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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Two forces, F1 and F2, are acting on a body, as shown in the figure. The resultant force, R, is
newtons.
Answer:
R ,is the Resultant of two forces,
∠ACB +50°=180°
∠ACB=180° -50°
∠ACB=130°
→Cos(130°)=Cos (180°-50°)= -cos 50°= -0.6427
Magnitude of resultant force =70.70 Newtons(Approx)
3. The function represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.
(a) During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
(b) Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
(c) When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
Answer:
a
Step-by-step explanation:
Another day, another math problem
Answer:
4x+2h+5
Step-by-step explanation:
[tex]\frac{(2(x+h)^{2}+5(x+h)) - (2x^{2} +5x) }{h} \\[/tex]
For now I'm just going to ignore the denominator for simplicity
[tex](2(x^{2}+2xh+h^{2})+5x+5h) - (2x^{2} +5x)\\(2x^{2}+4xh+2h^{2}+5x+5h) - (2x^{2} +5x)\\(4xh+2h^{2}+5h)\\\\\frac{(4xh+2h^{2}+5h)}{h}\\ 4x+2h+5[/tex]
Final step just distributes the division
50/22 as a decimal rounded to the nearest hundreth
Step-by-step explanation:
the answer is 2.27. hope this helps
Hassan put 437.2 grams of brown sugar into a canister. Then he carefully measured out 430.43 grams of it to use in a recipe for cookies. How much brown sugar is left in the canister?
How many units were started into production in a period if there were zero units of beginning work in process inventory, 4,714 units in ending work in process inventory, and 20,661 completed and transferred out units?
The number of the units were started into production in a period will be 25,375.
What is inventory?A industry's fully prepared kinds of goods, as well as the primary materials needed to make them, are considered to as inventory.
If there were zero units of beginning work in process inventory, 4,714 units of ending work in process inventory, and 20,661 completed and transferred out units.
Completed and transferred out = 20,661
Ending Inventory = 4,714
Units accounted for = 25,375
Beginning Inventory = 0
Units started into production = [Units accounted for – Beginning work in progress Inventory] = 25,375
Units accounted for = 25,375
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What is the range of the function g(x) = –3sec(2x + 4) – 1?
(–∞, –2] ∪ [0, ∞)
(–∞, –4] ∪ [0, ∞)
(–∞, –4] ∪ [2, ∞)
(–∞, –5] ∪ [1, ∞)
The range of the function g(x) will be (–∞, –4] ∪ [2, ∞). Option C is correct.
What is the difference between domain and range?The domain denotes all potential x values, while the range denotes all possible y values.
When we plot the graph of the given function we will get the maximum and the minimum value till we get the function plot. The difference in the value of those coordinates is the range of the function.
The range of the function g(x) will be (–∞, –4] ∪ [2, ∞).
Hence option C is correct.
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The vertex of the graph of y = -4(x + 3)² + 2 is
DONE
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola will lie at (-3,2).
What is the Equation of a parabola?A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Comparing the given equation with the equation of a parabola, we will get,
y = a(x -h)² + k
y = -4(x+3)² + 2
Hence, the vertex of the parabola will lie at (-3,2).
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Question 13 of 50
Choose two statements (the original conditional statement and its converse)
that could form the biconditional "The object weighs a ton if and only if the
scale reads 2000 pounds."
A. If the object weighs a ton, then the scale reads 2000 pounds.
B. If the scale does not read 2000 pounds, then the object does not
weigh 2000 pounds.
C. If the scale reads 2000 pounds, then the object weighs a ton.
D. The scale reads 2000 pounds if and only if the object weighs a
ton.
it can be more then one answer too
Conditional statements are ones that begin with a hypothesis and end with a conclusion. The correct option is A and C.
What are conditional Statements?Conditional statements are ones that begin with a hypothesis and end with a conclusion. It is sometimes referred to as a "If-then" statement. If the hypothesis is correct but the conclusion is incorrect, the conditional statement is incorrect.
The two statements that among which one is original and the other one is its converse is If the object weighs a ton, then the scale reads 2000 pounds, and If the scale reads 2000 pounds, then the object weighs a ton.
Hence, the correct option is A and C.
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Which of the following is the given function's
average rate of change on the interval
Sx≤1?
