[tex]~~~~\log_3 (x) = 4\\\\\implies x= 3^4 \\\\\implies x= 81[/tex]
Select the correct answer. what is the solution set of y = x2 2x 7 and y = x 7? a. {(0, 7), (-1, 6)} b. {(0, 7), (-7, 0)} c. {(0, 7), (1, 8)} d. {(-2, 0), (4, 0)}
Answer:
a. {(0, 7), (-1, 6)}
Step-by-step explanation:
[tex]y = x^{2} +2x+7\\y=x+7[/tex]
subtract the equations
[tex]y = x^{2} +2x+7 \\- \ \ \ \ \ y=x+7\\y - y =x^{2} +2x+7-(x+7)\\0=x^{2} +x\\x = 0 \ and \ x= -1[/tex]
for [tex]y = x^{2} +2x+7[/tex], substitute x = 0
[tex]y = (0)^{2} +2(0)+7\\y = 0 +0+7\\y=7[/tex]
for [tex]y = x^{2} +2x+7[/tex], substitute x = 0
[tex]y = (-1)^{2} +2(-1)+7\\y = 1 -2+7\\y=6[/tex]
Answer:
A
Step-by-step explanation:
A ___ is an instrument used to draw circles and arcs.
Answer: A compass.
Step-by-step explanation: an instrument for drawing circles and arcs and measuring distances between points, consisting of two arms linked by a movable joint, one arm ending in a point and the other usually carrying a pencil or pen.
Justin did push-ups for the past 555 days.The following data points are the number of push-ups he did each day.
21,24,24,27,29
Find the standard deviation of the data set.
Round your answer to the nearest hundredth.
push-ups
Answer: σ: 2.76
Step-by-step explanation:
Count, N: 5
Sum, Σx: 125
Mean, μ: 25
Variance, σ2: 7.6
Steps
look at attached pic for formula
σ^2 = [tex]\frac{Σ(xi - μ)^{2} }{N}[/tex]
[tex]\frac{(21 - 25)2 + ... + (29 - 25)2}{5}[/tex]
⇒ [tex]\frac{38}{5}[/tex]
⇒ 7.6
σ = [tex]\sqrt{7.6}[/tex]
⇒ 2.756809750418
⇒ or 2.76
What expression represents this description? Twice the quantity m plus n
Hi student, let me help you out! :)
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We are asked to find which expression represents the description "twice the quantity m plus n".
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Translate this phrase into an algebraic expression.First, add m and n:
[tex]\star~\large\pmb{m+n}[/tex]
Now, multiply two times this sum:
[tex]\star~\large\pmb{2(m+n)}[/tex]
See, the parentheses around the sum show that we multiply two times both m and n.
Hope it helps you out! :D
Ask in comments if any queries arise.
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Answer:
2(m + n)
Step-by-step explanation:
The words describe a quantity. "Twice" means two-times the previous amount. m and n are the unknown numbers that are being added, so you must put them in parentheses to indicate that they should be added first.
Kamaria opens a bank account with $300. Five weeks later, her account balance is $500. What was the average rate of change of her account balance in dollars per week?
Answer:
$40 average
Step-by-step explanation:
500-300=200
200/5=40
Which expression is equivalent to -6(-2+2x)?
O −4-12%
O −4+2%
O 4-12%
O 4+12%
Use distributive law
a(b+c)=ab+ac
-6(-2)-6(2x)12-12x12(1-x)Miguel and Lauren are testing two versions of a new video game. in Miguel's version he receives 25 points at the start of the game, plus one point for each level he completes. In Laurens version she receives 20 points at the start of the game, and 2 points for each level she completes. at what level will they have the same amount of points ?
Answer: 5 levels
Step-by-step explanation:
We will set up a system of equations and solve. Let x be the number of levels beaten, and let y be the number of total points.
Miguel's version:
y = 1x + 25
Lauren's version:
y = 2x + 20
Now, we will graph both equations. The x-coordinate of the point-of-intersection is the answer to our question.
See attached.
The lines intersect at (5, 30) meaning they will have the same number of points after 5 levels, with 30 points.
