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2 years ago

8

Jason wrote the mixed number 1 1/3 as the sum of three fractions. None of the fractions had a denominator of 3. How is this poss

ible? What fractions might jason have used?

2 answers:

UkoKoshka [18]2 years ago

5 0

Maybe 1 1/2
or try a number that makes that number

kipiarov [429]2 years ago

3 0

Convert 1/3 to 2/6
divide 1 to 1/2+1/2
3/6+1/2+1/2= 1 1/3

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In RST, RS = 7, RT = 10, and ST = 8. Which angle of RST has the smallest measure? A T BCANNT BE DETERMINDED C R D S

Scrat [10]

Answer:

Correct answer is option A. T

Step-by-step explanation:

Given that

In a $\triangle RST$ , RS = 7, RT = 10, and ST = 8.

To find:

Smallest angle = ?

Solution:

We can use cosine rule here to find the angle.

Formula for cosine rule:

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

Using the cosine rule:

$cos T = \dfrac{ST^{2}+RT^{2}-RS^{2}}{2\times ST \times RT}\\\Rightarrow cos T = \dfrac{8^{2}+10^{2}-7^{2}}{2\times 8 \times 10}\\\Rightarrow cos T = \dfrac{64+100-49}{160}\\\Rightarrow cos T = \dfrac{115}{160}\\\Rightarrow \angle T = cos^{-1}(0.71875)\\\Rightarrow \angle T = 44.05^\circ$

Now, let us use Sine rule to find other angles:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

$\dfrac{RS}{sinT} = \dfrac{ST}{sinR} = \dfrac{RT}{sinS}\\\Rightarrow \dfrac{7}{sin44.05} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow \dfrac{7}{0.695} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow sin R = \dfrac{8 \times 0.695}{7}\\\Rightarrow R = 52.58^\circ$

$\Rightarrow sin S = \dfrac{10 \times 0.695}{7}\\\Rightarrow S = 83.14^\circ$

Smallest angle is $\angle T$

Correct answer is option A. T

4 0

2 years ago

Aiden is replacing the tile in a rectangular kitchen. The length of the kitchen is nine feet shorter than three times its width,

julia-pushkina [17]

Answer:

Total Cost of tile = $273.28

Step-by-step explanation:

From the given information:

Let the width be = x

Then, the length of the rectangular kitchen is L = 3x - 9

The perimeter is = 6x

Suppose the cost of the tile = $1.69 a square foot.

Then the total costs to tile the kitchen is calculated as follows:

The Perimeter of the rectangle = 2(L + b)

The Perimeter of the rectangle = 2(3x - 9 + x)

The Perimeter of the rectangle = 2(4x-9)

6x = 8x - 18

- 2x = - 18

x = 18/2

x = 9

Thus, the width = x = 9 ft

the length = 3x - 9 = 3(9) - 9

the length = 27 - 9

the length = 18 ft

Area = L × W

Area = (18 × 9)ft

Area = 162 sq. ft.

Cost of a Tile = $1.69 per sq. ft.

Thus;

Total Cost of tile = $1.69 × 162

Total Cost of tile = $273.28

7 0

2 years ago

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The ratio of boys to girls in ms. zombo's class is 33 to 22. in mr. stolarski's class it is 55 to 33. if there are 15 students

Aloiza [94]

Zombo's class is 33:22 or 3:2
Stolarski's class is 55:33 or 5:3
15 students in Zombos
9 boys 6 girls
32 students in Stolarski
20 boys 12 girls
Together is 29 boys and 18 girls
29:18 boys to girls

4 0

2 years ago

What is the value of y?<br> y = <br><br> Find the following angle measures.<br> mJKM = °<br> mMKL

shusha [124]

Answer: ∠JKM = $106\textdegree$ and

∠JKM = $74\textdegree$

Step-by-step explanation:

Since we have given that

∠JKM=10y+6

∠MKL=8y-6

Since they are linear pairs ,

So, $10y+6+8y-6=180\textdegree \\\\18y=180\textdegree \\\\y=\frac{180\textdegree}{18\textdegree}\\\\y=10\textdegree$

∠JKM = $10\times 10+6=100+6=106\textdegree$

and

∠MKL = $8\times 10-6=80-6=74\textdegree$

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2 years ago

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Which expanded expressions represent the exponential expression (–4)3 · p4? Select all that apply. (–4) · (–4) · (–4) · (–4) · p

Alexxx [7]

Answer:

(-4)(-4)(-4)(p)(p)(p)(p)

Step-by-step explanation:

= $(-4)^3 * p^4$

The expanded form of it is:

= (-4)(-4)(-4)(p)(p)(p)(p)

4 0

2 years ago

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