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creativ13 [48]
3 years ago
15

Need help with this math lesson

Mathematics
1 answer:
ki77a [65]3 years ago
3 0

Rational numbers are numbers that can be turned into fractions. So A, C, D, E, F, G, H, and I are rational numbers

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Which of the following are solution to 2X squared minus 8X -90
svetlana [45]

Answer:

2(x+5)*(x-9)

Step-by-step explanation:

4 0
3 years ago
What is 58.65 with a 15% tip?
11111nata11111 [884]
X/58.65 = 15/100

(58.65*15)/100 = tip
6 0
2 years ago
Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B a
evablogger [386]

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1=\frac{1}{2} *PQ*RM

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2=\frac{1}{2} *SR*PN

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1=\frac{1}{2}*PQ*h

S2=\frac{1}{2}*SR*h

Adding them together, we get the area of the whole trapezoid:

S=S1+S2=\frac{1}{2} (PQ+SR)h,

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}

Simplifying, we have

=>A= \frac{ah+2b_{1+C} }{2}

Factoring we have,

=> A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2}  \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}

 But, a+ b_{1} + c  is equal to b_{2}, the longer base of our trapezoid.

Hence, A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}

We have discussed two ways by which we can derive area of a trapezoid.

Read to know more about Trapezoid

brainly.com/question/4758162?referrer=searchResults

#SPJ10

5 0
1 year ago
the first three terms of an arithmetic progression is (x + 1), (4 x - 2) and 6 x - 3 if the last term is 18 find the value of x​
lbvjy [14]

Answer:

2

Step-by-step explanation:

<u>Since it is AP, the common difference is same for any term:</u>

  • (4x - 2) - (x + 1) = (6x - 3) - (4x - 2)
  • 3x - 3 = 2x -1
  • 3x - 2x = 3 - 1
  • x= 2

<u>The first 3 terms are:</u>

  • 3, 6, 9

<u>Since the last term is 18, it means this AP has 6 terms:</u>

  • {3, 6, 9, 12, 15, 18}

<u>Answer: </u>as we need to find the value of x only, it is = 2

6 0
3 years ago
Lucy earns money babysitting. Her earnings and hours worked represent a direct variation. She worked for 4 hours and earned $25.
SashulF [63]

For this case we have that by definition, a direct variation is given in the form:

y = kx

Where:

k: It is the constant of proportionality

According to the statement we have to:

y = 25\\x = 4

Substituting:

25 = k4\\k = \frac {25} {4}k = 6.25\ for\ \frac {dollars} {hour}

On the other hand we have:

y = 4\\x = 25\\4 = k25\\k = \frac {4} {25}

k = 0.16\ for\ \frac {hours} {dollar}

Answer:

k = 6.25 for \frac {dollars} {hour}\\k = 0.16 for \frac {hours} {dollar}

7 0
3 years ago
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