CAN SOMEOBODY ANSWER MY QUESTIONS?? The area of the regular hexagon is 50 in sq. What is the measure of the apothem? 10 in 5 in 25 in 2 in

Answer:

a = 0.3 and b = - 1.1

Step-by-step explanation:

(x - 2)² = x² -4x + 4

Hence, x² - 4x + 4 = 3x - 6

x² - 7x + 10 = 0

(x - 5)(x - 2) = 0

∴ x = 5 or 2

f(5) = 25a + 5b = 2  ----- (i)

f(2) = 4a +  2b = -1  ------ (ii)

(i) X 2: 50a + 10b = 4 ----- (iii)

(ii) X 5: 20a + 10a = -5  ---- (iv)

Subtract (iv) from (iii): 30a = 9

a = 0.3

Substitute a into (ii) to obtain b

4(0.3) + 2b = -1

2b = -1 - 1.2 = -2.2

∴ b = -1.1

Step-by-step explanation:

great circle = 9[tex]\pi[/tex] = r^2.[tex]\pi[/tex] --> r = 3 m

Surface area S = 4[tex]\pi[/tex].r^2 = 36[tex]\pi[/tex] m^2

Volume V = 4/3[tex]\pi[/tex].r^3 = 36[tex]\pi[/tex] m^3

The volume of a sphere is 36π m³ and the Surface area of sphere 36π m². Therefore, option A is the correct answer.

The volume of sphere is the measure of space that can be occupied by a sphere.  If the radius of the sphere formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by: Volume of Sphere, V = (4/3)πr³

Given that, sphere with great circle area 9π m².

We know that, area of a circle = πr²

Now, πr²=9π m²

r=3 m

Here, volume of a sphere = 4/3 ×π×3³

= 36π m³

Surface area of sphere = A = 4πr²

= 4×π×3²

= 36π m²

Therefore, option A is the correct answer.

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Answer:

radius ≈ 17.0 units

Step-by-step explanation:

The radius is the distance from the centre of the circle to a point on it.

Calculate the radius r using the distance formula

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (7, 12)

r = [tex]\sqrt{(7+6)^2+(12-1)^2}[/tex]

  = [tex]\sqrt{13^2+11^2}[/tex]

  = [tex]\sqrt{169+121}[/tex]

   = [tex]\sqrt{290}[/tex] ≈ 17.0 ( to the nearest tenth )

The required radius of the circle whose center is at the point (-6,1). If the point (7, 12) lies on the circle is 17.0

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

The radius of the circle r, for the center (h, k) and point on the circle (x, y) is given by the distance formula,
[tex]r = \sqrt{(x-h)^2 +(y-k)^2}[/tex]
Since the center is at the point (-6,1). If the point (7, 12) lies on the circle,

[tex]r = \sqrt{(7+6)^2 +(12-1)^2}\\r = \sqrt{(13)^2 +(11)^2}\\r = \sqrt{169+121}\\r =\sqrt{290}[/tex]
r = 17.03
r ≈ 17.0 (to the nearest tenth)

Thus, the required radius of the circle whose center is at the point (-6,1). If the point (7, 12) lies on the circle is 17.0

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Answer:

a = 3

Substitute the value of point (a,7) in the equation and solve for a

5(a)-7=8

5(a)=8+7

5(a)=15

a = 15/5 = 3

God Bless and stay safe!

- Eli <3

Answer:

(i) 9

(ii) 12

Step-by-step explanation:

Comedy is 90 degrees out of 360 degrees or 1/4 of the circle.

36 students took the survey.

1/4 × 36 = 9

Horror is 120 degrees out of 360 degrees or 1/3 of the circle.

1/3 × 36 = 12

Answer:

9 comedy

12 horror

Step-by-step explanation:

First, there are 360 degrees in a circle.

Comedy = 90 degrees

Action and romance = 90 degrees combined

Horror = 120 degree

Science fiction = 60 degrees

To find sci fi : 90 +90 +120 = 300 - 360 = 60 degrees

36 students took the survey.

1/4 × 36 = 9

Horror is 120 degrees out of 360 degrees or 1/3 of the circle.

1/3 × 36 = 12

Answer:

Hey there!

You can use the ASA postulate, when two angles are congruent, and one side is congruent.

