Triangle ABC is shown:What statement must be true?cos(A) = sin(A)cos(A) = sin(B)cos(A) = cos(B)sin(A) = sin(B)
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The statement that must be true is;
[tex]\cos \text{ A = sin B}[/tex]Here, we want to select the correct option
The triangle we can see is a right-angled triangle
That means the two angles are complementary
When two angles are complementary, they add up to be 90
Thus, we have it that;
[tex]A\text{ + B = 90}[/tex]Now, let us consider the options.
a) The sine of an angle is not the same value as its cos, except if the angle is 45 degrees. Since we cannot ascertain that the angles are 45 degrees in value, then the statement must not be true
b) cos A = sin B
This is possible
This is because, the sine of an angle is equal to the cosine of its complement and also; the cosine of an angle is equal to the sine of its complement
We have this as;
[tex]\begin{gathered} A\text{ + B = 90} \\ A\text{ = 90-B} \\ \sin \text{ A = cos (90-A)} \\ 90-A\text{ = B} \\ \sin \text{ A = cos B} \end{gathered}[/tex]The last two cases are only true if A = B which means the angle is 45. Since we cannot confirm this, then we can say that only the second statement is a possibility
Related Questions
The length of a rectangle is five times its width. If the perimeter of the rectangle is 120 ft, find its area.
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Solution
The length of a rectangle is five times its width.
Let the length be represented by L
Let the width be represented by W
The length of the rectangle is five times the width i.e
[tex]L=5W[/tex]To find the perimeter, P, of a rectangle, the formula is
[tex]P=2(L+W)[/tex]Given that the perimeter, P, of the rectangle is 120ft,
Subsitute for length and width into the formula above
[tex]\begin{gathered} P=2(L+W) \\ 120=2(5W+W) \\ 120=2(6W) \\ 120=12W \\ \text{Divide both sides by 12} \\ \frac{12W}{12}=\frac{120}{12} \\ W=10ft \end{gathered}[/tex]Recall that, the length of the rectangle is
[tex]\begin{gathered} L=5W \\ L=5(10) \\ L=50ft \\ W=10ft \end{gathered}[/tex]To find the area, A, of a rectangle, the formula is
[tex]A=LW[/tex]Substitute the values of the length amd width into the formula above
[tex]\begin{gathered} A=(50)(10)=500ft^2 \\ A=500ft^2 \end{gathered}[/tex]Hence, the area of the rectangle is 500ft²
please help me understand how to graph this and what each part changes on the graph. thank you!
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SOLUTION
The plot the graph, we have the interval
[tex]0From the equation given, we have [tex]r=1+2\cos \theta[/tex]We have
[tex]\begin{gathered} 2\cos \theta\text{ changes as the angles changes } \\ \text{while } \\ 1\text{ remains unchange} \end{gathered}[/tex]Hence, the graph becomes
Find the sum of 738 and659
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Given that point D is in the interiro of
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Explanation
Step 1
draw a diagram of the described situation.
Now, we can see that due to point D is in the interior, the line BC divide the angle ABC into 2 angles, angles ABD and DBC
so, we can conclude
angle ABC is the sum of angles ABD and DBC
[tex]\measuredangle ABC=\measuredangle ABD+\measuredangle DBC[/tex]I hope this helps you
Determine of each equation represents a direct variation y equals 4X + 1
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The general form of the equation that represents a direct variation between y and x is as follows:
[tex]y=k\cdot x[/tex]Where k is the proportion constant
We will check the given equation:
a) y = 4x + 1
The equation doesn't have the general form
so, the answer is NO
b) y = 7.5x
It is like the general form and k = 7.5
so, the answer is Yes
c) y = (1/15)x
it is like the general form and k = 1/15
so, the answer is Yes
d) y = 6/x
It is not like the general form
So, the answer is No
Select the correct answer.What is the factored formed of b^3 - 1,000?
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Step 1: Concept/Formula
[tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex]Step 2: Express each term as a cube of a number.
[tex]\begin{gathered} b^3\text{ - 1000} \\ =b^3-10^3 \\ \end{gathered}[/tex]Step 3: Factor in the result.
