Answer:
Step-by-step explanation:
[tex]1+tan^2\theta=sec^2\theta\\tan^2\theta=sec^2\theta -1 \\tan^2\theta=(sec\theta-1)(sec\theta+1)\\\implies \frac{1}{sec\theta-1} =\frac{sec\theta+1}{tan^2\theta} \\\\and \quad \frac{1}{sec\theta+1} =\frac{sec\theta-1}{tan^2\theta} \\\\ \frac{1}{sec\theta-1} + \frac{1}{sec\theta+1} = \frac{sec\theta+1}{tan^2\theta} + \frac{sec\theta-1}{tan^2\theta}\\\\=\dfrac{2sec\theta}{tan^2\theta}\\\\=\dfrac{2cos^2\theta}{cos\theta.sin^2\theta}\\\\\\=2cos\theta.cosec^2\theta[/tex]
Vertical lines have an undefined slope.
True or False
Answer:
True
Step-by-step explanation:
The 'base' of the line has length zero.
Answer:
True.
Step-by-step explanation:
You take 2 points and find gradient of a line and if you get a constant. For example, m=5. Then 5 over 0 (the denominator is what matters, it must be 0) and that's how you know it's a vertical line and has undefined slope.
Circle Q is centered at the origin. Is point (-5, 0) on the circle? Justify your answer
Answer: D
Step-by-step explanation: I just took the quiz
30 points and mark brainlest
A rectangular picture has dimensions 3 inches by 2 inches. Find the dimensions of the pictures if it has to be enlarged with a scale factor of 5. Question 18 options: 15 inches × 10 inches 3 5 inches × 2 5 inches 8 inches × 7 inches 12 inches × 8 inches
The dimensions of the enlarged rectangular picture is 15 x 10 inches.
What are the dimensions of the enlarged rectangular picture ?When the dimensions of the enlarged rectangular picture is enlarged by a scale factor of 5, it means that the dimensions would be five times larger what they were initially.
New dimensions : (3 x 5) x (2 x 5)
15 x 10 inches
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Answer:
I’m just adding so you can mark brainliest
Step-by-step explanation:
A car travels 24 km between 9:30 am and 10:15 am. What is its average speed in km/h?
Answer:
32 km / hr
Step-by-step explanation:
930 to 1015 is 45 min = .75 hr
24 km / .75 hr = 32 km /hr
(x-2)(x+2)(x²+4)-(x²+3)(x²-3)+2022
The simplified form of the given expression is 2015
Simplifying expressionsThe given expression is (x-2)(x+2)(x²+4)-(x²+3)(x²-3)+2022
The expression can be simplified as shown below
(x-2)(x+2)(x²+4) - (x²+3)(x²-3) + 2022
x(x+2)-2(x+2)(x²+4) - x²(x²-3) +3(x²-3) + 2022
(x²+2x-2x-4)(x²+4) - (x⁴-3x²+3x²-9) + 2022
(x²-4)(x²+4) - (x⁴-9) + 2022
x²(x²+4) -4(x²+4) - (x⁴-9) + 2022
(x⁴+4x²-4x²-16) - (x⁴-9) + 2022
(x⁴-16) - (x⁴-9) + 2022
x⁴ -16 -x⁴ +9 + 2022
x⁴ -x⁴ -16 +9 +2022
= 2015
Hence, the simplified expression is 2015
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Suppose that x and y vary inversely, and x = 12 when y = 8 . Write the function that models the inverse variation.
Answer:
[tex]y=\frac{96}{x}[/tex]
Step-by-step explanation:
So when x and y, vary inversely, it means that the product of x and y will remain constant such that: [tex]xy=c[/tex]. This means that the function can be defined as [tex]y=\frac{c}{x}[/tex] by dividing both sides by x. In this case x=12, and y=8, this means the constant is equal to 12 * 8 which is 96. So we have the equation: [tex]xy = 96[/tex], which can be defined as [tex]y=\frac{96}{x}[/tex]
Simplify the ratio. 2 1/2: 3 1/3
Answer:
two and a half to three and one third
Step-by-step explanation:
A
Ф
Ф
center of triangle ABC.
