To plot more the points, we move up one and right two.
How to plot more the points?The ratios are given as:
(1, 0.5), (2, 1), and (5, 2.5)
Calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{1 - 0.5}{2 - 1}[/tex]
Evaluate
[tex]m = \frac{0.5}{1}[/tex]
This gives
[tex]m = \frac{1}{2}[/tex]
The above means
Vertical : Horizontal = 1 : 2
This means a vertical movement of 1, followed by an horizontal movement of 1
Hence, to plot more the points, we move up one and right two.
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Complete question
Three equivalent ratios are shown on the graph. On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted. Starting on one of the plotted points, how can you plot more equivalent ratio points?
inverse of y = 2x squared
The inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].
What is a Function ?A function is a mathematical statement used to relate a dependent and an independent variable.
The function given is
y = 2x²
To find the Inverse of a function ,
The x and y are interchanged and the function is again written in terms of x
Here
x = 2y²
y² = x/2
y = [tex]\rm \sqrt {x/2}[/tex]
Therefore the inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=21 miles and c=75 miles, what is b? If necessary, round to the nearest tenth.
Answer:
C = 29.7
Step-by-step explanation:
Remember to use a^2 + b^2 = c^2
21^2+ 21^2 = c^2
441 + 441 = c^2
882 = c^2
you square root both sides
c= 29.6984
Round it
C = 29.7
NEED HELP IMMEDIATELY PLS!
Answer:c
Step-by-step explanation:
c
Answer:
D.
Step-by-step explanation:
The equation must be true to have a proportion.
12/20 = 0.6
21/34 = 0.62
A. No
10/15 = 0.666666...
34/60 = 0.566666...
B. No
13/23 = 0.565217...
26/56 = 0.46428...
C. No
25/15 = 1.6666...
85/51 = 1.6666...
D. Yes
Answer: D
Stephen evaluated (6.34 times 10 Superscript negative 7 Baseline) (4.5 times 10 Superscript 3 Baseline). His work is shown below. Which two statements describe the errors Stephen made?
(6.34 times 10 Superscript negative 7 Baseline) (4.5 times 10 Superscript 3 Baseline). (6.34 times 4.5) (10 Superscript negative 7 Baseline times 10 Superscript 3 Baseline). 28.53 times 10 Superscript negative 4 Baseline. Negative 28.53 times 10 Superscript 4 Baseline. Negative 2.853 times 10 Superscript 3 Baseline.
He changed the sign of the coefficient. A negative exponent does not affect the sign of a coefficient in scientific notation. The sign of the exponent determines the direction the decimal is moved in.
He rewrote Negative 28.53 times 10 Superscript 4 incorrectly; 28.53 times 10 Superscript 4 Baseline = 2.853 times 10 Superscript 5. The exponent is increased to account for the extra place the decimal is moved.
He did not correctly evaluate the exponent. It should be evaluated as (10 Superscript negative 7 Baseline times 10 Superscript 3 Baseline) = 10 Superscript negative 21 since exponents are evaluated using the same operation as the coefficients.
He got the wrong value for the coefficients; 28.53 times 10 Superscript negative 4 is not possible. The coefficients in scientific notation are always greater than 1, but less than 10.
He multiplied the coefficients; he should have added 6.34 and 4.5. The product of powers rule states that coefficients are added.
Steps 4 and 5 describe the errors Stephen made.
Stephen evaluated [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex].
His work is shown below.
Which two statements describe the errors Stephen made?Step 1 - [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex]
Step 2 - [tex]=(6.34\times 4.5)(10^{-7} \times 10^3)[/tex]
Step 3 - [tex]=(28.53)(10^{-4})[/tex]
Step 4 - [tex]20.53\times 10^4[/tex]
Error is the step as 4 sign is negative.
So correct step is [tex]=(28.53)(10^{-4})[/tex]
Step 5 - [tex]=(28.53)(10^{-4})[/tex]
Error is the step as there are 4 in place of 3.
So correct step is [tex]=(28.53)(10^{-4})[/tex]
Steps 4 and 5 describe the errors Stephen made.
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For the following exercises, solve the inequality and express the solution using interval notation.
71. |3x − 2 | < 7
Answer:
In interval notation, the solution of |3 x-2|<7 is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex].
Step-by-step explanation:
The given absolute value function is |3 x-2|<7.
