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malfutka [58]
2 years ago
5

Find the area of the shaded region.

Mathematics
1 answer:
kondor19780726 [428]2 years ago
7 0

The region is made up of

• a right triangle with short leg 10 m and hypotenuse 26 m

• a parallelogram with sides 40 m and 26 m (the 26-m side corresponds to the aforementioned hypotenuse)

• another triangle with two known legs of length 20 m and 26 m

Find the height of the right triangle using the Pythagorean theorem. If the height is h, then

(10 m)² + h² = (26 m)²   ⇒   h² = 576 m²   ⇒   h = 24 m

This height is common to all three shapes.

Now find the area of each shape.

• right triangle:

1/2 × (10 m) × (24 m) = 120 m²

• parallelogram:

(40 m) × (24 m) = 960 m²

• other triangle:

• 1/2 × (20 m) × (24 m) = 240 m²

Then the total area of the shaded region is 1320 m².

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A chocolate bar 13cm long is cut into 2 equal pieces. How long will each piece be?
Mashcka [7]

Answer:

The answer is 6.5

Step-by-step explanation:

All you have to do is divide 13 by 2.

3 0
3 years ago
The function F is defined by F(x)=x^2+3X-10
vesna_86 [32]

Answer:

k = 13

smallest zero = -6

Step-by-step explanation:

f(x) is basically the function of x.

x could be any integer. f(x) is the solution of the function of x.

f(x) is defined as x² + 3x - 10

f(x) = x² + 3x - 10

Now, f(x+5) = x² + kx + 30

This statement here says that if the value of x is x+5, then the answer would be x² + kx + 30.

f(x) = x² + 3x - 10

f(x+5) = (x+5)² + 3(x+5) - 10

f(x+5) = x² + 10x + 25 + 3x + 15 - 10

f(x+5) = x² + 13x + 40 - 10

f(x+5) = x² + 13x + 30

x² + 13x + 30 = x² + kx + 30

hence, k = 13

Smallest zero = The smallest x value.

f(x+5) = x² + 13x + 30

Let's take f(x+5) = 0

x² + 13x + 30 = 0

which two numbers products give us 30 and add up to 13?

== 6 and 5

(x+6)(x+5) = 0

x+6 = 0

x = -6

x+5 = 0

x = -5

The two solutions are -6 and -5

The smallest out of these two is -6.  

7 0
4 years ago
In 7th grade there are 58 students with red-hair and 609 students with another color hair. The numbers of red-haired students in
mr_godi [17]

In 7th grade:

red-hair students =58

another color hair students =609

In 8th grade:

red-hair students =60

Let's assume

another color hair students =x

now, we are given

The numbers of red-haired students in 8th grade are proportional to the numbers in 7th

so,

\frac{60}{58} =\frac{x}{609}

now, we can solve for x

we get

x=609*\frac{60}{58}

we get

x=630

so, students have another color hair in 8th grade is 630.........Answer

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