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weeeeeb [17]
1 year ago
14

A 12-centimeter rod is held between a flashlight and a wall as shown. Find the length of the shadow on

Mathematics
1 answer:
choli [55]1 year ago
7 0

Answer:

48 cm

Step-by-step explanation:

Given:

Distance of rod from the wall = 45 cm

Distance of rod from the light = 15 cm

Length of rod = 12 cm

We can see that <DAM and <BAF are equal

Also, <DMA and <BFM are equal because they are corresponding angles

To find the length of the shadow, let's take the equation

\frac{DM}{BF} = \frac{AM}{A.F}

Where.:

DM = ½ of length of the rod = ½*12 = 6

A.F = 15 + 45 = 60 cm

AM = 15 cm

Therefore,

\frac{DM}{BF} = \frac{AM}{A.F}

= \frac{6}{BF} = \frac{15}{60}

Cross multiplying, we have:

15 * B.F = 60 * 6

15 * B.F = 360

BF = \frac{360}{15}

BF = 24 cm

The shadow on the wall =

2 * BF

= 2 * 24

= 48 cm

The shadow on the wall is 48 cm

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In Virginia, 120 lame dogs were tested for arthritis and Lyme disease. The results showed that 42 of the dogs had Lyme disease,
miskamm [114]

Answer:

The number of dogs that had both Lyme disease and arthritis is 18

Step-by-step explanation:

Let x represent dogs that have both Lyme disease and arthritis

Dog with only Lyme disease = 42 - x

Dog with only arthritis = 96 - x

The sum of the 3 category should give 120

x + (42 - x) + (96 - x) = 120

Collect like terms and solve

x - x - x + 42 + 96 = 120

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138 - 120 = x

x = 18

Dog with only Lyme disease = 42 - x = 42 - 18 = 24

Dog with only arthritis = 96 - x = 96 - 18 = 78

Therefore, the number of dogs with both Lyme disease and anthritis is 18.

4 0
2 years ago
There are 14 dogs in a particular class at a dog show. Blue, red, yellow, and white ribbons will be awarded to the first through
stira [4]
There are 14 possibilities for first place.
There are 13 possibilities for second place, since a dog can't get both first and second place.
There are 12 possibilities for third place, since a dog can't get both first, second, and third place.
There are 11 possibilities for fourth place, since a dog can't get both first, second, third, and fourth place.

Multiply them together and get 24024 possibilities.

Hope this helps!

4 0
1 year ago
Sam spent 5/6 of an hour at the dentist’s office. He spent 1/10 of the time in the waiting room. How much time did he spend at t
svp [43]
That is  5/6  - 5/6 * 1/10 = 5/6 - 5/60  = 50/60 - 5/60 = 45/60  = 3/4 hour answer
4 0
1 year ago
A restaurant buys 56 pounds of beef at $1.12/pound and 24 quarts of milk at $.90/quart. How much money was spent?
Gre4nikov [31]

Answer:

84.80

Step-by-step explanation: 62.72+22.08=84.80

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2 years ago
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saul85 [17]

Answer: Annabelle is using  the a measure of central tendency defined as the Mode.

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The mean, median and mode are commonly accepted measures of central tendency.

The mode is the most frequently occurring value in a given set of data. As such, the modal value is statistically acceptable as a representative of the entire set of values or data.

If Annabelle measures the sides of 15 right triangles and based on her observations, she concludes that for any right  triangle the sum of the squares of the two legs is equal to the square of the hypotenuse, what she has done is taking the most frequently occurring value, and in her experiment, the most frequent of all observed data satisfies the Pythagorean Theorem.

That is why Annabelle can confidently make her assumption.

6 0
2 years ago
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