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3 years ago

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The system of equations below represents the measures of 2 angles created by the diagonal of a rectangle: x + y = 90 y =1/5 What

is the measure of the greater angle? ° What is the measure of the smaller angle? °

1 answer:

madreJ [45]3 years ago

4 0

Answer:

The larger of the two angles is x, which is 75. y is the smaller angle at 15.

Step-by-step explanation:

In order to find these, we can use our solved value for y in the second equation to plug into the first equation. This method is called substitution.

x + y = 90

x + (1/5x) = 90

1.2x = 90

x = 75

Now we can plug that value into either equation to find y

y = 1/5x

y = 1/5(75)

y = 15

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A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. Th

Olegator [25]

Answer:

(a) 74553

(b) 172120

(c) 234802

Step-by-step explanation:

Given

$y = \frac{340110}{1 + 377e^{-0.259t}}$

Solving (a): 1998

Year 1998 means that:

$t =1998 - 1980$

$t =18$

So, we have:

$y = \frac{340110}{1 + 377e^{-0.259*18}}$

$y = \frac{340110}{1 + 377e^{-4.662}}$

$y = \frac{340110}{1 + 3.562}$

$y = \frac{340110}{4.562}$

$y = 74553$ --- approximated

Solving (b): 2003

Year 2003 means that:

$t = 2003 - 1980$

$t =23$

So, we have:

$y = \frac{340110}{1 + 377e^{-0.259*23}}$

$y = \frac{340110}{1 + 377e^{-5.957}}$

$y = \frac{340110}{1 + 0.976}$

$y = \frac{340110}{1.976}$

$y = 172120$ --- approximated

Solving (c): 2006

Year 2006 means that:

$t = 2006 - 1980$

$t =26$

So, we have:

$y = \frac{340110}{1 + 377e^{-0.259*26}}$

$y = \frac{340110}{1 + 377e^{-6.734}}$

$y = \frac{340110}{1 + 0.4485}$

$y = \frac{340110}{1.4485}$

$y = 234802$ --- approximated

3 0

2 years ago

The weight of a child in 1990 was 40 lb. By 2005, the child's weight

Maslowich

Answer:

225%

Step-by-step explanation:

1. Divide the new weight by the original weight.

90/40 = 2.25.

2. Multiply by 100 to get the percentage.

2.25 x 100 = 225%

5 0

3 years ago

Consider functions f and g.1 + 12f(1) = 12 + 4. – 12for * # 2 and 7 -64.2 – 16. + 1641 +48for a # -12 Which expression is equal

lisabon 2012 [21]

Given the following functions below,

$\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}\text{ and} \\ g(x)=\frac{4x^2-16x+16}{4x+48} \end{gathered}$

Factorising the denominators of both functions,

Factorising the denominator of f(x),

$\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}=\frac{x+12}{x^2+6x-2x-12}=\frac{x+12}{x(x+6)-2(x+6)}=\frac{x+12}{(x-2)(x+6)} \\ f(x)=\frac{x+12}{(x-2)(x+6)} \end{gathered}$

Factorising the denominator of g(x),

$\begin{gathered} g(x)=\frac{4x^2-16x+16}{4x+48}=\frac{4(x^2-4x+4)}{4(x+12)} \\ \text{Cancel out 4 from both numerator and denominator} \\ g(x)=\frac{x^2-4x+4}{x+12}=\frac{x^2-2x-2x+4}{x+12}=\frac{x(x-2)-2(x-2)}{x+12}=\frac{(x-2)^2}{x+12} \\ g(x)=\frac{(x-2)^2}{x+12} \end{gathered}$

Multiplying both functions,

$undefined$

4 0

1 year ago

In a survey of employees at a fast food restaurant, it was determined that 15 cooked food, 12 washed dishes, 21 operated the

andre [41]

This question is incomplete

Complete Question

In a survey of employees at a fast food restaurant, it was determined that 15 cooked food, 12 washed dishes, 21 operated the cash register, 7 cooked food and washed dishes, 6 cooked food and operated the cash register, 6washed dishes and operated the cash register, 4 did all three jobs, and 7 did none of these jobs

(a) Only cooked food?

(b) Only operate the cash register?

Answer:

(a) Only cooked food?

6

(b) Only operate the cash register?

13

Step-by-step explanation:

From the above question, we have the following information:

15 cooked food

12 washed dishes

21 operated the cash register

7 cooked food and washed dishes

6 cooked food and operated the cash register

6washed dishes and operated the cash register

4 did all three jobs

7 did none of these jobs

(a) Only cooked food?

This would be calculated as

Number of people that cooked food + Number of people that did all three jobs - Number of people that cooked food and washed dishes - Number of people that cooked food and operated the cash

= 15 + 4 - 7 - 6

= 19 - 13

= 6

Therefore ,only 6 people cooked food

(b) Only operate the cash register?

This would be calculated as

Number of people that operated cash register + Number of people that did all three jobs - Number of people that cooked food and operated the cash register - Number of people that washed dishes and operated the cash register

= 21 + 4 - 6 - 6

= 25 - 12

= 13

Therefore, only 13 people operated cash register.

7 0

3 years ago

Suppose ΔXYZ is given, and you want to construct ΔABC so that the triangles are congruent. Which constructions would guarantee t

bekas [8.4K]

Answer:

A: constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and CA ≅ ZX

C: constructing ΔABC so that AB ≅ XY, CA ≅ ZX, and ∠A ≅ ∠X

Step-by-step explanation:

* Lets revise the ways of constructing a triangle

- There are 3 ways to construct a triangle

# You must have length of one side and measures of two angles which

are the endpoint of the side

# You must have a length of two sides and the measure of the including

angle between the two sides

# You must have the length of the 3 sides

* Lets solve the problem

∵ Δ XYZ ≅ Δ ABC

∴ XY = AB , YZ = BC , ZX = CA

∴ m∠ X = m∠ A , m∠ Y = m∠ B , m∠ Z = m∠ C

- To construct Δ ABC You can use:

# The length of the 3 sides

∵ AB ≅ XY , BC ≅ YZ , CA ≅ ZX

∴ constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and CA ≅ ZX ⇒ A

# The length of two sides and the measure of the including angle

∵ AB ≅ XY , CA = ZX

∵ The including angles between the sides are ∠A and ∠X

∴ constructing ΔABC so that AB ≅ XY, CA ≅ ZX, and ∠A ≅ ∠X ⇒ C

# The length of one side and the measures of two angles which are

the endpoints of the side

∵ CA ≅ ZX

∵ The end points are C , A and Z , X

∴ constructing ΔABC so that CA ≅ ZX, ∠A ≅ ∠X, and ∠C ≅ ∠Z

- But this answer not in the choices

∴ The answer is A and C

4 0

3 years ago

Read 2 more answers