On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2). Which statement best explains the relationship between lines FG and HJ? They are perpendicular because their slopes are equal. They are perpendicular because their slopes are negative reciprocals. They are not perpendicular because their slopes are equal. They are not perpendicular because their slopes are not negative reciprocals.

Answer:

The completed proportions are;

ED/A_F = CE/CA = CF/CD

Step-by-step explanation:

The given m∠CED = m∠A

∴ Angle ∠CDE = Angle ∠A_FC, (corresponding angles)

Angle ∠ECD = Angle ∠ACF (reflexive property)

Triangle ΔDCE is similar to triangle ΔACF (Angle Angle Angle (AAA) similarity)

In triangle ΔDCE and triangle ΔACF

m∠A is bounded by CA and A_F

m∠CED is bounded by CE and ED

∠DCE is bounded by CE and DE

∠C is bounded by CA and CF

Based on the orientation of the two triangles, we have

ED is the corresponding side to A_F, CD is the  corresponding side to CF, CE is the corresponding side to CA

Therefore, we have;

ED/A_F = CE/CA = CF/CD.

Answer:

Option C is the correct option

Step-by-step explanation:

Let the points be A and B

A ( 4 , 5 ) ------> ( x1 , y1 )

B ( 10 , 13 ) ------> ( x2 , y2 )

Now, let's find the distance between these points:

[tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

plug the values

[tex] = \: \sqrt{(10 - 4) ^{2} + {(13 - 5)}^{2} } [/tex]

Calculate the difference

[tex] = \sqrt{ {(6)}^{2} + {(8)}^{2} } [/tex]

Evaluate the power

[tex] = \sqrt{36 + 64} [/tex]

Add the numbers

[tex] = \sqrt{100} [/tex]

Write the number in exponential form with. base of 10

[tex] = \sqrt{ {(10)}^{2} } [/tex]

Reduce the index of the radical and exponent with 2

[tex] = 10 \: units[/tex]

Hope this helps..

Best regards!!

Answer:

167.55

Step-by-step explanation:

so it varies jointly so

A-area if cylinder

so

[tex]a \: \alpha \: \pi \: r \: ^{2} h[/tex]

so

[tex]a = k\pi \: r^{2}h[/tex]

where k is the constant

so apply the first set of values to get k=2/3

then substitute the k with the second set of values

Answer: Ask the king to draw first and read it. Explain that if the king selects "leave" the PM's choice could only be "stay". It is then unnecessary for the PM to draw. It avoids embarrassing the king in his lie, demonstrates the PM's intelligence, and keeps his job.

Step-by-step explanation:

Answer:

Option A is the correct option.

Step-by-step explanation:

As PW is the median.

PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )

Plug the values

x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]

Calculate the sum

x = [tex] = \frac{1}{2} \times 17.6[/tex]

Calculate the product

x = [tex] = 8.8[/tex]

Hope this helps...

Best regards!

Answer:

-30

Step-by-step explanation:

7m + 2n - 8p/n

Let  m = –4, n = 2, and p = 1.5

7(-4) + 2 ( 2) -8*(1.5)/2

-28 + 4 - 4*1.5

-28+ 4 - 6

-30

Answer:

-30

Step-by-step explanation:

Hey there!

Well given,

m = -4

n = 2

p = 1.5

We need to plug those number into,

7m + 2n - 8p/n

7(-4) + 2(2) - 8(1.5)/(2)

-28 + 4 - 12/2

-28 + 4 - 6

-24 - 6

-30

Hope this helps :)

Answer:

B. 6sqrt(2).

Step-by-step explanation:

Since the two legs of the right triangle are congruent, this is a 45-45-90 triangle. That means that the hypotenuse will measure xsqrt(2) units, and each leg will measure x units.

In this case, x = 6.

So, the hypotenuse is B. 6sqrt(2).

Hope this helps!

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 4 and (a, b) = (- 3, - 4) , thus

y - (- 4) = 4(x - (- 3)) , that is

y + 4 = 4(x + 3) → C

Answer:

[tex]\boxed{\sf \ \ 28 \ \ }[/tex]

Step-by-step explanation:

Hello,

Please find attached the graph

AB = 6-2 = 4

DA = 7-0 = 7

So the area of the rectangle is AB * DA = 4 * 7 = 28

Hope this helps

Step-by-step explanation:

The dimensions are (8-2x) and (10-2x) We will say the depth of the box is x. The equation we use for the volume of the box is V=x(8-2x)(10-2x)

Answer:

part b of the answer is x=1.5 inches

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

< DBG = 1/2 ( DG)

< DBG = 1/2 ( 360 - BD - BG)

           = 1/2 ( 360 - 172 - 150)

           = 1/2 (38)

           = 19

Answer:

The correct option is

This is a polynomial function of degree 7 with a leading coefficient of -1

Step-by-step explanation:

Functions that consist of a variable such as x raised to positive integer powers which are equal to or larger than zero added together to make the function are known as polynomial functions

Therefore, the function in the question which is f(X) = x⁴ × (2 - x³) + 1

Which can be expanded as follows

f(x) = 2·x⁴ - x⁷ + 1, which is the same as given as follow equation;

f(x) = -x⁷ + 2·x⁴ + 1

Which is  polynomial function with a leading coefficient of -1 as it consists of only whole number positive powers of x including the powers of x 4 and 7  

Therefore, the correct option is that f(x) is a polynomial function of degree 7 with a leading coefficient of -1.

Answer:

518 / 3.

Step-by-step explanation:

(74 / 3) * 7 = (74 * 7) / 3 = 518 / 3 = 172 and 2/3 = 172.6666666667.

Hope this helps!

Answer: [tex]4\sqrt{3}[/tex] .

Step-by-step explanation:

Distance formula : Distance between points (a,b) and (c,d) is given by :-

[tex]D=\sqrt{(d-b)^2+(b-a)^2}[/tex]

Distance between points [tex](-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3})[/tex].

[tex]D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}[/tex]

Hence, the correct option is [tex]4\sqrt{3}[/tex] .

Without further context I can't say much other than the radius is perpendicular to the tangent. In other words, the radius and tangent line form a 90 degree angle. This is one particular radius and its not just any radius. The radius in question must have the point of tangency as its endpoint.

The radius, AB  is perpendicular to the tangent line,  BC  so their slopes are negative reciprocals of one another. Because I generated a circle at random for this activity, this conclusion likely applies to any tangent line to a circle. In other words, the tangent line to any circle is perpendicular to the radius at their point of intersection.

Answer:

D

Step-by-step explanation:

The chord- chord angle 105° is half the sum of the arcs intercepted by the angle and its vertical angle, thus

[tex]\frac{1}{2}[/tex](120 + x) = 105 ( multiply both sides by 2 )

120 + x = 210 ( subtract 120 from both sides )

x = 90 → D

Answer:

The slope is 1/3 and the y intercept is 6

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

3y -x =18

Add x to each side

3y = x+18

Divide each side by 3

3y/3 = x/3 +18/3

y = 1/3x +6

The slope is 1/3 and the y intercept is 6

We need to solve for y (y = mx + b):

3y - x = 18

~Add x to both sides

3y = 18 + x

~Divide 3 to everything

y = 6 + x/3 or y = 6 + 1/3/x

So... 1/3 is the slope and 6 is the y-intercept.

Best of Luck!

Answer:

Since ΔABC is equilateral, ∠ACB = 60°. Since ΔCED is isosceles (we know this because CE = ED from the graph), ∠ECD = ∠EDC from Base Angles Theorem, and since the sum of angles in a triangle is 180°, they measure (180 - 32) / 2 = 74° each. Since BCD is a straight line, it measures 180° so we can write:

60 + x + 74 = 180

134 + x = 180

x = 46°

Answer:

46 degrees

Step-by-step explanation:

Since triangle ABC is equilateral that means each angle in that triangle is 60 degrees.

We also know that for triangle ECD angle C and angle D have to be 74 degrees, because a triangle has 180 degrees in total and the only unique angle is at the top which is 32. So it is 180-32=148, than 148/2=74.

We than know that a half circle is 180 degrees aswell, so we do 180-60=120

120-74=46

Answer:

  £531.52

Step-by-step explanation:

We are given the profit in week 1 and information about week 2. We are asked for the difference between week 2 profit and week 1 profit.

__

In week 2, pizza is sold 4 ways. The diagram shows the numbers of pizzas sold each way. The table shows the profit made for each way the pizza was sold. We need to add up the profits from each of the sales to find the profit for week 2.

Then the total profit in week 2 is ...

  £1514.04 -175.42 +888.94 -5.68 = £2221.88

So, profit in week 2 exceeds profit in week 1 by ...

  £2221.88 -1690.36 = £531.52 . . . more profit in week 2

Answer: 1/5

Step-by-step explanation:

Given the following :

Total number of ducks in pool = 30

Mark 1 = 15 ducks

Mark 2 = 9 ducks

Mark 3 = 6 ducks

Probability of picking a duck with Mark 3:

Probability = (number of required outcomes / total possible outcomes)

Number of required outcomes = number of ducks with mark 3 = 6 ducks

P(picking a duck with Mark 3) = 6/30

6/30 = 1/5

= 1/5

Answer:

3.9

Step-by-step explanation:

Pythagorean theorem:

a^2 + b^2 = c^2

a^2 + 1^2 = 4^2

a^2 + 1 = 16

a^2 = 15

a = sqrt(15)

a = 3.9

Answer a = 3.9 yards

Answer:

[tex]\boxed{3.9}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

Apply Pythagorean theorem.

