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3 years ago

Can a translation and a reflection map TriangleQRS to TriangleTUV?

Mathematics

2 answers:

BartSMP [9]3 years ago

8 0

Answer:

Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map

△QRS to △TUV.

Step-by-step explanation:

andrey2020 [161]3 years ago

5 0

Answer:

Yes

Step-by-step explanation:

Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV. No, the triangles are obtuse. Yes, a translation mapping vertex S to vertex T and a reflection across the line containing RS will map △QRS to △TUV.

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X^2-10x = −16 solution??

Maru [420]

X^2-10x+16= 0
(x-8)(x-2)=0
x = 8 or 2

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3 years ago

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Another teacher has a monthly salary of $2000 She spends $943 per month on rent Her monthly salary then increases by 15% What pe

Aleks04 [339]

Answer:

47.15%

Step-by-step explanation:

Getting a raise of 15% would increase the teacher's salary by 300. 943 of 2300 is 47.15%.

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2 years ago

Find the length of the line PA.

Diano4ka-milaya [45]

RO divides the rectangle into two congruent right triangles.

The area of the one triangle is equal half area of the rectangle.

Calculate the area of rectangle:

$A_R=lw\\l=12,\ w=5\\\\A_R=12\cdot5=60$

The area of right triangle:

$A_T=\dfrac{1}{2}A_R\to A_T=\dfrac{1}{2}\cdot60=30$

Use the Pythagorean theorem to calculate the length of RO:

$|RO|^2=5^2+12^2\\\\|RO|^2=25+144\\\\|RO|^2=169\to|RO|=\sqrt{169}\to|RO|=13$

The formula of an area of this right triangle is:

$A_T=\dfrac{1}{2}|RO||PA|$

Therefore we have the equation:

$\dfrac{1}{2}(13)|PA|=30\qquad|\cdot2\\\\13|PA|=60\quad|:13\\\\|PA|=\dfrac{60}{13}\\\\|PA|\approx4.62$

8 0

3 years ago

How to find all real solutions

AlladinOne [14]

$\bf \sqrt{\sqrt{x-5}+x}=5\leftarrow \textit{squaring both sides}
\\\\
\sqrt{x-5}+x=25\implies \sqrt{x-5}=25-x\leftarrow \textit{squaring both sides}
\\\\
x-5=(25-x)^2\implies x-5=625-50x+x^2
\\\\
0=x^2-51x+630\implies 0=(x-30)(x-21)$

and surely you'd know what the roots are

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3 years ago

Compare the strengths and weaknesses of the horizontal and vertical methods for adding and subtracting polynomials. Include comm

Pavlova-9 [17]

Answer:

Overall vertical is visually better, if done correctly

it forces you to "line up" all the common exponents.

The disadvantage is that it usually requires re-writing the problem, and it takes up space.

most problems are presented horizontally, that becomes the issue to locate the common exponents.

in both cases the biggest issue is people forget

that when subtracting "subtracting a negative is like adding a positive"

-5x - (-8x) = 3x [that is a positive 3x]

or:

-7x

- - 10x

-------------

everyone misses those eventually so you have to watch out for that in both methods

Step-by-step explanation:

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3 years ago