Select the correct answer from the drop-down menu. Simplify the expression. (1-cot(r))^2/cot(r)
The simplified form of the given expression is tan(r) + cot(r) - 2
Simplifying trigonometric functionsFrom the question, we are to simplify the given trigonometric function
The given trigonometric function is
[tex]\frac{(1-cot(r))^{2} }{cot(r)}[/tex]
Expanding, we get
[tex]\frac{(1-cot(r))(1-cot(r)) }{cot(r)}[/tex]
Simplifying
[tex]\frac{1 - 2cot(r) +cot^{2}(r) }{cot(r)}[/tex]
[tex]\frac{1}{cot(r)} -\frac{2cot(r)}{cot(r)}+\frac{cot^{2}(r) }{cot(r)}[/tex]
[tex]\frac{1}{cot(r)} -2+cot(r)[/tex]
Recall: [tex]tan(x) = \frac{1}{cot(x)}[/tex]
Therefore, we get
[tex]tan(r) -2 + cot(r)[/tex]
[tex]tan(r) + cot(r)-2[/tex]
Hence, the simplified form of the given expression is tan(r) + cot(r) - 2.
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1.5 Determine the degree of the following algebraic expressions:
a. √3xyz - 5
b. y² - 3y5-y + 2y³ - 4
c. -10³
By identifying the largest exponent in each expression, we see that the answers are:
a) D = 3.
b) D = 5.
c) D = 0.
How to determine the degree of an expression?The degree is just the largest exponent of the variable in an expression.
First, we have:
a) √3xyz - 5
The largest exponent is on the term √3*xyz is 3 (because we add the 3 exponents 1 of x, y, and z) so this expression has a degree of 3.
b) y² - 3y⁵ -y + 2y³ - 4
Here the largest exponent is on the second term, so we can see that the degree is 5.
c) -10³
Here we don't have a variable, so this is a constant, which means that the degree is zero, because we could write:
-10³*x⁰
Where we use the fact that x⁰ = 1
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Kaminsky’s bronze sculpture is 5 feet in diameter, which is approximately 1.524 meters. If the sculpture was made of solid bronze, its weight could be approximated using the density of bronze , the volume, , in cubic meters, the mass, , in kilograms and applying the formula . Approximately, how many pounds would the sculpture weigh if it was made of solid bronze?
The weight of the spherical sculpture in pounds is approximately 251607 pounds
How to find the weight of the sculpture in pounds?
The sculpture is spherical and its made of solid bronze.
Therefore,
density = mass / volume
where
density = 7700 kg / m³
volume = 4 / 3πr³
volume = 4/ 3 × 3.14 × 1.524³
volume = 44.4574491494 / 3
volume = 14.8191497165 m³
Therefore,
mass = 7700 × 14.8191497165
mass = 114107.452817 kg
1 kg = 2.205 pounds
114107.452817 = ?
cross multiply
mass in pounds = 114107.452817 × 2.205
mass in pounds = 251606.933461
mass in pounds = 251607 pounds
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Is 3²+3³ equal to 3⁵?
( yes, no ) the expressions (are, are not ) equal
Answer: No the expressions are not equal
Work Shown:
3² = 3*3 = 9
3³ = 3*3*3 = 27
3²+3³ = 9+27 = 36
3⁵ = 3*3*3*3*3 = 243
The 3²+3³ = 36 doesn't match up with 3⁵ = 243
Therefore, the two expressions are not equal.
Answer:
Step-by-step explanation:
No, the expressions are not equal.
3^2 + 3^3 = 9 + 27 = 36
3^2 * 3^3 = 3^5
keep the base the same and add the exponents
guys omg please someone answer this asap this is due tmmr
Answer:
First, break the shape into smaller shapes.
Bigger rectangle: 5m, 8m
Thin rectangle: 7m, 3m
Thinner rectangle: 8m, 2m
We will call the bigger rectangle B, the thin rectangle R, and the thinner rectangle r.
Step-by-step explanation:
B = 8 • 5 = 40
R = 7 • 3 = 21
r = 2 • 8 = 16
Add the areas together:
40 + 21 + 16 = 77
Therefore, the area is 77 meters.
Each of the teams in a mixed volleyball league consists of 5 men and 5 women. there are 9 men and 10 women, including julia, who are trying out for a team. how many possible teams would include julia? 15,876 31,752 45,722,880 457,228,800
Using the combination formula, it is found that 15,876 teams would include Julia.
The order in which the people are chosen to the team is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
5 men are chosen from a set of 9.4 women are chosen from a set of 9(as Julia is already on the team).Hence the number of teams is given by:
[tex]C_{9,5} \times C_{9,4} = \frac{9!}{5!4!} \times \frac{9!}{5!4!} = 15876[/tex]
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Ann bought 2 pounds of cheese to make lasagna. the recipe gives the amount of cheese needed in ounces. how many did she buy?
Answer:
Ann bought 32 ounces of cheese.
Step-by-step explanation:
First of all, that is a lot of cheese, I hope she is not lactose intolerant.
Second of all, one pound is equivalent to 16 ounces. Given this, we can multiply the pounds of cheese by 16.
That would look like 2×16=32.
I hope this answer helped you and also made you laugh. It is correct though, despite the comedy.
((-7,1). (-3,2). (0, -2). (5, -5)}What are the domain and range of the function represented by the set of ordered pairs?
Answer:
Domain:{-7,-3,0,5}
Range:{1,2,-2,-5}
Step-by-step explanation:
i know because it works for me.
6. What is the measure of angle A rounded to two decimal places? 15 A) 25.02° B)27.82° C) 62.18° D)64.98°
sin A=Perpendicular/ Hypotenuse
sin A = 7/15
A= arcsin(7/15)
= 27,82 degree
Answer is option (B)
given the triangle below what is m<a, round to the nearest tenth?
The measure of angle A is 17.8
The correct option is (A)
What is angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
As, perpendicular from B to side AC
In triangle BDC,
its angles are 30°, 60° and 90°
So, the sides ratio be 1 :√3 : 2
Now,
BD : DC : BC = 1 :√3 : 2
= 11√3/2 : 11/2 : 11
Now, using trigonometry
Sin A = P /H
Sin A = BD/AB
=(11/2)/18
= 11/36
= 0.3055
m<A = 17.79 ≈ 17.8°
hence, the measure of A is 17.8°.
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round to 1 significant figure and estimate 423 x 764
Answer:
300,000
Step-by-step explanation:
423 x 764 = 323,172
If lines Joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one
represented in the table?
x y
5 11
10 22
15 33
10
9
3
022 Edmentum. All rights reserved.
The points (2, 8), (3, 9) and (4, 10) have a greater slope than the table
How to determine the points?The table and the graph that complete the question are added as an attachment
Start by calculating the slope of the table using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (22 - 11)/(10 - 5)
m = 2.2
Next, we calculate the slope of each point on the graph when connected to the origin using:
m = y/x
So, we have:
(2,8) ⇒ m = 8/2 = 4
(3,9) ⇒ m = 9/2 = 3
(4,10) ⇒ m = 10/4 = 2.5
(5,8) ⇒ m = 8/5 = 1.6
(6,7) ⇒ m = 7/6 = 1.2
(7,6) ⇒ m = 6/7 = 0.9
By comparing the slopes with 2.2, we can see that only points (2, 8), (3, 9) and (4, 10) have a greater slope than the table
Hence, the points are (2, 8), (3, 9) and (4, 10).
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Answer: The points: (5,8) (6,7) (7,6)
Step-by-step explanation: I took the test and the points going ↘️ (down) are correct but the points ↖️ (up) are incorrect
Find the mean, median, and mode(s) of the data with and without the outlier.
45, 52, 17, 57, 42, 54, 58
Answer:
Mean = 48.5, Median = 53, Mode = nothing, Outlier = 17
Step-by-step explanation:
Mean: Add all the numbers (388) then divide by how many numbers (8) are there. (= 48.5)
Median: Is the middle number () so you have to order them from least to greatest (17, 42, 45, 52, 54, 57, 58, 63) and then just keep marking them off left, right, left, right... until you get to the middle. But since there are two numbers (52, 54) you have to add them (106) then you divide by 2 (53).
Mode: Is the number that shows up the most. In this case none of them do.
Outlier: The number that is farthest from the other numbers (17).
A botanist wants to determine if a fertilizer is effective
in the growth of plants. He selects the first 100 plants
of the same type of seedling from a greenhouse and
assigns the first 50 to the group that uses the fertilizer
and remaining seedlings to the group that does not
use fertilizer. He makes sure the plants all have the
same amount of water, soil, and light for two months.
At the end of two months, he measures the heights of
the plants and finds that the ones receiving the
fertilizer are significantly taller.
Which of the following is a valid conclusion?
Inferences can be made for all plants, and the
conclusion can be drawn that the fertilizer will help
all plants grow taller.
Inferences cannot be made for all plants, and the
conclusion can be drawn that the fertilizer will help
all plants grow taller.
Inferences can be made for these types of plants,
and the conclusion can be drawn that the fertilizer
will help these types of plants grow taller.
Inferences cannot be made for these types of
plants, and the conclusion cannot be drawn that the
fertilizer will help these types of plants grow taller.
Based on the information provided, the statement which is a valid conclusion is only: option A.
What is a valid conclusion?A valid conclusion can be defined as a statement that is essentially based on empirical data, formulated hypotheses, facts, and prudent experimental design, which entails that relationship between data variables are reasonable, credible and valid.
Based on the information provided, the statement which is a valid conclusion is that the botanist can make inferences for all plants, and he can draw his conclusion that the fertilizer would help all plants grow taller.
