Solve using the elimination method, and also determine whether a system is consistent or inconsistent, and whether the equations are dependent or independent.
Please helppp <3
Answers
To solve using the elimination method, we need to eliminate one of the variables.
Multiplying the first equation by 3, we get:
9x = 165 - 21y
Now we can write the system as:
9x = 169 - 22y
9x = 165 - 21y
Subtracting the second equation from the first, we get:
0 = 4 - y
Solving for y, we get:
y = 4
Substituting y = 4 in the first equation, we get:
3x = 55 - 7(4)
3x = 27
x = 9
Therefore, the solution to the system is (x, y) = (9, 4).
The system is consistent and independent, since it has a unique solution.
Related Questions
Round each measurement to the nearest ten. Then estimate the area of the rectangle. 48 Inches 82 inches 4, 500 square inches. O 260 square inches O3,200 square inches. O 4,000 square inches. O
Answers
The solution is, : the area of the rectangle is 4000 sq inches.
Here, we have,
A rectangle is given with sides 82 and 48 inches
We have to round off these dimensions to the nearest 10.
82 inches ~80 inches
since 2 <5, we make it 0
Similarly 48 inches ~50 inches since 8>5
Now area
= length x width
=80(50)
=4000 square inches
Hence, the area of the rectangle is 4000 sq inches is correct answer.
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Problems 2 and 3 refer to the following drawing.
Answers
2. The side AC corresponds to side AE of the other triangle.
3. The length of side BC is 15.
What are similar triangles?Two or more triangles are said to be similar if on comparing their properties, there exist some common relations. Some of the common relations are; measure of internal angles, scale factor etc.
From the diagram given, we have;
2. Given that the triangles are similar, thus:
The side AC corresponds to side AE of the other triangle.
3. On comparing the corresponding length of the triangles, we have;
15/ 25 = 9/ BC
15BC = 9 x 25
= 225
BC = 225/ 15
= 15
The length of side BC is 15.
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In a large clinical trial, 395,487 children were randomly assigned to two groups. The treatment group consisted of 198,610 children given a vaccine for a certain disease, and 27 of those children
developed the disease. The other 196,877 children were given a placebo, and 104 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the
values of n₁. P. 9₁. ₂. P₂. Q2. P, and q
Answers
Answer:
n₁ = 198,610
P₁ = 27/198,610
n₂ = 196,877
P₂ = 104/196,877
q₁ = 1 - P₁
q₂ = 1 - P₂
Step-by-step explanation:
what is the mass per running metre of a copper bar with a uniform cross-section in the form of a triangle as shown in the figure? the density of copper is 8 850 kg/m³.
Answers
The mass per running metre of a copper bar with a uniform cross-section in the form of a triangle as shown in the figure when the density of copper is 8 850 kg/m³ is 3.
How to calculate the valueMass per running meter = density x area x length
Substituting the values for density, area, and length, you get:
Mass per running meter = 8,850 x [(b x h) / 2] x length
Simplifying the equation, you get:
Mass per running meter = 4,425 x b x h x length
Mass = 8850 / 4425
Mass = 2
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What is the probability that the total team time in the
400-meter freestyle relay is less than 215 seconds?
