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baherus [9]
3 years ago
13

Robin had 7/8 pound of butter when she started baking a cake. She used 1/4 pound of butter while baking. How much butter was lef

t after she was done baking?
Mathematics
1 answer:
8_murik_8 [283]3 years ago
3 0

Answer:

\dfrac{5}{8} butter was left after she was done baking.

Step-by-step explanation:

Robin had 7/8 pound of butter when she started baking a cake. She used 1/4 pound of butter while baking.

We need to find how much butter was left after she was done baking.

It can be calculated as follows,

Left =

=\dfrac{7}{8}-\dfrac{1}{4}\\\\=\dfrac{7}{8}-\dfrac{2}{8}\\\\=\dfrac{7-2}{8}\\\\=\dfrac{5}{8}

Hence, \dfrac{5}{8} butter was left after she was done baking

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Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list.
SOVA2 [1]

Answer:

23.92°, 78.503°, and 77.577°

Step-by-step explanation:

The coordinates of the vertices of the triangle are;

X(-3, -5), Y(2, 6), Z(6, 3)

The vectors are;

z = \left \langle 2 - (-3), 6 - (-5) \right \rangle = \left \langle 5, 11  \right \rangle

y = \left \langle 6 - (-3), 3 - (-5)  \right \rangle = \left \langle 9, 8 \right \rangle

x = \left \langle 2 - 6, 6 - 3  \right \rangle = \left \langle -4, 3  \right \rangle

cos (\alpha ) = \dfrac{z \cdot y}{\left |  z \right | \times \left | y  \right |}

Therefore, we get;

cos (\alpha ) = \dfrac{5 \times 9  + 11 \times 8 }{\left |  \sqrt{5^2 + 11^2}  \right | \times \left | \sqrt{9^2 + 8^2}   \right |} = \dfrac{133}{\sqrt{146} \times \sqrt{145} } \approx 0.91409

α = arccos(0.91490) ≈ 23.92°

γ = The angle between -y and x

-y = \left \langle -9, -8 \right \rangle

We get;

cos (\gamma) = \dfrac{-y \cdot x}{\left |  -y \right | \times \left | x  \right |}

Therefore;

cos (\gamma) = \dfrac{-9 \times -4  + -8 \times 3 }{\left |  \sqrt{(-9)^2 + (-8)^2}  \right | \times \left | \sqrt{(-4)^2 + 3^2}   \right |} = \dfrac{12}{\sqrt{145} \times \sqrt{25} } \approx 0.199309

γ = arccos(0.199309) ≈ 78.503°

γ ≈ 78.503°

By angle sum property, β = 180° - (α + β)

β ≈ 180° - (23.92° + 78.503°) = 77.577°

β ≈ 77.577°

The interior angles are;

23.92°, 78.503°, and 77.577°

4 0
3 years ago
50 POINTS what is the average rate of change of the function f(x)=3x^2 on the interval from 0 to 2?
Evgesh-ka [11]

Answer:

f=3x-2

Step-by-step explanation:

5 0
3 years ago
Assume that 0<br> a. 16/63<br> b. -16/63<br> c. 63/16<br> d. -63/16<br><br> please help
iVinArrow [24]
The answer to this question is B
3 0
3 years ago
A soft-drink vending machine is supposed to pour 500ml of the drink
guajiro [1.7K]

the answer is on chegg

4 0
3 years ago
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Help please! Need help solving
NISA [10]
For the perimeter you have to consider the EXTERNAL SHAPE ONLY:

a) the perimeter of half a circle WITHOUT ITS DIAMETER  is:
π.R - 2R → 3.14x1.5 - 2x1.5 → 1.71 cm

b) the perimeter of the rectangle WITHOUT THE UPPER SIDE is:
2.5+3+2.5 = 8 cm

Hence the perimeter of the figure is 1.71 + 8 = 9.71 cm

2) Area of the figure:
Area of half circle is π.R²/2 →3.14 x (1.5)²/2 → Area half circle = 3.5325 cm²
Area of rectangle = 2.5 x 3 = 7.5 cm²
Total area = 3.5325 + 7.5 = 11.0325 ≈ 11 cm²


3 0
4 years ago
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