Answer:
The y-intercept of function f(x) is 2.The y-intercept of function g(x) is -3.Therefore, we conclude that function f(x) has a greater y-intercept.
Step-by-step explanation:
The y-intercept of any function can be determined by checking the value of y at x = 0.
Important Tip
A point where the graph meets the y-axis — y-intercept.Determining the y-intercept of the function f(x)
Given the function f(x) passes through the point (0,2).
It means at x = 0, the value of y = 2
Thus, the y-intercept of function f(x) is 2.
Determining the y-intercept of the function g(x)
Given the function g(x)
[tex]g\left(x\right)=x^2-2x-3[/tex]
substitute x = 0 in the function equation
[tex]g\left(0\right)=\left(0\right)^2-2\left(0\right)-3[/tex]
[tex]g\left(0\right)=0-0-3[/tex]
[tex]g\left(0\right)=-3[/tex]
It means at x = 0, the value of y = -3
Thus, the y-intercept of function g(x) is -3.
Conclusion:
The y-intercept of function f(x) is 2.The y-intercept of function g(x) is -3.As 2 > -3
Therefore, we conclude that function f(x) has a greater y-intercept.
please help me with the question
Answer: [tex]\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]
Step-by-step explanation:
[tex]a \cdot b=(3)(0)+(-4)(5)+(-1)(2)=-22\\\\|a| |b|=\sqrt{3^2 +4^2 +1^2} \sqrt{5^2 +2^2}=\sqrt{754}\\\\\therefore \cos \theta=\frac{-22}[\sqrt{754}}\\\\\theta=\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]
A ladder is leaning against a building as shown in the
diagram.
How many feet up the side of the building is the top of
the ladder?
ft
10 feet
6 feet
The length of ladder is 30 ft.
How can the feet that made up the side of the building is the top of the ladder be known ?The formula below can be used in solving the problem
Tan (∅)= [tex]\frac{opposite}{adajacent}[/tex]
∅=70°
opposite = BC
Adjacent = 12 ft
70°= opposite/ 12
opposite= 32.96 ft
Therefore, The length of ladder is 30 ft.
NOTE; Since the actual diagram can not be found i solved another on on the same topic
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CHECK COMPLETE QUESTION BELOW:
Consider the diagram shown where a ladder is leaning against the side of a building. the base of the ladder is 12ft from the building. how long is the ladder? (to the nearest ft)
a. 25ft
b. 30ft
c. 35ft
d. 40ft
need help with this!
Answer:
1.The slope intercept- form of the function is:
y = x -2
2.The predicted length of the vine after 53 days is 51 cm.
Step-by-step explanation:
The slope is the [tex]\frac{change in length}{change in days}[/tex]
In the table, every time that the length increased by 5, the days also increased by 5. 5/5 = 1
Now we have to find the y-intercept, we can use the slope and one of the points that we know to do this. Let's use the first point (5,3). This is in the form (x,y).
y = mx + b
3 = (1)(5) + b
3 = 5 + b Subtract both sides by 5
-2 = b Now we can write the equation
y = mx + b
y = x -2. Plug 53 in for x and you will find your second answer.
y = 53 - 2
y = 51
1. The function's slope intercept form is y = x -2.
2. The vine should be 51 cm long in length after 53 days.
Determining the Slope Intercept Form:
The slope is given as,
m = (Change in length) / (Change in days)
In the table, it can be seen that,
The days climbed by 5 for every 5 that the length did as well [10-5 = 8-3 = 5].
∴ Slope, m =5/5 = 1
We may use the slope and one of the points we are familiar with to help us find the y-intercept. Utilizing the first point (5,3), this is how it looks for the point (x, y),
y = mx + c ..... (1)
3 = (1)(5) + c
3 = 5 + c
Subtract 5 from both sides to get c.
c = -2
Hence, from (1), the slope intercept form is given as,
y = x - 2 ...... (2)
Predicting the Vine Length:
Since x represents the number of days, put x = 53 in equation (2) to predict the vine length after 53 days.
y = (53) -2
y = 51 cm
Thus, the length of vine after 53 days would be 51 cm.
