Answer:
If you wish to find any term (also known as the {n^{th}}n
th
term) in the arithmetic sequence, the arithmetic sequence formula should help you to do so. The critical step is to be able to identify or extract known values from the problem that will eventually be substituted into the formula itself.
Step-by-step explanation:
How many 5 digit numbers have five distinct digits?
Answer:3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Which is the graph of linear inequality 6x + 2y > -10?
Answer:
The top left one.
Step-by-step explanation:
Fix this into y intercept form: y=mx+b
y>-3x-5
Because y is greater than 3x-5, the shaded area should be positive, so the top right and the bottom right will be eliminated. Now, looking at the y intercept which is the 'b' in the equation, it is -5. So the y intercept on the graph should be on negative 5, which means that the top left one is the correct answer!
Hope this helped, BRAINLIEST would really help me:)
Option 1 is the correct choice.
We have a linear inequality -
6x + 2y > -10
We have to determine which of the following graphs depicts the inequality given above.
What is an Inequality?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
6x + 2y > -10
Add - 6x on both sides of inequality, we get -
- 6x + 6x + 2y > - 10 - 6x
2y > - 6x - 10
Dividing both sides of the inequality by 2, we get -
y > - 3x - 5
Now, in order to plot the graph for this inequality, let -
y = - 3x - 5
Plot the line for the above equation. Remember to plot the graph in the form of dashed line since the inequality is strict inequality.
Consider the point (0, 0) -
Solve the inequality for the point (0, 0), we get -
0 > - 3 x 0 - 5
0 > - 5
Which is true.
Hence, shade the complete area on that side of line where the point
(0, 0) lies.
Therefore, Option 1 is the correct choice.
(Refer the image attached, for reference)
To solve more questions on Plotting inequalities, visit the link below -
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se technology to solve 4x−11=3.2x+13. Enter the solutions in the boxes. Write the lesser solution first. Round to the nearest tenth if needed.
Answer: x=30
Step-by-step explanation: if you were looking for the value of x, hope this helps!
first, you have to make sure that the correct values are on the right side to allow us to find the answer faster and easier. your modified formula should look like this: 4x-3.2x=11+13
if you do the operations on each side, it will look like this: 0.8x=24, from here, all you have to do now is divide 24 by 0.8 to get the X value, which will result in 30!
Kaylee has $4,500 for a down payment and thinks she can afford monthly payments of $300. If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate), what is the maximum amount Kaylee can afford to spend on the car? [use the calculation in the text or the online calculators in the resource section]
Answer:
$17,028.06
Step-by-step explanation:
Given that :
Kaylee's down payment = $4500
monthly payment = $300
If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate).
the maximum amount Kaylee can afford to spend on the car is being calculated as the present value for all the payments.
= [tex]=\$4,500 +\dfrac{\$300}{(1+\frac{0.07}{12})} + \dfrac{\$300}{(1+\frac{0.07}{12})^2} +\dfrac{\$300}{(1+\frac{0.07}{12})^3} + ....+ \dfrac{\$300}{(1+\frac{0.07}{12})^{46}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{47}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{48}}[/tex]
Using the online desmos calculator to determine the maximum amount Kaylee can afford to spend on the car; we have:
= $17,028.06
WILL GIVE BRAINLIEST PLZ HELP
Answer:
y = -5x - 9.
Step-by-step explanation:
(-2, 1)
(0, -9)
(1 - -9) / (-2 - 0) = (1 + 9) / (-2) = 10 / (-2) = 5 / (-1) = -5
Since -5 is the slope, and the y-intercept is at (0, -9), we have an equation of y = -5x - 9.
Hope this helps!
Answer:
y=-5x-9
Step-by-step explanation:
Change in x = +2
Change in y=-10
-10/2=-5
m=-5
plug in an point
example:
1=-5(2)+B
B=-9
To check your answer:
y=-5x-9
plug in an point for x given on the chart:
-5(0)-9=-9
Simplify this expression.
275(13 +2)
O 2765 + 2/10
O 25+277
O 2665 + 2/10
O 2675 +2V10
Hurrryyy
Answer:
2675 +2V10
Step-by-step explanation:
Answer:
D :)
Step-by-step explanation:
did on edge 2021
Consider the construction of a pen to enclose an area. You have 500 ft of fencing to make a pen for hogs. If you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area
Answer:
The dimensions of the rectangular pen that maximize the area are [tex]w = 125\,ft[/tex] and [tex]l = 250\,ft[/tex].