30° R
15
в
What is m/QOB?
0000
30°
60°
75°
90°
Answer:
75757575757575757575757575757575757575757575A certain big company classifies its employees according to gender, age-group (6 categories) and employment type (10 categories). How many classifications are there
We don’t know the number of employees remaining at the company.
We don’t know the total number of employees remaining at the company.
The classification consists of gender, division, and employment type.
It doesn’t matter what order those attributes come in. A person who is male, age group 6, and employment type 10 has the same classification as someone who is of employment type 6, male, and age group10.
Therefore since order does not matter it is a combination question.
Assuming only two genders are allowed (you didn’t say and some people think there are about 10 of them)
It is either 120 (2 times 6 times 10) or "None of the above" if you believe there are more than 2 genders.
2×6×10=120
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In circle O, R_T and S_U are diameters
Applying the vertical angles theorem, the measure of VU is determined as: 64°.
What is the Vertical Angles Theorem?If two angles lie directly opposite each other, they are vertical nagles and are therefore equal.
13x = 15x - 8 [vertical angles theorem]
13x - 15x = - 8
-2x = -8
x = 4
Let y represent m(VU). Since m(RV) = m(VU), therefore:
13x + 2y = 180 [angles on a straight line]
Plug in the value of x
13(4) + 2y = 180
52 + 2y = 180
2y = 180 - 52
2y = 128
y = 64°
m(VU) = 64°.
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Using the markings in the following image, answer the questions below:
a. Determine whether group A or group B (or both) show a pair of similar triangles or not. Tell how you know this.
b. For the group(s) with similar triangles, calculate all unknown side lengths. If possible, calculate the unknown angles. Explain your answers.
c. For the group(s) with similar triangles, calculate the scale factor. What is the relationship of the area of the original figure to the area of the translated figure? Explain.
d. For the group(s) with similar triangles, tell (roughly) what transformations would be needed to make one of the triangles carry onto the other triangle in its group.
The two triangles in group A are similar because two angles of one are congruent to two angles of the other.
How to explain the triangle?The two triangles in group A are similar because two angles of one are congruent to two angles of the other.
The two triangles in group B are not similar. The ratio of the short sides of the two triangles is 10:4 or 2.5:1, and that is the same ratio as the two sides 24 and 9.6.
However, using the fact that an angle bisector in a triangle divides the opposite side into two segments in the same ratio as the lengths of the two sides that include the angle, the length of the third side of the left triangle can be found to be about 25.12; and 9.25 times 2.5 is not close to 25.12.
b. In group A, the third side of the first triangle, by the Pythagorean Theorem, is sqrt(306).
The scale factor between the two triangles is 3:5, so the length of the third side of the second triangle is 15*(5/3) = 25.
In both triangles, the third angle measure is 31 degrees, since the sum of the three angles is 180.
c. The scale factor, again, is 3:5 which means the ratio of the areas of the two triangles is 3²:5² or 9:25.
d. The first triangle can be carried onto the second with the following transformations:
(1) dilate by a factor of 5/3 to make it the same size;
(2) rotate 90 degrees counterclockwise;
(3) translate so the hypotenuses of the two triangles are the same line segment; and
(4) reflect on the hypotenuse.
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Michael is renting a bicycle for $12 per hour.
Which of the following is equivalent to this rate?
a.)
20 cents per minute
b.)
14 cents per minute
c.)
5 cents per minute
d.)
7 cents per minute
Answer:
20 cents/minute
Step-by-step explanation:
We need to convert both units
1 dollar is 100 cents
12 dollars * 100 cents/1 dollar = 1200 cents
1 hour = 60 minutes
1 hours * 60 minutes / 1 hour = 60 minutes
12 dollars/ hour = 1200 cents / 60 minutes
Simplify
20 cents/minute
Answer: A. 20 cents per minute
Unit rate given: $12 per hour
Conversion:
$1 = 100 cents
$12 = 1200 cents
1 hour = 60 minutes
Solving steps:
amount in cents/time in minutes = 1200/60 = 20 cents per minute
Select the correct answer. This table represents a quadratic function. x y 1 3 3 -3 5 -5 7 -3 9 3 Which statement about this function is true? A. The value of a is negative, so the vertex is a maximum. B. The value of a is positive, so the vertex is a maximum. C. The value of a is positive, so the vertex is a minimum. D. The value of a is negative, so the vertex is a minimum. Reset Next
The statement "The value of a is positive, so the vertex is a minimum" is correct.
