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sp2606 [1]
3 years ago
5

Is it congruent or not ? Remember that the diagram may not be drawn to scale . justify your conclusion.

Mathematics
1 answer:
Leno4ka [110]3 years ago
4 0

Yes, we can see each triangle has congruent angle, side, angle, respectively (SAD). When two triangles have these correlating congruences, they can be determined as congruent.

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Jamarius just filled up his SUV for $58.56. If he put 24 gallons of gas in the tank, what was the cost per gallon?
Kazeer [188]
Answer:

$2.44/gal

Explanation:

$58.56/24gallon/
6 0
2 years ago
2x+3y=1 and y=-2 - 9 solve using linear combination method. Please explain steps.
kaheart [24]

Answer:

x=17

Step-by-step explanation:

2x+3y=1

y=-2-9

  • In order to combine these two equations, an idea you need to keep in mind is finding a way of setting these equations as equal to each other. I saw that each equation shared a common value, y. In this case, we need to isolate y in the first equation so that both equations =y.

2x+3y=1

3y=-2x+1

\frac{3y}{3}=\frac{-2x+1}{3}

y=-\frac{2}{3}x+\frac{1}{3}

  • With this, we now know that both -2-9 and -\frac{2}{3}x+\frac{1}{3} are equal to y, so we can set them equal to each other.

y=-\frac{2}{3}x+\frac{1}{3}

y=-11

-\frac{2}{3}x+\frac{1}{3}=-11

  • Reply to this if anything I'm saying or doing is confusing in any way, or if you find a mistake. :) Solve for x.

-\frac{2}{3}x+\frac{1}{3}=-11

-\frac{2}{3}x=-11-\frac{1}{3}

-\frac{2}{3}x =-\frac{33}{3}-\frac{1}{3}

-\frac{2}{3}x =-\frac{34}{3}

-\frac{2}{3}x(-\frac{3}{2})=-\frac{34}{3}(-\frac{3}{2})

x=\frac{102}{6}=17

x=17

  • Hopefully this answer is correct AND makes sense in terms of how I achieved it. Again, reply to this with any questions or mistakes I made and I'll do my best to answer or fix them.

 

4 0
3 years ago
Sum of exterior angles in a polygon?
soldi70 [24.7K]

Answer:

360

Step-by-step explanation:

The exterior angles always add up to 360 in a polygon because it's the sum of all the vertexes which would make a circle.

8 0
3 years ago
Peter has 100 dollars. His mom gives him x dollars more. Write an expression to represent the situation.
denis23 [38]

Answer:

100+x

Step-by-step explanation:

Peter starts out with 100 dollars and then gets X more meaning we have to add X to what he originally had and that looks like this 100+x

I hope this helps and please don't hesitate to ask if there is anything still unclear!

5 0
3 years ago
Read 2 more answers
A line tangent to the curve f(x)=1/(2^2x) at the point (a, f(a)) has a slope of -1. What is the x-intercept of this tangent?
kirza4 [7]

Answer:

x-intercept = 0.956

Step-by-step explanation:

You have the function f(x) given by:

f(x)=\frac{1}{2^{2x}}   (1)

Furthermore you have that at the point (a,f(a)) the tangent line to that point has a slope of -1.

You first derivative the function f(x):

\frac{df}{dx}=\frac{d}{dx}[\frac{1}{2^{2x}}]  (2)

To solve this derivative you use the following derivative formula:

\frac{d}{dx}b^u=b^ulnb\frac{du}{dx}

For the derivative in (2) you have that b=2 and u=2x. You use the last expression in (2) and you obtain:

\frac{d}{dx}[2^{-2x}]=2^{-2x}(ln2)(-2)

You equal the last result to the value of the slope of the tangent line, because the derivative of a function is also its slope.

-2(ln2)2^{-2x}=-1

Next, from the last equation you can calculate the value of "a", by doing x=a. Furhtermore, by applying properties of logarithms you obtain:

-2(ln2)2^{-2a}=-1 \\\\2^{2a}=2(ln2)=1.386\\\\log_22^{2a}=log_2(1.386)\\\\2a=\frac{log(1.386)}{log(2)}\\\\a=0.235

With this value you calculate f(a):

f(a)=\frac{1}{2^{2(0.235)}}=0.721

Next, you use the general equation of line:

y-y_o=m(x-x_o)

for xo = a = 0.235 and yo = f(a) = 0.721:

y-0.721=(-1)(x-0.235)\\\\y=-x+0.956

The last is the equation of the tangent line at the point (a,f(a)).

Finally, to find the x-intercept you equal the function y to zero and calculate x:

0=-x+0.956\\\\x=0.956

hence, the x-intercept of the tangent line is 0.956

5 0
3 years ago
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