Step-by-step explanation:
Let suppose that one side of the rectangular area to be fence coincides with the contour of the river, so that only three sides are needed to be enclosed. The equations of perimeter ([tex]p[/tex]) and area ([tex]A[/tex]), measured in feet and square feet, are introduced below:
[tex]p = 2\cdot w + l[/tex]
[tex]A = w\cdot l[/tex]
Where [tex]w[/tex] and [tex]l[/tex] are the length and width of the rectangle, measured in feet.
Besides, let suppose that perimeter is equal to the given amount of fencing, that is, [tex]p = 500\,ft[/tex]. The system of equations is:
[tex]2\cdot w + l = 500\,ft[/tex]
[tex]A = w\cdot l[/tex]
Let is clear the length of the rectangle and expand the area formula:
[tex]l = 500\,ft-2\cdot w[/tex]
[tex]A = w\cdot (500\,ft-2\cdot w)[/tex]
[tex]A = 500\cdot w -2\cdot w^{2}[/tex]
To determine the maximum area that can be enclosed, first and second derivatives to obtain the critical values that follow to an absolute maximum.
First derivative
[tex]A' = 500 - 4\cdot w[/tex]
Second derivative
[tex]A'' = -4[/tex]
Now, let equalize the first derivative to zero, the only critical value is:
[tex]500-4\cdot w = 0[/tex]
[tex]4\cdot w = 500[/tex]
[tex]w = 125\,ft[/tex]
Since the second derivative is a negative constant function, then, the previous outcome follows to an absolute maximum. The length of the rectangular area is: ([tex]w = 125\,ft[/tex])
[tex]l = 500\,ft - 2\cdot (125\,ft)[/tex]
[tex]l = 250\,ft[/tex]
The dimensions of the rectangular pen that maximize the area are [tex]w = 125\,ft[/tex] and [tex]l = 250\,ft[/tex].
There are 110 applicants for three cosmetology positions. How many different ways can the three positions be filled? Select one: 215,820 ways 3 ways 1,294,920 ways 1,331,000 ways
Answer: 215,820 ways
Step-by-step explanation:
There are 110 applicants for three cosmetology positions. How many different ways can the three positions be filled?
Number of positions = 110
Number of applicants = 3
Number of way in which the positions can be filled ;
This is a combination problem
nCr = n! ÷ (n-r)! r!
110C3 = 110! ÷ (110 - 3)! 3!
110C3 = 110! ÷ 107! 3!
110C3 = (110 * 109 * 108) / (3 * 2 * 1)
110C3 = 1294920 / 6
= 215820 ways
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 57:18 Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is 5 and the length of B D is 12. What is the length of Line segment B C, rounded to the nearest tenth? 13.0 units 28.8 units 31.2 units 33.8 units
Answer:
28.8 units
Step-by-step explanation:
In order to further explain the description of the right angled triangle ABC above, I have attached a hand drawn diagram for easier understanding.
The length of A D is 5 units
The length of B D is 12 units.
From the above triangle ABC, to solve for BC we have the following ratios.
BD : BC = AD : BD
Hence,
BD/ BC = AD/BD
= 12/BC = 5/12
Cross Multiply
12× 12 = BC × 5
BC = 12 × 12/ 5
BC = 144/5
BC = 28.8 units
Therefore, the length of Line segment B C, rounded to the nearest tenth is 28.8 units
Answer:
c.31.2
Step-by-step explanation:
Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes. Complete parts (a) through (e) below.
(a) What is the probability that a randomly selected time interval between eruptions is longer than 82minutes? The probability that a randomly selected time interval is longer than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes? The probability that the mean of a random sample of 13 time intervals is more than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(c) What is the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes? The probability that the mean of a random sample of 34 time intervals is more than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. Fill in the blanks below. If the population mean is less than 82 minutes, then the probability that the sample mean of the time between eruptions is greater than 82 minutes ▼ increases decreases because the variability in the sample mean ▼ decreases increases as the sample size ▼ decreases. increases.
(e) What might you conclude if a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes? Select all that apply.