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Follow the instructions below to show two different ways of filling a square that has sided of length a + b with triangles and squared without gaps or overlaps.
The proofing for the triangle is illustrated below.
How to illustrate the information?The proofing for a² + b² = c² in the triangle is illustrated.
It should be noted that the longest side in the triangle is the hypothenuse. The hypothenuse is gotten by finding the square root of the opposite and the adjacent.
Therefore, a² + b² = c²
Let's say a = 3 and b = 4, the value of c will be:
c² = a² + b²
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = ✓25
c = 5
Also, the square and triangle is illustrated and attached.
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Which choice is equivalent to the quotient shown here for acceptable
values of X?
√25(x-1) + √5(x-1)²
OA. √25(x-1)-5(x-1)²
OB.
5
1(x-1)
OC. √125(x-1)3³
OD. √5(x-1)
The equivalent to the quotient shown in the task content for acceptable values of x is; √(5/(x-1)).
What is the equivalent of the quotient?It follows from the task content that the expression given is; √(25(x-1)) ÷ √(5(x-1)²).
It therefore follows from the the laws of indices that the evaluation is thus;
= √{(25/5) ×(x-1)/(x-1)²}.
Ultimately, upon evaluation we have;
= √(5/(x-1))
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if sin just answer the please lol i don't feel like typing
ASAP
Considering that the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.
What are the signs of the sine and of the cosine in each quadrant?Quadrant 1: Both positive.Quadrant 2: Sine positive, cosine negative.Quadrant 3: Both negative.Quadrant 4: Sine negative, cosine positive.Hence, since the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.
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for csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
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Simplify the ratio 0.40 to 0.60
The ratio 0.40 to 0/60 is equivalent to a simplified ratio..?
(Simplify your answer. Type a whole number or fraction)
The simplified firm of the ratio 0.40 to 0.60 is 2 : 3
Ratio0.40 : 0.60
= 0.40 / 0.60
divide both numerator and denominator by 0.20
= 2 / 3
= 2 : 3
Therefore, the simplified form of the ratio 0.40 to 0.60 is 2 : 3
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ppose you have one quart of water/juice mix that is 40% juice, and you add 3
quarts of water. What percent juice is the final m
The final percent of juice is 10%
How to get the final percent?
We initially have one quart that is 40% juice and 60% water.
Then initially we have:
0.4 of quarts of juice.0.6 quarts of water.Then we add another 3 quarts of water, so the new mixture has:
0.4 quarts of juice.3.6 quarts of water.So we have 4 quarts of mixture.
The new percentage of juice will be:
P = (0.4 quarts/4 quarts)*100% = 10%
The final percent of juice is 10%
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What is the volume of a solid with dimensions 5 inches, 3 inches, and 4 inches? 15 cubic inches 30 cubic inches 45 cubic inches 60 cubic inches
Answer:
60 cubic inches
Step-by-step explanation:
You multiply 3 and 4 to get 12, then 12 and 5 to get 60
3 x 4 x 5 = 60
The volume of a solid exists the measurement of how much area an object brings up. It exists measured by the number of unit cubes it brings to fill up the solid.
Volume of a solid = 5 [tex]*[/tex] 3 [tex]*[/tex] 4 = 60 cubic inches
Therefore, the correct answer is option d) 60 cubic inches.
What is the volume in dimension?Volume exists as a three-dimensional measurement; that exists, it measures the collective length, width, and height of a figure. Because planes, polygons, and other two-dimensional figures don't contain height, they contain no volume. Only solids and figures with dimensions more significant than or equivalent to three have volume.
What is the volume of solid?The volume of a solid exists as the measurement of how much space an object brings up. It exists estimated by the number of unit cubes it brings to fill up the solid.
Volume of a solid = 5 [tex]*[/tex] 3 [tex]*[/tex] 4 = 60 cubic inches
Therefore, the correct answer is option d) 60 cubic inches.
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Can someone explain how to do this
The negative solution is -2.21 and positive solution is 12.21
Factorizing quadratic equationsGiven the quadratic equation expressed as:
x^2-10x-27 = 0
Find the solution using the general formula
x^2-10x-27 = 0
x = 10±√(10)²-4(1)(-27)/2
x = 10±√100+108/2
x = 10±√208/2
x = 10±14.422/2
Simplify
x = 10+14.422/2 and x = 10-14.422/2
x = 24.422/2 and -4.422/2
x = 12.21 and -2.21
Hence the negative solution is -2.21 and positive solution is 12.21
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The event of walking your dog is A and the event of electing a female as class president is B. If these events are independent events, using P(A)=0.35, and P(B)=0.54, what is P(B|A)?
The value of the probability is 0.54
How to determine the probability?The given parameters are:
P(A) = 0.35
P(B) = 0.54
From the question, we understand that the events are independent.
This means that
P(B|A) = P(B)
Substitute P(B) = 0.54
P(B|A) = 0.54
Hence, the value of the probability is 0.54
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suppose that you borrowed 2000 from a friend and promise to pay back 3600 in 4 years. What simple interest rate will you pay?
The simple interest rate that the money would be paid is 20%
Simple interestFrom the question, we are to determine the interest rate that the money would be paid
Using the formula for simple interest,
S.I = PRT/100
Where S.I is the simple interest
P is the principal
R is the rate
and T is the time
From the given information,
P = 2000
S.I = Amount - Principal = 3600 - 2000 = 1600
R = ?
T = 4
Putting the parameters into the equation, we get
1600 = (2000 ×R × 4) / 100
1600 = 20 × R × 4
1600 = 80R
R = 20%
Hence, the simple interest rate that the money would be paid is 20%
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You have $2000 to invest in an account and need to have $2500 in five years. What annual interest rate would you need to have in order to have this if the amount is compounded monthly?
a 3.77%
b4.47%
c2%
d5.5%
please answer
The annual interest rate needed to reach the given amount in five years is 4.47%.
Hence, option B) is the correct answer.
What is the annual interest rate needed?Compound interest is expressed as;
A = P( 1 + r/n )^(nt)
Making rate r the subject of the formula;
r = n[ (A/P)^(1/nt) - 1 ]
Given that;
Principal P $2000Final Amount A = $2500Number of times interest applied per time period n = monthly = 12Time t = 5We substitute into our formular above
r = n[ (A/P)^(1/nt) - 1 ]
r = 12[ (2500/2000)^(1/(12×5)) - 1 ]
r = 12[ (1.25^(1/60) ) - 1 ]
r = 12[ 1.0037598 - 1 ]
r = 12[ 0.0037598 ]
r = 0.447
Next we convert to percentage
r = 0.447 × 100%
r = 4.47%
The annual interest rate needed to reach the given amount in five years is 4.47%.
Hence, option B) is the correct answer.
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Please help Need answer Urgently.
give at least five problems solving about area of a sector of a circle.
five example of arc length
fixe example or arc of a circle
See below for the examples of sectors and arcs of a circle
Area of sector of a circleThe area of a sector is calculated as:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex] ---- when the angle is in degrees
[tex]A = \frac{\theta}{2} *r^2[/tex] ---- when the angle is in radians
Take for instance, we have the following problems involving sector areas
Calculate the area of a sector where the radius of the circle is 7, and
The central angle is 30 degreesThe central angle is π/12 radThe central angle is 90 degreesThe central angle is π/4 radThe central angle is 180 degreesUsing the above formulas, the sector areas are:
1. [tex]A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83[/tex]
2. [tex]A = \frac{\pi}{12} * 7^2 = 12.83[/tex]
3. [tex]A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5[/tex]
4. [tex]A = \frac{\pi}{2} * 7^2 = 38.5[/tex]
5. [tex]A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77[/tex]
Examples of arc lengthThe length of an arc is calculated as:
[tex]L= \frac{\theta}{360} * 2\pi r[/tex] ---- when the angle is in degrees
[tex]L = r\theta[/tex] ---- when the angle is in radians
Take for instance, we have the following problems involving arc lengths
Calculate the length of an arc where the radius of the circle is 7, and
The central angle is 30 degreesThe central angle is π/12 radThe central angle is 90 degreesThe central angle is π/4 radThe central angle is 180 degreesUsing the above formulas, the arc lengths are:
1. [tex]L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7[/tex]
2. [tex]L = \frac{\pi}{12} * 7 = 3.7[/tex]
3. [tex]L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0[/tex]
4. [tex]L = \frac{\pi}{4} * 7 = 11[/tex]
5. [tex]L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22[/tex]
Examples of the arcs of a circleThe examples include:
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PLEASE IF ANYONE CAN HELP JUST ANSWERS 1-8 (giving brainliset)
The computation of the equations is illustrated below.
How to illustrate the equation?a. x - y = 1 .... i
x + y = -9 ..... ii
Subtract the equations
-2y = 10
y = 10/-2 = -5
Since x - y = 1
x - (-5) = 1
x + 5 = 1
x = 1 - 5 = -4
b. 3x + 2y = -9
x - y = -13
Multiply equation i by 1
Multiply equation ii by 3
3x + 2y = -9
- 3x - 3y = -39
5y = 30
y = 6
Since x - y = 13
x - 6 = 13
x = 13 + 6 = 19
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Please help ASAP
What is the measure of YZ?
A.142
B.52
C.128
D.38
Work Shown:
(arc YZ + arc XU)/2 = angle YVZ
(arc YZ + 38)/2 = 90
arc YZ + 38 = 90*2
arc YZ + 38 = 180
arc YZ = 180 - 38
arc YZ = 142
mimi read 1/4 of a book on wednesday. she read 82 more pages on thursday, and she finished the book on friday by reading the last 98 pages. how many pages were in mimi's book.
Answer:
240 pages
Step-by-step explanation:
Let x = the TOTAL number of pages in the book. So we'll add up all her reading for the week and it should equal x, the total number of pages.
see image.
find the y intercept of 2x - 5y + 7 = 0
Write the following powers of 6 exponential form: 6 x 6
The exponential form of 6 × 6, is written as: 6².
How to Write an Expression in Exponential Form?Repeated multiplication involving base exponents and base can be written in exponential form, such as: a × a × a = a³.
Given the expression, 6 × 6, the number 6 will be the base while 2 will be the exponent if we want to express it in exponential form. Therefore:
6 × 6 = 6².
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Find a Cartesian equation for the curve.
r = 3 sec(θ)
Identify the curve.
▢ ellipse
▢ line
▢ hyperbola
▢ limaçon
▢ circle
[tex]r = 3sec( \alpha ) \\ r = \frac{3}{cos( \alpha )} [/tex]
[tex]x = rcos( \alpha ) \: \: \: \: \: \: \: cos( \alpha ) = \frac{x}{r} [/tex]
[tex]r = \frac{3}{ \frac{x}{r} } \\ r = \frac{3r}{x} \: \: \: \: \: \: x = 3 \\ line[/tex]
According to the American Community Survey, 27% of residents of the United States 25 years old or older had earned a bachelor degree. Suppose you select 12 residents of the United States 25 years old or older and recorded the number who had earned a bachelor degree. Round probabilities to 4 decimal places.
Explain why this is a binomial experiment.
Find and interpret the probability that exactly 5 of them had a bachelor degree.
Find and interpret the probability that fewer than 5 of them had a bachelor degree.
Find and interpret the probability that at least 5 of them had a bachelor degree.
Compute the mean and standard deviation of the binomial random variable.
a. The reason why this question is a binomial experiment is based on the fact that it is made up of an independent sample, it has a number that is fixed and a probability.
Each event is made up of two outcomes and they are random with the same success rate.
b. How to solve probability that exactly 5 had a bachelorwe have the following data n = 12, p = 0.27 and k = 5
We have to use the function to solve electronically
binompdf(n,p,k)
input the values
= binompdf(12,0.27,5)
This gives us
= 0.1255
(C) Probability that fewer than 5 have bachelorWe use the formula below
= binompdf(12,0.27,5-1)
This is = 0.7984
D. Probability of at least 5
1 - probability of fewer than 5
= 1 - 0.7984
= 0.2016
How to solve for the Mean = n*p
n = 12 , p = 0.27
Mean = 12*0.27 = 3.24
and
standard deviation = √npq
n = 12, p = 0.27 , q = 1- 0.27
= 0.73
sd = √12*.27*.73
= 1.54
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Find the measures of the right triangle that are not given.
The missing values of the right angle triangle are; a = 28 yds; c = 47 yds; ∠B = 54°
How to use Trigonometric Ratios?
From the attached image of the right angle ABC, we see that;
∠A = 36°
b = 38 yd
∠C = 90°
Using trigonometric ratios, we have;
a/38 = tan 36
a = 38 * tan 36
a = 27.61 yd ≈ 28 yds
Similarly;
38/c = cos 36
c = 38/cos 36
c = 46.97 yds ≈ 47 yds
∠B = 180 - (36 + 90)
∠B = 54°
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Evaluate each expression:
I-3|=
The value of the modulus function |-3| is 3.
What is the value of modulus?'Modulus' exists a Latin word, which signifies 'measure'. Absolute value is commonly referred to as numeric value or magnitude. The absolute value designates only the numeric value and does not contain the sign of the numeric value. The modulus of any vector quantity exists ever taken as positive and exists in its absolute value.
The absolute value (or modulus) | x | of a real number x stands as the non-negative value of x without regard to its sign.
For example, the absolute value of 5 stands at 5, and the absolute value of −5 exists also at 5. The absolute value of a number may be considered as its distance from zero along a real number line.
Therefore, the value of the modulus function |-3| is 3.
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Which parent function is f(x) = x²?
A. The quadratic parent function
B. The linear parent function
C. An exponential parent function
D. The absolute value parent function
Answer:
A
Step-by-step explanation:
It is the quadratic parent function
His wife makes a final test of Odysseus' identity by getting him to tell
about the building of his bed
the name or his favorite dog
about the day he went away
how he got a scar on his arm
Answer: About the building of his bed
Adult tickets to the fall play cost $8
and student tickets cost $4. The drama class
sold 20 more adult tickets than student tickets
to the fall play. If the class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution is
Solving a system of equations we will see that they sold 80 adult tickets.
how many adult tickets were sold?
To solve this, we need to solve a system of equations. To define said systems of equations, we first need to define the variables, we will use:
x = adult tickets sold.y = student tickets sold.They sold 20 more adult tickets than student tickets, then:
x = y + 20
And they collected a total of $880, then:
x*$8 + y*$4 = $880
The the system of equations is:
x = y + 20
x*$8 + y*$4 = $880
Isolating y on the first equation we get:
y = x - 20
Replacing that on the other equation we get:
x*$8 + (x - 20)*$4 = $880
Now let's solve that for x.
x*$12 - $80 = $880
x*$12 = $880 + $80 = $960
x = $960/$12 = 80
They sold 80 adult tickets.
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! PLEASE HELP ! Mr. Herman had $120 and Mr. Chandra had $80. After each of them had paid for a concert ticket,
Mr. Herman had 3 times as much money as Mr. Chandra. (a) How much was the ticket? (b) How
much money did Mr. Chandra have left?
Answer:
Step-by-step explanation:
let x be the price of ticket,then
120-x=3(80-x)
120-x=240-3x
3x-x=240-120
2x=120
x=120/2=60
Price of ticket=$60
Mr.Chandra has 80-60=20 $ after buying the ticket.
Draw the graph of changing length of shadow of a stick from 12pm to 5pm.
The graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.
When an object (like the stick in the cartoon) blocks some of the Sun's light, it casts a shadow. The shadow always points away from the Sun. How long the shadow is depends on how low or high the Sun is in the sky. If the Sun is low, we see a longer shadow. Is the Sun is high, we see a shorter shadow.
Length of shadow due to the Sun's light is smallest when the Sun is vertically above. This happens at 12 noon.
Thus the graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.
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