For the given equation, either 3x + 7 = 0 or x + 7 = 0
Now,
3x + 7 = 03x = -7 x = -7/3or
x + 7 = 0x = -7So, possible values of x is : -7 and -7/3
[tex](3x + 7)(x + 7) = 0 \\ \\ \\3x + 7 = 0 \\ \\ 3x = - 7 \\ \\ x = \frac{ - 7}{3} . \\ \\ \\ x + 7 = 0 \\ \\ x = - 7.[/tex]
Determine the domain of (g ∘ f)(x) if f (x) = x2 + x − 3 and g of x is equal to 1 over the quantity x plus 1 end quantity period {x ∈ ℝ| x ≠ −1} {x ∈ ℝ| x ≠ −2, 1} {x ∈ ℝ| x ≠ −2, −1, 1} {x ∈ ℝ}
The domain of gof(x) is {x ∈ ℝ| x ≠ −2, 1} .
What is domain?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.
given function:
f(x) = x² + x -3
g(x) = 1/x+1
Now, solving the equation
gof = g(f(x))
=g( x² + x -3)
=1/(x² + x -3)+1
=1/ x² + x -2
= 1/ x² +2x - x -2
= 1/ x( x+ 2) - (x +2)
=1/ (x+2)(x-1)
Hence, the domain of gof(x) is {x ∈ ℝ| x ≠ −2, 1} .
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Taylor's computer randomly generate numbers between 0 and 4, as represented by the given uniform density curve.
A graph titled Random number generated by computer has random number on the x-axis. A horizontal line is at y = one-fourth from 0 to 4.
What percentage of numbers randomly generated by Taylor's computer are less than 0.5?
12.5%
25%
50%
87.5%
Picture posted below
12.5% is the percentage of numbers randomly generated by Taylor's computer that is less than 0.5.
An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).
The percentage of numbers randomly generated by Taylor's computer are less than 0.5 is given by
P(0≤X≤0.5)
=[tex]\int_{0}^{0.5}\frac{1}{4}dx[/tex]
[tex]=\frac{1}{4}x|^{0.5}_{0}[/tex]
[tex]=\frac{1}{4}(0.5-0)[/tex]
[tex]=0.25(0.5)[/tex]
= 0.125
That is 12.5%
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Step-by-step explanation:
[tex]29 {}^{ \frac{x}{2} } [/tex]
[tex]((29) {}^{ \frac{1}{2} } ) {}^{x} [/tex]
The answer is A
little melinda has nickels and quarters in her bank she has 8 fewer than nickels she has 5.60 in the bank how many coins of each type does she have
Answer:
She has 20 coins in her bank, where she has 12 nickels and 8 quarters
Step-by-step explanation:
A quarter is 25 centsA nickel is 5 centsSince she has 8 fewer than nickels, we add 8 to the number of nickelsQ = N + 8, 25Q + 5N = 560
25(N + 8) + 5N = 560
25N + 200 + 5N = 560
25N + 200 - 200 + 5N = 560 - 200
30N = 360
30N / 30 = 360 / 30
N = 12 nickels
Finding amount of Quarters:
Q = N + 8 → Q = 12 + 8
Q = 20 quarters
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Sketch 0 = 11π/6 in standard position
Answer:
cuantos billetes de 100.son en .100000?
Mr. Tan, a manufacturer who produces
more medium-sized shirts than either
large-sized or small-sized T-shirts,
bases his decision on?
O A. Instinct
O B. Mean
O C. Median
O D. Mode
Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.
To determine whether Mr. Tan bases his decision on instinct, mean, median, or mode, we need to consider the given information that Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts.
Instinct refers to a natural or intuitive decision-making process that is not based on specific calculations or statistical measures. While Mr. Tan's decision-making process could involve some level of instinct, it is unlikely to be the primary basis for his decision.
The mean is the average value calculated by summing up all the values and dividing by the total number of values. However, the mean does not provide any information about the distribution of the sizes or the fact that Mr. Tan produces more medium-sized shirts.
The median is the middle value when the data is arranged in ascending or descending order. However, we do not have any information about specific values or the distribution of sizes, so we cannot determine the median.
The mode refers to the value or values that appear most frequently in a set of data. Since Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts, it implies that medium-sized shirts are the mode in his production. This suggests that Mr. Tan's decision is based on the mode, as he produces more shirts of this size than any other size.
Therefore, based on the given information, it can be inferred that Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.
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Given the functions, fx) = 3x-6 and g(x)= x² + 5x+7, perform the indicated operation. When applicable, state the
domain restriction.
f(g(x))
Hope this helps
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
I did this already
Based on the graph of g(x), on which intervals
are the function's values negative? Select all that
applv.
Answer:
[tex]\text{B}) \text{ } -3 < x < -1\\\text{D}) \text{ } 2 < x < \infty[/tex]
Step-by-step explanation:
The graph lies below the x-axis.
