The domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
We are given the two functions as:
f (x) = x - 4
g (x) = x² - 16
Now, first, we need to subtract f (x) from g (x).
So, we get that:
g (x) - f (x) = x² - 16 - (x - 4)
g (x) - f (x) = x² - 16 - x + 4
g (x) - f (x) = x² - x - 12
Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.
Therefore, we get that the domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
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round up 1.237 to the nearest hundredths
Answer:
1.24
Step-by-step explanation:
To round 1.237 to the nearest 100th ( you have to know the thousandth one. which the value is 1.237, ) which is 7 and equal to or more than 5. Therefore, the hundredths value of 1.237
if the mass is 12g and the volume is 13cm3 what is the density
[tex] \rho = \frac{mass}{volume} = \frac{12}{13} \approx0.923 \: g.cm {}^{ - 3} [/tex]
10. Three math teachers went to Office Depot to buy school supplies. Mr. Smith bought nine boxes of
pencils, three boxes of markers, and twelve packages of notebook paper for $45.75. Ms. Santana
purchased five boxes of pencils, six boxes of markers, and eight packages of notebook paper for
$41.50. While Mrs. Baker spent $128 on twenty boxes of pencils, four boxes of markers, and fifty
packages of notebook paper.
Which of the following systems of equations can determine the price of these items individually?
System of equation are,
9x + 3y + 12z = $45.75
5x + 6y + 8z = $41.50
12x + 4y + 50z = $128
Where, x is number of boxes of pencil,
y is number of boxes of markers.
z is number of packages of notebook paper.
What is System of equation?
System of equation is two or more equations to be solved together. For a system to have a unique solution, the number of equations must equal the number of unknowns.
Now, Let number of boxes of pencil = x
Number of boxes of markers = y
Number of packages of notebook paper = z
Since, Mr. Smith bought nine boxes of pencils, three boxes of markers, and twelve packages of notebook paper for $45.75.
Hence, In expression is written as;
9x + 3y + 12z = $45.75
Ms. Santana purchased five boxes of pencils, six boxes of markers, and eight packages of notebook paper for $41.50.
Hence, In expression is written as;
5x + 6y + 8z = $41.50
Mrs. Baker spent $128 on twenty boxes of pencils, four boxes of markers, and fifty packages of notebook paper.
Hence, In expression is written as;
12x + 4y + 50z = $128
So, System of equation are,
9x + 3y + 12z = $45.75
5x + 6y + 8z = $41.50
12x + 4y + 50z = $128
Where, x is number of boxes of pencil,
y is number of boxes of markers.
z is number of packages of notebook paper.
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20% of x is 15. What is x% of 120
Answer: x% of 120=3.6
Step-by-step explanation:
20% of x is 15---- .20*15=3, therefore x=3.
3%=0.03, 0.03*120=3.6
If x and y vary directly and y is 40 when x is 5, find y when x is 6.
The area of the rectangular arena can be represented as A = (8y2 - 18y) square feet.
Here, we are given the dimensions of a rectangular arena, which are as follows-
Length = 4y - 9 feet
width = 2y feet
The area of a rectangle is given by the formula-
Area of a rectangle = length x breadth
Thus, in this case, area (A) can be calculated as follows
A = (4y - 9) * 2y
Now, we simplify the equation-
A = (4y)(2y) - 9(2y)
A = 8[tex]y^{2}[/tex] - 18y
Thus, the area of the rectangular arena can be represented by the following equation- A = (8[tex]y^{2}[/tex] - 18y) square feet.
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If f(x) = 2x- + 1 and g(x) = x - 7, find (f- g)(x).
Answer:
hope this helps you
(f-g)(x)=2x+1-(x^2-7)
(f-g)(x)=2x+1-x^2+7
answer : (f-g)(x)= -x^2+2x+8
Brandon has a jar of quarters and dimes with a total value of $5.95. The number of quarters is 5 less than twice the number of dimes. How many quarters and how many dimes does Brandon have?
The quarters and dimes that Brandon have will be 13 quarters and 9 dimes.
How to illustrate the information?Based on the information given, the appropriate equation will be:
0.25q + 0.10d = 5.95 .... i
q = 2d - 5 .....
q = quarter
d = dime
From equation i, multiply through by 100
25q + 10 = 595
Put equation ii into i
25q + 10d = 595
25(2d - 5) + 10d = 595
50d - 125 + 10d = 595
Collect like terms
60d = 595 + 125
60d = 720
Divide
d = 720/60
d = 9
q = 2d - 5
q = 2(9) - 5
q = 18 - 5 = 13
Therefore, the quarters and dimes that Brandon have will be 13 quarters and 9 dimes.
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Let f(x)=2x-3. Write a function g whose graph is a reflection in the y axis of the graph of f
25%x4000=?
With explanation, please
Answer:
1,000
Step-by-step explanation:
25% as a decimal is .25
.25 x 4000
1,000
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{25\% \times 4,000}\\\\\mathsf{= \dfrac{25}{100}\times 4,000}\\\\\mathsf{= \dfrac{25\div25}{100\div25}\times \dfrac{4,000}{1}}\\\\\mathsf{= \dfrac{1}{4}\times \dfrac{4,000}{1}}\\\\\mathsf{= \dfrac{1\times4,000}{4\times1}}\\\\\mathsf{= \dfrac{4,000}{4}}\\\\\mathsf{= 4,000\div4}\\\\\mathsf{= 1,000}\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{1,000}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex] Jan invests $800 at a rate of 3% per year simple interest
Calculate the value of her investment at the end of 4 years.
first we need to know 3 percent of 800.
0.03 times 800 = 24.
we get about 24 interest every year.
now for four years. 800 + 24 = 824.
824 times 4(implying four years) = $3296
The value of her investment at the end of four years is $3296
find three consecutive odd integers such that the third is 9 more than twice the sum of the first and second
Answer:
Step-by-step explanation:
let the three consecutive odd numbers be x,x+2,x+4
9+x+4 = 2(x+x+2)
thus x =
Divide and simplify. ∛64 x⁹ y³ / ∛8 x³
Solving the problem by Dividing and simplifying we have as a result 2x⁶y³
What is a division?A division is a basic mathematical operation, which has the purpose of dividing a number or element into two or more equal parts, as follows:
Dividend |_divisor
Divisions can also be expressed as a fraction as : a/b
What is simplification?Simplification is a process of reducing terms to expressions, which do not generate changes or values.
The algebraic expression we will divide and simplify to its smallest expression is:
∛64x⁹y³ / ∛8 x³
We solve the cube roots and substitute results, to split terms
∛64 = 4∛8 = 24x⁹y³ / 2x³
we can see that it is an expression that has two variables
2x⁹⁻³y³
2x⁶y³
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5(10h²-20h -30) what’s the answer it’s dueee today
I could be wrong, but your answer should be: [tex]50h^2-100h-150[/tex].
--------------------------------------------
Hope this helps!
Have a great day and God bless! :)
Answer:
[tex]50h^{2} -100h -150[/tex]
Step-by-step explanation:
Assuming that h has no defined value, all we have to do here is multiply every defined number(non-variable numbers) in the parentheses here by 5.
[tex]5(10h^{2} -20h -30)[/tex] Given
[tex]50h^{2} -100h -150[/tex] 5x10=50, 5x(-20)=-100, and 5x(-30)=-150
a fruit salsa recipe calls for 2 cups finely chopped pineapple and 4 cups of finely chopped strawberries. isaiah only has 1 cup of pineapple. He reasons that because he subtracted 1 cup of pineapple he needs to use 3 cups of strawberries. is his reasoning correct? Explain.
The reasoning isn't correct.
How to explain the information?It should be noted that the fruit salsa recipe calls for 2 cups finely chopped pineapple and 4 cups of finely chopped strawberries
This implies that the ratio is:
= 2/4
= 1/2
= 1:2.
Therefore when Isaiah only has 1 cup of pineapple, the appropriate strawberry will be:
= 1 × 2 = 2
He's wrong as he doesn't need 3 cups.
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The scale drawing is a map of the campus of Central Middle School. The school board needs to know
the distance from the art room to the gym in order to build a walkway.
What is the scale factor from the map to the
actual school?
scale factor =?
Answer:Scale factor is 10 , the second part is 50
Step-by-step explanation:
what is 2.34 written as a percentage
Answer:
23.4%
Step-by-step explanation:
10 = (2.34 / 10) x 100% = 23.4%.
I’m slow asl bro istg help
Answer:
Area = 1725 ft²
Step-by-step explanation:
In this question, we have to calculate the area of the trapezoid. As mentioned in the hint, the formula for the area of a trapezoid is:
[tex]\boxed{\mathrm{Area = \frac{b_1 + b_2}{2} \times h}}[/tex],
where [tex]\mathrm {b_1}[/tex] and [tex]\mathrm {b_2}[/tex] are the two parallel bases of the trapezoid, and h is the height of the trapezoid.
As we can see in the diagram the two bases are 50 ft and 65 ft respectively, and the height is 30 ft. Using this information and the formula above, we can calculate the formula of the trapezoid:
[tex]\mathrm{Area = \frac{(50 + 65)\: \mathrm{ft}}{2} \times 30 \: \mathrm{ft}}[/tex]
[tex]= \frac{115 \: \mathrm {ft}}{2} \times 30 \: \mathrm{ft}[/tex]
[tex]= \bf 1725 \: ft^2[/tex]
Therefore, the area of the lawn is 1725 ft².
I've tried to solve this but I am still puzzled on what to do.
You are solving a measurement problem where the numbers 5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 are multiplied. How many significant digits should the product have?
A. 5
B. 3
C. 2
D. 1
Using scientific notation, the number of significant digits of the product is given as follows:
B. 3.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
When two numbers in scientific notation are multiplied, we have that:
The bases are multiplied.The power of 10 is kept.The exponents are added.For this problem, the product is given by:
[tex]5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3[/tex]
Multiplying the bases and adding the exponents, we have that:
[tex]5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3 = 5.2187 \times 2.05 \times 3.4 \times 10^{-3 + 7 + 3} = 42.8 \times 10^7[/tex]
42.8 has to be divided by 10 to assume for the base have only one digit, thus, to compensate, we have to add one to the exponent(equivalent to multiply by 10), hence:
[tex]42.8 \times 10^7 = 4.28 \times 10^8[/tex]
Hence, considering the rounding, the number has 3 significant digits(4, 2 and 8), and option B is correct.
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help me my son wont leave me alone!
Answer:
190 square feet
Step-by-step explanation:
25×4 + (25-5×2) × (10-4) = 25×4 + 15×6 = 100+90 = 190
check if each of the following equalities is true for all value of the variables (1-2b)(1-5b+b^2)+(2b-1)(1-6b+b^2)=b(1-2b)
The check done confirmed that the equality is true since the value arrived at while solving the expression is same as the given value
How to check if the equalities is true for all value of the variablesGiven data
[tex](1-2b)(1-5b+b^{2} )+(2b-1)(1-6b+b^{2} )=b(1-2b)[/tex]
breaking the expansion into 2 we have
[tex]=(1-2b)(1-5b+b^{2} )[/tex]
[tex]=(1)(1)+(1)(-5b)+(1)(b^2)+(-2b)(1)+(-2b)(-5b)+(-2b)(b^2)[/tex]
[tex]=1-5b+b^2-2b+10b^2-2b^3[/tex]
[tex]=-2b^3+11b^2-7b+1[/tex]
expanding this [tex](2b-1)(1-6b+b^2)[/tex] gives:
[tex]=2b^3-13b^2+8b-1[/tex]
adding both equation gives
[tex]= -2b^3+11b^2-7b+1 + 2b^3-13b^2+8b-1[/tex]
[tex]= -2b^2 + b[/tex]
[tex]= b - 2b^2[/tex]
[tex]= b (1 - 2b)[/tex]
Since the expansion gave same value we can say that the equality is true
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Please help im stuck
The table represents the direct relationship y = - 3 · x. (Correct choice: C)
How to determine whether a table represents a direct relationship
Two variables have a direct relationship if and only if the following model is observed:
y ∝ x
y = k · x
Where k is the constant of proportionality.