What is a quadratic function?
Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
From the table we can find the quadratic function:
f(x) = ax² + bx + c
Plug (x, y) on the above function.
a + b + c = 3 ...(1)
9a + 3b + c = -3 ...(2)
25a + 5b + c = -5 ...(3)
After solving the above equations:
a = 0.5
b = -5
c = 7.5
The value of a is positive.
Thus, the statement "The value of a is positive, so the vertex is a minimum" is correct.
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The purpose of statistical inference is to make estimates or draw conclusions about a _____. a. population based upon information obtained from the sample b. mean of the sample based upon the mean of the population c. sample based upon information obtained from the population d. statistic based upon information obtained from the population
a)The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.
Statistical inference is the process of drawing conclusions about populations or scientific truths from data. There are many ways to make inferences, including statistical modeling, data-driven strategies, and the explicit use of designs and randomization in analyses.
Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or population probability distribution.
First, a preliminary assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted H0.
An alternative hypothesis (denoted Ha) is then defined, which is the opposite of what is stated in the null hypothesis. The hypothesis testing procedure involves using sample data to determine whether or not H0 can be rejected. If H0 is rejected, the statistical conclusion is that the alternative hypothesis Ha is true.
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What number is it that, when multiplied by 18,27,36,45,54,63,72,81, or 99, gives a product in which the first and last figures are the same as those in the multiplier, but which when multiplied by 90 gives a product in which the last two figures are the same as those in the multiplier?
The given multipliers are factors of 9, the possible number will have 1 as first and last digit which gives the number as 101
How can the correct number be found?The given numbers are;
18, 27, 36, 45, 54, 63, 72, 81, 99
Given that the first and the last figures are those of the multipliers, we have;
The first and last and last digit of the number can be 1, which gives;
Possible numbers includes; 11 and 101
By trying the possible numbers, the difference found is presented as follows;
99 × 11 = 1089 (The first and the last digit are not the same as the multiplier)
99 × 101 = 9999 (First and last digit are not the same as the multiplier)90 × 11 = 990
90 × 101 = 9090
The correct option is therefore 101
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If I have 8$and I buy something 3$ how many change wil I get?
Answer:
5$
Step-by-step explanation:
it is 5 because the difference of 8 and 3 is 5
1) The dimensions of an irregular solid are as shown in the figure below.
a) Write a polynomial function, in standard form, to model the volume of this solid.
b) If the volume of the solid is 208 cubic inches, what is the value of x?
Hello,
a) Volume of the figure = Volume of light blue rectangular parallelepiped - volume of dark blue rectangular parallelepiped
Volume of rectangular parallelepiped = lengh × high × height
Volume of light blue rectangular parallelepiped :
V = (x + 2) × (x + 5) × (2x + 1)
V = (x² + 5x + 2x + 10) × (2x + 1)
V = (x² + 7x + 10) × (2x + 1)
V = 2x³ + 15x² + 27x + 10
Volume of dark blue rectangular parallelepiped :
V = x × 3 × (x + 5)
V = 3x(x + 5)
V = 3x² + 15x
Polynomial function, in standard form, to model the volume of this solid :
V = 2x³ + 15x² + 27x + 10 - (3x² + 15x)
V = 2x³ + 15x² - 3x² + 27x - 15x + 10
V = 2x³ + 12x² + 12x + 10
b) We have to solve 2x³ + 12x² + 12x + 10 = 208
⇔ 2x³ + 12x² + 12x - 198 = 0
⇔ 2(x - 3)(x² + 9x + 33) = 0
⇔ x = 3 or x² + 9x + 33 = 0
a = 1 ; b = 9 ; c = 33
Δ = b² - 4ac = 9² - 4 × 1 × 33 = -51 < 0 ⇔ Δ < 0 ⇒ no solution
So if the volume of the solid is 208 cubic inches, the value of x is 3
Adriana and Sophie have summer jobs selling newspaper subscriptions door-to-door, but their
compensation plans are different. Adriana earns a base wage of $6 per hour, as well as $2 for
every subscription that she sells. Sophie gets $3 per subscription sold, in addition to a base
wage of $4 per hour. If they each sell a certain number of subscriptions in an hour, they will
end up earning the same amount. How much would each one earn?
