All categories

2 years ago

The measures of the angles of a triangle are 2x+10, 3x, and 8x-25 what is the triangle

Mathematics

1 answer:

umka2103 [35]2 years ago

7 0

Answer:

40,45,95

Step-by-step explanation:

The sum of the angles of a triangle are 180

2x+10 + 3x + 8x-25 = 180

Combine like terms

13x - 15 = 180

Add 15 to each side

13x - 15+15 =180 +15

13x = 195

Divide by 13

13x/13 = 195/13

x =15

The angles are

2x+10 = 2(15)+10 = 30+10 = 40

3x = 3(15) = 45

8x-25 = 8(15) -25 = 120-25 = 95

You might be interested in

One reading at an Arctic research station showed that the temperature was -35 Celsius.what is this temperature in degrees Fahreh

dem82 [27]

-31F because of the formula.
-35°C multiplied by 9/5 +32 = -31°F
~JZ
Hope it helps

8 0

3 years ago

You decide to enter in a rowing competition. To train, you go to the boat house and begin rolling down stream. You row for the s

fredd [130]

Answer:

Time spent rowing down stream $=100\ seconds$

Speed of boat in still water $=14\ ms^{-1}$

Step-by-step explanation:

Let speed of boat in still water be $= x\ ms^{-1}$

Speed of current $= 10\ ms^{-1}$

Speed of boat down stream = $\textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}$

Distance rowed down stream = 2400 m

Time spent rowing down stream = $\frac{Distance}{Speed}=\frac{2400}{x+10}\ s$ = $\frac{Distance}{Speed}=\frac{2400}{x+10}\ s$

Speed of boat up stream = $\textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}$

Distance rowed up stream = $\frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m$

Time spent rowing up stream = $\frac{Distance}{Speed}=\frac{400}{x-10}\ s$

We know that,

$\textrm{Time spent rowing down stream =Time spent rowing up stream}$

So,

$\frac{2400}{x+10}=\frac{400}{x-10}$

Cross multiplying

$2400(x-10)=400(x+10)$

Dividing both sides by $400$

$\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}$

$6(x-10)=x+10$

$6x-60=x+10$

Adding 60 to both sides.

$6x-60+60=x+10+60$

$6x=x+70$

Subtracting both sides by $x$

$6x-x=x+70-x$

$5x=70$

Dividing both sides by 5.

$\frac{5x}{5}=\frac{70}{5}$

∴ $x=14$

Speed of boat in still water $=14\ ms^-1$

Time spent rowing down stream = $\frac{2400}{14+10}=\frac{2400}{24}=100\ s$

3 0

2 years ago

the length of one leg of a right triangle is 6 feet. the length of the hypotenuse is 2 ft longer than the other leg. Find the le

Minchanka [31]

Answer:

The missing leg is 8 feet and the hypotenuse is 10 feet.

Step-by-step explanation:

Use the Pythagorean theorem which is A²+B²=C².

So we know the first side is 6 so plug that into the equation which would now be 6²+B²=C².

Because the hypotenuse is 2 feet longer than the missing leg we can plug in C=B+2 which would now make it 6²+B²=(B+2)².

Now we solve what we have so far which would now make the equation 36+B²=B²+4B+ 4.

Now we can figure out that 4B=32.

Now isolate the variable, B, by divide both side of 4B=32 by 4.

This gives us B=8.

So the other side is 8 feet.

Since we know that the hypotenuse is 2 feet longer than the leg we just add 2 feet to the original 8 feet to find the hypotenuse to be 10 feet.

5 0

2 years ago

Birth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation of 15 oz. The propor

OLga [1]

Answer:

The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 110, \sigma = 0.15$

The proportion of infants with birth weights between 125 oz and 140 oz is

This is the pvalue of Z when X = 140 subtracted by the pvalue of Z when X = 125. So

X = 140

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{140 - 110}{15}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

X = 125

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{125 - 110}{15}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

0.9772 - 0.8413 = 0.1359

The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.

4 0

2 years ago

X+y+z=2 X-y-z=2 x-y+z=-6

likoan [24]

<h2>The first one:</h2>

solve for x.

Step 1: Add -y to both sides.

x+y+z+−y=2+−y

x+z=−y+2

Step 2: Add -z to both sides.

x+z+−z=−y+2+−z

x=−y−z+2

solve for y.

Step 1: Add -x to both sides.

x+y+z+−x=2+−x

y+z=−x+2

Step 2: Add -z to both sides.

y+z+−z=−x+2+−z

y=−x−z+2

solve for z.

Step 1: Add -x to both sides.

x+y+z+−x=2+−x

y+z=−x+2

Step 2: Add -y to both sides.

y+z+−y=−x+2+−y

z=−x−y+2

<h2>The second one:</h2>

solve for x.

Step 1: Add y to both sides.

x−y−z+y=2+y

x−z=y+2

Step 2: Add z to both sides.

x−z+z=y+2+z

x=y+z+2

solve for y.

Step 1: Add -x to both sides.

x−y−z+−x=2+−x

−y−z=−x+2

Step 2: Add z to both sides.

−y−z+z=−x+2+z

−y=−x+z+2

Step 3: Divide both sides by -1.

−y /−1 = −x+z+2 /−1

y=x−z−2

solve for z.

Step 1: Add -x to both sides.

x−y−z+−x=2+−x

−y−z=−x+2

Step 2: Add y to both sides.

−y−z+y=−x+2+y

−z=−x+y+2

Step 3: Divide both sides by -1.

−z /−1 = −x+y+2 /−1

z=x−y−2

<h2>The third one:</h2>

solve for x.

Step 1: Add y to both sides.

x−y+z+y=−6+y

x+z=y−6

Step 2: Add -z to both sides.

x+z+−z=y−6+−z

x=y−z−6

solve for y.

Step 1: Add -x to both sides.

x−y+z+−x=−6+−x

−y+z=−x−6

Step 2: Add -z to both sides.

−y+z+−z=−x−6+−z

−y=−x−z−6

Step 3: Divide both sides by -1.

−y /−1 = −x−z−6 /−1

y=x+z+6

solve for z.

Step 1: Add -x to both sides.

x−y+z+−x=−6+−x

−y+z=−x−6

Step 2: Add y to both sides.

−y+z+y=−x−6+y

z=−x+y−6

I hope this was helpful <3

3 0

3 years ago