The table may represent a direct relationship if and only if each ordered pair has the same constant of proportionality. Now we proceed to evaluate the table:
k₁ = - 3 / 1
k₁ = - 3
k₂ = - 9 / 3
k₂ = - 3
k₃ = - 15 / 5
k₃ = - 3
As k₁ = k₂ = k₃, then the table represents the direct relationship y = - 3 · x.
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Can anyone explain how to simplify the square root of 20, in a simple and detailed way?
Accoreding to the given statement,
The simple method to find the value of √20 is to factorise the number under the root.
What is Factorisation?The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.
According to the given value;
The prime factorisation of 20 = 2 x 2 x 5 = 2 2 x 5
Thus, here we can see, 20 is not a perfect square, because we cannot pair digit 5 after factoring 20.
Only 2 2 can be taken out of the root.
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The sum of 15 and the prodcut of 5 and z
the expression for the statement that is given will be 15 + 5 z.
We are given the statement that the sum of 15 and the product of 5 and z
We need to make the expression that represents the statement.
First we will find out that the product of 5 and z
So, we will multiply 5 with z.
We get that:
= 5 × z = 5 z
Now we have to find the sum of 15 and 5 z
For this, we will add both the numbers.
We get that:
= 15 + 5 z
Therefore. we get that, the expression for the statement that is given will be 15 + 5 z.
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When is a Fraction and ratio the same
it is actually 1:1 that is 1 all over one
2x-20 and x+20 that makes ab parallel
If the two angles corresponds, hence the value of x that makes them to be equal is 40
Lines and angles
An angle is a point where two lines meet or intersect
Using the diagram below such that if the line a and b are parallel to each other hence the given angles are corresponding angles.
Equate both angles
2x - 20 = x +20
Collect the like terms
2x - x = 20 + 20
x = 20 + 20
x = 40
Hence the value of x that will make both angles correspond is 40
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Compare square root of one hundred sixty and one hundred fifteen ninths using <, >, or =.
The comparison of the numbers are √160 > √115.1
How to compare the numbers?The numbers are given as
square root of one hundred sixty and one hundred fifteen ninths
Rewrite properly as
√160 and √115.11
By comparing the radical of both numbers, we have
160 and 115.11
160 is greater than 115.11
Hence, the comparison of the numbers are √160 > √115.11
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Help NEEDED PLEASE!!!!!!
Consider the sequence with first term 2 and second term 4. If these are the first two terms of a geometric sequence, what is the third term?
The third term of a given geometric sequence based on common ratio 2 is 8.
What is geometrical progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
Given a geometric sequence.
First term = 2
Second term = 4
Common ratio = Next term / previous term
Common ratio = 4/2 = 2
So,
Common ratio = Third term / second term
The third term = common ratio × second term
The third b = 2 × 4 = 8
Hence "The third term of a given geometric sequence based on common ratio 2 is 8".
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I need help with c and 3. I’ll give brainliest.
Answer:
This might help
Step-by-step explanation:
for C-The number of lines of symmetry in a regular polygon is equal to the number of sides.
for 3 I’m not as sure but all I know is that Y is greater than 90 degrees and x is also greater than 90 degrees
Are the ones with answers correct? I just want to make sure I’m right
Answer:
yes just make sure to pay close attention