Evaluate each using the values given.

1. 6c(a+a+a); use a=1, and c=3

The distance between the bottom of the ladder and the ground's surface is 24.7 feet.

Given that a is the ground, b is the building, and c is the ladder.

Also the ground is perpendicular to the building, the ladder, the building, and the ground form a right triangle.

Therefore, the Pythagorean theorem can be applied as follows:

c² = a² + b²

According to the information in the problem, c is 30 feet, b is 17 feet, and we solve for a as follows:

(30 ft)² = a² + (17 ft)²

900 ft² = a² ₊ 289 ft²

900 ft² ₋ 289 ft² = a²

611 ft² = a²

a² = 611 ft²

a = √611 ft²

a = 24.71

rounding off to nearest tenth, so a = 24.7

Hence the bottom of the ladder is 24.7 feet far away from the base of the ground.

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Your question is incomplete. Please find the missing content here.

A 23-foot ladder is placed against a building. If the top of the ladder will lean against the building 17-feet high, how far away from the base of the building is the bottom of the ladder located?

Answer:

a) S varies inversely as G

[tex]S\propto\frac{1}{G}[/tex]

or  [tex]S=\frac{K}{G}[/tex]

b) S=4 when G=7

Step-by-step explanation:

a) Write the variation.

S varies inversely as G

[tex]S\propto\frac{1}{G}[/tex]

So, We can write: [tex]S=\frac{K}{G}[/tex]

Where k is constant of proportionality

b) Find S when G is 7.

Now, if S=8, G = 3.5 we will find K

[tex]S=\frac{K}{G}\\K=SG\\K=8\times 3.5\\K=28[/tex]

So, value of K= 28

Now, find S when G is 7

[tex]S=\frac{K}{G}\\S=\frac{28}{7}\\S=4[/tex]

So, S=4 when G=7

Answer:

Slope = 3/1 or 3

Y intercept = (0, -5) or 5

Step-by-step explanation:

The slope intercept form : y = mx+b shows that the m represents the place of the slope and the b represents the place of the y intercept.

I wrote the answer using this app

hope it helps :D

Answer:

(-2, -5)

(-1, -2)

(0, 1)

(1, 4)

(2, 7)

Step-by-step explanation:

Substitute x with each number and solve equation.

Using the  system of equations x+y+z=7200, 0.04x+0.11y+0.14z=805 and z=x+y+200, the value of x=1400,y=2100 and z=3700

Given,

The equations

x+y+z=7200

0.04x+0.11y+0.14z=805

z=x+y+200

Substitute the value of z in the first and second equations

x+y+x+y+200=7200

2x+2y+200=7200

2x+2y=7000

x+y=3500   (1)

Similarly

0.04x+0.11y+0.14(x+y+200)=805

0.04x+0.11y+0.14x+0.14y+28=805

0.18x+0.25y=777

Multiply the equation by  4

0.72x+y=3108   (2)

We have to use elimination method here

Subtract the equation (1) from (2)

x-0.72x=3500-3108

0.28x=392

x=1400

Then,

x+y=3500

1400+y=3500

y=2100

z= x+y+200

z=1400+2100+200

z=3700

Hence, using the  system of equations x+y+z=7200, 0.04x+0.11y+0.14z=805 and z=x+y+200, the value of x=1400,y=2100 and z=3700

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[tex]\textsf{Hey there!}[/tex]

[tex]\mathsf{\dfrac{4}{25} - \dfrac{-1}{2}}[/tex]

[tex]\textsf{Cross\ multiply and you should see what the result comes}[/tex]

[tex]\mathsf{New\ equation: \dfrac{8}{50} + \dfrac{-25}{50}}[/tex]

[tex]\mathsf{8 - 25 = -17\leftarrow \text{\bf{{NUMERATOR}}}}[/tex]

[tex]\mathsf{50 + 0 = 50\leftarrow \text{\bf{DENOMINATOR}}}[/tex]

[tex]\boxed{\boxed{{\boxed{\textsf{Therefore, your answer is most likely: \boxed{\boxed{{\huge{\mathsf{\bf{\dfrac{-17}{50}}}}}}}}}}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

Answer:

Five less than twelve times a number is represented by  12n - 5

Expressing word problems as Equations

Let the unknown nmber be represented as n

Such that twelve times the  number will be represented as 12 n

There fore Five less than twelve times the  number becomes 12n - 5

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1600\\ r=rate\to 1.4\%\to \frac{1.4}{100}\dotfill &0.014\\ t=years\dotfill &3 \end{cases} \\\\\\ A=1600e^{0.014\cdot 3} \implies A \approx 1668.63[/tex]

Answer: 6i

Step-by-step explanation:

Answer:

I will give you the link below to a PDF that one of my young friends made for someone who had this exact question.

Step-by-step explanation:

The appropriate domain for this situation is [tex]\{t : 0 \leq t \leq 1.5\ \& \: t \in \mathbb R \}[/tex] (that means t can be any real number and between 0 and 1.5 (both endpoints included)

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

For this case, we have  only those values of 't' as appropriate value, which are from t = 0 till the time when ball hits the ground, since after that the height will be constantly 0, but the height function will give negative values which doesn't model the situation correctly.

Thus, those values of t for which the equation [tex]h(t) = -16t^2 + 24t[/tex] correctly models the real world situation are said to be appropriate values of domain of this function.

The time when the ball will reach the ground will be when the height will be 0, thus,:

[tex]0 = -16t^2 + 24t\\2t^2 - 3t = 0\\(2t-3)(t) = 0\\t = 0, t = 3/2 = 1.5 \: \rm sec[/tex]

The height is 0 when ball starts going up(t=0), and when t = 1.5 the ball reaches ground.

Thus, the appropriate domain for modelling the situation is values of t in the interval [0, 1.5] (both endpoints are inclusive, as shown by big bracket).

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Answer:

B

Step-by-step explanation:

if its less than 1 it shrinks

The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

If a polygon is dilated by a scale factor = k

Rule to be followed as;

(x, y) → (kx, ky)

Here, k = Scale factor

If 0 < k < 1, size of the image will be reduced.

Similarly, k > 1, size of the image will be enlarged.

We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.

Rule used for the transformation,

(x, y) → (1/4x, 1/4y)

Here, the scale factor through which MNPQR has been dilated is 1/4.

Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.

Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.

Option (2) is the answer.

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Answer:

I think the second one!

Step-by-step explanation:

Note: Consider the below figure attached with this question.

Given:

[tex]a=3\sqrt{3}[/tex]

To find:

The value of b.

Solution:

In a right angled triangle,

[tex]\tan \theta = \dfrac{Perpendicular}{Base}[/tex]

For the given right angled triangle,

[tex]\tan \theta = \dfrac{a}{b}[/tex]

[tex]\tan (30^\circ) = \dfrac{3\sqrt{3}}{b}[/tex]

[tex]\dfrac{1}{\sqrt{3}} = \dfrac{3\sqrt{3}}{b}[/tex]

On cross multiplication, we get

[tex]1\times b=3\sqrt{3}\times \sqrt{3}[/tex]

[tex]b=3(3)[/tex]

[tex]b=9[/tex]

Therefore, the value of b is 9.

Answer:

You still would have $1,000

Step-by-step explanation:

In April, you lost 13% of your fund. So we will subtract it.

In May, you gain 13% back. The rate of change was 0%.

Therefore, you still have $1,000 dollars.

Answer: The answer is that you have $983.

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Substitute 7 for b

6 + 7 = 13

Answer:

It's 13.

Step-by-step explanation:

6+7=13

Answer:

Step-by-step explanation:

for first,

then solving this we get

Answer:

8/7

Step-by-step explanation:

0.8/0.7=8/7

Answer:8/7

Step-by-step explanation:

Answer:

C. n^3 - 16 = 48

Answer:

17,070

Step-by-step explanation:

Continue to move the decimal point to the right, and it adds a zero when the decimal places are all taken.

