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3 years ago

Check all that are equivalent A=1/2h(b1+b2), 2A=hb1+b2, b1=2A/h-b2, b1=2(A-1/2hb2)/h

Mathematics

1 answer:

VMariaS [17]3 years ago

7 0

Answer:

(A) $A=\dfrac12h(b_1+b_2)$

(D) $b_1=\dfrac{2(A-\dfrac12 hb_2)}{h}$

Step-by-step explanation:

Given that:

$A=\dfrac12h(b_1+b_2)$

$2A=h(b_1+b_2)\\2A=hb_1+hb_2\\hb_1=2A-hb_2\\b_1=\dfrac{2A-hb_2}{h} \\b_1=\dfrac{2(A-\dfrac12 hb_2)}{h}$

Therefore, A and D are equivalent

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Unit 7: Polygons and Quadrilaterals Homework 6: Kites Need Help Stat PLEASE HELP!!!!! 20 POINTS

balu736 [363]

1) The measures of angles H and F are 121°, respectively.

2) The measures of angles U and V are 65° and 139°, respectively.

3) The missing angles are $m \angle 1 = 72^{\circ}$ , $m\angle 2 = 72^{\circ}$ , $m\angle 3 = 47^{\circ}$ , $m\angle 4 = 90^{\circ}$ , $m\angle 5 = 18^{\circ}$ , $m\angle 6 = 47^{\circ}$ and $m\angle 7 = 43^{\circ}$ .

4) The missing angles are $m \angle 1 = 55^{\circ}$ , $m\angle 2 = 35^{\circ}$ , $m\angle 3 = 35^{\circ}$ , $m\angle 4 = 90^{\circ}$ , $m \angle 5 = 55^{\circ}$ , $m \angle 6 = 67^{\circ}$ , $m\angle 7 = 67^{\circ}$ , $m\angle 8 = 23^{\circ}$ and $m \angle 9 = 23^{\circ}$ , respectively.

5) The measure of side $QT$ is $\sqrt{105}$ .

6) The measure of side $DF$ is $4\sqrt{26}$ .

7) The measure of side $NP$ is $3\sqrt{65}$ .

8) The value of $x$ is 17.

9) The value of $x$ is 6.

10) The measure of angle EDC is 107°.

11) The measure of angle RST is 122°.

<h3>How find missing angles and sides in rhombuses</h3>

1) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the measures of angles H and F are 121°, respectively. $\blacksquare$

2) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the measures of angles U and V are 65° and 139°, respectively. $\blacksquare$

3) According to geometry, the sum of internal angles in a triangle equals 180° and the sum of internal angles in a quadrilateral equals 360°. The missing angles are $m \angle 1 = 72^{\circ}$ , $m\angle 2 = 72^{\circ}$ , $m\angle 3 = 47^{\circ}$ , $m\angle 4 = 90^{\circ}$ , $m\angle 5 = 18^{\circ}$ , $m\angle 6 = 47^{\circ}$ and $m\angle 7 = 43^{\circ}$ , respectively. $\blacksquare$

4) According to geometry, the sum of internal angles in a triangle equals 180° and the sum of internal angles in a quadrilateral equals 360°. The missing angles are $m \angle 1 = 55^{\circ}$ , $m\angle 2 = 35^{\circ}$ , $m\angle 3 = 35^{\circ}$ , $m\angle 4 = 90^{\circ}$ , $m \angle 5 = 55^{\circ}$ , $m \angle 6 = 67^{\circ}$ , $m\angle 7 = 67^{\circ}$ , $m\angle 8 = 23^{\circ}$ and $m \angle 9 = 23^{\circ}$ , respectively. $\blacksquare$

5) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$QT = \sqrt{PQ^{2}-PT^{2}}$

$QT = \sqrt{13^{2}-8^{2}}$

$QT = \sqrt{105}$

The measure of side $QT$ is $\sqrt{105}$ . $\blacksquare$

6) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$DF = 2\cdot DH$ , $DH = \sqrt{DE^{2}-EH^{2}}$

$DF = 2\cdot \sqrt{DE^{2}-EH^{2}}$

$DF = 2\sqrt{15^{2}-11^{2}}$

$DF = 4\sqrt{26}$

The measure of side $DF$ is $4\sqrt{26}$ . $\blacksquare$

7) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$NK = 7\cdot x - 1$ , $NM = 10\cdot x - 13$ , $KM = 24$ , $NK = NM$ , $KP = \frac{KM}{2}$

$NP = \sqrt{NK^{2}-KP^{2}}$

$NP = \sqrt{[7\cdot (4)-1]^{2}-12^{2}}$

$NP = 3\sqrt{65}$

The measure of side $NP$ is $3\sqrt{65}$ . $\blacksquare$

8) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the value of $x$ is 17. $\blacksquare$

9) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the value of $x$ is 6. $\blacksquare$

10) According to geometry, the sum of internal angles in a triangle equals 180°. Hence, we have the following expressions:

$m\angle EDC = 180^{\circ}-90^{\circ}-[2\cdot (2)+13]$

$m\angle EDC = 107^{\circ}$

The measure of angle EDC is 107°. $\blacksquare$

11) According to geometry, the sum of internal angles in a triangle equals 180°. Hence, the angle RST is:

$m\angle RST = 2\cdot (3\cdot 12 +25)$

$m \angle RST = 122^{\circ}$

The measure of angle RST is 122°. $\blacksquare$

To learn more on quadrilaterals, we kindly invite to check this verified question: brainly.com/question/25240753

8 0

3 years ago

The equation ℎ = −162 + 32 + 9 gives the height of a ball, h, in feet above the ground, at t seconds after the ball is thrown up

Maru [420]

Answer:

time = 1secs

Max height = 25metres

Step-by-step explanation:

Let the equation that models the height of the ball be expressed as;

h(t) = −16t^2 + 32t + 9

t is the time in seconds

The velocity of the ball at its maximum height is zero i.e dh/dt = 0

dh/dt = -32t + 32

0 = -32t + 32

32t = 32

t = 32/32

t = 1 seconds

The ball will reach its maximum height after 1 seconds.

Get the maximum height reached. Substitute t = 1 into the modeled function;

h(t) = −16t^2 + 32t + 9

h(1) = −16(1)^2 + 32(1) + 9

h(1) = −16 + 32 + 9

h(1)= 16+9

h(1) = 25

Hence the maximum height reached is 25metres

4 0

3 years ago

How many 5/8-foot pieces of wood can you cut from a board 4 5/8 feet long

Leona [35]

Divide 4 and 5/8 by 5/8. you will get 7 and 2/5, or 7.4. since this you need whole pieces of wood, round down to 7.

final answer=7 pieces of wood

8 0

3 years ago

What multiples of 4 are not factors of 48?

MakcuM [25]

Multiples of four:
4, 8, 12, 16, 24, 28, 32, 36

Is 4 a factor of 48?
48/4=12
Yes, so that means 4 is not the answer.

Is 8 a factor of 48?
48/8=6
Yes, so that means 8 is not the answer.

Is 12 a factor of 48?
48/12=4
Yes, so that means 12 is not the answer.

Is 16 a factor of 48?
48/16=3
Yes, so that means 16 is not the answer.

Is 24 a factor of 48?
48/24=12
Yes, so that means 24 is not the answer.

Is 28 a factor of 48?
48/28= irrational number
No, so that means 28 is the answer.

Is 32 a factor of 48?
48/32= irrational number
No, so that means 32 is the answer.

Is 36 a factor of 48?
48/36= irrational number
No, so that means 36 is the answer.

Answer: 28, 32, 36

7 0

3 years ago

Read 2 more answers

Wayne Gretsky scored a Poisson mean six number of points per game. sixty percent of these were goals and forty percent were assi

BartSMP [9]

Answer:

a) The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

b) 0.05 = 5% probability that he has four goals and two assists in one game

Step-by-step explanation:

In hockey, a point is counted for each goal or assist of the player.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval. The standard deviation is the square root of the mean.

(a) Find the mean and standard deviation for the total revenue he earns per game.

60% of six are goals, which means that 60% of the time he earned 3K.

40% of six are goals, which means that 40% of the time he earned 1K.

The mean is:

$\mu = 6*0.6*3 + 6*0.4*1 = 13.2$

The standard deviation is:

$\sigma = \sqrt{\mu} = \sqrt{13.2} = 3.63$

The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

(b) What is the probability that he has four goals and two assists in one game

Goals and assists are independent of each other, which means that we find the probability P(A) of scoring four goals, the probability P(B) of getting two assists, and multiply them.

Probability of four goals:

60% of 6 are goals, which means that:

$\mu = 6*0.6 = 3.6$