f(h(x)) = -2x^2 + 12x + (-12) in terms of x.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
To find f(h(x)), we first need to substitute h(x) into f(x).
f(h(x)) = f(4(x-3)²)
Now we can substitute 4(x-3)^2 into f(x)
f(h(x)) = 6 - 1/2(4(x-3)^2)
= 6 - 2(x-3)^2
= 6 - 2(x^2 - 6x + 9)
= 6 - 2x^2 + 12x - 18
Hence, f(h(x)) = -2x^2 + 12x + (-12) in terms of x.
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i need help with this
3:7 = ___: 49
Answer:
3 : 7 = 21 : 49
Step-by-step explanation:
i need help with this
3:7 = ___: 49
3 : 7 = x : 49
x = 3 × 49 ÷ 7
x = 147 ÷ 7
x = 21
3 : 7 = 21 : 49 (your answer)
unit 10 test study guide circles geometry
Circle Terminology:
Center: The point at the center of the circle.
Radius: The distance from the center to any point on the circle.
Diameter: The distance across the circle passing through the center (2 times the radius).
Chord: A line segment connecting two points on the circle.
Arc: A part of the circumference of the circle.
Sector: The region enclosed by two radii and the corresponding arc.
Circle Formulas:
Circumference (C): C = 2πr or C = πd (where r is the radius and d is the diameter).
Area (A): A = πr^2.
Central Angles and Arcs:
Central Angle: An angle whose vertex is at the center of the circle.
Arc Measure: The measure of the central angle that intercepts the arc.
Arc Length: The distance along the circumference of the circle.
Arc Length = (Arc Measure / 360) * Circumference.
Inscribed Angles and Arcs:
Inscribed Angle: An angle formed by two chords with its vertex on the circle.
Inscribed Angle Theorem: An inscribed angle is half the measure of its intercepted arc.
Intercepted Arc: The arc that lies between the endpoints of the inscribed angle.
Tangents:
Tangent: A line that intersects the circle at exactly one point (the point of tangency).
Tangent Theorem: A tangent line is perpendicular to the radius drawn to the point of tangency.
Secants:
Secant: A line that intersects the circle at two points.
Intersecting Chord Theorem: The product of the lengths of the two segments of a secant is equal to the product of the lengths of its external segment.
Relationships Between Angles and Arcs:
Angle-Arc Relationship: The measure of an inscribed angle is half the measure of its intercepted arc.
Angle in a Semicircle: An angle inscribed in a semicircle is a right angle (90 degrees).
Circle Construction:
Circumscribed Circle: A circle that passes through all the vertices of a polygon.
Incircle: A circle that is tangent to all the sides of a polygon.
Remember to practice solving problems involving these concepts, including finding angles, arc measures, lengths, and areas of circles. Additionally, review the properties and relationships between angles and arcs in different scenarios. Good luck with your study and the test!
Given m ∥ n, find the value of x.
given that m is parallel to n,
the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.
using the corresponding angle rule we know that:
2x + 16 = 96
2x = 80
so x = 40
Does anybody know this? I feel like it it's easy but I can't seem to get it. Find the common difference of the arithmetic sequence -3.6,-3.9,-4.2,-4.5
Answer: Looks like its -.3
Answer:
Step-by-step explanation:
-3.6 + -0.3 = -3.9
-3.9 + -0.3 = -4.2
-4.2 + -0.3 = -4.5
you are adding - 0.3 to each number to get the next number in the sequence
=
+
Can someone answer this question?
The graph of the polynomial function y = f(x) in the xy plane could be the first graph.
Given a polynomial function f.
Range of the polynomial function is the set of all the real numbers less than or equal to 4.
So y values are y ≤ 4
So the vertex of the function will be at y = 4 and other value are less than 4.
So parabola is downwards.
Two options are there with the parabola folded downwards.
Now the zeroes of f are at -3 and 1.
Zeroes of f are the values of x where the function touches the X axis.
Hence the correct graph is first one.
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Please help me answer this question. Having a hard time with it.
(Sorry if it’s blurry)
The new price of the pants, after the discount is applied, is the one in option B:
P = $38.40
What is the price of the pants excluding the tax?We know that the original price of the pants is $64, and we have a discount of 40%.
Then to find the new price of the pants, we need to multiply the original price by a factor (1 - 40%/100%) = (1 - 0.4) = 0.6
Then the new price of the pants, exluding the taxes, we will get that the new price is:
P = $64*0.6
P = $38.40
Then we can see that the correct option is B.
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Please help me understand this problem!
The values of c on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].
According to the Mean Value Theorem for Integrals, if f(x) is continuous on the interval [a, b], then there exists a value c in [a, b] such that:
f(c) = 1/(b-a) . ∫(a to b) f(x) dx
For f(x) = x⁴ on the interval [-5, 5], we have:
∫(-5 to 5) x⁴ dx = (1/5) . (5⁵ - (-5)⁵)/5
= (1/5) . (3125 + 3125)
= 1250
So we need to find c such that f(c) = 1250/10 = 125.
f'(x) = 4x³, so we can use the Mean Value Theorem for Derivatives to find a value of c that satisfies the condition.
f'(c) = (1/(5-(-5))) . ∫(-5 to 5) f'(x) dx
= (1/10) . [f(5) - f(-5)]
= (1/10) . [(5⁴) - ((-5)⁴)]
= 100
Therefore, by the Mean Value Theorem for Derivatives, there exists a value c in [-5, 5] such that f'(c) = 100.
Now, we need to check if there exists a value c in [-5, 5] such that f(c) = 125.
f(c) = c⁴, so we need to solve the equation c⁴ = 125.
c = ±[tex]5^{1/4[/tex]
Both of these values are in the interval [-5, 5], so they satisfy the Mean Value Theorem for Integrals.
Therefore, the values of c that satisfy the Mean Value Theorem for integrals for f(x) = x⁴ on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Can someone answer this question
Answer: x+2
Step-by-step explanation:
It is not factorable through grouping method. You can test for factors if you divide the factor and it goes in evenly (no remainder) then, it is a factor.
I will use synthetic division to test:
X-8:
8 | 1 -14 56 -64
| 8 -48 64
1 -6 8 0 =>no remainder so yes this is a factor
X+2:
-2 | 1 -14 56 -64
| -2 32 -176
1 -16 88 -240 => remainder so NOT factor
X-2:
2 | 1 -14 56 -64
| 2 -24 64
1 -12 32 0 =>no remainder so yes this is a factor
X-4:
4 | 1 -14 56 -64
| 4 -40 64
1 -10 16 0 =>no remainder so yes this is a factor
zeus industries bought a conputer for $2500. it is ecpected to depreciate at a eate of 20% per year. what will the e value of the computers be in 2 years
Answer: Let me explain!
Step-by-step explanation:
Well, this is easy, I’ll explain it.
We know the value of these computers are going to go down 20% each year. So since we know that, we can multiply 20 percent by the amount of years, which is 2, so 20 times 2 is 40, so the computers decreased in value by 40 percent!
Now that that’s established, we need to subtract forty percent of 2500, from the original price, 2500.
(To do that, move the decimal place over one to get 250, which is 10%, then multiply by 4, to get 40 percent of 2500, which is 1000, in case you weren’t sure on how to do that :)
Then, subtract 1000 from 2500, and that is your answer!
$1,500
The radius of a circle is 14 yards. What is the circle's circumference?
Use 3.14 for .
pls help
a snail is 20 inches about the ground. It slips down 6 inches and the creeps up 12 inches. what is the snails height now?
Answer:
26 inches
Step-by-step explanation:
The snail starts 20 inches above the ground: +20
The snail slips (goes down) 6 inches: 20 - 6 = 14
The snail goes up 12 inches: 14 + 12 = 28
The snail is 28 inches above the ground.
Hope this helps!
What is true about the triangles shown in the diagram? Select all that apply.
Answers:
Choice A) Segment AC = 2*sqrt(17)
Choice B) Segment BD is 32 units long
Choice F) Segment AB is approximately 33 units long.
==========================================================
Explanation:
The triangles are similar, so we can form this proportion
CD/DA = DA/BD
2/8 = 8/x
2x = 8*8
2x = 64
x = 64/2
x = 32
BD is 32 units long
This means one of the answers is choice B. It rules out choice D.