Answer: 2
Step-by-step explanation:
[tex]g(-2)=-2\\\\g(1)=4\\\\\frac{g(-2)-g(1)}{-2-1}=\frac{-2-4}{-3}=\boxed{2}[/tex]
the height of a toy rocket
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable
solution if x represents the number of days that a library book is late and y represents the total fee?
The equivalent equation to find the ordered pair will be y=0.3x where x represents the number of days the book is late and y represents the total fine fee.
A linear equation is an equation where the highest degree in the equation is 1.
for example, y=mx,
where y and x is the variable and m, is the constant.
Given, that the librarian charges $0.30 per each day that the book is late to submit
for estimating the relation between the number of days the book is late and the total fine fee
Let's assume the number of days the book is late is x,
and the total fine is y
the librarian charges $0.30 per one day
so for x days, the total charge will be =0.30x
so from above, it is clear that the linear equation will be
y=0.3x
applying all the order pairs in this equation we can decide.
The equivalent equation to find the ordered pair will be y=0.3x
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again help me pease
Answer:
See below ~
Step-by-step explanation:
1) a) 50 km / 2 h
⇒ 25 km/h
b) 540 kg / 3 days
⇒ 180 kg/day
c) 125 m / 5 min.
⇒ 25 m/min.
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate…
a) 50km/2h
=> 25 kilometers per hour
b) 540kg/3d
=> 180 kilogram per day
c) 125m/5min
=> 25 meter per minute
can someone find the value of x?
Answer:
[tex]\boxed{\sf x=12}[/tex]
Step-by-step explanation:
By applying Similar Triangles Theorem:-
[tex]\sf \cfrac{x}{6} =\cfrac{6}{3}[/tex]
We'll multiply both sides of the equation by 6, the LCM of 6,3.
[tex]\sf x=2 \times 6[/tex]
[tex]\sf x=12[/tex]
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13%, percent monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck?
Thank you for asking this question. Here is your answer:
We will consider the price of the truck to be $x
And the amount of tax in the percentage would be 13%
13/100
= $ 0.13x (this is the actual amount of the tax)
Now we will calculate the total price of the truck =
$x + $ 0.13x
= $ x(1 + 0.13)
If there is any confusion please leave a comment below.
On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value? Find the t-table here. t = –1.85; the P-value is 0.9678. t = –1.85; the P-value is between 0.025 and 0.05. t = 1.85; the P-value is 0.9678. t = 1.85; the P-value is between 0.025 and 0.05.
Using the t-distribution, the correct option regarding the test statistic and the p-value is given as follows:
t = –1.85; the P-value is between 0.025 and 0.05.
What are the hypothesis tested?
The null hypothesis is:
[tex]H_0: \mu = 25[/tex]
The alternative hypothesis is:
[tex]H_1: \mu < 25[/tex]
What are the test statistic and the p-value?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 23.5, \mu = 25, s = 4.8, n = 35[/tex]
Hence the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{23.5 - 25}{\frac{4.8}{\sqrt{35}}}[/tex]
t = -1.85.
Using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.
Hence the correct statement is:
t = –1.85; the P-value is between 0.025 and 0.05.
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$30 is taken off the price of a dress. If the new price is now 60% off the original price, what was the original price of the dress.
4x^2 +16x -20 = 0
What is x
Answer:
x = 1, -5
Step-by-step explanation:
4(x^2 + 4x - 5) = 0
4(x - 1)(x + 5) = 0
x = 1, -5
Gianna is constructing a circle that passes through all three vertices of the triangle shown.
Where will the center of the circle be located?
OA. on a vertex of the triangle
OB. inside the triangle
OC. on a side of the triangle
OD. outside the triangle
B
Based on the definition of a circumcircle, the center of the circle as shown in the image below is located: B. inside the triangle.
What is a Circumcircle?A circumcircle, as shown in the diagram attached below, is a circle that is drawn so that all the vertices of a triangle touches the circumference of the circle.
Thus, as shown in the image attached below, the center of the circle is located: B. inside the triangle.
