The function g(x)=4(x+3)² - 68 is mapped to 32.
What is equation?An equation is a mathematical expression in terms of one or more unknown variable.
Given are the following functions:
f(x)= - 3x² - 4
g(x)= 4(x+3)²-68
f(x)= 3x
f(x)= 2x-62
To get the mapped function, we substitute the value of x in all function,
a) f(x)=-3x²- 4
Put x=2,
f(2)= -3 (2)² - 4
f(2)= -16
It is not mapped.
b) g(x)=4(x+3)² - 68
Put x=2,
g(2) = 4(2+3)² - 68
g(x) =32
It is mapped to 32.
c) f(x)=3x
Put x=2,
f(2) = 3 x 2 =6
It is not mapped.
d) f(x)=2x - 62
Put x=2,
f(2) =2x2 -62
f(2) = -58
It is not mapped.
Therefore, the function g(x)=4(x+3)² - 68 is mapped to 32.
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Solve the following system to find the point(s) of intersection.
y = x² - 2x - 3
y = 2x - 3
x=4 y=5
if we put two pharases together
the answer is as follows pic :
x=4 y=5
Will a stand that hold up to 40 pounds support a 21-kilograms television? Explain used 2.2 Lb = kg
Answer: No, the stand will not support the TV. It is too heavy.
Work Shown:
1 kg = 2.2 lbs approximately
21*1 kg = 21*2.2 lbs
21 kg = 46.2 lbs
A 21 kilogram tv is roughly equivalent to 46.2 pounds.
This exceeds the 40 pound weight limit, so this stand will not support it.
Answer: No
Step-by-step explanation:
Weight limit = 40 Lb
Weight given = 21 kg
Conversion factor
2.2 Lb = 1 kg
2.2 x 21 = 46.2
46.2 Lb = 21 kg
46.2 > 40, the stand cannot support the TV
Complete the steps to factor the polynomial by grouping. p(x) = x3 5x2 – x – 5 p(x) = x2 (x ) – (x 5) p(x) = (x2 – )(x 5) p(x) = (x – )(x 1)(x )
The polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
The given polynomial to us is p(x) = x³ + 5x² - x - 5.
We are asked to factor the polynomial by grouping.
We can do this by following these steps:
p(x) = x³ + 5x² - x - 5.We group the first two terms and the next two terms to get p(x) = (x³ + 5x²) + (-x -5).Now, we take x² common from the first group and -1 common from the second group to get p(x) = x²(x + 5) -1(x + 5)Now, we take (x + 5) common from both the terms to get, p(x) = (x + 5)(x² - 1).Now, we right (x² - 1) as (x + 1)(x - 1). to get the polynomial as, p(x) = (x + 5)(x + 1)(x - 1).Therefore, the polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
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Jean had $25.86 in her pocket. If shoes cost $7.50 a pair plus 10% of tax. How many pairs can she buy?
Answer:
3 pairs
Step-by-step explanation:
10% of 7.50 is 0.75. So one pair will cost $8.25. Now, 25.86/8.25 and you get 3 pairs
Answer:
[tex]\fbox {3 pairs}[/tex]
Step-by-step explanation:
Cost of 3 pairs with tax :
⇒ 7.50 × 3
⇒ 22.50
* Adding tax *
⇒ 22.50 + 22.5 (0.1)
⇒ 22.50 + 2.25
⇒ 24.75
∴ Since 24.75 is less than 25.86, Jean can buy 3 pairs of shoes.
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks. If at year’s end an auditor
checks your accounting records and randomly selects one week to check the company’s payroll, what is the probability that the auditor will select a week in which you paid overtime wages and hired
temporary help?
The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.
What is probablitity?
Probability, can be define as the ratio of favorable outcomes to the n number of total events.
Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
p(b) = temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
= 0.81 + 0.46 -1
= 0.28
The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
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a toolbox has 10 screwdrivers and 6 wrenches. bella put 8 more wrenches in the toolbox. how many more wrenches are in the toolbox than screwdrivers
Answer:
4 more wrenches than screwdrivers
Step-by-step explanation:
6+8=14
14-10=4
therefore there are 4 more wrenches than screwdrivers.
:)
Answer:
14
Step-by-step explanation:
solution
Screwdrivers- 10
wrenches- 6
if bella adds 8 more wrenches.
