The range of the composite function (w o r)(x) is (a) (-oo, 0)
How to determine the range of the composite function?From the function, the definition of the functions are given as:
r(x) = 2 - x²
w(x) = x - 2
The composite function (w o r)(x) is calculated as
(w o r)(x) = w(r(x))
This means that:
(w o r)(x) = w(2 - x²)
So, we have
(w o r)(x) = 2 - x² - 2
Evaluate the like terms
This gives
(w o r)(x) = -x²
The above function is a quadratic function, and the range is all set of negative numbers
This can be represented as (-oo, 0)
Hence, the range is (-oo, 0)
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For the line and point below, describe how the following equations would differ: A) A parallel line, through the given point B) A perpendicular line, through the given point (-2,1) slope 1
The linear functions would be given as follows:
a) Parallel: y = x + 3.
b) Perpendicular: y = -x - 1.
The equations have different slope and intercept.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).For item a, we consider that if two lines are parallel, they have the same slope, hence the line would also have a slope of 1, that is:
y = x + b.
From point (-2,1), we have that when x = -2, y = 1, hence we can solve and find the intercept b as follows:
1 = -2 + b
b = 3.
Hence:
y = x + 3.
For item b, we consider that if two lines are perpendicular, the multiplication of their slopes is of -1, hence:
m = -1.
Then:
y = -x + b.
From the point (-2,1), we can find b as we did above, hence:
1 = -(-2) + b
2 + b = 1
b = -1.
Hence the rule is:
y = -x - 1.
The equations have different slope and intercept, that is, their coefficients are different.
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If the volume of a prism is 64, its length 4, and its width 2, what is its height
Answer:
h=8
Step-by-step explanation:
there is a formula for a volume of a prism
Volume = length • width • height
for shortening purposes
V = L • W • H
we know the prism's length is 4, and it's width is 2 and we know it's volume is 64 but the height is missing
what we will do is say (since height is missing)
[tex]h = \frac{V}{l \: • \: w} [/tex]
v = 64
l = 4
w = 2
so, now plug in those values for your variables
[tex]h = \frac{64}{4 \: • \: 2} [/tex]
multiply 4 • 2
[tex]h = \frac{64}{8} [/tex]
divide by 8
[tex]h = \frac{8}{1} [/tex]
simplify
[tex]h = 8[/tex]
Check:V = l•w•h
v= 4 • 2 • 8
v = 8• 8
v = 64
hope this helped happy learning
what is the equation of a line that is parallel to the line y=2x+1 and passes through the point (4,6).
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line that has a slope of 2 and it passes thourhg (4 , 6)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{4}) \\\\\\ y-6=2x-8\implies {\Large \begin{array}{llll} y=2x-2 \end{array}}[/tex]
How much more will his shirt cost in Fresno than in Bakersfield (in dollars)? (Round each to the nearest cent and write your answer as a decimal). Do Not Put Units.
Using the properties of percentage we get that the shirt cost $0.25 more in Fresno than in Bakersfield.
A percentage is a figure or ratio stated as a fraction of 100 in mathematics.
Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A percentage lacks dimensions and has no associated unit of measurement.It is not always obvious from the context what a percentage is in relation to because of inconsistent usage. The typical meaning of a "10% rise" or "10% decline" in a quantity is that this refers to the quantity's starting value. As an illustration, the new price of a $200 item would be $220 if the price increased by 10%, or $20.Price of the shirt is Fresno
= 35 + 8.225% of 35
= 37.87875
≈ 37.88 dollars
Price of the shirt in Bakersfield
= 35 + 7.5% of 35
= 35 + 2.625
= 37.625
≈ 37.63 dollars
Difference in price after adding the sales tax percentage
= 37.88-37.63
= 0.25 dollars
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- (-5v - 4y + 6) use distributive property to remove the parenthesis
Answer:
(5v+4y+6)
Step-by-step explanation:
You have to distribute/multiply the negative sign (-) to all the values inside.
-(-5v-4y+6)=
-(-5v)=5v (-×- = +)
-(-4y)= 4y (-×- = +)
-(6)= -6 (-×+ = -)
The answer is:
(5v+4y+6)
Mandy bought 3 boxes of cupcakes to share with friends at work. Each box has 6 cupcakes inside.
The letter c stands for the total number of cupcakes. Which equation can you use to find c? Please answer quickly I need it for math. I'll give 20 points.
Answer:
c=3*6
Step-by-step explanation:
c=3 boxes * 6 cupcakes per box
Use cubes with the given edge length to find the volume of the rectangular prisim. Check your answer using the volume formula
The volume of the rectangular prism is 27 inch³.
Given that,
We are going to find the volume of the given rectangular figures in the picture.
The volume of a three-dimensional figure is the amount of rectangular units required to completely fill the interior space.
Volume of the rectangular prism is length×width×height.
Volume of a cube is (side length)³.
If we take each cube from a figure u will get the side length as 1 inches.
So, The 1 cube volume is S³
=1³=1 inch³
Now, we take each cube row's.
Each row as 9 cubes
We get the volume as 9 inch³.
Then there are 3 rows in the diagram.
=9+9+9
=27 inch³
Therefore, The volume of the rectangular prism is 27 inch³.
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(1)What are the two equations to set up to solve the equation
|3x -2| =19
3x -2=
(2) Solve.
-2|2x+3| + 14≥ - 16
The two equations to set up to solve the absolute value equation given are; 3x - 2 = 19 and 3x - 2 = -19.
The solution of the inequality given; -2|2x+3| + 14 ≥ - 16 is; x ≥ 6 OR x ≤ -9.
What are the two equations to set up in order to solve the absolute value equation?It follows from absolute value equations that;
| x | = ±x
Hence, | x | = x OR | x | = -x
Ultimately, the two equations to set up are; 3x - 2 = 19 and 3x - 2 = -19.
2. Also, the equation given; -2|2x+3| + 14≥ - 16 can be solved as follows;
-2|2x+3| ≥ - 16 - 14
-2|2x+3| ≥ - 30
|2x+3| ≥ 15
Hence, the equation can be solved as;
2x + 3 ≥ 15 OR 2x + 3 ≤ -15
2x ≥ 12 OR 2x ≤ -18
x ≥ 6 OR x ≤ -9.
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There are 30 fish in a pond. 9 of the fish are carp.
1/3
Of the fish that are not carp, are sticklebacks and the rest are tench.
What is the ratio of carp to sticklebacks to tench in the pond?
Give your answer in its simplest form.
Answer:
9:7:14
Step-by-step explanation:
where I got my answer
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21. Determine the measures of angles x, y, and z.
55⁰
80
100°
60°
4 = -(x + 3) implemented as a real life problem
8 Select the correct answer. Which inequality represents all the solutions of 10(3x + 2) > 7(2x - 4)? ОА. X> 4 OB. X
The given inequality is expressed as
10(3x + 2) > 7(2x - 4)
The first step is to open the brackets on each side of the inequality by multiplying the terms outside the bracket by the terms inside. Thus, we have
10 * 3x + 10 * 2 > 7 * 2x - 7 * 4
30x + 20 > 14x - 28
Collecting like terms, we have
30x - 14x > - 28 - 20
16x > - 48
Dividing both sides by 16, it becomes
16x/16 > - 48/16
x > - 3
solve each compound inequality. drag the correct solution and graph next to the inequality
A compound inequality is created by joining two or more inequalities together using or or and (also known as a combined inequality). For a value to be the answer to an or inequality, it simply needs to make one part of the inequality true. To be effective, a solution to an inequality must make both sides true. Examples are x3 or x>2.
Explain about the compound inequality?
A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. It is when the solution sets for the various statements cross over or intersect.
Divide a compound inequality into two independent ones before attempting to solve it. Choose either a union of sets ("or") and an intersection of sets as the appropriate response ("and"). Then, resolve the graph and all inequalities.
The values that belong to both graphs—where the graphs overlap—are found by first examining the graphs of each individual inequality in order to obtain the answer to a "and" compound inequality. We graph each inequality for the compound inequality x>3 and x2. Next, we search for areas where the graphs "overlap."
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How are the functions y=x and y=x-3 related? How are their graphs related?
Functions y=x and y=x-3 are related in a way that each output for y=x–3 is 3 units more than the corresponding output for y=x.
Their graphs are related in a way that the graph of y=x–3 is the graph of y=x translated down 3 units
A function will defines one variable in terms of the other. Functions y=x means that y will vary directly to whatever value x takes.
When the graph of function y=x is drawn, then it is a straight line through the origin.
Now, functions y=x and y=x-3 are closely related. The graphs of the two are almost the same, the only difference is that every point on function y=x has been lowered by 3 to be function y=x-3.
Hence, the output for y=x-3 is 3 units more than the output of y=x, and the graph of function y=x is translated down by 3 units to get function y=x-3
The graphs for functions y=x and y=x-3 are shown below:
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Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
1. sin0 = -2/3
2. sec0 = 2/1
3. tan0 = 4/5
4. csc0 = -3/2
5. cos0 = -3/5
The trigonometric functions sin θ = - 2 / 3 and csc θ = - 3 / 2 are related to each other in accordance with the trigonometric formula: sin θ · csc θ = 1. (Correct choices: 1, 4)
What two trigonometric functions have the same angle?
