This is a 30-60-90 triangle. What is the measure of x?

Answer:

Breadth = 15 cm

Step-by-step explanation:

Area = length x breadth

315 = 21 x breadth

[tex]\frac{315}{21} = \frac{21}{21} \times breadth[/tex]                 [ dividing both sides by 21 ]

[tex]15 = 1 \times breadth\\\\breadth = 15 \ cm[/tex]

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[tex]\quad\quad\quad\quad\tt{A = A rea}[/tex]

[tex]\quad\quad\quad\quad\tt{ l = length} [/tex]

[tex]\quad\quad\quad\quad\tt{ b \: = breadth} [/tex]

[tex]\quad\quad\quad\quad\tt{A = 315 {cm}^{2} }[/tex]

[tex]\quad\quad\quad\quad\tt{l = 21cm}[/tex]

[tex]\quad\quad\quad\quad\tt{b = \: ? }[/tex]

[tex]\quad\quad\quad\quad\tt{breadth = \frac{Area}{length} }[/tex]

[tex]\quad\quad\quad\quad\tt{b = \frac{315 {cm}^{2} }{21cm} }[/tex]

[tex]\quad\quad\quad\quad\tt \boxed{ \boxed{ \color{magenta}{b = 15cm }}}[/tex]

___________________________________

#CarryOnLearning

✍︎ C.Rose❀

Answer:

by using middle term break method

Step-by-step explanation:

9x^2 + 12x + 4

9x^2+ (6 + 6)x + 4

9x^2 + 6x + 6x + 4

3x(3x + 2) + 2(3x + 2)

(3x + 2)(3x + 2)

(3x + 2)^2

9514 1404 393

Answer:

  z = 20

  m∠A = 70°

Step-by-step explanation:

Step 0: read and understand the question. Identify the given information and the information requested.

Step 1: consult your knowledge of inscribed quadrilaterals to determine that opposite angles are supplementary.

Step 2: identify angles A and C as being marked with expressions in z.

Step 3: use those expressions and the relation in Step 1 to write an equation.

  A + C = 180°

  (4z -10)° +(10 +5z)°= 180°

Step 4: solve for z.

  9z = 180 . . . . simplify, divide by °

  z = 20 . . . . . . divide by 9

Step 5: use the relation between z and the measure of angle A to answer the question.

  m∠A = (4z -10)° = (4·20 -10)°

  m∠A = 70°

Step 6: check your answer. This can be done by making sure that angle C is supplementary to angle A.

  C = (10 +5z)° = (10 +5·10)° = 110° = 180° -70° ∴ answer checks OK

Answer:

Ok ☺️✌️✌️✌️Ok ok ok ok

Answer is

5 gives the range of possible values for x.

Answer:

$3.53 per lb of salami

Step-by-step explanation:

0.75 lb of salami for $2.65

The price per of salami will be :

0.75 lb = $2.65

1 lb = x

Using cross multiplication :

0.75 * x = $2.65 * 1

0.75x = $2.65

Divide both sides by 0.75

0.75x / 0.75 = $2.65 / 0.75

x = $3.533

This means that :

The price per unit of salami is $3.53

Answer:

0.75 lb of salami for $2.65 is $3.53 per lb of salami.

Answer:

A) The probability that Kevin will win the spring break cruise is 0.42%.

B) Kevin's expected earnings are $ 8.4.

C) Kevin effectively contributed with $ 50.

Step-by-step explanation:

Since the college student senate is sponsoring a spring break Caribbean cruise raffle, and the proceeds are to be donated to the Samaritan Center for the Homeless, ya local travel agency donated the cruise, valued at $ 2000, and the students sold 2357 raffle tickets at $ 5 per ticket, to determine A) if Kevin bought ten tickets, what is the probability that Kevin will win the spring break cruise to the Caribbean; B) Kevin's expected earnings and C) how much did Kevin effectively contribute to the Samaritan Center for the Homeless; the following calculation must be performed:

A) 10/2357 = 0.0042 x 100 = 0.42

Therefore, the probability that Kevin will win the spring break cruise is 0.42%.

B) 2000 x 0.0042 = 8.4

Therefore, Kevin's expected earnings are $ 8.4.

C) 5 x 10 = 50

Kevin effectively contributed with $ 50.

9514 1404 393

Answer:

  21.75 m

Step-by-step explanation:

The given relations tell us that ...

  VW = TV +3

  TW = VW +TV -19

  VW +TW +TV = 62

__

Solving the first equation for TW gives ...

 TV = VW -3

Substituting that into the second equation gives ...

  TW = 2VW -22

And using these expressions in the third equation, we have ...

  VW +(2VW -22) +(VW -3) = 62

  4VW = 87 . . . . . . . . collect terms

  VW = 21.75 . . . . . . divide by 4

The length of VW is 21.75 meters.

Answer: 1547 bricks are required to build the staircase.

