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Dmitry [639]
3 years ago
12

If the coordinates of point a are -3 and 2 and the coordinates of point B are 7 and 6 the x-intercept of CD is what

Mathematics
1 answer:
AveGali [126]3 years ago
3 0

Answer:

The x-intercept of CD is -19/5

Step-by-step explanation:

If the coordinates of the first point is (-3, 2) and the coordinates of the point B are (7, 6) then we need first to find the equation of the line CD:

We know that the general equation of the line is:

y-y0 = m(x-x0) where (x0, y0) represents a point that belongs to the line and m, is the slope which can be calculated by using the following formula:

m = (x1 - x0) / (y1 - y0)

In this case:

(x1, y1) = (7, 6)

(x0, y0) = (-3, 2)

Then:

m = (7 - (-3))/(6-2) = 10/4 = 5/2.

Then, the equation of the line is:

y-y0 = m(x-x0)

y - 2 = 5/2 (x -(-3))

y = 5/2(x+3) + 2

To find the x intercept we make y=0.

Then y = 5/2(x+3) + 2 = 0

Then:

x = -4/5 - 3 = -19/5

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∆ ABC is similar to ∆DEF and their areas are respectively 64cm² and 121cm². If EF = 15.4cm then find BC.​
lyudmila [28]

{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}

★ ∆ ABC is similar to ∆DEF

★ Area of triangle ABC = 64cm²

★ Area of triangle DEF = 121cm²

★ Side EF = 15.4 cm

{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}

★ Side BC

{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}

Since, ∆ ABC is similar to ∆DEF

[ Whenever two traingles are similar, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. ]

\therefore \tt \boxed{  \tt \dfrac{area( \triangle \: ABC )}{area( \triangle \: DEF)} =  { \bigg(\frac{BC}{EF} \bigg)}^{2}   }

❍ <u>Putting the</u><u> values</u>, [Given by the question]

• Area of triangle ABC = 64cm²

• Area of triangle DEF = 121cm²

• Side EF = 15.4 cm

\implies  \tt  \dfrac{64   \: {cm}^{2} }{12 \:  {cm}^{2} }  =  { \bigg( \dfrac{BC}{15.4 \: cm} \bigg) }^{2}

❍ <u>By solving we get,</u>

\implies  \tt    \sqrt{\dfrac{{64 \: cm}^{2} }{ 121 \: {cm}^{2} }}   =   \bigg( \dfrac{BC}{15.4 \: cm} \bigg)

\implies  \tt    \sqrt{\dfrac{{(8 \: cm)}^{2} }{  {(11 \: cm)}^{2} }}   =   \bigg( \dfrac{BC}{15.4 \: cm} \bigg)

\implies  \tt    \dfrac{8 \: cm}{11 \: cm}    =   \dfrac{BC}{15.4 \: cm}

\implies  \tt    \dfrac{8  \: cm \times 15.4 \: cm}{11 \: cm}    =   BC

\implies  \tt    \dfrac{123.2 }{11 } cm   =   BC

\implies  \tt   \purple{  11.2 \:  cm}   =   BC

<u>Hence, BC = 11.2 cm.</u>

{\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}

★ Figure in attachment.

\rule{280pt}{2pt}

4 0
2 years ago
Jenna drove 35 miles in 30 minutes. At this rate, how many miles will she drive in 1 hour?
Llana [10]

Answer:

70 miles

Step-by-step explanation:

30 minn+30 min=1 hour/60 min

30 min=35 miles

add the minutes together then add the miles together witch will give you

1 hour/60 min=70 miles

4 0
3 years ago
Read 2 more answers
Someone pls help me
Nat2105 [25]
The answer should be AC+BC

We can answer this by applying the rule called "Greater angle, greater side". This is where in any triangle, the opposite side of the larger angle is also longer.

So in this question, first we have to find the largest 2 angles, which is ∠ABC and ∠BAC with measures of 120° and 35° respectively. Therefore, from the diagram, the opposite sides of the angles are AC and BC. 

Therefore, the answer should be AC+BC.
7 0
3 years ago
The following table shows the number of classes that
Tresset [83]

Answer:

There are 6 classes we find the median by finding the middle number of the 3rd highest class and 4th highest class, even if this is a decimal.

6/3 = 3+ 0.5

The process would be different if some values are the same values already on the chart total of each class.

ie) 20  31  14  22 20 31

small data like this below you can rearrange

14  20  20  22  31 31  

and see that 21 is the correct value

as there are even numbers, so we choose 20 , 22

and select the middle value = 21

Step-by-step explanation:

If there is an even number of numbers locate the two middle numbers so that there is an equal number of values to the left and to the right of these two numbers. Step 3: If there is an odd number of numbers, this middle number is the median. If there is an even number of numbers add the two middles and divide by 2.

7 0
3 years ago
Kate has a rectangular garden that is 8 feet long by 3 feet wide. She wishes to extend the length and width by the same amount i
elena55 [62]
<span>Let the extension of the length and width be x.
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 Area of a rectangle = Length x Width
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(8+x)(3+x) = 104
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4 0
3 years ago
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