Answer:
(1, 1) is NOT a solution
Step-by-step explanation:
The only point of intersection of the graphs is (0, 2). The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection, so is NOT the solution to the system of equations.
The point (1,1) is not a solution to the system of equations because, when we substitute the coordinates into the equations, it matches the second equation but not the first.
Explanation:To determine whether point (1,1) is a solution to the system of equations, we need to substitute the x and y values of the point into each equation and see if they produce true statements.
The first equation in the system is '3 times x plus 2', which we can write as 3x + 2. Substituting x = 1 in this equation gives us 3*1 + 2 = 5, which is not equal to the y-coordinate (1) of our input point.
The second equation is the |x - 1| + 1, which refers to the absolute value of (x minus 1) plus one. If we input x = 1, we get |1 - 1| + 1 = 1, which equals the y-coordinate (1) of our point. However, because the point didn't satisfy both equations, (1,1) is not a solution to the system.
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Sandra's printer can print 5 pages in 2/3 of a minute (40s). Show different ways to determine how many pages her printer can print in 1 minute.
Answer:
[tex]7\frac{1}{2}[/tex] pages
Step-by-step explanation:
Method 1: Working with minutes
Let us assume that, Sandra's printer can print x pages in 1 minute.
Then we can write the equation:
[tex]x:1=5:\frac{2}{3}[/tex]
We can rewrite the ratios as a fraction.
[tex]\frac{x}{1}=\frac{5}{\frac{2}{3}}[/tex]
This simplifies to
[tex]x=\frac{15}{2}[/tex]
Or
[tex]x=7\frac{1}{2}[/tex]
Method 2: Working with seconds
If 5 pages corresponds to 40 seconds, then we can write: [tex]5:40[/tex]
Let y corresponds to 60 seconds (1 minutes).
Then:
[tex]y:60=5:40[/tex]
We rewrite as fraction:
[tex]\frac{y}{60}=\frac{5}{40}[/tex]
Multiply both sides by:
[tex]y=\frac{5}{40}\times 60[/tex]
[tex]y=\frac{300}{40}[/tex]
[tex]y=\frac{15}{2}[/tex]
[tex]y=7\frac{1}{2}[/tex]
Someone please help??
Answer:
x-axis
Step-by-step explanation:
The asymptote is a straight line that the curve gets closer and closer to but never touches it.
The given exponential function is [tex]f(x)=3^x[/tex].
The given graph has a horizontal asymptote,
The equation of this horizontal asymptote is y=0.
This is also refers to as the x-axis.
Therefore the asymptote is the x-axis.
How do I expand (x-2)^6
The expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64
How to expand the algebraic expression
From the question, we have the following parameters that can be used in our computation:
(x - 2)⁶
This is a binomial expression that can be expanded using Pascal triangle
The power of the expression is 6
At n = 6, we have the following coefficients
1 6 16 20 16 6 1
So, we have
(x - 2)⁶ = 1 * x⁶ + 6 * x⁵ * (-2) + 16 * x⁴ * (-2)² + 20 * x³ * (-2)³ + 16 * x² * (-2)⁴ + 6 * x * (-2)⁵ + 1 * (-2)⁶
Expand the exponents
(x - 2)⁶ = x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64
Hence, the expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64
Suppose a triangle has two sides of length 33 and 37 and that the angle between these two sides is 120 what is the length of the third side of the triangle
Answer:
60.65
Step-by-step explanation:
The Law of Cosines can help you figure this out. Call the given sides "a" and "b" and the given angle "C". Then the third side, "c" will satisfy the relation ...
c² = a² + b² -2ab·cos(C)
= 33² +37² -2·33·37·cos(120°) = 3679
c = √3679 ≈ 60.65476 ≈ 60.65
The length of the third side is about 60.65 units.
A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (–3, 1), (1, 1), and (1, –2). What is the perimeter of the triangle?
