What type of angle are angles 1 and 14

A school has 825 students and 55 teachers. How many students are there per teacher?

DochEvi [55]

15 students after dividing 825 with 55

3 0

3 years ago

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1/4 + 1/2 + x = −3/4

Ostrovityanka [42]

1/4 + 1/2 + x = −3/4

get a common denominator 1/4

1/4 +2/4 +x = -3/4

combine like terms

3/4 +x =-3/4

subtract 3/4 from each side

x = -3/4 -3/4

x = -6/4

divide top and bottom by 2

x = -3/2

x = -1 1/2

Answer : x = -1 1/2

7 0

3 years ago

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Find the length of diagonal HJ. Round to the nearest hundredth.

Alisiya [41]

Answer:

The length of the diagonal HJ is 10.82 units

Step-by-step explanation:

* Lets revise the rule of the distance between two points

- $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ , where

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ are the two points

* Lets use this rule to find the length of the diagonal HJ

∵ The coordinates of point H are (-4 , 3)

∵ The coordinates of point J are (5 , -3)

∴ $x_{1}=-4$ and $x_{2}=5$

∴ $y_{1}=3$ and $y_{2}=-3$

- Lets find the length of the diagonal HJ by using the rule above

∴ HJ = $\sqrt{(5-(-4))^{2}+(-3-3)^{2}}=\sqrt{(5+4)^{2}+(-6)^{2}}$

∴ HJ = $\sqrt{(9)^{2}+36}=\sqrt{81+36}=\sqrt{117}=10.81665$

∴ HJ = 10.82

* The length of the diagonal HJ is 10.82 units

7 0

3 years ago

Evaluate the line integral, where c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Arada [10]

The value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

<h3>What is integration?</h3>

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

The parametric equations for the line segment from (0, 0, 0) to (2, 3, 4)

x(t) = (1-t)0 + t×2 = 2t

y(t) = (1-t)0 + t×3 = 3t

z(t) = (1-t)0 + t×4 = 4t

Finding its derivative;

x'(t) = 2

y'(t) = 3

z'(t) = 4

The line integral is given by:

$\rm \int\limits_C {xe^{yz}} \, ds = \int\limits^1_0 {2te^{12t^2}} \, \sqrt{2^2+3^2+4^2} dt$

$\rm ds = \sqrt{2^2+3^2+4^2} dt$

After solving the integration over the limit 0 to 1, we will get;

$\rm \int\limits_C {xe^{yz}} \, ds = \dfrac{\sqrt{29}}{12} (e^{12}-1)$ or

= 73037.99 ≈ 73038

Thus, the value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Learn more about integration here:

brainly.com/question/18125359

#SPJ4

7 0

2 years ago

Find the scale factor of the smaller figure to the larger figure

guapka [62]

Answer:

#9: 1.2

#10: 1.25

Step-by-step explanation:

To find the scale factor of the smaller figure to the larger figure, we're going to be dividing the measurements of corresponding edges.

$\frac{larger figure}{smaller figure}$

If you wanted to find the scale factor of the larger figure to the smaller figure, you'd do: $\frac{smaller figure}{larger figure}$

Question #9:

Left edges: $\frac{larger figure}{smaller figure}$ ⇒ $\frac{24}{20}$ = 1.2

Bottom edges: $\frac{larger figure}{smaller figure}$ ⇒ $\frac{30}{25}$ = 1.2

<em>(You should get the same number as long as the figures are similar.)</em>

<em />

Question #10:

Bottom edges: $\frac{larger figure}{smaller figure}$ ⇒ $\frac{30}{24}$ = 1.25

<em>(There are no corresponding edges with measurements that we can compare.)</em>

<em />

~Hope this helps!~

4 0

3 years ago