--------------
The legs of right triangle ABD are
AD = 8BD = 32Use the pythagorean theorem to find hypotenuse AB.
a^2 + b^2 = c^2
(AD)^2 + (BD)^2 = (AB)^2
8^2 + 32^2 = (AB)^2
(AB)^2 = 64 + 1024
(AB)^2 = 1088
AB = sqrt(1088)
AB = sqrt(64*17)
AB = sqrt(64)*sqrt(17)
AB = 8*sqrt(17)
AB = 32.984845
Segment AB is approximately 33 units long.
This tells us another answer is choice F. Choice C is false because 4*sqrt(5) = 8.94427
--------------
BC = BD + DC
BC = 32 + 2
BC = 34
BC is the hypotenuse of triangle ABC
Use the pythagorean theorem to determine AC.
a^2 + b^2 = c^2
(AB)^2 + (AC)^2 = (BC)^2
(sqrt(1088))^2 + (AC)^2 = (34)^2
1088 + (AC)^2 = 1156
(AC)^2 = 1156 - 1088
(AC)^2 = 68
AC = sqrt(68)
AC = sqrt(4*17)
AC = sqrt(4)*sqrt(17)
AC = 2*sqrt(17)
Another answer is Choice A. It rules out choice E because 2*sqrt(17) = 8.2462 approximately.
Need help in solving this problem I’m stuck on it. Pls help me?????? If you can see the numbers it’s 3ft, 7ft, 5ft, 4ft.
Answer:
area=20ft^2
Step-by-step explanation:
3ft×4ft=12ft^2
12ft÷2=6ft is the area of the smaller triangle
7ft×4ft=28ft^2
28ft÷2=14ft is the area of the larger triangle
6ft+14ft=20ft^2
Enter the correct answer in the box. Write the sum of 12\sqrt{23x^{13}}+14\sqrt{23x^{13}} in simplest form, if x > 0.
The sum of the expressions 12√23x¹³ + 14√23x¹³ is in its simplest form if x > 0 is 26x⁶√23x
Calculating the sum of the radical expressionFrom the question, we have the following parameters that can be used in our computation:
12\sqrt{23x^{13}}+14\sqrt{23x^{13}}
Express the summation expression, properly
So, we have
12√23x¹³ + 14√23x¹³
Next, we add the terms of teh expression
Using the above as a guide, we have the following:
12√23x¹³ + 14√23x¹³ = 26√23x¹³
Take the square root of x¹³
12√23x¹³ + 14√23x¹³ = 26x⁶√23x
The above expression is in its simplest form if x > 0.
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how are the shapes alikei need to know
The similarity between the cube and cuboid is that both have 12 edges.
option C.
What is a cube and cuboid?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
So a cube is a three-dimensional solid figure, having 6 square faces and 12 edges.
A cuboid is a three-dimensional geometric shape that looks like a book or a rectangular box.
A cuboid can be defined as a three-dimensional solid shape that has 12 edges, 8 vertices, and 6 faces and each of its faces is rectangular in shape.
So the similarity between a cube and cuboid is that both have 6 faces and 12 edges.
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I’m particularl class of 33 students, 14 are men. What fraction of the students in the class are men?
_____________________________
= 14 ÷ 33 × 100= 42.4% ~ 43% The Fraction of Male Students Is 43%_____________________________
Step-by-step explanation:
the headline says "college". that cannot be.
14 out of 33 are men.
so,
14/33 of the students are men.
that's it. nothing else can be done.
let's add a little bit more spice to this and ask also what percentage of the students are men :
for % questions, always find 100% and correspondingly 1%.
everything else can be easily calcite out of this.
100% = 33
1% = 100%/100 = 33/100 = 0.33
how many % of these 33 are 14 ?
as many as times 1% fit into these 14 :
14/0.33 = 42.42424242...%
List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, and f. real numbers.