Hope this helps :)

The root of a number is equivalent of being raised to its inverT

11 cubic root is = 1/11

X = 1/11

Answer:

x = -3/4, 1

Step-by-step explanation:

Factor left side of the equation.

(4x + 3)(x - 1) = 0

Set factors equal to 0.

4x + 3 = 0

4x = -3

x = -3/4

x - 1 = 0

x = 1

Answer:

x₁ = -3/4

x₂ = 1

Step-by-step explanation:

4x² - x - 3 = 0

4x² + 3x - 4x - 3 = 0

xx(4x + 3) - 4x - 3 = 0

xx(4x + 3) - (4x + 3) = 0

(4x + 3) × (x - 1) = 0

4x + 3 = 0 → x = -3/4

x - 1 = 0 → x = 1

Hope this helps! :)

Answer:

  (4.4, 4.4)

Step-by-step explanation:

The point S can be found as the weighted average of the end points. The relative weights are the reverse of the distances to the end points:

  RS : ST = 1 : 4

  S = (4R +1T)/5

  S = (4(2, 2) +(14, 14))/5 = (22, 22)/5

  S = (4.4, 4.4)

Answer:

1. 4/5

2. 80%

Step-by-step explanation:

Answer:

40 km away.

Step-by-step explanation:

a^2 + b^2 = c^2

In this case, a = 16 * 2 = 32 km, since he travels 16 km per hour for 2 hours.

b = 12 * 2 = 24 km, since she travels 12 km per hour for 2 hours.

32^2 + 24^2 = c^2

1,024 + 576 = c^2

1600 = c^2

c^2 = 1600

c = plus or minus 40

Since distance cannot be negative, they will be 40 km away.

Hope this helps!

The required, after 2 hours, Rachel and Amos will be 40 kilometers apart.

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

Here,

We can use the Pythagorean theorem to solve this problem. After 2 hours, Rachel will have traveled 24 kilometers (12 km/hour x 2 hours) due east, and Amos will have traveled 32 kilometers (16 km/hour x 2 hours) due north. Let's call the distance between them after 2 hours "d".

Using the Pythagorean theorem, we can write:

d² = (24 km)²+ (32 km)²

Simplifying this expression:

d² = 576 km² + 1024 km²

d² = 1600 km²

Taking the square root of both sides,

d = 40 km

Therefore, after 2 hours, Rachel and Amos will be 40 kilometers apart.

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Answer:

Option B

Step-by-step explanation:

With a scale factor of 1/2, the dilated shape should be smaller because of the scale factor, So in Option B the dilated shape is smaller than the real one.

1) Option A is an enlargement

2) Option B is reduction

3) Option C is equality

Answer:

x = 1.

Step-by-step explanation:

y = k(x + 3)

When x = 3 y = 12 so

12 = k(3 + 3)

6k = 12

k = 2.

So the relation is y = 2(x + 3)

When y is 8:

8 = 2(x + 3)

2x = 8 - 2*3 = 2

x = 1.

Answer:

3/2

Step-by-step explanation:

Using two points we can find the slope of a line

(0,1) and  (2,4)

The slope is given by

m= (y2-y1)/( x2-x1)

   = (4-1)/(2-0)

   = 3/2

Answer:

I hope it will help you....

Distribute the sum:

[tex]\displaystyle\sum_{i=1}^{24}(3i-2)=3\sum_{i=1}^{24}i-2\sum_{i=1}^{24}1[/tex]

Use the following formulas:

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

[tex]\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2[/tex]

[tex]\implies\displaystyle\sum_{i=1}^{24}(3i-2)=3\cdot\frac{24\cdot25}2-2\cdot24=\boxed{852}[/tex]

In case you don't know where those formulas came from:

The first one is obvious; you're just adding n copies of 1, so 1 + 1 + ... + 1 = n.

The second can be proved in this way: let S be the sum 1 + 2 + 3 + ... + n. Rearrange it as S = n + (n - 1) + (n - 2) + ... + 1. Then 2S = (n + 1) + (n + 1) + (n + 1) + ... + (n + 1), or n copies of n + 1. So 2S = n(n + 1). Divide both sides by 2 and we're done.

Hey there! :)

Answer:

y = 5x + 10

Step-by-step explanation:

From the information given, we can derive the points (-2, 0) and (0, 10). Find the slope using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the points:

[tex]m= \frac{10 - 0}{0 - (-2)}[/tex]

Simplify:

[tex]m= \frac{10}{2}[/tex]

m = 5.

The equation in slope-intercept form is y = mx + b. We were already given the b value, or y-intercept as y = 10. Therefore:

y = 5x + 10 is the equation written in slope-intercept form.

Answer:

y=5x+10

Step-by-step explanation:

The base form of the equation is y=mx+b

B is always the y intercept so we can plug that in

y=mx+10

Then we can fine the slope by using the gradient formula

Change in y over change in x

The two points are (-2, 0) and (0, 10)

The result is 10/2 which can be simplified to 5

y=5x+10

Answer:

[tex]y=359x+1500[/tex]

Step-by-step explanation:

The data provided is as follows:

Months (x)     Costs  (y)

      1               $1,859

      3              $2,577

      8              $4,372

     12              $5,808

The slope intercept form is:

[tex]y = mx+b[/tex]

Here,

m = slope

b = intercept.

Compute the value of m and b as follows:

[tex]\begin{aligned} b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 14616 \cdot 218 - 24 \cdot 114262}{ 4 \cdot 218 - 24^2} \approx 1500 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 4 \cdot 114262 - 24 \cdot 14616 }{ 4 \cdot 218 - \left( 24 \right)^2} \approx 359\end{aligned}[/tex]

The equation in slope-intercept form to represent the total cost, y, of leasing a car for x months is:

[tex]y=359x+1500[/tex]

Answer:

4 ( -x^3 + 2x - x)

Step-by-step explanation:

refer the attachment

Answer:

[tex]\boxed{\mathrm{view \: attachment}}[/tex]

Step-by-step explanation:

The zeros of a function is where the function crosses the x-axis. The x-intercepts are the zeros of a function.

[tex]f(x) = (x - 1)(x - 7)[/tex]

Let output equal to 0.

[tex]0 = (x - 1)(x - 7)[/tex]

Set factors equal to 0.

[tex]x-1=0\\x=1[/tex]

[tex]x-7=0\\x=7[/tex]

The zeros of the function are [tex]x=1[/tex] and [tex]x=7[/tex].

Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

0.05 in per min.

Step-by-step explanation:

We simply divide 6 by 120 to find our unit rate:

6 in/120 min = 1/20 = 0.05 in/1 min

Answer:

1/20 Inch per. Minute

Step-by-step explanation:

6/120 -->

6/1 x 1/120 --> cancel out 6 and 120 for 1 and 20 respectively

1/1 x 1/20 --> 1 x 1/20 => 1/20

Hope this helps!

Answer:

a) 26

b) 50

Step-by-step explanation:

a ) 5^2 +1 =26

b ) 5 ^2*2=50

Answer:

261/44

Step-by-step explanation:

hope this helps. :)

Answer:

9 1/2

Step-by-step explanation:

7 1/2 - 1 5/8 + (1 3/8 × 2 7/11)​ =

= 7 4/8 - 1 5/8 + 11/8 * 29/11

= 6 12/8 - 1 5/8 + 29/8

= 5 7/8 + 3 5/8

= 8 12/8

= 8 + 8/8 + 4/8

= 9 1/2

Answer:

11.47

Step-by-step explanation:

Use SohCahToa. In this problem, you are given the hypotenuse and you are trying to solve for the adjacent side so it will be cosine. (cosine = [tex]\frac{adjacent}{hypotenuse}[/tex])

1. set up the equation

cos55 = [tex]\frac{x}{20}[/tex]

2. Multiply both sides by 20 to solve for x

20 · cos55 = 11.47

Answer:

Solution,

From the figure,

[tex]cos \: 55 = \frac{PQ}{PR} [/tex]

[tex]cos \: 55 = \frac{PQ}{20} [/tex]

[tex]PQ = 20 \: cos \: 55[/tex]

[tex]PQ= 11.472[/tex]

[tex]PQ= 11 .47[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

B. 8sqrt(2)

Step-by-step explanation:

The legs of an isosceles right triangle are congruent and measure 45 deg. The right angle measures 90 deg. The ratio of the lengths of the sides of a 45-45-90 deg triangle is 1 : 1 : sqrt(2).

Since the hypotenuse measures 8, then the legs measure 8/sqrt(2)

8/sqrt(2) * sqrt(2)/sqrt(2) = 8sqrt(2)/2 = 4sqrt(2)

Answer: B. 8sqrt(2)

Answer:

40/100 = 0.4

your welcome

Answer:

e)  (3.77%, 8.70%)

95% confidence interval for the percentage of all medical students who plan to work in a rural community

(3.83% , 8.69%)

95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices

(0.406 , 0.454)

Step-by-step explanation:

Step(i):-

Given random sample size 'n' = 369

Sample proportion

                              [tex]p = \frac{x}{n} = \frac{23}{369} = 0.0623[/tex]

95% confidence intervals are determined by

[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.0623 - 1.96 \sqrt{\frac{0.0623(1-0.0623)}{369} } , 0.0623 + 1.96\sqrt{\frac{0.0623(1-0.0623)}{369} })[/tex]

(0.0623 - 0.0246 , 0.0623 + 0.0246)

(0.0383 , 0.0869)

(3.83% , 8.69%)

95% confidence interval for the percentage of all medical students who plan to work in a rural community

(3.83% , 8.69%)

Step(ii):-

Given 43% of those polled blamed of companies the most for the recent increase in gasoline prices

sample proportion 'p' = 0.43

Given Margin of error (M.E) = 0.024

95% confidence intervals are determined by

[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.43 - 0.024 } , 0.43 +0.024 )[/tex]

(0.406 , 0.454)

Final answer:-

95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices

(0.406 , 0.454)

Answer:

Step-by-step explanation:

Solve 3x + 5y = 1 for y to obtain the slope of the given line:

5y = -3x + 1, or y = (-3/5)x + 1.

Any line perpendicular to this one has the slope which is the negative reciprocal of (-3/5):  That would be 5/3.

The desired line has slope 5/3 and passes through (2, 7);

Adapt y = mx + b by substituting the known values, to find b:

7 = (5/3)(2) + b.  The LCD is 3, so multiply each term by 3 to eliminate the fractional coefficient:

21 = 10 + 3b, or 11 = 3b.  Then b = 11/3, and the desired equation in slope intercept form is

y = (5/3)x + 11/3

To obtain the standard form, multiply all three terms by 3 again:

3y = 5x + 11, or

5x + 11 - 3y = 0, or

5x - 3y + 11 = 0

Answer:

[tex]m\angle 2=53^{\circ}[/tex]

[tex]m\angle 7=74^{\circ}[/tex]

Step-by-step explanation:

It is given that quadrilateral GHJK is a rectangle and [tex]n\angle 3=37^{\circ}[/tex].

All interior angles of a rectangle are right angles. Diagonals are equal and bisect each other.

Now,

[tex]m\angle HKJ+m\angle HKG=90^{\circ}[/tex]    (Interior angles of a rectangle are right angles)

[tex]m\angle 3+m\angle HKG=90^{\circ}[/tex]

[tex]37^{\circ}+m\angle HKG=90^{\circ}[/tex]

[tex]m\angle HKG=90^{\circ}-37^{\circ}[/tex]

[tex]m\angle HKG=53^{\circ}[/tex]

In an isosceles triangle, angle with equal sides are equal.

[tex]m\angle JGK=m\angle HKG[/tex]

[tex]m\angle 2=53^{\circ}[/tex]

Therefore, measure of angle 2 is 53 degrees.

Let the diagonals intersect each other at point O.

In triangle OGK,

[tex]m\angle OGK+m\angle OKG+m\angle GOK=180^{\circ}[/tex]    (Angle su property)

[tex]53^{\circ}+53^{\circ}+m\angle GOK=180^{\circ}[/tex]

[tex]106^{\circ}+m\angle GOK=180^{\circ}[/tex]

[tex]m\angle GOK=180^{\circ}-106^{\circ}=74^{\circ}[/tex]

Vertical opposite angles are equal. So,

[tex]m\angle 7=74^{\circ}[/tex]

Therefore, measure of angle 7 is 74 degrees.

Answer:

y=2x-8

Step-by-step explanation:

Every hour, temperatures INCREASE by two degrees, so 2x.

At the beginning (x=0), the temperature was -8 degrees, so -8.

So temperature as a function of time is y=2x-8

Answer:

y = 2x-8

Step-by-step explanation:

At the beginning = -8 F

Let y be the temperature and x be the no. of hours

So, the equation becomes

=> y = -8 + 2x

Writing it in proper form

=> y = 2x-8