[tex]\begin{gathered} b^3-10^3=(b-10)(b^{2\text{ }}+10b+10^2) \\ =(b-10)(b^2\text{ + 10b + 100)} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} (b-10)(b^2\text{ + 10b + 100)} \\ \text{Option B is the correct answer} \end{gathered}[/tex]8 Find the value of x in this equation. 3/4(6x + 1) - 3x = 1/4(2x-1)Fractions btw
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Find the value of x;
[tex]\begin{gathered} \frac{3}{4}(6x+1)-3x=\frac{1}{4}(2x-1) \\ \text{Expand the parenthesis and you now have;} \\ \frac{3(6x+1)}{4}-3x=\frac{(2x-1)}{4} \\ \frac{3(6x+1)}{4}-\frac{(2x-1)}{4}=3x \\ \frac{18x+3}{4}-\frac{2x-1}{4}=3x \\ \frac{18x-2x+3-1}{4}=3x \\ \frac{16x+2}{4}=3x \\ \text{Cross multiply and you have;} \\ 16x+2=3x\times4 \\ 16x+2=12x \\ \text{Collect like terms} \\ 16x-12x=-2 \\ 4x=-2 \\ \text{Divide both sides by 4} \\ x=\frac{-2}{4} \\ x=-\frac{1}{2} \end{gathered}[/tex]*Image of Graph and everything for this question in Jpeg image The tennis club is selling water bottles and hats to raise money for a tennis tournament. A water bottle costs $4 and a hat costs $6. The club wants to raise $1,200. 1. Write a linear equation that describes the problem.2. Graph the linear equation. Make sure to label both axes with appropriate titles. 3. Use the graph to approximate how many hats the tennis club must sell if it sells 150 water bottles are sold.
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15.
Given:
The cost of a water bottle = $4.
The cost of a hat = $ 6.
The total amount = $ 1,200.
Aim :
We need to find the linear equation for the given model.
Explanation:
Let x be the number of water bottles.
Let y be the number of hats.
The cost of the x number of water bottles = x time 4.
The cost of the x number of water bottles = 4x.
The cost of the y number of hats = y times 6.
The cost of the y number of hats = 6y.
Addition of 4x and 6y = the total amount
[tex]4x+6y\text{ =1200}[/tex]Answer:
The linear equation is
[tex]4x+6y\text{ =1200}[/tex]16.
Aim:
We need to graph the line equation.
Set x =0 and substitute in the eqaution to find the value of y at x =0.
[tex]4(0)+6y\text{ =1200}[/tex][tex]6y\text{ =1200}[/tex]Divide both sides of the equation by 6.
[tex]\frac{6y}{6}=\frac{1200}{6}[/tex][tex]y=200[/tex]We get the point (0,200).
Set x =150 and substitute in the eqaution to find the value of y at x =150.
[tex]4\times150+6y\text{ =1200}[/tex][tex]600+6y\text{ =1200}[/tex]Subtract 600 from both sides of the equation.
[tex]600+6y-600=1200-600[/tex][tex]6y=600[/tex]Dividing both sides of the equation by 6.
[tex]\frac{6y}{6}=\frac{600}{6}[/tex][tex]y=100[/tex]We get the point (150,100).
Mark the points (0,200) and (150,100) on the graph and join them by ray.
The graph of the line equation is
17.
The number of water bottles that sold = 150.
From the graph, we get the point (150,100).
The number of hats =100.
find the area of a triangle if the base is 6 units and the height is 9 units.
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A city council consists of 10 members. Four are Republicans, three are Democrats, and three are Independents. If a committee of three is to be selected, find the probability of selectinga. All Republicansb. All Democrats
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We have a total of 10 members to choose from, this means that we have a total of 10 possibilities.
a.
We have four republicans and we need to choose three of them, the number of ways to do this is:
[tex]_4C_3=\frac{4!}{3!(4-3)!}=4[/tex]Since we are going to choose 3 people of the total of 10 members the number of ways to do this is:
[tex]_{10}C_3=\frac{10!}{3!(10-3)!}=120[/tex]The probability of choosing all republicans is:
[tex]P=\frac{4}{120}=\frac{1}{30}[/tex]Therefore the probability is 1/30
b.
In this case we need to choose 3 people out of 3 people (since we only have 3 democrats) there's only one way to do this.
Then in this case the probability is:
[tex]P=\frac{1}{120}[/tex]Therefore the probability of choosing all democrats is 1/120
solve the right triangle. Round decimal answers to the nearest tenth.In ABC, b = .... , m
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Using Pythagorean Theorem, we can write:
[tex]\begin{gathered} \text{Leg}^2+\text{AnotherLeg}^2=\text{Hypotenuse}^2 \\ b^2+6^2=14^2 \\ b^2+36=196 \\ b^2=196-36 \\ b^2=160 \\ b=\sqrt[]{160} \\ b\approx12.6 \end{gathered}[/tex]Now, let's find the angles.