O 0.056
O 0.1665
O 0.8335
0.944
Answers
The probability that the total team time in the 400-meter freestyle relay is less than 215 seconds is: 0.8345
How to find the probability from z-score?From the table given the mean and standard deviation, we can say that:
Total time spent = 54.2 + 57 + 55.3 + 53.7
Total time spent = 220.2 secs
The total standard deviation is:
2.8 + 3 + 2.4 + 2.5 = 10.7 secs
Formula for z-score here is:
z = (x' - μ)/(σ/√n)
where:
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
Thus:
z = (220.2 - 215)/(10.7/√4)
z = 0.972
From online p-value from z-score calculator, we have:
p(x < 0.972) = 0.8345
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Answer: b
Step-by-step explanation: cause i just did it
what is this?? i will give extra points
Answers
↬ x² - 6x -5
Substituting x = 3:-
⟶ x² - 6x -5
⟶ (3)² - 6(3) -5
⟶ 9 - 6 × 3 - 5
⟶ 9 - 18 - 5
⟶ 9 - 23
⟶ -14
Answer:
[tex] \gg{ \underline{ \large \: \boxed { \bf {- 14}}}}[/tex]
Step-by-step explanation:
[tex] \large \: \sf { \underline{Given}}[/tex]
[tex] \sf \: x {}^{2} - 6x - 5[/tex][tex] \sf \: x = 3[/tex][tex] \large \sf \underline{Solution }[/tex]
[tex] \large \: \displaystyle \sf {x}^{2} - 6x - 5[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \large \bf \blue{ \underline{putting \: the \: value \: of \: x}}[/tex]
[tex]\large \: \displaystyle \sf \: {3}^{2} - 6(3) - 5 [/tex]
[tex]\large \: \displaystyle \sf \: = \: 9 - 18 - 5[/tex]
[tex]\large \: \displaystyle \sf \: = \: - 9 - 5[/tex]
[tex]\large \: \displaystyle \bf \red{= - 14}[/tex]
Select the correct answer.
Which of these statements defines the term resources?
O A. materials that help you achieve your goals
OB. all the goods and services provided to people
OC. the government's ability to deal with economic problems
Reset
Next
Answers
The statements that defines the term resources is A. materials that help you achieve your goals.
What is resources?Resource can be described as all the materials available that is available in individual environment and can be seen as one that is technologically accessible.
It should be noted that resources do help us to achieve most of our goals and can be seen as one that is economically feasible as welll as culturally sustainable and they serves as things that can help us and thjat can satisfy our needs and wants which is needed on daily basis.
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Can a rectangle be a parallelogram
Options
A. Sometimes
B. Always
C. Never
Answers
Answer:
B always because a rectangle has two sets of parallel sides
Hope this helps
use a unit 2 multiplayer to convert 5.4 square meters to square centameters
Answers
To convert 5.4 square meters to square centimeters is 54,000 cm²
How to convert convert 5.4 square meters to square centimeters?To convert 5.4 square meters (m²) to square centimeters (cm²),
We need to multiply it by 10,000 (since 1 meter = 100 centimeters).
5.4 m² = 5.4 x 10,000 cm² = 54,000 cm²
Therefore, 5.4 square meters is equal to 54,000 square centimeters.
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Find the missing side of the triangle . leave your answer in simplest radical form
Answers
Answer: B: [tex]\sqrt{65}[/tex]
Step-by-step explanation:
The figure indicates this is a right triangle. As such, we can use the pythagorean theorem:
a^2 + b^2 = c^2
16 + 49 = x^2
sqrt(65) = x
.: x = [tex]\sqrt{65}[/tex]
Rewrite the logarithmic equation below as an equivalent exponential equation.
log3(N) = x
Answers
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_3(N)=x\implies 3^x=N[/tex]
The list represents the number of students who checked books out of the library in a 10-day period.
48, 63, 75, 40, 32, 52, 35, 68, 83, 40
Find the median and interpret its meaning as it relates to the number of students checking out books.
A. The median is 32, and it represents the difference in the lowest and highest number of students who checked books out.
B. The median is 83, and it represents the highest number of students who checked books out.
C. The median is 40, and it represents the most common number of books that students checked out.
D. The median is 50, and it represents the typical number of students who checked books out.
Answers
The median number of students who checked books out of the library in a 10-day period is 50.
We have,
To find the median of the list, we need to first put the numbers in order from least to greatest:
32, 35, 40, 40, 48, 52, 63, 68, 75, 83
The median is the middle value in the list.
If there is an odd number of values, the median is the middle value.
If there is an even number of values, the median is the average of the two middle values.
There are 10 values, which is an even number.
The middle values are 48 and 52.
Median = (48 + 52) / 2
Median = 50
So the median number of students who checked books out of the library in a 10-day period is 50.
Interpretation:
The median represents the middle value in the list, which in this case is 50.
This means that half of the values in the list are greater than 50, and half of the values are less than 50.
In terms of the number of students checking out books, this means that 50 is the typical number of students who checked books out of the library during the 10-day period.
Thus,
The median number of students who checked books out of the library in a 10-day period is 50.
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Police body cameras: A survey of New York State residents asked about police officers having to wear video cameras on duty. The question stated, “Do you agree or disagree that police officers should carry video cameras for the purposes of filming their activities while on duty?” Most (88%) respondents agreed with this statement.
Do Californians share the same opinion? A California-based civil rights group conducted a similar survey by randomly selecting 500 California residents, and 425 agreed that police officers should carry video cameras for the purposes of filming their activities while on duty.
Conduct a hypothesis test to determine if the proportion of California residents who agree is different from New York residents. Use a 5% significance level to make your decision. Use the applet (at the top of this Checkpoint) to determine the P‐value.
Which of the following is an appropriate conclusion based on the results?
Group of answer choices
The survey provides strong evidence that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is significantly different from the proportion of New York residents.
The survey suggests that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is 85%.
Of the California residents surveyed, 85% agree that police officers should carry video cameras for the purposes of filming their activities while on duty, but this is not strong enough evidence to conclude that the proportion of California residents who agree is significantly different from the proportion of New York residents.
This survey suggests that 88% of California residents surveyed agree that police officers should carry video cameras for the purposes of filming their activities while on duty.
Answers
Based on my experiment, My appropriate conclusion based on the results is option A: The survey provides strong evidence that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is significantly different from the proportion of New York residents.
What was the survey about?This conclusion is based on the truth that the experiment conducted in California found that 85% of the respondents matches with the view, one that is diverse from the extent of Modern York inhabitants (88%) who concurred with the same conclusion .
The "strong evidence" based on the experiment shows that the findings are statistically significant and the conclusion will thus be that the extent of California inhabitants who agree is "essentially wide" from the extent of other York inhabitants, showing some differences between the two populaces.
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Question 1 نت You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 369 randomly selected caterpillars observed, 45 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and b. If many groups of 369 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion. Hint: Hints Video [+]
Answers
a) The 99% confidence interval for the proportion of all caterpillars that lived to become a butterfly is between 0.078 and 0.166.
b) About 99% of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The sample size and the estimate for this problem are given as follows:
[tex]n = 369, \pi = \frac{45}{369} = 0.122[/tex]
The lower bound of the interval is given as follows:
0.122 - 2.575 x sqrt(0.122 x 0.878/369) = 0.078.
The upper bound of the interval is given as follows:
0.122 + 2.575 x sqrt(0.122 x 0.878/369) = 0.166.
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Mia and Lia are competing in a race. 50 people are in the race and medals are given 1st, 2nd, and 3rd place. What is the likelihood that Mia and Lia place in 1st or 2nd?
Answers
The likelihood that Mia and Lia place in 1st or 2nd is unlikely
What is the likelihood that Mia and Lia place in 1st or 2nd?From the question, we have the following parameters that can be used in our computation:
People = 50
Positions = 1st, 2nd, and 3rd place
The probabilities are
P(1st) = 1/50
P(2nd) = 1/49
Using the above as a guide, we have the following:
P = 1/50 * 1/49
Evaluate
P = 0.00040816326
This value is less than 50%
So, the likelihood is unlikely or less likely
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Coordinate Proof!
Given: Isosceles ∆ABC; M is the midpoint of AC-.
Prove: area ∆ABM = area ∆CBM
Proof
AM = √(x₂ − x₁)² + (y₂-y₁)²
= √(4-0)² + (0-0)²
= √4² = _
BM = √(x2-x₁)² + (1₂-y₁)²
= √(4-4)² + (6-0)2
= √6² = _
AM- ≅ CM- ____
AM = CM ____
CM = 4. Subst.
area ∆ABM
A = 1/2 bh
= 1/2 ___
= ___
area ∆CBM
A = 1/2 bh
= 1/2 ___
= ___
Therefore: Area ∆ABM = area ∆CBM by ___
Answers
The completed calculation with regards to the area of the congruent triangles can be presented as follows;
The distance formula indicates;
AM = √((x₂ - x₁)² + (y₂ - y₁)²)
Therefore, we get;
AM = √((4 - 0)² + (0 - 0)²) = √(4²)
AM = √(4²) = 4
BM = √((x₂ - x₁)² + (y₂ - y₁)²)
BM = √((4 - 4)² + (6 - 0)²) = √(6²)
BM = √(6²) = 6
AM ≅ CM Definition of the midpoint of AC
AM = CM Definition of congruent segments
CM = 4 Substitution property
Area ΔABM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Area ΔCBM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Therefore Area ΔABM = area ΔCBM by congruence
What are congruent triangles?Triangles are congruent if they have the same size and shape.
The details of the reasons for the calculation steps and values are presented as follows;
Definition of midpoint of a segment
The midpoint of a line segment is the point that divides the segment into two parts of the same length
Definition of congruence?
Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement
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How much more total interest will you earn when interest is calculated on the new yearly amount, rather than the original principal? (Compare the last row of the tables). In the next section, we will get to “see” the larger snowball, called compound interest.
Answers
The rate of interest with the given amount and compound interest is 5 percent.
Given that,
After 1 year: compound interest = $30 and total amount=$630.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Here, principal = 630-30=600
630=600(1+r/100)¹
630/600 = 1+r/100
1.05=1+r/100
1.05-1=r/100
0.05=r/100
r=5%
Therefore, the rate of interest with the given amount and compound interest is 5 percent.
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A cone has an apex. True False
Answers
Answer:
True, a cone has an apex which is the point where the sides of the cone meet to form a tip.
QUESTION 5 - 1 POINT
Rebecca invests $700 into an account with a 2.9% interest rate that is compounded semiannually.
How much money will she have in this account if she keeps it for 5 years?
Round your answer to the nearest dollar.
Provide your answer below:
Answers
Answer:
$814 she kept for 5 years if she don't spend it
Step-by-step explanation:
(HURRY PLEASE!!) First, a graph of f(x) = -x + 3 is drawn. Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3. Which will be true of these three graphs? A. Their slopes will be the same as the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x). B. Their slopes will be the same as the slope of f(x), and their x-intercepts will be different from the x-intercept of f(x). C. Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x). D. Their slopes will be different from the slope of f(x), and their x-intercepts will be different from the x-intercept of f(x).
Answers
The true statement about the graphs:
Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x).
The correct answer is an option (C)
First we draw a graph of function f(x) = -x + 3.
Find the graph in attached figure.
the x-intercept of f(x) is:
0 = -x + 3
i.e., x-intercept = (3, 0)
Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3.
Let g(x) = -1(-x + 3)
The x-intercept of g(x) would be,
0 = -1(-x + 3)
i.e., x-intercept = (3, 0)
Let h(x) = -2(-x + 3)
The x-intercept of h(x) would be,
0 = -2(-x + 3)
2x = 6
i.e., x-intercept = (3, 0)
Let t(x) = -3(-x + 3)
The x-intercept of t(x) would be,
0 = -3(-x + 3)
3x = 9
i.e., x-intercept = (3, 0)
the graph of functions g(x), h(x) and t(x) is shown below.
We can observe that the x-intercept is same for all graphs but the slopes are different.
Therefore, the correct answer is an option (C)
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2. Tell if the number shown is written in scientific notation. If it is, write correct, if incorrect
explain why and correct the mistake.
A. 0.5045 x 10
B. 2.804 x 10"
C. 12.04 x 10
Answers
The number shown is not written in scientific notation because the 10 do not raise to power of any number, and exponential on the second value do not represent a particular power.