It is required to solve the inequality and express the solution using interval notation. -B<x-A<B and solving them separately for x
Step 1 of 3
Given absolute value equation is |3 x-2|<7.
It can be written as -7<3 x-2<7.
To solve for the equality, 3x-2=7 and
[tex]$$3 x-2=-7$$[/tex]
First, solve the equation 3x-2=7, then add 2 on both sides.
[tex]$$\begin{aligned}&3 x=7+2 \\&3 x=9\end{aligned}$$[/tex]
Step 2 of 3
Simplify 3x=9 further, by dividing each side with 3 .
[tex]$$\begin{aligned}&\frac{3 x}{3}=\frac{9}{3} \\&x=3\end{aligned}$$[/tex]
Step 3 of 3
Similarly, 3x-2=-7
From the above term 3x-2=-7,
Add 2 on each side.
[tex]$$\begin{aligned}&3 x=-7+2 \\&3 x=-5\end{aligned}$$[/tex]
Simplify $3 x=-5$ further, by dividing each side with 3 .
[tex]$$\begin{aligned}&\frac{3 x}{3}=-\frac{5}{3} \\&x=-\frac{5}{3}\end{aligned}$$[/tex]
Therefore, the solution is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex]
The speed that a tsunami can travel is modeled by the equation , where s is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?.
The approximate depth of water for a tsunami traveling at 200 kilometers per hour, given the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers, is 0.32 km. Hence, option A is the correct choice.
To solve for the average depth of water, when the water is traveling at 200 kilometers per hour, we substitute speed S = 200, in the relation S = 356√d.
This will be solved in the following way:
S = 356√d,
or, 200 = 356√d {Substituting S = 200},
or, 200/356 = (356√d)/356 {Dividing both sides by 356},
or, √d = 0.5618 {Simplifying},
or, d = 0.32 kilometers.
Therefore, the approximate depth of water for a tsunami traveling at 200 kilometers per hour, given the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers, is 0.32 km. Hence, option A is the correct choice.
The provided question is incomplete.
The complete question is:
"The speed that a tsunami can travel is modeled by the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?
A. 0.32 km
B. 0.75 km
C. 1.12 km
D. 3.17 km"
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What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%
-0.5244 will separates the highest 70% of the scores in a normal distribution from the lowest 30%
Normal Distribution is bell shaped and symmetrical in nature.
We use standard normal to find probabilities of normal distribution.
Fig 1 represents Graph of standard normal
and Fig 2 is % points Table for standard normal distribution.
From % points Table the value separates the highest 70% of the scores in a normal distribution from the lowest 30% is 0.5244 since 30% lies left side from 0 it will be negative
⇒ value separates the highest 70% of the scores in a normal distribution from the lowest 30% is -0.5244
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5
The equivalent equations to [tex]\frac{3}{5}(30x - 15) = 72[/tex] are given as follows:
18 x - 9 = 723(6x - 3) = 72x = 4.5.What are equivalent equations?Equivalent equations are equations that have the same solution.
First, we have to check the solution to [tex]\frac{3}{5}(30x - 15) = 72[/tex], hence:
[tex]\frac{3}{5}(30x - 15) = 72[/tex]
Applying the fraction:
18x - 9 = 72 -> first equivalent equation
Simplifying by 3:
3(6x - 3) = 72 -> second equivalent equation
The solution is:
18x - 9 = 72
18x = 81
x = 81/18
x = 4.5 -> third equivalent equation.
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PLS help fast this is urgent ty
For question 1 option C is the correct answer and for question 2 option A is the correct answer.
We need to find which transformation from the graph of a function f(x) describes the graph of 10f(x).
Here the transformation that describes the graph of g(x) is a vertical dilation of scale factor k = 10 of f(x).
We can start by defining the general vertical dilation.
For a given function f(x), a vertical dilation stretches or contracts the graph vertically, depending on the scale factor k.
And it is written as:
g(x) = k*f(x).
Then here we have:
g(x) = 10*f(x)
It is easy to see that this is a vertical dilation of scale factor k = 10. Therefore, option C is the correct answer.
We need to check from the given options which information is sufficient to prove that quadrilateral ABCD is a parallelogram.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Therefore, option A is the correct answer.
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What is the coefficient of the last term in the binomial expansion of (x 1)9? 0 1 9 10
The coefficient of the last term in the binomial expansion is 1.
Given term is (x + 1)⁹.
The algebraic expansion of a binomial's powers is expressed by the binomial theorem or binomial expansion. The process of expanding and writing terms that are equal to the natural number exponent of the sum or difference of two terms is known as binomial expansion.
The binomial expansion formula for (a + b)ⁿ= ⁿC₀(aⁿb⁰)+ⁿC₁(aⁿ⁻¹b¹)+ⁿC₂(aⁿ⁻²b²)+ⁿC₃(aⁿ⁻³b³)+...............+ⁿCₙ(a⁰bⁿ)
Here, a = x, b = 1 and n = 9.
Substituting the values in the formula,
⁹C₀(x⁹{1}₀)+⁹C₁(x⁹⁻¹{1}¹)+⁹C₂(x⁹⁻²{1}²)+⁹C₃(x⁹⁻³{1}³)+......+⁹C₉(x⁰{1}⁹)
The last term is ⁹C₉(x⁰{1}⁹)
The coefficient of the last term = ⁹C₉ = 1.
Hence, the coefficient of the last term in the binomial expansion of (x+1)⁹ is 1.
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A 2-column table with 9 rows. The first column is labeled x with entries negative 8, negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries negative 16, negative 8, 0, 8, 16, 32, 64, 128.
Which could be the entire interval over which the function, f(x), is negative?
(–8, –2)
(–8, 0)
(–∞, –6)
(–∞, –4
Answer: (–∞, –6)
Step-by-step explanation:
From the given information, the function is never non-negative over (-8,-6), which is the only subset of the interval that is given.
Explain the difference between SAS similiarity and SAS congruency.
Answer:
In the SAS congruence criterion, you must show that two pairs of sides are equal and their included angles are equal as well. But In the SAS similarity criterion, you must show that two pairs of sides are proportional and their included angles are equal.
Step-by-step explanation:
Solution: In the SAS congruence criterion, you must show that two pairs of sides are equal and their included angles are equal as well. But In the SAS similarity criterion, you must show that two pairs of sides are proportional and their included angles are equal.
The ratio of winning tickets to tickets sold is 2 to 5. If 3,500,000 are sold, how many tickets are winners?
Answer:
1400000
Step-by-step explanation:
This is very simple,
multiply the total tickets with this fraction which is
= 2/5x 3500000
= 1400000
Answer:
14,000,000.
Step-by-step explanation:
2 out 5 tickets are winners.
So number of winning tickets = 3,500,000 * 2/5
= 2 * 7,000,000
= 14,000,000
74. Real-World Applications
A town's population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation, P(t), for the population t years after 2003 .
Answer:
The linear equation modeling the given function is P(t)=1700t+45000.
Step-by-step explanation:
In the question it is given that a town's population has been growing linearly. In 2003, the population was 45000, and the population has been growing by 1700 people each year.
It is required to write an equation P(t), for the population t years after 2003.
To solve this question, substitute the given slope , or change in population in the equation with the initial population . Thus, formulate the equation modeling the given function.
Step 1 of 1
Formulate the equation in the slope-intercept form.
[tex]$$\begin{aligned}&y=m x+b \\&P(t)=1700 t+45000\end{aligned}$$[/tex]
Triangle H L I is shown. Line segment J K is drawn near point L to create triangle J L K.
If △HLI ~ △JLK by the SSS similarity theorem, then StartFraction H L Over J L EndFraction = StartFraction I L Over K L EndFraction is also equal to which ratio?
StartFraction H I Over J K EndFraction
StartFraction H J Over J L EndFraction
StartFraction I K Over K L EndFraction
StartFraction J K Over H I EndFraction
The correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent. Option A is correct.
Similarity theorem of trianglesFor two triangles to be similar, the ratio of the measure of similar sides of the triangle must be equal to a constant known as a scale factor.
From the given figures, the expression that can be used to prove that the triangles are similar is as shown;
HL/JL = IL/KL = HI/JK
Hence the correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent
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I can Confirm A is correct
Step-by-step explanation:
Find the probability of picking 4 consonant and 1 vowels when 5 letters are picked (without replacement) from a set of alphabet tiles
The required probability is 0.45
We have total 26 letters in english, of which 21 are consonants and 5 are vowels.
According to the question, we have to select 5 of them of which 4 will be consonants and 1 will be vowel.
Suppose we want to have the vowel in the first selection, so the probability of picking a vowel is equal to the quotient between the number of vowels and the number of total number of letters.
So the probability is 5/26
Now, a letter has been selected, so in the set, we have 25 letters left.
In the next 4 selections, we must select consonants.
In the second selection the probability is 21/25
In the third selection the probability is 20/24
In the fourth selection the probability is 19/23
In the last selection the probability is 18/22
So, the probability is (5/26)×(21/25)×(20/24)×(19/23)×(18/22)
Now, remember that we take that the vowel must be in the first place, but it can be in any five places, so if we add the permutations of the vowel letter we have,
P = 5×(5/26)×(21/25)×(20/24)×(19/23)×(18/22) = 0.45
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Use the drawing tools to form the correct answers on the graph.
Consider this linear function:
y =
x + 1.
Plot all ordered pairs for the values in the domain.
D: (-8, -4, 0, 2, 6}
Drawing Tools
Select
Point
Click on the Graph to
place a Point
Click on a tool to begin drawing.
-10 -9 -8
+7 -6
-5
H
-3
-2
10
9
8-
7-
6
5
4
3-
2
Delete
3
4
5
6
Undo
7 8
Reset
9 10
The function y = x + 1 has a slope (rate of change) of 1 as well as an y intercept of 1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form for a linear function is:
y = mx + b
Where m is the slope and b is the y intercept.
Given the function y = x + 1
The function y = x + 1 has a slope (rate of change) of 1 as well as an y intercept of 1.
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Dylan examines 10 different brands of yogurt. He lists the amount of yogurt in one container of each brand to the nearest 18 of a cup. The results are recorded in this frequency table. Create a line plot to display the data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
The attached graph represents the line plot of the dataset
How to create the line plot?The frequency table is given as:
Amount 3 3.5 4 4.5 5
Frequency 1 2 3 3 1
To create the line plot, we represent the frequency by dots.
Take for instance:
The amount 3 will be represented by 1 dot because it has a frequency of 1The amount 3.5 will be represented by 2 dots because it has a frequency of 2See attachment for the line plot
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how to get the answers?
By inclusion/exclusion,
[tex]n(P' \cup Q) = n(P') + n(Q) - n(P' \cap Q)[/tex]
We have
[tex]n(\xi) = n(P) + n(P') \implies n(P') = 28 - n(P)[/tex]
so that
[tex]n(P' \cup Q) = (28 - n(P)) + n(Q) - 2n(P) = 28 - 3n(P) + n(Q)[/tex]
Now,
[tex]n(\xi) = 28 \implies n(P \cup Q) = 28 - 7 = 21[/tex]
and by inclusion/exclusion,
[tex]n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)[/tex]
Decompose [tex]Q[/tex] into the union of two disjoint sets:
[tex]Q = (P \cap Q) \cup (P' \cap Q)[/tex]
Since they're disjoint,
[tex]n(Q) = n(P\cap Q) + n(P'\cap Q) \implies n(Q) = n(P\cap Q) + 2n(P)[/tex]
[tex]\implies n(P \cup Q) = n(P) + (n(P\cap Q) + 2n(P)) - n(P \cap Q)[/tex]
[tex]\implies 21 = 3n(P)[/tex]
[tex]\implies n(P) = 7[/tex]
From the Venn diagram, we see there are 3 elements unique to [tex]P[/tex] - by the way, this is the set [tex]P \cap Q'[/tex] - so [tex]n(P\cap Q) = 7-3 = 4[/tex], and it follows that
[tex]n(Q) = n(P\cap Q) + 2n(P) = 4 + 2\times7 = 18[/tex]
Finally, we get for (a)
[tex]n(P' \cup Q) = 28 - 3n(P) + n(Q) = 28 - 3\times7 + 18 = \boxed{25}[/tex]
For (b), we have by inclusion/exclusion that
[tex]n(P \cup Q') = n(P) + n(Q) - n(P \cap Q') = 7 + 18 - 3 = \boxed{22}[/tex]
PLEASE HELP URGENT!!!!
Answer:
(d) y≥-5
Step-by-step explanation:
first, we find the equation for the blue line:
a doesn't work as it goes diagonally, so as b, e, or f.
so it must be y≥-5 or y<-5
since the graph is shaded above the line, it must be greater than or greater than or equal to, so it must be D) y≥-5.
You can tell it must be D as greater or less than is dotted while greater equal or less equal would be a solid line.
Theo is using this spinner to predict the favorite movie genre of randomly chosen students in his school.
A spinner with 5 sections labeled action, drama, sci-fi, horror, comedy.
If Theo spins the spinner 60 times, how many times should he expect it to land on “Action”?
Theo should expect the spinner to land on "Action" 12 times.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
Given: A spinner with 5 sections labeled action, drama, sci-fi, horror, and comedy.
Theo spins the spinner 60 times.
We need to find the number of times, out of 60, the spinner lands on "Action".
Here, a total number of outcomes= 5
A number of favorable outcomes = 1
So, the probability that the spinner lands on "Action" = 1/5
Theo spins the spinner 60 times.
So, the number of times the spinner lands on "Action"
= 1/5 x 60 = 12
Hence, Theo should expect the spinner to land on "Action" 12 times.
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Can you see an easy way to work out the value of [tex]\sqrt{ 1^3 + 2^3 + 3^3 + 4^3 + 5^3[/tex] ? if so, describe it.
We have the sum of cubes identity
[tex]a^3 + b^3 = (a + b) (a^2 - ab + b^2)[/tex]
and observing that 1 + 4 = 2 + 3, we have
[tex]1^3 + 4^3 = (1 + 4) (1^2 - 4 + 4^2) = 5 \times 13[/tex]
and
[tex]2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7[/tex]
Then
[tex]\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}[/tex]
Alternatively, we have the well-known sum of cubes formula
[tex]\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4[/tex]
The sum under the square root is this sum with [tex]n=5[/tex]. Then
[tex]1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2[/tex]
and so the square root again reduces to 15.
Sherrie's biology class is studying the ability of a certain microbe to dissipate oil spilled in seawater. to be effective the population of microbes must grow exponentially. she has recorded the microbe population growth as follows: # days after march 1st 0, 1, 5, 10 population 57, 95, 700, 8525 a. using sherrie's data, find the best exponential equation for this growth using the substitution method. must show work. b. using the same data get an equation using calculator's regression feature. then estimate the microbe population on march 21st
The exponential equation for the growth is f(x)=57[tex]e^{0.51x}[/tex] where x is the number of days and the population on 21st march is 2069983.5 of microbes.
Given:
Days population
0 57
1 95
5 700
10 8525
We have to form exponential equation which shows the growth of microbes.
We know that exponential equation which shows the sum is as under:
f(x)=P[tex]e^{rt}[/tex] where r is the rate of growth and x is the number of days, months or years depending on how things grows.
In the question when x=0 population is 57.
f(0)=57
P[tex]e^{0}[/tex]=57
P=57
When x=1, population is 95.
f(1)=95
P[tex]e^{r}[/tex]=95
57 [tex]e^{r}[/tex]=95
57=95/[tex]e^{r}[/tex]----1
when x=5,population is 700.
f(5)=700
P[tex]e^{5r}[/tex]=700
57[tex]e^{5r}[/tex]=700
57=700/[tex]e^{5r}[/tex]-----2
Equating 1&2
95/[tex]e^{r}[/tex]=700/[tex]e^{5r}[/tex]
[tex]e^{5x} /e^{x} =700/95[/tex]
[tex]e^{5r-r}[/tex]=7.36
[tex]e^{4r}[/tex]=7.36
[tex](2.7182)^{4r}[/tex]=[tex](2.7182)^{2}[/tex]
equating both sides
4r=2
r=0.5
put the value of t=21 in the exponential equation
f(21)=57[tex]e^{0.5*21}[/tex]
=57[tex]e^{10.5}[/tex]
=57*36315.5
=2069983.5
Hence the population on 21st march is 2069983.5.
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Please help, i already tried and couldn't get it right
Answer:
3072
Step-by-step explanation:
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termr is the common ratioGiven values:
first term, a = 3common ratio, r = 4Substitute the given values into the formula to create an equation for the nth term:
[tex]\implies a_n=3(4)^{n-1}[/tex]
To find the 6th term, substitute n = 6 into the equation:
[tex]\implies a_6=3(4)^{6-1}[/tex]
[tex]\implies a_6=3(4)^{5}[/tex]
[tex]\implies a_6=3(1024)[/tex]
[tex]\implies a_6=3072[/tex]
Therefore, the 6th term of a geometric sequence whose 1st term is 3 and whose common ratio is 4 is 3072.
