Question 13 and 14 I need help

The value of x in the triangle is 100 units.

A right triangle is a triangle that has one of its angles as 90 degrees.

The triangles formed are similar, therefore, they form a ratio or proportion.

Therefore, using similarity principle of triangles,

36 / 60 = 60 / x

cross multiply

36x = 60 × 60

36x = 3600

divide both sides by 36

36x = 3600

36x / 36 = 3600 / 36

x = 100

Therefore, the value of x in the triangle is 100 units.

learn more on triangle here: https://brainly.com/question/10136448

#SPJ1

Based on the amount that Nick is left with at the end of the month, the amount he earns is $2,400

The amount of $300 that is left is 25% of 50% of Nick's income as the other 75% of the 50% went to paying for the car and other expenses.

25% of 50% is:

= 25% x 50%

= 12.5%

The amount Nick makes per month is:

= Amount remaining / Amount remaining in percentage terms

= 300 / 12.5%
= $2,400

Find out more on percentages at https://brainly.com/question/843074

#SPJ1

Answer:

21 hours

Step-by-step explanation:

If he worked 2/3 at home you need to divide 31.5 by 3 = 10.5

Then multiply by 2 = 21

Hope this helps! Have a great day :)

_what is this this is futo balis subina to amake dis_

answer: 8 wholes and 3/4

the answer is the 0,1 because the lines all have different slopes but always start at 1.

The line of the graph is a solid line and the region to be shaded depends on the type of the inequality

The graph represents the given parameter

On the graph, we have a straight continuous line

A straight continuous line is an illustration of a solid line

This means that the line of the graph is a solid line

Hence, the line of the graph is a solid line

The graph represents the given parameter

On the graph, we can see that no region of the graph is shaded

This means that the shaded region would be determined by the type of the inequality

≥ means that the region would be shaded above

≤ means that the region would be shaded below

Hence, the region to be shaded depends on the type of the inequality

Read more about inequality at

https://brainly.com/question/24372553

#SPJ1

Based on theword problem, the inequality of the word problem is 7/2 + 4h >=  1

Inequalities are used to represent expressions that do not have equal values i.e. unequal expression

The word problem is given as

Half of 7 added to product of h and 4 is at least 1

At least 1 means greater than or equal to 1

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to product of h and 4 >=  1

The product of h and 4 means 4h

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to 4h >=  1

Half of 7 means 7/2

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 added to 4h >=  1

added to means +

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 + 4h >=  1

Hence, the inequality of the word problem is 7/2 + 4h >=  1

Read more about inequality at

https://brainly.com/question/24372553

#SPJ1

Answer:

The frog will catch the fly after 2 seconds of his jump.

Step-by-step explanation:

It is given that a frog is about to hop from the bank of a creek. The path of the jump can be modeled by the equation h(x) = -x² + 4x + 1, where h(x) is the frog's height above the water and x is the number of seconds since the frog jumped and a fly is cruising at a height of 5 feet above the water.

Now, let us assume that the frog catches the fly that is cruising at a height of 5 feet above the water;

=> h = 5 feet

So, let us put the value of h = 5 for time x;

=> h(x) = -x² + 4x + 1

=> 5 = -x² + 4x + 1

=> x² - 4x - 1 + 5 = 0

=> x² - 4x + 4 = 0

Now, on solving the above equation we get;

=> x² - 4x + 4 = 0

=> x² - (2 + 2)x + 4 = 0

=> x² - 2x - 2x + 4 = 0

=> x (x - 2) - 2 (x - 2) = 0

=> (x - 2) (x - 2) = 0

On comparing and solving for the value of x we get;

=> (x - 2) = 0

=> x = 2

and

=> (x - 2) = 0

=> x = 2

Therefore, the frog will catch the fly after 2 seconds of his jump.

To know more about this topic, click here:

https://brainly.com/question/18514707

#SPJ9

The equation of the function given as (x)= 5 * 2^x is an exponential function

The equation of the function is given as

f(x)= 5 * 2^x

An exponential function is represented as

f(x) = a * b^x

Where

Initial value = a

Rate = b

This means that

a = 5

b = 2

Hence, the equation of the function given as (x)= 5 * 2^x is an exponential function

Read more about exponential function at

https://brainly.com/question/27161222

#SPJ1

The simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶

Given,

a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.

The expression : ( a⁻⁴ / 2 × b² )³

Simplify the expression :

( a⁻⁴ / 2 × b² )³

= a⁻⁴⁽³⁾ / 2³ ˣ b²⁽³⁾

= a⁻¹² / 2³ ˣ b⁶

= a⁻¹² / 8b⁶

Therefore, the simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶

Learn more about simplification of the expression here: https://brainly.com/question/28506189

#SPJ1

Answer:

C. 40 times greater is the distance of Pluto from the Sun than the distance of Venus from the sun.

Answer:

Two shapes are congruent if their corresponding sides and corresponding angles are congruent.

Step-by-step explanation:

This is the definition of congruency.