Sin is the ratio of opposite to hypotenuse
Cos is the ratio of adjacent to hypotenuse
Tan is the ratio of opposite to adjacent
Let's find angle B:
[tex]\begin{gathered} \cos B=\frac{BC}{AB} \\ \cos B=\frac{6}{14} \\ \cos B=0.42857 \\ B=\cos ^{-1}(0.42857) \\ B=64.6\degree \end{gathered}[/tex]Now, we know three angles in a triangle add to 180 degrees, thus we can say:
[tex]\begin{gathered} A+B+90=180 \\ A+B=180-90 \\ A+B=90 \\ A+64.6=90 \\ A=90-64.6 \\ A=25.4\degree \end{gathered}[/tex]The answers are:
b = 12.6A = 25.4°B = 64.6°What is the solution set for: 10x < 30 *OX > 10x < 30O x<3OX=3
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10x < 30°
Solve for x
x < 30/10
x < 3 This is the answer, I think is the third choice
Suppose the graph of a parent function f(x) is shifted to the left 1 unit, reflected vertically over the x-axis, and then shifted up three units. What equation models the transformed graph?o y = f (x - 1) + 3o y = -f (x- 1) + 3o y = f (x + 1) + 3o y = -f (x + 1) + 3
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If it is shifted to the left by 1 unit, the function becomes:
[tex]y=f(x+1)[/tex]It is reflected vertically over the x-axis; the function becomes:
[tex]y=-f(x+1)[/tex]It is, then, shifted up 3units, thus we have:
[tex]y=-f(x+1)+3[/tex]Hence, the correct option is option D
A set of equations is given below:Equation M: y = 3x + 4 Equation P: y = 3x + 7Which of the following options is true about the solution to the given set of equations? (4 points)No solutionOne solutionTwo solutionsInfinite solutions
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A line equation can be written in slope-intercept form, which is:
[tex]y=mx+b[/tex]where m represents the slope and b the y-intercept.
The solution of a linear system is given by the intercept between the line equations. A linear system can have one solution, when the lines cross each other, infinite solutions when they are the same, or none if they are parallel.
To determinate this, we can use the slope and y-intercept. Given two line equations, if their slopes are different the system has one solution, if the slopes are the same and the y-intercepts are the same the system has infinite solutions, and if the slopes are the same and the y-intercept are different the system has no solutions.
In our system, we have:
[tex]\begin{cases}y={3x+4} \\ y={3x+7}\end{cases}\implies\begin{cases}m_1={m_2}=3 \\ b_1={4\ne b_2=7}\end{cases}[/tex]We have the same slope and distinct y-intercepts, therefore, this system has no solution.
solve c=1/2 ab² for b
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First we have to divide both sides of the equation by 1/2a:
[tex]\frac{c}{\frac{1}{2}a}=\frac{\frac{1}{2}a}{\frac{1}{2}a}b^{2}[/tex]And we get
[tex]\frac{2c}{a}=b^{2}[/tex]finally we have to take square root on both sides:
[tex]\sqrt[]{\frac{2c}{a}}=\sqrt[]{b^2}[/tex]And we get that b is:
[tex]b=\sqrt[]{\frac{2c}{a}}[/tex]What transformation of the parent function f(x) is made to get f(-x) + 1?A. a reflection in the y-axis and 1 unit in the y-directionB. a reflection in the x-axis and 1 unit in the y-directionC. a reflection in the x-axis and -1 unit in the y-directionD. a reflection in the y-axis and -1 unit in the y-directionOsetion
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we have the parent function f(x)
so
First transformation
f(x) ---------> f(-x)
Reflection over the y-axis
Second transformation
f(-x) --------> f(-x)+1
Translation 1 unit up
therefore
The answer is option Acan someone help me graph this equation and solve it?
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3x + 8 <= 11 or 3x + 8 > 20
3x <= 3 or 3x > 12
x <= 1 or x > 4
The graph is a semi-line from negative infinity until 1 and another from 4 until positive infinity
The price of 9-volt batteries is increasing according to the function below,where is years after January 1, 1980. During what year will the prIce reach$5?
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Explanation
The price model is given by the exponential equation below.
[tex]P(t)=1.1e^^{0.047t}[/tex]When the price becomes $, we will have;
[tex]\begin{gathered} 5=1.1e^{0.047t} \\ Divide\text{ both sides by 1.1} \\ \frac{5}{1.1}=e^{0.047t} \\ take\text{ the natuaral logarithm of both sides} \\ ln(\frac{5}{1.1})=ln(e^{0.047t}) \\ ln(\frac{5}{1.1})=0.047t \\ t=ln(\frac{5}{1.1})\div0.047 \\ t=32.22\text{ years} \end{gathered}[/tex]Therefore, by adding 32 to the years 1980. The batteries will cost 5$ in the year
Answer: 2012.
which of the following is affected by extreme value.
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Mean
the mean of a given set of data can be affected by extreme values because it comprises of every single data in the given data set
8. The temperature at 4pm was -8 degrees F. The temperature fell 5 degrees by 7pm. What was the temperature at 7pm? *
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7 pm8. The temperature at 4 pm was -8 degrees F. The temperature fell 5 degrees by 7 pm. What was the temperature at 7 pm? *
___________________________
-8 º F - 5 = -13
_______________________________________
Answer
The temperature at 7pm is -13
___________
Unfortunately, I can help you with a question per session
What is the approximate value of tangent of the quantity 4 times pi over 5 end quantity question mark
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Given,
[tex]\tan (\frac{4\pi}{5})[/tex]It can be written as:
[tex]\tan (\pi-\frac{\pi}{5})=-\tan (\frac{\pi}{5})=-0.72[/tex]The answer is -0.727.
find the measure of PR given rectangle pqrs round answer to the nearest whole number
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We can draw the following picture:
where we can see that triangle PSR is a right one. Then, we can apply Pytagorean theorem to find PR:
[tex](2.6)^2+4^2=PR^2[/tex]then, PR is given by
[tex]PR=\sqrt[]{(2.6)^2+4^2}[/tex]which gives
[tex]\begin{gathered} PR=\sqrt[]{6.76+16} \\ PR=\sqrt[]{22.76} \end{gathered}[/tex]therefore, PR is equal to 4.77 m. By rounding up to the nearest whole number, the answer is PR= 5 m.
A camera is originally $150 The store gives a discount and the camera is now priced at $112.50 Write the percentage discount for the camera
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We are asked to determine the percentage of discount if the price for an item goes from $150 to $112.50. To do that we will use the following relationship:
[tex]150-\frac{150x}{100}=112.5[/tex]Where "x" is the percentage of the discount.
Now we solve for "x" first by subtracting 150 from both sides:
[tex]-\frac{150x}{100}=112.5-150[/tex]Solving the operations:
[tex]-\frac{150x}{100}=-37.5[/tex]Now we multiply both sides by 100:
[tex]\begin{gathered} -150x=-37.5\times100 \\ -150x=-3750 \end{gathered}[/tex]Now we divide both sides by -150:
[tex]x=-\frac{3750}{-150}[/tex]Solving the operations:
[tex]x=25[/tex]Therefore, the percentage of the discount is 25%.
What is the angle measure of the angle shown? Explainhow you know.
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110º, because the arrow on the left is pointing to 110º. You have to see the angle that is shown the closest to the arrow, because the angle started on the right, on the 0º, so we use the first line.
If the arrow were to stat on the left, then we have to use the outermost value
select two fractions that are equivalent to 3/4
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Let us simplify each answer to find the equivalent to 3/4
[tex]\frac{6}{12}=\frac{\frac{6}{6}}{\frac{12}{6}}=\frac{1}{2}[/tex][tex]\frac{9}{12}=\frac{\frac{9}{3}}{\frac{12}{3}}=\frac{3}{4}[/tex][tex]\frac{6}{16}=\frac{\frac{6}{2}}{\frac{16}{2}}=\frac{3}{8}[/tex][tex]\frac{6}{8}=\frac{\frac{6}{2}}{\frac{8}{2}}=\frac{3}{4}[/tex]The equivalents are B and D
Fresh Side Grocery sells 7 bagels for $4.41. Value Mart sells 5 bagels for $3.60. How does the unit rate compare?Option #1: The bagels at French Side Grocery are $0.09 less expensive than the bagels at Value Mart.Option #2: The bagels at French Side Grocery are $0.09 more expensive than the bagels at Value Mart.Option #3: The bagels at French Side Grocery are $0.07 less expensive than the bagels at Value Mart.Option #4: The bagels at French Side Grocery are $0.07 more expensive than the bagels at Value Mart.
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Answer:
The bagels at French Side Grocery are $0.09 less expensive than the bagels at Value Mart.
