[tex]\frac{1+\tan x}{\sin x+\cos x}=\sec x[/tex] is proved
Solution:Given that,
[tex]\frac{1+\tan x}{\sin x+\cos x}=\sec x[/tex] ------- (1)
First we will simplify the LHS and then compare it with RHS
[tex]\text { L. H.S }=\frac{1+\tan x}{\sin x+\cos x}[/tex] ------ (2)
[tex]\text {We know that } \tan x=\frac{\sin x}{\cos x}[/tex]
Substitute this in eqn (2)
[tex]=\frac{1+\frac{\sin x}{\cos x}}{\sin x+\cos x}[/tex]
On simplification we get,
[tex]=\frac{\frac{\sin x+\cos x}{\cos x}}{\sin x+\cos x}[/tex]
[tex]=\frac{\sin x+\cos x}{\cos x} \times \frac{1}{\sin x+\cos x}[/tex]
Cancelling the common terms (sinx + cosx)
[tex]=\frac{1}{c o s x}[/tex]
We know secant is inverse of cosine
[tex]=\sec x=R . H . S[/tex]
Thus L.H.S = R.H.S
[tex]\frac{1+\tan x}{\sin x+\cos x}=\sec x[/tex]
Hence proved
The volume of a cube is 15.625cm3. Find the length of its edge
The edge of cube is: 2.5 cm
Step-by-step explanation:
Let V be the volume of cube
V = 15.625 cm^3
Let x be the side of the cube then
[tex]V = x^3\\15.625 = x^3[/tex]
Taking cube root on both sides
[tex]\sqrt[3]{x^3} = \sqrt[3]{15.625} \\x = 2.5\ cm[/tex]
The edge of cube is: 2.5 cm
Keywords: Volume, Cube
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Please answer this correctly is the answer
3:37pm
6:37pm
8:37pm
5:37pm
Answer: 5:37
Step-by-step explanation:
The answer is d/5:37pm
Step-by-step explanation:
2:07+2:30=4:37
Cheyenne is 1 he ahead
4:37+1:00=5:37
Henry and his children went into a grocery store and where they sell peaches for $2
each and mangos for $1.25 each. Henry has $20 to spend and must buy no less than
10 peaches and mangos altogether. If Henry decided to buy 4 peaches, determine all
possible values for the number of mangos that he could buy. Your answer should be a
comma separated list of values. If there are no possible solutions, submit an empty
answer.
Answer:
6, 7, 8, 9
Step-by-step explanation:
There ya go. The numbers of possible amounts of mangos he could buy without exceeding his budget.
The possible values of mangos if, The cost of peaches is $2, The cost of the mangos is $1.25, and the Total money is $20, are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
What is equation?
A formula known as an equation uses the equals sign to denote the equality of two expressions. In other terms, it is a mathematical statement stating that "this is equivalent to that."
Given:
The cost of peaches =$2,
The cost of the mangos = $1.25,
Total money = $20,
Write the equation, if Henry buys 10 peaches,
10 × 2 + 1.25x = 20
Here, x is the number of mangos,
1.25x = 20 - 20
x = 0
Write the equation when Henry buys 4 peaches,
4 × 2 + 1.25x = 20
8 + 1.25x = 20
x = 20 - 8 / 1.25
x = 9.6 or 9 mangos
Thus, Henry can buy a maximum of 9 mangos if he buys at least 4 peaches.
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What is the unknown term.
in the seqpence 4.5, 5.4,____7.2
A.6.2 or B. 63
Answer:
6.3
Explanation:
To get from 4.5 to 5.4, you need to add 0.9. If you add 0.9 two more times, you get 7.2. Therefore, the middle term should be 6.3. I don't know if you made a typo and forgot the decimal when writing the options cause it says "63", but I believe the answer is 6.3.
Nathan estimated 67*36 by finding 70*40. Nathan’s estimate be greater than or less than the actual product? Explain.
Answer:
Nathan's estimate would be greater than the actual product.
Step-by-step explanation:
Let a, b, c, d be natural numbers such that a<c and b<d
Multiplying a positive number on both sides doesn't affect the inequality
⇒a×b < c×b and c×b < c×d
⇒a×b < c×d
Here 67<70 and 36<40
∴67×36<70×40
Hence, Nathan's estimate would be greater than the actual product.
The sum of 4 times a number and 7 equals 9
Answer:
0.5
Step-by-step explanation:
0.5 x 4 = 2, 2 + 7 = 9
Answer:n=1/2
Step-by-step explanation:
4n+7=9
-7 -7
4n=2
divide by 4 on both sides
n=1/2
There are 12 pupils in a class.
They are each asked whether they have a brother or a sister.
9 say they have a brother.
7 say they have a sister.
2 say they have neither.
Fill in the Venn diagram.
Answer:
The value in box of circle B is 3 and the value in box which belongs in both circle B and S is 6 and value which belongs in circle S is 1 and the value of box outside both the circle is 2.
Step-by-step explanation:
In given Venn diagram
ε = class of 12 pupils
pupils who have brother B = 9
pupils who have sister S = 7
pupils who have neither brother nor sister = 2
Hence the Venn diagram is drawn in the attachment for your reference.
n(E) =12
n(neither B nor S) = 2
So, n(B or S)= n(E) - n(neither B nor S)= 12-2=10
n(B) = 9
n(S) = 7
Now, addition theorem,
n(B or S) = n(B) + n(S) - n(B and S)
[tex]10=9+7-n(B\ and \ S)\\n(B\ and \ S) = 6[/tex]
So the value in box which is in both circle B and S is 6.
So the Box which contains only brothers = n(B) - n(B and S) = 9 - 6 = 3
Value in box of circle B is 3.
So the Box which contains only Sisters = n(S) - n(B and S) = 7 - 6 = 1
Value in box of circle S is 1.
There are 12 pupils in a class so, the number of pupils having both brother and sisters are 6 and the pupils had either brother or sister are 10.
Given :
There are 12 pupils in a class.9 say they have a brother. 7 say they have a sister. 2 say they have neither.Given that there are pupils in a class that is, n(E) = 12
Pupils who have brother, n(B) = 9
Pupils who have sister, n(S) = 7
Pupils who have neither brother nor sister, n(neither B nor S) = 2
So, n(B or S) = n(E) - n(neither B nor S)
= 12 - 2 = 10
n(B or S) = 10
Now, through the addition theorem:
n(B or S) = n(B) + n(S) - n(B and S)
10 = 9 + 7 - n(B and S)
n(B and S) = 6
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Evaluate the expression. 8 x 7 - 12 ÷ 6 please anwser fast
Answer:
54
Step-by-step explanation:
8*7-12/6=56-2=54
Answer:
56-2=54
Step-by-step explanation:
8×7 - 12÷6 =56 - 2= 54
Solve 3x - 5 = 16.
9
8
6
7
Answer:
7
Step-by-step explanation:
3(7)=21-5=16
is abc = dce? justify your answer below, please explain why! please help :)
Answer:
Step-by-step explanation:
∡ECD = 90°
∡DCA= 90°
∡BCA=90°
∡BCE =90°
⇔ ABC=DCE
Solve for x in the following situation. Show your work.
11x-4/50=70/60
Answer:
x=17/150
Step-by-step explanation:
11x-4/50=70/60
11x-2/25=7/6
11x=7/6+2/25
11x=187/150
x=(187/150)/11
x=(187/150)(1/11)
x=187/1650
simplify,
x=17/150
Answer:
x=17/150
Step-by-step explanation:
5 divide 3/4 in simplest
Answer:
20/3
Step-by-step explanation:
5/(3/4)=(5/1)(4/3)=20/3
What is the minimum cuts
needed to cut a circle into 8
equal parts?
What is the minimum cuts needed to cut a circle into 8 equal parts ?
A : 4 cuts
Answer:
4 cuts.Step-by-step explanation:
When we have a circle, each cut (supposing the curst are in the exact middle) which give use two haves. So, if we cut one time, we'll have two equal parts, if we cut a second time, we'll have 4 equal parts, a third time, we'll get us 6 equal parts, and if we cut a fourth time, we'll have 8 equal parts.
So, whenever we have this kind of problem dividing circles, we just say that each cut in the exact middle equals two equal haves, so if we have 4 cuts, we just multiply them by 2, 4(2)=8. Therefore, we have 8 equal parts.
Find the length of RS
Answer:
grab a ruler and put the 0 on the inches side up to the R and she what it's at when it hits S and do it again at T
Last Monday, two law students met up at café Literatura after school to read the pages they were assigned in the legal methods class. Alejandro can read 1 page per minute, and he has read 28 pages so far. Carly, who has a reading speed of 2 pages per minute has read 12 pages so far.
Part A: Define the variables and write two equations to represent the number of pages that each student read.
Variables:
Alejandro:
Carly:
Answer:
Step-by-step explanation:
Variables:
let x be the number of minutes
let y be the total number of pages read
Use the form y = mx + b
"b" is irrelevant in this context because the initial value is 0 (they have not read it before or it is not given)
m is the rate, how fast they can read, how many pages each minute
Alejandro:
28 = 1x <=Simplify because any number multiplied by 1 is itself.
28 = x
Carly:
12 = 2x
Somebody help quick please
Answer:
106°
Step-by-step explanation:
For the equilateral ΔBCD all angles are 60° (180/3 = 60).
m∠ADB is 67° Since the triangle is isosceles the base angles are =.
m∠ ABD will be 180 - (67+67) = 46°.
m∠DBC = 60° so m∠ABC = 46 + 60 = 106°
Answer:
For the equilateral ΔBCD all angles are 60° (180/3 = 60).
m∠ADB is 67° Since the triangle is isosceles the base angles are =.
m∠ ABD will be 180 - (67+67) = 46°.
m∠DBC = 60° so m∠ABC = 46 + 60 = 106°
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Step-by-step explanation:
Graph the solutions of the inequality
Answer:
The graph in the attached figure
Step-by-step explanation:
Graph the solution of the inequality
[tex]t\leq -4[/tex]
we know that
The solution is the interval ---> (-∞,-4]
All real numbers less than or equal to -4
In a number line the solution is the shaded area at left of t=-4 (closed circle, because the number -4 is included in the solution))
using a graphing tool
The graph in the attached figure
15. Which of the following equations was
used to graph the line shown?
A. y=6 + x
B. y=6 - x
C. y=x- 6
D. y=6x
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c (m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 0)
m = [tex]\frac{0-6}{6-0}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1
Note the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = - x + 6 or y = 6 - x ⇒ B
The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,80) and (7,140) to find the number of soda bottles the machine can make each minute.
This is a mathematics problem involving the calculation of the slope of a line graph. The machine produces 20 soda bottles per minute as concluded from the given coordinates (4,80) and (7,140).
Explanation:The subject of this question falls under Mathematics, specifically the topic of linear relationships or functions. The task is to calculate the rate at which soda bottles are made per minute using the given coordinates of the graph, (4,80) and (7,140).
First, we need to calculate the slope of the line represented by these points since the slope corresponds to the number of soda bottles produced per minute. In a linear relationship, the slope of the line can be found using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, (x1, y1) is (4,80) and (x2, y2) is (7,140). Plugging these values into the slope formula, we get: slope = (140 - 80) / (7 - 4) = 60 / 3 = 20.
So, the machine produces 20 soda bottles per minute.
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Three consecutive integers have a sum of 132
Answer:
43+44+45
Step-by-step explanation:
X + X + 1 + X + 2 = 132
3X + 3 = 132
3X + 3 - 3 = 132 - 3
3X = 129
3X/3 = 129/3
X = 43
consecutive means numbers after
HELP WITH THIS???????????????????Will mark brainliest
Answer:
(1,c) (2,b) (3,A)
Step-by-step explanation:
May be right or worng i just read thought it better.
Sandria earned $24 babysitting. She owes her friend $7 for dinner, and she owes her mom $4. She will make $15 later this week for mowing the yard.
How much money will she have at the end of the week?
Answer:
28
Step-by-step explanation:
24-7-4=13
13+15=28
A jacket that originally cost 20 is on sale for 75% off what is the sale price of the jacket? What was the amount of the discount?
Thus, a product that normally costs $20 with a 75 percent discount will cost you $5.00, and you saved $15.00. You can also calculate how much you save by simply moving the period in 75.00 percent two spaces to the left, and then multiply the result by $20 as follows: $20 x .75 = $15.00 savings.
Answer: $35
Step-by-step explanation:
20(75%)=15+20= $35
A long-distance telephone company charges a rate of 8 cents per minute or a 50-cent minimum charge per completed call, whichever is greater. Find the cost, in cents per minute, for a 3-minute call.
Answer:
Cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.
Step-by-step explanation:
We are given the following in the question:
Plan A
A rate of 8 cents per minute.
Plan B
A 50-cent minimum charge per completed call.
We have to find the cost, in cents per minute, for a 3-minute call.
Cost according to plan A:
[tex]\text{Cost per minute}\times \text{Call length in minutes}\\= 8 \times 3\\=24 \text{cents}[/tex]
Cost according to plan B:
50 cents for a 3 minute call
Rate =
[tex]\displaystyle\frac{\text{Total cost}}{\text{Duration of call}} = \frac{50}{3} = 16.67 \text{ cents per minute}[/tex]
The company chooses the plan with greater cost, thus, it chooses plan B.
Thus, cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.
Kayla is buying fruit for packed lunches. She needs to buy an assortment of at least 15 apples and oranges and spend less than $20.00. Apples (x) cost $0.65 each, an oranges (y) cost $0.78 each. Which system of linear inequalities models this situation?
Final answer:
The system of linear inequalities for Kayla's fruit purchase is x + y ≥ 15 to represent the quantity of fruit, and 0.65x + 0.78y < 20 to represent the budget constraint.
Explanation:
The student's question is asking for a system of linear inequalities that would model the situation in which Kayla wants to buy at least 15 fruits consisting of apples and oranges, without spending more than $20. Given that apples (x) are $0.65 each and oranges (y) are $0.78 each, we can set up the following inequalities:
x + y ≥ 15
0.65x + 0.78y < 20
The first inequality represents the requirement that Kayla needs to buy at least 15 pieces of fruit. The second inequality represents the constraint that she needs to spend less than $20 on her purchase.
Evaluate the expression for x = 5, y = 3, and z = 1/4 . 5x−6y+20z4yz Enter your answer in the box.
To evaluate the given expression 5x−6y+20z4yz, for x = 5, y = 3, and z = 1/4, we substitute the given values and apply the order of operations to solve the problem.
Explanation:The question requires us to evaluate the mathematical expression given as 5x−6y+20z4yz with provided values of x = 5, y = 3, and z = 1/4. Let us substitute the values into the expression as follows:
First, replace each 'x', 'y', 'z' in the expression with the given values:
= 5×5 - 6×3 + 20×(1/4) / (4×3×(1/4))
= 25 - 18 + 20 / (3)
= 7 + 20/3
Finally, you can calculate the exact numerical result depending on whether you are allowed to leave it as an improper fraction or if you need to convert it to a mixed number or decimal form.
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In January Jennifer was allowed to use 150 text messages. If she is allowed to use the same amount of text messages every month. How many text messages would she have used in all by the month of August?
She would have used 1200 messages in all by the month of August.
Step-by-step explanation:
Messages allowed per month = 150
There will be 8 months starting from January to August, therefore,
Time period = 8 months
Messages in 8 months = Messages per month * Time period
[tex]Messages\ in\ 8\ months=150*8\\Messages\ in\ 8\ months=1200[/tex]
She would have used 1200 messages in all by the month of August.
Keywords: Multiplication
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What is the factored form of 8x^2+ 12x? 4(4x^2+8x) 4x(2x+3) 8x(x+4) 8x(x^2+4)
Answer:
4x(2x+3)
Step-by-step explanation:
The answer is 4x(2x+3)
A scientist has two solutions which she has labeled solution A and solution B. Each contains salt. She knows that solution A is 30% salt and solution B is 55% salt. She wants to obtain 60 ounces of mixture that is 45% salt. How many ounces of each solution should she use?
Answer:
A= 24 ounces and B= 36 ounces.
Step-by-step explanation:
Given: Solution A contain 30% salt= 0.30 salt.
Solution B contain 55% salt= 0.55 salt.
New mixture should be of 60 ounces with 45% salt.
Let x be the amount of mixture for solution A. Let y be the amount of mixture of solution B.
Scientist need to to obtain 60 ounce of mixture from solution A and B.
∴ [tex]x+y= 60\ ounces[/tex]
y= [tex]60-x[/tex] equation 1
Now, solving to get final solution.
∴ [tex]0.3x+0.55y=0.45\times 60\ ounces[/tex]
Substituting the value of y from equation 1
⇒ [tex]0.3x+ 0.55\times (60-x)= 27[/tex]
⇒ [tex]0.3x+33-0.55x= 27[/tex]
⇒ [tex]-0.25x= -6[/tex]
∴ x= 24 ounces
Next, finding y
y= 60-x
∴ y= [tex]60-24= 36\ ounces.[/tex]
y= 36 ounces.
Now, we can say scientist would require 24 ounces of solution A and 36 ounces of solution B to obtain mixture of 60 ounces with 45% salt.
Eli took out a 20-year loan for $135,000 at 4.8% interest, compounded
monthly. If his monthly payment on the loan is $876.09, how much of his first
payment went toward note reduction?
O A. $876.09
B. $336.09
O
c. $540.00
D. $420.48
Answer:
B. $336.09
Step-by-step explanation:
Monthly payment = $876.09
Interest rate = 4.8%
Convert the annual interest rate to monthly rate = 4.8% / 12
Monthly rate = 0.4% or 0.004
Amount going towards interest payment = 0.004* loan amount
Interest = 0.004 * 135,000
Interest = $540
Therefore, from the monthly payment of $876.09 , $540 goes towards paying interest and the balance is the note reduction;
Note reduction = $876.09 - $540 = $336.09
Answer:
336.09
Step-by-step explanation:
this is the right anwser