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Answer: OUTSIDE THE TRIANGLE
Step-by-step explanation: ANSWER ON EDMENTUM/PUTO
2/5x - 1/2 = 1/3 + 5/6x
Answer:
[tex]x = \frac{25}{13} [/tex]
Step-by-step explanation:
Given:
[tex] \frac{2}{5} x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6} x[/tex]
Combine like terms:
[tex] \frac{2}{5} x - \frac{5}{6} x = \frac{1}{3} + \frac{1}{2} [/tex]
Find GCF :
[tex] \frac{12}{30} x - \frac{25}{30} = \frac{2}{6} + \frac{3}{6} [/tex]
Subtraction and Addition :
[tex] \frac{13}{30} x = \frac{5}{6} [/tex]
Divide both sides by 13/30 :
[tex] \frac{ \frac{13}{30} }{ \frac{13}{30} } x = \frac{ \frac{5}{6} }{ \frac{13}{30} } [/tex]
Simplify :
Multiplication (Reciprocal) :
[tex]x = \frac{5}{6} \times \frac{30}{13} [/tex]
[tex]x = \frac{150}{78} [/tex]
[tex]x = \frac{25}{13} [/tex]
Answer :
[tex]x = \frac{25}{13} [/tex]
Hope it helps
In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = x^2 - 12, and CE = 4x What is AC?
The length of the AC is x^2 + 4x - 12.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given :
In Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
AE = x^2 - 12,
CE = 4x
We know that the diagonal of a parallelogram bisect each other.
x^2 - 12 = 4x
x^2 - 4x - 12= 0
(x-6)(x-2) = 0
Hence, the value of x = 6, 2.
AC = AE + CE = x^2 + 4x - 12.
The length of the AC is x^2 + 4x - 12.
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my sis needs help asap
Answer:
3/4 - 5/12
Step-by-step explanation:
first you make the demoninators the same so 3*4=12
and if you *3 you do it to the numerator
so its 9/12-5/12
the unsimplified fraction is 4/12
if wanted simplified version its 1/3
[tex]\frac{3}{4}-\frac{5}{12}\\[/tex]
First make the denominators equal so you can easily add the numerators
Common Factor of 4 and 12: 12
So multiply [tex]\frac{3}{4}[/tex] with 3 for both numerator and denominator (4*3=12, to make denominator equal)
[tex]\frac{9}{12} - \frac{5}{12} =\frac{4}{12}[/tex]
Simplify further
[tex]\frac{4}{12} =\frac{1}{3}[/tex]
[tex]\frac{1}{3}[/tex] is the answer
Hope it helps!
Jacob spends 13/4 dollars to paint 9/3 square feet. Find the cost to paint a
square feet per dollar.
The cost to paint a is 12/13 square feet per dollar.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Jacob spends 13/4 dollars to paint 9/3 square feet.
[tex]\dfrac{\dfrac{9}{3}}{ \dfrac{ 13}{4}} = \dfrac{9}{3} \times \dfrac{ 4}{13}\\\\= \dfrac{ 36}{39}\\\\= \dfrac{ 12}{13}[/tex]
Hence, the cost to paint a is 12/13 square feet per dollar.
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In ABC, m<2=70 and m
The measure of the third angle in the ΔABC is 70 degrees
Complete questionIn ΔABC, m∠2 = 70 and m∠1 = 40, find the measure of all third angle of ΔABC.
How to determine the third angle?The given parameters are:
m∠2 = 70
m∠1 = 40
The sum of angles in a triangle is:
m∠1 + m∠2 + m∠3 = 180
So, we have:
70 + 40 + m∠3 = 180
Subtract 110 from both sides
m∠3 = 70
Hence, the measure of the third angle in the ΔABC is 70 degrees
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PLEASE HELP
True or false
False
Step-by-step explanation:
Answer:
true.
Step-by-step explanation:
[tex]b^t=\frac{n}{a}; \ = > \ t=log_b\frac{n}{a}; \ = > \ t=\frac{log\frac{n}{a}}{logb}.[/tex]
3y + 9x = 21 Graph A On a coordinate plane, a line goes through (negative 3, negative 2) and (0, 7). Graph B On a coordinate plane, a line goes through (0, negative 7) and (3, 2). Graph C On a coordinate plane, a line goes through (0, 7) and (3, negative 2). Graph D On a coordinate plane, a line goes through (negative 3, 2) and (0, negative 7). a. Graph A c. Graph C b. Graph B d. Graph D Please select the best answer from the choices provided
Answer:
Graph C
Step-by-step explanation:
Graph A (-3, -2) (0, 7)
3(7) + 9(0) = 21
21 = 21 ✓
3(-2) + 9(-3) = 21
-6 - 27 = 21
-33 = 21 ✖
Graph B (0, -7) (3,2)
We know from above that (0, 7) is a point on the line 3y + 9x = 21, therefore point (0, -7) cannot be on that line.
3(2) + 9(3) = 21
6 + 27 = 21
33 = 21 ✖
Graph C (0, 7) (3, -2)
We know from above that (0, 7) is a solution.
3(-2) + 9(3) = 21
-6 + 27 = 21
21 = 21 ✓
Since both points on graph C is a solution to the equation of the line given, it is the answer (looking at graph D is not necessary unless you want to double check your answer).
2, 9, 11, 18, 20, 27,
the next 3 numbers.
Answer:
29, 36, 38
Step-by-step explanation:
The pattern is add 7 then 2, then 7, then 2, then 7, then 2. You should get the hang of it. All you have to do is just do the same thing for the next three numbers.
sin theta = 1/4, tan theta > 0
Find cos theta/2
Answer:
Step-by-step explanation:
sin θ=1/4,tan θ>0
so θ lies in first quadrant.
cos θ=√(1-sin²θ)=√(1-(1/4)²)=√(1-1/16)=√(15/16)=√15/4
[tex]2cos^2 \frac{\theta}{2} =1+cos \theta[/tex]
[tex]2~cos^2\frac{\theta}{2} =1+\frac{\sqrt{15} }{4} =\frac{4+\sqrt{15}}{4} \\cos~\frac{\theta}{2} =\sqrt{\frac{4+\sqrt{15} }{4 \times 2} } \\cos\frac{\theta}{2} =\frac{\sqrt{8+2\sqrt{15}} }{4}[/tex]
Using a sequencing method called "RNAseq," a researcher determines the level of FOXP2 expression
The Z-score is 2.306 to three decimal places. However, the Z-test statistic value shows that it is greater than the Z-critical value, so we reject the null hypothesis [tex]\mathbf{H_o}[/tex]
What is the Z-score of a test statistic?A z-score is a measurement of how often standard deviations the score obtained from a z-test is beyond or under the mean population.
From the given data information, let us find the mean and the standard deviation.
[tex]\mathbf{Mean (\bar x) = \dfrac{1154+5998+1007+...3987+4187+887}{10}}[/tex]
[tex]\mathbf{Mean (\bar x) = \dfrac{24256}{10}}[/tex]
Mean (x) = 2425.6
The hypothesis testing can be computed as:
[tex]\mathbf{H_o: \mu = 2425.6}[/tex]
[tex]\mathbf{H_1: \mu \ne 2425.6}[/tex]
The standard deviation (σ) is:
[tex]\mathbf{=\mathbf{ \sqrt{\dfrac{(1154-2425.6)^2+....+(887-2425.6)^2}{10-1}}}}[/tex]
[tex]\mathbf{= \sqrt{3199489}}[/tex]
= 1788.71
Now, the Z-test statistic is determined using the formula:
[tex]\mathbf{|Z| = |\dfrac{\bar x - \mu }{\sigma}| }[/tex]
[tex]\mathbf{|Z| = |\dfrac{2425.6 -6550 }{1788.71}| }[/tex]
[tex]\mathbf{|Z| = |-2.3058| }[/tex]
Z ≅ 2.306
Therefore, at a 0.05 level of significance, the Z-critical value is 2.306. However, since the Z-test statistic value shows that it is greater than the Z-critical value, so we reject the null hypothesis [tex]\mathbf{H_o}[/tex]
The complete question is given as:
Using a sequencing method called "RNAseq," a researcher determines the level of FOXP2 expression in 10 different samples of lung tissue, and obtains these data:
1154 5998 1007 2501 1000 988 2547 3987 4187 887Scientist has previously determined that FOXP2 is expressed in brain tissue at a level of 6,550. Calculate the Z-score associated with a test to see if the average expression of FOXP in her lung tissue samples is different from the levels she measured from brain tissue.
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What is the measure of complemnt angle 42
Answer:
Complemetry angle = 90° - 40°
= 50°
Hii!
___________________________________________________________
Answer:
[tex]\sf 48\textdegree[/tex]
Step-by-step explanation:
The sum of complementary angles is always 90 degrees.
We can find the complement of 90 by setting up an equation; (let x be the unknown angle).
[tex]\implies[/tex] 42+x=90
Subtract 42 from both sides
x=48
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Hope that this helped! Best wishes.
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