Answer:
All values of x make the equation true. It is an infinite solution.
What are the roots of the polynomial equation?
–12, 12
–4, 3
–3, 4
–1, 1
8.04 A
Graph each pair of parametric equations.
(2 points each)
x = 3 sin3t
y = 3 cos3t
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 7 sin t + sin 7t
y = 7 cos t + cos 7t
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 2t
y = t + 5, -2 ≤ t ≤ 3
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 2t – 1
y = t2 + 5, -4 ≤ t ≤ 4
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 6 sin t
y = 6 cos t, 0 ≤ t ≤ 2π
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
If the domain is {0, 2, -6}, what is the range of y = -2x + 3?
The range of the function is {-1, 3, 15}.
What is the range of the function?The set of a function's potential output values is known as its range.
Given that, the domain of the function is {0,2,-6}.
The range is the set of the output of the functions for the given domain values.
The value of y for x = 0 is:
y = -2(0) + 3
y = 3
Similarly, the values of y for x = 2 and x = -6 are:
y = -2(2) + 3
y = -1, and
y = -2(-6) + 3
y = 15
Hence, the range of the function is {-1, 3, 15}.
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Which ordered pair will be the solution for the function y = 12 - x?
(7, 4)
(6, 6)
(4, 9)
(2, 14)
The solution to the function y = 12 - x is the ordered pair (6, 6) because when we substitute x = 6 into the function, the result, y, is also 6, which matches the given y-value in the pair.
Explanation:To find the ordered pair that is a solution for the function y = 12 - x, we need to substitute the x-values of each given ordered pair into the equation and see which one gives a resulting y-value that matches the one in the pair.
(7, 4): y = 12 - 7 = 5 – This does not match the y-value of 4.(6, 6): y = 12 - 6 = 6 – This is correct, as it matches the y-value of 6.(4, 9): y = 12 - 4 = 8 – This does not match the y-value of 9.(2, 14): y = 12 - 2 = 10 – This does not match the y-value of 14.Therefore, the solution to the function is the ordered pair (6, 6).
Segment AB has endpoints A(–4, 6) and B(1, 4). After a dilation, centered at the origin, the image of A is (–6, 9). Without measuring the distance, explain how you could find the image of B
Answer:
To find the image of B, first find the scale factor for the dilation. The scale factor should be greater than 1 because the image of A is farther from the origin than A. Divide the coordinates of the image of A by the coordinates of A: –6/–4 = 3/2 and 9/6 = 3/2, so the scale factor is 3/2. Now, apply the dilation to B by multiplying the coordinates by 3/2 to get ((3/2)(1), (3/2)(4)), or (3/2, 6).
Step-by-step explanation:
A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?
A)53.53 feetB)74.62 feetC)126.11 feetD)322.75 feet
The sum of the first 30 terms of the sequence an=6n+5 is
Answer:
[tex]S_{30}=2940[/tex].
Step-by-step explanation:
Given : [tex]a_{n} =6n+5[/tex].
To find : The sum of the first 30 terms .
Solution: We have given [tex]a_{n} =6n+5[/tex].
For n = 1
[tex]a_{1} =6(1)+5[/tex].
[tex]a_{1} =6+5[/tex].
[tex]a_{1} =11[/tex].
For n =2
[tex]a_{2} =6(2)+5[/tex].
[tex]a_{2} =17[/tex].
Common difference = 17 - 11 = 6.
Sum of nth term : [tex]S_{n} =\frac{n}{2}[2a+(n-1)d][/tex].
d = common difference = 6.
For n = 30 .
[tex]S_{30} =\frac{30}{2}[2(11+(30-1)6][/tex].
[tex]S_{30} =15[22+29 *6][/tex].
[tex]S_{30} =15[22+29 *6][/tex].
[tex]S_{30} =15[22+174][/tex].
[tex]S_{30} =15[196][/tex].
[tex]S_{30}=2940[/tex].
Therefore, [tex]S_{30}=2940[/tex].
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Triangle HJK is transformed to similar triangle H’J’K’:
What is the scale factor of dilation?
1/2
1/3
1/4
1/5
Answer:
The scale factor of the dilation is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor
Let
z------> the scale factor
so
[tex]z=\frac{K'J'}{KJ}=\frac{K'H'}{KH}=\frac{J'H'}{JH}[/tex]
substitute the values
[tex]z=\frac{K'J'}{KJ}[/tex] -----> [tex]z=\frac{1}{4}[/tex]
The scale factor is less than 1
therefore
The dilation is a reduction
Sakura speaks 150150150 words per minute on average in hungarian, and 190190190 words per minute on average in polish. she once gave cooking instructions in hungarian, followed by cleaning instructions in polish. sakura spent 555 minutes total giving both instructions, and spoke 270270270 more words in polish than in hungarian. how long did sakura speak in hungarian, and how long did she speak in polish?
Answer:
3 minutes polish 2 minutes hungarian
Step-by-step explanation:
I just did it on Kahn Academy, and this was correct.
Please help i'll give you brainliest answer!
1. Astronomers measure large distances in light-years. One light year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light years from Earth. In scientific notation, approximately how many miles is it?
A. 5.88 x 10^13 miles
B. 5.76 x 10^14 miles
C. 5.88 x 10^12 miles
D. 9.8 x 10^12 miles
2. A 1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?
A. $4,979.11
B. $14,920.54
C. $112,992.00
D. $15,494.70
Answer:
1. B. 5.76 × 10¹⁴ miles.
2. D. $15,494.70
Step-by-step explanation:
Question 1: We have,
Distance light traveled in one year = 5.88 × 10¹² miles.
Since, the star is 9.8 × 10¹ light years away.
So, we get,
Total number of miles the star is away = 5.88 × 10¹² × 9.8 × 10¹ = 57.62 × 10¹³ miles.
Hence, the total number of miles are 5.76 × 10¹⁴ miles.
Question 2: We have,
Principle amount, P= $1,600
Rate of interest, r = 7% = 0.07
Time period, t = 33 years
Moreover, the interest is compounded twice per year i.e. n=2.
Since, Amount = [tex]P(1+\frac{r}{n})^{nt}[/tex]
i.e. Amount = [tex]1600(1+\frac{0.07}{2})^{2\times 33}[/tex]
i.e. Amount = [tex]1600(1+\frac{0.035)^{66}[/tex]
i.e. Amount = [tex]1600(1.035)^{66}[/tex]
i.e. Amount = [tex]1600\times 9.68418}[/tex]
i.e. Amount = $15,494.70
Hence, the balance in the account is $15,494.70.
Please help and show all work thank you!
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A packet contains 24 pens.
Henry and Alice share them in the ratio 3 : 5
How many does Alice receive?
On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis. What are the coordinates of Q and S?
Answer:
Q(2, −1), S(−6, 5)
Step-by-step explanation:
The original ordered pairs were (2, 1) and (−6, −5). When you reflect across the x-axis the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).
so since the original ordered pairs were (2, 1) and (−6, −5), the reflected ordered pairs would be Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.
Hope this helped fellow FLVS student!!
The coordinates are Q(2, −1) and S(−6, 5)
What is reflection of points?A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side. Under the point of reflection, the figure does not change its size and shape.
Given that, On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis.
We know that, when you reflect across the x-axis, the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).
So, since the original ordered pairs were (2, 1) and (−6, −5), the reflected ordered pairs would be Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.
Hence, The coordinates are Q(2, −1) and S(−6, 5)
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box. °
Each trapezoid in the figure below is congruent to trapezoid ABDC.
What is the perimeter of hexagon ACEFGH?
1)28 cm
2)32 cm
3)36 cm
4)64 cm
Answer:
The answer is the second option
[tex]32\ cm[/tex]
Step-by-step explanation:
we Know that
Each trapezoid in the figure below is congruent to trapezoid ABDC
so
[tex]CE=AC=3\ cm[/tex]
[tex]EF=AB+CD=4+6=10\ cm[/tex]
[tex]FG=AC=3\ cm[/tex]
[tex]GH=AC=3\ cm[/tex]
[tex]AH=AB+BH=AB+CD=4+6=10\ cm[/tex]
the perimeter is equal to
[tex]P=AC+CE+EF+FG+GH+AH[/tex]
substitute the values
[tex]P=3+3+10+3+3+10=32\ cm[/tex]
Function f, shown below, is translated down 3 units and left 4 units to create function g. f(x)=3|x-2|-5. Fill in the values of a, h, and k to write function g.
Answer:
g (x) = 3lx+2l-8
Step-by-step explanation:
Carlosego made a mistake on the horizontal shift.
y = f (x + c) shifts the graph c units to the left.
Therefore, g (x) = 3lx - 2 + 4l - 8 is
g (x) = 3lx+2l-8
find the measure of side c.
The length of side AB (c) in triangle ABC is 31.38 m.
In triangle ABC, angle BCA is a right angle with a measure of 90 degrees, and angle CAB has a measure of 42 degrees.
The side BC has a length of 21 m and the side AB has a length of c.
