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2 years ago

5x10 but showing your work

Mathematics

1 answer:

prohojiy [21]2 years ago

8 0

Answer: 50

Step-by-step explanation: 5 times 10 means that there is going to be 5 10’s added together, so 10+10 = 20 + 10 + 10 = 40 + 10 = 50 so 5 times 10 is 50

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X+8=-15 help again sorryyy

suter [353]

X by its self is always 1x

1x+8=-15 you have to get rid of 8 by subtracting on both sides

1x=-23 now get rid of 1 by dividing on both sides

x=-23

8 0

2 years ago

Find m∠STU and m∠TUA

PIT_PIT [208]

Answers:

angle STU = 65 degrees
angle TUA = 123 degrees

=========================================================

Explanation:

Let's find the expression for angle TUS in terms of x

Angle TUA has the expression 11x+2. It will add to angle TUS to get 180 degrees

(angle TUS) + (angle TUA) = 180

angle TUS = 180 - (angle TUA)

angle TUS = 180 - (11x + 2)

angle TUS = 180 - 11x - 2

angle TUS = -11x + 178

Now focus on the interior angles of triangle TUS. We have these three angles

T = 5x+10
U = -11x+178
S = 58

For any triangle, the interior angles always add to 180, so,

T+U+S = 180

(5x+10) + (-11x+178) + (58) = 180

(5x-11x) + (10+178+58) = 180

-6x + 246 = 180

-6x = 180-246

-6x = -66

x = -66/(-6)

x = 11

Use this x value to find the angle measures we're after:

angle STU = 5x+10 = 5*11+10 = 55+10 = 65 degrees
angle TUA = 11x+2 = 11*11+2 = 121+2 = 123 degrees

--------------------------

As an alternative route, you can apply the remote interior angle theorem. This says that adding two interior angles leads to the exterior angle that isn't adjacent to either one.

In this case, we would say

(angle STU) + (angle TSU) = angle TUA

that leads to the equation

(5x+10) + (58) = 11x+2

Solving this should lead to x = 11 to generate the angles mentioned earlier.

6 0

2 years ago

Find the average rate of change of the function over the given interval

sattari [20]

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\$

$\bf h(t)=cot(t)\implies h(t)=\cfrac{cos(t)}{sin(t)}\quad 
\begin{cases}
t_1=\frac{\pi }{4}\\
t_2=\frac{3\pi }{4}
\end{cases}\implies \cfrac{h\left( \frac{3\pi }{4} \right)-h\left( \frac{\pi }{4} \right)}{\frac{3\pi }{4}-\frac{\pi }{4}}
\\\\\\$

$\bf \cfrac{\frac{cos\left( \frac{3\pi }{4} \right)}{sin\left( \frac{3\pi }{4} \right)}-\frac{cos\left( \frac{\pi }{4} \right)}{sin\left( \frac{\pi }{4} \right)}}{\frac{\pi }{2}}\implies \cfrac{-1-1}{\frac{\pi }{2}}\implies \cfrac{-2}{\frac{\pi }{2}}\implies -\cfrac{4}{\pi }\\\\\\
-------------------------------\\\\$

$\bf h(t)=cot(t)\implies h(t)=\cfrac{cos(t)}{sin(t)}\quad 
\begin{cases}
t_1=\frac{\pi }{3}\\
t_2=\frac{3\pi }{2}
\end{cases}\implies \cfrac{h\left( \frac{3\pi }{2} \right)-h\left( \frac{\pi }{3} \right)}{\frac{3\pi }{2}-\frac{\pi }{3}}
\\\\\\$

$\bf \cfrac{\frac{cos\left( \frac{3\pi }{2} \right)}{sin\left( \frac{3\pi }{2} \right)}-\frac{cos\left( \frac{\pi }{3} \right)}{sin\left( \frac{\pi }{3} \right)}}{\frac{9\pi -2\pi }{6}}\implies \cfrac{\frac{0}{-1}-\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}}{\frac{7\pi }{6}}\implies\cfrac{-\frac{1}{\sqrt{3}}}{\frac{7\pi }{6}}\implies -\cfrac{\sqrt{3}}{3}\cdot \cfrac{6}{7\pi }
\\\\\\
-\cfrac{2\sqrt{3}}{7\pi }$

8 0

3 years ago

The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18

kogti [31]

Answer: One side could be 18 and the other side will be 33.

Step-by-step explanation:

Side #1 = 18
Side #2 = 2x - 3
Side #3 = x

One way of setting up the inequality is: Side #2 + Side #3 > Side #1

$2x-3+x>18\\3x-3>18\\3x>18+3\\3x>21\\x>7$

Another way of setting up the inequality is: Side #1 + Side #3 > Side #2

$18+x>2x-3\\18+3>2x-x\\x$

Final way of setting up the inequality is: Side #1 + Side #2 > Side #3

$18+2x-3>x\\15>x-2x\\15>-x\\x>-15$

Therefore, we have the range for our value of x, which is between 7 and 21. Any possible value between works. Negative measurements are rejected. One of the sides would equal the x-value, while the other side would equal the value of 2x-3.

3 0

3 years ago

Find the fifth term in the sequence that is defined as follows an=n^2+2

Vedmedyk [2.9K]

Answer:

a(5) = 2 + 5^2 = 2 + 25 = 27

Step-by-step explanation:

This sequence is defined as a(n) = 2 + n^2.

Thus, a(1) = 2 + 1^2 = 2 + 1 = 3

Then a(5) = 2 + 5^2 = 2 + 25 = 27

8 0

3 years ago