= 6 + 8
=14
Now, there are 14 wrenches in the box
The table below shows the results of a survey that asked 1052 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at
random. Complete parts (a) through (c).
(a) Find the probability that the person opposed the tax or is female.
P(opposed the tax or is female) =
(Round to the nearest thousandth as needed.)
(b) Find the probability that the person supports the tax or is male.
P(supports the tax or is male) =
(Round to the nearest thousandth as needed.)
(c) Find the probability that the person is not unsure or is female.
P(is not unsure or is female)=
(Round to the nearest thousandth as needed.)
The complete options are P(opposed the tax or is female) = 0.28, b. P(supports the tax or is male) = 0.15, c. P(is not unsure or is female) 0.025.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
(a) The probability that the person opposed the tax or is female.
P(opposed the tax or is female) = 298 / 1052 = 0.28
(b) The probability that the person supports the tax or is male.
P(supports the tax or is male) = 168/1052 = 0.15
(c) The probability that the person is not unsure or is female.
P(is not unsure or is female) = 27 / 1052 = 0.025
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The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score? A) 20 B) 24 C) 32 D) 36
The highest score is 32.
What is mean?The mean refers to the average of a set of values.
Total players = 8
Mean= 14.5
Now, total score of 8 players,
= 14.5*8
=116
and, Total score for the remaining 7 players
= 12 * 7
= 84
Hence, the highest score is 116-84 =32
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The fences will be aligned with the exterior angles 1 and 2. what are some other relationships you can see between 1,2,a, and b? (2 points)
please help
1.8.4
The relationships between angles 1, a, b, and 2 can be defined using the angles between parallel lines.
In the diagram, we can see the fences, making angles 1 and 2 with the parallel lines X and Y respectively.
Using the angles among parallel lines, we can state the relationships between angles 1, a, b, and 2 as follows:
Angle 1 and Angle a are adjacent angles, thus their sum is 180°, that is m∠ 1 + m∠ a = 180°.Angle 2 and Angle b are adjacent angles, thus their sum is 180°, that is m∠ 2 + m∠ b = 180°.Angle 1 and Angle b are corresponding angles, thus they are equal, that is m∠1 = m∠ b.Angle 2 and Angle a are corresponding angles, thus they are equal, that is m∠2 = m∠ aAngle 1 and angle 2 are co-exterior angles, thus their sum is 180°, that is, m∠ 1 + m∠ 2 = 180°.Angle a and angle b are co-interior angles, thus their sum is 180°, that is, m∠ a + m∠ b = 180°.These were the relations among angles 1, a, b, and 2, using the parallel lines X and Y.
Refer to the diagram for a better understanding.
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Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.
Answer:
Step-by-step explanation:
Equation of the line in slope- intercept form:[tex]\sf \boxed{\bf y = mx +b}[/tex]
Here, m is the slope and b is the y-intercept
Find the slope with the given two points.
[tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]
Slope = -2/3 and choose any one the given points.
Substitute m = -2/3 and (5,6) in the above equation and find 'b'
[tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]
Equation of the line:
[tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]
Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ? Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4) A. Both the reflection and dilation preserve the side lengths and angles of triangle . B. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths. C. The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles. D. Neither the reflection nor the dilation preserves the side lengths and angles of triangle .
Answer: B. The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths.
Step-by-step explanation:
Reflections are congruency transformations, but dilations are similarity transformations.
find x if 2+x = -2/3
The pipe has a length 29cm, internal diameter 6.5cm and thickness 0.5cm. What is the Volume
Answer:
Length of pipe = 21 cm
Internal diameter = 4 cm
Internal radius = \frac{4}{2} = 2 cm24=2cm
Thickness = 0.5 cm
Outer radius = 2+0.5=2.5 cm
Volume of pipe =\pi R^2 h - \pi r^2 hπR2h−πr2h
Volume of pipe =\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3
=\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3722(2.5)2(21)−722(2)2(21)=148.5cm3
Hence The volume is 148.5 cubic cm.
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The thickness of a metal pipe is 1.5cm. The inner diameter is 21cm. What is the volume of metal required for a pipe of length 7cm
The average time between accidents in a factory is 5 weeks.
