Answer:
(2)
Step-by-step explanation:
by substituting the values of x into f(x) and evaluating
f(0) = 3(0) - 5 = 0 - 5 = - 5 ≠ 0
f(3) = 3(3) - 5 = 9 - 5 = 4 ← True
f(4) = 3(4) - 5 = 12 - 5 = 7 ≠ 3
f(5) = 3(5) - 5 = 15 - 5 = 10 ≠ 0
Hence, statement 2 is true for the equation f(x) = 3x-5
What is equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Types of Equations:
Linear Equation: More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1.
Quadratic Equation: This equation is of second order. At least one of the variables in a quadratic equation needs to be raised to exponent 2.
Cubic Equation: A third-order equation is this one. At least one of the variables in cubic equations needs to be raised to exponent 3.
Rational Equation: A fractional equation having a variable in the numerator, denominator, or both is referred to as a rational equation.
Substituting the values of x into f(x) and evaluating
f(x) = 3x - 5
put x = 0
f(0) = 3(0) - 5
= 0 - 5 = - 5
put x = 3
f(3) = 3(3) - 5
= 9 - 5
= 4
put x = 4
f(4) = 3(4) - 5
= 12 - 5
= 7
put x = 5
f(5) = 3(5) - 5
= 15 - 5
= 10
hence statement 2 is true.
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I offer to give you $40 if you can flip a coin and have it land on heads 2 times in a row. If you get tails, you have to pay me $10. What is the probability that you will win this bet
Answer:
25%
Step-by-step explanation:
Each flip has a 50% probability of landing heads. Two in a row would be (50%)*(50%) = 25%
[Note: 25% of $40 is $10]. Don't waste your time.
What is the equation of the vertical asymptote of g(x)=4log2(x−2) 5 ? enter your answer in the box.
The equation of the vertical asymptote of the function [tex]g(x)=4log_{2} (x-2)+5[/tex] is x=2.
What is vertical asymptote of a function?Vertical asymptotes are vertical lines that represent the zeros of a rational function's denominator. Asymptotes can also occur in other situations, such as logarithms. It occurs at the x-value that is outside the domain of the function, therefore the graph can never cross it.
How to find vertical asymptotes from graph?There may be a vertical asymptote along the vertical line if a portion of the graph is about to turn vertical. At the point of x along which you discovered the vertical asymptote, the function's value changes to either ∞ or -∞. A vertical asymptote, however, must never touch the graph.
Graph the function [tex]g(x)=4log_{2} (x-2)+5[/tex]
(x,y)= (3,5), (4,9), (6,13)
From graph we can see that the graph is turning to be vertical from x=2. So, the equation of vertical asymptote of the function is x=2.
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The complete question is:
“What is the equation of the vertical asymptote of [tex]g(x)=4log_{2} (x-2)+5[/tex]? enter your answer in the box.”
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
The surface area of the pyramid is 34.8 in²
How to find the surface area of the figure?Since the figure is a square pyramid, its surface area, A = 4 × area of triangular face + area of square base.
The area of triangular face
Area of triangular face A' = 1/2bh where
h = height = 4.3 in and b = base = 3 in.So, A' = 1/2 × 4.3 in × 3 in
A' = 1/2 × 12.9 in²
A' = 6.45 in²
The area of square base
Area of square base A" = L² where L = length of base = 3 in
So, A" = (3 in)²
= 9 in²
The Surface area of pyramid.
Surface area of pyramid, A = 4A' + A"
= 4 × 6.45 in² + 9 in²
= 25.8 in² + 9 in²
= 34.8 in²
So, the surface area of the pyramid is 34.8 in²
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Shaking wants to write 2/6 as a decimal. which method could she use divide 6 by 2. divide 2 by 6. multiply 6 by 2. multiply 2 by 6
she should use 2 by 6
Step-by-step explanation:
2 divided by 6 will give 0.3 in 1d.p
If a 650-cm leader is placed against a building at a certain angle, it just reaches a point on the building that is 520 cm above the ground. If the ladder is moved to reach a point 80 cm higher up, how much closer will the foot of the ladder be to the building
Answer:
140 cm
Step-by-step explanation:
The distance of the foot of the ladder from the building can be found using the Pythagorean theorem (or your knowledge of Pythagorean triples). Once the two distances are found, their difference can be found.
