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3 years ago

13

A carpenter trims a triangular peak of a house with three 7-ft pieces of molding. The carpenter uses 21 ft of molding to trim a

second triangular peak. Are the two triangles formed congruent? Explain.

1 answer:

Burka [1]3 years ago

5 0

They should be, 3 pieces of 7ft is 21ft, and if the other triangle is 21ft then they should be congruent.

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Lisa, an experience shipping clerk, can fill a certain order in 10 hours. Bill, a new clerk, needs 13 hours to do the same job.

Lelu [443]

I think 11 hours and 30 minutes

7 0

3 years ago

Which equation represents a parabola that opens upward has a minimum at x=3 and has a line of symmetry at x=3

umka2103 [35]

Answer:

$y=x^2-6x+5$

Step-by-step explanation:

Let us consider the equation $y=x^2-6x+5$

For a quadratic equation in a standard form, $y=ax^2+bx+c$ , the axis of symmetry is the vertical line $x = \frac{-b}{2a}$ .

Here in this case we have, $a=1, b=-6 , c =5$

Putting the values we get,

$x = \frac{-(-6)}{2\times 1} = \frac{6}{2} =3$

We can see that the axis of symmetry is x=3 and the graph is giving minimum at x=3.

Therefore, the required equation is $y=x^2-6x+5$ . Refer the image attached.

4 0

3 years ago

Read 2 more answers

Convert 14ML (megalitres) iinto kilolitres

irakobra [83]

Answer:

14000Kilolitres

Step-by-step explanation:

$1megalitre = 1000kilolitres \\$

$14megalitres = xkilolitres$

Cross multiply

$14 \times 1000 = xkilolitres$

$14megaitres = 14000kilolitres$

6 0

3 years ago

What is the area of the composite figure? (use 3.14 for pi). Explain how you arrived at your answer. Please round to the nearest

maksim [4K]

The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.

Step-by-step explanation:

The given is,

Given diagram is combination of Rectangle and Semi circle.

Step:1

Res the attachment,

Area of given diagram = Area of A + Area of B..............(1)

Step:2

For A,

The A section in the given diagram is semi circle,

Diameter of semi circle = Total distance - ( 2+3)

( ∵ 2, 3 are top distance in the given diagram)

$= 10 - 5$

Diameter, d = 5 cm

Radius, $r = \frac{d}{2}$

$r = \frac{5}{2}$

r = 2.5 cm

Area, $A_{A} = \frac {\pi r^{2} }{2}$ ........................(2)

$A_{A} = \frac {\pi (2.5)^{2} }{2}$

$= \frac {\pi ( 6.25) }{2}$

$= \frac{19.63}{2}$

$A_{A} = 9.8174 cm^{2}$

Step:3

For B,

Area of rectangle is,

$A_{B} =lb$ .....................(3)

Where, l - Length = 10 cm

b - Width = 2 cm

Equation (3) become,

$= (10)(2)$

$= 20$

Area of B, $A_{B}$ = 20 $cm^{2}$

Step:4

From the equation (1),

Area of given diagram = 20+ 9.81747

Area = 29.817 square centimeters

Result:

The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.

5 0

3 years ago

A new movie is released each year for 8 years to go along with a popular book series. Each movie is 5 minutes longer than the la

Georgia [21]

Answer:

The total length of all 8 movies is 740 minutes

Step-by-step explanation:

* Lets revise the arithmetic series

- In the arithmetic series there is a constant difference between

each two consecutive numbers

- Ex:

# 2 , 5 , 8 , 11 , ………………………. (constant difference is 3)

# 5 , 10 , 15 , 20 , ………………………… (constant difference is 5)

# 12 , 10 , 8 , 6 , …………………………… (constant difference is -2)

* General term (nth term) of an Arithmetic series:

- If the first term is a and the common diffidence is d, then

U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d

So the nth term is Un = a + (n – 1)d, where n is the position of the

number in the series

- The formula to find the sum of n terms is

Sn = n/2 [a + l] , where l is the last term in the series

* Lets solve the problem

- A new movie is released each year for 8 years to go along with a

popular book series

∴ n = 8

- Each movie is 5 minutes longer than the last

∴ d = 5

- The first movie is 75 minutes long

∴ a = 75

- To find the total length of all 8 movies find the sum of the 8 terms

∵ Un = a + (n - 1)d

∵ The last term l is u8

∵ a = 75 , d = 5 , n = 8

∴ l = 75 + (8 - 1)(5) = 75 + 7(5) = 75 + 35 = 110

∴ l = 110

∵ Sn = n/2 [a + l]

∴ S8 = 8/2 [75 + 110] = 4 [185] = 740 minutes

* The total length of all 8 movies is 740 minutes

7 0

3 years ago