A park ranger standing in a 146-foot lookout tower sees the beginning of a forest fire. she measures the angle of depression from the tower to the fire to be 12 degrees. Assuming that the ground is horizontal, calculate the distance from the tower to the fire. *Round to the nearest hundredth

Answer: $2294 should be invested in the simple interest account while $4588 should be invested in the certificate of deposit.

Step-by-step explanation:

Let x represent the amount that he would deposit in the simple interest account.

Let y represent the amount that he would deposit in the certificate of deposit.

she will deposit twice as much in the certificate of deposit. It means that

y = 2x

Interest from the simple interest account would be 7%. This mean that the interest would be 7/100 × x = $0.07x

Interest from the certificate of deposit account would be 5%. This mean that the interest would be 5/100 × y = $0.05y.

The total interest from both accounts would be $390. It means that

0.07x + 0.05y = 390- - - - - - - - - - 1

Substituting y = 2x into equation 1, it becomes

0.07x + 0.05 × 2x = 390

0.07x + 0.1x = 390

0.17x = 390

x = 390/0.17 = $2294

y = 2x = 2 × 2294

y = 4588

Answer:

y = 6x + 1

Step-by-step explanation:

Use the point slope equation:

y - y1 = m( x - x1 )

y - 1 = 6 ( x - 0)

y - 1 = 6x

y = 6x + 1

Answer:

Independent variable is tickets.

Dependent variable is cost(dollars).

Step-by-step explanation:

Dependent variable depends on independent variable.

In this question, the total amount deoend on number of ticket bought. As number of tickets increases, the total cost will also increase.

Answer:

Third graph in the image attached

Step-by-step explanation:

Let's rewrite the first inequality:

x - 4y < 4

-4y < 4 - x

4y > x - 4

y > x/4 - 1

We can draw the line y = x/4 - 1, then all values above this line will be solution for this inequality (check first graph in the image attached)

Now, for the second inequality, we have:

y < x+1

We can draw the line y = x + 1, then all values below this line will be solution for this inequality (check second graph in the image attached)

Now, if we combine these solutions, we have the third graph in the image attached.

The crossing point can be found making the value of y from one line equal the value of y from the other line:

[tex]x/4 - 1 = x + 1[/tex]

[tex]x - x/4 = -2[/tex]

[tex]3x/4 = -2[/tex]

[tex]3x = -8[/tex]

[tex]x = -8/3[/tex]

[tex]y = x + 1 = -5/3[/tex]

The crossing point is (-8/3 , -5/3)

Answer:

its c

Step-by-step explanation:

edge

Answer:

3 acute angles with different measures and 1 right angle and 2 acute angles with same measures

Answer:

8%

Step-by-step explanation:

The Cost price is = 49.31

The Selling price is = 41.91

The profit is =-7.4

The percentage decrease of the price of the shirt is hence=

=41.31/49.31 * 100

= 8%

Hence, 8% is the percentage of the decrease of the price of the shirt.

Answer:

b) 1.6 units

    y = 1.586 ≅ 1.6 units

Step-by-step explanation:

Explanation:-

step(i):-

The sine rule

[tex]\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]

Given  a = 2 and b = y

∠A = 75° and ∠ B = 50°

Step(ii):-

by sine rule

              [tex]\frac{a}{Sin A} = \frac{b}{Sin B}[/tex]

            [tex]\frac{2}{Sin 75} = \frac{y}{Sin 50}[/tex]

Cross multiplication , we get

         2 × sin 50° = y  sin 75°

          2 × 0.766 = y  × 0.9659

           [tex]y = \frac{ 2 X 0.766}{0.9659} = 1. 586[/tex]

           y = 1.586 ≅ 1.6 units

Answer:

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

[tex]7\sqrt{3}+2\sqrt{9}= \\\\7\sqrt{3}+2(3)= \\\\6+7\sqrt{3}[/tex]

Therefore, this is irrational. Hope this helps!

Answer:

Step-by-step explanation:

What we do is to divide 1500 by 4 = $1500/4 = $375

Answer:375

Step-by-step explanation:

1500/4=375

Answer:

(x+3)^2+(y+1)^2=25

Step-by-step explanation:

the distance of the center and the point is the radius of the circle

distance=(4^2+3^2)^(1/2)=5

(x+3)^2+(y+1)^2=25

Answer:

41

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

[tex]f(x)=3x+5 \\\\g(x)=x^2 \\\\(f-g)(x)=(3x+5)-(x^2)=-x^2+3x+5[/tex]

Therefore, the correct answer is choice D. Hope this helps!

Answer:

16

Step-by-step explanation:

1/2*1/2*1/2 = 1/8 cubic units

2/(1/8) = 16

Answer:

16

Step-by-step explanation:

[tex](\frac{1}{2})^3 = \frac{1^3}{2^3} = \frac{1}{8}\\\frac{2}{\frac{1}{8}} = 2 \cdot 8 = 16[/tex]

Step-by-step explanation: The account started at $34. Three $50 credits were added. Indicate the withdrawal by subtracting $60 or adding –$60. The check is also represented by subtracting $22 or by taking the additive inverse and adding –$22.

Sample Response: The account started at $34. Three $50 credits were added. Indicate the withdrawal by subtracting $60 or adding –$60. The check is also represented by subtracting $22 or by taking the additive inverse and adding –$22.

Answer:

  2. ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36

  3. see below for synthetic division

  4. complex roots: ±3i

  5. see the second attachment for a graph (has no symmetry)

Step-by-step explanation:

2. The Rational Root Theorem tells you possible rational roots are the form of ...

  ±(divisor of constant term) / (divisor of leading coefficient)

Here, we're lucky in that the leading coefficient is 1. The constant is 36, and its divisors are 1, 2, 3, 4, 6, 9, 12, 18, 36. Possible rational roots, according to the Rational Root Theorem are ...

  ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36

__

3. When actually searching for possible roots, it is useful to narrow down this list of 18 candidates. We can do this using Descarte's Rule of Signs and a couple of other simple tests. The rule of signs has us look at the signs of the coefficients. They are ...

  + + + + +

There are no sign changes, hence no positive real roots. This means we're looking at negative roots only.

We know that p(0) = 36, the constant term. We can evaluate p(-1) simply, by reversing the signs of the odd-degree coefficients and adding them up:

  1 -4 +13 -36 +36 = 10

So p(0) = 36 and p(-1) = 10. The average rate of change is -26, so we expect p(-2) to be zero or less. That value (-2) may be a good first choice for a possible root.

The synthetic division for the root -2 is shown in the first attachment. It shows a remainder of 0, so -2 is a root. The polynomial with the corresponding factor divided out is ...

  q(x) = x^3 +2x^2 +9x +18

__

We can apply the above steps to this polynomial. It will have no positive real roots. The value of q(0) is 18, and the value of q(-1) is -1 +2 -9 +18 = 10. The average rate of change between these points is (18 -10)/(0 -(-1)) = 8, so we expect the function to be zero or negative between x=-2 and x=-3.

Further, we observe that the ratio of the first two coefficients is 1 : 2, the same as the 9 : 18 ratio of the last two coefficients. This suggests we can factor this polynomial by "grouping."

  q(x) = (x^3 +2x^2) +(9x +18) = x^2(x +2) +9(x +2) = (x^2 +9)(x +2)

So, without doing any more synthetic division, we have found a second root at x = -2. This means -2 is a double root.

Our factorization so far is ...

  p(x) = (x +2)^2(x^2 +9)

__

4. The remaining polynomial factor (x^2 +9) has only complex roots:

  x^2 +9 = 0

  x^2 = -9

  x = ±√(-9)

  x = ±3i . . . . the complex roots

__

5. The graph is shown in the second attachment, along with the graph of the final quadratic factor.

The leading coefficient is positive and p(x) is of even degree, so it will have a general U shape, going to +∞ for large positive and negative values of x.

Since x = -2 is a double root, the graph touches the x-axis there, but does not cross it.

The graph of p(x) shows no symmetry.

______

Comment on the graph

With modern graphing calculator software it is entirely feasible to start by graphing the polynomial, then reading the (rational) roots from the graph. The same calculator can effectively divide out those roots. If the result is a quadratic, its vertex form equation can be read from the graph, making it easy to find any additional real or complex roots.

This graph shows ...

  p(x) = (x +2)^2·q(x)

  q(x) = x^2 +9

Answer:

195

Step-by-step explanation:

The area of a rhombus is the product of the two diagonal lengths / 2. The two diagonals measure 15 and 26 respectively. Therefore, the rhombus' area is 390/2=195

Answer:

no solutions

Step-by-step explanation:

Subtract the two equations

3x+y=18

-(3x+y=16)

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

0 + 0 = -2

0 does not equal negative 2

This is never true so there are no solutions

Answer:

The number of solutions is 0.

Step-by-step explanation:

The x and y terms are equal. The constants are different. The lines are parallel. No solution.

Answer:

I think its wrong. For g(5)=(5/5)^2=1 and in your graph is something close to 3. The correct graph for [tex]g(x)=(\frac{1}{5}x)^2[/tex] is

Answer:

False

Step-by-step explanation:

Took the test and this is what I got

Answer:

Download this mm file

Answer:

x = -1 or x = -7

Step-by-step explanation:

y = (x + 4)^2 - 9​

To find x-intercept, set y = 0

=>  (x + 4)^2 - 9​ = 0

=>  ( x + 1)( x + 7) = 0

=> x = -1 or x = -7

To find the x intercepts, plug in y = 0 and solve for x

y = (x+4)^2 - 9

0 = (x+4)^2 - 9 ... replace y with 0

9 = (x+4)^2

(x+4)^2 = 9

x+4 = plus/minus sqrt(9)

x+4 = sqrt(9)  or   x+4 = -sqrt(9)

x+4 = 3   or   x+4 = -3

x = 3-4    or   x = -3-4

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

Checking each answer:

Plug x = -1 into the original equation. You should get y = 0 as a result

y = (x+4)^2 - 9

y = (-1+4)^2 - 9

y = (3)^2 - 9

y = 9-9

y = 0 .... so this confirms x = -1 as a solution

The same should apply for the other potential solution x = -7

y = (x+4)^2 - 9

y = (-7+4)^2 - 9

y = (-3)^2 - 9

y = 9-9

y = 0 .... this confirms x = -7 as well

7 multiply by three u get 21 then add it to the number 28 add u get the answer 49

Answer: 48 red drops

Step-by-step explanation:

ratio of yellow food drops to red food drops is 8:12

8:12 simplifies to 2:3

2:3 = 2/5:3/5

2x/5 = 32 = # of yellow drops (where x is the total # of drops)

2x/5 = 32

2x = 160

x = 80

Since there are 80 total drops and 32 yellow drops, there must be 48 red drops (80-32=48)

Answer:

1.13 cm

Step-by-step explanation:

V=1/3 * pi*r^2*h

h=12 cm (assuming, since that's what you gave)

V=16

r=1.13 cm

Answer: [tex]-1\frac{1}{5}[/tex]

Step-by-step explanation:

[tex]2(P +1) + 3(P + 2 ) > 2[/tex]

Distribute 2 and 3

[tex]2P+2+3P+6>2[/tex]

Combine like terms;

[tex]5P+8>2[/tex]

Subtract 8

[tex]5P>2-8[/tex]

[tex]5P>-6[/tex]

Divide by 5

[tex]P>-\frac{6}{5}[/tex]

Convert to a mixed number by dividing. However, when we have the numerator greater than the denominator, we must find a way to make the numerator lower. We can achieve this by separating it into 2 fractions.

[tex]-\frac{6}{5}=-\frac{5}{5}-\frac{1}{5}[/tex]

When we do this, we can see that 5/5 = 1

[tex]-1-\frac{1}{5}=-1\frac{1}{5}[/tex]

Answer:

C

Step-by-step explanation:

For Youfang, the time spent running is equal to 15 times the week

Answer: x = 4

Step-by-step explanation:

You basically want to solve for the angle A. Do arcsin of 1/3, which is approximately 19.47 degrees. In this triangle, we are missing the adjacent and opposite, but we do have the angle luckily. Lets use SOH-CAH-TOA.

[tex]sin(theta) = \frac{opposite}{hypotenuse}[/tex]

We can see here that doing sine will give us the length of the opposite

[tex]sin19.47 = \frac{x}{12}[/tex]. Do sine of 19.47, then multiply by 12. I got 4

Answer:

Distance between 2 stations= 8.94 miles

Step-by-step explanation:

The coordinates of Symphony Station is given by:

Symphony Station: (x₁ , y₁) : (1,2)

The coordinates of Elm station is given by:

Elm Station: (x₂ ,y₂) : (-3,-6)

We know that the distance formula can be used to find distance between these 2 points. Distance formula is given as

d= √((x₂ - x₁)² + (y₂ - y₁) ²)

Substitute values

d= √((-3 - 1)² + (-6 - 2) ²)

d= √((-4)²+(-8)²)

d= √(16+64)

d=√80

d= 8.94 miles