Answer:
The given lines are un-related.
Step-by-step explanation:
In the question two functions are given as h(t)=3t-4 and j(t)=5-t.
It is required to find whether these lines are perpendicular, parallel or neither.
Step 1 of 1
Find the slope of two lines by comparing these to the standard form.
y=mx+b
Then, [tex]$m_{1}[/tex]=3
And [tex]$m_{2}[/tex]=-1
Since, both slopes are neither equal nor reciprocal of each other.
Therefore, the lines are un-related.
What is the measure of the central angle of a circle with radius 18 centimeters that intercepts a12π centimeters arc?
Answer: [tex]120^{\circ}[/tex]
Step-by-step explanation:
[tex]12\pi=2(\pi)(18)\left(\frac{\theta}{360} \right)\\\\12\pi =36\pi \left(\frac{\theta}{360} \right)\\\\\frac{1}{3}=\frac{\theta}{360}\\\\\theta=120^{\circ}[/tex]
If measure of AC= 50 degrees, then…
1) How many degrees measures the central angle O?
2) How many degrees measures the inscribed angle B?
1) Because [tex]\angle AOC[/tex] is a central angle, the answer is 50 degrees.
2) By the inscribed angle theorem, the answer is 25 degrees.
Please assist me with this question
Answer:
? = 45
Step-by-step explanation:
the inner and outer triangles are similar ( AA postulate )
Then the ratios of corresponding sides are in proportion, that is
[tex]\frac{56}{56+24}[/tex] = [tex]\frac{105}{105+?}[/tex] , that is
[tex]\frac{56}{80}[/tex] = [tex]\frac{105}{105+?}[/tex] ( divide numerator/denominator by 8 to simplify left side )
[tex]\frac{7}{10}[/tex] = [tex]\frac{105}{105+?}[/tex] ( cross- multiply )
7(105 + ? ) = 1050 ← distribute parenthesis on left side
735 + 7? = 1050 ( subtract 735 from both sides )
7? = 315 ( divide both sides by 7 )
? = 45
construct a right angle triangle abc where m b is equal to 90 degree BC is equal to 4.5 cm and ac is equal to 7 cm
The triangle will be computed based on the information illustrated below.
How to compute the triangle?The steps needed for the construction will be:
Draw a segment XY.
Locate B, C on XY such that BC = 4.5cm.
Construct a line segment such that B = 90°.
With C as center and radius 7cm, draw a arc cutting BD at A.
Then, the required triangle ABC will be gotten.
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Kelly offers to pay for 9 of her friends to play laser tag, but 2 of them don't want to play.
if laser tag costs $4 per person, how much will Kelly spend on her friends /
Answer:
$28Step-by-step explanation:
If she offers to 9, but 2 reject, that means she paid for 7 friends.
If each friend costs $4, multiply 4 by 7.
The answer is $28
Hope this helps! (:
Find F(5) for f(x)= 1/4(2)^x
If we have a function f(x), f(5) is f(x) but replacing x with 5. The result give us a value of y and a point of the function, (x, y).
[tex]f(5) = \frac{1}{4} ({2})^{5} = \frac{32}{4} = 8[/tex]
ANSWER A
Hello!
Substitute x = 5 to find f(5).
⇒ f(5) = 1/4(2)⁵
⇒ f(5) = 32/4
⇒ f(5) = 8
∴ The correct option is A.
The sum of two numbers is 8 and sum of their reciprocal is 8/15. Find the numbers.
Answer:
The 2 numbers are 3 and 5.
Step-by-step explanation:
x + y = 8
1/x + 1/y = 8/15
From first equation y = 8 - x so
1/x + 1 / (8-x) = 8/15
Multiply through by the LCM 15x(8-x):-
15(8 - x) + 15x = 8x(8-x)
120 - 15x + 15x = 64x - 8x^2
8x^2 - 64x + 120 = 0
x^2 - 8x + 15 = 0
(x - 3)(x - 5) = 0
x = 3 or 5
so y = 8-3 = 5 or 3.
. A new employee at an auto detailing shop is offered one of three options for earning pay: Option 1: Receive an hourly rate of $15.25 for 8 hours plus $0.50 per bottle of wax sold to customers. Option 2: Receive $38.75 per automobile detailed in a day. Option 3: Receive $100 per day plus 2% of sales in a day. A typical day consists of 12 bottles of wax sold per detailer, 4 automobiles detailed per employee, and average daily sales are $1,500. Which option should the new employee choose in order to make the most money on an typical day, and how much will he earn in a 20-day month at this rate?
The new employee should choose the second option to make the most money on a typical day. The amount that the new employee will earn 20-day at this rate is $3,100.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
For Option 1,
Receive an hourly rate of $15.25 for 8 hours plus $0.50 per bottle of wax sold to customers. Also, A typical day consists of 12 bottles of wax sold per detailer.
Earning = ($15.25 × 8) + ($0.50×12)
= $122 + $6
= $128
For Option 2,
Receive $38.75 per automobile detailed in a day. Also, 4 automobiles are detailed per employee. Therefore, the earnings are,
Earning = $38.75 × 4
= $155
For Option 3,
Receive $100 per day plus 2% of sales in a day. Also, the average daily sales are $1,500. Therefore, the earnings are,
Earning = $100 + 0.02($1500)
= $130
Hence, The new employee should choose the second option to make the most money on a typical day.
2.)
The amount that the new employee will earn 20-day at this rate is,
Amount earned = $155 × 20 days
= $3,100
Hence, The amount that the new employee will earn 20-day at this rate is $3,100.
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What is the vertex of the graph of the function below?
y=x²-4x+3
O A. (1,-1)
OB. (2,-1)
O C. (2,0)
O D. (1.0)
Answer:
B
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² - 4x + 3 ← is in standard form
with a = 1, b = - 4 , then
x = - [tex]\frac{-4}{2}[/tex] = 2
substitute into the equation for corresponding y- coordinate
y = 2² - 4(2) + 3 = 4 - 8 + 3 = - 1
vertex = (2, - 1 )
and the other answer that you didnt see is ( 2+3×2+5+6+7+9 units ) .
pls give me the answer .. and ty <3 .
There is a rule for finding perimetre of all polygons that perimetre is the sum of all the side's lengths ; according to this rule add the length of the sides of this polygon and you'll get the answer , the answer is the choice that you've written ( 2+3×2+5+6+7+9 ) or ( 2+3+3+5+6+7+9 ) both are correct because 3+3 is same as 3×2
perimetre is 2+3×2+5+6+7+9 = 35 units
HOPE IT HELPS
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer to all of them, Tysm!
#1
No
#2
We can see f(1) has 3 values so it's not a function as it's failed in vertical line test
#3
f(10) has two values -2 and 11
So not a function
#4
As per definition of function
every domain has an unique rangeSo it's not a function
The inverse of F(x) is a function.
-5
OA. True
OB. False
The inverse of any function F(x) is also a function.
A function is an abecedarian notion in mathematics and computer programming. In both contexts, a function is a regulation or relationship that maps input values to corresponding output values. It takes one or more input values, performs a set of operations or calculations, and produces a single output value.
There are many types of functions such as trigonometric function, logarithmic function, exponential function, and so on.
If a function f(x) gives output y then its inverse will be [tex]f^{-1}(y)[/tex] and will return x as output.
So, the statement is true.
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Find the value of X.
Answer:
151°
Step-by-step explanation:
The above shape is a quadrilateral.
sum of exterior angle of a quadrilateral is 360°.The exterior angles are :
82°, 70°, 62°, and (x -5)°
Therefore,
82 + 70 + 62 + x - 5 = 360
214 -5 + x = 360
209 + x = 360
x = 360 - 209
x = 151°
66. Extensions
Find the equation of the line that passes through the following points: (2a, b) and (a, b + 1)
Answer:
The equation of the line that passes through the points (2a, b) and (a, b+1) is [tex]$y=-\frac{1}{a} x+2+b$[/tex].
Step-by-step explanation:
The given points are (2a, b) and (a, b+1).
It is required to find the equation of the line that passes through the points. the slope-intercept form.
Step 1 of 4
Using the given two points, to find the slope.
Given points are (2a, b) and (a, b+1).
Substitute [tex]$x_{1}[/tex]=2a,
[tex]$$\begin{aligned}&y_{1}=b \\&x_{2}=a \text { and } \\&y_{2}=b+1\end{aligned}$$[/tex]
into the formula, [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Step 2 of 4
Simplify [tex]$m=\frac{b+1-b}{a-2 a}$[/tex], further
[tex]$$\begin{aligned}m &=\frac{b+1-b}{a-2 a} \\m &=-\frac{1}{a}\end{aligned}$$[/tex]
As a result, the slope is [tex]$m=-\frac{1}{a}$[/tex].
Step 3 of 4
Use the slope [tex]$m=-\frac{1}{a}$[/tex] and the coordinates of one of the points (2a, b) into the point-slope form, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex].
Substitute [tex]$m=-\frac{1}{a}$[/tex],
[tex]x_{1}=2 a$ and$y_{1}=b$[/tex]
into the formula, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$y-b=-\frac{1}{a}(x-2 a)$[/tex]
[tex]$y-b=-\frac{1}{a} x+2$$[/tex]
Step 4 of 4
Rewrite the above equation as a slope-intercept equation. So, from the above term [tex]$y-b=-\frac{1}{a} x+2$[/tex], Add b on each side.
[tex]$$\begin{aligned}&y-b=-\frac{1}{a} x+2 \\&y=-\frac{1}{a} x+2+b\end{aligned}$$[/tex]
Therefore, the equation of the line that passes through the points is [tex]$y=-\frac{1}{a} x+2+b$[/tex].
what does 160=7x+6 equal to?
Answer:
x=22
Step-by-step explanation:
7x+6=160.
Lets start by moving 6 over to the other side. We can do this by subtracting 6 from both sides of the equation.
7x+6-6=160-6
7x=154
Now, let's isolate x by getting rid of the 7. The 7 is being multiplied with x, so to get rid of it we have to divide both sides by 7.
7x/7 = 154/7
x=22
Look Below :
Step-by-step explanation:
160 - 6 = 7x
154 = 7x
Or
7x = 154
x = 22
Please help me out. im struggling
Answer: 48
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{x}{36}=\frac{64}{x}\\\\x^{2}=36 \cdot 64\\\\x=\sqrt{36 \cdot 64}\\\\x=\sqrt{36} \sqrt{64}=48[/tex]
Write a piecewise-defined step function f(x) that has the following characteristics:
f(x) has more than one x intercept.
The domain of f(x) is the real numbers.
The range of f(x) consists of four unique integers.
Here use general math mind
F(x) has more than one x inetercept .
We shall take one quadratic function in which will give 2 intercepts(Real)Domain is for real numbers
Four unique numbers?
Add 4 constants for 4 unique definations and that shouldn't fall under quadratic regionLets see
[tex]\sf f(x)=\begin{cases}\sf (x+2)²,x\neq \left\{0,-1,1,2,3\right\}\\ \sf 0,x=0\\ \sf 1,x=-1\\ \sf 9,x=1\\ \sf 16,x=4\\ \sf 25,x=5\end{cases}[/tex]
Has 2 x interceptsFor -2
y=(0)²=0(-2,0)For 0 it's (0,0)
And for extra ,it's discontinuous on x=0
. The Pancake Restaurant served 348 pancakes. If 87 customers ate an equal number of pancakes, how many did each person eat?
Answer:
4
Step-by-step explanation:
348 / 87 = 4
There are 87 Customers. The restauraunt served 348 pancakes. You divide 348 by 87 and conclude that each customer ate 4 pancakes.
Answer:
4
Step-by-step explanation:
348 ÷ 87 = 4
each person ate 4 pancakes
In circle N with the measure of arc \stackrel{\Large \frown}{MP}= 114^{\circ} MP ⌢ =114 ∘ , find \text{m} \angle MNPm∠MNP
According to the central angle theorem, the measure of angle MNP = 114°.
What is the Central Angle Theorem?According to the central angle theorem of a circle, the measure of central angle MNP equals the measure of intercepted arc MP.
Measure of arc MP = 114°
Measure of angle MNP = arc MP
Measure of angle MNP = 114° [central angle theorem]
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Find the area of the figure to the nearest square unit
Answer:
357 mi²
Step-by-step explanation:
A = LW + 0.5πr²
A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²
A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²
A = 357 mi²
What are domain and range of these two and how step by step please?
Answer:
Step-by-step explanation:
[tex]\sf f(x) = \dfrac{1}{Sin \ x}[/tex]
f(x) does not contain values where sin x = 0. Sin x is 0 at integral multiples of π.
Domain = R - nπ , n is integers.
The range of Sin x is [-1 , 1] and in this range we cannot find 1/sin x .
Range = (-∞, -1] U [1,∞)
[tex]\sf f(x) =\dfrac{1}{Cos x}[/tex]
f(x) does not contain values where Cos x = 0 . Cos x is 0 at integral of multiples of (π/2)
[tex]\sf Domiain =R -\dfrac{(2n+1)\pi }{2}[/tex]
The range of Cos x is [-1,1] and in this range we cannot find 1/Cos x.
Range = (-∞, -1] U [1,∞)
Points U, M, And D are collinear with U between U and D.
Given:
UM=5x+30
MD=3x+80
UD=10x+20
What is x
The value of x from the given equation is 5/3
How to determine the valueSince the three points are collinear to U, they are on a straight line which equals 0
Then we have,
UM + UD = MD
5x+30 + 10x+20 = 3x+80
Collect like terms
5x + 10x + 50 = 3x + 80
15x - 3x = 80 - 50
12x = 30
x = 30/12 = 15/6 = 5/3
Thus, the value of x from the given equation is 5/3
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How to find minimum and maximum of this equation.
Using it's vertex, the maximum value of the quadratic function is -3.19.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the equation is:
y + 4 = -x² + 1.8x
In standard format:
y = -x² + 1.8x - 4.
The coefficients are a = -1 < 0, b = 1.8, c = -4, hence the maximum value is:
[tex]y_v = -\frac{1.8^2 - 4(-1)(-4)}{4(-1)} = -3.19[/tex]
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After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly. The relationship between the elapsed time, t in seconds, and the number of bacteria, Bsecond(t) in the petri dish is modeled by the following function:
Using the given exponential function, we have that:
Every minute, the number of bacteria decays by a factor of 0.98.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the function is, for the amounts each second:
[tex]Bs(t) = 6000\left(\frac{15}{16}\right)^{t}[/tex]
The initial amount is of 6000 bacteria. After 60 seconds = 1 minute, the amount will be of:
[tex]Bs(60) = 6000\left(\frac{15}{16}\right)^{60} = 125[/tex]
The decay factor after 1 minute is:
(6000 - 125)/6000 = 98% = 0.98.
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How can the basic fact help find 3,000 divided by 5?? I need help
Answer:
3000/5 = 600
Step-by-step explanation:
Every multiplication fact is equivalent to two (2) division facts:
a·b = c ⇒ c/a = b and c/b = a
Multiplication or division by 10 involves moving the decimal point one place to the right or left (respectively).
Recasting the problemThe division ...
[tex]\dfrac{3000}{5}[/tex]
is fully equivalent to ...
[tex]\dfrac{30}{5}\times 100[/tex]
Using the basic factWe assume your "basic fact" is 5×6 = 30. In accordance with the above equivalence to division problems, this tells you ...
[tex]\dfrac{30}{5}=6\\\\\dfrac{30}{5}\times100 = 6\times100\\\\\dfrac{3000}{5}=600[/tex]
Someone please help !! :(
Question 22 of 25
What is the average rate of change for this quadratic function for the interval
from x = 0 to x = 2?
Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
No this is not a function because the x-values repeat. In a function you can have the the output duplicate but not the input. The input at 3 has duplicates s o this is not a function.
Step-by-step explanation:
Definition
A relation is called to be a function if every domain has an unique range
f(x)=yHere
f(3)=-9,4As
f(3) has 2 corresponding values it's not a function
In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is
The 95% confidence interval of voters not favoring the incumbent is (0.0706, 0.1294).
Sample size, n=400
Sample proportion, p = 40 / 400
= 0.1
We use normal approximation, for this, we check that both np and n(1-p) >5.
Since n*p = 40 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.1 and standard deviation = root( p * (1-p) /n )
= 0.015
For constructing Confidence interval,
Margin of Error (ME) = z x SD = 0.0294
95% confidence interval is given by Sample Mean +/- (Margin of Error)
0.1 +/- 0.0294 = (0.0706 , 0.1294)
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3. This is a graph of the function f(x) = -3x + 1.
-2
8
4f(x) = -3x + 1
0
y
4
2
X
a) Determine the range value when the
domain value is 1.
b) Determine the domain value when the
range value is 4.
a) [tex]-3(1)+1=\boxed{-2}[/tex]
b) [tex]4=-3x+1 \longrightarrow -3x=3 \kongrightarrow x=\boxed{-1}[/tex]
Describe fully the single transformation which takes shape A to shape B
Shape A was reflected over the y axis and translated 1 unit down to get shape B.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation is the movement of a point either up, down, left or right on the coordinate plane.
Shape A was reflected over the y axis and translated 1 unit down to get shape B.
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