math please help me :)

[tex]\frac{1+\tan x}{\sin x+\cos x}=\sec x[/tex] is proved

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

Answer:

Graph A is the correct answer.

explanation of the answer:

the line starts between 10 and 15 and continues to increase to the top of the graph.

The equation y = 12 + 2x represents the cost of a pizza given the number of additional toppings. The corresponding graph would be a straight line which starts at $12 on the y-axis (no toppings) and goes up by $2 on the y-axis for each increment of 1 on the x-axis (each additional topping).

The equation given in the problem, y = 12 + 2x, is a linear equation that represents the cost of a pizza with an increasing number of toppings.

In this equation, 'x' represents the number of additional toppings and 'y' represents the total cost of the pizza. The graph representing this equation would be a straight line that starts at $12 on the y-axis (representing the cost of a medium
pizza without any additional toppings).

Then, for each increment of 1 on the x-axis (representing adding one topping), the line goes up by $2 on the y-axis (representing the additional cost).

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Answer:

-20 feet

Reasoning:

When your going down when your talking about water the answer is negative.But when your going up the answer will be positive

Answer:

- 20 feet

Step-by-step explanation:

Its also negative because the dolphin is going not up if the dolphin did go up then it positive.

Answer:

5

Step-by-step explanation:

Expected value = probability × number of trials

X = 1/4 × 20

X = 5

Answer:

18

Step-by-step explanation:

I'm 90% sure I'm right but I could be wrong

4 × 18 = 72

6 × 18 = 108

72 + 108 = 180 degrees

Which means the opposite angle diagonal from 6x would also equal 108 degrees

Same thing for 4x, 72 degrees

72° + 72 ° + 108° + 108° = 360 degrees

Answer:

The quantity of lobster which are sold live each year in the United States and  Canada are 46 million pounds (approximately).

Step-by-step explanation:

Given:

Each year, 183 million pounds of lobster are caught in  the United States and Canada. Twenty-five percent of this amount is  sold live.

Now, to find how  many pounds of lobster are sold live each year in the United States and  Canada.

According to question:

25% of 183 million pounds.

[tex]\frac{25}{100}\times 183[/tex]

[tex]=0.25\times 183[/tex]

[tex]=45.75[/tex]

Each year 45.75 million pounds of lobster are sold live in the United States and Canada.

Therefore, the quantity of lobster which are sold live each year in the United States and  Canada are 46 million pounds (approximately).

Answer:

B. 10

Step-by-step explanation:

x + y = 21

xy = 110

Rewrite first equation. x + y = 21 becomes y = -x + 21

Now substitute this new equation in the second equation.

x(-x+21) = 110

-x^2 + 21x - 110

Divide by -1

x^2 - 21x + 110

(x - 10)(x - 11)

x = 10, 11

10 is less, so the youngest daughter is 10

Answer:15

Step-by-step explanation:you multiply m=5 to n=3 so what is 5 times 3? so 5 times 3 = 15

Final answer:

When m=5 and n=3, the value of mn is found by multiplying the two numbers, resulting in mn=15.

Explanation:

To find the value of mn when m=5 and n=3, you simply need to multiply the two numbers together:

1. multiply m and n-

mn = m × n

2. m= 5 and n= 3, so the expression will be as follows-

mn = 5 × 3

3. Multiplying 5 and 3, the following is obtained-

mn = 15

Therefore, the value of mn is 15.

Answer: Need help with this too

Step-by-step explanation:

Answer: 18 question correct

Step-by-step explanation:

if she got 100% on the test:

100% x 25 question = 25 questions correct

so,

72% x 25 questions = 18 question correct

Answer:

The amount of numbers that have a G C F of 7 and a product of 490 is 2.

Step-by-step explanation:

On Prime Factorization 490   =   2   x   5   x   7   x   7

G CF = Greatest Common Factor

So, here the possible number who have products as 490 and G C F as 7 is

(a)  2 x 7 = 14  and   5 x 7  = 35

As, 14 and 35 on multiplication,gives 490 as a  product.

And, G C F  of 14 and 3 5 is also 7.

(b)  7  and   5 x 7 x  2  = 70

As, 7 and 70 on multiplication,gives 490 as a  product.

And, G C F  of 7  and 70 is also 7.

⇒ (14, 35) and (7,70) are the only such pairs.

Hence, the amount of numbers that have a G C F of 7 and a product of 490 is 2.

Final answer:

The question seeks the number of number pairs with a GCF of 7 and a product of 490. There are only two pairs that meet the criteria: (7, 70) and (10, 49). Each pair multiplies to 490 and has a GCF of 7.

Explanation:

The question asks for the number of pairs of numbers that have a Greatest Common Factor (GCF) of 7 and a product of 490. First, we must note that any pair of numbers with a GCF of 7 must be multiples of 7. So, we divide 490 by 7 to find another factor that is also a multiple of 7, which gives us 70. Now, we have two pairs of numbers that satisfy the condition: (7, 70) and (10, 49) because each pair when multiplied gives 490, and the GCF of each pair is 7. It's important to note that 490 is equal to 7^2 times 10, which means we won't find more than these two pairs without repeating the same factors in a different order.