In this question we must look for two trigonometric functions that are associated to one and same angle. This can be done by relations between fundamental and derivate trigonometric functions. There are two fundamental trigonometric functions (sine, cosine) and four derivate trigonometric functions (tangent, cotangent, secant, cosecant).
After a quick inspection, sin θ = - 2 / 3 is related to csc θ = - 3 / 2 as it fulfill the following trigonometric formula: sin θ · csc θ = 1
RemarkThe graph is missing and cannot be found, so we decided to change the intend of the question to find two trigonometric functions associated with the same angle.
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I NEED THESE IN 7 MINS PLEASE SOMEONE ANSWER THIS ILL GIVE U EXTRA POINTS!!! ANSWER THEM ALL PLEASE!!!
The circumference of the circle is 62.8 feet.
In geometry, the circumference of a circle or ellipse is referred to as its perimeter (from the Latin circumference, meaning "carrying around").
In other words, the circumference would match the length of the circle's arc if the circle were spread out and straightened into a line segment. The perimeter of any closed figure is more frequently used terminology for the length of the curve around. The exact location of the circle, which corresponds to the edge of a disc, can also be referred to as the "circumference." Any one of the great circles has a length equal to the circumference of a sphere.The diameter of the circle = 20 ft
radius (r) = 20 ÷ 2 = 10 ft
Circumference = 2πr = 2 × 3.14 × 10 = 62.8 feet.
For the second problem
The circumference is 17 feet
∴2πr=17
or, 2r = 17 ÷ 3.14 = 5.414... ≈5.41 feet
Hence the diameter is 5.41
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i neeed help again:( pweaseee help
Answer:
[tex]a) n =\dfrac{c}{d}\\\\\\b) b= 2A -a\\\\c) m_1=\dfrac{Fr^2}{Gm_2}[/tex]
d) z = 10
Step-by-step explanation:
Solve for the given variable:a)
[tex]\sf d = \dfrac{c}{n}\\\\\text{Mulitply the entire equation by 'n',}\\\\n*d=n*\dfrac{c}{n}\\\\nd =c\\\\\text{Now, divide the entire equation by 'd',}\\\\n =\dfrac{c}{d}[/tex]
b)
[tex]\sf A = \dfrac{a+b}{2}\\\\\text{Multiply the entire equation by 2,}\\\\2*A = 2*\dfrac{a+b}{2}\\\\2A = a+b\\\\\text{Now subtract 'a' from both sides,}\\\\2A - a = b\\\\\boxed{b=2A - a}[/tex]
c)
[tex]\sf F =\dfrac{Gm_1m_2}{r^2}[/tex]
Multiply the entire equation by r²,
[tex]\sf Fr^2=r^2*\dfrac{Gm_1m_2}{r^3}\\\\Fr^2=Gm_1m_2[/tex]
Divide the entire equation by Gm₂,
[tex]\sf \dfrac{Fr^2}{Gm_2}=m_1\\\\\boxed{m_1=\dfrac{Fr^2}{Gm_2}}[/tex]
D) A = 7 ; y =4
Substitute in the equation and find the other number.
[tex]\sf A = \dfrac{1}{2}(y+z)\\\\7=\dfrac{1}{2}(4+z)\\\\Multiply \ both \ sides \ by 2,\\\\7*2 = 4 +z[/tex]
14 = 4 + z
Subtract 4 from both sides,
14 - 4 = z
z = 10
What is the equation of the line that passes through the point (−7,−4) and has an undefined slope?
Naomi added three mixed numbers as shown below.
Add: 358+(216+238)
Step 1 =358+(238+216)
Step 2 =(358+238)+216
Step 3 =6+216
Step 4 =816
Which statement best evaluates Naomi’s work?
1. She used the commutative and distributive properties correctly and got the correct answer.
2. She used the commutative and distributive properties correctly and got the correct answer.
3. She used the commutative and associative properties correctly and got the correct answer.
4. She used the commutative and associative properties correctly and got the correct answer.
5. She used the commutative and distributive properties correctly but got an incorrect answer.
6. She used the commutative and distributive properties correctly but got an incorrect answer.
7. She used the commutative and associative properties correctly but got an incorrect answer.
8. She used the commutative and associative properties correctly but got an incorrect answer.
The correct option about Naomi is that dhe used the commutative and associative properties correctly but got an incorrect answer.
What are the properties about?It should be noted that the commutative property states that that order of mathematical operations don't matter. The associative property illustrates that the grouping of numbers such that:
(a + b) + c = a + (b + c)
The steps given are:
Add: 358+(216+238)
Step 1 =358+(238+216)
Step 2 =(358+238)+216
Step 3 =6+216
Step 4 =816
You can see that the step 3 is incorrect as well as the final answer. In this case, (358+238)+216 will be 812.
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Which of the following inequalities is represented by the number line?
A) x > 4.5
B) x ≤ 4.5
C) x ≥ 4.5
D) x < 4.5
Answer:
A
Step-by-step explanation:
i took this test
Answer: B) x ≤ 4.5
Step-by-step explanation:
Closed circles either mean “less than or equal to” or “greater than or equal to,” which would be marked as either
≤ or ≥. Since the number line includes values that are less than 4.5, the ≤ symbol would have to be used.
how do I find which two further transformations will carry rectangle P'Q'R'S back onto rectangle PQRS
Reflection across the x axis involve negating the value of the y axis but the value of the x axis remain the same. Reflection across the y axis negate the x coordinates but the y values remains the same. When you reflect across the line y=x the coordinate and the y coordinates change places. Whe it rotate 180 degree around the origin the x and y values are negated. The transformation is interpreted as follows.
The answer is C which is reflection across the y axis followed by a 180 degree rotation around the origin.
The logic here is that PQRS is first reflected across the x axis which makes the y values negative. Then it reflect across the y axis which makes the value of x negative. So both x and y values are negative at this point. The rotation of 180 degree around the origin negates both the x and y values to make it all positive like the initial values of PQRS.
-7 -3 2/3 write as mixed number
Answer: 3 1/3
Step-by-step explanation:
-7 - (-3 2/3)
-7 = -6 -3/3
-6 -(-3) = -3
-3/3 -(-2/3) = -1/3
-3 + (-1/3) = -3 1/3
|-3 1/3| = 3 1/3
The distance between the two numbers is 3 1/3
what is three hundred thousand twelve in standard form?
A bakery sold a total of 300 cupcakes in a day, and 252 of them were chocolate flavored. what percentage of cupcakes sold that day were chocolate flavored?
Answer:
84% of the cupcakes were chocolate- flavored.
Step-by-step explanation:
[tex] \frac{252}{300} = \frac{84}{100} = 84\%[/tex]
pls help will mark brainliest
Answer:
I think your answer is A.
Step-by-step explanation:
10=x 15=y
The amount spent is $220
so
10x +15y = 220
Which of the following describes the location of the opposite of the number that R represents on this line? please help someone . Thanks
A) at a distance of 8 tick marks above 0
B) at a distance of 4 tick marks above 0
C) at a distance of 8 tick mark below 0
D) at a distance of 4 tick mark below 0
Answer:
B) at a distance of 4 tick marks above 0
Step-by-step explanation:
The dot represents the number on the line, R, and the opposite of -4 is positive 4, which is 4 tick marks above 0.
what are the factors of the quadratic function represented by this graph
The factors of the quadratic function represented by the graph is (x+1) and (x+5)
What is a Quadratic Function?A quadratic Function is an Algebraic equation in which the highest degree of the variable is 2.
Quadratic functions when plotted on graphs appear as curves and which cuts through the X-axis of the graph.
From the graph, the roots of the function are x = -1 and x = -5,
If x = -1 is a root then taking -1 to the left x+1 = 0
Also if x = -5, then X+5 = 0
so since x+5 = 0 or x +1 = 0
Then (x+5)(x+1) = 0 is the required function.
Therefore (x+5)(x+1) are factors of the Quadratic function
In conclusion, the Factors of the Quadratic functions are (x+1)(x+5)
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Please help me with this question asap the test is about to close in 20 minutes
Number of cubic feet water is passing through dam in 3 second = 4 cubic ft
Therefore, amount of water passes through dam in 1 seconds
= \frac{\text{Amount of water passing through dam}}{\text{Duration}}
Duration
Amount of water passing through dam
= \frac{4}{3}
3
4
cubic feet per seconds
help mee!!
7|5p−7| = −21
Answer:
p=-1.25
Step-by-step explanation:
first, we do the absolute value so we get 7x5p+7=-21
now we subtract 7 on each side so now it is 7x5p=-28
now we multiply the 7 and 5p so no it is 35p=-28
now we divide both sides by 35 now the answer is p=-1.25
Order the following numbers from least to greatest: 6.5, -26, -1.3, 0, 2.6, 12
Answer: least to greatest:
-26, -1.3, 0, 2.6, 6.5, 12
Step-by-step explanation:
We can start by putting the negative numbers last (-26, -1.3) the greater a negative number is the smaller it actually is! so -26 would be the least followed by -1.3
0 would be after because well it's zero. then we can go least to greatest, 2.6, 6.5, 12.