A. The population mean may be less than 72.
B. The population mean must be more than 72, since the probability is so low.
C. The population mean cannot be 72, since the probability is so low.
D. The population mean is 72, and this is just a rare sampling.
E. The population mean may be greater than 72.
F. The population mean is 72, and this is an example of a typical sampling result.
G. The population mean must be less than 72, since the probability is so low.
Answer:
(a) The probability that a randomly selected time interval between eruptions is longer than 82 minutes is 0.3336.
(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 minutes is 0.0582.
(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is 0.0055.
(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.
(e) The population mean must be more than 72, since the probability is so low.
Step-by-step explanation:
We are given that a geyser has a mean time between eruptions of 72 minutes.
Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.
(a) Let X = the interval of time between the eruptions
So, X ~ N([tex]\mu=72, \sigma^{2} =23^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
Now, the probability that a randomly selected time interval between eruptions is longer than 82 minutes is given by = P(X > 82 min)
P(X > 82 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{82-72}{23}[/tex] ) = P(Z > 0.43) = 1 - P(Z [tex]\leq[/tex] 0.43)
= 1 - 0.6664 = 0.3336
The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.
(b) Let [tex]\bar X[/tex] = sample mean time between the eruptions
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
n = sample of time intervals = 13
Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes is given by = P([tex]\bar X[/tex] > 82 min)
P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{13} } }[/tex] ) = P(Z > 1.57) = 1 - P(Z [tex]\leq[/tex] 1.57)
= 1 - 0.9418 = 0.0582
The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.
(c) Let [tex]\bar X[/tex] = sample mean time between the eruptions
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
n = sample of time intervals = 34
Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is given by = P([tex]\bar X[/tex] > 82 min)
P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{34} } }[/tex] ) = P(Z > 2.54) = 1 - P(Z [tex]\leq[/tex] 2.54)
= 1 - 0.9945 = 0.0055
The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.
(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.
(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 minutes, then we conclude that the population mean must be more than 72, since the probability is so low.
Answer:
The probability that a randomly selected time interval between eruptions is longer than 82minutes = [tex]0.3336[/tex]The probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes = [tex]0.0594[/tex]The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes = [tex]0.0057[/tex]Step-by-step explanation:
From the given data
mean, u = 72
Standard deviation [tex]\rho[/tex] = 23
A) Probability that a randomly selected time interval between eruptions is longer than 82minutes
[tex]P (x > 82) = P[\frac{x-u}{\rho} > \frac{82-72}{23}]\\\\P (x > 82) = P[z > 0.43]\\\\P (x > 82) = 0.3336[/tex]
B)
[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{13}}}]\\\\P (x > 82) = P[z > 1.5676]\\\\P (x > 82) = 0.0594[/tex]
C)
[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{34}}}]\\\\P (x > 82) = P[z > 2.5351]\\\\P (x > 82) = 0.0057\\\\[/tex]
D) If the mean is less than 82minutes, then the probability that the sample mean of the time between eruptions is greater than 83 minutes decrease because the variability in the sample mean decrease as the sample size increases
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1. A wine store conducted a study. It showed that a customer does not tend to buy more or fewer bottles when more samples are offered. What can we conclude?
>There is no correlation between number of bottles bought and number of samples offered.
>There is a correlation between number of bottles bought and number of samples offered. However, there is no causation. This is because there is probably an increase in the number of bottles bought with an increase in the number of samples offered.
>There is a correlation between number of bottles bought and number of samples offered. There may or may not be causation. Further studies would have to be done to determine this.
2. Felipe compared the player statistics from his team's soccer season. He determined that having less playing time implies that a player scores fewer goals. What should he say based on his findings?
>There is no correlation between playing time and number of goals.
>There is a correlation between playing time and number of goals. There may or may not be causation. Further studies would have to be done to determine this.
>There is a correlation between playing time and number of goals. However, there is no causation. This is because there is a decrease in the number of goals with a decrease in playing time.
Answer:
>There is a correlation between number of bottles bought and number of samples offered. However, there is no causation. This is because there is probably an increase in the number of bottles bought with an increase in the number of samples offered.
>There is no correlation between playing time and number of goals.
Hope this helps....
Have a nice day!!!!
Determine the equation of the line that is parallel to y=23x+4 and passes through the point (3,7).
