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3 years ago

If arc AB = 70°, how many degrees are in ∠ ADB?

Mathematics

1 answer:

tankabanditka [31]3 years ago

5 0

If D is the center of the circle, ∠ADB = 70°, as that is where the arc gets its measure.

If D is on the circle and not on the arc, ∠ADB = 35°, half the measure of the arc's central angle.

If D is on arc AB, then ∠ADB = 145°, half the measure of the corresponding central angle.

If D is inside or outside the circle (and not one of the above), we need to know more about the measures of arcs intercepted by lines AD and BD.

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Finding the Vertex What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)? (,)

Rama09 [41]

Answer:

(5, -9)

Step-by-step explanation:

Let's multiply the function out:

f(x) = (x-8)(x-2)

$f(x)=x^2-2x-8x+16\\f(x)=x^2-10x+16$

The vertex is (h, k), where

h = -b/2a

and

k is plugging in h into the equation

a is the number before the x^2 term, hence a = 1
b is the number before x term, hence b = -10
c is the constant , hence c = 16

Plugging these into the formula for h, we get:

$h=-\frac{b}{2a}\\=-\frac{-10}{2(1)}\\=5$

Now pluggin in 5 into the equation we get:

$x^2-10x+16\\(5)^2-10(5)+16\\=-9$

Hence, vertex is (5, -9)

5 0

3 years ago

Read 2 more answers

There are 12 baseball trading cards in 4 packages. each package has the same number of cards. Write a rule in words for the numb

Tamiku [17]

Answer:

Rule in words:

The number of packages Justin needs to buy to get x cards is x divided by 3.

Rule as an algebraic expresssion:

$y=x/3$

Explanation:

This is a direct variation problem.

Since each package has the same number of cards, the number of cards is proportional to the number of packages.

12 baseball cards in 4 packages means that there are 12/4 = 3 cards per package, so:

The number of cards is 3 times the number of packages.

The number of packages is the number of cards divided by the number of 3.

So, the rule in words for the number of packages Justin needs to buy x cards is one third of x. This table may help you to visualize it:

Number of packages: 1 2 3 4 5

Number of cards: 3 6 9 12 15

To find the algebraic expression that describes the same rule, you can set the following proportion:

$\frac{12}{4} =\frac{x}{y}$

Where y is the number of packages and x is the number of cards.

And from that you solve for y:

$\frac{12}{4} =\frac{x}{y}\\ \\ 12y=4x\\ \\ y=4x/12\\ \\ y=x/3$

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4 years ago

A confectioner has 300 pounds of a chocolate that is 1 part cocoa butter to 7 parts caramel. How much chocolate that is 1 part c

anygoal [31]

Let's call our unknown quantity $n$ . We'll need to add $n$ lbs of chocolate with a 1/15 ratio of cocoa butter to caramel to 300 lbs of chocolate with a 1/7 ratio of cocoa butter to caramel to yield $300+n$ lbs of chocolate with a 1/9 ratio of cocoa butter to caramel. We can set this up as an equation, but it's important to note something first: the ratio of the caramel to the cocoa butter is provided, but this is not the same thing as the fraction of the chocolate the cocoa butter takes up.

The 300 pounds of chocolate have 1 + 7 = 8 parts of cocoa butter and caramel total, which means that cocoa butter takes up 1/8 of those total parts; the $n$ pounds we're adding on has 1 + 15 = 16 total parts, which means the cocoa butter takes up 1/16 of those; and the $300+n$ pounds being produced have 1 + 9 = 10 total parts, so the cocoa butter takes up 1/10 of those parts. With this in mind, we can set up the following equation:

$300\big( \frac{1}{8}\big)+n\big( \frac{1}{16}\big)=(300+n)\big( \frac{1}{10}\big)$

which we can rewrite as

$\frac{300}{8}+ \frac{n}{16}= \frac{300+n}{10}$

From here, it would be helpful to combine the fractions on the left side of the equation. To do this, we'll convert the denominator of $\frac{300}{8}$ to 16, multiplying it by $\frac{2}{2}$ to obtain the fraction $\frac{600}{16}$ . Combining that with $\frac{n}{16}$ , we have:

$\frac{600+n}{16}= \frac{300+n}{10}$

To get rid of the denominator on the left, we'll multiply both sides of the equation by 16, and to eliminate the one on the right, we'll multiply both sides by 10:

$(10)(16)\big( \frac{600+n}{16}\big)=\big( \frac{300+n}{10}\big)(10)(16)$

Simplifying:

$10(600+n)=(300+n)16\\ 6000+10n=4800+16n$

And finally, we solve for $n$ :

$6000-4800=16n-10n\\ 1200=6n\\ 200=n$

So, the confectioner needs 200 lbs of chocolate that's 1 part cocoa butter and 15 parts caramel.

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4 years ago

What is the tangent of angle P? 12/13 5/13 12/5 5/12

scoundrel [369]

Tangent is opposite side/ adjacent side
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3 years ago

A tennis ball has a radius of 6.7 centimeters. What is the volume of a tennis ball? Use 3.14 for pi. Round your answer to the ne

ANEK [815]

Answer:

The answer would be B) 1259.19 cm3

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3 years ago

Read 2 more answers