Position 1The 650 cm ladder reaches 520 cm up the side of the building. The ratio of these side lengths is 650/520 = 5/4, suggesting these are the sides of a 3-4-5 right triangle. The distance from the building is ...
(3/5)×650 cm = 390 cm.
Alternatively, the distance (a) from the building can be found using the Pythagorean relation ...
a² +b² = c²
a² +520² = 650²
a = √(422500 -270400) = √152100 = 390 . . . cm
Position 2The 650 cm ladder reaches 520 +80 = 600 cm up the side of the building. The ratio of these side lengths is 650/600 = 13/12, suggesting these are the sides of a 5-12-13 right triangle. The distance from the building is ...
(5/13)×650 cm = 250 cm
Again, the Pythagorean theorem can be used to obtain the same result:
a = √(422500 -360000) = √62500 = 250 . . . cm
DifferenceThe difference between the two distances is ...
390 cm -250 cm = 140 cm
The foot of the ladder will be 140 cm closer to the building.
What is the slope of the line that passes through the points (6, 2) and
(
-18, 2)? Write your answer in simplest form.
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 2 ) and (x₂, y₂ ) = (- 18, 2 )
m = [tex]\frac{2-2}{-18-6}[/tex] = [tex]\frac{0}{-24}[/tex] = 0
The slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
m = ( y₂ - y₁) / (x₂ - x₁)
It is given that the two points are (6, 2) and (-18, 2).
The two-point can be represented as,
(x₁, y₁ ) = (6, 2)
(x₂, y₂ ) =(-18, 2)
The slope of the line can be obtained as,
m = ( y₂ - y₁) / (x₂ - x₁)
m = (2-2) / (-18-6)
m =0 / -24
m =0
Thus, the slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.
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Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:
A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 6 feet..
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. (5 points)
Part B: The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)
Part A
Using the Pythagorean on the right triangle PQR, with PQ and QR as the legs and PR as the hypotenuse,
[tex]14^2 +6^2 =(PR)^2\\\\(PR)=\sqrt{14^2 +6^2}\\\\PR \approx \boxed{15.23 \text{ ft}}[/tex]
Part B
[tex](QR)^2 +6^2 =16^2\\\\(QR)^2 =16^2 -6^2\\\\QR=\sqrt{16^2 -6^2}\\\\QR \approx \boxed{14.83 \text{ ft}}[/tex]
A bucket contains exactly 3 marbles, one red, one blue and one green. a person arbitrarily pulls out each marble one at a time. What is the probability that the last marble removed is non-red?
The probability that the last marble removed is non-red is 2/3.
According to the given question.
Total number of marbles in a bucket = 3
And, a person arbitary pulls out each marble one at a time.
So, there are 6 possible sequences of removing 3 marbles.
Let R be the red marble, B be the blue marble and G be the green marble.
The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.
Let A denotes the event of removing the non-red marbles at the last.
The favorable cases for event A are: RBG, RGB, BRG and GRB.
As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.
Thereofre,
The probability that the last marble removed is non-red
= 4/6
= 2/3
The probability that the last marble removed is non-red is 2/3.
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find the gradient of 15y-6x=8
Answer:
2/5 or 0.4
Step-by-step explanation:
First we have to make equation into the gradient slope form :
y=mx+c m is gradient and c is y-intercept
15y-6x=8
First we add 6x to both sides :
15y = 6x+8
Now we divide both sides by 15 :
y = 6x+8 / 15
Split the fraction on the right :
y = 6x/15 + 8/15
6x/15 = 6/15x
Our gradient will be 6/15 = 2/5 or 0.4
Hope this helped and have a good day
mr thapa travelled 5km by a taxi the minimum fare of rs 14 apperared immediately after the meter was flagged down, then the fare went on rs 7.20 per 200m. calculate the total fair paid by her
The total price paid by Mr. Thapa as per the new rating will be equal to Rs 180.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Total distance traveled by Mr. Thapa = 5 km = 5000 meters.
