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3 years ago

Solve for x, please help

Mathematics

1 answer:

IRISSAK [1]3 years ago

8 0

Answer:

x = 18

Step-by-step explanation:

ΔABC ≅ ΔDEC

∠ B ≅ ∠E

40 = 2x + 4

-2x = 4 - 40

-2x = -36

2x = 36

x = 36/2

x = 18

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the annual interest on 17,000 investment exceeds the interest on an 11,000 investment by 308 . the 17,000is invested at a 0.4% h

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keeping in mind that

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}$

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now, regardless of what "x" and "y" are, we know that the interest from the 17000 is higher by 308 bucks, therefore 170x = 110y + 308.

we also know that the rate of <u>x</u> is higher as well than <u>y</u> by 0.4%, so then x = y + 0.4.

$\bf \begin{cases} 170x=110y+308\\ \boxed{x}= y +0.4\\[-0.5em] \hrulefill\\ 170\left( \boxed{y+0.4} \right)=110y+308 \end{cases} \\\\\\ 170y+68=110y+308\implies 60y=240\implies y=\cfrac{240}{60}\implies \blacktriangleright y=\stackrel{\%}{4} \blacktriangleleft \\\\\\ x=y+0.4\implies \blacktriangleright x=\stackrel{\%}{4.4} \blacktriangleleft$

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4 years ago

Graph the image of this figure after a dilation with a scale factor of 13 centered at the point (4, −2) .

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Answer:

From the given triangle figure;

Labelled the triangle as A , B and C.

The coordinates of this triangle ABC are;

A = (1, 10) ,

B = (-2, 4)

C = (7, 4).

Given : Scale factor(k) = $\frac{1}{3}$ and centered at point (4, -2).

The rule of dilation with $k= \frac{1}{3}$ and center at point (4,-2) is:

$(x, y) \rightarrow (\frac{1}{3}(x-4)+4 , \frac{1}{3}(y+2)-2)$

$(x, y) \rightarrow (\frac{1}{3}x-\frac{4}{3}+4 , \frac{1}{3}y+\frac{2}{3}-2)$

$(x, y) \rightarrow (\frac{1}{3}x+\frac{8}{3} , \frac{1}{3}y-\frac{4}{3})$

then, the dilation of the given figure are;

$A(1, 10) \rightarrow (\frac{1}{3}\cdot 1+\frac{8}{3} , \frac{1}{3} \cdot 10-\frac{4}{3})$ = $(\frac{1}{3}+\frac{8}{3} , \frac{10}{3}-\frac{4}{3})$ = $(\frac{9}{3} , \frac{6}{3})$ = A'(3 , 2)

$B(-2, 4) \rightarrow (\frac{1}{3}\cdot -2+\frac{8}{3} , \frac{1}{3} \cdot 4-\frac{4}{3})$ = $(-\frac{2}{3}+\frac{8}{3} , \frac{4}{3}-\frac{4}{3})$ = $(\frac{6}{3} , \frac{0}{3})$ =B'(2 , 0)

$C(7, 4) \rightarrow (\frac{1}{3}\cdot 7+\frac{8}{3} , \frac{1}{3} \cdot 4-\frac{4}{3})$ = $(\frac{7}{3}+\frac{8}{3} , \frac{4}{3}-\frac{4}{3})$ = $(\frac{15}{3} , \frac{0}{3})$ = C'(5 , 0)

The coordinates of dilation images are:

A' = (3,2) , B' = (2, 0) and C' = (5, 0)

You can see the graph of the dilated image as shown below:

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