Answer:
The perimeter of the triangle is [tex]12\ units[/tex]
Step-by-step explanation:
Let
[tex]A(-3,1),B(1,1),C(1,-2)[/tex]
we know that
The perimeter of triangle is equal to
[tex]P=AB+BC+AC[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(-3,1),B(1,1)[/tex]
substitute in the formula
[tex]AB=\sqrt{(1-1)^{2}+(1+3)^{2}}[/tex]
[tex]AB=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]AB=4\ units[/tex]
step 2
Find the distance BC
[tex]B(1,1),C(1,-2)[/tex]
substitute in the formula
[tex]BC=\sqrt{(-2-1)^{2}+(1-1)^{2}}[/tex]
[tex]BC=\sqrt{(-3)^{2}+(0)^{2}}[/tex]
[tex]BC=3\ units[/tex]
step 3
Find the distance AC
[tex]A(-3,1),C(1,-2)[/tex]
substitute in the formula
[tex]AC=\sqrt{(-2-1)^{2}+(1+3)^{2}}[/tex]
[tex]AC=\sqrt{(-3)^{2}+(4)^{2}}[/tex]
[tex]AC=5\ units[/tex]
step 4
Find the perimeter
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=4+3+5=12\ units[/tex]
Develop a 95% confidence interval for the expected value of y when x = 8. estimate the standard deviation of an individual value of y when x = 8.
Final answer:
To create a 95% confidence interval for y when x=8, we need the sample mean and the standard deviation to calculate the Error Bound for the Mean (EBM). The CI is the sample mean ± EBM. Estimating the standard deviation of y involves using the sample standard deviation as an estimate or the known population standard deviation.
Explanation:
To develop a 95% confidence interval for the expected value of y when x = 8, we first need to know the sample mean (μ) and the standard deviation of the population or an estimate from the sample (known as σ or s, respectively). When we have these statistics, we can use the normal distribution to calculate the error bound for the mean (EBM), which is the margin of error. The confidence interval (CI) is then constructed as (sample mean - EBM, sample mean + EBM).
To estimate the standard deviation of an individual value of y when x = 8, which is essentially the standard deviation of the population (σ), you need to use the sample standard deviation (s) as an estimate unless the population standard deviation is known.
Remember, the EBM for the confidence interval depends on the chosen confidence level, the standard deviation, and the size of the sample. With a higher confidence level, you get a wider interval. In practice, the confidence interval gives us a range where we expect the true population parameter lies with a certain level of confidence, acknowledging there's still a small chance the true value lies outside of this range.
The table of values represents the function g(x) and the graph shows the function f(x).
Which statements are true?
Select EACH correct answer.
A. g(x) has fewer x-intercepts than f(x).
B. f(x) and g(x) have a common x-intercept.
C. The maximum value of g(x) is greater than the maximum value of f(x) .
D. f(x) has a greater y-intercept than g(x).
Answer:
B, C
Step-by-step explanation:
x-intercepts are when y=0. f(x) has two x-intercepts at (1, 0) and (5, 0). g(x) also has two x-intercepts; (-3, 0) and (5, 0). So the first one is false, and the second one is true.
The maximum value of f(x) is 2. The maximum value of g(x) is 4. So the third one is true.
The y-intercept is the value of y when x=0. So the y-intercept of f(x) is -1, and the y-intercept of g(x) is 3. So the fourth one is false.
The statement which is true are f(x) and g(x) have a common x-intercept (B) and the maximum value of g(x) is greater than the maximum value of f(x) (C).
What is x-intercept?The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis. The value of y is equal to zero at x-intercept.
The function f(x) shown in the graph has two x intercept (5,0) and (1,0). The x intercept of g(x) are (-3, 0) and (5, 0).
Similarly, the y-intercept is the point on the coordinate at which a line, curve or plane intersect with the y-axis. The value of x is equal to zero at y-intercept.
The function f(x) shown in the graph has one y intercept (0,-1). The y intercept of g(x) is (0, 3). Here the maximum value of f(x) is 2 while g(x) is 4.
Thus, the statement which is true are f(x) and g(x) have a common x-intercept (B) and the maximum value of g(x) is greater than the maximum value of f(x) (C).
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Chance has hired a construction crew to renovate his kitchen. They charge $3.92 per square foot for materials and $124.26 per day of labor. Chance spent $3,233.54 on the renovation. If the number of square feet is 269 more than the number of days it took for the renovation, how long did the renovation take?
A. 20 days
B. 17 days
C. 3 days
D. 15 days
Please show your work so I can understand how you got the answer. :)
Answer:
B. 17 days
Step-by-step explanation:
We want to know how many days it took, so it is convenient to define the variable x as the number of days. Then the number of square feet is (x+269) and the total cost is ...
124.26x +3.92(x+269) = 3233.54
128.18x + 1054.48 = 3233.54 . . . . . . . . simplify
128.18x = 2179.06 . . . . . . . . . . . . . . . . . . subtract 1054.48
2179.06/128.18 = x = 17 . . . . . . . . . . . . . divide by the coefficient of x
The renovation took 17 days.
For solving the problem, we first divide the question into two equations, and then substitute and solve the equations. The renovation took around 17 days that is option B)
Explanation:This is a system of equations problems in Mathematics. Let's denote the number of days as 'd' and the square footage as 'f'. According to the problem, we know that:
1. Costs of materials + Costs of labor = Total spent
$3.92f + $124.26d = $3233.542. The square footage is 269 more than the number of days. So:
'f = d + 269'We can replace 'f' from the second equation with the first one: $3.92(d + 269) + $124.26d = $3233.54. Simplifying this, we get $1052.48 + $4.93d = $3233.54, and solving for 'd', we get 'd' approximately equal to 17 days, so the answer is (B).
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The area of a square is A = s?, where s is the length of one side of the square. What is the side length s for each square?
Answer:
s = +√A
Step-by-step explanation:
Start with the area formula, A = s². Solve this for the side length, s, as follows:
s = +√A
In words, if you're given the area of a square, find the square root of this area to determine the side length.
It costs 9.95 for 1 ticket to the movies. If 3 people go, how much would the total price of 3 tickets be?
It would be $9.95 x 3
A car loses its 15% of its current value every year. What is the value of a car that was bought for $20,000 in two years?
Answer:
$14,450
Step-by-step explanation:
y=20,000(1-0.15)^x
Hope This Helps :D
what is the area of isosceles trapazoid MNOP?
Answer:
340 units squared
Step-by-step explanation:
in the trapezoid, there is a square and an isosceles triangle
find the area of the square: 17×(23-6) =17×17 =289
find area of the triangle: 17×6 /2 =51
add the two together: 289 +51 =340
Answer:
Line MN = 23 -3 -3 = 17
Middle Area = 17 * 17 = 289
Area of BOTH Ends = 17 * 3 = 51
TOTAL Area = 289 + 51 = 340
Step-by-step explanation:
The lines shown below are perpendicular. If the green line has a slope of -1/4 what is the slope of the red line
Answer:
4
Step-by-step explanation:
Since perpendicular lines have negative reciprocals, we have to find out the negative reciprocal of -1/4.
To get the negative reciprocal of -1/4, we have to switch the numbers in the numerator and denominator.
That becomes 4/-1, and then we have to remove the negative, which makes the final answer 4/1.
4/1 = 4
Therefore, the negative reciprocal of -1/4 is 4.
Hope this Helps!
The slope of the red perpendicular line is 4.
What is slope of a perpendicular line ?Slope of a straight line is defined as the inclination of the line with respect to the coordinate axis. The slope is also measure of the tangent of angle with which the line is inclined to the axis.
If the slope of a given straight line is m then the slope of its corresponding perpendicular line will be negative reciprocal of the given slope which is -(1/m).
How to find the slope of the given curve ?It is said that the lines shown below are perpendicular. Also it is mentioned that the green line has a slope of -1/4 .
As the red line is perpendicular to the green line, thus its slope is negative reciprocal of the given slope of green line.
Slope = -(-4) = 4 .
Therefore, the slope of the red perpendicular line is 4.
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Look at the two circles below . They share a center point . The larger circle has a radius of 10 inches . The distance between the smaller circle and the larger circle is 2 inches . Which best represents the shaded area between the two circles
Answer:
π(10 in)² - π(8 in)²
Step-by-step explanation:
Area between the two circles=
Area of larger circle less area of smaller circle, or
π(10 in)² - π(8 in)² Since the difference in the radii of the
two circles is 2, that means the smaller
circle has radius 10 - 2, or 8 (inches)
Next time, please share the answer choices. Thank you.
