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3 years ago

PLEASE HELP

Mathematics

1 answer:

Georgia [21]3 years ago

6 0

Answer:

Option A and Option C

Step-by-step explanation:

Given:

IJ ≅ LM

∠J ≅ ∠M

To Prove:

ΔHIJ ≅ ΔKLM

Statements Reasons

1). IJ ≅ LM 1). Given

2). ∠J = m∠M 2). Given

3). ΔHIJ ≅ ΔKLM 3). By HA property Or AAS property of

congruence

Therefore, Option A and Option C are the correct options.

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3 years ago

Find the height of a cylinder with a volume of 367 cm and a base with a radius of 3 cm.

Bingel [31]

Answer:

The height is 5.11, if rounded to the nearest whole number it would be 5.

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4 years ago

Read 2 more answers

The bar graph shows the numbers of reserved campsites at a campground for one week. What percent of the reservations were for Fr

Slav-nsk [51]

Answer:

66.67 %

Step-by-step explanation:

As we can see from the figure

We are given a bar graph in which bars represent the number of reserved campsites at a camp ground for one week from Monday to Sunday.

First of all

Lets the count the total number of reservations made by campsites during the week.

Total Number of campsite reservations = 5+3+4+7+26+30+9

Total Number of campsite reservations =84

Now

we have to calculate what percent of reservations were made for friday or saturday.

% of reservations made on friday or saturday = $\frac{total-numer-of-reservations-on-friday-or-saturday}{total-number-of reservations}$

% of reservations made on friday or saturday = $\frac{26+30}{84}$

% of reservations made on friday or saturday = $\frac{56}{84}$

% of reservations made on friday or saturday = 66.67 %

So in total 66.67 % reservations are on friday and saturday.

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3 years ago

Read 2 more answers

C. A circular puzzle is 20 inches in diameter. All of the pieces are about the same

Kay [80]

Answer:

Circumference if the diameter is 20 the radius is 10 so if all the pieces are equal to 20 you have to find the radius(10) so the answer is 125 pieces

Step-by-step explanation:

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3 years ago

A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the

Kay [80]

Answer: The required number of quarters in the collection is 11.

Step-by-step explanation: Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = $ 0.05, 1 dime = $ 0.10 and 1 quarter = $0.25.

Then, according to the given information, we have

$x+y+z=20\\\\\Rightarrow x=20-y-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.05x+0.10y+0.25z=3.35\\\\\Rightarrow 5x+10y+25z=335\\\\\Rightarrow x+2y+5z=67~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\0.05y+0.25x+0.10z=2.75\\\\\Rightarrow 5y+25x+10z=275\\\\\Rightarrow y+2z+5x=55~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of x from equation (i) in equations (ii) and (iii), we have

$(20-y-z)+2y+5z=67\\\\\Rightarrow y+4z=47\\\\\Rightarrow y=47-4z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

and

$y+2z+5(20-y-z)=55\\\\\Rightarrow -4y-3z=-45\\\\\Rightarrow y=\dfrac{45-3z}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Comparing the values of y from equations (iv) and (v), we get

$47-4z=\dfrac{45-3z}{4}\\\\\Rightarrow 188-16z=45-3z\\\\\Rightarrow 16z-3z=188-45\\\\\Rightarrow 13z=143\\\\\Rightarrow z=\dfrac{143}{13}\\\\\Rightarrow z=11.$

Thus, the required number of quarters in the collection is 11.

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3 years ago