One number is 3 less than twice another. If their sum is 39, find the numbers.
Which of the following systems of equations represents the word problem?

y = 2x - 3 and y = x + 39
y = 2x - 3 and x + y = 39
y = 2(x - 3) and x + y = 39

Answer:

The answer is sin^2 (theta)  cos (theta) .

Step-by-step explanation:

We need to rewrite tan (theta)  as sin (theta) /cos (theta)

tan^2 (theta) = sin^2 (theta)/ cos^2 (theta)

We also need to rewrite sec (theta) as 1/ cos(theta)

sec^3 = 1 / cos^3( theta)

tan^2 (theta)       sin^2 (theta)

------------------ =    ----------------

sec ^3 (theta)      cos ^ 2(theta)

                           ---------------------------

                               1

                             -----------

                                 cos ^3 (theta)

Remember when dividing fractions, we can use, copy dot flip

sin^2 (theta)           cos^3 (theta)    

------------------    *   -------------------

  cos ^ 2(theta)           1

Canceling a cos^2(theta)  from the top and bottom,

sin^2 (theta)           cos (theta)    

------------------    *   -------------------

  1                             1

we are left with

sin^2 (theta)  cos (theta)

The answer is sin^2 (theta)  cos (theta) .

The answer is sin^2

Answer:

$132.90

Step-by-step explanation:

Answer:

$120.86

Step-by-step explanation:

Answer:

Divide 5.4 by 0.5

Step-by-step explanation:

It's says to find the number of laps she swam. It doesn't ask us to figure out how many laps she could have run with the amount of laps she did.

To find the number of laps Flo swam, divide the total distance Flo swam (5.4 km) by the length of one lap in the pool (0.05 km). This results in 108 laps.

To find out the number of laps Flo swam, we must take the total distance she swam and divide it by the length of one lap in the pool. According to the chart, the length of one lap in a standard-sized pool is 0.05 kilometers. Therefore, the best method would be to divide 5.4 (the total distance Flo swam in kilometers) by 0.05 (the length of one lap in kilometers).

So, we take 5.4/0.05 = 108. This means that Flo swam 108 laps in the pool. Remember, when you want to find how many times a certain distance fits into another, you should utilize division.

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If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

A) 10, 14, 26

10 + 14 = 24 < 26   INCORRECT  :(

B) 10, 14, 16

10 + 14 = 24 > 16  CORRECT :)

C) 10, 10, 14

10 + 10 = 20 > 14  CORRECT :)

D) 8, 10, 14

8 + 10 = 18 > 14   CORRECT :)

E) 5, 10, 14

5 + 10 = 15 > 14   CORRECT :)

F) 2, 10, 14

2 + 10 = 12 < 14   INCORRECT :(

Options B, C, D and E are correct answers.

Given that, a triangle has two sides of lengths 10 and 14.

We need to find what value could the length of the third side be and check all that apply.

Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

Now, from the given options:

A) 10, 14, 26

10 + 14 = 24 < 26 the triangle can not be formed

B) 10, 14, 16

10 + 14 = 24 > 16 the triangle can be formed

C) 10, 10, 14

10 + 10 = 20 > 14 the triangle can be formed

D) 8, 10, 14

8 + 10 = 18 > 14 the triangle can be formed

E) 5, 10, 14

5 + 10 = 15 > 14 the triangle can be formed

F) 2, 10, 14

2 + 10 = 12 < 14 the triangle can not be formed

Therefore, options B, C, D and E are correct answers.

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Answer:

He needs to save $90.75 each month to reach his goal.

Step-by-step explanation:

We have the cost of his vacation that is $1089.

We know that Todd has a year to save the money.

We know that a year in terms of time is twelve months (12 months).

If we want to calculate how much does he need to save each month we need to divide the total cost of his vacation by the amount of months in a year ⇒

[tex]\frac{1089}{12}=90.75[/tex]

We find that Todd needs to save $90.75 per month to reach his goal.

Question: Explain how you would use the result of finding the ground speed to find the course of the airplane.