Answer: OPTION D.

Step-by-step explanation:

The rate of change of a linear function is also known as "Slope".

The slope can be calculated with the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Choose two points on the function "R" graphed:

[tex](1,0)\\(0,-3)[/tex]

You can say that:

 [tex]y_2=-3\\y_1=0\\\\x_2=0\\x_1=1[/tex]

Substituting values into the formula, you get:

[tex]m=\frac{-3-0}{0-1}=3[/tex]

Choose two point from the table that models the function "S":

[tex](4,21)\\(6,31)[/tex]

You can say that:

 [tex]y_2=31\\y_1=21\\\\x_2=6\\x_1=4[/tex]

Substituting values into the formula, you get:

[tex]m=\frac{31-21}{6-4}=5[/tex]

Therefore, you can conclude that the function "S" has a greater rate of change than Function "R".

Answer:

D: Function S has a greater rate of change than Function R.

Step-by-step explanation:

Function S has a greater rate of change than Function R.

Function R → m =

rise

run

=

6

2

= 3. Function S → m =

change in y

change in x

=

31 − 21

6 − 4

=

10

2

= 5

Since 5 > 3, function S has a greater rate of change.

Word problem - Jose played soccer for 5 hours every afternoon for 8 days. How many hours did Jose play soccer in all?

So this problem is about Jose and the amount of time he spends playing soccer.

Next, let's pick out what we know and what we want to find out.

We know that Jose played soccer for 5 hours every afternoon for 8 days. We want to find out how many hours of soccer he played in all so we need to multiply.

We multiply the amount of time he spent playing soccer each afternoon which is 5 hours by the number of days which is 8 days.

(8) (5) = 40

This means that Jose played 40 hours of soccer in all.

Answer:

yes

Step-by-step explanation:

Answer:

two  significant figures

Step-by-step explanation:

Answer:

there is an infinite amount of solutions

Step-by-step explanation:

negative 6t and positive 6t cancel each other out

plug in any number for t, and you will always get 0

Answer:

C

Step-by-step explanation:

If $500 is deducted for each 1,000 miles, and 10,000 miles are being driven per year, that is -$5,000 each year. Therefore your equation would be $23,000-$5,000y.

Answer:

Step-by-step explanation:

Answer:

She bought 3 large frames and 14 small frames

Sigma notation of sequence −10, −13, −16, … is [tex]\sum_{n=1}^{6}-(3 n+7)[/tex]

Need to determine the sigma notation for the following sequence  

−10, −13, −16, …

Let's try to build a generic formula for given sequence  

The given sequence is in Arithmetic progression where first term = -10 and common difference = -3

The formula for arithmetic progression is given as:

[tex]a_n = a_1 + (n - 1)d[/tex]

Where,

[tex]a_n[/tex] is the nth term in the sequence

[tex]a_1[/tex] is the first term in the sequence

d is the common difference between the terms

Here in this sequence [tex]a_1[/tex] = -10 and d = -3

[tex]a_n = -10 + (n - 1)(-3)\\\\a_n = -10 - 3n + 3\\\\a_n = -3n - 7[/tex]

So generic formula for a term is – ( 3n + 7 )

[tex]\begin{array}{l}{\text { For } \mathrm{n}=1, \text { term is }-(3 \times 1+7)=-10} \\\\ {\text { For } \mathrm{n}=2, \text { term is }-(3 \times 2+7)=-13} \\\\ {\text { For } \mathrm{n}=3, \text { term is }-(3 \times 3+7)=-16}\end{array}[/tex]

And so on

Using sigma notation for arithmetic sequence:

[tex]\sum_{k=1}^{n} a_{k}[/tex]

So for first six terms value of n will vary from 1 to 6 and in sigma notation it can be represented as

[tex]\sum_{n=1}^{6}-(3 n+7)[/tex]

1 + 2 = 21 (reversing numbers)

2 + 3 = 32 (reversing numbers) + 4 = 36

3 + 4 = 43 (reversing numbers)

4 + 5 = 54 (reversing numbers) + 4 =58

Answer:

Step-by-step explanation:

This is a sequence using reversed numbers, and alternating a summing fixed amount.

In the first one you can see that it's only numbers being reversed.

The second one is also reversing numbers but adding 4 units, 32+4=36.

The third one has the same pattern in the first one, just numbers being reversed.

The fourth has the same pattern than the second one, reversed numbers and add 4 units. So, it would be 54+4=58.

Therefore, the answer is 58.

the solution for ( x ) in the equation [tex]\( x^{12} = 17 \)[/tex] is approximately [tex]\( x \approx 1.170092 \).[/tex]

To solve ( x ) in the equation [tex]\( x^{12} = 17 \),[/tex] follow these steps:

1. Take the 12th root of both sides.

2. Simplify the expression.

Step 1: Take the 12th root of both sides:

[tex]\[ x^{12} = 17 \][/tex]

[tex]\[ x = \sqrt[12]{17} \][/tex]

Step 2: Simplify the expression:

To find the 12th root of 17, you can use a calculator or approximation methods.

[tex]\[ x \approx \sqrt[12]{17} \][/tex]

Using a calculator or approximation methods, we find:

[tex]\[ x \approx 1.170092 \][/tex]

So, the solution for ( x ) in the equation [tex]\( x^{12} = 17 \)[/tex] is approximately [tex]\( x \approx 1.170092 \).[/tex]

The cost of the nylon rope is $0.8 per meter. For $1, you can purchase 1.25 meters of nylon rope.

The given equation is p=0.8L. Here, 'p' stands for the price in dollars and 'L' is the length of the nylon rope in meters.

A. To determine the cost per meter, we look at the coefficient in front of 'L' in our equation. Here, it is 0.8, signifying that the nylon rope costs $0.8 per meter.

B. To find out the length of rope that could be bought for $1, we use the equation by setting 'p' equal to 1 and solving for 'L'. Doing this gives us 'L' = 1 / 0.8 which equals to 1.25 meters.

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If 2a−b/6 = b/3, then ratio a:b = 3 : 2

Given that 2a−b/6 = b/3

We have to find the ratio of a:b

In mathematics, a ratio indicates how many times one number contains another

A ratio between two or more quantities is a way of measuring their sizes compared to each other

let us first solve the given expression

[tex]\frac{2a -b}{6} = \frac{b}{3}[/tex]

On cross multiplication we get,

6a - 3b = 6b

6a = 6b + 3b

6a = 9b

[tex]a = \frac{9b}{6}\\\\\frac{a}{b} = \frac{3}{2}[/tex]

To convert a fraction to a ratio, first write down the numerator, or top number. Second, write a colon. Thirdly, write down the denominator, or bottom number

Therefore ratio a:b = 3 : 2

Answer:

a) x=4  b) x=17.5

Step-by-step explanation:

a)5x/2+1=11             b)2x/7-3=2

5x/2=11-1                    2x/7=2+3

5x/2= 10                     2x/7=5

5x= 10x2                    2x=35

5x=20                         x=35/2

x=20/5                        x=17.5

x=4

Answer:

Step-by-step explanation:

[tex]a)\\\\\dfrac{5x}{2}+1=11\qquad\text{subtract 1 from both sides}\\\\\dfrac{5x}{2}+1-1=11-1\\\\\dfrac{5x}{2}=10\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\dfrac{5x}{2\!\!\!\!\diagup_1}=(2)(10)\\\\5x=20\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{20}{5}\\\\\large\boxed{\boxed{x=4}}[/tex]

[tex]b)\\\\\dfrac{2x}{7}-3=2\qquad\text{add 3 to both sides}\\\\\dfrac{2x}{7}-3+3=2+3\\\\\dfrac{2x}{7}=5\\\\\dfrac{2x}{7}=\dfrac{5}{1}\qquad\text{cross multiply}\\\\(2x)(1)=(7)(5)\\\\2x=35\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{35}{2}\\\\\large\boxed{\boxed{x=17.5}}[/tex]

Answer:

Each shirt costed $27

each

Step-by-step explanation:

HOPE IT HELPS!!! please mark brainliest :)

Answer:

Answer (d):  (5, -2)

Step-by-step explanation:

Let's use the substitution method.  Eliminate "x" in the second equation.  Solving the first equation for x, we get  x = -3y - 1.  Subbing this for x in the second equation, we get:

2(-3y - 1) + 2y = 6, or, after multiplying as indicated,

-6y - 2 + 2y = 6.

Combining like terms,

-4y = 8, so that y = -2.  If y = -2, then x is found from x = -3y - 1 (see above):

x = -3(-2) -1 = 5

Then the solution is (5, -2)  (Answer d)

Answer:

Because Alternate Interior angles are equal.

Step-by-step explanation:

STEP - I:

[tex]$ m \angle {5} = 3 . m \angle {\{3}\} $[/tex]

Reason:

This is the given data.

STEP - II:

It has multiplied and the reason is mentioned as well.

STEP - III:

[tex]$ m \angle{3} + m \angle{5} $[/tex] = 45° + 135° = 180°

Reason:

It has substituted the value of [tex]$ m\angle{5} $[/tex] from the previous step. The sum of [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle{5} $[/tex] is 180°.

STEP - IV:

[tex]$ a \parallel b $[/tex]

Reason:

We calculated [tex]$ m\angle{5}[/tex] to be 135°.

Note that [tex]$ \angle {5} $[/tex] and [tex]$ \angle{6} $[/tex] are on the same line. That means their sum should be 180°.

i.e., [tex]$ m\angle{5} + m\angle{6} $[/tex] = 180°.

[tex]$ \implies $[/tex] 135° + [tex]$ m\angle{6} $[/tex] = 180°.

[tex]$ \implies m\angle{6} = $[/tex] 45°.

One of the ways to prove [tex]$ a \parallel b $[/tex] is to check if alternate interior angles are equal.

Here, [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle {6} $[/tex] are alternate interior angles and they are equal.

[tex]$ \implies a \parallel b $[/tex].