a. Natural numbers: 0, 4.2, √9
b. Whole numbers: -8, 0, 4.2, √9
c. Integers: -8, 0, 4.2, √9
d. Rational numbers: -8, 5/6, 0, 4.2, √9
e. Irrational numbers: √2, π
f. Real numbers: -8, 5/6, 0, 0.1, √2, π, 4.2, √9
We have,
a. Natural numbers:
5/6, 0, 4.2, √9 (The natural numbers are positive integers excluding zero)
b. Whole numbers:
-8, 0, 4.2, √9 (Whole numbers include zero and all positive integers)
c. Integers:
-8, 0, 4.2, √9 (Integers include positive and negative whole numbers, including zero)
d. Rational numbers:
-8, 5/6, 0, 4.2, √9 (Rational numbers can be expressed as a fraction of two integers)
e. Irrational numbers:
√2, π (Irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal expansions)
f. Real numbers:
-8, 5/6, 0, 0.1, √2, π, 4.2, √9 (Real numbers include all rational and irrational numbers)
Thus,
a. Natural numbers: 0, 4.2, √9
b. Whole numbers: -8, 0, 4.2, √9
c. Integers: -8, 0, 4.2, √9
d. Rational numbers: -8, 5/6, 0, 4.2, √9
e. Irrational numbers: √2, π
f. Real numbers: -8, 5/6, 0, 0.1, √2, π, 4.2, √9
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The complete question.
-8, 5/6, 0, 0.1, √2, π, 4.2, √9
List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, and f. real numbers.
Find value of X. Round to the nearest tenth. right Triangle 36° , 10, x
●Problem #8
Answer:
x ≈ 8.1
Step-by-step explanation:
using the cosine ratio in the right triangle
cos36° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex] ( multiply both sides by 10 )
10 × cos36° = x , then
x ≈ 8.1 ( to the nearest tenth )
subtraction property of equality
multiplication property of equality
17
3
3
4
3
X-
Step
3
X=
17 3 17
7--7-x+5-77
3
5x.-
4
4
-2/x-12x X=
1 2
X= X-
2
X=-
4
5
-
-
X=
division property of equality
X+5
2
-/3/33
addition property of equality
2
3
8
15
-²333
x-²/3-1/2 x
-
17
4
5
3
given
simplification
Justification
The required justification for the solution to the equation is shown in the solution part.
As per the given equation, the required solution would be as follows:
Given:
17/3 - (3/4)x = 1(/2)x + 5
Subtraction property of equality:
17/3 - (3/4)x - 17/3 = 1(/2)x + 5 - 17/3
- (3/4)x = 1(/2)x - 2/3
Addition property of equality:
- (3/4)x - 1(/2)x = 1(/2)x - 2/3 - 1(/2)x
-(5/4)x = -2/3
Multiplication property of equality:
-(5/4)x × -4/5 = -2/3 × -4/5
Simplification:
x = 8/15
The required justification for the solution to the equation is shown in the solution part.
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Answer:
Answer shown in picture.
What is the measurement of N?
Please help me it’s due today!!!!
The value of x in trapezoid KFGJ is 40.
Given information:
KFGJ is a trapezoid.
KF = 20
JG = x
MN is midsegment of trapezoid KFGJ.
MN = 30
To find the value of x in trapezoid KFGJ, we can use the fact that the midsegment MN of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the bases.
In this case, MN is given as 30, and we know that KF is one of the bases with a length of 20. To find the length of the other base JG, we can use the formula for the midsegment of a trapezoid:
MN = (KF + JG) / 2
Substituting the given values, we have:
30 = (20 + x) / 2
To solve for x, we can multiply both sides of the equation by 2:
60 = 20 + x
Subtracting 20 from both sides:
x = 60 - 20
x = 40
Therefore, the value of x in trapezoid KFGJ is 40.
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Solve and graph on number line. |6x-3|<21
The solution of the given inequality is -3<x<4.
The given inequality is,
|6x-3| < 21
Here absolute function is applied in the given expression,
Therefore,
Case 1
⇒ (6x-3) > -21
⇒ 6x-3 > -21
Add 3 both sides,
⇒ 6x > -18
⇒ 6x > -3
Divide by 6 both sides we get,
⇒ x > -3
Case 2:
⇒ (6x-3) < 21
⇒ 6x-3 < 21
Add 3 both sides,
⇒ 6x-3+3 < 21+3
⇒ 6x < 21+3
⇒ 6x < 24
Divide by 6 both sides we get,
⇒ x < 4
Now plotting the graph of this inequality we get:
-3<x<4 is the solution.
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principal $45,687.23 annual interest rate 7.555% interest period monthly. What is the first period interest?
