Condense the expression to the logarithm of a single quantity.

​

Use the law

√a√b=√ab

So

Graph attached

Answer:

  x ≈ 8.99

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.

__

The tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(angle of elevation) = (tower height)/(length of shadow)

Solving for the length of shadow, we have ...

  length of shadow = (tower height)/tan(angle of elevation)

The difference in shadow lengths is 2x for the two different angles, so we have ...

  2x = 24.57/tan(30°) -24.57/tan(45°)

__

Dividing by 2 and factoring out the tower height, we have ...

  x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)

  x ≈ 8.993244

The value of x is about 8.99.

Answer:

see explanation

Step-by-step explanation:

a translation of 3 squares right means add 3 to the x- coordinate

a translation of 3 squares up means add 3 to the y- coordinate

then

(1, 1 ) → (1 + 3, 1 + 3 ) → (4, 4 )

(3, 1 ) → (3 + 3, 1 + 3 ) → (6, 4 )

(1, 4 ) → (1 + 3, 4 + 3 ) → (4, 7 )

Answer:

Equation:  24x + 2(36) = 6(6x) or 24x + 72 = 36x Answer: x = 6

Step-by-step explanation:

24x + 72 = 36x
-24x           -24x
         72 = 12x
         /12    /12
           6 = x

Explanation:

The value of 'a' out front in y = a sin(bx) determines the amplitude.

The b term helps us compute the period, which is 2pi/b for sine, cosine, secant, and cosecant functions.

For example, y = 2sin(3x) has an amplitude of 2 and period of 2pi/3

For tangent and cotangent functions, the period would be pi/b.

Answer:

3.61cm^2

Step-by-step explanation:

1.9 * 1.9 = 3.61

Answer:

y = 40 degrees

Step-by-step explanation:

All three interior angles of a triangle sum to 180 degrees.

2y   + y+10  + 50 = 180

3y + 60 = 180

3y = 120

y = 40  

Answer:

1

Step-by-step explanation:

Raise -2 to the power of 3 = -8

9-8= 1

Answer:

1

Step-by-step explanation:

A number raised to the 3rd power is equal to that number multiplied by itself twice. Below I have expanded the expression to visualize this process. If this makes it more confusing, the main way is just to go from line 1 to line 4.

9 + (-2)³                          <---- Original expression

9 + (-2 x -2 x -2)             <---- (-2)³ expanded

9 + (4 x -2)                     <---- -2 times -2

9 + (-8)                           <---- 4 x -2                    

1                                     <---- 9 - 8

Considering the given function, we have that:

a) D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.

b) D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.

The distance that the family is from home, after t hours of driving, is given by:

D(t) = 3260 - 55t.

Then, after 12 hours, the distance is given by D(12), that is:

D(12) = 3260 - 55 x 12 = 2600.

D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.

D(t)=2490, hence:

3260 - 55t = 2490

55t = 770

t = 770/55

t = 14

D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.

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Answer:

15

Step-by-step explanation:

Let 2n+1 be the first odd integer.

Therefore, the consecutive odd integers will be 2n+3 and 2n+5

If the sum of the consecutive odd integers is 51 then:

⇒ 2n + 1 + 2n + 3 + 2n + 5 = 51

⇒ 6n + 9 = 51

⇒ 6n = 42

⇒ n = 7

To find the values of the integers, substitute the found value of n into the expressions:

Therefore, the three consecutive odd integers that sum to 51 are 15, 17 and 19.  The smallest of which is 15.

Answer:

[tex](5x+3)(2x+1)[/tex]

Step-by-step explanation:

- Sum-product method

For a polynomial of the form [tex]ax^2+bx+c[/tex]

We rewrite the middle term as a sum of two terms whose product is

[tex]a*c = 10*3 = 30[/tex] and whose sum is [tex]b = 11[/tex]

[tex]10x^2 + 11x + 3[/tex]

[tex]10x^2 + 6x + 5x + 3 -- > (3*10 = 6*5), (6+5 = 11)[/tex]

- Factor using the greatest common factors (GCF)

[tex]2x(5x + 3) + 1(5x + 3)[/tex]

- Final Answer

[tex]= (5x+3)(2x+1)[/tex]

Answer:

no c is write

Step-by-step explanation:

10+5≥ 25

10-10+5≥ 25-10

0+5≥ 15

≥3 ans…

Answer: The correct answer choice A: ≥2

Step-by-step explanation:

10+5>25 is false

Let's solve your inequality step-by-step.

10x+5 ≥ 25

Subtract:

[tex]10x+5-5[/tex] ≥ [tex]25-5[/tex]

[tex]10x[/tex] ≥ [tex]20[/tex]

Divide:

[tex]\frac{10x}{10}[/tex] ≥ [tex]\frac{20}{10}[/tex]

[tex]x[/tex]≥[tex]2[/tex]

10+5≥25 is False: The left side 15 is less than the right side 25, which means that the given statement is false.

you may mean 10x+5≥25, if so your answer is A.

Answer:

8+7=15

Step-by-step explanation:

15-8=7

so if she adds 8 to 7 and she gets 15 she did it right.

Answer: Julia can use 7 + 8 = 15 to check her work.

Step-by-step explanation: As fifteen minus eight equals seven, Julia can check her work by performing the inverse operation of seven plus eight to check her work. This is true as when c - b = a, a + b = c.

Answer:

y[tex]\leq[/tex]-2/5x + 2

Step-by-step explanation:

-2/5x + 2 would be the slope and y intercept of the line

The line is solid, so it has to be either less than or equal to or greater than or equal to

It is shaded below the line, which means it has to be less than.  you can tell this by looking at the closed end of the inequality sign. If it points left, you shade below, if it points right, you shade above.

The independent variable represents the number of years that Daniel has worked.

