All categories

4 years ago

If you know that two triangles are congruent, you know that any unmarked corresponding parts are also congruent by

1 answer:

6 0

<span>The SSS, SAS, ASA, AAS, and HL theorems. These theorems state that if any of those combinations of angles or sides are congruent, the triangles are congruent. That means that you can apply it in reverse, because if two triangles are congruent then SSS, SAS, ASA, AAS, and HL (if a right triangle) are also all congruent.</span>

You might be interested in

I think I need to find x

ozzi

Answer:

-6

Step-by-step explanation:

the x value is just plugging that number in for x so

-3x-8=10 (add 8 to both sides) so

-3x=18 (divide by -3 on both sides) so

x=-6

7 0

3 years ago

Read 2 more answers

What function can be used to model data pairs that have a common ratio?

liubo4ka [24]

Correct answer is C.

For example 2, 4, 8, 16, 32...

$2=\frac{4}{2} = \frac{8}{4} = \frac{16}{8} = \frac{32}{16} =...$

$y=2^x$

4 0

4 years ago

Read 2 more answers

A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

8 0

3 years ago

Whats the answer to these? (These are called Proper fractions.)

Darya [45]

Answer to the first question: 7/10ths of a mile

Explaination: When adding fractions, you need to have a common denominator. Since dividing 3/10 by 2 to get a denominator of 5 makes 3 a decimal, it's easier to multiply 2/5 by 2 to get a denominator of 10. You do the same to the top that you do to the bottom: $\frac{2*2}{5*2} = \frac{4}{10}$ . From there, just add 4/10 and 3/10 to get the answer: 7/10ths of a mile.

Answer to the second question: Daniel read three (3/10) more books

Explaination: Since you can't evenly multiply 5 or 2 to get the opposite number, it's easier to multiply to the lowest common multiple. The easiest way to find that is to multiply both denominators (5*2=10). You'll have to multiply the numerator by the same amount you multipled the denominator by. For Daniel, that would mean: $\frac{4*2}{5*2} = \frac{8}{10}$ . For Edgar, that would mean: $\frac{1*5}{2*5} = \frac{5}{10}$ . So, Daniel read 3 more books than Edgar.

Answer to the third question: 2/4 mile (or 1/2 a mile)

Explaination: 2/8 can be simplified, by dividing the top and bottom by 2, resulting in 1/4. Since both fractions have the same denominator (/4), you can add them to get 2/4ths. This can be simplified further to half (1/2) a mile.

5 0

3 years ago

Read 2 more answers

PLEASE HELP ME PLEASE!!!

AleksAgata [21]

Answer:

cant not see the photo honey

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers