Solution
For this case the unitary circle is given by:
[tex]x^2+y^2=1[/tex]this unitary circle is important for the trigonometric identities
Can be used also to solve inequalities
Can be used also in physics applications and in linear algebra
Susan runs 4 miles in 30 minutes. At the same rate, how many minutes would she take to run 10 miles?
Answer:
It would take 75 minutes for Susan to run 10 miles.
Step-by-step explanation:
10 miles divided by 4 = 2.5
30 min. x 2.5 = 75 minutes
Find 2 conservative numbers whose square differs by 25
The 2 conservative numbers whose square differs by 25 are 12 and 13.
How to illustrate the information?It should be noted that consersative numbers simply refer to the numbers hat follow each other continuously in a particular order. They include 1, ,2, 3, etc.
In this case, the two conservative numbers whose square differs by 25 are 12 and 13. This will be illustrated as:
= 13² - 12²
= 169 - 144
= 25
Therefore, the numbers are 12 and 13
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I heard that I received a fourth rating from a customer on our customer service survey . What is my average monthly rating ?
Supervisor : “ you have been doing really well . You received ratings of 85, 90, 100 and 90 . What’s your monthly average ?
The average monthly rating is 91.25.
How to estimate averages?By adding a set of integers and then dividing by their count, the average, or arithmetic mean, is determined.Finding an average helps us determine a general pattern of behavior or trend.To compare different quantities of the same category, averages are utilized.In other words, the average is the proportion between the total number of observations and the sum of all observations presented.The common formula of average is:Average = Sum of the Observations/Number of Observations
Given:
The received ratings are 85, 90, 100, and 90.
Average monthly rating = Sum of ratings/ total number of ratings
= (85 + 90 + 100 + 90)/ 4
= 365/ 4
= 91.25
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y varies directly with x, and y = 40in when x = 15in
If y varies directly with x, that means there is going to be a constant that connects both the x and y variable.
[tex]\begin{gathered} \text{When x=15, and y=40, then} \\ k=\frac{y}{x} \\ k=\frac{40}{15} \\ k=\frac{8}{3} \\ \text{Therefore, the equation is going to be;} \\ y=\frac{8}{3}x \end{gathered}[/tex]The appropriate direct variation equation is stated above, and that is;
y = 8/3x
The recipe for junk crunchies requires a total of 8 cups of sugar and flour together. If the recipe had called for 1/4 cup more sugar, the amount of sugar would be half the amount of flour. How many cups of sugar does the recipe call for?
The recipe of the junk calls for 16/7 cups of sugar
How to determine the number of cups of sugar in the recipe?From the question, the given parameters are:
Total number of cups = 8
Let the number of cups of sugar be x and the number of cups of flour be y
So, we have the following equation
x + y = 8
Also, we have:
The recipe uses 1/4 cup more sugar, so the amount of sugar equals half the amount of flour
This means that
(1 + 1/4) * x = 1/2 * y
Evaluate the sum and the products
So, we have
5/4x = 1/2y
Make y the subject
y = 5/2x
Substitute y = 5/2x in x + y = 8
x + 5/2x = 8
Evaluate the sum
3.5x = 8
Divide by 3.5
x = 16/7
Hence, the cups of sugar is 16/7
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What is the missing step in the sequence of transformations that will map figure 1 onto figure 2?
1.?
2. translation 3 units to the right
3. translation 4 units down
A. reflection across the x-axis
rotation 90° clockwise about the origin
rotation 270° clockwise about the origin
reflection across the origin
Answer: rotation 90° clockwise about the origin
The missing step is rotation 90° clockwise about the origin.
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
In the graph, triangle 1 is translated to triangle 2.
Triangle 1 has three transformations, rotation 90° clockwise, translation 3 units to the right and 4 units down.
Therefore, the missing step is rotation 90° clockwise about the origin.
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Marie is calculating an annuity payment. Her mortgage of $200,000 compounds monthly for 30 years. What is the nt value she will use in her formula?
Based on the annuity payment that Marie will make and the number of years, the nt value that she will use in her formula is 360 months.
How to find the nt value?The nt value is the number of periods that Marie will need to pay her annuity payment. This value can be yearly, monthly, weekly and even daily.
As the mortgage compounds monthly in this instance, the nt value will need to be monthly as well.
To find the nt value, the formula is:
= Number of years x number of compounding periods per year
= 30 x 12 times a year
= 360 months
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Answer:
360
Step-by-step explanation:
i did that and i got it right
Convert (2,210 °) to rectangular form.
A. (1,-√3)
B. (-√3,-1)
C. (-√3,1)
D. (-1,-√3)
E. (√3,-1)
The answer is D. -1,-3. i just finished and got it right
You are considering a 5/1 arm what does 5 represent
Your rate is temporarily fixed for a total of five years under a 5/1 ARM, indicated by the "5".
An adjustable-rate mortgage is what?A loan for a home is a mortgage with an adjustable interest rate (ARM). An ARM's initial interest rate is fixed for a specific period of time.
The "1" indicates the number of times the rate may change after the initial fixed-rate term expires; in this instance, the "1" equals one year, therefore the rate changes once a year.
The "5" in the word represents the period during which the rate will be fixed, and the "1" denotes the interval between adjustments after that (once per year). Therefore, it is already apparent how crucial insurance is.
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what is equivalent to (x+7)^2 ?
1. x^2+49
2. (x-7)(x+7)
3. (x+7)(x+7)
4. (7x)(7x)
⇒In this case what is in the brackets is being treated as being the term . so this means that if we are to expand then we expand the whole term in full detail.
⇒In this case we have x+7 as the term of the expression which means when we expand we are going to expand the whole term x+7
[tex]=(x+7)^{2} \\=(x+7)(x+7)[/tex]
The third option is the answer.
GOODLUCK!!
What is the value of c?
14=-2c-6-3c
Answer:
-4
Step-by-step explanation:
14= -5c-6
+6 +6
________
20 = -5c
÷-5 ÷-5
________
-4 = c
10. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle.
Round answers to the nearest tenth of a centimeter.
O 44.4 cm, 11.1 cm
11.1 cm 49 cm
O 24 cm 49 cm
444 cm, 3.2 cm
The longest and shortest possible lengths of the third side of the triangle are 4.9 cm and 11.1 cm.
What does the Angle Bisector Theorem state?It states that the opposite side of a triangle is divided into segments by each angle bisector that are proportional in length to the adjacent sides.
Given:
An angle bisector divides the opposite side of the triangle into segments 6 cm and 4 cm long.
Second side of the triangle is 7.4 cm.
We have to calculate the longest and shortest possible lengths of the third side of the triangle.
By Angle Bisector Theorem we can solve this problem,
In the triangle ABC, AD is the angle that bisects angle A, placing D on side BC.
Now, BD / DC = AB / AC
BC = 6 + 4 = 10 cm
Angle bisector divides BC into 2 segments,
BD = 6 cm
CD = 4 cm
If AB = 7.4 cm,
6/4 = 7.4 / AC
AC = 7.4(4) / 6
AC = 29.6 / 6
AC = 4.94 cm (shortest possible length of the third side of the triangle)
If AC = 7.4 cm
6/4 = AB/7.4
AB = 6(7.4)/4
AB = 44.4/4
AB = 11.1 cm (longest possible length of the third side of the triangle)
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A figure is dilated by a factor of 3. Which of following statements about the image of the figure is true?
When an image is dilated by a factor of 3, the statement about the image of the figure that is true is Both the area and the perimeter increase.
What happens when a shape is dilated?When a shape is dilated, the effect on the shape is that its dimensions are made to be longer. For instance, a shape dilated by 2 would see all its dimensions increase by 2.
In the case of a figure that is dilated by a factor of 3, it means that the shape would increase by 3 in size.
The effect of this is that the perimeter would increase by 3. The area of the figure would also increase thanks to the increase in dimensions by 3.
Options for this question include:
The perimeter decreases.The area decreases.Both the area and the perimeter decrease.Both the area and the perimeter increase.Find out more on dilation at https://brainly.com/question/3457976
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To use the law of sines, which of the following statements must be true?
A. At least one side length and opposite angle pair must be known.
B. At least two angles must be known.
C. The triangle must be a right triangle.
D. All three side lengths must be known.
For the application of the law of sine the true statement is that at least one side length and opposite angle pair must be known.
How to use the law of sine to solve triangle?The law of sine is used to solve the sides and angles of a triangle.
Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.
In other words, the law of sines is defined as the ratio of side length to the sine of the opposite angle.
It holds for all the three sides of a triangle respective of their sides and angles.
Therefore, the law of sine can be expressed as follows:
a / sin A = b / sin B = c / sine C
Hence, the statement that is true is at least one side length and opposite angle pair must be known.
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A restaurant is having a deal for Valentine's day and is offering a 4-course meal for $27.00. If there is a sales tax of 8 percent, what is the actual cost of the meal?
Answer:
$29.16
Step-by-step explanation:
You want the total cost of a $27 meal after 8% tax is added.
TaxThe amount of added tax is found by multiplying the meal cost by the tax rate:
0.08 × $27.00 = $2.16
TotalThe total cost is the meal cost plus the tax:
$27 +2.16 = $29.16 . . . . actual cost of the meal
__
Additional comment
The sum 27 + 0.08×27 can also be found by factoring out the 27:
= 27(1 +0.08) = 27×1.08
WILL GIVE BRAINLYEST 100 POINTS 3 QUESTIONS WILL GIVE EXTRA POINTS
Answer:
The answer to the first question is the first option
The answer to the second question is the third option
the answer to the third one is the second option
Step-by-step explanation:
*I'm not 100% sure about these but it's probably right*
Answer:
1. First one
2. Third one
3. Second on
Step-by-step explanation:
(★ ω ★)
6. The table shows the equations Ms. Valer discussed in math class
Equations
6 x 10° 6
6 10¹ -60
6 x 10-600
6x 10³6,000
Explain the pattern of zeros in the product when multiplying
by powers of 10.
The product when multiplying by powers of 10 is 6 ×[tex]10^{10}[/tex] = 60000000000
What is multiplication ?The fundamental concept of repeatedly adding the same number is embodied in the process of multiplication. The outcome of multiplying two or more numbers is known as the product of those numbers, and the factors that are multiplied are referred to as the factors. The process of repeatedly adding the same number is made easier by multiplication.
Finding the product of two or more numbers is done by multiplication. It is a fundamental mathematical operation that is frequently applied in everyday situations. When combining groups of similar sizes, multiplication is utilized.
Given that :The table shows the equations Ms. Valer discussed in math class Equations
6 x 10°= 6
6× 10¹ =60
6 x 10=600
6x 10³=6,000
6 ×[tex]10^{10}[/tex] = 60000000000
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A. Write the decimals in words.
Example: 32.76-thirty-two point seven six
1. 60.03 -
2. 209.11 -
Answer:
1. sixty point zero three OR sixty and 3 hundredths
2. two hundred and nine point one one OR two hundred nine and 11 hundredths
Select the correct answer from each drop-down menu.
In a city, Broadway, Main Street, and Water Street all intersect to form a triangle. Broadway is 2000 m from Main Street to Water Street, Main Street
is 1600 m from Broadway to Water Street, and Water Street is 1200 m from Main Street to Broadway.
Complete the statement below.
In the triangle formed by the three streets, the greatest angle is the one formed by the intersection of
smallest angle is the one formed by the intersection of
Reset
Next
The
Using the Law of Sines, it is found that:
The greatest angle is formed by the intersection of Main Street and Water Street.The smallest angle is formed by the intersection of Broadway and Main Street.What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is given by a.The length of the side opposite to angle B is given by b.The length of the side opposite to angle C is given by c.The lengths and the sine of the angles are proportionally related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
From this relation, we have that:
The greatest angle is opposite the largest side.The smallest angle is opposite the smallest side.In this problem, we have that:
Broadway is the hypotenuse, hence the greatest angle is formed by the intersection of Main Street and Water Street.Due to the smaller distance, of 1200 m, compared to 1600 m and 2000 m, the smallest angle is formed by the intersection of Broadway and Main Street.More can be learned about the Law of Sines at https://brainly.com/question/27174058
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[tex]5(\frac{x+5}{9} )-9[/tex]
Answer:
I don't know
Step-by-step explanation:
I don't know
A small order coffee company charges $12 for each bag of coffee +3 dollars shipping no matter how many bags are ordered. Describe the function that this situation gives rise to. make a table for this function, sketch a graph for this function, and find an equation for this function. Is the function linear or not? How can you tell?
A small order coffee company charges $12 for each bag of coffee +3 dollars shipping no matter how many bags are ordered. Describe the function that this situation gives rise to. make a table for this function, sketch a graph for this function, and find an equation for this function. Is the function linear or not? How can you tell?
Step 1
Describe the function,
.
Let
x, the number of bags
shipping = 3 dollars
Charges=$12 for each bag, then
charges=12*x
Now, the total is
total=charges + shipping
total=12x +3
now, we have a function ( the total (y) depends on the number of bags)
[tex]y=12x+3[/tex]where
y is the total charge, and x is the numbers of bags
Step 2
assume values for x, replace and find y
x=-3
then y=12(-3)+3, y=-36+3, y=-33
so, when x=-3, y=-33
2
then y=12(-2)+3, y=-24+3, y=-21
so, when
x=-2, y=-21
1
then y=12(-1)+3, y=-12+3, y=-9
so, when
x=-1, y=-9
0
then y=12(0)+3, y=+3, y=3
so, when
x=0, y=3
1
then y=12(1)+3, y=12+3, y=15
so, when
x=1, y=15
the table is
x y
-3 -33
-2 -21
-1 -9
0 3
Step 3
, just sepick two cooridnadinates from the table mak, then mark those pintsoints, and finally, dwr in the planeaaw a line conceeecting he connectingnts
Step 4
as you can see, when we take the points of the table and we unite them, a line appears
so , this is a linear function
Also, the exponent of the variable ( x) is cero, which means it is a linear function.
List 3 points that are on the line 5y= 3x - 7.
List 3 points that are on the line 5y= 3x - 7.
We know that the y-intercept is (0, -7)
We know that slope = 3 and slope = rise / run or 3 y for every 1 x
We can add 1 for the x and 3 for the y: (0, -7) to (1, -4).
We can do that again:add 1 for the x and 3 for the y: (1, -4) to (2, -1).
(0, -7)
(1, -4)
(2, -1)
The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That is, find the probability that the subject lied, given that the test yields a positive result.
_ No_(Did_Not_Lie) Yes_(Lied)
Positive_test_results 10 45
Negative_test_results 34 12
Using it's concept, the probability that the subject lied, given that the test yields a positive result is of 9/11 = 0.8182 = 81.82%.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In this problem, we want to find the probability that the subject lied, given that the test yields a positive result, hence:
The total outcomes are the tests resulting in a positive.The desired outcomes is the number of tests out of those positive in which the subject lied.From the table, we have that:
There were 10 + 45 = 55 positive test results.In 45 of those tests, the subject lied.Hence the probability is given as follows:
p = 45/55 = 9/11 (simplifying by 5)
p = 9/11 = 0.8182 = 81.82%.
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based on the infomation in the table , is the cost of the apples proportional to the weight of apples?
pounds of apples cost of apples
2 3.76
3 5.64
4 7.53
5 9.40
The given table shows that does not show a proportional relationship, as the ratio between the output and the input is not the same for all terms of the table.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as defined below.
y = kx
In this problem, we have that:
The input x is the number of pounds of apples.The output y is the cost of the apples.To verify if it shows a proportional relationship, we have to divide the output by the input in each case, hence:
k = 3.76/2 = 1.88.k = 5.64/3 = 1.88.k = 7.53/4 = 1.8825.k = 9.40/5 = 1.88.Due to the different constant for 4 pounds, the table does not show a proportional relationship,
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m - a + n + p , for a
The expression m = a + n + p can be written as a = m - n - p after making the subject a.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The expression is:
m = a + n + p
To solve for a make the subject as a:
a = m - n - p
Thus, the expression m = a + n + p can be written as a = m - n - p after making the subject a.
The question is incomplete.
The complete question is:
Solve for a, if the expression is m = a + n + p.
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The graph shows the number of states and Washington, DC, within each range of electoral votes for the 2020 presidential election. Which interval contains 11 states? Check all that apply.
0 to 3
3 to 6
6 to 9
9 to 12
12 to 15
15 to 18
18 to 21
Based on the number of states and their electoral votes in the 2020 presidential election, the intervals with 11 states are:
3 to 66 to 9How to find the intervals?The graph on electoral votes by state in 202, gives the number of electoral votes as a range from 0 to 21 but in intervals of 3.
In 0 - 3 electoral votes, the number of states is 16.
In 3 - 6 electoral vote interval, number of states is 11.
In 6 - 9 electoral vote interval, number of states is 11.
In 9 - 12 electoral vote interval, number of states is 3.
In 12 - 15 electoral vote interval, number of states is 3.
In 15 - 18 electoral vote interval, number of states is 3.
In 18 - 21 electoral vote interval, number of states is 4.
The two intervals with 11 states are therefore 3 - 6 and 6 - 9.
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Which ratio is equivalent to 9/78.
A: 1/8
B: 3/26
C: 1/3
D: 3/18
Answer:
3/26
Step-by-step explanation:
you simply divide both numbers by there largest lcm which is 3
9/3=3
78/3=26
Together 3/26
Use synthetic division to find the quotient and remainder when
2x^3-9x² +14x-2 is divided by x-1.
Dividing (2x³ - 9x² + 14x - 2) by (x - 1) with synthetic division method given the remainder 5 and the quotient 2x² - 7x + 7 + (5/x-1).
What is synthetic division?One unique way to divide polynomials is by using the synthetic division method. This approach, where the leading coefficient should be equal to 1, is a special case of multiplying a polynomial expression by a linear factor. In the specific case of dividing by a linear factor, the synthetic division is a shorthand, or shortcut, method of polynomial division. However, the synthetic division is typically used to locate polynomial zeroes (or roots), not to divide out factors.So, 2x³ - 9x² + 14x - 2 ÷ x - 1 by synthetic division as follows:
(Refer to the images attached below for calculations)2x³ - 9x² + 14x - 2 ÷ x - 1:
Remainder: 5Quotient: 2x² - 7x + 7 + (5/x-1)Therefore, dividing (2x³ - 9x² + 14x - 2) by (x - 1) with synthetic division method given the remainder 5 and the quotient 2x² - 7x + 7 + (5/x-1).
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The sum of 5 times the first number and 6 times the second number is 235. The difference between 7 times the first number and 17 is 2 times the second number. Find both the numbers.
a) Using the variable x to represent the first number and y to represent the second number, write the information given in the first sentence, "The sum of 5 times the first number and 6 times the second number is 235."
Correct
b) Using the variable x to represent the first number and y to represent the second number, write the information given in the second sentence, "The difference between 7 times the first number and 17 is 2 times the second number."
Correct
c) Find both the numbers.
The first number is:
Correct
The second number is:
Correct
By using the elimination method, the numbers are 11 and 30
Consider the first number as x and the second number as y
Sum of 5 times the first number and 6 times the second number is 235
The linear equation will be
5x+6y = 235
The difference between 7 times the first number and 17 is 2 times the second number
7x-17 = 2y
Rearrange the terms
7x-2y = 17
The both equations are
5x+6y = 235
7x-2y = 17
Multiply the first equation by 2 and second equation by 6
10x+12y = 470
42x-12y = 102
Here we have to use the elimination method
Add both equation and y term will cancelled
10x+42x = 470+102
52x = 572
x = 11
Substitute the value of x in any equation
5x+6y =235
5(11)+6y = 235
55+6y = 235
6y = 180
y = 30
Hence, by using the elimination method, the numbers are 11 and 30
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Consider the matrices.
What operations are defined for these matrices?
Drag the operation to the boxes to correctly complete the table.
[0]. and Q = []
00
Answer:
Defined: M-N
Not defined: Q+P, M+P, L-N
Step-by-step explanation:
Just took the test