Johnny measured a city park and made a scale drawing. The soccer field is 6 millimeters wide in the drawing. The actual field is 60 meters wide. What scale did Johnny use for the drawing?

Given:

In a right angle triangle ABC, altitude BD drawn to hypotenuse AC.

AD=3 and, AC=27.

To find:

The length of AB.

Solution:

Draw a figure by using the given information as shown below.

In triangle ABC and ADB,

[tex]\angle ABC\cong \angle ADB[/tex]              (Right angles)

[tex]\angle BAC\cong \angle DAB[/tex]              (Common angle)

[tex]\triangle ABC\sim \triangle ADB[/tex]              (AA similarity postulate)

We know that the corresponding parts of congruent triangles are proportional. So,

[tex]\dfrac{AC}{AB}=\dfrac{AB}{AD}[/tex]

After substituting the given values, we get

[tex]\dfrac{27}{AB}=\dfrac{AB}{3}[/tex]

[tex]27\times 3=AB\times AB[/tex]

[tex]81=AB^2[/tex]

Taking square root on both sides, we get

[tex]\sqrt{81}=AB[/tex]

[tex]9=AB[/tex]

Therefore, the length of AB is 9 units.

Answer:

53.63 feet

Step-by-step explanation:

Answer:

she needs at least a 93 on her next quiz

Step-by-step explanation:

hope this helps mate

Answer:

AB

Step-by-step explanation:

Definition of a chord

Answer:

[tex]y=18[/tex]

Step-by-step explanation:

[tex]y=x4-3x+18[/tex]

[tex]y=(0)4-3(0)+18[/tex]

[tex]y=0-0+18[/tex]

[tex]y=18[/tex]

Hope this helps

Answer:

6'12 inches long might be the answer

Step-by-step explanation:

Answer:

45 = ABD

Step-by-step explanation:

ABC = ABD + DBC

115 = ABD + 70

Subtract 70 from each side

115 - 70 = ABD

45 = ABD

Answer:

80% increase

Step-by-step explanation:

First, divide $0.25/$0.45, you get 0.8, turn it into a percent. 0.8=80%

There is an 80% increase.

Check work:

0.25x1.8=0.45

We multiply by 1.8 because 80% increase means 100% (itself) multiplied by 80% of itself, which gives us 180% or 1.8.

0.25x1.8=0.45 ✔️

Hope this helps!

:)

Answer:

Standard form: 62,080,126

Word form: Sixty-two million, eighty thousand, one hundred twenty-six

Expanded form: 60,000,000 + 2,000,000 + 80,000 + 100 + 20 + 6

Answer:

this means that for just an hour or 2 you're going to pay $25/hour which would be the initial value...but if you keep it for 5 hours you only pay $16/hour...the more you buy the less you pay per thing you're buying. ...this is a partial relationship, because there is an initial value greater than 0, and has a constant rate of change. a direct relationship would be when one variable did affects the other, meaning when one changes, so does the other ....it would mean the price got cheaper by a certain amount with every hour added ...in this example, the price doesn't get cheaper until hour 5, meaning the initial value is affected by the variable of hours rented...but is not a constant change, it is a partial change because it only changes under certain circumstances, (5 hours) rather than changing constantly with each passing hour....

Answer:

1/7^10

Step-by-step explanation:

7^-10

=1/7^10

Answer:

15

Step-by-step explanation:

According to propagation rule,

[tex]\frac{9}{3} =\frac{x}{5} \\45=3x\\x=15[/tex]

Therefore, option (B) is correct

Answer:

7.6 inches

Step-by-step explanation:

We solve the above question using the Law of Cosines.

The formula is given as:

h² = i² + j² - 2ij Cos H

h = √i² + j² - 2ij Cos H

From the above question:

i = 6.6 inches

j = 6.4 inches

Length h = ?

Angle H=62º.

