solve for x 3(x+2) = 12

Answer:

AandB=80miles

Total=240miles

Step-by-step explanation:

Draw the figure first indicating the figures then find the distance each degrees then find the total

The distance ship travels from A to B is 273.2 miles and total distance covered by ship is  707.82 miles.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given distance from C to A = 100 miles north

From B to A ship travels 60° east of north,

and From B to C 45° west of south,

the figure for problem is attached,

from figure we can  calculate the angles of A, B and C

so ∠A makes supplementary with 60°

∠A + 60° = 180°

∠A = 120°

for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get

∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)

∠B = 90 - 75 = 15°

and ∠C can be found by,

∠A + ∠B + ∠C = 180°

∠C = 180 - 15 - 120

∠C = 45°

now use sine formula for triangles,

sinA/a = sinB/b = sinC/c

where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.

a = BC, b = AC, and c = AB

so

sinA/BC = sinB/AC = sinC/AB

we have AC = 100 miles

substitute the values

sinC/AB = sinB/AC

sin(45)/AB = sin(15)/100

AB = 100/(√2sin(15))

AB = 100/0.3659

AB = 273.298 miles

and sinA/BC = sinB/AC

BC = AC sinA/sinB

BC = 100(sin 120/sin15)

BC = 100(0.866/0.2588)

BC = 100 x 3.3462

BC = 334.62 miles

total distance = AB + BC + AC

total distance = 334.62 + 273.2 + 100

total distance =  707.82 miles

Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.

Learn more about  laws of sines;

https://brainly.com/question/17289163

#SPJ2

Answer:

75 cm

Step-by-step explanation:

∅=90° , r = 21 cm

Arc length= (2πr∅)/360

=(2π×21×90)/360

=33 cm

Perimeter= arc length + 2(radius)

=33+2(21)

=33 + 42

= 75 cm

Answer:

22 units²

Step-by-step explanation:

1/2b*h=area

You can either count the units or use the distance formula.

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

b = 4 units

h = 11 units

area = (1/2*4)*11 = 22 units²

Answer:

Step-by-step explanation:

When the quadratic is written in vertex form:

  x = a(y -k)^2 +h

the vertex is (x, y) = (h, k), and the length of the latus rectum is 1/a.

For your given equation, ...

  x = (1/2)(y -5)^2 +7

you have a=1/2, k = 5, h = 7, so ...

  the vertex is (7, 5)

  the length of the latus rectum is 1/(1/2) = 2

Answer:

C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The lower quartile range is shown by the bottom of the box which is at 10.

The median is shown in the middle line, which is closer to 18 than 18.5.

The upper quartile range in the end of the box, which is at 22!

(You can also look at the picture attached if that helps.)

Answer:

It is reduced to the equation of the Theorem of Pythagoras.

Step-by-step explanation:

Any triangle can be modelled by this formula under the Law of Cosine:

[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.

[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.

Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:

[tex]\cos B = 0[/tex]

And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:

[tex]b = \sqrt{a^{2}+c^{2}}[/tex]

Answer: $10

Step-by-step explanation:

let x = the price of green fabric, then x+2 = blue fabric price

8x+5(x+2)=62

8x+5x+10=62

    13x+10=62

          13x=52

              x=4

price of green fabric=$4

price of blue fabric=$6

4+6=$10

Answer:

[tex]\huge\boxed{Supplementary \ Angle}[/tex]

Step-by-step explanation:

118 is a supplementary angle. It is not a complementary angle because complementary angles add up to 90 and 118 is greater than 90 degrees. So, 118 is a supplementary angle and it is an angle adding up to 180 degrees with any other angle measuring 62 degrees.

Answer:Supplementary

Step-by-step explanation:You should remember that complementary refers to any number from 0-90 and supplementary refers to any number from 90 onwards..

Hereby giving the answer as ''Supplementary''

Answer:

To find the median you cross off the first few numbers and the last few until you get to the middle then when you get the middle number that will be your median

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

It's the middle value of a list of numbers arranged in order.

For example the median of the list 1 2 3 4 5 is 3.

If there are an even number of values, the median is the mean of the middle two. For example:

1 3 4 5 7 9:

The middle 2 numbers are 4 and 5 so

the median is  (4 + 5) / 2 = 4.5

Answer:

GREAT QUESTION!!

Step-by-step explanation:

Bases of exponential functions CANNOT be 1.

It the base was between 0 and 1, .25 for example, then it would be exponential decay, because as x would increase y would decrease.

Just search up exponential decay to see what it looks like, or type in y=.25^x in google search bar.

if this helped, Please give brainly, I need it! Thank you!

Answer:

If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.

Step-by-step explanation:

If the base were 1, the function would be constant.

If the base were 1, the graph would be a horizontal line.

If the base were between 0 and 1, the function would be decreasing.

Answer:

Given the information above, the area of the square is 361 cm²

Step-by-step explanation:

A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.

The perimeter of the square is 76. So, let's divide 76 by 4.

76 ÷ 4 = 19

So, the lengths of each sides in the square is 19cm.

In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.

19 × 19 = 361

So, the area of the square is 361 cm²

Answer:

361 cm^2

Step-by-step explanation:

The area of a square can be found by squaring the side length.

[tex]A=s^2[/tex]

A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.

[tex]s=\frac{p}{4}[/tex]

The perimeter is 76 centimeters.

[tex]s=\frac{76 cm}{4}[/tex]

Divide 76 by 4.

[tex]s=19 cm[/tex]

The side length is 19 centimeters.

Now we know the side length and can plug it into the area formula.

[tex]A=s^2\\s=19cm[/tex]

[tex]A= (19 cm)^2[/tex]

Evaluate the exponent.

(19cm)^2= 19 cm* 19cm=361 cm^2

[tex]A= 361 cm^2[/tex]

The area of the square is 361 square centimeters.

Answer:

Since both companies have a different plan, two equations are created to determine which company Jonas should choose with respect to the number of messages sent.

Step-by-step explanation:

- Sprint = $ 29.95 * X (0.15)

- AT & T = $ 4.95 * X (0.39)

One dollar equals 100 cents, so 0.15 cents equals $ 0.0015 dollars.

- Sprint = $ 29.95 * X (0.0015)

- AT & T = $ 4.95 * X (0.0039)

Si Jonas envía 500 mensajes de texto el valor mensual de cada empresa sería de:

- Sprint = $ 29.95 * 500 (0.0015)  = 22.46 dollar per month.

- AT & T = $ 4.95 * 500 (0.0039)  = 9.65 dollar per month.

The company Jonas should choose is AT&T.

AT&T also charges a little more per number of text messages, but since the phone's value is so low it would take thousands of text messages to compare to Sprint's monthly value.

Answer:

The word problem is "How many $25 are there in $125?"

Step-by-step explanation:

Given

[tex]n(\$25) = \$125[/tex]

Required

Write a word problem for the expression

We start by solving the given equation

[tex]n(\$25) = \$125[/tex]

Divide both sides by $25

[tex]\frac{n(\$25)}{\$25} = \frac{\$125}{\$25}[/tex]

[tex]n = \frac{\$125}{\$25}[/tex]

[tex]n = 5[/tex]

This implies that there are 5, $25 in $125

Hence; The word problem is "How many $25 are there in $125?"

Answer:

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Step-by-step explanation:

For a relation to be proportional

a:b = c:d

in other form

a/b = c/d

______________________________________________

Ratio for first type of fabric

cost of fabric/ area of fabric = 31.25/5 = 6.25

Ratio for other type of fabric

cost of fabric/ area of fabric = 71.50/11 = 6.5

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Answer:

[tex]\huge\boxed{9,40,46}[/tex]

Step-by-step explanation:

Let's check it using Pythagorean Theorem:

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

Where c is the longest sides, a and b are rest of the 2 sides

1) 9 , 40 , 46

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

=> [tex]46^2 = 9^2 + 40^2[/tex]

=> 2116 = 81 + 1600

=> 2116 ≠ 1681

So, this is not a Pythagorean Triplet

2) 16, 30 and 34

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

=> [tex]34^2 = 16^2 + 30^2[/tex]

=> 1156 = 256 + 900

=> 1156 = 1156

No need to check more as we've found the one which is not a Pythagorean Triplet.

Answer:

Option A is the correct option.

Step-by-step explanation:

1. Let h , p and b are the hypotenuse , perpendicular and base of a right - angled triangle respectively.

From Pythagoras theorem,

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Here, we know that the hypotenuse is always greater than perpendicular and base,

h = 46 , p = 40 , b = 9

⇒[tex] \sf{ {46}^{2} = {40}^{2} + {9}^{2} }[/tex]

⇒[tex]2116 = 1600 + 81[/tex]

⇒[tex] \sf{2116  ≠ 1681}[/tex]

Thus , the relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is not satisfied by h = 46 , p = 40 , b = 9

So, The set of numbers 9 , 40 , 46 is not Pythagorean triple.

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

2. 16 , 30 , 34

h = 34 , p = 30 , b = 16

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {34}^{2} = {30}^{2} + {16}^{2} }[/tex]

⇒[tex] \sf{1156 = 900 + 256}[/tex]

⇒[tex] \sf{1156 = 1156}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 34 , p = 30 , b = 16

So, the set of numbers 16 , 30 , 34 is a Pythagorean triple.

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

3. 10, 24 , 26

h = 26 , p = 24 , b = 10

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {26}^{2} = {24}^{2} + {10}^{2} }[/tex]

⇒[tex] \sf{676 = 576 + 100}[/tex]

⇒[tex] \sf{676 = 676}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and h i.e h = 26 , p = 24 , b = 10

So, the set of numbers 10, 24 , 26 is the Pythagorean triple.

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

4. 50 , 120 , 130

h = 130 , p = 120 , b = 50

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {130}^{2} = {120}^{2} + {50}^{2} }[/tex]

⇒[tex] \sf{16900 = 14400 + 2500}[/tex]

⇒[tex] \sf{16900 = 16900}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 130 , p = 120 , b = 50

So, the set of numbers 50, 120 , 130 is the Pythagorean triple.

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

In this way, to satisfy the Pythagoras Theorem , the hypotenuse ( h ) , perpendicular ( p ) and the base ( b ) of a right - angles triangle should have the particular values in order. These values of h , p and b are called Pythagorean triple.

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

23x +2 = 15x+48x+6

To solve for x group like terms

That's

Send the constants to the right side of the equation and those with variables to the left side

We have

23x - 15x - 48x = 6 - 2

Simplify

- 40x = 4

Divide both sides by -40

We have the final answer as

Hope this helps you

Answer:

JK = 6.86

Step-by-step explanation:

The parameters given are;

LJ = 14

JM = 48

LM = 50

[tex]tan(\angle JML )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{LK}{JM} = \dfrac{14}{48} = \dfrac{7}{24}[/tex]

[tex]tan \left( \dfrac{7}{24} \right)= 16.26 ^{\circ }[/tex]

∠JML = 16.26°

Given that ∠JML is bisected by KM, we apply the angle bisector theorem which states that a ray that bisects an interior angle of a triangle bisects the opposite (bisected angle facing side) in the proportion of the ration of the other two sides of the triangle.

From the angle bisector theorem, we have;

LM/JM = LK/JK

50/48 = LK/JK................(1)

LK + KJ = 14.....................(2)

From equation (1), we have;

LK = 25/24×JK

25/24×KJ + JK = 14

JK×(25/24 + 1) = 14

JK × 49/24 = 14

JK = 14×24/49 = 48/7. = 6.86.

JK = 6.86

Answer:

6 sacks

Step-by-step explanation:

Buying Price = $1200

Selling Price = $1500

Total profit = Selling price - Buying Price

= $1500 - $1200

= $300

Given that the profit on each sack of tea is $50

Number of Sacks of Tea = Total Profit ÷ profit per sack

= $300 ÷ 50

= 6 sacks

The number of sacks of tea he has is 6.

The first step is to determine the total profit earned by the trader. Profit is the selling price less the cost price.

Profit = selling price - cost price

$1500 - $1200 = $300

The second step is to divide the total profit by the profit made per sack of tea.

Number of sacks = $300 / $50 = 6

To learn more about division, please check: https://brainly.com/question/194007

Answer:

3x+11y-3

Step-by-step explanation:

Hey! So here is what you do to solve the problem-

Combine like terms:

(x) 5x-2x=3x

(y) 3y+8y=11y

(#) 7-10 =-3

So....

3x+11y-3 is your answer!

Hope this helps!:)

hope it helps.I was reading the same chapter

Answer:

4.44 pints

Step-by-step explanation:

7.4 times 3/5

Answer:

[tex]\large \boxed{1296}[/tex]

Step-by-step explanation:

6 raised to 4 indicates that the base 6 has an exponent or power of 4.

[tex]6^4[/tex]

6 is multiplied by itself 4 times.

[tex]6 \times 6 \times 6 \times 6[/tex]

[tex]=1296[/tex]

Answer:

Hey there!

The overlapping part is the product.

Thus, the product is 1/8.

Hope this helps :)

Answer & Step-by-step explanation:

For this problem, we have two inequalities to solve for x.

3x - 91 > -87

17x - 16 > 18

Now that we know what our inequalities are, we will solve them as if we are solving for the value of x.

3x - 91 > -87

Add 91 on both sides.

3x > 4

The solution for the first inequality is 3x > 4

Now let's do the second inequality.

17x - 16 > 18

Add 16 on both sides.

17x > 34

Divide by 17 on both sides.

x > 2

The soultion for the second inequality is x > 2

Answer:

The answer is x>2

Step-by-step explanation:

Answer:

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= 2000π unit³

Volume= 6284 unit³

Step-by-step explanation:

The decimal value of the volume already given= 600π

The decimal value of the volume already given= 600*3.142

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= πr²h/3

Volume= 11²*12/3 *π

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume = πr²h/3

Volume= 4²*6/3(π)

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= πr²h/3

Volume= 20²*15/3(π)

Volume= 2000π unit³

Volume= 6284 unit³

Here's the right answer.

Answer:

I hope this will help!

Step-by-step explanation:

Answer:

2 hrs, 24 min

Step-by-step explanation:

Sally:  in one hour, she can paint 1/4 of the room.

Joe: in one our, he can paint 1/6 of the room

Hour one: 1/4+1/6=3/12+2/12=5/12

1÷5/12=1*12/5=12/5

12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes

Answer: 2.4 hours

Step-by-step explanation:

1/4 1/6

LCM

3/12+2/12=5/12 repricical 12/5 =2.4

distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$

so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$

Answer:

Distance=17 units

Step-by-step explanation:

Coordinates of the origin: (0, 0)

Coordinates of the point in question: (-15, 8)

Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:

[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]

Answer:

1) B. The differences are normally distributed or the sample size is large

C. The  sample size mus be large

E. The sampling method results in an independent sample

2) The null hypothesis H₀:  [tex]\bar x_1[/tex] =  [tex]\bar x_2[/tex]

The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] <  [tex]\bar x_2[/tex]

Test statistic, t = -0.00693

p- value = 0.498

Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers  at 0.10 level of significance

Step-by-step explanation:

1) B. The differences are normally distributed or the sample size is large

C. The  sample size mus be large

E. The sampling method results in an independent sample

2) The null hypothesis H₀:  [tex]\bar x_1[/tex] =  [tex]\bar x_2[/tex]

The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] <  [tex]\bar x_2[/tex]

The test statistic for t test is;

[tex]t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]

The mean

Height of Father, h₁,  Height of Son h₂

72.4,      77.5

70.6,      74.1

73.1,       75.6

69.9,      71.7

69.4,      70.5

69.4,      69.9

68.1,       68.2

68.9,      68.2

70.5,       69.3

69.4,       67.7

69.5,       67

67.2,       63.7

70.4,       65.5

[tex]\bar x_1[/tex]  = 69.6      

s₁ = 1.58

[tex]\bar x_2[/tex] = 69.9

s₂ = 3.97

n₁ = 13

n₂ = 13

[tex]t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}[/tex]

(We reversed the values in the square root of the denominator therefore, the sign reversal)

t = -0.00693

p- value = 0.498 by graphing calculator function

P-value > α Therefore, we do not reject the null hypothesis

Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers  at 0.10 lvel of significance

[tex](-3+5,10-7)=(2,3)[/tex]