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Readme [11.4K]
3 years ago
12

What is the area of this composite shape?

Mathematics
2 answers:
jasenka [17]3 years ago
8 0

Answer:

52 in^2

Step-by-step explanation:

8 times 7 equals 56 ( larger square part)

1/2(3 times 4) equals 6

White raven [17]3 years ago
4 0

Answer:

Labeled the diagram as shown below.,

In rectangle ABCD:

Area of the rectangle(A) is given by:

From the diagram:

AB = DC = 8 in. and AD = BC = 7 in.

⇒Length = 7 in. and width = 8 in.

then;

Next, find the area of triangle OAE:

In triangle OAE

Base = AE = 3 in.

Height = OA = 4 in.

then;

Area of this composite figure = area of rectangle ABCD+ area of triangle OAE

⇒Area of this composite figure = 56 +6 = 62 square inches.

therefore,  area of this composite shape is, 62 in²

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What is the y-intercept, axis of symmetry and vertex of the following function.
Pepsi [2]

Complete the square:

F(x) = -3x² - 6x - 5

F(x) = -3 (x² + 2x) - 5

F(x) = -3 (x² + 2x + 1 - 1) - 5

F(x) = -3 ((x + 1)² - 1) - 5

F(x) = -3 (x + 1)² + 3 - 5

F(x) = -3 (x + 1)² - 2

The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :

F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5

The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.

The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from

(x + 1)² ≥ 0   ⇒   -3 (x + 1)² ≤ 0   ⇒   -3 (x + 1)² - 2 ≤ -2

This is to say, every point on the parabola has a y-coordinate no greater than -2.

As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.

4 0
2 years ago
Read 2 more answers
Evaluate x^2 − 4x + 5, when x = − 3
Gnom [1K]

Answer:

\huge\boxed{26}

Step-by-step explanation:

\sf x^2-4x+5\\Given \ that \ x = -3\\(-3)^2-4(-3)+5\\9+12+5\\26

3 0
3 years ago
Read 2 more answers
Please help if you can!
Dima020 [189]

Answer:

m' (-2, 4)

n' (-2, 1)

o' (3, 1)

p' (3, 4)

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
A truck can be rented from Company A for ​$70 a day plus ​$0.50 per mile. Company B charges ​$20 a day plus ​$0.60 per mile to r
r-ruslan [8.4K]

Answer:

The rental cost for Company A and Company B will be the same after 500 miles

Step-by-step explanation:

The total cost of renting a truck from Company A can be expressed as;

Total rental cost(Company A)=Cost per day+Total rate

where;

Cost per day=70

Total rate=rate per mile×number of miles (m)=(0.5×m)=0.5 m

replacing;

Total rental cost(Company A)=70+0.5 m...equation 1

2. The total cost of renting a truck from Company B can be expressed as;

Total rental cost(Company B)=Cost per day+Total rate

where;

Cost per day=20

Total rate=rate per mile×number of miles (m)=(0.6×m)=0.6 m

replacing;

Total rental cost(Company B)=20+0.6 m...equation 2

Equating equation 1 to equation 2

70+0.5 m=20+0.6 m

0.6 m-0.5 m=70-20

0.1 m=50

m=50/0.1

m=500 miles

The rental cost for Company A and Company B will be the same after 500 miles

7 0
3 years ago
a 12-ft-long ladder is leaning against a building. the ladder makes a 45 degree angle with the building. how far up the building
zhuklara [117]
12 cos45degree=8.486 ft
6 0
3 years ago
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