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2 years ago

Find 10-3. Write the subtraction fact two ways.

1 answer:

4 0

This is a problem of fact families, but what is fact families? Well it is a family of four things. Two of them are additions and two of them are subtractions. So this question asks about fact families by writing the subtraction fact two ways. So we have:

 $10-3$

First way. So let's take the number 10 and explain this problem using triangles. Let's say that we have 10 triangles in the beginning:

Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ

So I want to take away 3 triangles, then by taking away 3 what is left? Well the answer is 7:

Δ Δ Δ Δ Δ
Δ Δ

That is, if we subtract 3 from 10 then the result is:

$10-3=7$

Second way. In this subtraction we take the same 10 triangles:

Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ

Now I want to take away 7 triangles, then by taking away 7 what is left is 3:

Δ Δ Δ

That is, if we subtract 7 from 10 then the result is:

$10-7=3$

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The ball bearing have volumes of 1.6cm cube and 5.4cm cube . Find the ratio of their surface area.

Korvikt [17]

Answer:

4/9

Step-by-step explanation:

The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:

k = ∛(1.6/5.4) = 2/3

Then the scale factor for the areas will be the square of this scale factor:

ratio of surface area = (2/3)² = 4/9

_____

The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.

Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.

8 0

2 years ago

Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant

Viktor [21]

Answer:

Therefore $k= \frac{ln2 }{18}$ , A=184

Step-by-step explanation:

Given function is

$T(t)=230 -e^{-kt}$

where T(t) is the temperature in °C and t is time in minute and A and k are constants.

She noticed that after 18 minutes the temperature of the pie is 138°C

Putting T(t) =138°C and t= 18 minutes

$138=230 -Ae^{-k\times 18}$

$\Rightarrow -Ae^{-18k}=138-230$

$\Rightarrow Ae^{-18k}=92$ .....(1)

Again after 36 minutes it is 184°C

Putting T(t) =184°C and t= 36 minutes

$184=230-Ae^{-k\times 36}$

$\Rightarrow Ae^{-36k}=230-184$

$\Rightarrow Ae^{-36k}=46$ .......(2)

Dividing (2) by (1)

$\frac{Ae^{-36k}}{Ae^{-18k}}=\frac{46}{92}$

$\Rightarrow e^{-18k}=\frac{46}{92}$

Taking ln both sides

$ln e^{-18k}=ln\frac{46}{92}$

$\Rightarrow -18k =ln (\frac12)$

$\Rightarrow -18k= ln1-ln2$

$\Rightarrow k= \frac{ln2 }{18}$

Putting the value k in equation (1)

$Ae^{-18\frac{ln2}{18}}=92$

$\Rightarrow A e^{ln2^{-1}}=92$

$\Rightarrow A.2^{-1}=92$

$\Rightarrow \frac{A}{2}=92$

$\Rightarrow A= 92 \times 2$

⇒A= 184.

Therefore $k= \frac{ln2 }{18}$ , A=184

7 0

2 years ago

For the sequence an = 2n + 1, identify the values of a0 = _____, a1 = _____, a2 = _____, and a3 = _____.

Tresset [83]

Answer:

Option A - $a_0= 2,a_1= 3,a_2= 5,a_3= 9$

Step-by-step explanation:

Given : For the sequence $a_n= 2^n + 1$

To find : Identify the values of following?

Solution :

The nth term of the sequence is $a_n= 2^n + 1$

Substitute n=0,1,2 and 3

When n=0,

$a_0= 2^0+ 1$

$a_0= 1+1$

$a_0=2$

When n=1,

$a_1= 2^1+ 1$

$a_1= 2+1$

$a_1=3$

When n=2,

$a_2= 2^2+ 1$

$a_2=4+1$

$a_2=5$

When n=3,

$a_3= 2^3+ 1$

$a_3= 8+ 1$

$a_3= 9$

Therefore, The value is $a_0= 2,a_1= 3,a_2= 5,a_3= 9$

So, Option A is correct.

4 0

2 years ago

The slope of diagonal OA is ? and its equation is ?

Nimfa-mama [501]

Answer:

Slope = $\frac{4}{3}$

Equation of the line → $y=\frac{4}{3}x$

Step-by-step explanation:

Let the equation of diagonal OA is,

y = mx + b

Here, m = Slope of the line OA

b = y-intercept

Slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

m = $\frac{y_2-y_1}{x_2-x_1}$

Therefore, slope of the line passing through O(0, 0) and A(3, 4) will be,

m = $\frac{4-0}{3-0}$

m = $\frac{4}{3}$

Since, line OA is passing through the origin, y-intercept will be 0.

Therefore, equation of OA will be,

$y=\frac{4}{3}x$

3 0

2 years ago

Shelly bought a house five years ago for $150,000 and obtained an 80% loan. Now the home is worth $140,000 and her loan balance

LiRa [457]

Answer:

The current equity is $32,000

Step-by-step explanation:

Here, we are to calculate the current equity of the House

Value of house initially is $150,000

loan borrowed is 80% of this

= 80/100 * 150,000 = $120,000

Now the house value is 140,000 and the loan amount is reduced to 12,000

The outstanding loan amount to pay would be 120,000-12,000 = 108,000

The current equity is thus = Assets - liability = 140,000-108,000 = $32,000

5 0

2 years ago