Find the probability that more than 7 weeks pass between accidents.
Answer:
The probability that more than 7 weeks pass between accidents is 4.0551 .
Step-by-step explanation:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes
A Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period.
mean = 5 weeks
rate = 1/5 = 0.2
x = average time
P(x > 7) = e^(0.2×7) = 4.0551
The probability that more than 7 weeks pass between accidents is 4.0551 .
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Which of the following is needed to construct a hexagon?
OA. Six obtuse triangles
OB. Six isosceles triangles
OC. Six right triangles
OD. Six equilateral triangles
The answer choice which represents the what is needed to construct a hexagon is Choice B; Six isosceles triangles.
What is needed to construct a hexagon?
By definition, an hexagon is a closed figure with six equal sides and six congruent interior angles.
On this note, upon assembly of six isosceles triangle s in which cases, the excluded side of the isosceles triangles form the sides of the hexagon and the congruent sides represents lines joining each vertex to the center of the hexagon, an hexagon is formed.
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Answer:
The correct answer is six equilateral triangles.
Step-by-step explanation:
The angle at the center of the hexagon is 360°, which is being divided into 6 equal parts. The value of each angle at the center is equal to 60°. All three angles of the 6 triangles formed in the given hexagon are equal to 60°. This proves that there are 6 equilateral triangles.
I need help lol xoxoxo
A book seller a book for Rs 70 at a gain of 40 percent find the profit
Answer:
Rs 20
Step-by-step explanation:
140%=Rs 70
100%
(100%×Rs 70)÷140%=50
Rs 70-Rs 50=Rs 20
if the unit rate is 30 miles per hour , then how much miles is traveled in 9 hours
Answer:
270 miles
Step-by-step explanation:
Since the unit rate is 30 miles per hour, the miles on 9 hours will be:
= 30 × 9
= 270 miles.
A randomly generated list of integers from 1 to 5 is being used to simulate an event, with the numbers 1 and 2 representing a success. What is the estimated probability of a success?
A.50%
B.30%
C.40%
D.20%
Y W P 8 cm E R WERP is a square. Find.
1. m2WER=
2. measure of PE =_______
3. measure of WA =
4. Value of y=
1) All interior angles of a square are right angles, so angle WER measures 90°
2) All squares are parallelograms, and diagonals of a parallelogram bisect each other, meaning PA=AE=8 cm. Thus, PE=16 cm
3) All squares are rectangles, and diagonals of a rectangle are congruent, meaning WR=16 cm. Then, using the fact that the diagonals bisect each other, we get that WA=8 cm
4) If we consider right triangle WPR, we know it is isoceles because all sides of a square are congruent. So, the length of WP is:
[tex] \frac{16}{ \sqrt{2} } = 8 \sqrt{2} [/tex]
Express 10cm as percentage of 50cm
Answer:
10 cm is 20% of 50 cm.
Step-by-step explanation:
1) Put the "question" into fraction form: 10/50
2) Divide the numerator by the denominator (essentially changing the fraction into the decimal form): 10 ÷ 50 = 0.2
3) Multiply the quotient by 100: 0.2 × 100 = 20
4) Slap a "%" on the end and you're good to go!! : 20%
Subtract the equations. Two-Variable Systems: Elimination
(screenshot of the question below)
Answer:
4x = 14
Step-by-step explanation:
7x + 2y = 17
– (3x + 2y = 3)
- - -
4x = 14
So, the correct option is A. 4x = 14
Hope it helps!
For a given interest rate, simple interest varies jointly as principal and time. If $2000 left in an account for 4 yr earned interest of $280, how much interest would be earned in 6 yr?
What are the exact solutions of x2 − 3x − 5 = 0? (1 point) a x = the quantity of negative 3 plus or minus the square root of 29 all over 2 b x = the quantity of 3 plus or minus the square root of 29 all over 2 c x = the quantity of 3 plus or minus the square root of 11 all over 2 d x = the quantity of negative 3 plus or minus the square root of 11 all over 2
x = the quantity of 3 plus or minus the square root of 29 all over 2. Then the correct option is B.
What is the solution of the quadratic equation by formula method?The quadratic equation is given as ax² + bx + c = 0.
Then the solution is given as
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic equation is given below.
x² – 3x – 5 = 0
Then the solution of the equation will be
[tex]\rm x = \dfrac{-(-3)\pm \sqrt{(-3)^2 - 4 *1*(-5)}}{2*1}\\x = \dfrac{3 \pm \sqrt{29}}{2}[/tex]
Then the correct option is B.
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if the exterior angles of a pentagon are x° 2x° (x+30)°,(x-10)° and (x+40)° find x
a) 30
b) 50
c) 60
d) 80
Answer:
[tex]\fbox {b) 50}[/tex]
Step-by-step explanation:
The sum of the exterior angles of any polygon (including a pentagon) is equal to 360 degrees.
Then :
⇒ x + 2x + x + 30 + x - 10 + x + 40 = 360
⇒ 6x + 60 = 360
⇒ 6x = 300
⇒ x = 50
Answer:
[tex]\huge\boxed{\sf x = 50}[/tex]
Step-by-step explanation:
Statement:The exterior angles of a pentagon add up 360 degrees.Given angles:x°2x°(x+30)°(x-10)°(x+40)°Solution:x + 2x + x + 30 + x - 10 + x + 40 = 360
6x + 60 = 360
Subtract 60 to both sides
6x = 360 - 60
6x = 300
Divide 6 to both sides
x = 300/6
x = 50
[tex]\rule[225]{225}{2}[/tex]
one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?
After 3 months memberships will cost the same.
We have,
Cost of Membership of 1st gym = $ 10 per month
And, the Cost of the sign-up fee for 1st gym = $ 45
And,
Cost of Membership of 2nd gym = $ 25 per month
And, the Cost of the sign-up fee of the 2nd gym = $ 0
Now,
Let the number of months = m
So,
According to the question;
45 + 10m = 25m
⇒
25m - 10m = 45
15m = 45
m=3
So, After 3 months memberships will cost the same.
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Given: AC and BD are parallel. BX and CY are parallel. AX = DY.
Prove: AYC is congruent to DXB
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Using the ASA congruency the triangles are congruent.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
For the two of the given triangles ΔACY and ΔDXB,
∠A = ∠D {Alternate Interior Angles}∠DXB = ∠ACY {Alternate Interior Angles}AY = YD ⇒ (AX + XY) = (DY + XY) {Given AX=DY}Since the measure of the two angles and one side of the two triangles are equal, therefore, using the ASA congruency the triangles are congruent.
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Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| + 1 > 7/2
The graph is shown below:
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Rearrange unknown terms to the left side of the equation:
|x| > 7/2-1
Now,
|x| > (7-2)/ 2
Calculate the sum or difference:
|x| > 5/ 2
Convert the absolute inequality to standard inequality:
x> 5/2 or x< -5/2
Solve the inequality:
x> 5/2
Solve the inequality:
x< -5/2
Graph on number line is attached
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PLEASE HELP!!!!! ASAP
[tex]\text{Let's factor this quadratic.}\\\text{ We can start by thinking of two numbers such that,}\\\text{ if they are multiplied together, the product is 9}\\\text{if they're added together, the sum is -10, the middle term.}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{These numbers are -9 and -1.}\\\text{Checkup::}\\\text{-9*(-1)=9 and -9+(-1)=-10. The answer is good}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now, write these numbers as factors::}\\\text{(x-9)(x-1)=0 (make sure that the equation is \textbf{set to zero})}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now we can solve these mini equations in terms of x::}\\\text{x-9=0; \, x=9}\\\text{x-1=0; x=1}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Our factors are:: \textsl{9 and 1}}[/tex]
Answer:
x=1
Step-by-step explanation:
Pls help and explain tyyy
Answer:
11) 195312
13) 5461
Step-by-step explanation:
11)
15÷(-3) = -5
(-75)÷15 = -5
375÷(-75) = -5
It’s clear that the common ratio of this geometric sequence is -5
Then using the sum formula for geometric sequences :
[tex]S_{11}=\left( -3\right) \times \frac{1-\left(-5 \right)^{8} }{1-(-5)} =-\frac{1}{2}\times(1-(-5)^8)=195312[/tex]
……………………………………………………
13)
[tex]S_{13}=1\times \frac{1-4^{7}}{1-4} =-\frac{1}{3} \times(1-4^{7})=5461[/tex]
