An architect build a scale model of a sports stadium that was 12 inches. The actual height of the building was 180 feet.


Which scale did the architect use to create the scale of the sports stadium?

Answer:

y = ¾x  

Step-by-step explanation:

y = mx + b, where

m = slope and

b = y-intercept

If slope = ¾ and y-intercept =0,  the equation is

y = ¾x

Answer:

Area of trapezoid = 32√3

Step-by-step explanation:

Using Pythagoras theorem

8² = (4√3)² + x²

64 = 48 + x²

x² = 64 - 48

x² = 16

x = √16

x = 4

Area of trapezoid = ½(a + b) h

Where a = 10 - 4 = 6

b = 10

h = 4√3

Area of trapezoid = ½(6 + 10) × 4√3

= ½ × 16 × 4√3

= 8 × 4√3

= 32√3

Answer:

NO SOLUTION

Step-by-step explanation:

Step 1:  Subtract 5 from both sides

|x| + 5 - 5 ≤ 1 - 5

|x| ≤ -4

x ≤ NO SOLUTION

Answer:  NO SOLUTION

A square root can’t be a negative value, so the root would be greater than or equal to zero.

Range:

Y>=O

[O, infinity)

Answer:

83

Step-by-step explanation:

Add the numbers together

Answer:

80

Step-by-step explanation:

14 + 16 = 30

30 + 11 = 41

41 + 2 = 43

43 + 6 = 49

49 + 6 = 55

55 + 15 = 70

70 + 2 = 72

72 + 11 = 83, which, rounded to the nearest tenth, is 80

Answer:

x < -6

Step-by-step explanation:

X/4 < -1.5

Multiply each side by 4

X/4*4 < -1.5*4

x < -6

Answer:

$449.8

Step-by-step explanation: 450-0.2

The question is about calculating the new price of a Hamilton multitouch watch which was priced originally at $450, and is reduced by 20%. The new selling price of the watch is $360.

The problem at hand is telling us that a Hamilton multitouch watch, which originally costs $450, is experiencing a price reduction of 0.2 or 20%. To calculate the new selling price, we need to multiply the original price of $450 by the reduction rate of 0.2 and then subtract that value from the original price.

The calculation would look like this: $450 * 0.2 = $90. This suggests that the watch is being discounted by $90.

Following, to calculate the new selling price, subtract the discount from the original price: $450 - $90 = $360. Thus, the new selling price of the Hamilton multitouch watch is $360.

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Answer:

its C or 16

Step-by-step explanation:

15 ft. 7 in is the sum of 6 feet 10 inches and 8 feet 9 inches.

6 feet 10 inches + 8 feet 9 inches

= 14 feet 19 inches

= 15 feet 7 inches

Mercury's distance = 5.8 x 10¹⁰

Venus' distance = 1.86 farther or more than Mercury's, namely 1.86(5.8 x 10¹⁰)

Earth's distance = 2.58 farther or more than Mercury's, namely 2.58(5.8 x 10¹⁰)

[tex]\bf \stackrel{\textit{venus' distance}}{1.86(5.8\times 10^{10})}\implies \begin{cases} 1.86(58000000000)\\ 107880000000\\ 1.0788\times 10^{11} \end{cases} \\\\\\ \stackrel{\textit{earth's distance}}{2.58(5.8\times 10^{10})}\implies \begin{cases} 2.58(58000000000)\\ 149640000000\\ 1.4964\times 10^{11} \end{cases}[/tex]

about how many meters farther is Earth's than Venus?  well, we can simply get their difference, we know the Earth is farther than Venus, so we can just subtract Venus' distance from Earth's to get the difference, namely 149640000000 - 107880000000.

[tex]\bf \stackrel{earth}{149640000000} - \stackrel{venus}{107880000000}~~ = ~~41760000000\implies \stackrel{\textit{rounded up}}{4.2\times 10^{10}}[/tex]

Answer:3xy

Step-by-step explanation:18x^2y^3= 3,6,x,x,y,y,y

6xy^2=. 3,2,x,y,y

3x^3y=. 3,x,x,x,y

All three have this in common a 3xy

The greatest common factor of the given polynomial's terms 18x^2y^3-6xy^2+3x^3y is 3xy. This is determined by factoring each term, and finding the greatest factor that occurs in all of the lists.

In mathematics, the greatest common factor (GCF) of a set of terms in a polynomial, is the largest term that divides each term exactly. To find the greatest common factor for the given polynomial 18x^2y^3-6xy^2+3x^3y, first, we list the factors for each term.

The term 18x^2y^3 factors as 2*3*3*x*x*y*y*y, the term -6xy^2 factors as -2*3*x*y*y, and the term 3x^3y factors as 3*x*x*x*y.

The greatest factor that occurs in all three lists is 3*x*y, so 3xy is the greatest common factor of the polynomial’s terms.

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f(–2) = 1

Solution:

The table represents a function.

            x               f(x)

           –6               3

           –2                1

             0                4

             3               –2

To find the value of f(–2):

f(–2) means the value of f(x) for the corresponding x value –2.

In the table, if the x value is –2, then f(x) is 1.

See the value of f(x) which correspond to x = –2.

Hence f(–2) = 1.

Answer:

x = 3

Step-by-step explanation:

(x - 1)2 = 4

how to get this solved is very simple.

first step to apply is the BODMAS RULE

B..................... bracket

O..................... of

D.....................Division

M.................... multiplication

A..................... addition

S.................... Subtraction

so (x - 1)2 = 4

we have,

2x - 2 = 4 ( by opening the bracket)

collect the like terms

2x = 4+2

divide both sides by 2

2x/2 = 6/2

x = 3

to check if your answer is correct put the value of x = 3 into the question and see if the right hand side will equal to the left handside

(x - 1)2 = 4

(3-1)2=4

2(2)=4

4=4.............................. proved

Answer

Distributive Property.

Step-by-step explanation:

First you solve for the first equation by multiplying 2 by 18 which is 36. Then 3 times 18 which is 54. Then you add them together to get 90.

Next you solve for the second equation by multiplying 5 by 18 which is 90.

Both of these equations are solved by the distributive property because your distributing the number outside of  the parenthesis.

Answer:

Answer : A   x=0

Step-by-step explanation:

hello :

f(x)= 2e^x + 1      graph red

g(x)= 1/2e^x + 5/2   graph bleue

2e^x + 1

= 1/2e^x + 5/2

by graphic solution   one solution x=0

Answer:

d) x=3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

[tex]\\4x^2-2x=30\\\\x=3\\4(3)^2-2(3)=30\\4(9) - 6 =30\\36 - 6 = 30\\30 = 30 \\\\x=4\\4(4)^2-2(4)=30\\4(16) - 8 =30\\64 - 8 = 30\\56\neq 30[/tex]

56  is not equal to 30

Answer:

[tex]\frac{3}{(2x+7)}[/tex]

Step-by-step explanation:

[tex]\frac{3x +3}{2x^2 + 9x + 7}[/tex]

[tex]\frac{3(x + 1)}{(2x + 7)(x + 1)}[/tex]

[tex]\frac{3}{(2x+7)}[/tex]

Answer:  [tex]\frac{3}{(2x+7)}[/tex]

GRAPH BELOW:

Answer:

A) -1

Step-by-step explanation:

The missing graph is attached.

The possible answers were:

-1

-2

-3

-4

The average rate of change of a function f(x) on a≤x≤b is given by:

[tex] \frac{f(b) - f(a)}{b - a} [/tex]

We want to find the best estimate of the average rate of change for the quadratic function on the interval 0 ≤ x ≤ 4.

From the graph, f(0)=0 and f(4)=-4

[tex] \frac{f(4) - f(0)}{4 - 0} = \frac{ - 4 - 0}{4 - 0} = \frac{ - 4}{4} = - 1[/tex]

The range of Ervin's scores is 55.

Range is the difference between the largest number and the smallest number.

To find the range of a set of values, first sort the values numerically (smallest to largest). With this set, it would look like this: 138, 142, 155, 165, 172, 193. Lastly, subtract 138 from 193 to find the range. By doing so, you will get 55 as an answer.

I hope this helps!

The range of ErvIn's scores is 55.

The range of ErvIn's scores is calculated by finding the difference between the highest and lowest scores.

Arrange the scores in numerical order: 138, 142, 155, 165, 172, 193.

Find the highest score: 193.

Find the lowest score: 138.

Subtract the lowest score from the highest score to find the range: 193 - 138 = 55.

Answer:

Supplementary

Step-by-step explanation:

Since the two angles add up to 180 degrees, they are supplementary

Answer:

y= 4x-6

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is its gradient and c is its y-intercept.

Let's find the gradient, m, first.

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Using the above formula,

[tex]m = \frac{10 - ( - 6)}{4 - 0} \\ m = \frac{10 + 6}{4} \\ m = \frac{16}{4} \\ m = 4[/tex]

Subst. the value of m into the equation.

y=4x+c

To find c, substitute a coordinate into the equation.

When x=0, y= -6,

-6= 4(0) +c

c= -6

Thus, the equation of the line is y= 4x -6.

Answer:

B

Step-by-step explanation:

From annual salary of 42,600, we have to subtract the following percentages:

Social Security:

0.062 * 42,600 = 2641.2

Medicare:

0.014 * 42,600 = 596.4

State Income Tax:

0.03 * 42,600 = 1278

Federal Income Tax:

0.13 * 42,600 = 5538

Total Deductions (from percentages) = 2641.2 + 596.4 + 1278 + 5538 = 10053.6

Now, remaining salary:

42,600 - 10053.6 = 32546.4 (annual)

Divided by 12 to get monthly:

32546.4 / 12 = 2712.2 (monthly)

Now, monthly deductions are:

260 + 280 = 540

Net Salary: 2712.2 -  540 =2172.2

Based on the information given his monthly net paycheck is: b. $2172.20.

Deduction

Social security=42,600×62%

Social security = 2641.2

Medicare=42,600×1.4%

Medicare = 596.4

State Income Tax= 42,600×3%

State Income tax = 1278

Federal Income Tax=42,600×13%

Federal Income Tax = 5538

Total Deductions = 2641.2 + 596.4 + 1278 + 5538

Total deduction= 10053.6

Net paycheck:

Net paycheck=(42,600 - 10,053.6)/12- (260 + 280)

Net paycheck=32,546.4/12-540

Net paycheck= 2712.2 -  540

Net paycheck=$2172.2

Therefore, his monthly net paycheck is: b. $2172.20.

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N = N₀* [tex](\frac{1}{2} )^{\frac{t}{h} }[/tex]

where N is how much you currently have

N₀ is the starting amount

t is the time

and h is the half life of the substance.

The half-life formula for a radioactive isotope is amount remaining = (amount initial) × e^(-t/t1/2), where e is the base of natural logarithms, t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. The formula can be used to calculate how much of a radioactive isotope remains after a certain amount of time.

The half-life formula for a radioactive isotope is given by:

amount remaining = (amount initial) × e^(-t/t1/2)

Here, e is the base of natural logarithms (approximately 2.71828182), t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. To evaluate the exponential function, you may need to use a calculator or an inverse logarithm function. It is important to note that the length of time t does not need to be an exact multiple of half-lives.

Answer:

After 4 more days

Step-by-step explanation:

The remaining amount of money needed to reach the goal is $200 this is because 1000-800=200

Now we divide the 200 by the amount Karen  earns a day

200/50=4

That means after 4 more days Karen will have $1000

C. Is your answer

y=−52+8x

following expression  [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] is equal to  [tex]-4x[/tex] . Kindly match with your options!

Step-by-step explanation:

Here we have , following expression to evaluate . 1/3(9 - 18x) + 1/4(8x - 12 or , [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] :

⇒ [tex]\frac{1}{3}(9 - 18x) + \frac{1}{4}(8x - 12)[/tex]

⇒ [tex]\frac{1(4)}{3(4)}(9 - 18x) + \frac{1(3)}{4(3)}(8x - 12)[/tex]

⇒ [tex]\frac{(9 - 18x)(4)}{3(4)} + \frac{(8x - 12)(3)}{4(3)}[/tex]           { Making denominator of both terms same ! }

⇒ [tex]\frac{(9 - 18x)(4)+(8x - 12)(3)}{12}[/tex]

⇒ [tex]\frac{9(4) - 18(4)x+8(3)x - 12(3)}{12}[/tex]

⇒ [tex]\frac{36- 72x+24x - 36}{12}[/tex]

⇒ [tex]\frac{ -48x}{12}[/tex]           { Simplifying even further }

⇒ [tex]-4x[/tex]

Therefore , following expression  [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] is equal to  [tex]-4x[/tex] . Kindly match with your options!

Final answer:

The equivalent expression for 1/3(9 - 18x) + 1/4(8x - 12) is -4x.

Explanation:

The given expression is 1/3(9 - 18x) + 1/4(8x - 12).

We need to distribute the fractions across the terms inside the parentheses:

Therefore, the equivalent expression is -4x.

24h=d.

if you multiply 24 by the number of hours than you will get the distance.

if you traveled for 2hours than you would have traveled 48miles because if you multiply 24 by 2 you get 48.

In the equation 24 is distance traveled in 1 hour.

Answer:

24h=d

Step-by-step explanation:

0=0

2=48

4=96

7=168

its just multiples of 24 :)