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3 years ago

A chocolate maker melts three blocks of chocolate weighing 5.4 ounces, 6.1 ounces, and 5.7 ounces. If

Mathematics

1 answer:

Nady [450]3 years ago

4 0

Answer:

43 truffles

Step-by-step explanation:

First add all of the weights together

5.4+6.1+5.7=17.2

Divide the total chocolate by the weight of a truffle

17.2/0.4=43

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X f(x) -2 -1/200 -1 -1/20 0 -1/2 1 -5 2 -50

Hitman42 [59]

9514 1404 393

Answer:

f(x) = -1/2·10^x

Step-by-step explanation:

The y-intercept is -1/2.

The common ratio is (-1/20)/(-1/200) = 10, so the exponential function can be written as ...

f(x) = -1/2·10^x

6 0

3 years ago

Rewrite in simplest terms: -2(5d-9f)+7f-10(-9f-7d)

Afina-wow [57]

Answer:

= 5 ( 12d + 23f )

Step-by-step explanation:

-2(5d-9f)+7f-10(-9f-7d

Open parenthesis

= -10d + 18f + 7f + 90f + 70d

Collect like terms

= -10d + 70d + 18f + 7f + 90f

= 60d + 115f

Factorise

= 5 ( 12d + 23f )

Therefore,

-2(5d-9f)+7f-10(-9f-7d) in its simplest form is 5 ( 12d + 23f )

4 0

2 years ago

What is the vertex of the graph of the function below? y = x2 + 8x + 12

Vera_Pavlovna [14]

Hello,

$The\,\,formula\,\,for\,\,the\,\,vertex\,\,of\,\,a\,\,quadratic\,\,equation\,\,is: \\ V=( -\frac{b}{2a},f(-\frac{b}{2a}) )$

That means that we must first obtain x, then we replace x in the function to get y, so:

$x=- \frac{b}{2a} \\ \\ x=- \frac{8}{2*(1)} \\ \\ \boxed{x=-4} \\ \\ Reeplacing \,\,x: \\ y=(-4)^{2} +8*(-4)+12 \\ y=16-32+12 \\ \boxed{y=-4}$

Answer: V=(-4 , -4)

5 0

3 years ago

X = ? y = ? 16 45 degrees

mezya [45]

Let's put more details in the figure to better understand the problem:

Let's first recall the three main trigonometric functions:

$\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}$ $\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}$ $\text{ Tangent }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Adjacent Side}}$

For x, we will be using the Cosine Function:

$\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}$ $Cosine(45^{\circ})\text{ = }\frac{\text{ x}}{\text{ 1}6}$ $(16)Cosine(45^{\circ})\text{ = x}$ $(16)(\frac{1}{\sqrt[]{2}})\text{ = x}$ $\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}$ $\text{ 8}\sqrt[]{2}\text{ = x}$

Therefore, x = 8√2.

For y, we will be using the Sine Function.

$\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}$ $\text{ Sine }(45^{\circ})\text{ = }\frac{\text{ y}}{\text{ 1}6}$ $\text{ (16)Sine }(45^{\circ})\text{ = y}$ $\text{ (16)(}\frac{1}{\sqrt[]{2}})\text{ = y}$ $\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}$ $\text{ 8}\sqrt[]{2}\text{ = y}$

Therefore, y = 8√2.

5 0

1 year ago

BD is tangent to circle O at C, m(arc AEC) = 280, and m(arc ACE) = 140. Find m (The figure is not drawn to scale.)

Zepler [3.9K]

Answer:

The correct answer is second option 60°

Step-by-step explanation:

From the figure we can write,

measure of arc AEC = measure of arc AE + measure of CE

measure of arc ACE = measure of AC + measure of CE

measure of arc AEC + measure of arc ACE = 280 + 140 = 420°

measure of arc AE + measure of CE + measure of AC + measure of CE = 420

measure of arc AE + measure of CE + measure of AC = 360°

measure of CE = 420 - 360 = 60°

The correct answer is second option 60°

8 0

3 years ago