Find the diameter of the circle. Assume the leg of the triangle is tangent to the circle. Round any decimals to the nearest tenth.

Answer:

x = 2

Step-by-step explanation:

[tex] log_{3}x(x+ 30) = log_{3}64 \\ x(x + 30) = 64 \\ {x}^{2} + 30x - 64 = 0 \\ x = 2 \: or \: x = - 32[/tex]

-32 is rejected because in logarithms you cannot use negative value so x=2

Answer:

1.70

Step-by-step explanation:

Logarithmic functions are the inverses of exponential functions. Hence, exponential functions can be expressed in logarithmic form whereas logarithmic function can be expressed in exponential form. Since log is a function, it is most correctly written as log.

Given that f(x) = log₁₀(x)

To find the value of f(50), we substitute x to be 50 in the logarithm function and solve:

f(50) = log₁₀(50)

f(50) = log₁₀(5 * 10) = log₁₀(5) + log₁₀(10)  

f(50) = 1 + log₁₀(5) = 1 + 0.70

f(50) = 1.70

Answer: 0; -2

Step-by-step explanation:

Data: y-intercept=x and slope=x

Equation=y=-2

Only step, Point out the y-intercept and slope

-2=y-intercept

0=slope

Reason: Since there is no visible slope, the placeholder would be 0 therefore the slope would be 0, -2 is the only number left so that means the only number that can be y-intercept is -2.

That is why the slope is 0 and the y-intercept is -2

I hope this helps!

Responder:

15 m e 75 m

Explicação passo a passo:

Deixar :

Largura = x

Comprimento = 5x

Perímetro = 180

Já o terreno tem uma forma retangular; usamos a relação;

Perímetro = 2 (comprimento + largura)

180 = 2 (5x + x)

180 = 2 (6x)

180 = 12x

180/12 = x

15 = x

Largura = x = 15 metros

Comprimento = 5x = 15 * 5 = 75 metros

Medida de largura e comprimento, respectivamente:

15 m e 75 m

Answer:

(a) The ball will hit the ground after 3 seconds

(b) The maximum height is 6.125

Step-by-step explanation:

Given

[tex]h(t) = -2t^2 +5t +3[/tex]

Solving (a): When the frisbee will hit the ground?

To do this, we set h(t) to 0

So, we have:

[tex]h(t) = -2t^2 +5t +3[/tex]

[tex]-2t^2 +5t +3=0[/tex]

Expand

[tex]-2t^2 +6t-t +3=0[/tex]

Factorize

[tex]-2t(t - 3) -1(t - 3) = 0[/tex]

Factor out t - 3

[tex](-2t -1)(t - 3) = 0[/tex]

Split:

[tex]-2t -1= 0\ or\ t - 3 = 0[/tex]

Solve for t in both equations

[tex]-2t =1\ or\ t = 3[/tex]

[tex]t =-\frac{1}{2}\ or\ t = 3[/tex]

Time can't be negative; So:

[tex]t = 3[/tex]

Solving (b): How height the frisbee will go?

First, we calculate time to reach the maximum height

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

Where:

[tex]h(t) = at^2 + bt + c[/tex]

By comparison:

[tex]a = -2,\ b =5,\ c =3[/tex]

So:

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

[tex]t = -\frac{5}{2*-2}[/tex]

[tex]t = \frac{5}{4}[/tex]

[tex]t = 1.25[/tex]

So, the maximum height is:

[tex]h_{max} = -2 * 1.25^2 + 5 * 1.25 + 3[/tex]

[tex]h_{max} = 6.125[/tex]

Answer:

a+4=11b

Step-by-step explanation:

Distributive property in mathematics means to multiply the sum by a number of two or more add-ons will provide the same result that each add-on multiplies by a single number and then together add the products.

for example a( b+c) = ab+ac

Therefore, applying distributive property in asked eapression

12(2a - 6b+ 8) = 21(2a−6b+8)

24a+72b+96 = 42a-126b+168

198b=18a+72

9a +36=99b

3a+12=33b

a+4=11b

The product of the two given fractions is 1/12.

Given that, 1/4 of 1/3.

The product of two fractions is the product of the numerators and the product of the denominators.

Product of two fractions = Product of their numerators / Product of their denominators

1/4 × 1/3

= (1×1)/(4×3)

= 1/12

Therefore, the product of the two given fractions is 1/12.

To learn more about the product of two fractions visit:

https://brainly.com/question/7335118.

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Answer:

[tex]x=4.02[/tex]

Step-by-step explanation:

The given triangle is a right triangle, this is indicated by the box around one of the angles, signifying that the angle is a (90) degree angle. Therefore, to solve this problem one must use trigonometric ratios. These ratios are used to describe the relationship between an angle and the sides in a right triangle.

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

Bear in mind, the names of the sides of the triangle are relative to the angle that one uses to describe it in the triangle. Therefore the (opposite) and (adjacent) sides will change depending on the angle one chooses to look at it from.

In this case, one is given the length of the side opposite the given angle. One is asked to find the measure of the side adjacent to the angle. Therefore, it would make the most sense to use the tangent (tan) ratio.

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

Substitute,

[tex]tan(20)=\frac{9}{x}[/tex]

Manipulate the equation such that it is solved for (x),

[tex]x=\frac{9}{tan(20)}[/tex]

Solve,

[tex]x=4.02[/tex]

Answer:

1) if he wants to do that he needs 0.6 gallons x 14 days = 8,4 gallons.

If the car starts with 14 gallons then he is able to ride 14 days without the warning light.

2) now he would need 0.6 gallons x 25 days = 15 gallons.

he only has 14 gallons so that is not possible.

3) no clue sorry

4) x= the days he can drive without the warning light

14-1,5 = 0,6.x

<=>12,5= 0,6.x

<=>20,833... = x

He can go 20 days without the warning light.

5) x= the days he can drive his car without seeing the warning light.

x.0,6<12,5

<=> x<20,833...

If he drives 20,833... days he will see the warning light so everything before that he won't see it.

Answer:

ummmmmm

Step-by-step explanation:

I don't know

Answer:

A

Step-by-step explanation:

c and d cannot be since the answer to sqrt((900f^6)/(100g^4)) is 3f³/g²

and not 30f something.

the best answer I see is correct is a.

Answer:

2 or -2

Step-by-step explanation:

x²+y²=2

(x+y)²-2xy=2

(x+y)²=4

x+y=±2

Answer: you're screwed dude. i had trouble with that two. you should pack up your stuff and run away before your mom finds out that you failed.

Step-by-step explanation:

Answer:

[tex]\frac{3}{4}[/tex] liter

Step-by-step explanation:

Given:

The given expression is:

[tex]\log_44[/tex]

To find:

The simplified value for the given expression.

Solution:

According to the property of logarithm,

[tex]log_aa=1[/tex]

We have,

[tex]\log_44[/tex]

Here, the base of the logarithm is 4 and the value inside the log is also 4, since these two values are same therefore the value of this expression is 1 by using the above property of logarithm.

[tex]\log_44=1[/tex]

Hence, the correct option is D.

By evaluating log4 4 without a calculator, we discover that it is equal to 1.

Step-by-step explanation:

everything can be found in the picture

Answer:

p = -6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

-5p = 24 - p

Step 2: Solve for p

howdy!!

yr answer is A. -6!!!!

goodluck!!! <33

Answer:

A) 2

Step-by-step explanation:

The law of sines is based on the proportionality of sides and angles in triangles. The law states that for the angles of a non-right triangle, each angle of the triangle has the same ratio of angle measure to sine value.

sin(A)/a=sin(B)/b=sin(C)/c

Substitute the known values into the law of sines to find a.

sin(60)/a=sin(60)/2

Answer:b im not sure

Step-by-step explanation:

ur welcome .  

By using substitution method, the number of nickels is 8 and the number of dimes is 13.

The substitution method is one of the algebraic methods to solve simultaneous linear equations. It involves substituting the value of any one of the variables from one equation into the other equation.

Representing the nickels as n and the dimes as d, and knowing that a nickel is 5 cents and a dime is 10 cents, we can write two equations from the given data.

n + d = 21

5n + 10d = 170

We use the first equation to derive a value for n.

n + d = 21

Subtract d from each side.

n + d - d = 21 - d

n = 21 - d.........................(1)

We now simplify the second equation by dividing all terms by 5.

5n + 10d = 170

[tex]\frac{5n}{5} +\frac{10d}{5} =\frac{170}{5}[/tex]

n + 2d = 24

substitute n = 21 - d in above equation

(21 - d) + 2d = 24

21 -d +2d = 24

21 + d = 24

d = 24 - 21

d = 13

n = 21 - d

n = 21 - 13

n = 8

Thus, the number of nickels is 8 and the number of dimes is 13.

Find out more information about substitution method here:

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Answer:24.5

Step-by-step explanation:30% of 35 is 10.5.  To find the 30% off- you multiply 35 times 0.3 which is 10.5.  Then you subtract the 10.5 from 35 for the total cost.  35-10.5=24.50

Answer:

the answer is 24.5

First you multiply 35 x 0.3 = 10.5, then subtract 10.5, 35-10= 24.5

Which in total the answer is 24.5

Answer:

144.84

Step-by-step explanation:

Answer:

No solution is possible from the information provided.

Step-by-step explanation:

"A floor plan of the room is shown below. "

You failed to provide the floor plan so it is not possible to answer your question.

Answer:

7 n and -4 I hope it will help you please follow me

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

−8(z+4)=−7(z+−4)+−3

Step 1: Simplify both sides of the equation.

-8z-32=-7z+25

Step 2: Add 7z to both sides.

-z-32=25

Step 3: Add 32 to both sides.

-z=57

Answer:-57

Step-by-step explanation:

-8(z+4) = -7(z+-4)+-3

-8z-32= -7z+28-3

-8z-32=-7z+25

-57=z

Answer:

[tex]A = 43.0^o[/tex]

[tex]B = 55.0^o[/tex]

[tex]BC = 20.0[/tex]

Step-by-step explanation:

I will solve this question with the attached triangle

From the attachment, we have:

[tex]\angle C =82^o[/tex]

[tex]AB = 29[/tex]

[tex]AC = 24[/tex]

Required

Solve the triangle

First, we calculate [tex]\angle B[/tex] using sine law:

[tex]\frac{AC}{\sin(B)} = \frac{AB}{\sin(C)}[/tex]

This gives:

[tex]\frac{24}{\sin(B)} = \frac{29}{\sin(82^o)}[/tex]

[tex]\frac{24}{\sin(B)} = \frac{29}{0.9903}[/tex]

Cross multiply

[tex]\sin(B) * 29 = 24 * 0.9903[/tex]

[tex]\sin(B) * 29 = 23.7672[/tex]

Divide both sides by 29

[tex]\sin(B) = 0.8196[/tex]

Take arcsin of both sides

[tex]B = \sin^{-1}(0.8196)[/tex]

[tex]B = 55.0^o[/tex]

Next, calculate [tex]\angle A[/tex] using:

[tex]A + B + C = 180^o[/tex] --- angles in a triangle

[tex]A + 55^o + 82^o = 180^o[/tex]

Collect like terms

[tex]A = 180^o-55.0^o - 82^o[/tex]

[tex]A = 43.0^o[/tex]

Next, calculate BC using sine laws

[tex]\frac{BC}{\sin(A)} = \frac{AB}{\sin(C)}[/tex]

This gives:

[tex]\frac{BC}{\sin(43.0)} = \frac{29}{\sin(82)}[/tex]

[tex]\frac{BC}{0.6820} = \frac{29}{0.9903}[/tex]

Make BC the subject

[tex]BC = \frac{29*0.6820}{0.9903}[/tex]

[tex]BC = 20.0[/tex]

Given:

In circle F, [tex]m\angle EFG=122^\circ,\ EF=16[/tex] units.

To find:

The length of arc EG.

Solution:

It is given that, [tex]m\angle EFG=122^\circ,\ EF=16[/tex] units. It means the central angle of arc EG is 122 degrees and the radius of the circle F is 16 units.

Formula for arc length is:

[tex]s=2\pi r\times \dfrac{\theta}{360^\circ }[/tex]

Where, r is the radius and [tex]\theta [/tex] is the central angle in degrees.

Putting [tex]r=16,\ \theta=122^\circ,\ \pi=3.14[/tex], we get

[tex]s=2(3.14)(16)\times \dfrac{122^\circ}{360^\circ }[/tex]

[tex]s=100.48\times \dfrac{61}{180}[/tex]

[tex]s=34.0515556[/tex]

[tex]s\approx 34.05[/tex]

Therefore, the length of arc EG is 34.05 units.

Answer:

8

Step-by-step explanation:

7779.949783~7779.94978

Answer:

The missing digit is 8

Step-by-step explanation:

An educated guess, but i'm pretty sure it's right

Answer:

2x-10

Step-by-step explanation:

2(x) - 2(5) = 2x - 10