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3 years ago

Solve for x: 4x(3y-2)=7x+11

Mathematics

2 answers:

kupik [55]3 years ago

7 0

Answer:

x=11(12y-15)

Step-by-step explanation:

4x(3y-2)=7x+11

12xy-8x=7x+11

12xy-8x-7x=11

12xy-15x=11

x(12y-15)=11

x(12y-15)/(12y-15)=11/(12y-15)

x=11/(12y-15)

g100num [7]3 years ago

7 0

Answer: $x=\frac{11}{12y-15}$

Step-by-step explanation:

To solve for x, we want to isolate the variable.

$4x(3y-2)=7x+11$ [distribute]

$12xy-8x=7x+11$ [subtract both sides by 7x]

$12xy-8x-7x=11$ [combine like terms]

$12xy-15x=11$ [factor out x]

$x(12y-15)=11$ [divide both sides by 12y-15]

$x=\frac{11}{12y-15}$

Now, we know that $x=\frac{11}{12y-15}$ .

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3 years ago

Find all values of x that make the triangles congruent. Explain your reasoning.

RSB [31]

Answer:

x = $\frac{4}{5},5$

Step-by-step explanation:

If both the triangles ΔABC and ΔBCD are congruent,

Corresponding sides of both the triangles will be proportional.

$\frac{AB}{BD}=\frac{AC}{CD}$

$\frac{5x}{3x+10}=\frac{5x-2}{4x+3}$

5x(4x + 3) = (5x - 2)(3x + 10)

20x² + 15x = 15x² + 50x - 6x - 20

20x² + 15x = 15x² + 44x - 20

20x² - 15x² = 44x - 15x - 20

5x² = 29x - 20

5x² - 29x + 20 = 0

5x² - 25x - 4x + 20 = 0

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3 0

3 years ago

what is the coordinate of the vertex of the parabola y-2=1/12(x+10) a. ( 10,-2) b. (-10,2) c. (-2,10) d. (2.-10)

solniwko [45]

Answer:

$y-a= c(x-b)^2$

With the vertex $V= (b,a)$

We see that b = -10 and a = 2 and then the vertes wuld be:

$V= (-10,2)$

And the best option is:

b. (-10,2)

Step-by-step explanation:

For this problem we have the following function:

$y-2 = \frac{1}{2} (x+10)$

And if we compare this expression with the general expression for a parabola given by:

$y-a= c(x-b)^2$

With the vertex $V= (b,a)$

We see that b = -10 and a = 2 and then the vertes wuld be:

$V= (-10,2)$

And the best option is:

b. (-10,2)

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3 years ago

Someone please help me out with these questions . I don’t get them at all.

iVinArrow [24]

Answer:

a)similar; b)similar; c)similar; d)NOT similar

Step-by-step explanation:

>In general if

all corresponding angels are ≅, and

all corresponding sides are in proportion

then the Δs are similar

>we have 3 similarity theorems AA, SSS, and SAS

we can use that sum of angles in a triangle is 180 to find the missing angles

180-96-32 = 52

so in the smaller triangle the angles are 96°-52°-32°

in the larger triangle the angles given are 52°-32°

Since there are 2 corresponding angles congruent, AA theorem of similarity says that the 2 triangles are similar. The transformations were that the big triangle was shrunk and rotated

here we are given a pair of congruent angles and we need to check if the sides are in proportion, is 14/44.8 equal to 20/64?

14/44.8 =.3125 is equal to 20/64=.3125

since we have two corresponding sides in proportion and the angles in between them congruent the SAS theorem says that the 2 triangles are similar. The transformation was that the small triangle was dilated.

because we are given the 2 angles are congruent we can conclude that the lines NH and SL are parallel. NH║SL let us conclude that ∡H and ∡ L are congruent because 2 parallel lines cut by a transversal (ML in our case) form congruent angles. So ΔMNH is similar to ΔMSL because of AA theorem of similarity (one pair of A was given congruent, one other pair of A we concluded was congruent)

here we have to check if all the sides are in proportion to see if SSS theorem of similarity applies here

18/90 = .2

44/202.4≈.22

58.5/211.2≈.28

.2≠ .22 ≠ .28

since the sides are not in proportion the 2 triangles are NOT similar.

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3 years ago