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Black_prince [1.1K]
3 years ago
14

Find the x- and y-intercept of the line x+4y=36

Mathematics
1 answer:
blagie [28]3 years ago
4 0

Answer:

x=36

y=9

Step-by-step explanation:

Plug in 0 for x to find the y-intercept

0 + 4y = 36

4y = 36

y = 9

y-intercept (0, 9)

Plug in 0 for y to find the x-intercept

x + 4(0) = 36

x = 36

x-intercept (36, 0)

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6 0
2 years ago
In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm
tangare [24]

Answer:

AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD

Consider right triangle CAH.By the Pythagorean theorem,

CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8

The length cannot be negative, so CD=8 cm and

CA=\sqrt{3}CD=8\sqrt{3}\ cm

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

AB=2CA=16\sqrt{3}\ cm

By the Pythagorean theorem,

BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm

3 0
2 years ago
The figure below shows a rectangle ABCD having diagonals AC and DB: A rectangle ABCD is shown with diagonals AC and BD. Jimmy wr
yaroslaw [1]

Answer:

C. DC = DC. By reflexive property of equality.

Step-by-step explanation:

We are given that,

In step 4, Jimmy proved ΔADC ≅ ΔBCD by the SAS Congruence Postulate.

For that, the previous steps states,

Step 1: AD = BC, as opposite sides of a rectangle are congruent.

Step 2: ∠ADC = ∠BCD

So, in order to satisfy the SAS Postulate, we must have another pair of sides equal from the respective rectangles.

As, we can see that in ΔADC and ΔBCD, the side DC is a common side.

Thus, in the missing step, we get,

Step 3: DC = DC, By the reflexive property of equality.

Hence, option C is correct.

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2 years ago
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Mrrafil [7]
105 is the product of 15 and 7.
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3 years ago
Please help i dont wanna fail this time
mezya [45]

Answer:

Step-by-step explanation:

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you would add -4 and -2 1/2 giving the total of -6 1/2.

All thats left is for you to graph it:)

(Please mark brainliest)

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2 years ago
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