The dependent variable is the total salary of Daniel. This is because it depends on the number of years worked.

M(5) is $80,000.

The independent variable is that is given. The dependent variable is the variable that is being  determined. It is usually affected by the independent variable.

M(5) = $60,000 + (4000 X 5) = $80,000

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Answer:

  (a)  SV/VW

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides in a right triangle. This problem also makes use of the properties of similar triangles:

__

The sine of angle U is given by ...

  Sin = Opposite/Hypotenuse

The side opposite angle U in ΔTUS is ST. The hypotenuse of that right triangle is side TU. This means the desired ratio is ...

  sin(U) = Opposite/Hypotenuse = ST/TU

In similar ΔVWS, angle W has the same measure as angle U. Its sine will be the ratio of the corresponding sides. The similarity statement ΔTUS~ΔVWS tells you that the side corresponding to ST is SV, and the side corresponding to TU is VW.

  sin(U) = sin(W) = SV/VW

Answer:

z=98 degrees

x=64 degrees

y=18 degrees

Step-by-step explanation:

y is congruent to 18 since theyre opposite of eachother, same with x and 64. find z by using the straight 180 line. (180=64+18+z, so z=98)

Answer:

v = 130

Step-by-step explanation:

substitute the given values for u, a and t into the equation

v = 32 + ( 9.8 × 10) = 32 + 98 = 130

Answer:

the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal

Answer:

I was taught like this.

Corresponding has emphasis on the word pond

Fish live in a pond

Therefore, it has to be an angle F

The geometric figures which could be this three-dimensional figure are:

A cross section can be defined as an exposed surface or shape that is formed when a cut is made through a three-dimensional figure.

In this scenario, the geometric figures which could be this three-dimensional figure are:

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Answer:

Below in bold.

Step-by-step explanation:

Total surface area = 1/2 * area of a sphere + area of the side o a cone

=  1/2 * 4 π r^2 + π r L

= 1/2 * 4 π 7^2 + π*7*25

=  307.876 + 549.779

= 857.65 in^2 to nearest hundredth.

Answer:

  36 tablets

Step-by-step explanation:

We are asked to find the number of tablets of a particular mass that are required to give a specific mass-to-volume ratio for a given volume of solution. The units used are all SI (metric) units.

__

The International System of units (abbreviated SI in all languages) defines seven base units and a number of derived units. The base unit for length is the meter. For mass, the base unit is the kilogram. The derived unit for volume is the liter, which is 1/1000 of a cubic meter.

Currently, there are 20 prefixes defined that signify powers of 10 ranging from 10^-24 to 10^24. These are used in front of the abbreviations for units. Useful here are the prefixes kilo- and milli-, standing for 10^3 and 10^-3, respectively. The relevant abbreviations are ...

In this problem, the volume of syrup used is 180 ml, or 180×10^-3 liters. The mass of medicine in one tablet is 10 mg, or 10×10^-3 grams.

__

We desire a solution with a concentration of 2 mg/ml. We want 180 ml of the solution, so the mass of medicine that needs to be incorporated is ...

  (180 ml)×(2 mg/ml) = 360 mg

number of tablets

Each tablet supplies 10 mg of medicine. To get 360 mg of medicine, we need n tablets, such that ...

  n(10 mg) = 360 mg

  n = (360 mg)/(10 mg) = 36 . . . . tablets

36 tablets of 10 mg each are needed to mix with 180 ml of syrup to give 2 mg/ml.

2y=x+10

3y=3x+15

2y-10=x

3y=3(2y-10)+15

2y-10=x

3y=6y-30+15

2y-10=x

0=3y+15

2y-10=x

3y=15

x=2y-10

y=5

2y=x+10

2×5=x+10

x=0

x=0, y=5

Answer:

35°

Step-by-step explanation:

If 2 angles are supplementary, that means they add up to 180 :

Now we make an equation and solve for x :

(4x+9) + (x+1) = 180

5x+10 = 180

5x = 170

x = 34

Now we find the measure of the smaller angle using our value of x :

x+1 = 34 +1

x+1 = 35

Hope this helped and have a good day

Answer:

1 / 1024

Step-by-step explanation:

Each flipping has 1/2 chance

In ten flippings:

[tex](\frac{1}{2} )^{10} =\frac{1^{10} }{2^{10} } =\frac{1}{1024}[/tex]

Hope this helps

The area of the circle formed when the plane passes through the center of the given sphere is: 15π cm².

Area of a circle = πr² (radius of the circle = r).

Given the following:

Radius of the circle = √((radius of sphere)² - (distance of the  plane  from  the  center of sphere²)) = √(8² - 7²)

Radius of the circle = 3.87 cm

Area of the circle = π(3.87²) ≈ 15π cm².

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By using the Pythagoras theorem, the length of the ladder will be 13.6 feet.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Jennifer needs to use a ladder to clean a second-floor window on a building.

If the window is 13 ft above the ground and the base of the ladder is 4 ft from the building.

Then the length of the ladder will be

H² = 13² + 4²

H² = 169 + 16

H² = 185

H = 13.6 ft

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Answer: 4^2+13^2=x^2

Step-by-step explanation:

trust

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the slope of (-4, -7) and (-2, -19).

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's the slope formula:

[tex]\star~\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]

Where

y2 and y1 are y-coordinates

x2 and x1 are x-coordinates

Input the values, which are:

-19: y2

-2: x2

-7: y1

-4: x1

[tex]\star~\mathrm{\cfrac{-19-(-7)}{-2-(-4)}}[/tex]

[tex]\star~\mathrm{\cfrac{-19+7}{-2+4}}[/tex]

Simplify!

[tex]\star~\mathrm{\cfrac{-12}{2}}[/tex]

[tex]\star~\mathrm{-6}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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