Which of the following would best be solved using completing the square?
2x^2 + 15x = 6
x^2 = 36
x^3 - 3x^2 + 4x - 12 = 0
x^2 - x - 20 = 0
Answer:
2x^2 +15x = 6
Step-by-step explanation:
the form of this equation makes it easier to use the completing the square method
P is a polynomial of degree 4 with three zeros: -1 and 2 are zeros of multiplicity one, and 3 is a zero with multiplicity two. If P(0) = 90, what is the lead coefficient of P ?
Answer:
[tex]P(x) = (x+1)(x-2)(x-3)^2 + 108[/tex]
Step-by-step explanation:
let me know if you want an explanation
(a) {(1)¹⁰⁰ + (−1)¹⁰¹+(2500)⁰} x2³
Answer:
8
Step-by-step explanation:
You should have this in mind , one raise to the power of any number is one and also any number with the power zero is 1.
{(1)¹⁰⁰ + (−1)¹⁰¹+(2500)⁰} x2³
= 1 - 1 + 1 × 8
= 1 - 1 + 8
= 1 +7
= 8
What is the inverse of f(x)=9x-3
Answer:
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x9+13 f - 1 ( x ) = x 9 + 1 3 is the inverse of f(x)=9x−3 f ( x ) = 9 x - 3
Answer:
y = x + 3/9
Step-by-step explanation:
Change f(x) y = 9x-3Solve for y +3 +3
x+3 = 9y = y=x+3/9
The number 900 is increased by 20% and then decreased by 20%. Find the new number.(the ans is 864 apparently:/ I need steps)
Step-by-step explanation:
if 900 is increased by 20% then
120/100×900=1080
Decreasing it by 20% then
80/100×1080=864
4. In 2010, the amount in Raja's account was 40 Lakhs. He debited 8000 in 2011, and in 2012, he debited 2,07,000. In 2013, he credited 1,16,000, and in 2014 he credited 12,000. How much more he has to credit to be worth what it was at at the start of 2010
Answer:
don't know is is mathematics or any other subject
Select the solution(s) of the original equation.
0 x = √√√2
x = 1
X=1
x = -1
0 *=-√√2
X = -1
DONE ✔
0000
Answer:
the first,second,forth and fifth.
Step-by-step explanation:
I got it off of edg.
What is the main difference between confirmatory and exploratory factor analysis? (CFA vs EFA)
O a. In CFA, SPSS is required to build the model
O b. In CFA, the researcher does not define the model
O c. In CFA, the researcher defines the model
O d. In CFA, factor rotation is required
Oe In CFA, there is no model
Answer:
in exploratory factor analysis all the measures variables are related to every legend variable but in confirmatory factor analyse CFA research 10 specifically the number of factors required in the data in which measures variable is related with talent variable
Sum of 1/2*3 +1/3*4 +1/4*5 ..1/99*100
Answer:
11∗2+13∗4+15∗6+⋯+199∗100=?
=(1−12)+(13−14)+(15−16)+⋯+(199−1100)
=(1+13+15+17+⋯+199)−(12+14+16+⋯+1100)
=(1+13+15+17+⋯+199)−12(1+12+13+⋯+150)
=∑k=15012k−1−∑k=15012k
Continue further.
This.is my question
Since we have given that
Measure of revolution = 360°
Now, the measure of [tex]\frac{3}{4}[/tex] of revolution.
So, it becomes,
[tex]\frac{3}{4}[/tex]×360
= 3 × 90
= 270
Hence, the measure of 3/4 of revolution is 270°.
Hope this helped and have a good day
Match each equation below with its solution(s).
1. x² =4
2.x² = -4
3.x² +2=0
4.x²-2=0
5.x² = -18
6.x²=18
8.x+2=0
7.x-2=0
+2i +3i√√2 +√√2 2 ±2 -2 ±i√√2 +3√√2
Drag each solution above to the matching equation below.
1.
2.
3.
4.
5.
6.
7.
8.
[tex]1) \pm 2 \\\\2) \pm 2i\\\\3) \pm i\sqrt{2}\\\\4) \pm \sqrt{2}\\\\5) \pm 3i\sqrt{2}\\\\6) \pm 3\sqrt{2}\\\\7) 2\\\\8) -2[/tex]
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
A and B
Step-by-step explanation:
Vertical angles are angles that are opposite of each other on two crossing lines.
They have equal angle measure.
When we look at the image, we can tell that, from the given options:
A. <LRA and <FRA and
B. <TRF and <NRL are vertical angles.
A merchant has 120 liters of oil of one kind, 180 liters of another kind, and 240
liters of the third kind. He wants to sell the oil by filling the three kinds of equal
capacity. What should be the greatest capacity of such a tin?
The merchant needs to fill 60 litres of all types of oils .
What is HCF ?
HCF is the highest common factor, it is the factor in common in more than two numbers.
It is given in the question that
A merchant has 120 litres of oil of one kind, 180 litres of another kind, and 240 litres of the third kind.
He wants to sell the oil by filling the three kinds of equal capacity.
To find the greatest capacity of such a tin , we have to find the highest common factor of the individual capacity.
120=2×2×2×3×5
180=2×2×3×3×5
240=2×2×2×2×3×5
HCF=2×2×3×5=60
The greatest capacity = 60 litres
So the merchant needs to fill 60 litres of all types of oils .
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9 is subtracted from 3 times the sum of 4 and 2.
Answer:
9
Step-by-step explanation:
This problem is represented below.
=3(4+2)-9
=3(6)-9
=18-9
=9
Please help me with this problem!
If you could please graph it that would be awesome!
The graph of the function is drawn. The open circle at -1 and 4 for -2x + 3.
The complete question is attached below.
What is a piecewise function?The function that is transformed into the number of pieces is known as piecewise function.
The piecewise function is given below.
[tex]f(x)=\left\{\begin{matrix}3x-5 & x\leq -1 \\\\-2x+3 & -1 < x < 4 \\\\2 & x\geq 4 \\\end{matrix}\right.[/tex]
The graph of the function is drawn.
The open circle at -1 and 4 for -2x + 3.
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The surface area of a cone is 250 square centimeters. The height of the cone is double the length of its radius.
What is the height of the cone to the nearest centimeter?
A.
10 centimeters
B.
20 centimeters
C.
15 centimeters
D.
5 centimeters
Answer: C
Step-by-step explanation:
just took it
The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.
Given that, the surface area of a cone is 250 square centimetres. The height of the cone is double the length of its radius.
We need to find what is the height of the cone to the nearest centimetre.
What is the surface area of a cone?The area occupied by the surface/boundary of a cone is known as the surface area of a cone. It is always measured in square units. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as a curved surface area.
If the radius of the base of the cone is "r" and the slant height of the cone is "l", the surface area of a cone is given as total surface area, T = πr(r + l) square units
Now, let the radius of a cone be x.
Then the height of the cone is 2x.
Slant height=√x²+4x²
=√5x
So, the surface area of cone=πx(x+2.24x)
⇒250=3.14 × 3.24x²
⇒x²=24.57
⇒x=4.95≈5 centimetre
So, height=2x=10 centimetre
The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.
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What expression is equivalent to ten square root five
The expression 10√5 can be written as √500 because √(10×10) = 10 option (A) √500 is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
= 10√5
We can write the above equation:
= √(10×10×5)
Because √(10×10) = 10
= √(100×5)
= √500
Thus, the expression 10√5 can be written as √500 because √(10×10) = 10 option (A) √500 is correct.
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Consider the given density curve.
A density curve is at y = StartFraction 1 Over 8 EndFraction and goes from negative 10 to negative 2.
What is the value of the median?
–10
–7
–6
–2
Picture posted below…
Answer: -6
Step-by-step explanation:
[tex]\frac{-10-2}{2}=\boxed{-6}[/tex]
The Median of the density is -6.
An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).
It is clearly visible from the uniform density curve given in the question that the median of the population density is -6.
Because the area to the left and right of the density curve is the same.
Hence, the Median of density is -6.
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Another job is advertising leaflets printed on sheets of A4 paper (210 x 297 mm).
The sheets are then folded into thirds as shown.
What are the measurements in millimetres of each folded leaflet?
5%3×4+14-15 answers thes questions
How can the logarithmic expression be rewritten?
Select True or False for each statement.
Answer:
True, True, False
Step-by-step explanation:
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ALMNOPQ?
Check all that apply.
M
AA
A. HL
B. SAS
C. AAS
D. ASA
E. LA
F. LL
Answer:
It has been a while. I think it is ASA and AAS
The triangles ΔLMN and ΔOPQ are congruent triangles by the ASA and AAS postulates
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔLMN
Let the second triangle be represented as ΔOPQ
Now , the measure of ∠MNL = 90°
The measure of ∠PQO = 90°
And , the measure of side MN = measure of side PQ
And , the measure of ∠MLN = measure of ∠POQ
So , the two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Therefore , the triangles are congruent by AAS and ASA theorems
Hence , the ΔLMN and ΔOPQ are congruent triangles
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Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)
2. Jay Smith deposited $5,000 into an annuity due at the beginning of each quarter for 3 years at 6%
compounded quarterly.
Answer:
value: $66,184.15interest: $6,184.15Step-by-step explanation:
The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.
__
formulaThe formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...
FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148
FV ≈ 66,184.15
calculatorThe attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.
__
a)The future value of the annuity due is $66,184.15.
b)The total interest earned is the difference between the total of deposits and the future value:
$66,184.15 -(12)(5000) = 6,184.15
A total of $6,184.15 in interest was earned by the annuity.
