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4 years ago

Which shapes are congruent? (See attachment)

Mathematics

2 answers:

sasho [114]4 years ago

8 0

Hello!

The 2nd, 3rd, and last choices are congruent. The rest are not congruent.

I hope this helps! -Wajiha

Andre45 [30]4 years ago

3 0

Hello! Congruent figures are those with the same size and shape. With that being said, if you look at the shapes correctly, here are your answers:

Quad 1 & 2: Not Congruent
Quad 1 & 3: Congruent
Quad 1 & 4: Congruent
Quad 2 & 3: Not Congruent
Quad 2 & 4: Not Congruent
Quad 3 & 4: Congruent

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Find the vertex of this parabola:<br> y = -x2 - 4x - 2

VikaD [51]

<h3>Hello!</h3>

$===============================$

In order to find the vertex of a parabola, we use the following formula:

$\bold{\displaystyle\frac{-b}{2a} }}$

Remember, a parabola looks like so:

$\tt{y=ax^2+bx+c}$

Now we know what a and b stand for.

In this case, b is -4, and a is -1:

$\hookrightarrow\sf{\displaystyle\frac{-(-4)}{2(-1)}$

Simplify:

$\hookrightarrow\sf{\displaystyle\frac{4}{-2} }}$

Divide:

$\hookrightarrow\sf{-2}$

$===================================$

<h3>Notes:</h3>

Hope everything is clear.
Let me know if you have any questions!
Enjoy your day!
Always remember: Knowledge is power!

<h3>Answered by:</h3>

$\mathbb{DiAmOnD}\\{\boxed{An~Emotional~And~Creative~Helper}}}}$

3 0

3 years ago

An architectural firm wants to replicate a nearby estate with some changes. The new estate will be larger than the original by a

Oduvanchick [21]

Answer:

Option B.

Step-by-step explanation:

It is given that the new estate will be larger than the original by a scale factor of 1:10.

A section of the roof in the original estate is constructed using 45-45-90 triangles. The hypotenuse of the triangle is 10 meters long.

Two angles are equal and one angle is a right angle, it means it is an isosceles right-angled triangle.

Let $x$ be the length of the legs of the triangle for the larger estate.

The hypotenuse of larger estate = 10 × 10 = 100

Using Pythagoras triangle,

$perpendicular^2+base^2=hypotenuse^2$

$x^2+x^2=(100)^2$

$2x^2=10000$

Divide both sides by 2.

$x^2=5000$

Taking square root on both sides.

$x=\sqrt{5000}$

$x=70.71\text{ meters}$

Hence, the correct option is B.

8 0

4 years ago

4x2 + 4x - 1, evaluate and fully simplify each of the - For the function f(0) following f(s + h) f(x + h) - f(5) h 10

Andrew [12]

Given the function f(x);

$f(x)=-4x^2+4x-1$

Evaluating the function f(x+h);

$\begin{gathered} f(x+h)=-4(x+h)^2+4(x+h)-1 \\ f(x+h)=-4(x^2+2xh+h^2)^{}+4(x+h)-1 \\ f(x+h)=-4x^2-4h^2-8xh^{}+4x+4h-1 \end{gathered}$

So;

$f(x+h)=-4x^2-4h^2-8xh^{}+4x+4h-1$

Evaluating the second function;

$\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-4h^2-8xh^{}+4x+4h-1-(-4x^2+4x-1)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-4h^2-8xh^{}+4x+4h-1+4x^2-4x+1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{-4x^2+4x^2-4h^2-8xh^{}+4x-4x+4h-1+1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{-4h^2-8xh^{}+4h}{h} \end{gathered}$

simplifying further;

$\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4h^2-8xh^{}+4h}{h}=-4h-8x+4 \\ \frac{f(x+h)-f(x)}{h}=-4h-8x+4 \end{gathered}$

Therefore, we have;

$undefined$

7 0

1 year ago

The science club purchased tickets for a magic show. They paid $108 for 6 tickets in section A and 10 tickets in section B.

san4es73 [151]

Let x is the price for one ticket in section A and y for section B.
In first week they paid <span>$108 for 6 tickets in section A and 10 tickets in section B.
So,
6x + 10y = 108
And in t</span><span>he following week, they paid $104 for 4 tickets in section A and 12 tickets in section B.
So,
4x + 12y = 104
12y = 104 -4x
y= (104 -4x) /12
now, put this value for y in first equation
6x +10(104 - 4x / 12) = 108
multiplying all terms with 12
72x +10(104 -4x) = 1296
72x + 1040 -40x = 1296
32x = 256
x = 8
So, price for one ticket in section A is $8.

</span>

6 0

3 years ago

Which ordered pair is a solution to the system of linear equations -4x+y= 8 and X-5y=17?

iren [92.7K]

C is the correct answer.
Plug the x & y values for x and y in the equation and you'll get true statements. For example:
-4(-3) -4 = 8
12-4=8

And in the second equation:
-3 -5(-4) = 17
-3 +20 = 17

5 0

3 years ago