[tex]a^2 + b^2 = c^2[/tex]

[tex]a^2 + 1^2 = 4^2[/tex]

[tex]a^2 + 1 = 16[/tex]

[tex]a^2 = 15[/tex]

[tex]a=\sqrt{15}[/tex]

[tex]a \approx 3.872983[/tex]

Answer: -1.8

Step-by-step explanation:

Start at -5.5 and move the point on the number line up 3.7 spaces.

Hope it helps <3

Answer:

Your correct answer is -1.8

Step-by-step explanation:

−5.5 + 3.7

= −5.5+3.7

= −1.8

Answer:

P(X ≤ 94) =  0.09012

From what we observe; There is a probability  of less than 94 people who voted for the referendum is 0.09012

Comment:

The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.

Step-by-step explanation:

From the information given :

An exit poll of 200 voters finds that 94 voted for the referendum.

How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52​? Based on your​ result, comment on the dangers of using exit polling to call elections.

This implies that ;

the Sample size n = 200

the probability p = 0.52

Let X be the random variable

So; the Binomial expression can be represented as:

X [tex]\sim[/tex] Binomial ( n = 200, p = 0.52)

Mean [tex]\mu[/tex] = np

Mean [tex]\mu[/tex]  = 200 × 0.52

Mean [tex]\mu[/tex]  = 104

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{np(1-p)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(1-0.52)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(0.48)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{49.92}[/tex]

The standard deviation [tex]\sigma[/tex] = 7.065

However;

P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .

The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5

Now;

x = 94.5

Therefore;

[tex]z = \dfrac{x- \mu}{\sigma}[/tex]

[tex]z = \dfrac{94.5 - 104}{7.065}[/tex]

[tex]z = \dfrac{-9.5}{7.065}[/tex]

z = −1.345

P(X< 94.5) = P(Z < - 1.345)

From the z- table

P(X ≤ 94) =  0.09012

From what we observe; There is a probability  of less than 94 people who voted for the referendum is 0.09012

Comment:

The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.

Answer:

2x-(3x+5) = -x-5

Step-by-step explanation:

     2x + 0

-

     3x + 5

-———————-

     -x - 5

Answer:

Step-by-step explanation:

m∠UTV = 112°  ⇒  m∠WTV = 180° - 112° = 68°

sin(68°) ≈ 0.9272

sin(∠WTV) = WV/TV

WV/10 ≈ 0.9272

WV ≈ 9.272

WV ≈ 9.3

Answer:

Hey there!

Sine is equal to opposite/hypotenuse

Tangent is equal to opposite/adjacent

opposite=a

hypotenuse=b

adjacent=c

Thus, tangent x= a/c.

Hope this helps :)

Answer:

tan x = a/sqrt(b^2 - a^2)

Step-by-step explanation:

sin x = a/b = opp/hyp

tan x = opp/adj

adj^2 + opp^2 = hyp^2

adj^2 + a^2 = b^2

adj = sqrt(b^2 - a^2)

tan x = a/sqrt(b^2 - a^2)

Answer:

10

Step-by-step explanation:

[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^2[/tex]

[tex]\left(x-6\right)^{2}+\left(y-0\right)^{2}=r^2\\[/tex]

We used (2,-3)

[tex]\left(2-6\right)^{2}+\left(-3-0\right)^{2}=25[/tex]

[tex]r^2=25\\[/tex] , so [tex]r = 5[/tex]

But this one is asking for the diameter, and to find it. It's simply 2r.

2*5 = 10

Answer:

The answer is 0.133

Step-by-step explanation:

All you have to do is take 2/3 as if it was a whole number and divide it by 5, or if you are able to use a calculator, you can just but it in as 2 divided by 3 and then divide 5 by whatever answer you get.

Answer:

Hello! 2/3 divided by 5 in fraction will be 2/15

Step-by-step explanation:

Since we have a 5 we need to change that into a fraction

5 would turn into 1/5

Now you have to multiply both of the fractions to get your answer.

2/3 x 1/5

= 2/15

(So 2/15 will be your answer.)

Hope this helps! :)

Answer:

6π

Step-by-step explanation:

First we need to find the circumference of the circle. We know that the radius is 4 and the formula is πd or 2πr

Leaving it in terms of pi, the circumference is 8π

Now we need to find the length of the arc.

Since the missing part of the circle is labeled with a right angle, we know that it's exactly 1/4 of the whole circle. That means the arc we need to find is 3/4 of the circumference.

3/4 of 8π is 6π