All categories

2 years ago

Jefferson High School is looking to expand its student parking lot by expanding the existing lot as

Mathematics

2 answers:

marissa [1.9K]2 years ago

3 0

brainly.com/question/3577543

This was already answered.

N76 [4]2 years ago

3 0

Answer:

The value of x is 60 ft.

Step-by-step explanation:

The area of a rectangle is

$A=length \times width$

The area of school is

$A=165\times 300=49500$

The area of old lot with school is

$A=(165+75)(300+75)=90000$

The area of old lot without school is

$A_1=90000-49500=40500$

The area of new lot with school is

$A=(165+75+x)(300+75+x)=x^2 + 615 x + 90000$

The area of old lot without school is

$A_2=x^2 + 615 x + 90000-49500=x^2 + 615 x + 40500$

It is given that the area of new parking lot will be twice the size of the old parking lot.

$2A_1=A_2$

$2(40500)=x^2 + 615 x + 40500$

$0=x^2 + 615 x -40500$

$0 = (x - 60) (x + 675)$

$x=60,-675$

The value of x can not be negative. Therefore the value of x is 60 ft.

You might be interested in

Applying the the properties of Congruence.

kolbaska11 [484]

Answer:

$LM = 35cm$ and $m \angle H = 98^o$

Step-by-step explanation:

For this problem, it is critical to understand what the opening statement means.

$Quadrilateral GHJK \cong quadrilateral LMNP$ means that each pair of <u>corresponding sides</u> between shapes are congruent (they have equal length), and each pair of <u>corresponding angles</u> between shapes are congruent (they have equal measure -- or same number of degrees when measured with a protractor).

So, it's important to be able to determine which pairs are the <u>corresponding</u> parts. When the congruence is given like $Quadrilateral GHJK \cong quadrilateral LMNP$ the letters are in a particular order. That order explains the order in which the shape is drawn out, and they put them in the same order for both shapes to mean that those are the letters that correspond with each other.

So, the first letter of each are a corresponding pair, the second letter of each are a corresponding pair, ... etc

In other words, point G and L correspond, point H and K correspond, etc.

To find the corresponding sides, the sides for these shapes are defined by a two adjacent letters (two letters next to each other in the name, or ... as it wraps around the end of the name... the first and last letter).

$\overline{GH} \cong \overline{LM}\\ \overline{HJ} \cong \overline{MN} \\\overline{JK} \cong \overline{NP}\\\overline{KG} \cong \overline{PL}$

While all of that is true, we only have a few sides with any information in them. Notice that side GH in the first shape, and sides PL & LM in the second shape are the only sides with anything written. So, we just need to determine which sides correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent sides above, we see that $\overline{GH} \cong \overline{LM}$

Since the sides (line segments) are congruent, their lengths are equal

$GH = LM$

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "x"

$GH = LM\\(4x+3)=(6x-13)$

$(4x+3)+13=(6x-13)+13\\4x+16=6x$

$(4x+16)-4x=(6x)-4x\\16=2x$

divide both sides by 2

$\frac{16}{2}=\frac{2x}{2}\\8=x$

So, to find the length, LM, we just need to look back at the expression for LM:

$LM = 6x-13\\LM = 6(8)-13\\LM = 48-13\\LM = 35$

remembering that the lengths are measured in centimeters (as indicated on the diagram): $LM = 35cm$

To find the corresponding angles, the angles for these shapes are defined by a single letter, so since the points correspond in order, the names of the shapes tell which angles are congruent.

$\angle G \cong \angle L\\\angle H \cong \angle M\\\angle J \cong \angle N\\\angle K \cong \angle P$

While all of that is true, we only have a few angles with any information in them. Notice that ∠H in the first shape, and ∠L & ∠M in the second shape are the only angles with anything written. So, we just need to determine which angles correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent angles above, we see that

$\angle H \cong \angle M$

Since the angles are congruent, their measures are equal

$m\angle H = m\angle M$

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "y"

$m\angle H = m\angle M\\(9y+17)=(11y-1)$

subtract 1 from both sides

$(9y+17)+1=(11y-1)+1\\9y+18=11y$

subtract 9y from both sides

$\\(9y+18)-9y=(11y)-9y\\18=2y$

divide both sides by 2

$\frac{18}{2}=\frac{2y}{2}\\9=y$

So, to find angle H, we just need to look back at the expression for the measure of angle H:

$m\angle H = 9y+17\\m\angle H = 9(9)+17\\m\angle H = 81+17\\m\angle H = 98$

remembering that the angle is measured in degrees (as indicated on the diagram): $m \angle H = 98^o$

6 0

1 year ago

Colleen is making raffle tickets for the school's give-away drawing. She wants to use the digits 2, 5, and 7 to make three-digit

daser333 [38]

Answer:

You can make 9 three Digit numbers

Step-by-step explanation:

The 9 three digit numbers are:

257

275

752

725

527

572

This can also be easily found out by multiplying the number of digits to the number of digits needed for the number, in this case, there are 3 digits, and the number must have 3 digits in them (without them repeating).

3 digits x 3 needed for the numbers = 9 three digit numbers

8 0

2 years ago

Jorge bought 6 large balloons for a party. This was 25% of all the balloons he bought. How many total balloons did Jorge buy sho

riadik2000 [5.3K]

Answer:

The answer would be 24 balloons in total.

Step-by-step explanation:

Jorge bought 6 large balloons, which was 25% of ALL the balloons he bought.

Meaning that since 6 is 25% of the number 24, he bought 24 balloons in total.

PROOF:

25% * 24 = 6

24 / 6 = 4

6 * 4 = 24

<h2>Mark me Brainliest Please.</h2>

8 0

2 years ago

Sum of two consercutive integers is -49

lianna [129]

The answer is B. Hard to explain but it is B.

8 0

2 years ago

The circumference of a circle varies directly as the diameter of a circle. When the diameter of a circle is 5, the circumference

Naya [18.7K]

Answer:

20.3 units

Step-by-step explanation:

Write and solve an equation involving ratios:

5 units 15.7 units

------------- = ----------------

9 units C

Cross-multiplying, we get 5C = 9(15.7), with C measured in "units."

Then 5C = 141.3, so that C = 141.3 units / 5 = 20.3 units.

5 0

2 years ago

Read 2 more answers