Question 1:
Substitution.
x+y=2
y=-x+2
2x+(-x+2)=4
x=2
(2)+y=2
y=0
Solution: (2,0)
There is one solution
Question 7 is too confusing, just find where the points intersect at (-5,2).
Question 9:
Elimination.
(-1)y=2x+6
y=2x+2
New: -y=-2x-6
0=-4
No Solution
Question 11:
Just look at explanations.
It's (5,17) both lines etc..
Final answer:
The set of equations for Line A and Line B has one solution. The graph correctly represents the solution (-5, 2) if the lines intersect 5 units to the left and 2 units up. Equations C and D have no solution since the lines are parallel, and the solution to Lines C and D is (5, 17), with both lines passing through this point.
Explanation:
Question 1: To determine the relationship between Line A: x + y = 2 and Line B: 2x + y = 4, we can solve for y in both equations.
For Line A, y = 2 - x.
For Line B, y = 4 - 2x.
Since the coefficients of x are different in the two equations, and the y-intercepts are also different, the lines are not parallel nor identical. Therefore, they intersect at exactly one point, which means there is one solution to the set of equations.
Question 7: The coordinates of the solution is given as (-5, 2). Among the options, the one showing the lines intersecting at the point 5 units to the left and 2 units up represents the correct set of lines, so the graph that corresponds to this description contains the solution.
Question 9: Comparing the two equations: Equation C: y = 2x + 6 and Equation D: y = 2x + 2, we see that both have the same slope but different y-intercepts. Because they have the same slope but different y-intercepts, these lines are parallel and never intersect. Hence, there is no solution to this set of equations.
Question 11: To find the intersection point, we set the equations of Line C: y = x + 12 and Line D: y = 3x + 2 equal to each other and solve for x:
x + 12 = 3x + 2
Subtract x from both sides: 12 = 2x + 2
Subtract 2 from both sides: 10 = 2x
Divide by 2: x = 5
We then substitute x = 5 into one of the equations to find y:
For Line C: y = 5 + 12 = 17.
Hence, the solution to the set of equations is (5, 17), and both lines pass through this point, which lies between the two axes, but that is irrelevant to why it is the solution.
A rectangular garden sits next to a house. Three sides of the garden are fenced, and the fourth side is the house. The length of the garden is 9 meters. A total of 21.5 meters of fencing is used. If w stands for the width of the garden in meters, which equation can be used to find its width?
A. 2w+9=21.5 C. 2w - 21.5 = 9
B. 2w + 18 = 21.5 D. 2w +21.5=18
the equation that can be used to find width is B
Answer:
It's a
Step-by-step explanation:
I did it
solve this inequality. 1/3x-3<-1
Answer:
x < 6
Step-by-step explanation:
Let's isolate x first. Add 3 to both sides, obtaining (1/3)x < 2. Now multiply both sides by 3 to eliminate the fraction: x < 6
the area of a square is 64 cm. what is the length of one side of the square?
Answer:
8cm
Step-by-step explanation:
Since the area of a square is Side X Side (s x s) it is also s². The s² is also equivalent = 64cm². To find the length of a side you do the √64cm² and you get 8cm for a side. Great Job!
If f(x)= 3/x+2-sqrt x-3, complete the following statement:
The domain for f(x) is all real numbers____ than or equal to 3.
Answer:
all real numbers greater than or equal to 3
Step-by-step explanation:
There's some ambiguity in your "3/x+2-sqrt x-3." I will assume that you meant:
3
---------- - sqrt(x - 3). Using parentheses often changes everything.
x + 2
Here we see that x cannot = -2, because x + 2 would be zero then. And x must be greater than or equal to 3, so that the input to the sqrt function will be 0 or greater. The domain for f(x) is all real numbers greater than or equal to 3. The prohibition against x = -2 has no bearing on the overall domain of this function.
Answer:
The domain for f(x) is all real numbers GREATER than or equal to 3
Step-by-step explanation:
3. What’s the answer to this question?
Answer:
Opt B. y=5-3x
Step-by-step explanation:
We need to write the given equation in slope-intercept form, so we can obtain the slope and the 'y' axis intercept point.
To do this, we need to isolate 'y' variable with a possitive sign, hence we perform the following operation:
Subtraction of -5 in both sides of equality sign.
-y=3x-5
Lets multiply by -1 the equation from above:
y= 5-3x.
From the above we can find the slope, is the coefficient of x. in this case -3
And the y-intercept point is 5.
How do you find the length if you already know the perimeter? This is what I mean:
Morgan is ordering carpet for her bedroom. She measures the room and finds a width of 22 feet and a perimeter of 66 feet.
