de las dos cantidades
Yoooo help
A ball is thrown starting at a time of O and a height of 2 meters. The height of the ball follows the function
H(t)= -4.9t^2 +25t +2. What is the height of the ball at each second from 0 to 5?
Answer:
0 - 1 - 2 - 3 - 4 - 5
2 - 22.1 - 32.4 - 32.9 - 23.6 - 4.5
Step-by-step explanation:
The function is:
H(t) = -4.9t^2 +25t +2Calculating the value of H for each value of t from 0 to 5
H(0) = 2H(1) = -4.9*1^2 + 25*1 + 2 = 22.1H(2) = - 4.9*2^2 + 25*2 + 2 = 32.4H(3) = -4.9*3^2 + 25*3 + 2 = 32.9h(4) = -4.9*4^2 + 25*4 + 2 = 23.6H(5) = - 4.9*5^2 + 25*5 + 2 = 4.5Correct answer choice is the 3rd one or C
Which of the following functions describes the sequence 4, –2, 1, –12, 14, . . .? A. f(1) = 4, f(n + 1) = –2f(n) for n ≥ 1 B. f(1) = 4, f(n + 1) = f(n) – 2 for n ≥ 1 C. f(1) = 4, f(n) = 12f(n + 1) for n > 1 D. f(1) = 4, f(n) = –12f(n – 1) for n > 1
Answer: D. [tex] f(1) = 4,\ \ f(n+1)=\dfrac{-1}{2}f(n) [/tex]
Step-by-step explanation:
The given sequence: [tex]4, -2,1,\dfrac{-1}{2},\dfrac14,....[/tex]
Here, first term: [tex]f(1)=4[/tex]
Second term: [tex]f(2)=-2[/tex]
Third term : [tex]f(3)=\dfrac{-1}{2}[/tex]
It can be observed that it is neither increasing nor decreasing sequence but having the common ratio.
Common ratio: [tex]r=\dfrac{f(2)}{f(1)}=\dfrac{-2}{4}=\dfrac{-1}{2}[/tex]
So, [tex]f(n+1)=\dfrac{-1}{2}f(n)[/tex] [as in G.P. nth term= [tex]a_{n+1}=ar^n[/tex]]
Hence, correct option is D. [tex] f(1) = 4,\ \ f(n+1)=\dfrac{-1}{2}f(n) [/tex]
Solve for x:
5x – 1 = x+ 27
Hey mate!
Question:
5x – 1 = x+ 27
Answer:
x=7
Step-by-step explanation:
Step 1:
5x-x=27+1
Step 2:
4x=28
step 3:
x=28÷4
step 4:
x=7
hope it helped you:)
Which Natural Numbers are not Integers?
Answer:
Step-by-step explanation:
fraction are not integers
Someone help me solve this expression please
Step-by-step explanation:
To solve, we have to remember PEMDAS (Parenthesis, Exponent, Multiply / Divide, Add or Subtract).
Here, the curly brackets act as parenthesis, so we solve that first.
• 3 + 7 = 10
Then, we multiply by 4.
• 10 • 4 = 40
Finally, we add 6 to 40.
• 40 + 6 = 46.
Our final answer: 46
Answer:
46
Step-by-step explanation:
We are asked to evaluate the expression. Remember to solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
[tex]6+4 * (3+7)[/tex]
Solve inside the parentheses. Add 3 and 7.
⇒3+7=10
[tex]6+4*(10)[/tex]
Multiply 4 and 10.
⇒4*10=40
[tex]6+40[/tex]
Add 6 and 40.
⇒6+40=46
[tex]46[/tex]
When the expression 6+4*(3+7) is evaluated, the result is 46.
In a city, the record monthly high temperature for March is 56 degrees Fahrenheit. The record monthly low temperature is -4 degrees Fahrenheit. What Is the range of temperature for March?
Answer:
60 degrees.
Step-by-step explanation:
In mathematics, a "range" is described as the difference between the lowest and highest numbers in a data set. To find the range, we must subtract. (This is what the word "difference" indicates in math)
56 - (-4) =
56 + 4 = 60 (the negative signs cancel out)
Thus, the range of temperature for March is 60 degrees :) Hope this helped!
God bless and stay safe.
Stronomers estimate the internal temperature of the sun is 15,000,000 K. What is 15,000,000 written in scientific notation? 1.5 x 10^8 1.5 x 10^8 1.5 x 1^7 1.5 x 1^7 1.5 x 1^6 1.5 x 1^6 1.5 x 1^ 5
Answer:
Scientific notation for 15,000,000
[tex] = 1.5 \times {10}^{7} [/tex]
Which function is not defined at 0? Please help urgent
Answer:
b and g
Step-by-step explanation:
a. is y = 0³ = 0
b. is y = ln(0), which is undefined because ln(x) is only defined for x > 0
c. is y = 1 / (1 + e^-0) = 1 / (1 + 1) = 1/2
d. is y = 0
e. is y = 0² = 0
f. is y = sin(0) = 0
g. is y = 1/0, which is undefined because division by 0 is undefined
h. is y = e^0 = 1
i. is y = |0| = 0
j. is y = √0 = 0
X-32>32+9x Thx help ASAP
Answer:
Step-by-step explanation:
hello :
x-32>32+9x
means : x-9x>32+32
-8x >64
dvid by :8 -x >8 .......continu
For altitudes up to 36,000 feet, the relationship between ground temperature and atmospheric
temperature can be described by the formula t = -0.0035a +g, in which t is the atmospheric
temperature in degrees Fahrenheit, a is the altitude, in feet, at which the atmospheric temperature is
measured, and g is the ground temperature in degrees Fahrenheit. Solve the equation for a. If the
atmospheric temperature is -17.4°F and the ground temperature is 40 °F, what is the altitude?
The equation for a is a =
If the atmospheric temperature is -17.4 °F and the ground temperature is 40 °F, then
a= feet.
Answer:
a=16400 feet
Step-by-step explanation:
t = -0.0035 a +g
-17.40 = -0.0035 a+40
-17.40-40=-0.0035a+40-40
-57.40=-0.0035a
a = -57.40/-0.0035
a=16400 feet
Which of the following is an irrational number? (1 point)
OO
O 0.100100010000...
14
O
O 1,483,292
Answer:
0.100100010000...
Step-by-step explanation:
becoz in irrational numbers decimal goes on forever
evaluate the expression
Answer: 85
Step-by-step explanation:
To solve this problem, we want to use the order of operations, or PEMDAS.
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
To be more specific, you evaluate the expression in the order from top to bottom. To clarify, it is multiply OR divide, depending on which comes first, left to right. This also applies to add OR subtract.
------------------------------------------------------------------------------------------------------------
20÷(5-3)+5²(3) [solve parenthesis]
20÷(2)+5²(3) [solve exponent]
20÷2+25(3) [solve multiply or divide, left to right]
10+75 [solve add or subtract]
85
Answer:
85
Step-by-step explanation:
To evaluate the expression, follow the rule of PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
[tex]20 \div (5-3) +5^2(3)[/tex]
Solve inside the parentheses first by subtracting 3 from 5.
5-3 = 2
[tex]20 \div (2) +5^2(3)[/tex]
Next, evaluate the exponent.
5² = 5*5= 25
[tex]20 \div 2+25(3)[/tex]
Next, multiply 25 and 3.
25 *3 =75
[tex]20 \div 2+75[/tex]
Then, divide 20 by 2.
20/2=10
[tex]10+75[/tex]
Finally, add 10 and 75.
[tex]85[/tex]
The expression [tex]20 \div (5-3) +5^2(3)[/tex] evaluated is 85.
Find the product. √3(5+√2) A)5√3+√5 B)5√3+√6 C)5√9 D)√15+√6
Answer:
B. [tex] 5 \sqrt{3} + \sqrt{6} [/tex]
Step-by-step explanation:
[tex] \huge\sqrt{3} (5 + \sqrt{2} ) = 5 \sqrt{3} + \sqrt{6} [/tex]
10. While at the beach, Daniel buys lunch for
his family from a food stand. He purchases
one hot dog for $2.50 and 3 hamburgers. If he
spent $ 13 total, write and solve an equation to
find h, the amount each hamburger cost.
Answer: Each hamburger cost $3.50
Step-by-step explanation:
He spent $13 in total and bought one hot dog for $2.50 and 3 hamburgers but we don't know the price of one hamburger so we could represent it by the equation,
2.50 + 3h = 13 Now solve for x
-2.50 2.50
3h = 10.50
h = 3.50
Check:
2.50 + 3(3.50) = 13
2.50 + 10.50 = 13
13= 13
}
ons Help
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Problem Solving
D A farmer watered 10/82 of a field. What decimal is
equivalent to the fraction of the field the farmer
watered?
type here
Answer:
0.1219512195122
Step-by-step explanation:
To write 10/82 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 10 by 82 what we write down as 10/82 and we get 0.1219512195122
what is half the sum of x and y decreased by one-third y as a algebraic expression
Answer:
1/2(x+y) - 1/3
Step-by-step explanation:
I think this may be the answer based on the info you've given
Answer:
[tex]\frac{1}{2}(x+y) - \frac{1}{3}y[/tex]
Step-by-step explanation:
We can translate these words into an expression by just reading them and interpreting them.
Half the sum of x and y.
We know that it's going to include [tex](x+y)[/tex], and if we're taking half of that, we multiply that by [tex]\frac{1}{2}[/tex], so [tex]\frac{1}{2}(x+y)[/tex]
We also know that one third of y will be multiplying y by [tex]\frac{1}{3}[/tex], so [tex]\frac{1}{3}y[/tex].
Since we are decreasing [tex]\frac{1}{2}(x+y)[/tex] by [tex]\frac{1}{3}y[/tex], there's a minus sign between the terms.
So, [tex]\frac{1}{2}(x+y) - \frac{1}{3}y[/tex].
Hope this helped!
3/2x+1 = 13
find x.
What is x?
Answer:
8
Step-by-step explanation:
Please write this as (3/2)x + 1 = 13.
Start the process of solving for x by subtracting 1 from both sides:
(3/2)x = 12
Eliminate the fractional coefficient by multiplying both sides by 2/3:
(2/3)(3/2)x = (2/3)(12), or
x = 8
QS bisects PQR. If PQS = 5x and RQS = 2x + 6, then what is PQR?
m PQR is____
HELP PLEASE
Answer:
20°
Step-by-step explanation:
i just did it. got it correct
73) Find the surface area. Don't forget your
label.
8 cm
10 cm
18 cm
8 cm
Answer:
512cm²
Step-by-step explanation:
1/2bh*2 = 1/2(4)(10)(2)=40
Each triangle is 40
18*8=144
Each rectangle is 144
144+144+144+40+40=512cm²
«
-7 1/3 written as a fraction is
Answer:
-22/3
Step-by-step explanation:
-22/3 is the answer as a improper fraction.
Step 1
Multiply the denominator by the whole number
3 × 7 = 21
Step 2
Add the answer from Step 1 to the numerator
21 + 1 = 22
Step 3.
Write answer from Step 2 over the denominator
22/3
Answer:
-22/3
Step-by-step explanation:
7x3= 21
Solve the equation. 1/4 + w = 6 1/3
Answer:
6.08333....
Step-by-step explanation:
.25 +w = 19/3
19/3=6.3333
6.3333-.25=6.08333....
Check:
.25+6.08333....=6.3333...
please help :) Which expression is equal to 6+4×5 ? A 10 times 5 B 6 plus 20 C 6 plus 9
Answer:
B)
Step-by-step explanation:
6 + 4*5 = 6 + 20
= 26
According to BODMAS, multiplication should be done and then addition
Answer:
B
Step-by-step explanation:
By pemdas - multiplication first
6+4x5
6+(20)
so, b - 6 + 20 is the answer