Answer: 181.2

Explanation:  vertical speed of 20.78 knots  

new course is (-148 , 20.78) = inverse tan ( 20.78 / -148) = 172° or 8° N of East at 149.45 knots

New speed (- 148)² + ( 20.28)² = 149.45 knots round and you get 181.2

question answered by

(jacemorris04)

The ground speed of the airplane is 181.18 knots (approx).

The formula of ground speed of a airplane is given below,

[tex]v_{g} =\sqrt{}[/tex][tex](v_{a} ^{2}+v_{w} ^{2}-2v_{a} v_{w}cos\alpha)[/tex]

where, [tex]v_{g}[/tex] = Ground speed of airplane

[tex]v_{a}[/tex] = Speed of the airplane relative to the air

[tex]v_{w}[/tex] = Wind speed

[tex]\alpha[/tex] =  Internal angle

Given, [tex]v_{a}[/tex] = 160 knots, [tex]v_{w}[/tex] = 24 knots

Here, the angles increase clockwise and east is 90° heading.

The airplane is flying a heading of 90° at 160 knots speed & wind is blowing from 240° at 24 knots speed.

So, the internal angle[tex](\alpha)[/tex] = 240°-90° = 150°

∴ Ground speed, [tex]v_{g} =\sqrt{}[/tex][tex](v_{a} ^{2}+v_{w} ^{2}-2v_{a} v_{w}cos\alpha)[/tex]

⇒ [tex]v_{g}[/tex] [tex]=\sqrt{}[/tex][tex](160^{2}+24^{2}-2*160*24*cos(150))[/tex]

⇒ [tex]v_{g}[/tex] = 181.18 knots (approx)

Hence the ground speed of airplane is 181,18 knots (approx).

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Divide total full time employees by 20 to find how many groups of 20 there are, then multiply that number by 3 to find total part time employees:

250,000 / 20 = 12,500

12,500 x 3 = 37,500 part time employees.

Answer:

I think it's c.

Step-by-step explanation:

A graph usually stands as a representation for functions.

Answer:

-1/6

Step-by-step explanation:

Parallel lines are lines which have the exact same slope but different y-intercepts. This means any line which is parallel and does not cross will have the exact same slope of -1/6.

The correct way to rewrite the expression 5a + 5b + 5c + 5d using the distributive property is option C) 5(a + b + c + d).

The expression given is 5a + 5b + 5c + 5d. This is a sum where each term is multiplied by 5. According to the distributive property, also known as the distributive law of multiplication, a common factor can be factored out of a sum. The distributive property is represented as (A + B)C = AC + BC. In this case, the common factor is 5, and the sum of the variables a, b, c, and d is grouped, giving us 5(a + b + c + d).

So, the correct representation of the expression is 5(a + b + c + d), which corresponds to option C).

Answer: 1%

Explanation:

Add up the frequencies in the bottom row: 350+200+245+125+66+10+4 = 1000

There are 1000 families total. Of this total, 10+4 = 14 families have more than six people. I added up the frequency counts for "7 people" and "8 people" to get 14.

Divide 14 over 1000 and we get 14/1000 = 0.014 = 1.4% which rounds to 1%

Step-by-step explanation:

We are asked to write a system of equations using our given information.

Let x be number of small dogs and y be number of large dogs.

We have been given that paws at play made a total of $1,234 grooming 22 dogs, which means that number of small dogs and large dogs is 22. We can represent this information as:

[tex]x+y=22...(1)[/tex]  

We have been given that paws at play charges $43 to groom each small dog and $75 for each large dog. So the total grooming charges for grooming x small and y large dogs will be 43x+75y, that is equal to total charges for grooming $1234.

We can represent this information as:  

[tex]43x+75y=1234...(2)[/tex]

Therefore, our desired system of equations is:

[tex]x+y=22...(1)[/tex]

[tex]43x+75y=1234...(2)[/tex]    

Answer:

Number of chores done by Janie are 5.

Step-by-step explanation:

Janie's allowance per week is $3.

For each chore she earns $2.

Now we assume that number of chores in a week she does = c

Then total earning from chore = $2 × c

So for the purchase of CD total earning this week inequality will be

⇒ 3 + 2c [tex]\geq[/tex]13

⇒ 2c [tex]\geq[/tex] 13-3

⇒ c [tex]\geq[/tex] 10÷2

⇒ c [tex]\geq[/tex] 5

The speed that describes how fast the car was traveling when the driver applied the brakes is 49 mph.

What was the speed?

The formula that is often used by police officers to determine the speed from a skid mark is this s = √21d.

So, in this case, the length or distance of the skid mark is 115 feet. We can substitute this value in the formula to get;

Speed of car = √21(115)

Speed of car = √2,415

Speed of car = 49.1426 approximately 49 mph.

So, the speed that describes how fast the car was traveling when the driver applied the brakes is 49 mph.

Complete Question:

A police officer investigating an accident finds a skid mark 115 feet long. Approximately how fast was the car traveling when the driver applied the brakes?

Answer:

Jayda can cut 14 slices of dough that are 3/4 inches thick.  

Step-by-step explanation:

In order to solve this problem, we need to take the total amount of dough at 10 1/2 inches and divide it by the thickness of one slide, 3/4 inches, to find the number of slices that can be made from the total amount.  You can solve this two different ways.  You can either convert your fractions to decimals so that 10 1/2 becomes 10.5 and 3/4 become 0.75 and then divide 10.5/0.75 to get 14.  However, you can also keep them as fractions converting 10 1/2 to 21/2 and dividing by 3/4.  When we divide with fractions with keep-change-flip, or keep the first fraction-change the sign to multiplication-flip the second fraction.  So, we multiply 21/2 x 4/3 and get 84/6, or 14.  

Answer:

Not true

Step-by-step explanation:

It is in fact an expression with 4 factors, each with 3 terms.

Factors are things you multiply, terms are things you add.

Answer:

(B , D) = (-2,5)

Step-by-step explanation:

The given quadratic expression is

[tex]3x^{2} -x-10[/tex]

compare the given expression with [tex]ax^{2} +bx+c[/tex]

so we have [tex]a = 3 , b = -1 ,c = -10[/tex]

now [tex]ac=3 (-10)=- 30[/tex] and [tex]b= -1[/tex]

we need to find two numbers such that their product is -30 and sum is -1

-6 and 5 are such numbers

so we have

[tex]3x^{2} -6x+5x-10[/tex]

grouping first two terms and last two terms

[tex](3x^{2} -6x)+(5x-10)[/tex]

factor out 3x from first two terms and 5 from last two terms

[tex]3x(x-2) +5(x-2)[/tex]          

[tex](x-2)(3x+5)[/tex]        ( factor out (x-2))

[tex](x+(-2))(3x+5)[/tex]

hence B =-2 and D= 5

(B,D)= (-2,5)

[tex]f(x)=x^3+2x^2-x-2\\\\f(x)=0\iff x^3+2x^2-x-2=0\\\\x^2(x+2)-1(x+2)=0\\\\(x+2)(x^2-1)=0\iff x+2=0\ \vee\ x^2-1=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\\\boxed{x=-2}\\\\x^2-1=0\qquad\text{add 1 to both sides}\\\\x^2=1\to x=\pm\sqrt1\\\\\boxed{x=-1\ \vee\ x=1}\\\\Answer:\ -2,\ -1,\ 1[/tex]

Answer:  -2, -1, 1

Step-by-step explanation:

f(x) = x³ + 2x² - x - 2

 0 = x³ + 2x²   - x - 2

    = x²(x + 2)  -1(x + 2)

   = (x² - 1) (x + 2)

   = (x - 1) (x + 1) (x + 2)

0 = x - 1       0 = x + 1        0 = x + 2

1 = x           -1 = x             -2 = x

Answer:

The correct options are A: x+8 and C: x+2.

Step-by-step explanation:

We are given the following expression and we are to factorize it:

[tex]x^2+10x+16[/tex]

We are to find such factors that when multiplied they give a result of 16 (1 x 16 = 16) and when added they give a result of 10.

The two such factors of 16 are positive 2 and positive 8.

Factorizing the given expression to get:

[tex]x^2+10+16\\\\x^2+2x+8x+16\\\\x(x+2)+8(x+2)\\\\(x+2)(x+8)[/tex]

Therefore, the two binomial factors of the given expression [tex]x^2+10x+16[/tex] are (x+8) and (x+2).

Answer: x+6 x+2

tell me if I’m wrong because I put x+8 and x+2 and got it wrong it told me it was x+6 and x+2

Answer:

Option (a)

Step-by-step explanation:

The given equation is  

y = 4 (2ˣ)

To find y-intercept, substitute x=0 in the equation.

y = 4 (2⁰) = 4 (1) =4

Hence y-intercept is 4.

Since y-intercept is 4, the equation should pass through the point (0,4).

The only graph passing through the point (0,4) is the graph in option (a).

Hence the answer is option (a).

Answer:

a

Step-by-step explanation:

Look at the picture.

[tex]\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}[/tex]

We have the right triangle x, y and r. From the Pythagorean theorem we have:

[tex]r^2=x^2+y^2\to r=\sqrt{x^2+y^2}[/tex]

We have the point

[tex]\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)[/tex]

Substitute:

[tex]r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1[/tex]

[tex]\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}[/tex]

The cosine of the angle is -2/3, the sine is √5/3, and the cosecant, being the reciprocal of the sine, is √5/5 after rationalization.

The point (-2/3,√5/3) on a unit circle represents the cosine and sine of a specific angle. Here, the x-coordinate is the cosine of the angle, and the y-coordinate is the sine of the angle.

Therefore, the cosine of the angle is -2/3, and the sine is √5/3.

To find the cosecant of the angle, we take the reciprocal of the sine, which gives us 3/√5 or √5/5 after rationalizing the denominator.

Answer:

11

Step-by-step explanation:

I guessed

Answer:

A 1367

Step-by-step explanation:

Answer:

A)84 – 73 = 11 miles

Step-by-step explanation:

On Tuesday she drove 84 miles  (rounding to the nearest mile)

On Monday she drove 73 miles (rounding to the nearest mile)

Tuesday's mileage - Mondays miles = difference in miles

84-73 = 11 miles

Answer: A. 84 – 73 = 11 mi

Answer: (C) 7 and (D) 8

Step-by-step explanation:

5w - 10 > 20

      +10  +10  

5w        > 30

÷5           ÷5  

 w         > 6

Anything GREATER than 6 will work.

Answer:

c = 2

Step-by-step explanation:

(x, y) = (-1, 3)

3 = c - (-1)^2 - 2(-1)

3 = c - 1 + 2

3 = c + 1

2 = c

Answer:

Negative Correlation

Step-by-step explanation:

As you can see in the image I added, a negative correlation happens when the variables move in opposite directions, in other words, one variable increases as the other decreases. We can see this correlation represented by a value of -1 slope.

I hope you find this information useful and interesting! Good luck!

Answer: That's negative.

Step-by-step explanation: hope this helps.

[tex]a_1=-2\\\\a_n=3\cdot a_{n-1}\\-----------------------------------\\a_1=-2\\\\a_2=3\cdot a_{2-1}=3\cdot a_1\to a_2=3(-2)=-6\\\\a_3=3\cdot a_{3-1}=3\cdot a_2\to a_3=3(-6)=-18\\\\a_4=3\cdot a_{4-1}=3\cdot a_3\to a_4=3(-18)=-54\\\\a_5=3\cdot a_{5-1}=3\cdot a_4\to a_5=3(-54)=-162\\\\a_6=3\cdot a_{6-1}=3\cdot a_5\to a_6=3(-162)=-486\\\\Answer:\ \boxed{-2,\ -6,\ -18,\ -54,\ -162,\ -486}[/tex]

Answer:

$30

Step-by-step explanation:

Mark up is the profit on cost. if the pair of jeans was $45 after a 50% markup

Let the price of the jeans before the markup be p then;

p + 50%p = 45

1.5p =45

p = 45/1.5

p = 30

The price before mark up was $30, while the mark up or profit  is $15. This shows 50% of the price before mark up.