Answer: y = 23x - 62
Step-by-step explanation:
Parallel lines have the same slope.
y = 23x + 4
m=23 b=4
Input x = 3, y = 7, & m = 23 into the Point-Slope formula to find the equation or the Slope-Intercept formula to find b (you already have m). I will choose the latter.
y = mx + b
7 = 23(3) + b
7 = 69 + b
-62 = b
m = 23, b = -62 --> y = 23x - 62
Given the coordinate points of the preimage, use the transformation given to provide the points of the image. E(−5,−1) D(−5,1) C(−1,0) B(−2,−3) Rotation: 180∘ about the origin
Answer:
The points of the image are;
E'(5, 1), D'(5, -1), C'(1, 0), E'(-2, -3)
Step-by-step explanation:
The coordinates of the preimage are E(-5, -1) D(-5, 1) C(-1, 0) B(-2, -3)
Rotation of a point 180° about the origin gives;
Coordinates of the point of the preimage before rotation = (x, y)
The coordinates of the image after rotation = (-x, -y)
Therefore, the coordinates of the points EDCB after 180° rotation about the origin are;
E(-5, -1) rotated 180° becomes E'(5, 1)
D(-5, 1) rotated 180° becomes D'(5, -1)
C(-1, 0) rotated 180° becomes C'(1, 0)
B(-2, -3) rotated 180° becomes E'(-2, -3).
what is the lengthy of side s of the square below
Answer:
D. 4√2
Step-by-step explanation:
A triangle with 45°, 45°, and 90° is a special right triangle.
hypotenuse = √2 · leg
1. Set up the equation
8 = √2 · x
2. Divide by √2 and solve
x = [tex]\frac{8}{\sqrt{2} }[/tex] · [tex]\frac{\sqrt{2} }{\sqrt{2}}[/tex] = [tex]\frac{8\sqrt{2} }{2}[/tex] = 4√2
HELPPPPPPPPPPPPPPPpppp
Answer:
Option (A)
Step-by-step explanation:
Two bases of the the given cylinder are circular in shape in the given picture.
When we take a cross-section of the cylinder parallel to the bases or perpendicular to the height, we get a circle exactly same as the bases (As shown on the rectangular slide).
Cross-section will have the same radius as the bases of the cylinder.
Therefore, Option (A) will be the answer.
Find the Equation of the Parallel Line
2
of
Instructions: Find the equation of the line through point (-7,2) and parallel to
= x - 1. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 1).
Y=
y =
Answer:
y = 2/5x + 4/5
Step-by-step explanation:
We'll begin by calculating the slope of the equation: y = 2/5x – 1/2
The slope of the above equation can be obtained as follow:
y = mx + c
Where m is the slope.
c is the y-intercept.
y and x are the coordinate.
Comparing:
y = 2/5x – 1/2 with y = mx + c
The slope of y = 2/5x – 1/2 is 2/5.
Now, let us determine the equation parallel to y = 2/5x – 1/2.
This is illustrated below:
The coordinate of the line => (–7, 2)
x1 = –7
y1 = 2
Slope (m) = 2/5 => Since the lines are parallel, their slope are equal.
y – y1 = m (x – x1)
y – 2 = 2/5(x – –7)
y – 2 = 2/5(x + 7)
Clear bracket
y – 2 = 2/5x + 14/5
Rearrange
y = 2/5x + 14/5 + 2
y = 2/5x + 4/5
Therefore, the equation is:
y = 2/5x + 4/5
work out the value of x and y in this diagram. All measurement are in centimeters
Answer:
X = 5
Y = 7
Step-by-step explanation:
First we will find x
4x + 2 = 3x + 7
x + 2 = + 7
x = 5
Next we will find y
2y + 9 = 4y - 5
-2y + 9 = -5
-2y = -14
y = 7
A rope that is 245 cm long is cut into three pieces. The ratio of the lengths of the first piece to the second piece is 2:3, and the ratio of the lengths of the second piece to the third piece is 4:5. What is the length of the longest of the three pieces?
Answer:
The length of longest piece is 105 cm.
Step-by-step explanation:
Given:
Rope is 245 cm long.
Ratio of lengths of first to second piece = 2:3.
Ratio of lengths of second to third piece = 4:5.
To find:
Length of longest piece = ?
Solution:
We are given the ratio of first and second pieces AND
ratio of second and third pieces.
Common link is second piece.
We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.
