In the diagram below, the area of $\triangle BCD$ is 60. What is the length of side $\overline{BC}$?

Answer:

x° ≈ 60.4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = x°

Adjacent Leg = 43

Hypotenuse = 87

Step 2: Solve for x

Answer:

(12,0)

Step-by-step explanation:

So whenever you are asked for an "intercept" it is the point where a line crosses the axis. The x intercept is where the line crosses at the x axis (horizontal line on the graph) and the y intercept is where the y axis crosses (vertical axis).

So this question is really asking where is the point when y = 0

The x values in the chart are 5 apart-- 22 +5 = 27, 27+ 5 = 32

The y values are 18 apart --> 36 + 18 = 54, 54+ 18 = 72

Make a little chart where y = 0 (this is where the x crosses) and you can see

there is a point at (17, 18) and then (12, 0) and that point is the x intercept.

Answer:

(12, 0)

Step-by-step explanation:

the x-intercept is the point, where y=0.

so, the second coordinate is therefore 0, no matter what.

now, at what x is that ?

let's find the line function.

a line is

y = a×x + b

let's use the first point (22, 36)

36 = a×22 + b

a = (36 - b)/22

let's use the second point (27, 54)

54 = a×27 + b

now we use the first expression describing a in terms of b and insert that into the second expression.

54 = 27×(36 - b)/22 + b

54×22 = 27×(36 - b) + 22b = 972 - 27b + 22b

1188 = 972 - 5b

216 = -5b

b = -43.2

=>

a = (36 - -43.2)/22 = (36 + 43.2)/22 =79.2/22 = 3.6

our line is

y = 3.6x - 43.2

so, now back to the question, at what x is y=0 ?

0 = 3.6x - 43.2

3.6x = 43.2

x = 12

Answer:

4x² -4xy -4y -4

Step-by-step explanation:

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

In this case, a= 2x -y and b= y +2.

(2x -y)² -(y +2)²

= (2x -y +y +2)[2x -y -(y +2)]

= (2x +2)(2x -y -y -2)

= (2x +2)(2x -2y -2)

= 2x(2x) +2x(-2y) +2x(-2) +2(2x) +2(-2y) +2(-2) (expand)

= 4x² -4xy -4x +4x -4y -4

= 4x² -4xy -4y -4

Alternatively, start by expanding the brackets.

[tex]\boxed{(a - b)^{2} = {a}^{2} - 2ab \: + {b}^{2} }[/tex]

[tex]\boxed{(a + b)^{2} = {a}^{2} + 2ab \: + {b}^{2} }[/tex]

(2x -y)² -(y +2)²

= 4x² -4xy +y² -(y² +4y +4)

= 4x² -4xy +y² -y² -4y -4 (expand)

= 4x² -4xy -4y -4 (simplify)

Answer:

X=3

Y=1

Step-by-step explanation:

Vertex A forms dilation F

9514 1404 393

Answer:

  (C) Thursday on the playing fields

Step-by-step explanation:

The surface area of A is ...

  SA = 6s² = 6(5 cm)² = 150 cm² = 150(0.01 m)² = 0.015 m²

This matches Monday and Thursday.

The volume of D is ...

  V = Bh = (1/2bh)·h'

where b is the triangle base, h is the triangle height, and h' is the prism height.

  V = (1/2)(15 cm)(8 cm)(10 cm) = 600 cm³

This matches Thursday only.

__

The Accusation: Thursday on the playing fields.

Answer:

Answer:

Children= 384      Adults= 170

Step-by-step explanation:

First, write a system of algebraic equations:

[tex]1.75x+2.50y=1097[/tex]

[tex]x+y=554[/tex]

Second, use linear combination to eliminate one variable (I will eliminate x, or children.)

[tex]1.75x+2.50y=1097[/tex]

[tex]-1.75(x+y=554)[/tex]

[tex]1.75x+2.50y=1097[/tex]

[tex]-1.75x+-1.75y=-969.5[/tex]

[tex]0.75y=127.5[/tex]

Divide both sides by 0.75

[tex]0.75y=127.5[/tex]

[tex]/0.75[/tex]        [tex]/0.75[/tex]

[tex]y=170[/tex], there are 170 adults

Now, plug in 170 for [tex]x+y=554[/tex]

[tex]x+170=554[/tex]

Subtract 170 from both sides

[tex]x+170=554[/tex]

      [tex]-170[/tex]   [tex]-170[/tex]

[tex]x=384[/tex], there are 384 kids.

Hope this helps!!!

Answer:

384 children and 170 adults

Step-by-step explanation:

if x is children and y is adults

1.75x+2.5y=1097

x+y=554

1.75x=1097-2.5y

x=554-y

1.75x=1097-2.5y

1.75x=1.75(554-y)

1097-2.5y=969.5-1.75y

1097-969.5=2.5y-1.75y

127.5=0.75y

127.5/0.75=y

170=y

x+y=554

x=554-y

x=554-170

x=384

to prove these are correct just do 1.75(384)+2.5(170) and see if it equals 1097, and do 384+170 to see if its the amount of people

1.75(384)+2.5(170)

672+425

1097

384+170=554

Answer:

1. plants

2. together

3. is

4. family

5. talking

6. weeds

7. experience

8. planter

9. on

10. fields

11. too

12. method

13. around

14. react.

Explanation:

The given passage talks about the impact of chemicals on the ecosystem. The speaker narrates how the ecology belongs to plants, animals, and humans, though man seemed intent to destroy it for himself.

The blanks in the given passage are filled with the appropriate words as follows-

Ecology is the study of how (1) plants, animals, and people live (2) together and help each other. But man sometimes forgets he (3) is a part of the (4) family of all living things. Here is an example. A planter is (5) talking about killing (6) weeds on his land. He remembers his first (7) experience with a weedicide. He was a (8) planter then, working (9) on a rubber plantation. He had a problem with weeds. The cost of weeding of the (10) fields by hand was getting (11) too high. So he used a new, cheap, and effective (12) method, good old Sodium Arsenate. He sprayed plenty of this (13) around to kill the weeds. The first thing to (14) react were the frogs.

Answer:

1. mode

2. median, mode, mode interval

3. stem and leaf graph

4. not sure (try using a median calculator)

5. 80 or 90 (not exactly sure)

Step-by-step explanation:

Answer:

I've attached the Answer

Answer:

56Pi

Step-by-step explanation:

Area of small circle:

Pi*r^2

25Pi

Area of large circle:

Pi*r^2

81Pi

Area of the 2D doughnut :

Large -small circle = 81Pi-25Pi

Answer:

35m^2

Step-by-step explanation:

4×2.5=10 10×2=20

3×2.5=7.5 7.5×2=15

20+15=35

Hope this helps! :)

Neva is hungry and she buys a snack from the concession stand event is independent.

It is a branch of mathematics that deals with the occurrence of a random event.

Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.

Based on this definition, the scenario that depicts two independent events is Neva is hungry and she buys a snack from the concession stand.

The fact that Neva is hungry and decides to buy a snack from the concession stand is not affected by any other event.

The occurrence of one event (Neva buying a snack) does not affect the probability of the other event occurring.

Therefore, the Neva is hungry and she buys a snack from the concession stand. event is independent.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ5

Answer:

25%

Step-by-step explanation:

Probability = # of favorable outcomes / possible outcomes

favorable outcomes is what we want to happen ( throwing more than 3 pitches )

So to find the # of favorable outcomes we must find the frequency that the pitcher throws more than 3 pitches ( note: frequency of throwing 3 pitches is not included)

There are two possible outcomes of the pitcher pitching more than 3 pitches, 4 pitches having a frequency of 15, and 5 pitches which has a frequency of 10

So # of favorable outcomes = 10 + 15 = 25

Now we want to find the # of possible outcomes.

To do so we simply add the frequencies of each possible outcome.

15 + 20 + 40 + 15 + 10 = 100

So there are a total of 100 possible outcomes

Finally to find the probability of the pitcher throwing more than 3 pitches we divide favorable outcomes ( 25) by possible outcomes (100)

Our answer = 25/100 which can be converted into a percentage as 25%

Answer:

a = 78.5 cm²

Step-by-step explanation:

a = πr²

a = 3.14 * 5²

a = 3.14 * 25

a = 78.5 cm²

Answer:

$425.6 should be budgeted for weekly repairs and maintenance.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean $400 and standard deviation $20.

This means that [tex]\mu = 400, \sigma = 20[/tex]

How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?

This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 400}{20}[/tex]

[tex]X - 400 = 20*1.28[/tex]

[tex]X = 425.6[/tex]

$425.6 should be budgeted for weekly repairs and maintenance.

☆Amy is 9 years older than her younger sister.

[tex]\\ \sf\longmapsto Age\:of\:Amy=1+9=10years[/tex]

Let after x years Amy will be 4times old as her sister.

ATQ

[tex]\\ \sf\longmapsto \dfrac{1+x}{9+x}=\dfrac{1}{4}[/tex]

[tex]\\ \sf\longmapsto 4(1+x)=1(9+x)[/tex]

[tex]\\ \sf\longmapsto 4+4x=9+x[/tex]

[tex]\\ \sf\longmapsto 4x-x=9-4[/tex]

[tex]\\ \sf\longmapsto 3x=5[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{5}{3}[/tex]

[tex]\\ \sf\longmapsto x=1.6[/tex]

[tex]\\ \sf\longmapsto x=2(approx)[/tex]

Answer:

165.47≈165 Gallons of Water

Step-by-step explanation:

According To the Question,

The pool is filled with water to 2/3 of its height (H= 2/3 feet) .

Volume of Cylinder = π×R²×H , now put values, we get

Volume = 3.14×3.25²×2/3

Volume = 22.122 foot³ .

And, One cubic foot equals 7.48 gallons of water

Thus, 22.122 cubic foot equals to 165.47≈165 gallons of water .

Answer:

4.1 hours each day

Step-by-step explanation:

20.5 ÷ 5

= 4.1

Therefore 4.1 hours was spent on studying each day.

Answer:

Step-by-step explanation:

Middle point of AB

x(m) = (6+1)/2 = 7/2

y(m) = (7+4)/2 = 11/2

slope of the line that contains AB

(4-7)/(6-1) = -3/5

eqaution of the perpendicular bisector

y-11/2 = 5/3(x-7/2)

y = 5/3x -35/6 + 11/2

y = 5/3x + (-35 + 33)/6

y = 5/3x -1/3

Middle point of AC

x(m) = (1+5)/2 = 3

y(m) = (7+5)/2 = 6

Slope of the line that contains AC

(5-7)/(5-1) = -1/2

equation of the perpendicular bisector

y-6 = 2(x-3)

y = 2x -6 + 6

y = 2x

Point of intersection

y= 5/3x -1/3

y = 2x

2x = 5/3x - 1/3

6x = 5x - 1

x = -1

y = -2

P(-1,-2)

Answer:

(1,7)

Step-by-step explanation:

Given:

A(1,7)

B(6,4)

C(5,5)

Solution:

Mid point of AB = M((1+6)/2,(7+4)/2) = M(3.5,5.5)

Slope of AB = (4-7)/(6-1) = -3/5

Perpendicular bisector of AB:

L1: y -  11/2 = -(3/5)(x-7/2) ............(1)

Mid point of AC, m= N((1+5)/2,(7+5)/2) = N(3,6)

Slope of AC, n = (5-7)/(5-1) = -2/4 = -1/2

perpendicular bisector of AC:

L2: y-6 = -(1/2)(x-3) ..........."(2)

To find the point of intersection,

(1)-(2)

-5.5 - (-6) = -(3/5)x +12/5 + x/2 - 3/2

1/2 = -x/10 + 6/10

x/10 = 1/10

x = 1

substitute x in (1)

y = 3/2+11/2 =7

Therefore Point of intersection is (1,7)

Answer:

3. 0.00035

Step-by-step explanation:

Answer:

Step-by-step explanation:

Prime factorize 75

[tex]\sqrt{75x^{7}}=\sqrt{5*5*3* x * x * x * x * x * x *x}\\\\ =5*x *x *x \sqrt{3x}\\\\= 5x^{3}\sqrt{3x}[/tex]

Note: Let us consider, we need to find the [tex]m\angle ABC[/tex] and [tex]m\angle DBC[/tex].

Given:

In the given figure, BD is the angle bisector of ABC.

To find:

The [tex]m\angle ABC[/tex] and [tex]m\angle DBC[/tex].

Solution:

BD is the angle bisector of ABC. So,

[tex]m\angle ABD=m\angle DBC[/tex]

[tex]3x=x+20[/tex]

[tex]3x-x=20[/tex]

[tex]2x=20[/tex]

Divide both sides by 2.

[tex]x=\dfrac{20}{2}[/tex]

[tex]x=10[/tex]

Now,

[tex]m\angle DBC=(x+20)^\circ[/tex]

[tex]m\angle DBC=(10+20)^\circ[/tex]

[tex]m\angle DBC=30^\circ[/tex]

And,

[tex]m\angle ABC=(3x)^\circ+(x+20)^\circ[/tex]

[tex]m\angle ABC=(4x+20)^\circ[/tex]

[tex]m\angle ABC=(4(10)+20)^\circ[/tex]

[tex]m\angle ABC=(40+20)^\circ[/tex]

[tex]m\angle ABC=60^\circ[/tex]

Therefore, [tex]m\angle DBC=30^\circ,m\angle ABD=30^\circ[/tex] and [tex]m\angle ABC=60^\circ[/tex].

Answer:

4cm

Step-by-step explanation:

first find the length of the side of one square

the length of the rectangle will be twice the width

let y represent the width

area of a rectangle=length x width

2cm²=2yxy

2cm²=2y²

2cm²/2=2y²/2

1cm²=y²

1√cm²=√y²

1cm=y

perimeter of a square=4xside

4x1cm

4cm

Answer:

third one....domain starts  negative (-7/3)

and range starts at -5

Step-by-step explanation:

Answer:

May I ask what subject you are behind in?

Answer:

a. $354

b.$34.05p

Step-by-step explanation:

10 monthly instalments

10x28.5=280

plus the deposit 280+69=354

The difference between 354 and 319.95 is 34.05  

a. The total hire purchase price of the bicycle is $354.

b. The difference between the hire purchase price and the cost price of the bicycle is $34.05.

Total hire purchase price=(10 months×$28.5)+$69

Total hire purchase price=$285+$69

Total hire purchase price=$354

Difference=$354-$319.95

Difference=$34.05  

Inconclusion the total hire purchase price of the bicycle is $354 and the difference between the hire purchase price and the cost price of the bicycle is $34.05.

Learn more about  hire purchase price here:https://brainly.com/question/24730392

Answer:D. The answer is 3.

Step-by-step explanation:

Answer:

a. 74°

Step-by-step explanation:

Angle BCD and angle ACB are supplementary because they form a straight line. This means they add up to 180. We can write an equation to model the situation:

m<BCD + m<ACB = 180

106 + m<ACB = 180

m<ACB = 74

Since we are given two sides of the triangle are congruent, the triangle is isosceles. The base angles of an isosceles triangle are congruent, so we can say:

m<ACB = m<A

This means m<A is equal to 74°

Answer:

3x+34+23y, You can not add in this equation as there are no like numbers.

Step-by-step explanation:

Answer:

isnt it 60xy

Step-by-step explanation: