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3 years ago

How can you check the correctness of a division answer that has no remainder?

Mathematics

1 answer:

Arada [10]3 years ago

8 0

Multiply the quotient and dividend to get the divisor<span />

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Express the sum 7 + 14 + 21 + 28 + . . . + 105 using sigma notation.

olasank [31]

7+14+21+28+...+105=1*7+2*7+3*7+4*7+...+15*7

15
∑7*n=7*1+7*2+7*3+7*4+...+15*7=7+14+21+28+...+105
n=1

6 0

2 years ago

The product of negative 5 and negative 4 increased by 3 equals

Goryan [66]

Answer : 23

-5 * -4 = 20 ( when you multiply 2 negatives the answer is always positive )

20 + 3 = 23

8 0

2 years ago

Craig has a building block in the shape of a rectangular pyramid. A net of which is shown below.

Alex787 [66]

Answer:

the answer is D: 294 sq. cm

Step-by-step explanation:

first you want to split the net into 4 triangles and 1 rectangle

a = 12 cm

b = 6 cm

d = 13 cm

calculate the surface area of the pyramid...

1st find the area of the rectangle base

Rectangle base area

b x a = (6 cm) (12 cm)

= 72 sq. cm

next find the area of the triangle on the left

Left triangle

1/2(b)(d) = 1/2 (6 cm)(13 cm)

= 1/2 (78 sq cm)

= 39 sq. cm

Since all the triangles are congruent (same), you will need to multiply by 2 to get the combined area of the triangle on the left and on the right.

Area of left & right triangles

= 2 (39 sq. cm)

= 78 sq. cm

Find the area of the triangle on the bottom

Bottom triangle area = 1/2 (a)(a)

= 1/2 (12 cm) (12 cm)

= 1/2 (144 sq. cm)

= 72 sq. cm

Since the bottom of the triangle is congruent to the top triangle, multiply that by 2 to get a combined area of the triangle on the bottom and top

Area of top & bottom triangles

2 (72 sq. cm) = 144 sq. cm

Finally...add the area of the 4 triangles to the area of the rectangular base

72 + 78 + 144 = 294 sq. cm

3 0

3 years ago

The function A(b) relates the area of a trapezoid with a given height of 10 and

Natali [406]

Answer:

$B(a)=\frac{a}{5} -7$

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height $*$ ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 $*$ ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 $*$ ( ( y + 7 ) / 2 ) or $b=\frac{\left(y+7\right)\cdot \:10}{2}$ - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

$y+7=\frac{a}{5}$ ,

$y^{-1}=\frac{a}{5}-7 = B(a)$

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

8 0

2 years ago

If f(x) is differentiable for the closed interval [−4, 0] such that f(−4) = 5 and f(0) = 9, then there exists a value c, −4 <

Pavel [41]

$\bf \textit{mean value theorem}\\\\
f'(c)=\cfrac{f(b)-f(a)}{b-a}\qquad 
\begin{cases}
a=-4\\
b=0
\end{cases}\implies f'(c)=\cfrac{f(0)-f(-4)}{0-(-4)}
\\\\\\
f'(c)=\cfrac{9-5}{0+4}\implies f'(c)=\cfrac{4}{4}\implies f'(c)=1$

4 0

3 years ago