To find the length of side c, we can use the trigonometric function sine.
By using the sine function and the given angle CAB, we can calculate the length of side c as follows:
c = AB = BC * sin(CAB) = 21 * sin(42) = 31.38 m
Therefore, The length of side AB (c) in triangle ABC is 31.38 m.
The probable question may be:
In triangle ABC, Angle BCA= 90 degree, angle CAB=42 degree, Side BC (a)=21 m, Side AB=c, find the measure of side c.
Jerry goes to the bank and borrows $9,000 for farm equipment. The simple yearly interest is 9.5% and he pays off the loan over a period of 2 years with 24 equal monthly payments. What’s Jerry’s monthly payment
Jerry's monthly payment can be calculated using the formula for the monthly payment on a loan. Plugging in the given values will give the exact monthly payment amount.
Explanation:To calculate Jerry's monthly payment, we can use the formula for the monthly payment on a loan:
Monthly Payment = P × r × (1 + r)^(n) / ((1 + r)^(n) - 1)
Where:
P is the principal amount borrowed, which is $9,000r is the monthly interest rate, which is calculated by dividing the annual interest rate by 12 and converting it to a decimal. In this case, it would be 9.5% / 12 = 0.0079 (rounded to four decimal places)n is the total number of payments, which is 2 years × 12 months = 24 monthsPlugging in the values:
Monthly Payment = $9,000 × 0.0079 × (1 + 0.0079)^(24) / ((1 + 0.0079)^(24) - 1)
Simplifying this equation will give us the monthly payment amount.
suppose you invest $500 in a savings account that pays 3.5% annual interest. when will the account contain $650
Make this equation true by rearranging the numbers.... 26=74
What is the value of n?
Enter your answer in the box.
n =____m
police can estimate the speed of a vehicle before the brakes are applied using the formula 0.75d = s^2 / 30.25 where is the speed in miles per hour d is the length of the vehicle's skid marks. What was the approximate speed of a vehicle that left a skid mark measuring 160 feet?
1.about 36 miles per hour
2."" 60 ""
3."" 13 ""
4"" 54 ""
The answer would be ≈60mph, hence the answer is B.
The solution set for 7q2 − 28 = 0 is { }. (Separate the solutions with a comma) NextReset
Answer:
{ 2,-2}
Step-by-step explanation:
In order to solve this set we just have to first clear the "q":
[tex]7q^{2} -28=0\\7q^{2} -28+28=+28\\7q^{2} =28\\\frac{7q^{2}}{7} =\frac{28}{7} \\q^{2}=4\\\sqrt{q^{2}} =\sqrt{4} \\q= 2, -2[/tex]
So as we know the solution for a square root is always a negative and positive number, so the solutions ser for 7q2-28=0 is 2 and -2
The math test scores of Mrs. Hunter's class are shown below. 48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100 What is the range of the scores? A) 44 B) 52 C) 54 D) 62
The range of the scores is B) 52.
What is the range of the function?The range of a function is defined as the set of all the possible output values that are valid for the given function.
Since the range would be the difference between the highest and the lowest score
WE are given that the math test scores of Mrs. Hunter's class are shown below.
48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100
Highest = 100
lowest = 48
here, we have,
range = 100 - 48 = 52
Hence, The solution is, range = 52.
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When dividing which number goes first in the calculator?
The height and radius of a right cylinder are each 8 cm. what is its volume
A company has found that the demand for its product varies inversely as the price of the product. when the price x is 3.5 dollars, the demand yy is 450 units. find a mathematical model that gives the demand y in terms of the price x in dollars.
The mathematical model that gives the demand, y, in terms of the price, x, is y = 1575/x.
Explanation:To find a mathematical model that gives the demand, y, in terms of the price, x, we can use the formula for inverse variation. Inverse variation is described by the equation y = k/x, where k is a constant. To find the value of k, we can use the given information: when x = 3.5, y = 450. Substituting these values into the equation, we get 450 = k/3.5. Solving for k, we find that k = 1575. Therefore, the mathematical model that gives the demand, y, in terms of the price, x, is y = 1575/x.
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Ava rounded 19,350 to the nearest thousand and got 20,000. Which of the following statements is true? Ava rounded correctly. Ava rounded incorrectly; the answer should be 19,400. Ava rounded incorrectly; the answer should be 19,000. Ava rounded incorrectly; the answer should be 19,300.
A grocer wants to make a 10 pound mixture of cashews and peanuts that he can sell for $3.64 per pound. If cashews cost $5.80 per pounds and peanuts cost $2.20 per pound how many pounds of each nuts must he mix?