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gayaneshka [121]
3 years ago
13

Consider adjacent angles that measure (2x+45)∘ and (3x+55)∘. The sum of the measures of these two angles is 135∘.

Mathematics
1 answer:
bulgar [2K]3 years ago
3 0
Is there a picture?
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Need help parabola and its vertex
AVprozaik [17]
y + 13 = 2(x - 1)^2

use the equation: (y_{2} - y_{1}) = m({x_{2} - x_{1})^2

(-11 + 13) = m(0 - 1)^2

2 = m(1)^2

m = 2

y + 13 = 2(x - 1)^2

substitute y for 0, since x-intercepts occur on the x-axis, or the line y = 0 

0 + 13 = 2(x - 1)^2

13 = 2(x - 1)^2

13 = 2(x^2 - 2x + 1)[tex]\\[tex]13 = 2x^2 - 4x + 2

2x^2 - 4x - 15

use the quadratic equation (can't type it out on brainly, if you don't know, look it up)

x = 1 -  \sqrt{ \frac{13}{2} }, 1 +  \sqrt{ \frac{13}{2} }

The answer is: (1 -  \sqrt{ \frac{13}{2} },0) and (1 +  \sqrt{ \frac{13}{2} },0)
8 0
3 years ago
What is the y-intercept of the graph of the equation y=4(3^x)?
eimsori [14]

Answer:

The y-intercept is (0, 4).

Step-by-step explanation:

At the y-intercept x = 0 so

y = 4(3^0)

y = 4*1 = 4.

So the y-intercept is (0, 4).

8 0
3 years ago
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If sin 0 = -<br> and 270º &lt; 0&lt; 360°, what is cos 0?
Alik [6]

Answer:

  cos(θ) > 0

Step-by-step explanation:

In Quadrant IV, the cosine is positive.

__

In the attached, trig functions not listed are negative.

7 0
3 years ago
Rebecca has 3 pairs of running shoes.She bought new shoelaces for each pair.How many shoelaces did she buy?
kvasek [131]

Answer: 6 shoelaces

Step-by-step explanation:

Since 1 pair of shoes has 2 shoelaces, 3 x 2 = 6

3 pairs x 2 shoelaces = 6 shoelaces

Hope this helped!

P.S. PLS give brailiest! I only have one brainliest!!

4 0
3 years ago
Read 2 more answers
In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm
jeyben [28]

Answer:

The length of the legs is 8.64cm and 14.64cm respectively

Step-by-step explanation:

I've added an attachment to aid my explanation.

At different intervals, I'll be making reference to it.

Given

AB = 17

PAMC = 32

PBMC = 25

From the attachment, we have:

y + z = AB

Since, M is the Midpoint

y = z = \½AB

Substitute 17 for AB

y = z = \½ * 17

y = z = 8.5

Also, from the attachment

v + x + z = PAMC

v + x + y = 32

Substitute 8.5 for y

v + x + 8.5 = 32

v + x = 32 - 8.5

v + x = 23.5 --------- (1)

Also, from the attachment

v + w + z = 25

Substitute 8.5 for z

v + w + 8.5 = 25

v + w = 25 - 8.5

v + w = 17.5 ----------- (2)

Subtract (2) from (1)

v - v + x - w = 23.5 - 17.5

x - w = 6

Make x the subject

x = 6 + w

Apply Pythagoras Theorem:

We have that:

AB^2 = AC^2 + BC^2

The above can be replaced with

17^2 = x^2 + w^2 (see attachment)

289 = x^2 + w^2

Substitute 6 + w for x

289 = (6 + w)^2 + w^2

289 = 36 + 12w + w^2 + w^2

289 - 36 = 12w + 2w^2

253 = 12w + 2w^2

Reorder

2w^2 + 12w - 253 = 0

Solve using quadratic equation:

w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}

Where

a = 2

b = 12

c = -253

w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}

w = \frac{-12 \± \sqrt{144 + 2024}}{4}

w = \frac{-12 \± \sqrt{2168}}{4}

w = \frac{-12 \± 46.56}{4}

Split:

w = \frac{-12 + 46.56}{4} or w = \frac{-12 - 46.56}{4}

w = \frac{34.56}{4} or w = \frac{-58.56}{4}

w = 8.64 or w = -14.64

But length can't be negative

So:

w = 8.64

Recall that: x = 6 + w

x = 6 + 8.64

x = 14.64

<em>Hence, the length of the legs is 8.64cm and 14.64cm respectively</em>

5 0
3 years ago
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