Hence:

h= √6.6² + 6.4² - 2 × 6.6 × 64 × Cos 62

h = √43.56 + 40.96 - 84.48 × Cos 62

h = 7.64292 inches

Approximately to the nearest tenth, Length h = 7.6 inches

Answer:

6.7

Step-by-step explanation:

square root and round

Answer:

For each ticket sold they earned 3 dollars

Step-by-step explanation:

Answer:

1 + 1= 2

Step-by-step explanation:

because if u add 1 + 1 u will get 2

Answer:

hope it helps

Answer:

53,901

Step-by-step explanation:

Here is the complete question :

In which number does the digit 5 have a value that is ten times greater than the value of the digit 5 in the number 245,093?

43,567

45,248

53,901

562,011

In the number 245,093 :

3 = units

9 = tens

0 = hundred

5 = thousand

4 = ten thousand

2 = hundred thousand

the value of 5 in the number is 5000. the number that would have a value that it 10 times greater than 5 in 245,093 must occupy the value  of ten thousand.

looking through the options, it is only in 53,901 that 5 occupies a value of ten thousand

Answer:

The equation has 0 solutions (answer C).

Step-by-step explanation:

Starting with x = x - 9, we subtract x from both sides.  This leaves us with:

0 = -9,

which is never true.

The equation has 0 solutions (answer C).

Answer:

?

Step-by-step explanation:

?????????????????????????????

Answer:

[tex]y=-5x+2[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that the line passes through are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (1,-3) and (-3,17)

[tex]=\frac{17-(-3)}{-3-1}\\=\frac{17+3}{-3-1}\\=\frac{20}{-4}\\=-5[/tex]

Therefore the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-5x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-5x+b[/tex]

Plug in one of the given points and solve for b

[tex]-3=-5(1)+b\\-3=-5+b[/tex]

Add 5 to both sides of the equation to isolate b

[tex]-3+5=-5+b+5\\2=b[/tex]

Therefore, the y-intercept of the equation is 2. Plug this back into [tex]y=-5x+b[/tex]:

[tex]y=-5x+2[/tex]

I hope this helps!

Answer: 24/87 or 8/29

Step-by-step explanation:

24+13+15+10+15+10=87, the total amount of M&M's.

24 are brown, so 24/87 chance that he will draw a brown one.

24/87 = 8/29 simplified.

Answer:

I hope the above picture help you mate

have a great day

I did it in white board so that I can explain better.i hope you understand if u have any problem in understanding be sure to reach out

#liliflim

Answer:

see below

Step-by-step explanation:

all formulas of exponent given by:

[tex] \displaystyle {x}^{1} = x \stackrel{ \rm example}{ \iff} 2^{1} = 2[/tex]

[tex] \displaystyle{x}^{0} = 1\stackrel{ \rm example}{ \iff} 2^{0} = 1[/tex]

[tex] \rm \displaystyle {x}^{m} \cdot { x }^{n} = {x}^{m + n} \stackrel{ \rm example}{ \iff} x^{1 } \cdot {x}^{2} = x^{1 + 2 } = {x}^{3} [/tex]

[tex] \displaystyle \sqrt[n]{{x} }= x^{1/n} \stackrel{ \rm example}{ \iff} \sqrt[3]{x} = x^{1/3}[/tex]

[tex] \rm \displaystyle \frac{{x}^{m} }{ { x }^{n}} = {x}^{m - n} \stackrel{ \rm example}{ \iff} \frac{x^{3} }{ {x}^{1} } = x^{3 - 1} = {x}^{2} [/tex]

[tex] \rm \displaystyle ({x}^{m} {)}^{n} = {x}^{m n} \stackrel{ \rm example}{ \iff} (x^{1 } {)}^{2} = x^{ 2 } [/tex]

[tex] \rm \displaystyle ({x}^{m} {y}^{m} {)}^{n} = {x}^{m n} {y}^{mn} \stackrel{ \rm example}{ \iff} (x^{1 } { {y}^{1} )}^{2} = x^{ 2 } {y}^{2} [/tex]

[tex] \rm \displaystyle \left(\frac{{x}^{} }{ { y }^{}} \right) ^{m} = \frac{{x}^{m} }{ { y }^{n} } ^{} \stackrel{ \rm example}{ \iff} = \left(\frac{ {x}^{2} }{ {y}^{2} } \right)^{2} = \frac{ {x}^{4} }{ {y}^{4} }[/tex]

[tex] \displaystyle {x}^{ - n} = \frac{1}{ {x}^{n} } \stackrel{ \rm example}{ \iff} x^{ - 2} = \frac{1}{ {x}^{2} } [/tex]

Answer:

100 students were asked.