To find the shaded area between the two circles, subtract the area of the smaller circle from the area of the larger circle. The area of a circle is calculated using the formula A = πr^2. By finding the radius of the smaller circle, we can calculate its area and subtract from the larger circle's area to find the shaded area.
Explanation:The shaded area between the two circles can be found by subtracting the area of the smaller circle from the area of the larger circle. The radius of the larger circle is given as 10 inches and the distance between the two circles is given as 2 inches. To find the area of the shaded region, we first need to find the radius of the smaller circle. Since the distance between the two circles is equal to the sum of their radii, the radius of the smaller circle is 10 inches - 2 inches = 8 inches.
The area of the larger circle is calculated using the formula A = πr^2, where r is the radius. Therefore, the area of the larger circle is A = π(10 inches)^2 = 100π square inches.
The area of the smaller circle is calculated in the same way, using the radius of 8 inches. Therefore, the area of the smaller circle is A = π(8 inches)^2 = 64π square inches.
To find the shaded area, we subtract the area of the smaller circle from the area of the larger circle: 100π square inches - 64π square inches = 36π square inches.
Find an equation equivalent to r=5/1+cos0 in rectangular coordinates
A. x^2=25-10y
B. X^2=10y-25
C.y^2=10x-25
C. Y^2= 25-10x
[tex]r=\dfrac5{1+\cos\theta}\implies r(1+\cos\theta)=5\implies r+r\cos\theta=5[/tex]
In converting between polar and rectangular coordinates, we take
[tex]x^2+y^2=r^2\implies r=\sqrt{x^2+y^2}[/tex]
[tex]x=r\cos\theta[/tex]
so that the equation becomes
[tex]\sqrt{x^2+y^2}+x=5[/tex]
which we can rewrite as
[tex]\sqrt{x^2+y^2}=5-x[/tex]
[tex]x^2+y^2=(5-x)^2[/tex]
[tex]x^2+y^2=25-10x+x^2[/tex]
[tex]\implies\boxed{y^2=25-10x}[/tex]
so the answer is C.
The graph of which equation below is a horizontal line?
Answer:
2
Step-by-step explanation:
The equation of a horizontal line is y = c
where c is the value of the y- coordinates the line passes through
Thus y = 3 ← is the equation of a horizontal line
Determine whether the situation involves a permutation or a combination, and how many possibilities are there are?
A team of six students is chosen from a class of 36.
Answer:
This situation involves a combination as the team will be the same no matter what order the students are chosen in.
There are 1402410240 possibilities for the six student team
Step-by-step explanation:
Each time a student is chosen, they cannot be chosen again, so the number of available students decreases each time that one is chosen.
[tex]36*35*34*33*32*31=1402410240[/tex]
Please help me out please
Answer is A) Acute due to the lengths
Answer:
A
Step-by-step explanation:
Matt paid $55 at a restaurant. That amount included a 10% tip. What was the check amount before the tip? A. $40 B. $43 C. $45 D. $50 E. $52
Answer:
D $50
Step-by-step explanation:
50x.10=5
5+50=55
For this case we propose a rule of three:
$ 50 -------------> 100%
x -----------------> 10%
Where the variable "x" represents the amount of the tip.
[tex]x = \frac {10 * 50} {100}\\x = 5[/tex]
So, the tip was 5 dollars.
If we subtract that amount to what Matt paid at the restaurant we will have the amount of the check before the tip.[tex]55-5 = 50[/tex]
ANswer:
Option D
Are data at the nominal level of measurement quantitative or qualitative?
a. both qualitative and quantitative
b. qualitative
c. quantitative
d. neither qualitative nor quantitative
Answer:
B. qualitative
Step-by-step explanation:
The double number line shows that 444 pounds of almonds cost \$34$34dollar sign, 34. Based on the ratio shown in the double number line, what is the cost for 555 pounds of almonds?
Answer:
$42.5
Step-by-step explanation:
Answer:
42.5
Step-by-step explanation:
Please help with this !!
Answer:
A
Step-by-step explanation:
The graph of the parabola has no points of intersection with the real x- axis
and therefore has no real solutions
Complex roots occur in conjugate pairs so cannot be C
The solution would be 2 complex roots → A
Answer:
A
Step-by-step explanation:
The graph has no intersection with x-axis therefore has no real roots.
