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3 years ago

Find angle X in the angle diagram.

Mathematics

2 answers:

Rasek [7]3 years ago

6 0

Answer:

80°

Step-by-step explanation:

160 is vertically opposite the x and 80, which means they have the same value. This makes x+80=160.

This can be solved to x=80.

miss Akunina [59]3 years ago

5 0

Answer:

80*

Step-by-step explanation:

Angle x + 80* add up to the vertical angle of 160*

So, 160* = x + 80*

80* = x

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3x=4(c-d)/d make d the subject

MissTica

Answer:

$d = \frac{4c}{3x + 4}$

Step-by-step explanation:

$3x = \frac{4(c - d)}{d}$

Multiply both sides by d:

$3xd = 4(c - d)$

Expand:

$3xd = 4c \: - 4d$

+4d on both sides:

$3xd + 4d = 4c$

Factorise d out of the left-hand side:

$d(3x + 4) = 4c$

Divide both sides by (3x +4):

$d = \frac{4c}{3x + 4}$

8 0

3 years ago

What is the slope intercept form of the equation for the line?

Leni [432]

The slope intercept form is:

$y=mx+b$

Where is $m$ the slope of the line and $b$ the intercept with the y-axis.

To find the slope, take any two points from the table provided. For example:

(1, 1/5)

(3, 1)

So:

$m = \frac{1- 1/5}{3-1}$

$m = \frac{2}{5}$

Now we find b substituting any point of the table in the equation:

$y_0 = \frac{2}{5}x_0 + b$

We substitute the poiunt (3, 1) for example:

$1 = \frac{2}{5}(3) + b$

Now we solve for b:

$b = 1 -\frac{6}{5}\\\\b = -\frac{1}{5}$

Finally, the equation is:

$y = \frac{2}{5}x -\frac{1}{5}$

The answer is the last option

5 0

3 years ago

The data given below contain the state cigarette taxâ€‹ (in $) for all 20 regions of a country.

g100num [7]

Answer:

(a) $\bar x= 1.583$ -- Population Mean

(b) $s = 1.032$ --- Population standard deviation

Step-by-step explanation:

Given:

Cigarette tax for 20 regions

Solving (a): The population mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

$\sum x = 1.36 + 1.70 + 2.50 + 0.45 + 1.18 + 0.64 + 3.46 + 0.57 + 2.00 + 0.80 + 1.60 +0.98 + 0.36 + 2.24 + 4.35 + 0.62 + 2.70 + 1.78 + 1.53 + 0.84$

$\sum x = 31.66$

$n = 20$

So, we have:

$\bar x= \frac{31.66}{20}$

$\bar x= 1.583$

Solving (b): The population standard deviation

This is calculated as:

$s = \sqrt{\frac{\sum( x - \bar x)^2}{n}$

$\sum (x -\bar x)^2 = (1.36 - 1.583)^2 + (1.70 - 1.583)^2+ (2.50 - 1.583)^2+ (0.45 - 1.583)^2+ (1.18 - 1.583)^2+ (0.64 - 1.583)^2+ (3.46 - 1.583)^2+ (0.57 - 1.583)^2+ (2.00 - 1.583)^2+ (0.80 - 1.583)^2+ (1.60 - 1.583)^2+(0.98 - 1.583)^2+ (0.36 - 1.583)^2+ (2.24 - 1.583)^2+ (4.35 - 1.583)^2+ (0.62 - 1.583)^2+ (2.70 - 1.583)^2+ (1.78 - 1.583)^2+ (1.53 - 1.583)^2+ (0.84- 1.583)^2$

$\sum (x -\bar x)^2 = 21.29222$

So:

$s = \sqrt{\frac{21.2922}{20}$

$s = \sqrt{1.06461}$

$s = 1.032$

Solving (c):

Population mean tells the average amount while the standard deviation represents the spread from the calculated mean

Option (4) is correct

6 0

3 years ago

To go to a beach party 600 yd away, you kayak against the ocean current for 2 h. The trip back takes 1 h. Write and solve a syst

Mice21 [21]

Answer: the paddling speed is 450 yards per hour.

The speed of the ocean current is 150 yards per hour.

Step-by-step explanation:

Let x represent the paddling speed.

Let y represent the speed of the ocean current.

To go to a beach party 600 yd away, you kayak against the ocean current for 2 h. This means that the total speed at which you kayaked is (x - y) yards per hour.

Distance = speed × time.

Distance travelled while going to the party is expressed as

600 = 2(x - y)

Dividing through by 2, it becomes

300 = x - y - - - - - - - - - - -1

The trip back takes 1 h. Assuming you traveled with the ocean current. The total speed at which you returned is (x + y) yards per hour. Distance travelled while going to the party is expressed as

600 = 1(x + y)

600 = x + y - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

900 = 2x

x = 900/2

x = 450 yards per hour

Substituting x = 450 into equation 2, it becomes

600 = 450 + y

y = 600 - 450

y = 150 yards per hour

8 0

3 years ago

Solve the inequality. 2(4x – 3)-3(3x) + + 5x?

sashaice [31]

Answer:

2 (2 x - 3)

Step-by-step explanation:

Simplify the following:

2 (4 x - 3) - 3×3 x + 5 x

-3×3 = -9:

2 (4 x - 3) + -9 x + 5 x

Grouping like terms, 2 (4 x - 3) - 9 x + 5 x = 2 (4 x - 3) + (5 x - 9 x):

2 (4 x - 3) + (5 x - 9 x)

5 x - 9 x = -4 x:

2 (4 x - 3) + -4 x

2 (4 x - 3) = 8 x - 6:

8 x - 6 - 4 x

Grouping like terms, 8 x - 4 x - 6 = (8 x - 4 x) - 6:

(8 x - 4 x) - 6

8 x - 4 x = 4 x:

4 x - 6

Factor 2 out of 4 x - 6:

Answer: 2 (2 x - 3)

3 0

3 years ago