What is Scientific notation?Scientific notation can be described as the way of writing very large as well as very small numbers.
It should be noted that the number is written in scientific notation which is been done as a result of the number falling between 1 and 10 and then this number is been multiplied by a power of 10 instance of this is 6.5 ✕ 10^8, then we can see that none of the given values have the sa,me expresion with this example.
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n + 8 => 14
what makes it false
6, 8, 22, or 10
Answers
Answer:6
Step-by-step explanation: It’s 6 because it’s only greater than, not greater than or equal to
Answer this please for LARGE REWARD
Answers
Answer:
19.5625
Step-by-step explanation:
[tex]\frac{2(12) + 4(15) + 16 +18 + 2(20) + 22 +3(25) +2(29)}{16}[/tex] = [tex]\frac{313}{16}[/tex] = 19.5625
We add up all the numbers that are represented on the graph and then divide that by 16 because there are 16 numbers.
Helping in the name of Jesus.
Find the exact volume of a cylinder with radius 4 ft. and height 10 ft.
Answers
Question 1(Multiple Choice Worth 2 points) (Theoretical Probability MC) When rolling a 6-sided die twice, determine P(sum of 4). 1. 3/36 2. 5/36 3 8/36 4. 2/6
Answers
Answer:
5/36
Step-by-step explanation:
hope this helps
A wooden block measures 2cm by 5cm by 10cm and has a density of 18.2 g/ cm3. What is the mass?
Answers
The mass of the wooden block is given by the formula M = V*d, where d is the density of the wooden block. Substituting the given values, we get M = 100 cubic cm * 18.2 g/cubic cm = 1820 g.
Therefore, the mass of the wooden block is 1820 grams.
Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?
Answers
Answer:
19cm
Step-by-step explanation:
I think it's 19cm as sides BC on the green triangle measure 15cm, and EF is 25cm on the blue triangle. It also mentions that they are similar, meaning that ∆ DEF is just a translated and enlarged version of ∆ ABC
25 - 15 = 10cm
9 + 10 = 19cm
Hope this helped :)
The circle above has a radius of 3 cm. What is the area of the circle?
Answers
Answer:
Step-by-step explanation:
Answer:
28.27 CM ^2
Step-by-step explanation:
The formula for area of a circle is pi * r^2 where r = the radius.
Plugging the radius into the formula we get pi3^2, which equals 28.274 cm ^2 (and change)
Solve the following for θ, in radians, where 0≤θ<2π.
4sin2(θ)−7sin(θ)−4=0
Select all that apply:
0.4
3.61
1.66
5.81
1.4
3.07
Answers
Answer:
3.615.81Step-by-step explanation:
You want solutions to the equation 4sin(θ)² -7sin(θ) -4 = 0 on the interval [0, 2π].
GraphA graph of the left-side expression shows it has a value of 0 at ...
θ ≈ 3.61 or 5.81.
CheckUsing a calculator to check the offered answer choices, we find the values of θ that best satisfy the equation are θ = 3.61 or 5.81. (For this purpose, ±0.02 ≈ 0.)
Algebraic solutionWe can let x = sin(θ). Then the equation is ...
4x² -7x -4 = 0
x² -7/4x = 1
(x -7/8)² = 1 +(7/8)² = 113/64
x = (7 ±√113)/8
The value (7+√113)/8 is greater than 1, so the only value of x that is useful here is x = (7-√113)/8. The angles in the desired range are ...
{π - arcsin((7 -√113)/8), 2π +arcsin((7 -√113)/8)} ≈ {3.61, 5.81} . . . radians
Consider the sequence {3, 12, 21, 30, 39, 48, 57} What is a5
Answers
The value of the term a5 is 39
Calculating the value of a5From the question, we have the following parameters that can be used in our computation:
{3, 12, 21, 30, 39, 48, 57}
The expression a5 means the 5th term of the sequence
In {3, 12, 21, 30, 39, 48, 57} , the fifth eterm is 39
Hence, a5 = 39
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