Answer:

10,070

Step-by-step explanation:

so 10 to the power of three is 1 with three 0s

so 1000

remember 10 cubed is 10 times 10 times 10 that equals 1000

then 1000 times 17.07 is 17070

this is a 2 step equation

Answer:

multiplication

Step-by-step explanation:

cuz it says "times greater"

Answer:

It means how may times can the other variable fit into that variable, so you would divide.

- For example: Bob has 6 flowers in his basket, but Sally has only 2 flowers in her basket.

    Q: How many times greater is Bob's basket of flowers than Sally's?

    A: Bob's basket is 3 times greater than Sally's (bc 6/2 = 3, or 2 can fit into 6           three times)

**please mark brainliest!!

Answer:

This expression can be written as 53-2m

Step-by-step explanation:

Sometimes it can help to reword the sentence...

2 times Mai's score is being subtracted from 53.

Use 'M' for Mai's score:

53-2m

Answer:

$140

Step-by-step explanation:

Orignal Price: $200

200 x 0.3

= 60

200 - 60

= 140

Answer:the phone will cost 140

Step-by-step explanation:

Answer:

y = 3x

Step-by-step explanation:

Equation of a Line

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

We are given the following values of the function: f(-1)=-3 and f(2)=6. The points are (-1,-3) and (2,6). The slope is:

[tex]\displaystyle m=\frac{6+3}{2+1}=\frac{9}{3}=3[/tex]

Now find the equation of the line using the second point:

y - 6 = 3 ( x - 2 )

Operating:

y - 6 = 3x - 6

Simplifying:

y = 3x

Answer:

The youth group bought 35 geraniums and 45 daisy plants.

Step-by-step explanation:

We can solve this using a system of equations:

x + y = 80

4x + 6y = 410

X = Geraniums

Y = Daisies

First, let's solve for a variable in the first equation. I am going to solve for y in the first equation:

x + y = 80

y = -x + 80

Now that we have solved for y we can plug that back in to the 2nd equation:

4x + 6(-x + 80) = 410

4x - 6x + 480 = 410

-2x + 480 = 410

-2x = -70

x = 35

Now that we have found the amount of geraniums we can plug it back into the first equation and solve for y:

35 + y = 80

y = 45

Therefore the youth group bought 35 geraniums and 45 daisy plants.

Check:

(35) + (45) = 80

80 = 80

4(35) + 6(45) = 410

140 + 270 = 410

410 = 410

I hope this helps!!

- Kay :)

Answer:

6800

Step-by-step explanation:

Answer:

A:90

B:120

Step-by-step explanation:

all you have to do is divide 360 by 4 and then divide 360 by 3

Answer:

The steps are :

[tex] {tan}^{2} θ - {cot}^{2} θ = {sec}^{2} θ(1 - {cot}^{2} θ)[/tex]

[tex]RHS = {sec}^{2} θ(1 - {cot}^{2} θ)[/tex]

[tex]RHS = (1 + {tan}^{2} θ)(1 - \frac{1}{ {tan}^{2} θ} )[/tex]

[tex]RHS = (1 + {tan}^{2} θ)( \frac{ {tan}^{2}θ - 1}{ {tan}^{2} θ} )[/tex]

[tex]RHS = - \frac{(1 + {tan}^{2}θ)(1 - {tan}^{2} θ)}{ {tan}^{2} θ}[/tex]

[tex]RHS = - \frac{(1 - {tan}^{4} θ)}{ {tan}^{2} θ} [/tex]

[tex]RHS = \frac{ {tan}^{4} θ - 1}{ {tan}^{2}θ } [/tex]

[tex]RHS = {tan}^{2} θ - \frac{1}{ {tan}^{2}θ } [/tex]

[tex]RHS = {tan}^{2} θ - {cot}^{2} θ[/tex]

[tex]RHS = LHS (proven)[/tex]