Explanation:
From the question, we're told that Fresh Side Grocery sells 7 bagels for $4.41. Therefore, the unit rate here is;
[tex]Unit\text{ rate}=\frac{4.41}{7}=0.63\text{ per bagel}[/tex]So each bagel at Fresh Side Grocery costs $0.63.
Value Mart sells 5 bagels for $3.60, so the unit rate;
[tex]\frac{3.60}{5}=0.72\text{ per bagel}[/tex]So each bagel at Value Mart costs $0.72.
So if we subtract the cost of a bagel at French Side from that of Value Mart, we'll have ($0.72 - $0.63 = $0.09). It means that the bagels at French Side Grocery are $0.09 less expensive than the bagels at Value Mart.
4. Solve each equation for x. (8 points: 2 points each)a.) 3x-12y=27b.) 6x-7y=-2c.) 4x-k=17d.) kx+c=9
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A) The initial equation is:
[tex]3x-12y=27[/tex]now to solve for x, we have to add 12y in bout sides and divide by 3 so:
[tex]\begin{gathered} 3x=27+12y \\ x=\frac{27+12y}{3} \\ x=9+4y \end{gathered}[/tex]B) the inital equation is:
[tex]6x-7y=-2[/tex]To solve it we have to add 7y and divide by 6 so:
[tex]\begin{gathered} 6x=-2+7y \\ x=\frac{-2+7y}{6} \end{gathered}[/tex]C) the initial equation is:
[tex]4x-k=17[/tex]To solve it we have to add k and divide by 4 so:
[tex]\begin{gathered} 4x=17+k \\ x=\frac{17+k}{4} \end{gathered}[/tex]D) the initial equation is:
[tex]kx+c=9[/tex]To solve it we have to rest c and divide by k so:
[tex]\begin{gathered} kx=9-c \\ x=\frac{9-c}{k} \end{gathered}[/tex]Solve the inequality and graph the solution.–5(z–3)≥5
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5 (z–3) ≥5
Apply distributive property:
5(z)+5(-3) ≥ 5
5z-15 ≥ 5
Add 15 to both sides of the inequality:
5z-15+15≥ 5+15
5z ≥ 20
Divide both sides by 5
5z/5 ≥ 20/5
z≥ 4
graph:
Which conic section does the equation below describe? (x - 9) + (+2) . v = 1 4 25 O A. Parabola O B. Circle O c. Ellipse O D. Hyperbola
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Answer
The vertices of the ellipse are:
[tex](2,-8),(2,-2)[/tex]SOLUTION
Problem Statement
The question gives us the equation of an ellipse. We are asked to find the coordinate of the vertices of the major axis.
Method
The equation of the ellipse given is:
[tex]\frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1[/tex]The major axis of the ellipse is the term with the larger denominator. The larger denominator is 9, thus the y-axis is the major axis.
This thus implies that the coordinates we are most interested in are the topmost and bottom vertices of the ellipse.
To find the coordinates of this axis, we just need to know the formula stated below:
[tex]\begin{gathered} \text{Given the equation of an ellipse:} \\ \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \\ where, \\ (h,k)\text{ is the center of the ellipse} \\ a,b\text{ represent the minor and major axes.} \\ \\ \text{Topmost point = }(h,k+b) \\ \text{Bottom most point }=(h,k-b) \end{gathered}[/tex]Using the formula for the Topmost point and the Bottom most point, above, we would find the coordinate of the vertices of the ellipse
Implementation
[tex]\begin{gathered} \text{Comparing the equation of the ellipse given to the general formula in the Method section:} \\ h=2,k=-5 \\ a^2=4,a=\pm2 \\ b^2=9,b=\pm3 \\ \\ \text{Topmost point }=(h=2,k+b=-5+-3)=(2,-8) \\ \text{Bottom most point}=(h=2,k-b=-5-(-3))=(2,-2) \end{gathered}[/tex]
Final Answer
Therefore, the vertices of the ellipse are:
[tex](2,-8),(2,-2)[/tex]Hello! May I please have some guidance. I think I have it right but I'm not sure
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STEP - BY - STEP EXPLANATION
What to find?
The number of faces a polyhedron with 5 vertices and 8 edges have.
Given:
[tex]V-E+F=2[/tex]Vertices (V) = 5
Edges (E)=8
Step 1
Substitute the values into the formula above.
[tex]\begin{gathered} 5-8+F=2 \\ \\ -3+F=2 \end{gathered}[/tex]Step 2
Add 3 to both-side of the equation.
[tex]\begin{gathered} F=2+3 \\ \\ =5 \end{gathered}[/tex]ANSWER
5