I know for sure that the first thing I need to do is find the length, but how do I do that with only knowing the width and perimeter?
You can find length by knowing the formula for perimeter: 2l+2w= p; where l= length, w= width, and p= perimeter. Substitute the things you know and solve.
In this case, the length would be 11 feet.
A group surveyed a mix of people below and above 40 years old about whether or not they visit a dentist once a year. This table gives the survey results.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Which table shows the relative frequency of people above 40 years old who do not visit a dentist once a year? Round your answers to the nearest hundredth.
Answer: is D
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
Work: 8+22=30 17+13=30 turn into a fraction then simplify to get answer;
22/30 simp= 73.0 (0.73)
13/30 simp= 43.0 (0.43)
8/30 simp= 26.667 (0.27)
17/30 simp= 56.667 (0.57)
Answer with Step-by-step explanation:
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Relative frequency of people above 40 years old who do not visit a dentist once a year
=Number of people above 40 years old who do not visit a dentist yearly/Number of people above 40
=13/(17+13)
=13/30
=0.43
Hence, Relative frequency of people above 40 years old who do not visit a dentist once a year is:
0.43
The data represents the number of traffic tickets written by two police officers in one day over the course of a week. Officer 1: 21, 11, 14, 16, 10, 18, 5 Officer 2: 16, 19, 20, 17, 6, 13, 23
(a) Draw a box and whiskers plot for each officer (b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent?
Answer and Explanation :
Given : The data represents the number of traffic tickets written by two police officers in one day over the course of a week.
Officer 1: 21, 11, 14, 16, 10, 18, 5
Officer 2: 16, 19, 20, 17, 6, 13, 23
To find : (a) Draw a box and whiskers plot for each officer
(b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent?
Solution :
a) We plot the box plot with the help of graphing calculator of both data.
Refer the attached figure below.
Figure 1 shows the data 1 with Median 14.
Figure 2 shows the data 2 with Median 17.
b) On comparing the median of both Officer's are different first officer has 14 median and second officer has 17 median.
****BRAINLIEST The graph shows the solution for which inequalities?
y ≥ x + 2 and y ≤ 2x + 3
y ≥ x - 2 and y ≤ 2x - 3
y ≥ 3x - 2 and y ≤ x + 3
y ≤ 3x - 2 and y ≥ x + 3
Answer:
[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]
Step-by-step explanation:
Blue:
The inequality for the blue line is
[tex]y\geq 3x-2[/tex]
Yellow
The inequality for the yellow line is
[tex]y\leq \frac{1}{2} x+3[/tex]
This means that the correct answer is the third option,
[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]
The graph shows the solution for the inequalities y ≥ 3x - 2 and y ≤ x + 3.
How can find the inequalities?The inequalities can be found by substituting the coordinates of a point within the shaded area in both inequalities and seeing if they are satisfied.
We can find the inequalioties as follows:The options are given.
Let us take the options one by one:
Option A: y ≥ x + 2 and y ≤ 2x + 3Now, substitute (0,0) in the inequalities:
0 ≥ 2 and 0 ≤ 3
This is not true.
Option B: y ≥ x - 2 and y ≤ 2x - 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ - 3
This is not true.
Option C: y ≥ 3x - 2 and y ≤ x + 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ 3
This is true.
Option D: 0 ≤ - 2 and 0 ≥ 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ - 3
This is not true.
Therefore, we have found that the inequalities are y ≥ 3x - 2 and y ≤ x + 3. The correct answer is option C.
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2200 dollars is placed in an account with an annual interest rate of 7.25%. How much
will be in the account after 29 years, to the nearest cent?
Answer:
A = $2200(7.612) = $16,747.28
Step-by-step explanation:
You don't say whether this is simple interest or compound interest. I will assume you meant compound interest, for which the appropriate formula is
A = P(1 + r)^t, where P is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years. Then:
A = $2200(1 + 0.0725)^29, or
A = $2200(1.0725)^29, or
A = $2200(7.612) = $16,747.28
The amount in the account after 29 years will be approximately $8484.64.
Explanation:To calculate the amount of money that will be in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount ($2200 in this case), r is the annual interest rate (7.25% or 0.0725 as a decimal), n is the number of times interest is compounded per year (in this case, it's compounded annually, so n is 1), and t is the number of years (29 in this case). Plugging in the values, we get:
A = 2200(1 + 0.0725/1)^(1*29)
A = 2200(1.0725)^29
A ≈ $8484.64
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Write these numbers in order from least to greatest
0.65, 2/3, 3/5 , 0.5
Answer:
0.5, 3/5, 0.65, 2/3Step-by-step explanation:
Convert the fractions to the decimals (you can use the calculator):
2/3 = 2 : 3 = 0.6666...
3/5 = 3 : 5 = 0/6
We have
0.65
0.666...
0.6
0.5
The order from least to greatest:
0.5
0.6
0.65
0.666..
[tex]\begin{array}{c|c|c|c|c}0&.&5\\0&.&6\\0&.&6&5\\0&.&6&6&6...\end{array}[/tex]
Write 1,000 as a power of 100
Answer:
10 or 100
Step-by-step explanation:
Answer:
100^1,000 if that's what you mean or 100 ^10 to make 1,000
Step-by-step explanation:
IF RIGHT PLZ MARK BRAINLIEST!! PLZZZ!!!!!!!!!!!!!
The cost of renting a car is a flat $44, plus an additional 0.24 cents per mile that you drive. How far can you drive for $89?
Answer:
Subtract the flat fee from the total amount, then divide that amount by the cost per mile.
89 - 44 = 45
45 / 0.24 = 187.5 miles total.
there are some roses,lilies, and orchids in the vase. The number of roses is twice the number of lilies and the number of orchids is 5 more than the number of roses. if the total is 45, find the number of each type of flower
Answer:
Step-by-step explanation:
Let's say R is roses, L is lilies, and O is orchids.
R = 2L
O = R + 5
R + L + O = 45
Let's substitute the second equation into the third:
R + L + (R + 5) = 45
2R + L = 40
Now substitute the first equation:
2(2L) + L = 40
4L + L = 40
5L = 40
L = 8
Therefore:
R = 2L = 16
O = R + 5 = 21
There are 16 roses, 8 lilies, and 21 orchids.
PLEASE HELP FAST In the diagram below, Xy and yz are tangent to o. What is the measure of
Xwz?
Answer:
240
Step-by-step explanation:
since that arc is 120 you subtract that form 360 and voila!
Solve this quadratic equation using factorization
8xsquared-14x-4=0
Answer:
x = - [tex]\frac{1}{4}[/tex], x = 2
Step-by-step explanation:
Given
8x² - 14x - 4 = 0 ( divide through by 2 to simplify )
4x² - 7x - 2 = 0
To factorise the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 2 = - 8 and sum = - 7
The factors are - 8 and + 1
Use these factors to split the x- term
4x² - 8x + x - 2 = 0 ( factor the first/second and third/fourth terms )
4x(x - 2) + 1(x - 2) = 0 ← factor out (x - 2) from each term
(x - 2)(4x + 1) = 0
Equate each factor to zero and solve for x
4x + 1 = 0 ⇒ 4x = - 1 ⇒ x = - [tex]\frac{1}{4}[/tex]
x - 2 = 0 ⇒ x = 2
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?
To change the graph of f(x) = [tex]x^2[/tex] into g(x) = 4[tex]x^2[/tex] + 24x + 30, the transformations include a vertical stretch by a factor of 4 and a shift to the left by 3 units and up by 6 units. Completing the square helps identify these shifts.
Explanation:To transform the graph of f(x) = [tex]x^2[/tex] into the graph of g(x) = 4[tex]x^2[/tex] + 24x + 30, we can analyze the changes applied. First, the coefficient of x2 in g(x) is 4, which means the original parabola is vertically stretched by a factor of 4. Second, the term 24x indicates a horizontal transformation, specifically a shift, which is revealed when we complete the square.
To complete the square for the quadratic part of g(x), we rewrite the equation as 4([tex]x^2[/tex] + 6x) + 30 and add and subtract the square of half the coefficient of x inside the parentheses, giving us 4((x + 3)2 - 9) + 30. This simplifies to 4(x + 3)2 + 6, indicating that the graph of f(x) was also shifted to the left by 3 units and up by 6 units.
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6,15,16,20,13,5,10,16 find the mean
Hello There!
To find the mean we have to add up all the numbers and divide by how many numbers there are.
6+15+16+20+13+5+10+16
Now, I will add 2 numbers at a time to make it easier for myself.
21+36+18+26
Once I add up these numbers, I will get a sum of 101
Finally, I divide 101 by 8 and get a quotient of 12.625
6 + 15 + 16 + 20 + 13 + 5 + 10 + 16 = 101/8 = 12.6
mean: 12.6
Use synthetic substitution to find g(3) and g(–5) for the function g(x) = x5 – 8x3 – 2x + 7.
Let's do the same thing to evaluate g(-5):
-5Answer:
Step-by-step explanation:
Never heard of "synthetic substitution." I think you meant "synthetic division," which is a great method of evaluating polynomials for given input values.
g(x) = x^5 – 8x^3 – 2x + 7 is missing two terms.
With all terms showing, it would read:
g(x) = x^5 – 0x^4 + 8x^3 – 0x^2 - 2x + 7. The coefficients are {1, 0, 8, 0, -2, 7}.
Let's evaluate g(3). Use 3 as divisor in synth. div.:
3 ) 1 0 8 0 -2 7
3 9 51 153 453
------------------------------
1 3 17 51 151 460 Since the remainder is 460, the value of g(3) is also 460.
-5 ) 1 9 8 0 -2 7
-5 -20 60 -300 1510
----------------------------------
1 4 -12 60 -302 1517
The remainder is 1517, and so g(-5) = 1517.
Answer:
28, -2,108
Step-by-step explanation:
You have 100 feet of fencing to build a circular sheet pen. what is the diameter of the largest pen you can build?
Answer:
The diameter of the largest pen you could build is [tex]\frac{100}{\pi }[/tex] or [tex]31.8309[/tex] ft
Step-by-step explanation:
As the equation for the circumference of a circle is
[tex]C=d\pi[/tex]
We can plug in the known value for C, which is 100 and solve for d
[tex]100=d\pi[/tex]
[tex]d=\frac{100}{\pi }[/tex]
ANSWER
The diameter of the largest pen you can build is 31.8 feet to the nearest tenth.
EXPLANATION
You have 100 feet of fencing to build a circular sheet pen.
The largest diameter you can get is when you use all the 100 feet of fencing to build the sheet pen.
The circumference of the circular sheet pen must then be 100 feet.
Then using the formula for circumference, we have:
C=πd
100=πd
[tex]d = \frac{100}{\pi} [/tex]
d=31.83 ft.
What are the zeros of the polynomial function f(x)=x(x-4)(x+9)? HELP NEEDED!!!!
A. 0,-4,9
B. 1,-4,9
C. 0,4,-9
D. 1,4,-9
Answer: 0, 4, -9
Set the equation equal to zero.
x(x - 4)(x + 9) = 0
Solve for x by setting each factor equal to zero.
The factors in the equation are x, (x - 4), and (x + 9).
x = 0(x - 4) = 0x = 4
(x + 9) = 0x = -9
The zeros of the function are 0, 4, and -9.
formula for area of polygon
Answer:
The formula for the area of a polygon is 1/2*a*p.
a = apothem, which is a line segment that is the shortest distance from the center to a side.
p = perimeter
Hope this helps. :)
Answer:
Step-by-step explanation:
There's no one formula for finding the area of any polygon.
There are specialized formulas for finding the area of a square, of a triangle, of a trapezoid, etc. Beyond these, you have to invent approaches, such as breaking up an octagon into 8 triangles, finding the area of 1 such triangle, and then multiplying that area by 8.
Which one show factor pairs of 16
Answer:
There is not enough information
Step-by-step explanation:
If you wanted to find all the factors, here’s a list.
1,2,4,8,16
1 year, 27 weeks =
weeks
Answer:
Around 79.17 weeks
Step-by-step explanation:
Answer:
if you want to know how many weeks are in one year and 27 weeks, i can help out
Step-by-step explanation: 1 year has 365 days in it and one week has 7 days in it. Divide 365 by 7.
365/7= about 52 weeks.
52+27=79 weeks.
The exact amount of weeks is 79.177457
hope this helped!!
Consider this function.
f(x) = |x – 4| + 6
If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?
1.Since the domain of the original function is limited to x> 6, the range of the inverse function is y ≤ 6.
2.Since the domain of the original function is limited to x> 4, the range of the inverse function is y ≤ 1.
3.Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.
4.Since the range of the original function is limited to y> 4, the domain of the inverse function is x ≥ 1.
Answer:
3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.
Step-by-step explanation:
The domain of a function is the range of its inverse, and vice versa. The only answer choice that expresses this relationship is choice 3.
__
Comment on the answer choice:
The slope of the function is undefined at x=4, so restricting the function domain to the portion with positive slope means the domain restriction of the function is x > 4. That also means the range restriction of the function is y > 6. The domain restriction of the inverse function is the same: x > 6, not x ≥ 6. The answer choice has an error.
The domain of the original function with the positive slope is restricted to x > 4, and the range of f(x) is y ≥ 6. Therefore, the domain of the inverse function is x ≥ 6.
Explanation:The function given is f(x) = |x – 4| + 6. When restricting the domain to the portion of the graph with a positive slope, the function increases. In the absolute value function, the slope changes at the vertex, which here is when x = 4. For x > 4, the slope is +1 because the graph of the function is increasing. So, considering the domain x > 4 makes the graph of the function only represent the portion with a positive slope.
The range of the original function with the restricted domain is f(x) ≥ 6, because the lowest value of |x – 4| is 0 when x ≥ 4, which results in f(x) = 0 + 6 = 6 when x = 4. Consequently, the corresponding range of the inverse function must be the domain of the original function, and thus, the domain of the inverse function must be x ≥ 6.
For the simple harmonic motion equation d=4sin(pi/8t) what is the maximum?
Answer:
Maximum value of the function is 4.
Step-by-step explanation:
Given function of simple harmonic motion is [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].
Now we need to find about what is the maximum value of [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].
We know that value of sine function varies from -1 to 1.
that means for any value of t, maximum value of sine function is 1.
[tex]\sin\left(\frac{\pi}{8}t\right) \leq 1[/tex]
[tex]4 \sin\left(\frac{\pi}{8}t\right) \leq 4[/tex]
[tex]d \leq 4[/tex]
Hence maximum value of the function is 4.
What is the equation of the line that passes through (5,-2)and(-3,4)
The equation of the line that passes through (5,-2) and (-3,4) is y = (-3/4)x + 7/4.
Explanation:To find the equation of the line that passes through (5,-2) and (-3,4), we can use the formula for the equation of a straight line, which is y = mx + b.
First, calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). In this case, (x1, y1) = (5, -2) and (x2, y2) = (-3, 4). So the slope is m = (4 - (-2)) / (-3 - 5) = 6 / (-8) = -3/4.Next, plug in the values of one of the given points and the slope into the equation. Let's use (5, -2) and the slope m = -3/4: y = (-3/4)x + b. Substitute x = 5 and y = -2.Now solve for b: -2 = (-3/4)(5) + b. Multiply -3/4 and 5: -2 = -15/4 + b. Add 15/4 to both sides: -2 + 15/4 = b. Convert -2 to a fraction with a common denominator: -8/4 + 15/4 = b. Simplify: 7/4 = b.Finally, substitute the value of b back into the equation: y = (-3/4)x + 7/4. This is the equation of the line that passes through (5,-2) and (-3,4).
Pizza Palace has a small business loan for 30 months at 6% interest. The expression for the total loan amount to be paid is p (1+r)^t, where:
t is time in years,
r is interest rate as a decimal, and
p is the principal of the loan.
Find the principal of the loan, to the nearest dollar, when the total loan amount to be paid is $404,886 at 30 months.
A manager says, “If the interest rate was cut in half, the difference between the total loan amount and the principal would also be cut in half.”
The statement is not always true.
Provide a specific example to refute the manager’s statement.
Answer:
The principal of the loan is $350000
$26844 is not half 54886 so the statement is not true
Step-by-step explanation:
* Lets use the given rule to solve the question
- The total loan amount to be paid = p (1 + r)^t , where
# t is time in years,
# r is interest rate as a decimal
# p is the principal of the loan
- To find t divide the number of months by 12
∵ t = 30/12 = 2.5 years
∵ r = 6/100 = 0.06 ⇒ the interest rate in decimal
∵ The total loan amount to be paid = $404,886
∴ 404,886 = p (1 + 0.06)^2.5
∴ 404,886 = p (1.06)^2.5 ⇒ divide both sides by (1.06)^2.5
∴ p = 404,886 ÷ [(1.06)^2.5] ≅ $350,000
* The principal of the loan is $350,000
- To check the statement of the manager lets find the difference
between the total loan amount and the principal
∵ The principal of the loan is $350,000
∵ the total loan amount to be paid is $404,886
∴ The difference = 404,886 - 350,000 = $54886
- Lets find the total loan amount to be paid when the interest rate
was cut in half
∵ The total loan amount to be paid = p (1 + r)^t
∵ t = 30/12 = 2.5 years
∵ The half of 6% is 3%
∴ r = 3/100 = 0.03 ⇒ the interest rate in decimal
∵ p = $350,000
∴ The total loan amount to be paid = 350,000 (1 + 0.03)^2.5
∴ The total loan amount to be paid = 350,000 (1.03)^2.5
∴ The total loan amount to be paid = $376,844
- Lets find the difference between the total amount to be paid and
the principal
∴ The difference = 376,844 - 350,000 = $26844
∵ $26844 is not half 54886
* The statement is not true
Solve x⁄6 = 20.
A. x = 14
B. x = 26
C. x = 120
D. x = 3
Answer:
120
Step-by-step explanation:
x/6=20
×=20×6
=120
Helppppppppppppppppppppp!!!!
Answer:
±i√55
Step-by-step explanation: