The surface area of a rectangular prism that has height of 4 inches, width of 9 inches and length of 3 inches

The angles ∠1 ≅ ∠4 since the line BD bisects ∠ABC, AD║ BC, and AB ║ CD. This is obtained by using the angle bisector theorem, alternate interior angles, and the transitive property of congruence.

Transitive property:

If ∠a and ∠b are congruent and ∠b and ∠c are congruent, then ∠a and ∠c are also congruent.

I.e., If ∠a ≅ ∠b and ∠b ≅ ∠c, then ∠a ≅ ∠c.

The angles bisector theorem states that the ray or line which bisects the angle divides the angle into two equal parts.

I.e., If line BD bisects the angle ∠ABC, then ∠B = ∠B1 + ∠B2

(where ∠B1 = ∠B2)

The line BD bisects ∠ABC, AD║BC, and AB║CD

The line BD bisects ∠ABC. So,

∠B = ∠3 + ∠4

According to the angle bisector theorem, ∠3 ≅ ∠4.

Since AD║BC and AB║CD, the alternate angle are congruent.

I.e., ∠3 ≅ ∠1

Thus, by the transitive property of congruence,

∠1 ≅ ∠4

Hence proved.

Learn more about the transitive property of congruence here:

https://brainly.com/question/2437149

#SPJ1

Hello,

I think it is 9y² + 21y - 18 = 0

we have a = 9 ; b = 21 and c = -18

∆ = b² - 4ac = 21² - 4 × 9 × (-18) = 1089 > 0

x1 = (-b - √∆)/2a = (-21 - 33)/9 = 6

x2 = (-b + √∆)/2a = (-21 + 33)/9 = 12/9 = 4/3

S = {4/3 ; 6}

Answer: -x

Apply Multiplicative Distribution Law:- 1/5 * 5x - 1/5 * 20 - 1/2 * 4x - 1/2 *(-8)

Determine the sign for multiplication or division: 1/5 * 5x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8

Cross out the common factor: x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8

Cross out the common factor: x - 4 - 1/2 * 4x + 1/2 * 8 - 4 - 2x + 1/2 * 8

Cross out the common factor: x - 4 - 2x + 1/2 * 8

Cross out the common factor:  x - 4 - 2x + 4

Reorder and gather like terms: (x - 2x) + (- 4 + 4)

Collect coefficients for the like terms: (1 - 2) * x + (- 4 + 4)

Calculate the sum or difference :  - x + (- 4 + 4)

The sum of two opposites equals 0: -x

Answer: -x

Learn more about Multiplicative Distribution Law here:https://brainly.com/question/2898526

#SPJ4

Answer:

D) Substitute 5 into each expression and evaluate them.

Step-by-step explanation:

Answer: D and B

Step-by-step explanation:

Formula for two terms = a + b

Therefore,

D and B have two terms aka one plus sign

D. a + c

B. m^4 + 6m

Hi! ❄

  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  

The sum of two terms is what we get after adding these two terms.

If you add two positive terms, you put a + sign in between these terms.

[tex]\sf{Example\!\!:a+b}[/tex]

If you add two negative terms, you put a - sign in between these terms.

[tex]\sf{Example\!\!:a-b}[/tex] (this is the same as [tex]\sf{a+-b}[/tex])

Let's look at the provided choices to see which one works.

It doesn't, because [tex]\sf{xy\neq x+y}[/tex]. In this expression a number x was multiplied by a number y. So this one doesn't check.

One down, three to go.

It does, because [tex]\sf{m^4+6m\stackrel\checkmark{=}m^4+6m}[/tex]. A number m was multiplied by itself 4 times, and then the product of that samee number m and 6 was added to it.

So this one checks.

It doesn't. It is indeed a sum, but we need 2 terms, not 3

So this one doesn't work.

It does, because [tex]\sf{a+c\stackrel\checkmark{=}a+c}[/tex]. So Choice D. also works.

Hope that made sense !!

  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\star\tiny\pmb{calligraphy}\star[/tex]

Answer:

1/12

Step-by-step explanation:

the chances of rolling a 3 is 1/6

there are 3 numbers more than 3 on a number die, 4,5, and 6

which is 3/6 or 1/2 if you decide to simplify

to find the probability you want you have to multiply the fractions by each other

1/6x1/2=1/12

Given that the distance and angle of elevation of the tree from P are 50 m. and 32°, and Q is 100 m. from P, we have;

a. The height of the tree is approximately 31.2 m.

b. i. The distance of Q from the base of the tree is 50•√5 m.

ii. The angle of elevation of the top of the tree from Q is approximately 15.6°

iii. The bearing of the tree from Q is 296.565°

a. tan(32°) = Height/50

Height = 50 × tan(32°) = 31.243 m.

b. i. The distance, d, of Q from the base of the tree is given by Pythagorean theorem as follows;

d = √(100² + 50²) = 50•√5

ii. The angle of elevation is given by trigonometric ratios as follows;

[tex]tan (\theta) = \frac{31.243}{50 \cdot \sqrt{5} } [/tex]

Which gives;

[tex]\theta= arctan \left( \frac{31.243}{50 \cdot \sqrt{5} } \right) \approx 15.6 ^{ \circ} [/tex]

iii. The angle formed at Q by the lines from Q to the point P and Q to the tree is found as follows;

Angle = arctan(50/100) ≈ 26.565°

The angle between the direction north of Q and a line from Q to the tree is therefore;

90° - 26.565° = 63.435°

The bearing, which is the angle described clockwise from the direction north of Q and the direction from Q to the tree, is therefore;

Bearing = 360° - 63.435° = 296.565°

Learn more about bearings in mathematics here:

https://brainly.com/question/23427938

#SPJ1

The total number of bars of kitkat Mr hassell had in total is 3 1/2 bars

Total bars of KitKat = 6 × 3/4

= (6×3)/4

= 18/4

= 9/2

= 4 1/2 bars

Number of bar remaining after eating 1 bar = 4 1/2 - 1

= 3 1/2 bars

Learn more about algebra:

https://brainly.com/question/723406

#SPJ1

Answer:

80

Step-by-step explanation:

Answer:

80 balls

Step-by-step explanation:

Julie's brother's balls x 20 = Julie's balls

4 x 20 = 80

Brainliest, please :)

Applying the trigonometric ratios, the equations that can be used are:

sin 45 = BC/9

cos 45 = BC/9

In the given image below, to find the unknown lengths of the triangle, we would apply the following trigonometric ratios:

To find AC, use the cosine ratio, CAH.

To find BC, use the sine ratio, SOH.

sin 45 = opp/hyp = BC/9

sin 45 = BC/9

cos 45 = adj/hyp = BC/9

cos 45 = BC/9

Learn more about the trigonometric ratios on:

https://brainly.com/question/10417664

#SPJ1

Answer: A, E

Step-by-step explanation: Sin(45)=BC/9 ; cos(45)=Bc/9

Answer:

  10.  20.9°

  11.  73.2°

Step-by-step explanation:

The inverse sine function is used to find the angle from its sine value.

In each case, the equation is of the form ...

  a/sin(x) = b/c

Multiplying both sides by c/b·sin(x), we find the solution is ...

  sin(x) = ac/b . . . . . find sin(x)

  x = arcsin(ac/b) . . . . . find the corresponding angle

For the given values a=7.2, b=13, c=sin(40°), we have ...

  x = arcsin(7.2sin(40°)/13) ≈ 20.9°

For the given values a=6.53, b=√40, c=sin(68°), we have ...

  x = arcsin(6.53sin(68°)/√40) ≈ 73.2°

Using the Pythagorean theorem and the law of sines, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are: A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°

The theorem states that the square of the longest side of a right triangle equals the sum of the squares of the lengths of the other two smaller sides of the right triangle.

The points, M(3,2), E(3,−3), and R(9,−3) has been plotted on the graph which shows that angle E  is a right triangle, therefore:

m∠E = 90 degrees.

Find ME and ER:

ME = 5 units

ER = 6 units.

Using the Pythagorean theorem, find MR:

MR = √(ME² + ER²)

MR = √(5² + 6²)

MR = √(25 + 36)

MR = 7.81 units

Using the law of sines, find m∠M:

sin M/ER = sin E/MR

sin M/6 = sin 90/7.81

sin M = (sin 90 × 6)/7.81

sin M = 0.7682

M = sin^(-1)(0.7682)

m∠M ≈ 50°

m∠R = 180 - 50 - 90

m∠R = 40°

Thus, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are:

A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°

Learn more about the Pythagorean theorem on:

https://brainly.com/question/343682

#SPJ1

The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

Polynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.

ax^2+bx+c and;

mx^2+nx+p

Take the sum of the polynomials

P(x) =. ax^2+bx+c

f(x) = mx^2+nx+p

Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.

Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

Learn more on polynomial function here: https://brainly.com/question/24380382

#SPJ1

The sample size needed to obtain a margin of error of 0.05 for the estimation of a population proportion is 384.

Given margin of error of 0.05 and confidence interval of 95%.

We have to find the sample size needed to obtain a margin of error of 0.5 with confidence level of 95%.

Margin of error is the difference between real values and calculated values.

The formula of margin of error is as under:

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where

z is the critical value of z for given confidence level

n is sample size

σ is population standard deviation

We have not given population standard deviation so we will use the following formula:

Margin of error=z*[tex]\sqrt{p(1-p)}[/tex]/[tex]\sqrt{n}[/tex]

We have to find z value for 95% confidence level.

z value=1.96

We know that [tex]\sqrt{p(1-p)}[/tex]<=1/2

put [tex]\sqrt{p(1-p)}[/tex]=1/2

Margin of error=1.96*1/2/[tex]\sqrt{n}[/tex]

0.05=1.96*0.5/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=0.98/0.05

[tex]\sqrt{n}[/tex]=19.6

squaring both sides

n=384.16

After rounding off we will get

n=384.

Hence the sample size needed to obtain a margin of error of 0.05 is 384.

Learn more about margin of error at https://brainly.com/question/10218601

#SPJ4

table 1, and table 2 are the answers.

we know that any function is increasing when for an increase in x-values, y-value should also increase

we will verify each table

table-1:

we can see that

x increase as -3, -2, -1 , 0, 1,2

y is also increasing -6,-3,-1,1,3,6

so, this is increasing

table-2:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but it is asking between -2 to 1

y-values are -4,-1,1,4.....which is increasing

so, this is  increasing

table-3:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but y changes from -3 to -5 .....which is decreasing

so, this is not increasing

table-4:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but y changes from 7 to 1 .....which is decreasing

so, this is not increasing

Learn more about function here:https://brainly.com/question/25638609

#SPJ4

The equation in slope intercept form is y = -4x/3 + 10

The representations are given as:

So, we have:

2 * x + 1.5 * y = 15

Evaluate the product

2x + 1.5y = 15

Subtract 2x from both sides

1.5y = -2x + 15

Divide through by 1.5

y = -4x/3 + 10

Hence, the equation in slope intercept form is y = -4x/3 + 10

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

The value of y from the given figure is 6√3

From the given figure, according to the theorem;

H² = 6² - 3²

H² = 36 - 9

H²  = 27

H = 3√3

Determine the value of y using the same theorem;

y² = 9² + ( 3√3)²

y² = 81. + 27

y = √108

y = 6√3

Hence the value of y from the given figure is 6√3

Learn more on Pythagoras theorem here: https://brainly.com/question/654982

#SPJ1

The population after 20 minutes is 14.

We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-        

            After 1 hour, the population is 3*10

            After 2 hours, -> 3*3*10

            After 3 hours, -> 3*3*3*10

Make a function from above observation in the increasing

              number of the  insects per hour

              This can be generalized as a function of t, the time in hours:

              f(t) = (3^t) * 10

putting the values in the function and get the desired answer,

                             P = (3^t) * 10

             Since 20 minutes is equal to (1/3) hours, t can be substituted for

             (1/3) in order to calculate the population size after 20 minutes:

                  P = (3^(1/3)) * 10 = 14.422 ≈ 14

The population after 20 minutes is 14.

Learn more about this here:

https://brainly.com/question/22809798

#SPJ1

Answer:The population after 20 minutes is 14.

We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-        

           After 1 hour, the population is 3*10

           After 2 hours, -> 3*3*10

           After 3 hours, -> 3*3*3*10

Make a function from above observation in the increasing

             number of the  insects per hour

             This can be generalized as a function of t, the time in hours:

             f(t) = (3^t) * 10

putting the values in the function and get the desired answer,

                            P = (3^t) * 10

            Since 20 minutes is equal to (1/3) hours, t can be substituted for

            (1/3) in order to calculate the population size after 20 minutes:

                 P = (3^(1/3)) * 10 = 14.422 ≈ 14

The population after 20 minutes is 14.

Step-by-step explanation:

The double number line that shows the other values of packages and pencils is A. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48.

It should be noted that a number line simply means a line which numbers are marked a intervals to illustrated numerical operations.

In this case, the double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48 illustrate this information

Learn more about number line on:

brainly.com/question/12399107

#SPJ1

The probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen is 0.031 or 3.1%. The events are dependent events.

Given that there are five vowels, which come from the letters A, E, I, O, and U, the likelihood of drawing a vowel is:

5/26

since there are a total of 26 alternatives available. After choosing that, we are left with 25 alternatives, 4 of which are vowels, thus the probability is:

4/25

The final likelihood is thus:

5/26 * (4/25) = 0.031

In other words, the likelihood is 3.1% when choosing a vowel and then another (without replacement).

The first event has an impact on the second event since there are fewer vowels and overall possibilities, hence the events are dependent.

Learn more about probability here :

https://brainly.com/question/16812448

#SPJ1

Answer:

2/x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution

You want to find the probability of one certain event happening. For example, you want the die to come up 5 and you want the 6 to be drawn from the cards.

The total number of outcomes is 6 (for the die) times 10 for the cards.

One 1 outcome is possible.

So the vent probability is 1/6*10 = 1/60. You will have to translate this to the choices you have been given. 1/60 = 0.0167 is another possibility.

Answer

1/60 or 0.0167

Using proportions, it is found that each farmer bought 68,008 kg.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each t has 1000 kg, hence the amount of maize seeds in kg is given as follows:

6460 x 1000 + 760 = 6,460,760 kg

The amount per farmer is:

6,460,760/95 = 68,008 kg.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

[tex]ac {}^{2} = cb {}^{2} + ba {}^{2} - 2(cb)( ba)(cos \alpha ) \\ ac {}^{2} = 21 {}^{2} + 26 {}^{2} - 2(21)(26)(cos112) \\ ac {}^{2} = 441 + 676 - 1092(cos112) \\ ac {}^{2} = 1526.07 \\ ac = 39.065[/tex]

Answer:

Step-by-step explanation:

Q14)

a) The smallest prime number is 2. The smallest composite number is 4.

b) Rs 720 - 20 [as loss]

=> Rs 790 = SP

c) Rs 500 - 30 [as profit]

=> Rs 470 = CP

d) a° + b° = 180°

Hope it helps you!

The length of the wall = 125m

The area of the Playground = 10000[tex]m^{2}[/tex]

What is geometry?

A branch of mathematics that broadly deals with the measurement, properties, and connections of points, lines, angles, surfaces, and solids: the investigation of qualities of given elements that hold true even after being subjected to predetermined transformations.

Given data:

Perimeter of the playground=410m

length of the wall = 80m

The playground's width can be calculated as follows if its length is 80 meters:

(Formula of Perimeter of a rectangle)

P=2(L+B)              

410=2(80 +B)

410= 160 + 2B

2B= 410-160

2B= 250

B= 125 m

This results in a 125 m length for the playground.

The area of playground.

Area = Length x Width

Area = 80 x 125

area = 10000[tex]m^{2}[/tex]

To know more about geometry visit:

https://brainly.in/question/6710595

#SPJ4

Based on the angle of the seesaw and the height off the ground, the maximum length of the seesaw is 2 meters.

This can be found as:

Sin 30° = 1 / Maximum length

Solving gives:

Sin 30° = 1 / Maximum length

Ml = 1 / Sin 30°

= 1 / 0.5

= 2 meters

Find out more on maximum length at https://brainly.com/question/24259483

#SPJ1

Step 1

Using the points (2,0) and (-2, -3), we get the slope is

[tex]\frac{-3-0}{-2-2}=\frac{3}{4}[/tex]

Step 2

Using the point (2,0), the equation is

[tex]y=\frac{3}{4}(x-2)[/tex]

Step 3

Using the distributive property, we get [tex]y=\frac{3}{4}x-\frac{3}{2}[/tex].

The equation of the perpendicular bisector of BC with B(-2, 1), and C(4, 2) is y = 7.6 - 6•x

The slope, m, of the line BC is calculated as follows;

The slope of the perpendicular line to BC is -1/(1/6) = -6

The midpoint of the line BC is found as follows;

[tex] \left( - 2 + \frac{4 - ( - 2)}{2}, \: 1 + \frac{2 - 1}{2} \right) = (1,\: 1.5)[/tex]

The perpendicular bisector is the perpendicular line constructed from the midpoint of BC.

The equation of the perpendicular bisector in point and slope form is therefore;

(y - 1.5) = -6•(x - 1)

y - 1.6 = -6•x + 6

y = -6•x + 6 + 1.6 = 7.6 - 6•x

Which gives;

Learn more about equations of perpendicular lines here:

https://brainly.com/question/11635157

#SPJ1