The distance from a ship to two lighthouses on the shore are 4 miles and 7 miles respectively. If the angle between the two lines of sight is 45, find the distance between the lighthouses

Answer:

this problem is not factorable.

Step-by-step explanation:

Final answer:

The factored form of the quadratic expression x^2 + 9x + 16 is (x + 7)(x + 2), found by identifying two numbers that multiply to 16 and add up to 9.

Explanation:

To find the factored form of the expression x2 + 9x + 16, we are looking for two binomials that when multiplied together will yield the original quadratic expression. Since the coefficient of x2 is 1, we only need to find two numbers that add up to the coefficient of x (which is 9) and multiply together to get the constant term (which is 16).

To factor the quadratic expression, we look for two numbers that multiply to 16 and add to 9. These numbers are 7 and 2. Therefore, the factored form of the expression is (x + 7)(x + 2).

Answer:

a. 26° C

b. 40m

c. Yes

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo.

a. What was the approximate temperature at a depth  of 70 m? At the surface?  

26° C

b. At what depth was the temperature  a little more than 27°C?

40 m

c. Do the points in the scatter plot show a relationship?  Explain your thinking.

Yes, the scatter plot show a relationship between the depth and the temperature of Lake Turkana. It shows a negative correlation between the two variables. The deeper the lake is, the cooler the temperature .

Hope it will find you well.

Answer: The value of a is the number that the​ x-values are multiplied by to get to the corresponding​ y-values. So, a equals 5

We have

y=ax  

so a is clearly the number we multiply by the x values.

Substituting either  points (2,10) and (-2,-10),

10 = a(2)

a = 10/2 = 5

Answer:

120 different ways

Step-by-step explanation:

For the first lunch, Emilce has 5 options to choose,

In the second lunch, now she has only 4 options, as one was already chosen.

Then, in the third lunch, she has 3 options.

In the fourth lunch, she has 2 options.

In the last lunch, she has just 1 option.

So, the number of different ways she can order her lunches in the week is:

5 * 4 * 3 * 2 * 1 = 120

She can order in 120 different ways.

Final answer:

In a triangle, the sum of all interior angles is always 180 degrees. Given the ratio of the other interior angles, we can find their measures.

Explanation:

In a triangle, the sum of all interior angles is always 180 degrees. Given that one of the interior angles is 40 degrees, let's denote the measures of the other two angles as 3x and 5x. The sum of all three angles is 40 + 3x + 5x = 180. Simplifying this equation, we get 8x + 40 = 180. Subtracting 40 from both sides gives us 8x = 140. Dividing both sides by 8, we find x = 17.5.

Now, we can substitute the value of x back into the expressions for the other two angles. So, the first angle is 3x = 3(17.5) = 52.5 degrees, and the second angle is 5x = 5(17.5) = 87.5 degrees.

Answer:

Correct answer: a) m = 9 ; b) m = 2 and n = 3

Step-by-step explanation:

Given:

a) m x² - 36  = (3 x + 6) (3 x - 6)  ⇒ m = ?

b) (m x + n y)² = 4 x² + 12 x y + 9 y²  ⇒ m, n = ?

a)  m x² - 36 (3 x + 6) (3 x - 6)  

The right side of the equation is the difference of the square, so we will present the left side in the same way:

(√m x)² - 6² = (3 x + 6) (3 x - 6)

(√m x + 6) (√m x - 6) = (3 x + 6) (3 x - 6)

√m = 3 /²  when we square both sides of the equation we get:

m = 9

b)

(m x + n y)² = 4 x² + 12 x y + 9 y²

The left side of the equation is the complete square of the binomial, so we will present the right side in the same way:

(m x + n y)² = (2 x)² + 2 · 2 x · 3 y + (3 y)² = (2 x + 3 y)²

(m x + n y)² = (2 x + 3 y)²  ⇒

m = 2 and n = 3

God is with you!!!

For part (a), m must be 9 to make the equation true. For part (b), m can be 2 or -2, and n can be 3 or -3 to satisfy the equation.

To find values for m and n to make the statements true, we must compare coefficients or recognize patterns in the given equations.

Part (a)

We have the equation mx^2 - 36 = (3x + 6)(3x - 6). We can expand the right side to get 9x^2 - 36. To make this equation true, we need the coefficient of x^2 on the left to be equal to the coefficient on the right, which is 9. Therefore, m must be 9 for the equation to be true.

Part (b)

We have (mx + ny)^2 = 4x^2 + 12xy + 9y^2. Expanding the left side, we get m^2x^2 + 2mnxy + n^2y^2. To equate it to the right side, we need m^2 = 4 and n^2 = 9. This gives us two possibilities each for m and n: m can be 2 or -2 and n can be 3 or -3.

Answer:

range:{0,15}

Step-by-step explanation:

y=x²-2x

domain:{-3,0,5}

for range

when x=-3

y=(-3)²-2×(-3)=9+6=15

when x=0

y=0-0=0

when x=5

y=5²-2×5=25-10=15

range:{0,15}

or

y=x²-2x+1-1=(x-1)²-1

when x=-3

y=(-3-1)²-1=16-1=15

when x=0

y=(0-1)²-1=1-1=0

when x=5

y=(5-1)²-1=16-1=15

The student's question involves calculating the output values of a quadratic function for a given domain. The specific output values for the domain {-3, 0, 5} of the function y = x^2 - 2x are 15, 0, and 15, respectively.

The student is dealing with a question that involves the evaluation of a quadratic function y = x^2 - 2x at different values within its domain. Here, the domain is specified as the set {-3, 0, 5}. To answer the student's question, we calculate the value of y for each x in the domain:

Therefore, the corresponding output values for the function at the points in the domain are 15, 0, and 15, respectively.

Answer:

Included in screenshot

Answer:

The mean temperature is 31.

Step-by-step explanation:

The formula for the z-sore is

          x - mean

z = ----------------------

        (std dev)

In this case let's multiply both sides by (std dev), obtaining:

x - mean = z*(std dev).

Solving for (mean), we get

mean = x - z*(std dev)

Substituing 37 for x, 2.4 for z and 2.5 for (std dev), we get:

mean = 37 - (2.4)(2.5) = 31

The mean temperature is 31.

Final answer:

To find the mean temperature with the given z-score and standard deviation, the z-score formula is used. After calculation, the mean temperature in Philadelphia for the first 15 days of February is determined to be 31°.

Explanation:

The question is asking us to find the mean temperature in Philadelphia for the first 15 days in February, given that the daily high temperatures are normally distributed with a standard deviation of 2.5° and that on Valentine's Day (February 14th), the temperature was 37° with a z-score of 2.4. To solve for the mean temperature, we can use the z-score formula:

Z = (X - μ) / σ

Where:
Z is the z-score,
X is the value in the dataset,
μ is the mean, and
σ is the standard deviation.

We know Z = 2.4, X = 37°, and σ = 2.5°. Plugging these values into the z-score formula, we can solve for the mean (μ).

2.4 = (37 - μ) / 2.5

Multiplying both sides by 2.5, we get:

2.4 x  2.5 = 37 - μ
6 = 37 - μ
μ = 37 - 6
μ = 31°

Therefore, the mean temperature in Philadelphia for the first 15 days in February is 31°.

Answer:

2.57

Step-by-step explanation:

1/4×22/7×3×3=7.07

1/2×9=4.5

7.07-4.5=2.57

Answer:

shed get $1.82 back

Step-by-step explanation:

Answer:

She would get $1.82 back

Step-by-step explanation:

If she bought 3 cartons costing $1.06 each, you would have to multiply $1.06 by 3

$1.06 x 3 = $3.18

Then if she paid with a five dollar bill you have to subtract $3.18 from 5

5 - 3.18 = 1.82

$1.82 is the answer

Answer:

approximately 462.24

Step-by-step explanation:

Answer:

Judy spent 55 min at the gym.

Step-by-step explanation:

From the three people that are listed in the problem Mary is the only one we know the actual time she was at the gym which is 3 h. Sandy on the other hand spent 50 minutes less sprinting than Mary, so we have:

Sandy = Mary - 50 minutes

Sandy = 3h - 50 minutes

Sandy = 3*60 - 50

Sandy = 180 - 50 = 130 minutes

Judy spent 1h and 15 min less than Sandy exercising so we have:

Judy = Sandy - 1h 15min

Judy = 130 min - (60 min + 15 min)

Judy = 130 min - 75 min = 55 min

Judy spent 55 min at the gym.

Answer:

26 trees.

Step-by-step explanation:

The number of trees Ben, Cam, and Justin can chop down is given by:

b+2c+3j

Where:

b is the number of hours Ben spends chopping.

c is the number of hours Cam spends chopping.

j is the number of hours Justin spends chopping.

We want to determine the number of trees they chop down after Ben spends 8 hours chopping, Cam spends 3 hours chopping, and Justin spends 4 hours chopping.

b=8, c=3, j=4

Substituting these in the given equation

b+2c+3j=8+2(3)+3(4)=8+6+12 = 26

They chop down a total of 26 trees.

Answer:

26 trees chopped altogether

Step-by-step explanation:

We are given that;

-Ben, Cam, and Justin are lumberjacks.

-The number of trees they chop down is given by b+2c+3j

where;

b is the number of hours Ben spends chopping

c is the number of hours Cam spends chopping

j is the number of hours Justin spends chopping.

We are told that;

Ben spends 8 hours to chop

Cam spends 3 hours to chop

Justin spends 4 hours to chop

Thus, Substituting in the given equation we get

Total nmber of trees chopped = b + 2 c + 3 j = 8 + 2(3) + 3(4) = 8 + 6 + 12

 = 26

They have chopped 26 trees altogether

Answer:

According to my calculation, the two possible coordinates of vertex C, is [tex](1,\sqrt{27}) and (1,-\sqrt{27})[/tex].

Answer:

According to my calculation, the two possible coordinates of vertex C, is .

Step-by-step explanation:

Answer:

Increases

Step by Step Explanation:

More time on your homework means more time to cheat/figure the answer out.

Answer:

Improved

Step-by-step explanation:

The more you study or do homework, the more you learn, and the better your grade

9514 1404 393

Answer:

  12

Step-by-step explanation:

The applicable relationship here is ...

  AD² = AB·AC

  AD = √(AB·(AB +BC)) = √(6·(6+18)) = √144

  AD = 12

Answer:

32%

Step-by-step explanation:

Total animals: 45 + 30 = 75

Coloured: 16 + 8 = 24

24/75 × 100

32%

Answer:

one solution

Step-by-step explanation:

5x + 6 = 2 + 3x

Subtract 3x from each side

5x-3x + 6 = 2 + 3x-3x

2x +6 = 2

Subtract 6 from each side

2x+6-6 = 2-6

2x = -4

Divide each side by 2

2x/2 = -4/2

x = -2

There is one solution

Answer:

One solution

Step-by-step explanation:

To solve, we need to isolate the variable, x

5x+6=2+3x

Subtract 2 from both sides

5x+4=3x

Subtract 5x from both sides

4= -2x

Divide both sides by -2

x= -2

There is one solution to this equation,  -2

Answer:

Yes

Step-by-step explanation:

( x^3 + x^2) (-4x - 4)

x^2 ( x+1) -4 (x+1)

(x^2 - 4) (x+1)

(x-2) (x+2) (x+1)

X= 2 x=-2 x=-1

Answer:

Yes

Step-by-step explanation:

f(x) = x^3 + x^2 −4x − 4

Factor by grouping  taking x^2 out of the first group and -4 out of the second

0 = x^3 + x^2      −4x − 4

     x^2(x+1)     -4(x+1)

Factor out (x+1)

0=(x+1)(x^2-4)

Now we have the difference of squares

0=(x+1) (x-2)(x+2)

x+1 is a factor

Answer:

114

Step-by-step explanation:

find the solution below

Answer:

36

Step-by-step explanation:

6 9 15 24 ...

The sequence goes like this:

+3, +6, +9, +12, +15 (Adding 3 each time)

For example:

6 + 3 = 9  (First +3)

9 + 6 = 15  (Then +6)

15 + 9 = 24 (Then +9)

24 + 12 = 36

The next term of this quadratic sequence will be 36.

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The quadratic sequence is,

⇒ 6, 9, 15, 24

Now,

The first term = 6

The second term = 6 + 3 = 9

The third term = 9 + 6 = 15

The fourth term = 15 + 9 = 24

Thus, The pattern of adding are;

3 , 6 , 9, ..

So, For next term we add 12 in fourth term, we get;

The next term = 24 + 12

                      = 36

Thus, The next term of this quadratic sequence will be 36.

Learn more about the quadratic equation visit:

https://brainly.com/question/28038123

#SPJ3

Answer:

7/22

Step-by-step explanation:

Drama or Sports:

85 + 200 - 60

225

330 - 225 = 105

Probability: 105/330

7/22

Answer: cc

Step-by-step explanation:

Answer:

670.32

Step-by-step explanation

[tex] {4}^{2} \times {5}^{2} + 30 = 16 \times 2 5+ 30 = \\ = 400 + 30 = 430[/tex]

or

[tex] {4}^{2} \times {5}^{2} + 30 = (4 \times 5)^{2} + 30 = \\ = 20^{2} + 30 = 400 + 30 = 430 [/tex]

Answer:

10

Step-by-step explanation:

Answer:

Step-by-step explanation:

3+1.5*4

3+6

9 inches in total 4 hours from now

Answer:

3 + 1.5(4) = 9

then the second one will be: 3 + 1.5t

Step-by-step explanation:

1.5t is increasing do therefore that is the answer.

Answer:

No, because the inequality symbol should be less than or equal to 650.

Step-by-step explanation:

it should be "No, because the inequality symbol should be less than or equal to 650." because the statement says she gets the accessories without spending MORE than the amount she received, it says nothing about spending the exact amount.

Answer:

No, because the inequality symbol should be less than or equal to 650.