2:3
4:5
Multiply 1st ratio by 4 and 2nd ratio by 3:
Now, the ratio becomes:
8:12 and 12:15
And the ratio of three pieces can be represented as:
8: 12: 15, this ratio is the first piece: second piece: third piece
[tex]\Rightarrow 8x+12x+15x = 245\\\Rightarrow 35x = 245\\\Rightarrow x = \dfrac{245}{35}\\\Rightarrow x = 7[/tex]
So, the pieces lengths will be
First piece = [tex]8 \times 7 = 56[/tex] cm
Second piece = [tex]12 \times 7 = 84[/tex] cm
Third piece = [tex]15 \times 7 = 105[/tex] cm
So, the length of longest piece is 105 cm.
you have 12 monkey but 5 were taken away how much do you have
Answer:
12-5=7
unless it's not a prank or a joke question
Answer:
7
Step-by-step explanation:
Original number of monkeys = 12
Number taken away = 5
So, number left = 12-5 = 7.
Hope this helps.
A number is divided in the ratio 7:2. If the second part is 34, find the number.
Answer:
153.
Step-by-step explanation:
If the second part is 34 units, then the 2 of the ratio is equal to 34 / 2 = 17.
That means the first part will be 7 * 17 = 119.
119 + 34 = 153.
Hope this helps!
Please help this is a new topic for me.
Answer:
last answer
Step-by-step explanation:
P' (2, -4)
Q' (-2, -5)
R' (1, -8)
Answer:
C. P'(2, -4) Q'(-2, -5) R'(1, -8)
Step-by-step explanation:
When you reflect something across the y-axis you change (x,y) to (-x,y).
For each point, change the x to a negative x.
P(-2, -4) --> P'(2, -4)
Q(2, -5) --> Q'(-2, -5)
R(-1, -8) --> R'(1, -8)
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
Write the algebric expression of the difference of 'a' and 'b'
Step-by-step explanation:
An algebraic expression haa atleast one variable and operator sign such as (+,-,×,÷)
According to the question, an algebraic expression should be made from difference of 'a' and 'b'
so, the expression is (a - b) or a - b.
Hope it helps!!!!
Please answer this question now in two minutes
Answer:
q = 4 mi
Step-by-step explanation:
Using the sine or cosine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{4\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × q = 4[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
q = 4
Which of the following are solutions to the quadratic equation? Check all that apply.
x2 + x-12 = 0
A. -1
B. 28
C. 2
D. 4
E. 3
F. -4
Answer:
x= -4 x= 3
Step-by-step explanation:
x2 + x-12 = 0
Factor
What 2 numbers multiply to -12 and add to 1
4 * -3 = -12
4+3 = 1
( x+4) ( x-3) =0
Using the zero product property
x= -4 x= 3
Answer:
E, F
Step-by-step explanation:
x² + x - 12 = 0
Let’s factor left side.
Find 2 numbers that multiply to get -12 and add to get 1
4 × -3 = -12
4 + 3 = 1
x² - 3x + 4x - 12 = 0
x(x - 3) + 4(x - 3) = 0
(x + 4)(x - 3) = 0
Set factors equal to 0.
x + 4 = 0
x = -4
x - 3 = 0
x = 3
Please help me asap!!!
Answer:
HL theorem
Step-by-step explanation:
Since this is a right triangle, we can use the HL ( hypotenuse leg theorem)
We know that one of the legs are equal to each other by the lines on the legs and the hypotenuse is congruent by the reflexive property
Which function is increasing?
A. f(x)=(1/6)
B.f(x) = (0.6).
C. f(x)=(1/60)
D. f(x)=6
Answer:
Option D. f(x) = 6^x
Step-by-step explanation:
To know which of the function is increasing, let us obtain f(1) and f(2) for each function.
This is illustrated below:
f(x) = (1/6)^x
f(1) = (1/6)¹ = 1/6
f(2) = (1/6)² = 1/36
Therefore, f(x) = (1/6)^x is decreasing.
f(x) = (0.6)^x
f(1) = (0.6)¹ = 0.6
f(2) = (0.6)² = 0.36
Therefore, f(x) = (0.6)^x is decreasing.
f(x) = (1/60)^x
f(1) = (1/60)¹ = 1/60
f(2) = (1/60)² = 1/3600
Therefore, f(x) = (1/60)^x is decreasing.
f(x) = 6^x
f(1) = 6¹ = 6
f(2) = 6² = 36
Therefore, f(x) = 6^x is increasing.
Answer:
Option D
Step-by-step explanation:
The reason why it is D is because if it was something below 1, such as 0.6, it would be decreasing. That is why 6 is the answer.
Pete grabbed 18 mixed nuts, 2/9 of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed? A.18 divided by 2/9 =81
Answer:
18 multiplied by 2/9 = 4
Step-by-step explanation:
To determine the number of almonds that Pete grabbed, you have to multiply how much of the nuts were almonds by the total number of nuts that he grabbed. So,
2/9 × 18
= 0.2222 × 18
= 4
Pete grabbed 4 almonds out of the 18 mixed nuts that he grabbed.
Hope that helps.
Answer:
Amount of almonds = 18 × [2/9]
Amount of almonds = 4 almonds
Step-by-step explanation:
Given:
Number of mixed nuts = 18
Probability of almonds = 2/9
Find:
Amount of almonds
Computation:
Amount of almonds = Number of mixed nuts × Probability of almonds
Amount of almonds = 18 × [2/9]
Amount of almonds = 36 / 4
Amount of almonds = 4 almonds
Find the angle between the given vectors to the nearest tenth of a degree. u = , v = (2 points)
Answer:
3.6°Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the angle between the given vectors to the nearest tenth of a degree.
u = <8, 7>, v = <9, 7>
we will be using the formula below to calculate the angle between the two vectors;
[tex]u*v = |u||v| cos \theta[/tex]
[tex]\theta[/tex] is the angle between the two vectors.
u = 8i + 7j and v = 9i+7j
u*v = (8i + 7j )*(9i + 7j )
u*v = 8(9) + 7(7)
u*v = 72+49
u*v = 121
|u| = √8²+7²
|u| = √64+49
|u| = √113
|v| = √9²+7²
|v| = √81+49
|v| = √130
Substituting the values into the formula;
121= √113*√130 cos θ
cos θ = 121/121.20
cos θ = 0.998
θ = cos⁻¹0.998
θ = 3.6° (to nearest tenth)
Hence, the angle between the given vectors is 3.6°
K here’s another one please help
Answer:
Both the relations are functions, the correct answer is a.
Step-by-step explanation:
In order to solve this problem we will first find the inverse relation as shown below:
[tex]y = 3x^2 + 5\\x = 3y^2 + 5\\3y^2 = x - 5\\y^2 = \frac{x - 5}{3}\\y = \sqrt{\frac{x - 5}{3}} = \frac{\sqrt{x - 5}}{\sqrt{3}}\\y = \frac{\sqrt{x - 5}\sqrt{3}}{\sqrt{3}\sqrt{3}} = \frac{\sqrt{3x - 15}}{3}[/tex]
Functions are relations between two groups of numbers, for which the input must generate only one output. Using this definition we can classify both the relation and its inverse as a function, therefore the correct answer is a.
Help me please ty ty ♀️❤️
Answer:
AHH! Geometry!
Thanks for this problem. Needed to refresh my skill for similarity and rations.
First, notice the lines that are on sides of the triangles. Lines with the same number of marks are the same measure. You may have already known this, but I'll just tell you for reference.
That means both of those pair of sides have equal length. What does this mean though?
Imagine that each of the line segments(the ones with two marks) are... 1 cookie (Their lengths, also, I really want a cookie.)
Now, this is where ratios come into play. Consider only the top triangle to the entire triangle. The Top Triangle has a side with the length of one cookie. That corresponding side on the entire large one is 2 cookies (because they are the same measure, and 1*2=2).
Thus, we can make a ratio, comparing the lengths of a corresponding sides.
(BTW, these are similar triangles, meaning that they have all the same angle measures, but different side lengths.)
[tex]\frac{1Cookie}{2Cookies}[/tex]
Now. (Refer to above) Similar triangles have ratios of similarity. Meaning that: Corresponding sides have a 1/3 ratio. This means, also, that all the other corresponding sides have a 1/3 ratio. Neat, huh?
Putting into other words, we can compare CB and RT with the same 1/2 ratio!(Just cancel out the cookies, its still the same ratio)
Now, that we have all our needed information, let's solve!(Also, remember to match it up properly, or else it won't work: Small triangle side/Small Triangle side=Large Triangle Side/Large Triangle Side, or something like that).
[tex]\frac{1}{3x-8} =\frac{2}{2x+4} \\2x+4=6x-16\\4x=20\\x=5[/tex]
^ ANSWER
So there you go! X is equal to 5. I'm sure you can solve the rest on your own!
Hope this helps!
Stay Safe! I'm going to get that cookie now...