In the game Yahtzee, players roll five dice. There are 13 rounds per game. In each round, each player can roll the dice up to three times. In a player's first roll of each round, he or she rolls all five dice. The second and third rolls, the player can choose to roll any subset of the dice again (any or all the dice). Yahtzee is a bit like poker with dice. An especially valuable roll is 5 of a kind (all 5 dice show the same number of spots), called a Yahtzee. The next two questions are about Yahtzee. Problem 3 The chance of rolling a Yahtzee (5 of a kind) on the first roll of a turn is closest to
Answer: 13
Step-by-step explanation: because I have the whole bookanswer duh
Please help me please !!!!!
Answer:
215.6 m²
Step-by-step explanation:
The area (A) of the polygon is
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
perimeter = 7 × 7.7 = 53.9 m, so
A = 0.5 × 53.9 × 8 = 215.6
The area of regular polygon with 7 sides is 215.6 m².
What is Polygon?Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.
Here, the area (A) of the polygon is
A = 1/2 × perimeter × apothem
perimeter = length X width
= 7 × 7.7
= 53.9 m,
so, A = 0.5 × 53.9 × 8
= 215.6 m²
Thus, the area of regular polygon with 7 sides is 215.6 m².
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The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is:
The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is 4.35.
What is a critical value?A critical value can be calculated for different types of hypothesis tests. The critical value of a particular test can be interpreted from the distribution of the test statistic and the significance level.
Test of significance of linear regression between x and y.
Null hypothesis: There is no significant linear relationship between x and y.
Alternative hypothesis: There is a significant linear relationship between x and y.
Test statistic:
F0 = Mean square due to regression/ mean squared error ~ F(1, n-2)
Critical value: [tex]F_{\alpha}(1, n-2) = F_{0.05}(1,20) = 4.35[/tex]
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Please select the best answer from the choices provided
A is the correct answer but I did do it in my head so fair warning
Please please help me
Answer:
31%
Step-by-step explanation:
Of the 6101 students on financial aid, 1879 are graduates. This fraction is ...
1879/6101 × 100% ≈ 30.798% ≈ 31%
Each edge of a wooden cube is 4 centimeters long. The cube has a density of 0.59 g/cm3 . What is the mass of the wooden cube?
Answer:
37.76
Step-by-step explanation:
(What we know)
V = 4*4*4 = 64
Density = 0.59
___________________
Density = Mass/Volume
Mass = (Density)(Volume)
So
Mass = (0.59)(64)
or
Mass = .59 * 64
Mass = 37.76
_____________________________
So the answer would be 37.76
Hope this helps, if you see an error please correct me.
Solve the system of equations. y = -6x + 9 y = -3x + 3 a. ( 3, -2) c. ( 2, -3) b. ( -2, -3) d. No solution
For this case we have the following system of equations:
[tex]y = -6x + 9\\y = -3x + 3[/tex]
Equating the equations we have:
[tex]-6x + 9 = -3x + 3[/tex]
Adding 3x to both sides of the equation:
[tex]-6x + 3x + 9 = 3\\-3x + 9 = 3[/tex]
Subtracting 9 from both sides of the equation:
[tex]-3x = 3-9\\-3x = -6[/tex]
Dividing between -3 on both sides of the equation:
[tex]x = \frac {-6} {- 3}\\x = 2[/tex]
We look for the value of "and":
[tex]y = -3 (2) +3\\y = -6 + 3\\y = -3[/tex]
Thus, the solution of the system is (2, -3)
Answer:
(2, -3)
question 70 true or false
Answer:
true
Step-by-step explanation:
For this case we have that by definition:
[tex]Sin (90) = 1\\Cos (90) = 0[/tex]
Now, the tangent of 90 is given by:
[tex]tg (90) = \frac {Sin (90)} {Cos {90}} = \frac {1} {0}[/tex]
Thus, it is observed that the tangent of 90 degrees is not defined. Is obtained ∞.
Similarly:
[tex]Sin (-90) = - 1\\Cos (-90) = 0[/tex]
Now, the tangent of -90 is given by:
[tex]tg (-90) = \frac {Sin (-90)} {Cos {-90}} = \frac {-1} {0}[/tex]
Thus, it is observed that the tangent of -90 degrees is not defined.
Answer:
False