The initial price paid for the taxi = Rs 14
Then, the meter was flagged down, then the fare went to rs 7.20 per 200 m.
Let the price paid after 5 km is x.
So, the ratio will be,
200 m = Rs 7.20
5000 m = x
Perform cross-multiplication,
200x = 5000 × 7.20
200x = 36000
x = 36000/200
x = Rs 180
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The height and weight of adults can be related by the equation y=48.3x−127 where x is height in feet and y is weight in pounds.
What does the slope of the line represent?
A. the average number of pounds per foot tall
B. the number of pounds heavier an adult one foot taller would weigh
C. the height of an adult weighing zero pounds
D. the number of adults in the sample
we conclude that the correct option is A, the slope is:
"the average number of pounds per foot tall"
What does the slope of the line represent?The linear equation:
y = 48.3*x - 127
Relates the height, x, and the weight, y of an adult.
Then the slope, which is 48.3, should have units of mass over height.
Now, if x is in feet and y is in pounds, then the slope has units of pounds/feet.
Then it represents the mean number of pounds per feet. So we conclude that the correct option is A:
"the average number of pounds per foot tall"
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At a sale this week, a desk is being sold for $336. This is a 36% discount from the original price.
What is the original price?
Answer:
$525
Step-by-step explanation:
We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:
[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]
To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:
525 * 0.36 = 189
525 - 189 = 336
Modeling the first formula gives us:
525 - (0.36 * 525) = 336
525 - 189 = 336
PLEASE HELP QUICK, I need to know the answer.
Answer:
Your answer is 7^2.
Step-by-step explanation:
-------------------------
Have a great day,
Nish
The equivalent expression is [tex]7^{2}[/tex].
We have the following expression -
[tex]\frac{7^{-3} }{7^{-5} }[/tex]
We have to find its equivalent value.
What is the equivalent expression of the following expression-[tex]f(x, y) =\frac{A^{x} }{A^{y} }[/tex]
In order to divide two exponents with same base, we use the 'Quotient property of exponents.
The equivalent expression can be written as -
f(x, y) = [tex]A^{x} A^{-y} = A^{x-y}[/tex]
In the question given we have -
[tex]\frac{7^{-3} }{7^{-5} }[/tex]
Using the property discussed above -
[tex]7^{-3}\;7^{5}[/tex] = [tex]7^{-3+5}[/tex] = [tex]7^{2}[/tex]
Hence, the equivalent expression is [tex]7^{2}[/tex].
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10. A circular Harkness table is placed in a comer of a room so that it touches both walls. A mark is made on the
edge of the table, exactly 18 inches from one wall and 25 inches from the other wall. What is the radius of the
table?
The radius of the table can be either 13 inches or 73 inches.
How to estimate the radius of the table?Let the radius of the table be r inches and the corner be the origin.
The coordinates of the center of the table exist (r, r).
The equation for the circumference of the table exists (x−r)²+(y−r)²=r².
The mark at the edge of the table exists 18 inches from one wall and 25 inches from the other wall. Therefore, the coordinates of this point exist (18, 25). It could also be (25, 18) but it does not make any difference to our estimations.
As the mark exists on the edge, it meets the requirements of the equation of the circumference of the table.
(18−r)² + (25−r)² = r²
324−36r+r²+625−50r+r² = r²
r²−86r+949 = 0
(r − 13)(r − 73) = 0
r = 13 inches and r = 73 inches
Therefore, the radius of the table can be either 13 inches or 73 inches.
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I NEED HELP ASAP! The two cylinders below are similar. What is the volume of the larger cylinder?
Answer:
E
Step-by-step explanation:
We can find the volume either by finding the scale factor between the two figures and multiplying the first cylinder's volume by it or simply finding the diameter of the second cylinder and doing the equation for volume of a cylinder.
I chose the second way to work out.
Since the two cylinders are similar, we can simply set up a proportion to find the diameter, d, of the second cylinder:
[tex]\frac{6}{d}=\frac{4.5}{6}\\ \\ 4.5d=36\\ d=8[/tex]
The formula for volume of a cylinder is [tex]V=\pi r^2h[/tex]
The radius is simply d/2 so the radius of the second cylinder is 8/2 or 4.
Thus, we have
[tex]V=\pi *4^2*6\\V=\pi *16*6\\V=96\pi \\V=301.59[/tex]
G(x)=2x-8, f(x)=5-g(x) what is the value of f(10)
Answer:
-7
Step-by-step explanation:
[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]
If you have 66 data observations in a sample, how many classes (bins) does the sturges' rule recommend for you to construct a frequency distribution?
According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7
Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.
Given,
n = 66
We know that,
According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:
[tex]k=1+log_{2} n[/tex]
Here, n is equal to 66 and by substituting the value to the equation we get:
[tex]k=1+log_{2} (66)[/tex]
k = 7.0444
k ≈ 7
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Which situation will likely have no correlation?
Answer:
The third one as they have no links really
The length of a spring with no applied force acting on it is 10.00 centimeters. Juanita applied different forces to the spring and recorded the new lengths of the spring in a table. She also graphed a scatterplot from the results in the table. Based on the scatterplot, which equation BEST represents these data?
Answer:
the second option L = 0.05F + 10
Step-by-step explanation:
the first one
F = 0.05L + 10
does not make any sense, as for length = 10 the force has to be 0. but this function here gives us
0.05×10 + 10 = 0.5 + 10 = 10.5
which is clearly not 0. so, this is wrong.
the second one is correct.
L = 0.05F + 10
it is not perfect, but it is the only one describing the first data points well. like, when F = 0, then L = 10.
the third
L = 0.05F
fails already at the beginning F = 0, as it gives us L = 0 instead of 10. this is wrong.
the fourth
F = 0.05L
fails also already at the beginning. for L = 10 we need to have F = 0. but instead we get F = 0.5. this is wrong.
My family was so excited to see the new movie, Thor: Love and Thunder. I decided to go and take my
two boys and four of their friends. The adult ticket price was $11.00 and only 3 of the kids were able to
get the children's ticket price. If the total bill was $62.00, how much was each children's ticket?
Answer:$6
Step-by-step explanation:
If only 3 got the children's price, that means there were 4 adult tickets.
4*11=44
62-44=18
18/3=6
$6 per child ticket
Write the equation of the line shown
Answer:
y = [tex]\frac{1}{2}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 1) ← 2 points on the line
m = [tex]\frac{1-0}{0-(-2)}[/tex] = [tex]\frac{1}{0+2}[/tex] = [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, 1 ) ⇒ c = 1
y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line
The straight line equation is :
[tex]\boxed {y = mx + c}[/tex]
Here, c = 1 as it intersects (0, 1) on the y-axis.
The slope is :
m = 1 ÷ 2m = 0.5Hence, the equation will be :
y = 0.5x + 1
I hope it helped you solve the problem.
Good luck in your studies!
Area=
Help me please thanks :)
Answer:
16 square units
Step-by-step explanation:
You find the area by multiplying the base times the height. The base or horizonal length is 4. You get this from the ordered point x (4,0). The x coordinate 4, tells us that the point x is 4 spaces to the right of zero, so the length or base is 4.
The height is also 4. You get this from the point S (2,4) The y coordinate of 4 tells you how high up the point is.
4 x 4 = 16
Find a power series representation for the function. (give your power series representation centered at x = 0. ) f(x) = ln(5 − x)
Recall that for [tex]|x|<1[/tex], we have the convergent geometric series
[tex]\displaystyle \sum_{n=0}^\infty x^n = \frac1{1-x}[/tex]
Now, for [tex]\left|\frac x5\right| < 1[/tex], we have
[tex]\dfrac1{5 - x} = \dfrac15 \cdot \dfrac1{1 - \frac x5} = \dfrac15 \displaystyle \sum_{n=0}^\infty \left(\frac x5\right)^n = \sum_{n=0}^\infty \frac{x^n}{5^{n+1}}[/tex]
Integrating both sides gives
[tex]\displaystyle \int \frac{dx}{5-x} = C + \int \sum_{n=0}^\infty \frac{x^n}{5^{n+1}} \, dx[/tex]
[tex]\displaystyle -\ln(5-x) = C + \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]
If we let [tex]x=0[/tex], the sum on the right side drops out and we're left with [tex]C=-\ln(5)[/tex].
It follows that
[tex]\displaystyle \ln(5-x) = \ln(5) - \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]
or
[tex]\displaystyle \ln(5-x) = \boxed{\ln(5) - \sum_{n=1}^\infty \frac{x^n}{5^n n}}[/tex]
A triangle is shown.
What is the unknown side length, to the nearest tenth, in the triangle?
Using the Pythagorean Theorem, it is found that the unknown side length of the triangle is of 7.9 cm.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Researching this problem on the internet, we have that:
The unknown side length is of a leg of x.The other leg is of 9 cm.The hypotenuse is of 12 cm.Hence:
x² + 9² = 12²
x = sqrt(12² - 9²)
x = 7.9 cm.
The unknown side length of the triangle is of 7.9 cm.
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Solve the right triangle. Round decimals to the nearest tenth
Answer: 42
Step-by-step explanation:
angle t is 42 degrees
Answer:
∠T = 42°
PT = 14.4
QT = 19.4
Step-by-step explanation:
An angle and its adjacent side are given in the right triangle. The other two sides can be found using trig relations. The third angle can be found using the angle sum theorem.
Trig relationsThe mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and the trig functions of its angles. The relations relevant to this triangle are ...
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos
Tan = Opposite/Adjacent ⇒ Opposite = Adjacent×Tan
Then the missing side lengths are ...
QT = QP/cos(Q) = 13/cos(48°) ≈ 19.4282 ≈ 19.4
PT = PQ×tan(Q) = 13×tan(48°) ≈ 14.43796 ≈ 14.4
Angle sumThe angle sum theorem tells you the sum of angles in a triangle is 180°. This means the acute angles in a right triangle are complementary.
∠T = 90° -48° = 42°
The solution to the triangle is ...
∠T = 42°
PT = 14.4
QT = 19.4
__
Additional comment
The attachment shows the solution from one of many available triangle solvers. Some calculators have triangle solver functions built in.
g(x)=2x-8, f(x)=5-g(x) what is the value of f(10)
By evaluating the function, we conclude that f(10) = -7
How to evaluate the function f(x)?
Here we know that:
g(x) = 2x - 8
And f(x) = 5 - g(x).
Then we can write:
f(x) = 5 - (2x - 8) = 5 - 2x + 8 = -2x + 13
Now we want ot evaluate it in x = 10, this means replace the variable by the number 10.
f(10) = -2*10 + 13 = -20 + 13 = -7
Then, we conclude that f(10) = 7
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NEED HELP ASAP
let h(x)=-1/3x+2. Find -4h(9)
Answer:
4
Step-by-step explanation:
h(x) = -1/3x+2 where we need to find -4h(9)
h(9): x = 9
h(x) = -1/3(9) + 2
h(x) = -3 + 2
h(x) = -1
-4h(9) is -4h(x):
-4(-1) = 4
I NEED HELP WITH MY MATH PLEASE
use an integer to represent 15 feet and below sea level
Answer:
-15 would be the answer because if it's below sea level it would have a negative sign in front of 15
Step-by-step explanation:
Amanda increased the amount of protein she eats every day from 48 g to 54 g. what percentage did Amanda increase the amount of protein she eats
Step-by-step explanation:
I just answered this. how often did you post that question ?
she added 54-48 = 6g.
how many % of 48g are these 6g ?
100% = 48
1% = 100%/100 = 48/100 = 0.48g
how many % are 6g ?
as many as how often 1% (0.48g) fits into 6g :
6 / 0.48 = 12.5%