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sergeinik [125]
3 years ago
5

If 20% of a school was made up of out-of-district students last year, but the number of out-of-district students increased by 50

% this year, without any change in total enrollment, what percent of the students is out-of-district this year?
Mathematics
1 answer:
Nadya [2.5K]3 years ago
4 0

Answer:

<h2>30% is enrolled out-of-district.</h2>

Step-by-step explanation:

According to the word problem, the number is increased by 50%.

To increase a number by a percent, multiply the number and the percent.

We can do this by changing both percents to decimals.

To change a percent to a decimal, divide it by 100.

20/100 = 0.2

50/100=0.5

The number is INCREASED by 50% so 0.5 would become 1.5.

0.2 * 1.5=0.3

<h2>0.3 = 30%.</h2>
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Two farmers each have triangular plots of land in the diagram below with approximate values shown for lengths in feet
Ray Of Light [21]

Answer:

  • a) Plots are similar
  • b) x= 5577 feet

Step-by-step explanation:

<em>Refer to attached</em>

<h3>Question</h3>
  • a) Are the plots of land similar?  
  • b) Find to the exact value of x and rounded to the nearest tenth?
<h3>Solution</h3>

The small triangle have missing angle of 180° - (52° + 58°) = 70°

This is indicating both triangles have same 3 angle measures.

Since all angles are same, the triangles are similar.

<u>Corresponding sides, against corresponding angles are:</u>

  • 6180 and 8240
  • x and 7436

<u>As per property of similarity, the ratio of corresponding sides is same</u>

  • 6180/8240 = x/7436
  • x = 6180*7436/8240
  • x = 5577 feet

4 0
4 years ago
Write a quadratic equation given the roots -1/3 and 5, show your work
Travka [436]

\boxed{(x - a)(x - b) = 0}

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

x =  -  \frac{1}{3}  \\ x = 5

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

(x +  \frac{1}{3} )(x -  5) = 0

Here we can convert the expression x+1/3 to this.

x +  \frac{1}{3}  = 0 \\  3x + 1 = 0

Rewrite the equation.

(3x + 1)(x - 5) = 0

Simplify by multiplying both expressions.

3 {x}^{2}  - 15x + x - 5 = 0 \\ 3 {x}^{2}  - 14x  - 5 = 0

<u>Answer</u><u> </u><u>Check</u>

Substitute the given roots in the equation.

3 {(5)}^{2}  - 14(5)  - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0

3( -  \frac{1}{3} )^{2}  - 14( -  \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) +  \frac{14}{3}  - 5 = 0 \\  \frac{1}{3}  +  \frac{14}{3}  -  \frac{15}{3}  = 0 \\  \frac{15}{3}  -  \frac{15}{3}  = 0 \\ 0 = 0

The equation is true for both roots.

<u>Answer</u>

\large \boxed {3 {x}^{2}  - 14x - 5 = 0}

8 0
3 years ago
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Mila [183]
It would be a lot better if you zoomed in for these since it’s nearly impossible to read.
4 0
3 years ago
Ryan has shells and 4 equal groups tanner has 9 more than Ryan tanner has 3 fewer shells than parker. Parker has 48 shells. How
Nataly [62]

Answer:

9.75

Step-by-step explanation:

48-3=45

45-9=38

38÷4=9.75

3 0
3 years ago
How to write 0.997 as a fraction?
cluponka [151]
997/1000, or just round it to 1. <em>If I helped click thanks please  (:</em>
6 0
4 years ago
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