Given:
[tex]\tan \theta<0\text{ and }\sin \theta>0[/tex][tex]\text{ we know that }\tan \theta=\frac{\sin \theta}{\cos \theta}\text{.}[/tex][tex]\text{ Replace tan}\theta=\frac{\sin \theta}{\cos \theta}\text{ in tan}\theta<0\text{ as follows.}[/tex][tex]\frac{\sin \theta}{\cos \theta}<0[/tex][tex]\text{Multiply cos}\theta\text{ on both sides.}[/tex][tex]\frac{\sin\theta}{\cos\theta}\times\cos \theta<0\times\cos \theta[/tex][tex]\sin \theta<0[/tex][tex]\text{But given that sin}\theta>0[/tex]hence sine value should be equal to 0.
[tex]\sin \theta=0[/tex][tex]\theta=\sin ^{-1}0[/tex][tex]\theta=\sin ^{-1}\sin (n\pi)[/tex][tex]\theta=n\pi\text{ where n is integer.}[/tex]i dont know how to answer part b, but you need part a to answer it so that's at the top
GIVEN:
We are told that the original price of a sofa is $500 and rthen it has been reduced by 20%, leaving the new price at $400.
The company cant sell the sofa after 3 weeks so they reduce the price to $320.
Required;
To find the percentage decrease.
Step-by-step solution;
At the point of reducing the price further, the original price has now been put at $400 and the new price has been set at $320. We take note that in terms of percentage, the original price is 100% while the new price will be represented by x (that is, yet unknown).
With this information we can set up an equation based on the ratio of the two prices as compared to the two percentages.
This means;
[tex]\begin{gathered} Original\text{ }price=400(100\%) \\ \\ New\text{ }price=320(x\%) \end{gathered}[/tex]Therefore;
[tex]\frac{400}{320}=\frac{100}{x}[/tex]Now we cross multiply;
[tex]\begin{gathered} x=\frac{100\times320}{400} \\ \\ x=\frac{320}{4} \\ \\ x=80 \end{gathered}[/tex]The new price is now given as 80% which simply means 20% was deducted from the original price. In other words, there was a 20% price reduction.
ANSWER:
There was a 20% decrease.
22. QRST is a rectangle. If RU = 3x - 6 and UT = x + 9, find x and the length of QS.RUx= 5QS =TS
We are given two lengths of the rectangle:
RU=3x-6
UT=x+9
These two lengths are shown in the following diagram:
Since this is a rectangle, the lengths of RU and UT must be equal:
[tex]RU=UT[/tex]Thus
[tex]3x-6=x+9[/tex]We need to solve this equation for x.
We start by subtracting x to both sides of the equation:
[tex]\begin{gathered} 3x-x-6=9 \\ 2x-6=9 \end{gathered}[/tex]Now, add 6 to both sides:
[tex]\begin{gathered} 2x=9+6 \\ 2x=15 \end{gathered}[/tex]Finally, divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{15}{2} \\ x=7.5 \end{gathered}[/tex]We have the value of x: x=7.5
Now we have to find the length of QS. Since QS and RT are diagonals of the same rectangle, they have to be equal:
[tex]RT=QS[/tex]This means that we can find RT by adding RU and UT, and the result will be equal to QS:
[tex]QS=RU+TU[/tex]substituting the given expressions for RU and TU:
[tex]QS=3x-6+x+9[/tex]And now, substitute x=7.5 and solve for QS:
[tex]QS=3(7.5)-6+7.5+9[/tex][tex]\begin{gathered} QS=22.5-6+7.5+9 \\ QS=33 \end{gathered}[/tex]Answer:
x=7.5 and QS=33
An ice company charged $8.16 for 6 bags of ice. If a convenience store bought 7 bags ofice, how much would it have cost them?
In order to solve this problem, we need to use proportions.
We have:
cost in dollars number of bags of ice
8.16 6
x 7
We are assuming that the cost is proportional to the number of bags of ice. So, to find the value x that represents the cost for 7 bags of ice, we can cross multiply the proportions above:
x * 6 = 8.16 * 7
Now if we divide both sides by 6, we isolate the variable x on the left side of the equation, and find its value:
x * 6 = 8.16 * 7
x * 6/6 = 8.16 * 7/6
x = (8.16/6) * 7
x = 1.36 * 7
x = 9.52
Therefore, it would have cost them $9.52.
A new video game has been released. The table shows the proportional relationship between the number of levels completed and the time it should take to complete them. Number of Levels 4 5 Time (hours) ? 2.5 How many minutes should it take to complete 4 levels? 180 minutes 120 minutes 60 minutes 50 minutes
Proportionately, the number of minutes it should take to complete 4 levels is B. 120 minutes.
What is the proportion?Proportion is the ratio between one value and another.
Proportions show the relative amount of a variable or value contained in the whole or another variable.
Proportions as fractional values are depicted using fractions, decimals, or percentages.
Number Time
of Levels (hours)
4 ?
5 2.5
The proportion of hours for level 5 = 0.5 (2.5/5) for each level.
If every level takes 0.5 hours or 30 minutes, level 4 will take 2 hours (0.5 x 4).
Or:
If level 5 takes 2.5 hours, level 4 will take 2 hours (2.5/5 x 4).
Thus, proportionately, to complete level 4 will take Option B.
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Translate the sentence into an equation.Three times the sum of a number and 9 equals 8.Use the variable y for the unknown number.
The Solution:
Given:
Let the unknown number be y.
Three times the sum of a number and 9 equals 8.
Putting the above statement in equation form, we get:
[tex]3(y+9)=8[/tex]Therefore, the correct answer is:
[tex]3(y+9)=8[/tex][tex]3(y+9)=8[/tex]Juan made a scale drawing of his garden below. The scale of his drawing is 1 cm = 5 ft. What is the perimeter of his garden in feet
First let's find the perimeter of the scale drawing. The perimeter is the sum of all sides of the figure.
Looking at the figure, there are two sides without the length. The length of the vertical missing side can be calculated as 8 - 2 = 6 cm, and the length of the horizontal missing side can be calculated as 20 - 9 = 11 cm.
So the perimeter of the scale drawing is:
[tex]20+8+9+2+11+6=56[/tex]Now, to find the perimeter of the garden, we can use a rule of three:
[tex]\begin{gathered} 1\text{ cm}\to5\text{ ft} \\ 56\text{ cm}\to x\text{ ft} \\ \\ \frac{1}{56}=\frac{5}{x} \\ x=56\cdot5 \\ x=280 \end{gathered}[/tex]So the perimeter of the garden is 280 ft.
A loan of $14,354 was repaid at the end of 16 months. What size repayment check (principal and interest) was written, if a 7.4% annual rate of interest was charged?
Principal = P = $14,354
Rate = r
I need help. I have no idea on this question
ANSWER:
The total surface area is 450 mm^2
STEP-BY-STEP EXPLANATION:
We have a pyramid with a triangular base, which the formula to calculate the total surface area is the following
[tex]\begin{gathered} A_T=A_B+A_L \\ A_B=\frac{b\cdot h}{2} \\ A_L=3\cdot\frac{b\cdot l}{2} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} A_T=\frac{20\cdot15}{2}+3\cdot\frac{20\cdot10}{2} \\ A_T=150+300 \\ A_T=450 \end{gathered}[/tex]A model of a crayon is shown. The base is a cylinder with a radius of 1 cm and a height of 6 cm. The tip is a cone with a radius of 1 cm and a height of 2 cm. What is the total volume of the crayon? 6 CN Do not enter any spaces. Round to the nearest hundredths. Use 3.14 for 7.
ANSWER:
20.93 cubic cm
STEP-BY-STEP EXPLANATION:
We can calculate the volume of the crayon by adding the volume of the cone and the volume of the cylinder.
First the volume of the cylinder would be:
[tex]\begin{gathered} V_1=\pi\cdot r^2\cdot h \\ \text{replacing:} \\ V_1=3.14\cdot1^2\cdot6 \\ V_1=18.84 \end{gathered}[/tex]Now, the volume of the cone:
[tex]\begin{gathered} V_2=\frac{1}{3}\cdot\pi\cdot r^2\cdot h \\ V_2=\frac{1}{3}\cdot3.14\cdot1^2\cdot2 \\ V_2=2.09 \end{gathered}[/tex]Now we add them and we have:
[tex]\begin{gathered} V_T=V_1+V_2 \\ V_T=18.84+2.09 \\ V_T=20.93 \end{gathered}[/tex]The volume of the crayon is 20.93 cubic cm
Diameter = 9 ftMarci purchased the rug shown. To the nearest hundredth, what area of floor space will the rug cover? (1 = 3.14)A)28.26 ft?B)58.54 ft?C) 63.59 ft2D)254.34 ft2
Given:
a.) A rug with a diameter of 9 ft.
Since the rug appears to be a circle, we will be using the following formula:
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex]Where,
D = diameter
We get,
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex][tex]\text{= }\frac{\pi(9)^2}{4}[/tex][tex]\text{= }\frac{81(3.14)}{4}[/tex][tex]\text{ Area = }63.585\text{ }\approx63.59ft.^2[/tex]Therefore, the rug will cover 63.59 ft.^2 of the floor area. The answer is letter C.
In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true?
Option-D is correct, m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.
Given that,
This is about angle theorems.
Option A: m∠1 = m∠2. This is untrue since the sum of all angles on a straight line is 180° and the line that separates these two angles is not parallel to the horizontal straight line to evenly divide it.
Option B: m∠4 = m∠6; This statement is not true because though their sum is 180° but again they are transverse angles which are not equal from the line that forms them.
Option C: m∠1 + m∠5 = 90°; This is incorrect since the line that forms each of them is not at a 45° angle and m∠1 = m∠5
Option D; m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.
Option E; m∠7 = m∠8. The assertion is false for the same reason as in option A.
That means only option D is true.
Therefore, Option-D is correct, m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.
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Select all that function with -4x+5=y (-4,5)(-19,6)(9,-31)(8,-27)
Answer
(9, -31) and (8, -27)
Step-by-step explanation:
Given the following function
y = -4x + 5
Testing the options
Using (9, -31)
let x = 9 and y = -31
-31 = -4(9) + 5
-31 = -36 + 5
-31 = -31
Hence, (9, -31) satisifies the function y= -4x + 5
Using (8, -27)
let x = 8 and y = -27
-27 = -4(-8) + 5
-27 = -32 + 5
-27 = -27
Hence, (8, -27) satisfy the function y = -4x + 5
Please do it in such a way where you draw a line from A to C to use in your explanation. Also please draw the diagram so I can visualize.
We have to prove that triangles ABC and ADC are congruents.
We can draw a driagram of the triangles as:
As AB and AD are radius of the same circle, we have:
[tex]AB\cong AD[/tex]The same can be said for CB and CD, so:
[tex]CD\cong CD[/tex]Then, we have a shared side between the two triangle. Then, given the reflexive property we have:
[tex]AC\cong AC[/tex]Then, as we have 3 pair of congruent sides, by the SSS postulate, we can conclude that the triangles ABC and ADC are congruent. Then, all three pair of angles are also congruent.
NOTE:
If we just want to prove that the angles Then, we four right triangles (or a rhombus). Then, each angle of the erhombus is bisected.
The left angle at vertex D is complementary to the lower angle at A. The left angle at vertex B is complementary to the upper angle at A. As both angles at A are equal, The left angle at D and the left angle at B are complementary to the same angle.
Then, they have the same measure.
The same analysis can be done for the right angles.
Then, as both halves of the angles are equal, then the total angle
In △KLM, the measure of ∠M=90°, ML = 28, LK = 53, and KM = 45. Find tan L and cos K.
The triangle KLM can be drawn as,
The value of tan L and cosK can be determined as,
[tex]\begin{gathered} \tan L=\frac{KM}{ML} \\ =\frac{45}{28} \\ =1.6 \\ \cos K=\frac{KM}{KL} \\ =\frac{45}{53} \\ =0.85 \end{gathered}[/tex]Thus, the required value of tanL is 1.6 and cosK is 0.85.
7) The diameter on a scale drawing of a circular clock is 11 inches. Find the area, in square inches, of theactual clock if the scale on the drawing is -inches represents inches of the actual clock. Round to thenearest tenth.1lin
we know that
3/4 inches represents 3 inches of actual clock ----> given
so
Applying proportion
Find out how much represents 11 inches in the actual
3/0.75=x/11
solve for x
x=(3/0.75)*11
x=44 in
that means
The diameter of the actual clock is 44 inches
so
the radius of the actual clock is
r=44/2=22 in
Find out the area
[tex]\begin{gathered} A=pi*r^2 \\ A=pi*22^2 \\ A=1,520.5\text{ in}^2 \end{gathered}[/tex]The area is 1,520.5 square inchesif a coin was flipped 30 times, how many times would it land on tails?
It is expected that it would land on tails 15 times
Here, we want to get the number of times the coin will land on it tail
Mathematically, the probability that a coin will land on its head or on its tail is the same at 1/2
So the number of times out of 30 flips will be;
[tex]\frac{1}{2}\times30\text{ = 15 times}[/tex]3. (a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down. (b) What was the equation of your linear function in slope-intercept form? (c) What was the equation of the transformed function in slope-intercept form?
The required solution,
(a) the graph has been shown,
(b) The slope-intercept equation of linear function is y = x,
(c) The slope-intercept form of transformed equation is y = x + 2 and y = x - 3
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Let's consider a linear function y = x,
The equation of the trasformation in slope-intercept form is given as
For 2 units up
y = x + 2
For 3 units down
y = x - 3
Thus, the required graph has been attached and the solution is determined.
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I'm working on a practice quiz I'm confused about this question
In this problem we have to use the Hero formula so first we have to find s:
[tex]s=\frac{a+b+c}{2}[/tex]and then we replace the sides of the triangle:
[tex]s=\frac{12+11+7}{2}=\frac{30}{2}=15[/tex]and with s we can use the formula of A so:
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]and replace the data so:
[tex]A=\sqrt[]{15(15-12)(15-11)(15-7)}[/tex]and we simplify it so:
[tex]\begin{gathered} A=\sqrt[]{15(3)(4)(8)} \\ A=\sqrt[]{1440} \\ A\approx37.95 \end{gathered}[/tex]The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 432 feet long and 4 millimeters in diameter has a resistance of 1.26 ohms, find the length of a wire of the same material whose resistance is ohms and whose diameter is millimeters.
Let
R ----> resistance in ohms
L ---> the length of the wire in ft
D ---> the diameter of the wire in mm
In this problem, the equation is of the form
[tex]R=K\frac{L}{D^2}[/tex]we have
L=432 ft
D=4 mm
R=1.26 ohms
so
Find out the value of K (constant of proportionality)
substitute the given values
[tex]\begin{gathered} 1.26=K\frac{432}{4^2} \\ \\ K=\frac{1.26*16}{432} \\ \\ K=0.0467 \end{gathered}[/tex]Part 2
The formula is
[tex]R=0.0467\frac{L}{D^2}[/tex]For
R=1.41 ohms
D=5 mm
substitute in the formula above
[tex]\begin{gathered} 1.41=0.0467\frac{L}{5^2} \\ solve\text{ for L} \\ L=\frac{1.41*25}{0.0467} \\ L=754.8\text{ ft} \end{gathered}[/tex]The answer is 754.8 feetSilvia manages a sub shop and needs to prepare smoked turkey sandwiches. She has 3 lb of turkey in the cooler, and each sandwich requires3lb of turkey. How many sandwiches can she make?
Silvia manages a sub shop and needs to prepare smoked turkey sandwiches. She has 3 lb of turkey in the cooler, and each sandwich requires 3 lb of turkey. How many sandwiches can she make?
we have that
each sandwich requires 3 lb of turkey
She has 3 lb of turkey in the cooler
therefore
3/3=1
Only she can make 1 sandwichHow much would you need to deposit in an account now in order to have $2000 in the account in 5 years? Assume the account earns 5% interest compounded continuously.
The total amount of money that you can deposit in the account would be = $ 8,000
What is interest?Interest is defined as the amount of money that an individual earns from an investment made after a particular period of time.
The formula for calculating simple interest;
simple interest (SI) = Principal×time ×rate/100
The principal amount = $x
time = 5 years
Rate = 5%
simple interest = $2000
From the formula, make principal the subject of formula:
Principal= SI × 100/T ×R
Principal= 2000×100/5 × 5
principal= 200000/25
Principal=$ 8,000.
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17. Simplify the expression.1.7m² +6.5n - 4n+ 2.5m² – n1.5m² -4.2n1.5m +4.2n4.2m² + 1.5n4.2m² -1.5n
Given:
an expression is given as below
1.7m² +6.5n - 4n+ 2.5m² – n
Find:
we have to simplify the given expression.
Explanation:
we will simplify the given expression as following
1.7m² + 6.5n - 4n+ 2.5m² – n = (1.7 + 2.5)m² + (6.5 - 4 - 1)n = 4.2m² + 1.5n
Therefore, we get
1.7m² +6.5n - 4n+ 2.5m² – n = 4.2m² + 1.5n
Therefore, correct option is 4.2m² + 1.5n.
f(x) = x + 6f(x) = x - 6What’s the answers
Question:
Solution:
Consider the following function:
[tex]f(x)\text{ = x+6}[/tex]this is equivalent to:
[tex]y\text{ = x+6}[/tex]solving for x, we get:
[tex]x\text{ = y - 6}[/tex]exchanging the notation we get:
[tex]f(x)\text{ = x- 6}[/tex]The same procedure is applied analogously for the function f(x) = x-6.
We can conclude that the correct answer is:
YES
which equation can be used to determine the cost c
c = 8t + 12 (option C)
Explanation:
The equation will be in the form of equation of line:
y = mx + c
where y = cost
m = slope, x = change for calls, c = intercept
m = change for calls/change in lenght of call
m = slope = (28-20)/(2-1) = (36 -28)/(3-2)
m = 8/1 = 8
So we know the rate of change is 8
for t = 1, = 8 *1 = 8
for t = t , 8*t =8t
The option in the question with 8t is c = 8t + 12
To confirm if the option is correct, we use any of the value of time:
when t = 2
c = 8(2) + 12 = 16 + 12
c = $28
This is correct from the table. Hence, the equation can be used to determine the cost c is c = 8t + 12 (option C)
Find the length of the segment connecting (-2, 1) and (6. - 1) Round your answer to the nearest tenth. -6 -4 - 2 6
SOLUTION
Find the length of the segment connecting (-2, 1) and (6. - 1) .
In this question, we have the formulae for length segment
D^2 = ( x 2 - x 1 ) ^2 + ( y2 - y 1 )^2
( x 1 , y 1 ) = (-2, 1) , ( x 2 , y 2 ) = ( 6 , -1 )
D^2 = ( 6 - - 2 ) ^2 + ( -1 - 1 ) ^2
D^2 = ( 8 ) ^2 + ( -2 )^2
D^2 = 64 + 4
D^2 = 68
square- root both sides, we have
D = 8.246
D = 8 . 2 ( nearest tenth)
The student Fun Club plans to go to the movies. At the matinee, tickets cost $6 and popcorn is $3. At evening shows, tickets cost $9 and popcorn is $4. The Fun Club attends a matinee and spends less than $60, and then attends an evening show and spends more than $36. If they purchased the same number of tickets and popcorns at each show, which of the following is a possible solution for the number of tickets and popcorns purchased?3 tickets and 2 popcorns7 tickets and 5 popcorns9 tickets and 3 popcorns8 tickets and 6 popcorns
MAtine:
each ticket = $6
Each popcorn = $3
Evening:
Each ticket = $9
Each popcorn = $4
Number of tickets = t
Number of popcorns = p
Fun club attends at matinee, spends less than $60
6t + 3p < 60
Then attends an evening show and spends more than $36
9t + 4p > 36
The system of inequations:
6t + 3p < 60
9t + 4p > 36
Graph each and find the solution
6x + 3y < 60
9x + 4y > 36
Where both areas overlap is the solution:
Answer: 7 tickets and 5 popcorns
There are 50 students in a class. Can the teacher make them sit in a rows of having six students in each row? Use divisibility test to answer
Step 1. There are 50 students and we need to answer of the teacher can make rows of 6 students in each row.
To check if this can be done, divide 50 by 6 and if the residue is 0, there can be rows of 6 and if the residue is not 0 there cannot be rows of 6 students.
Step 2. D
Use the graph and the translation (x,y) → (x+2, y + 5) to answer parts a and b below.
A → A' (-7, 10)
B → B' (1, 5)
C → C' ( -3, 3)
Explanations:The translation rule is:
(x+2, y+5)
We are going to get the coordinates of the vertices A, B, and C.
We will also get the coordinates of the vertices A', B', and C' after translation.
A (-9, 5)
B (-1, 0)
C (-5, -2)
After the translation (x+2, y+5)
A' (-9+2, 5+5)
A' (-7, 10)
B' (-1+2, 0+5)
B' (1, 5)
C' (-5+2, -2+5)
C' (-3, 3)
Therefore:
A → A' (-7, 10)
B → B' (1, 5)
C → C' ( -3, 3)
solve the problem and show your work below. I have a rectangular garden. i usually grow cucumbers in2/3 of my garden but i want to take 3/4 of the cucumber section to grow radishes. After i make the change, how much of my whole garden will be radishes?
Given data;
The area in which cucumbers usually grown are 2/3 x.
Here, x is the total area of the garden.
The area of the cucumber taken to grow raddish are,
[tex]\begin{gathered} R=\frac{3}{4}\times\frac{2}{3}x \\ =\frac{1}{2}x \end{gathered}[/tex]Thus, the area of the raddish is 50% of the total area of the garden sfter the changes.
ExpenseYearty costor rateGasInsurance$425.00$400,00$110.00$100.00What is the cost permile over the course ofa year for a $20,000 carthat depreciates 20%,with costs shown in thetable, and that hasbeen driven for 10,000miles?OilRegistrationDepreciation20%A $1.10 per mileB, SA. 10 per mileD. $0.50 per mileC. $0.25 per mile
First, we will find 20% of the cost of the car which is $20,000.
Thus, we have:
[tex]\begin{gathered} 20\text{\% of 20,000} \\ \Rightarrow\frac{20}{100}\times20000 \\ \Rightarrow\text{ \$4000} \end{gathered}[/tex]Adding the $4000 to the other expenses provided in the table:
[tex]4000+425+400+110+100=\text{ \$5035}[/tex]To get the cost per mile, we are going to divide the total cost of $5035 by the number of mies, 10,000.
Thus, we have:
[tex]\frac{5035}{10000}=\text{ \$0.50 per mile}[/tex]Hence, the correct option is Option D