Write a system of equations, graph them, and type the solution.
Answer:
The each have to place 2 subscriptions
Step-by-step explanation:
Adriana
E (earnings) = 6 + 2*x where x is the number of subscriptions
Sophie
E (earnings) = 4 + 3x
For them to earn the same amount, their right sides must be equated.
4 + 3x = 6 + 2x Subtract 2x from both sides
4 + 3x - 2x = 6+ 2x - 2x Combine
4 + x = 6 Subtract 4 from both sides
4 - 4 + x = 6 - 4
x = 2
Question 3 (Essay Worth 10 points)
(05.07 MC)
The scatter plot shows the number of strawberries that have been picked on the farm during the month of February:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Strawberries and the x axis is labeled Days in February
Part A: Using computer software, a correlation coefficient of r = 0.01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm. (5
It's not an accurate value for the data based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means practically no correlation, while the points on the graph are moderately correlated
How to illustrate the information?1. Part A:
Since the points in the scatter plot shows a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.
The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to 1.
Here, r = - 1 is a perfect negative correlation as the points will adjust perfectly to a line with a negative slope.
r = + 1 is a perfect positive correlation: the points will adjust perfectly to a line with a positive slope.
r = 0 means that the variables are not correlated at all.
Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows another thing.
Therefore, the calculated value of r = 0.01 is not accurate for this scatter plot.
2. Part B.
A causal relationship means that the explanatory variable (the independent variable) is the cause of the dependent variable.
Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.
Thus, the scenario could be:
Amount of rainfall in mm (x) Number of strawberries picked (y)
100 20
50 40
25 80
12.5 160
6.25 320
The amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.
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Flying against the wind, an airplane travels 6230 kilometers in 7 hours. flying with the wind, the same plane travels 10,480 kilometers in 8 hours. what is the rate of the plane in still air and what is the rate of the wind?
The speed (rate) of the plane in still air is 1100 kilometers per hour and the speed (rate) of the wind is 210 kilometers per hour.
We assume the speed (rate) of the plane in still air to be x kilometers per hour, and the speed (rate) of the wind to be y kilometers per hour.
Thus, flying against the wind, the acting speed (rate) for the plane will be x - y kilometers per hour.
Flying with the wind, the acting speed (rate) for the plane will be x + y kilometers per hour.
We are given that flying against the wind, the airplane travels 6230 kilometers in 7 hours.
Thus, speed (rate) = 6230/7 kilometers per hour = 890 kilometers per hour.
Equating this to the derived speed of the airplane flying against the wind, we get x - y = 890 ... (i).
We are given that flying with the wind, the airplane travels 10480 kilometers in 8 hours.
Thus, speed (rate) = 10480/8 kilometers per hour = 1310 kilometers per hour.
Equating this to the derived speed of the airplane flying with the wind, we get x + y = 1310 ... (i).
Now, on adding equations (i) and (ii), we get:
2x = 2200,
or, x = 1100.
Substituting x = 1100 in (ii), we get:
x + y = 1310,
or, 1100 + y = 1310,
or, y = 1310 - 1100 = 210.
Thus, the speed (rate) of the plane in still air is 1100 kilometers per hour and the speed (rate) of the wind is 210 kilometers per hour.
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PLEASE HELP
Select the correct answer.
Which statement is true about this function for all values of x<4
A) The function is negative
B) The function is decreasing
C) The function is positive
D) the function is increasing
Answer: B) The function is decreasing
Step-by-step explanation:
As x increases, y decreases.
Write an equation for the nth term of the given arithmetic sequence. 7, 13, 19, 25
Hello,
U (n +1) = Un + 6
Un = Uo + nr
U9 = 7 + 9 × 6 = 7 + 54 = 61
Answer:
nth term = 6n + 1.
Step-by-step explanation:
The first term a1 = 7 and the common difference d = 6.
nth term = a + d(n - 1)
= 7 + 6(n - 1)
= 6n + 1.
When two musical notes are a "fifth" apart, the frequency of the lower note is 2/3 the frequency of the higher note. Using f as the frequency of the higher note, write an expression for the frequency
of the lower notes
Frequency is a physical quantity that relates to the number of cycles made by a wave per second. Therefore the required expression for the frequency of the lower note is: [tex]\frac{2}{3}[/tex] f
A wave is a phenomenon that propagates through a material medium without any permanent effect on the molecules of the medium. It transmits energy from one end of the medium to another. Examples are sound waves, light waves, electromagnetic waves, etc.
The propagation of a wave gives rise to frequency. Which can be defined as the number of cycles made by a wave per second. And it is measured in Hertz.
Let the frequency of the higher note be represented by f, and that of the lower note by [tex]f_{l}[/tex]. Thus, we have;
[tex]f_{l}[/tex] = [tex]\frac{2}{3}[/tex] f
Therefore, the expression for the frequency of the lower notes is [tex]\frac{2}{3}[/tex] f.
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If a ⊥ y and x ∥ y, then _____
Answer:
x⊥a
Step-by-step explanation:
If we draw this out, we see that x is perpendicular to a as well.
Triangles J K L and M N R are shown.
In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?
∠J ≅ ∠M
∠L ≅ ∠R
∠K ≅ ∠N
∠R ≅ ∠K
The correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.
Here we are given that
KL = NR
JL = MR
Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.
So for the triangles to be congruent by SAS, angle L must be congruent to angle R.
∠L=∠R
Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
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Answer:
B
Step-by-step explanation:
L=R
How many sides would there be in a convex polygon if the sum of all but one of its interior angles is $1070^{\circ}$
As Convex polygon:
A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The
Convex Polygon:
A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°.
Lets simplify the given problem,
If we try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:
1070 =[n - 2] x 180, where n = number of sides
[tex]1070 =180n - 360180n =1070+360180n =1430n = 1430 / 180[/tex]
n = 7.94 number of sides. Since this is not a whole number, will simply round it up to 8.
Hence the number of sides is 8
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The triathletes were offered water as they rode by the volunteer station. The volunteers handed them cones with the dimensions shown. If each triathlete sloshed 1/3 of the water out before they drank it, how many cubic cm of water did they slosh out? Round to the nearest tenth.
Height 7cm
radius 3.5cm
The slosh-out water is 29.9 cubic cm.
What is volume?Volume is defined as the space covered by any solid body in the three-dimensional plane. For the cylinder, the parameters are height and radius.
The volume of the cone is calculated as:-
V = ⅓r^2h
V = ⅓r^2h
V = ⅓(3.5)^2(7)
V = ⅓(12.25)(7)
V = 1/3(85.75)
V = 85.75/3
1/3 cup of water is sloshed out:
Sloshed water = (85.75/3 )/3
Sloshed water = 29.9 cubic cm
Therefore, the sloshed-out water is 29.9 cubic cm.
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I need a helping hand!
Answer:
x = 145°
Step-by-step explanation:
x and 35° are a linear pair and sum to 180° , that is
x + 35° = 180° (subtract 35° from both sides )
x = 145°
GEOMETRY - FIND X ON THIS TRIANGLE
Answer: [tex]\frac{7\sqrt{3}}{2}[/tex]
Step-by-step explanation:
[tex]\sin 60^{\circ}=\frac{x}{7}\\\\\frac{\sqrt{3}}{2}=\frac{x}{7}\\\\x=\frac{7\sqrt{3}}{2}[/tex]
Complete the input-output table for linear function y=3x
The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the linear function y = 3x:
When x = -2; y = 3(-2) = -6
When x = -1; y = 3(-1) = -3
When x = 0; y = 3(0) = 0
When x = 1; y = 3(1) = 3
When x = 2; y = 3(2) = 6
The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).
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Answer: ( -6/ 6/ 9
Step-by-step explanation: