MATHEMATICS HIGH SCHOOL

Find the product. Do not round.

2.78 · 9.3 =

Answers

Answer 1

Answer:

Answer:

25.854

Step-by-step explanation:

We are given that

$2.78\cdot 9.3$

We have to find the given product.

To find the product we will remove the decimal.

In 2.78 when we remove the decimal then we write 100 in denominator because here is decimal after two digit from right side.

In 9.3, when we remove the decimal then we write 10 in denominator because decimal after one digit from right side.

$(278)/(100)* (93)/(10)$

Multiply numerator with numerator and denominator with denominator

$(25854)/(1000)=25.854$

We write decimal after three digits from right side because denominator is 1000.

Hence, $2.78\cdot 9.3=25.854$

Answer 2

Answer: the answer is 25.854

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One of the corners of a cube is sliced off. The resulting cross section will have a minimum of how many sides?

Answers

3, because you cut a corner, you cut through where 3 sides meet.

3 sides

Answer:

The resulting cross-section will have a minimum of three sides.

i.e. a triangle will be formed.

Step-by-step explanation:

Because on cutting a cube along the corner we will obtain a triangle and thus a triangle has three sides.

Hence, the resulting cross section will have minimum of three sides.

( Also we can obtain many other figures on slicing a cube in different ways.

If we slice a cube parallel to the base we will obtain a square.

when we will slice the cube to it's diagonal we will obtain a rectangle.

and in many other ways)

Jack ate 3 chocolate squares after school. Each chocolate square had a mass of 8 grams.How many grams of chocolate did Jack eat in all?

Answers

Answer:

24 grams

Step-by-step explanation:

Since there are three of them, I multiply by the mass, which is 8, and get 24 grams. Hope this helps!

Jack ate 24 grams in total.

You can get this answer my multiplying 8x3 because he ate three pieces and each of the three had eight grams.

If 2 is added to seven times a number and equals 8 more than six times a number what is the number

Answers

Seven times a number is 7x; 6 times a number is 6x and then solve7x+2=6x+8X+2=8X=6

Your word equation turned into an operation would be: 2+7n=8+6n. To complete this equation you have to balance it out so only n would be put on one side. So, try subracting 6n on both sides so it can be on the same side as 7n:2+7n-6n=8+6n-6n.Therefore the 6n on the right side has now switched over to the left. Then, you need to switch the 2 onto the right side by subtracting it on both sides as well:2+7n-6n-2=8-2The 2 has now been switched. After, subtract 7n-6n=1n, and 8-2=6. The equation then becomes:1n=6.To isolate n from 1, divide 1n by 1 and 6 by 1. Your equation afterwards should be: n=6/1, or as simplified: n=6.

Which is an equation in point-slope form for the given point and slope?Point: (1, –7); Slope:

A.
y-7=-2/3(x+1)

B.
y-7=2/3(x-1)

C.
y+7=-2/3(x-1)

D.
y+7=2/3(x+1)

Answers

$\sf~y-y_1=m(x-x_1)$

Where y1 is the y-value of the point, x1 is the x-value, and 'm' is the slope.

In this case:

y1 = -7
x1 = 1
m = -2/3

Plug them in:

$\sf~y-(-7)=-(2)/(3)(x-1)$

or

$\boxed{\sf~y+7=-(2)/(3)(x-1)}$

The sides of a quadrilateral are 3, 4, 5, and 6. Find the length of the shortest side of a similar quadrilateral whose area is 9 times as great.

Answers

Answer:

9 units.

Step-by-step explanation:

Let us assume that length of smaller side is x.

We have been given that the sides of a quadrilateral are 3, 4, 5, and 6. We are asked to find the length of the shortest side of a similar quadrilateral whose area is 9 times as great.

We know that sides of similar figures are proportional. When the proportion of similar sides of two similar figures is $(m)/(n)$ , then the proportion of their area is $(m^2)/(n^2)$ .

We can see that length of smaller side of 1st quadrilateral is 3 units, so we can set a proportion as:

$(x^2)/(3^2)=(9)/(1)$

$(x^2)/(9)=(9)/(1)$

$x^2=9\cdot 9$

$x^2=81$

Take positive square root as length cannot be negative:

$√(x^2)=√(81)$

$x=9$

Therefore, the length of the shortest side of the similar quadrilateral would be 9 units.

Answer:

the answer is 9

Step-by-step explanation:

Just did the lesson

. Allison drew a triangle with 2 congruent sides and 1 obtuse angle. Which terms accurately describe the triangle? Select all that apply.

Answers

Answer:

obtuse triangle

isosceles triangle

Step-by-step explanation:

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees

Area of a triangle = 1/2 x base x height

the perimeter of a triangle = sum of the side lengths

An isosceles triangle has two opposite sides. If the two angles are equal , it means the triangle is an isosceles. Because 90 degrees is greater than 45 degrees, the two sides with the same length, would have a smaller length than the third side.

Answer:

obtuse triangle

isosceles triangle

Step-by-step explanation:

hope it helps

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