Step-by-step explanation:

We are given:

Number of bricks in the first step, [tex]a_1[/tex] = 131

Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126

Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121

Sequence become:

131, 126, 121, .....

These are in arithmetic progression where a = 131 and d (common difference) = -5

To calculate the sum of an AP, we use the formula:

[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]

where,

n = number of terms = 17

Putting values in above equation, we get:

[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]

Hence, 1547 bricks are required to build the staircase.

Answer:

-21

Step-by-step explanation:

4(x+9) = 4x+36

4x+36 = 2x-6

    -36        -36

minus 36 from both sides

4x = 2x-42

2x = -42

-42/2 = -21

x = -21

Hi there!

We are given the equation below:

[tex] \large \boxed{4(x + 9) = 2x - 6}[/tex]

1. Expand 4 in the expression.

[tex] \large{(4 \times x) + (9 \times 4) = 2x - 6} \\ \large{(4x) + (36) = 2x - 6}[/tex]

Cancel the brackets.

[tex] \large{4x + 36 = 2x - 6}[/tex]

2. Isolate x-term and solve for the variable.

[tex] \large{4x - 2x = - 6 - 36}[/tex]

Finally, combine like terms.

[tex] \large{2x = - 42}[/tex]

Then divide both sides by 2 so we can finally leave only x-term.

[tex] \large{ \frac{2x}{2} = \frac{ - 42}{2} } \\ \large \boxed{x = - 21}[/tex]

3. Check the solution if it is right or wrong.

To check the answer, we simply substitute the value of x which is -21 in the equation and see if both sides are equal or not. If both sides are equal then the answer is correct, if not then the answer is wrong. Therefore,

[tex] \large{4(x + 9) = 2x - 6 \longrightarrow 4( - 21 + 9) = 2 ( - 21) - 6} \\ \large{4( - 12) = - 42 - 6} \\ \large{ - 48 = - 48}[/tex]

Since both sides are equal when substitute in x = -21.

4. Answer

I hope this helps and let me know if you have any doubts!

Answer:

7

Step-by-step explanation:

|-7|  means find the distance from 0

We take the non negative value

|-7| = 7

Answer:

D

Step-by-step explanation:

Plug in the numbers for the x-value and solve the equation.

| 3(80/3)/4 + 1 | = 16

| 3(-40/3)/4 + 1 | = 16

Answer:

3.6

Step-by-step explanation:

set-up percentage like this!

[tex]\frac{part}{whole} =\frac{part}{whole}[/tex]

Then use what you know from the question to fill in the blanks

Answer: [tex]\frac{6}{100} =\frac{?}{60}[/tex]

Then: [tex]60[/tex] × 6 ÷ 100 = 3.6

Final Answer: 3.6

Answer:

x = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

2(x + -5) + x = x + (-6)

Step 2: Solve for x

Answer:

x=2 ( see Image below)

Step-by-step explanation:

cancel equal terms on both sides of the equation

2(x-5)=-6

move the constant to the right -hand side and change its sign

2x= -6 +10

Calculate the sum

2x=4

divide both sides of the equation by 2

x=2

Answer:

The answer is 3.

Step-by-step explanation:

What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.

Answer:

3

Step-by-step explanation:

What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.

Answer:

[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]

Step-by-step explanation:

U can reduce this into

[tex](4x + 3y) {}^{2} [/tex]

Which is a square.

Now,

16x^2 + 24xy + 9y^2

16x^2 + 12xy + 12xy + 9y^2

4x ( 4x + 3y ) + 3y ( 4x + 3y )

( 4x + 3y ) ( 4x + 3y )

( 4x + 3y )^2

I hope you understand...

Mark me as brainliest...

Answer:

10145

Step-by-step explanation:

5 times 950 equals 4750

and 6.5 times 830 equals 5395

add first and second value

4750 + 5395 equals 10145

there is no arguing

Answer:

10145 km

Step-by-step explanation:

Time x speed = Distance

5 x 950 = 4750

6.5 x 830 = 5395

add together = 10145

Answer:

x = 7.2

y = 10

z = 6

Step-by-step explanation:

Since ABCD ~ JKLM, therefore, the ratio of their corresponding sides would be equal. Thus:

JK/AB = KL/BC = LM/CD = JM/AD

Substitute

12/x = y/6 = 15/9 = 10/z

✔️Find x:

12/x = 15/9

12/x = 5/3

Cross multiply

x*5 = 3*12

5x = 36

x = 36/5

x = 7.2

✔️Find y:

y/6 = 15/9

y/6 = 5/3

Cross multiply

y*3 = 5*6

3y = 30

y = 30/3

y = 10

✔️Find z:

15/9 = 10/z

5/3 = 10/z

Cross multiply

5*z = 10*3

5z = 30

z = 30/5

z = 6

Step-by-step explanation:

I suppose you mean find the range for the following domain. Because when

g(x) is given the value of X

we are trying to solve the output value which is range.

If you want to solve for the domain, the question should give

g(x) = y

and provide the value of y.

X³+X²-X-2

Substitute

X=(-1)

-1+1-(-1)-2

= -1

g(-1)= -1

Substitute

X=(2)

8+4-2-2

=8

g(2)= 8

Substitute

X=(1)

1+1-1-2

=-1

g(1)= -1

g(2)+g(1)

=8-1

=7

Answer: (f)

Step-by-step explanation:

Given

The growth equation is [tex]y=50(1.05)^x[/tex]

When population becomes 1500

[tex]\Rightarrow 1500=50(1.05)^x\\\Rightarrow 30=(1.05)^x\\\text{Taking log both sides}\\\Rightarrow \ln (30)=x\ln (1.05)\\\\\Rightarrow x=\dfrac{\ln (30)}{\ln (1.05)}\\\\\Rightarrow x=69.71[/tex]

Thus, after 69.71 years of year 2015 i.e. [tex]2015+69.71=2084.71[/tex]. In year 2084, it becomes 1500.

option (f) is correct.

Answer:

$6.65

Step-by-step explanation:

You could start by seeing the price of a 1 minute phone call. if you divide 1.75 by 5 it is 0.35. that means 1 minute costs $0.35. so the equation would be 0.35 times 19. which is 6.65 dollars.

5 minutes call = $1.75

1 minute call = $1.75/5 = $0.35

19 minutes call = $0.35 × 19 = $6.65

Answer:

58.3

Step-by-step explanation:

divide 700 by 12

Answer:

$50

Step-by-step explanation:

The equation for this is:

700 = 12m + 100, where $700 is the total cost, m is the monthly fee, 12 is the number of months in a year, and $100 is the starting fee

Solve the equation:

700 = 12m + 100

12m = 600

m = 50

Answer:

Hi im not got with graphs

Step-by-step explanation:

Answer :

Let in Triangle abc,

a=90,

b = (we have to find)

c = (we have to find)

c + 144=180 (linear pair)

c = 180 - 144

c = 36

a + b + c = 180 (Angle sum property)

90 + b + 36 = 180

126 + b = 180

b = 180-126

b = 54

9514 1404 393

Answer:

  C.  Matrix C

Step-by-step explanation:

The usual form for an augmented matrix representation of a system of linear equations has the variable coefficients listed in a square matrix with an additional column at the right containing the constants in the standard-form equations. This is illustrated in Matrix C.

__

The variables in the equations are usually left out of the matrix. That is, the system of equations AX= B is usually represented by the augmented matrix A|B, rather than (AX)|B. Thus "Matrix B" is not the best choice.

Here, we have to classify each differential equation based on their characteristics:

This is a separable differential equation because the variables can be separated on different sides of the equation.

It's of the form dy/dx = g(x) - f(y)/h(y), where g(x) = x/x and h(y) = 1.

This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/(x + 1) and Q(x) = 20/(x + 1).

This is a separable differential equation because the variables x and y can be separated on different sides of the equation.

This is a separable differential equation because the variables x and y can be separated on different sides of the equation.

This is a Bernoulli differential equation because it is of the form [tex]dy/dx = p(x)y + q(x)y^n[/tex], where p(x) = 0 and q(x) = 5x, n = 2.

This is a separable differential equation because the variables x and y can be separated on different sides of the equation.

This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/x and [tex]Q(x) = e^{(xy)} - x^{(-1)[/tex].

This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -2/x and Q(x) = 2x.

This is a separable differential equation because the variables x and y can be separated on different sides of the equation.

This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), although it's not immediately obvious what P(x) and Q(x) are.

This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where [tex]P(x) = -1/x^2[/tex] and [tex]Q(x) = -e^{(2x^3)} - y^2[/tex].

To know more about differential equation, visit:

brainly.com/question/1164377

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Answer:

y = 64°

Step-by-step explanation:

From the picture attached,

m(∠E) = 90°

m(∠E) = m(∠D)

m(∠B) + 67° = 180° [pair of linear angles]

m(∠B) = 113°

m(∠C) + 75° = 180°

m(∠C) = 180° - 75°

           = 105°

Since, sum of interior angles of a polygon = (n - 2) × 180°

Here, n = number of sides

For n = 5,

Sum of interior angles = (5 - 2) × 180°

                                     = 540°

m(∠A) + m(∠B) + m(∠C) + m(∠D) + m(∠E) = 540°

m(∠A) + 113° + 105° + m(∠D) + 90° = 540°

(m∠D) + m(∠D) = 540 - 308 [Since, m(∠A) = m(∠D)]

2(m∠D) = 232

m(∠D) = 116°

m(∠D) + y° = 180° [Linear pair of angles]

116 + y = 180

y = 64°

The last equation says z = 3, so that in the second equation we get

y + 2z = y + 6 = 5   ==>   y = -1

and in turn, the first equation tells us

x - 2y + 2z = x + 2 + 6 = x + 8 = 9   ==>   x = 1

So the solution to the system is (x, y, z) = (1, -1, 3).