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I really need help with this please.
Answer:
y = - 6x + 7.5
Step-by-step explanation:
the perpendicular bisector of BC passes through the midpoint of BC at right angles to BC.
calculate the slope m of BC using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B (- 2, 1 ) and (x₂, y₂ ) = C (4, 2 )
[tex]m_{BC}[/tex] = [tex]\frac{2-1}{4-(-2)}[/tex] = [tex]\frac{1}{4+2}[/tex] = [tex]\frac{1}{6}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{6} }[/tex] = - 6
the midpoint of BC is the average of the x and y coordinates
midpoint = ( [tex]\frac{-2+4}{2}[/tex] , [tex]\frac{1+2}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = ( 1, 1.5 )
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 6 , then
y = - 6x + c ← is the partial equation
to find c substitute (1, 1.5 ) into the partial equation
1.5 = - 6 + c ⇒ c = 1.5 + 6 = 7.5
y = - 6x + 7.5 ← equation of perpendicular bisector of BC
The concession stand at a local high school sells nachos for $4 each and popcorn for $2 each. At the next event, the manager of the stand expects sales of a minimum of 100 items, totaling at least $225. Let x represent the number of nachos sold and let y represent the number of popcorn sold. Which of the following systems correctly represents the scenario?
The system of inequalities that correctly represents this scenario is given by:
[tex]x + y \geq 100[/tex].[tex]4x + 2y \geq 225[/tex].What is a system of inequalities?A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: number of nachos sold.Variable y: number of popcorn sold.The manager of the stand expects sales of a minimum of 100 items, hence:
[tex]x + y \geq 100[/tex].
The concession stand at a local high school sells nachos for $4 each and popcorn for $2 each. The manager wants a total of at least $225, hence:
[tex]4x + 2y \geq 225[/tex]
More can be learned about a system of inequalities at brainly.com/question/3656398
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if ace had 6 grapes and he gave 3 to mason how many will he have left
Answer:
its 3 grapes
Step-by-step explanation:
6-3=3 therefore the answer is 3
Answer:
3 grapes are left
Step-by-step explanation:
if you subtract 3 from 6 (6 - 3) you will find the answer you need to find how many grapes you have left.
ASAP! FIND THE AREA OF THE SECTOR
Answer:
probably B
Step-by-step explanation:
Using the formula pi*r^2, we plug in our values
pi*49=49pi mi^2
but, we still have one more step, as we are calculating for three quarters of a circle, not a full circle.
To find the area for 3/4 of a circle, we just multiply 3/4 by the area of the circle
49pi*3/4=147pi/4
A quick way (though not always accurate) to guess the answer in a multiple choice like this is to see that someone might find the area of the full circle as their final answer, not multiplying by 3/4, so there's a good chance that 49pi mi^2 would be an answer in the multiple choice. since we know that there is a correct answer that is exactly 3/4 of that answer, we can take the ratios of the answers and check if any of them equal 3/4. indeed, after checking a bit, answer B divided by answer A equals 3/4 exactly, and no other answer combination equals 3/4 (D/B is about equal to 4/5). So, we can guess that B is the answer.
Still better to actually do the problem though
Solve this system of equations by
using the elimination method.
x - 5y = 16
4x - 2y = -8
( , )
Answer:
[tex]x = - 4[/tex]
[tex]y = - 4[/tex]
Step-by-step explanation:
Looking at these equations, we can see neither x or y have the same coefficient. Therefore, we need to multiply or divide, to make either the x or the y the same. It's less of a hassle to make the Xs the same, so let's do that. Taking the top equation and multiplying it by 4, we get:
[tex]4x - 20y = 64[/tex]
Now let's subtract the top equation from the bottom equation, leaving us with a third equation:
[tex] - 18y = 72[/tex]
Divide 72 by -18 to get
[tex]y = - 4[/tex]
Now let's substitute into our first equation to find X:
[tex]x + 20 = 16[/tex]
Leaving us with:
[tex]x = - 4[/tex]
Now let's substitute into the second equation to check our solution is correct:
[tex] - 16 + 8 = - 8[/tex]
This is correct, so the answer is X and Y are both equal to -4
Find x if 2x - 9 = 0
Answer:
2x-9=0
2x-9+9=0+9.add the inverse of subtraction /addition/ (+9)
2x=9....then divide by 2
x=9/2
x=4.5. will the final answer