Step-by-step explanation:

11+21+ 33+ 23+ 12

11+12=  23

23+ 23= 46

46+ 21= 67

67+ 33= 100

Answer:

A.

Step-by-step explanation:

Answer:

19.8 m

Step-by-step explanation:

To find the height of the tree, we can use the trig ratio tangent:

θ = angle, h = height

tan θ [tex]= \frac{opposite}{adjacent}[/tex]

tan 33° = h / 30.5

h = (tan 33°)(30.5)

h = (0.6494)(30.5)

h = 19.8 m

Answer:

His time would be least likely greater than 27.9 minutes or smaller than 21.5 minutes.

Step-by-step explanation:

With an standard deviation of 3.2 minutes, it is clear that the maximum time taken by Roman to complete his run of 3 miles would be

Average time + standard deviation = 24.7 minutes + 3.2 minutes = 27.9 minutes

The minimum time taken by Roman to complete his run of 3 miles would be

Average time - standard deviation = 24.7 minutes  - 3.2 minutes = 21.5 minutes

Hence, his time would be least likely greater than 27.9 minutes or smaller than 21.5 minutes.

Answer:

x = -30

Step-by-step explanation:

g(x)= -2/3x+5

Let g(x) = 25

25= -2/3x+5

Subtract 5 from each side

25-5= -2/3x+5-5

20 = -2/3x

Multiply each side by -3/2

-3/2 * 20 = -3/2 * -2/3 x

-30 = x

Answer:

x = -30

Step-by-step explanation:

g(x)= -2/3x+5

25 = -2/3x + 5

20 = -2/3x

x = -30

Answer:

Al 8

Step-by-step explanation:

The minute hand is pointing to 20 minutes later at the number 8.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The minute hand is pointing to the 4.

Now,

Since, The minute hand is pointing to the 4.

Hence, The value of number after pointing to 20 minutes later is,

We know that;

Every 5 minutes gives 1 point.

⇒ 20 / 5

⇒ 4

Thus, The minute hand is pointing to 20 minutes later is,

⇒ 4 + 4

⇒ 8

Learn more about the multiply visit:

https://brainly.com/question/14176303

#SPJ2

Answer: 3 ohms

Step-by-step explanation:

Answer:

The angles are 78° and 102°.

Step-by-step explanation:

Let the one angle is y and the other number if y + 24.

The sum of the angles of the linear pair is 180°.

So, according to the question

y + y + 24 = 180

2 y = 180 - 24

2 y = 156

y = 78°

So, one angle is 78° and the other is 78° + 24° = 102°.

Answer:

y=3/5x+1

Step-by-step explanation:

Hi there!

We are given the equation -3x+5y=-8 and we want to find the equation of the line that is parallel to -3x+5y=-8 and contains the point (-15,-8)

parallel lines have the same slopes, but different y intercepts.

So let's first find the slope of -3x+5y=-8

We can do this by converting the equation from standard form (ax+by=c where a, b, and c are free coefficients (numbers)) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

add 3x to both sides

5y=3x-8

divide by 5 on both sides

y=3/5x-8/5

3/5 is in the place of where m is, so that means that 3/5 is the slope of the line

we can write the equation of the new line in slope-intercept form.

Here it is so far:

y=3/5x+b

we need to find b

Because the line will pass through the point (-15,-8), we can use it to solve for b

substitute -15 as x and -8 as y

-8=3/5(-15)+b

multiply

-8=-9+b

add 9 to both sides

1=b

substitute 1 as b into the equation

y=3/5x+1

There's the equation of the line :)

Hope this helps!