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Answer: C
Step-by-step explanation:
Inferences can be made for these types of plants, and the conclusion can be drawn that the fertilizer will help these types of plants grow taller
Nick wants to write a 1,260 page science-fiction novel.
How many pages will Nick need to write each month to finish his novel in 1 year?
1 year = 12 months
Pages to write in 12 months = 1260
Pages to write in 1 month = 1260/12
= 105 pages per month
Gerrie collects honey from a few
beehives. She scoops out the honey
with a small jar that holds of a cup.
Over the last two weeks Gerrie has
filled this jar 158 times. How many
cups of honey has she collected?
The number of the cups of honey has she collected will be 52 and 2/3 cups.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Gerrie collects honey from a few beehives.
She scoops out the honey with a small jar that holds 1/3 of a cup.
Over the last two weeks, Gerrie has filled this jar 158 times.
1 small jar = 1/3 cup
But we have done this for 158 times. Then we have
158 small jar = 158 x 1/3 cups
158 small jar = 52 and 2/3 cups
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Parallel to y=−3/4x, through (4, -1)
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
y = ___x + ___
Answer:
[tex]y=-\frac{3}{4}x+2[/tex]
Step-by-step explanation:
The slope-intercept form is given by y=mx+c, where m is the slope and c is the y-intercept.
Slope of given line= [tex]-\frac{3}{4}[/tex]
Parallel lines have the same slope. Thus, the slope of the line would also be [tex]-\frac{3}{4}[/tex].
[tex]y=-\frac{3}{4}x +c[/tex]
The value of c can be found by substituting a pair of coordinates.
When x= 4, y= -1,
[tex]-1=-\frac{3}{4} (4)+c[/tex]
-1= -3 +c
Add 3 to both sides:
c= -1 +3
c= 2
Thus, the equation of the line is [tex]\bf{y=-\frac{3}{4}x+2[/tex].
Additional:
Do check out the following for a similar question on slope-intercept form!
https://brainly.com/question/25549430A ride ticket usually costs
$1.50, but if you buy 10 tickets, you get
a 5% discount. Find the sale price of 10 tickets
Answer: Hope this helps if this is what you want.
$14.25
Step-by-step explanation:
$1.50 = 1 ticket
1.50 * 10 = 15
$15 = 10 tickets
100% - 5% = 95% (0.95)
15 * 0.95 = 14.25
$14.25
What is the difference of the fractions? Use the number line to help find the answer.
StartFraction 1 over 5 EndFraction minus three-fourths
A number line going from negative 1 to positive 1 in increments of StartFraction 2 over 20 EndFraction.
Negative StartFraction 19 over 20 EndFraction
Negative StartFraction 11 over 20 EndFraction
StartFraction 11 over 20 EndFraction
StartFraction 19 over 20 EndFraction
The result of the expressionn 1/5 - 3/4 will be negative 11/20. Then the correct option is C.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The expression is given below.
⇒ 1/5 - 3/4
⇒ (4 - 15) / 20
⇒ -11 / 20
Then the correct option is C.
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Answer:
c
Step-by-step explanation:
What is the difference between the highest and lowest points in a data set?the mean the median the mode the range
Answer:
Range
Step-by-step explanation:
Range is found by subtracting the highest and lowest point in the dataset
Mode is the number that occurs most frequently in the set
Median is the central number in the dataset when arranged from lowest to highest
Mean is the sum of all the numbers in the dataset divided by how many numbers there are.
For example, take this list of numbers: 10, 10, 20, 40, 70.
The mean (also known as average) is found by: 10 + 10 + 20 + 40 + 70 / 5 = 30.
The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.
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The attached graph represent the points in the domain -6 < x ≤ -2
How to graph the points?The function is given as:
[tex]f(x) = \left[\begin{array}{ccc}-2&-6 < x \le -1\\1&-1 < x \le 2 & \\5 & 2 < x \le 4\end{array}\right[/tex]
The question says that we plot two points in the domain -6 < x ≤ -2
The domain -6 < x ≤ -2 means that the values of x are greater than -6, but they do not exceed -1
The function at this interval means that all values of x have an output value of -2
So, the two points to plot could be (-5,-2) and (-1,-2)
See attachment for the graph of the points
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In the figure, line p || line q. Find the measure of each angle if m<8 = 115
Answer:
65, 65, 115
Step-by-step explanation:
Attached image
Ten cars were recently assembled at a factory. Of these
cars, 3 will be picked at random for inspection. Of the
10 cars, 5 are blue and 5 are grey. What is the
probability that all 3 cars picked for inspection will be
blue?
Answer:
1/12
Step-by-step explanation: