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Ksenya-84 [330]

2 years ago

9

A children's birthday party at an indoor play center costs $50 to rent the space and $6.25 per child. Gina wants to spend no mor

e than $100 on her son's fourth birthday party. Write an inequality for the number of children who can attend the birthday party, and solve the inequality.
A) 50 + 6.25x 100; x>8
B) 50 + 6.25x 100; x 8
D) 50 + 6.25x 100; x<8

1 answer:

Vedmedyk [2.9K]2 years ago

5 0

Answer:

D

Step-by-step explanation:

100>50 +6.25x, subtract 50 from both sides

50>6.25x, divide both sides by 6.25

8>x or x<8

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The difference of the squares of two positive consecutive even integers is 44 find the integers use the fact that if X represent

TiliK225 [7]

Answer:

The 2 integers are 10 and 12

Step-by-step explanation:

Translate it into english

"The difference (some subtraction) of the squares of two positive consecutive integers ( $x^2$ and $(x+2)^2$ ) is (=) 44 (44)"

this means the following:

$(x+2)^2-x^2=44$

solve for x to find the smaller integer

first, expand

$(x^2+4x+4)-x^2=44$

$x^2+4x+4-x^2=44$

$4x+4=44$

$4x=40$

$x=10\rightarrow x+2=10+2=12$

The 2 integers are 10 and 12

3 0

2 years ago

∆ ABC is similar to ∆DEF and their areas are respectively 64cm² and 121cm². If EF = 15.4cm then find BC.

lyudmila [28]

${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

★ ∆ ABC is similar to ∆DEF

★ Area of triangle ABC = 64cm²

★ Area of triangle DEF = 121cm²

★ Side EF = 15.4 cm

${\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}$

★ Side BC

${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

Since, ∆ ABC is similar to ∆DEF

[ Whenever two traingles are similar, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. ]

$\therefore \tt \boxed{ \tt \dfrac{area( \triangle \: ABC )}{area( \triangle \: DEF)} = { \bigg(\frac{BC}{EF} \bigg)}^{2} }$

❍ <u>Putting the</u><u> values</u>, [Given by the question]

• Area of triangle ABC = 64cm²

• Area of triangle DEF = 121cm²

• Side EF = 15.4 cm

$\implies \tt \dfrac{64 \: {cm}^{2} }{12 \: {cm}^{2} } = { \bigg( \dfrac{BC}{15.4 \: cm} \bigg) }^{2}$

❍ <u>By solving we get,</u>

$\implies \tt \sqrt{\dfrac{{64 \: cm}^{2} }{ 121 \: {cm}^{2} }} = \bigg( \dfrac{BC}{15.4 \: cm} \bigg)$

$\implies \tt \sqrt{\dfrac{{(8 \: cm)}^{2} }{ {(11 \: cm)}^{2} }} = \bigg( \dfrac{BC}{15.4 \: cm} \bigg)$

$\implies \tt \dfrac{8 \: cm}{11 \: cm} = \dfrac{BC}{15.4 \: cm}$

$\implies \tt \dfrac{8 \: cm \times 15.4 \: cm}{11 \: cm} = BC$

$\implies \tt \dfrac{123.2 }{11 } cm = BC$

$\implies \tt \purple{ 11.2 \: cm} = BC$

<u>Hence, BC = 11.2 cm.</u>

${\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}$

★ Figure in attachment.

$\rule{280pt}{2pt}$

4 0

2 years ago

The drill team at Hill Middle School made 120 spirit pins to sell for a fundraiser. After the fundraiser, the team had 18 pins l

Marizza181 [45]

no 1) is 85%

no 2) is 32 - 80 = -48

3 0

3 years ago

Solve 9/10=z/8 . Round to the nearest tenth.

kompoz [17]

$\boxed {Question}$
$\frac{9}{10} = \frac{z}{8}$

$\boxed {Cross \ multiply}$
$10z = 8 \times 9$

$\boxed {Evaluate}$
$10z = 72$
$z = 72 \div 10$
$z = 7.2$

$\Longrightarrow \bf \ Answer \ : \ z = 7.2$

4 0

3 years ago

-3(-5)(-4)<br><br> i need help

tamaranim1 [39]

Answer:

If you are asking -3 times -5 times -4, then the answer -60

Step-by-step explanation:

-3*-5=15

15*-4=-60

5 0

3 years ago

Read 2 more answers