The interest rate for the first period is $287.22
Using the Simple Interest PrincipleTo obtain the first period interest, we use simple interest formula;
Simple Interest = Principal * Rate * Time
Given:
Principal = $45,687.23
Annual interest rate = 7.555%
Interest period = Monthly
Convert the annual interest rate to a monthly interest rate.
Monthly interest = Annual interest/ 12 = 7.555/12 = 0.6295%
First period interest:Interest = Principal * Monthly interest rate * Time
Since it's the first period, the time is 1 month:
Interest = $45,687.23 * 0.62958333% * 1
Interest = $45,687.23 * 0.0062958333
Interest ≈ $287.22
Therefore, the first period interest is $287.22.
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A random survey of 495 adults found that 59 had dietes. Which of the following is a 98% confidence interval for the population proportion of adults with diabetes?
Answer:
{0.0853,0.1531}
Step-by-step explanation:
[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}\bigr(1-\hat{p}\bigr)}{n}}[/tex]
[tex]\displaystyle CI_{98\%}=\frac{59}{495}\pm2.326\sqrt{\frac{\frac{59}{495}\bigr(1-\frac{59}{495}\bigr)}{495}}\approx\{0.0853,0.1531\}[/tex]
Use the diagram to find x and y
The values of x and y is x=8 and y=12.
We are given that;
The dimensions=7 and 24
Now,
(x+y)^2= 7^2 + 24^2
x^2+y^2+2ab=49+416
x^2+y^2+2xy=465
Also, 7^2=x2+h2
49=x2+15
x2=49+15
x2=64
x=8
Substituting the values of x
8+y=20
y=12
Therefore, by Pythagoras theorem the answer will be x=8 and y=12.
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Dos horas y media ¿A cuántos minutos equivale?
Answer:
90 minutos
Step-by-step explanation:
una hora es 60 minutos y media es 30 minutos.
HELP!
To keep fish in an aquarium healthy, the aquarium must maintain an average water temperature of 67°F. For 14 hours of the day, no hearing is required as the aquarium is naturally at 69°F. However, if left unheated for the remaining hours the temperature would drop to 50°F. How many degrees (during heating hours) should the tank temperature increase to maintain the average temperature?
Answer:
Step-by-step explanation:
To find out how many degrees the tank temperature should increase during the heating hours to maintain the average temperature, we need to calculate the temperature difference between the target average temperature of 67°F and the temperature during the unheated hours (50°F).
The difference in temperature is:
67°F - 50°F = 17°F
Since the heating hours account for the remaining hours of the day, which is 24 hours minus the 14 hours when no heating is required, we have:
24 hours - 14 hours = 10 hours
To maintain the average temperature of 67°F, the tank temperature should increase by 17°F during the 10 hours of heating.
To find the increase per hour, we divide the total temperature increase by the number of heating hours:
17°F / 10 hours = 1.7°F
Therefore, the tank temperature should increase by 1.7°F per hour during the heating hours to maintain the average temperature of 67°F.
his composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units. 2 identical pyramids with rectangular bases are connected at their base. The height of the pyramid is 2. The lengths of the sides of the rectangle are 5 and 0.25 units. Which expression represents the volume, in cubic units, of the composite figure? One-half (One-third (5) (0.25) (2) ) One-half (One-third (5) (0.25) (4) ) 2(One-third (5) (0.25) (2) ) 2(One-third (5) (0.25) (4) )
The expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.
How to evaluate the expression for the volume of the identical pyramidTo calculate for the volume of a rectangular base pyramid, we use the formula:
volume = 1/3 × area of base rectangle × height
volume of one identical pyramid = (1/3 × 5 × 0.5 × 2)cubic units
volume of the two identical pyramid = 2(1/3 × 5 × 0.5 × 2)cubic units.
Therefore, the expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.
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10. Find measure of arc JK
pls help ASAP
The value of arc JK is determined as arc JK = 28⁰.
What is the value of arc JK?
The value of arc JK is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc JK = m∠JNK
From the diagram, we have N = 152⁰
m∠JNK = ¹/₂ ( 360 - (152 + 152) (sum of angles at a point)
m∠JNK = 28⁰
The value of arc JK is calculated as follows;
arc JK = 28⁰
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