Answer: that’s easily C because look down

Step-by-step explanation:

calculator lol I saw it don’t worry niu

Answer:

B

Step-by-step explanation:

calculate the distance between A and B using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (1, 6 ) and (x₂, y₂ ) = B (x, - 2 )

d = [tex]\sqrt{(x-1)^2+(-2-6)^2}[/tex]

   = [tex]\sqrt{(x-1)^2+(-8)^2}[/tex]

   = [tex]\sqrt{(x-1)^2+64}[/tex]

given AB = 10, then equating gives

[tex]\sqrt{(x-1)^2+64}[/tex] = 10 ( square both sides to clear the radical )

(x - 1)² + 64 = 10² = 100 ( subtract 64 from both sides )

(x - 1)² = 36 ← take square root of both sides

x - 1 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 1 to both sides )

x = 1 ± 6

then

x = 1 - 6 = - 5

x = 1 + 6 = 7

from the list then x = - 5 is a possible value

The product is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.

We are provided with expressions in three brackets. Performing multiplication between first two brackets first. This will be followed by multiplication of the product of first two brackets with the expression of third bracket.

For multiplication, the rule of exponents to be used is -

aᵇ×aⁿ = aᵇ⁺ⁿ

Rewriting the expression

Product = (p³)(2p² - 4p) (3p² - 1)

Performing multiplication of first two brackets -

Product = (p³ × 2p² - p³ × 4p) (3p² - 1)

Product = (2p⁵ - 4p⁴) (3p² - 1)

Further performing multiplication of product with third bracket -

Product = (2p⁵ × 3p² - 2p⁵ × 1 - 4p⁴ × 3p² - 4p⁴ × - 1)

Product = 6p⁷ - 2p⁵ - 12⁶ + 4p⁴

Hence, the product of given expressions is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.

Learn more about calculations on product -

https://brainly.com/question/25301924

#SPJ4

Answer:

C: 6p7 - 12p6 - 2p5 + 4p4

Step-by-step explanation:

Source: Trust me bro

Answer:

that is definitaly 18

Step-by-step explanation:

i will break it down 3+3+3=9    3+3+3=9 again  9+9=18

[tex]answer[/tex]

18

Break it down: 3+3+3= 9, Another 3+3+3= 9 (3 addition in 6 places will give 18). 9+9 = 18

x = 13/2 is not an extraneous solution.

[tex](2x+3)^{3/4}[/tex] - 3 = 5

Adding 3 on both the sides of the equation, we get

[tex](2x+3)^{3/4}[/tex] - 3 + 3= 5 + 3

[tex](2x+3)^{3/4}[/tex] = 8

On the right hand side of the equation, 8 can also be written as

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

Taking power 4/3 on both the side of the equation, we get

(2x + 3) = 2⁴

2x + 3 = 16

2x = 13

x = 13/2

Check for extraneous solution and putting x = 13/2 in the original equation, we get

[tex](2(13/2) + 3)^{3/4}[/tex] - 3 = 5

[tex]16^{3/4}[/tex] - 3 = 5

8 - 3 = 5

5 = 5

⇒ LHS = RHS

∴   x = 13/2 is not an extraneous solution.

Know more about Extraneous Solution:

brainly.com/question/4563555

#SPJ4

Answer:

-10 and -10

Step-by-step explanation:

Can you use the same number twice?

Answer:

-10

Step-by-step explanation:

[tex]2\left(-5\right)\left(-1\right)\left(-1\right)\\(-5)(-1) = |5|\\= 2 \times 5\left(-1\right)\\2 \times 5 = 10\\10 \times |-1| = -10\\= -10[/tex]

Answer:

-10

Step-by-step explanation:

Let's solve the problem,

→ 2(-5)(-1)(-1)

→ (2 × -5) × (-1 × -1)

→ -10 × 1 = -10

Thus, the answer is -10.

Given that  ∠ABC and ∠DEF are supplementary, the numerical value of ∠ABC and ∠DEF are 68° and 112° respectively.

Supplementary angles are angles that sum up to 180 degrees.

Given the data in the question;

Since ∠ABC and ∠DEF are supplementary, it means they sum up to 180 degrees.

Measure of ∠ABC + Measure of ∠DEF = 180°

Plug in the given values and solve for x

(6x + 8) + (12x − 8) = 180

6x + 8 + 12x − 8 = 180

6x + 12x + 8 - 8 = 180

18x + 0 = 180

18x = 180

x = 180/18

x = 10

Now, the numerical measure of each angle will be;

Measure of ∠ABC = (6x + 8)° = 6(10) + 8 = 60 + 8 = 68°

Measure of ∠DEF = (12x − 8)° = 12(10) - 8 = 120 - 8 = 112°

Given that  ∠ABC and ∠DEF are supplementary, the numerical value of ∠ABC and ∠DEF are 68° and 112° respectively.

Learn more about supplementary angles here: https://brainly.com/question/18164299

#SPJ1

Charlotte traveled in 414.44 feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

The first step is to convert miles per hour to feet per second.

(69.6 mi/hr)* (5280 feet/mi)*(1 hr/3600 sec) = 102.08 feet/sec

We know that,

Speed = [tex]\frac{Distance}{Time}[/tex]

Here, we have given,

Time = 4.06 s

Speed (feet/sec) = 102.08 feet/sec

We need to find, the distance charlotte traveled in feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

Putting the values in the formula, we get

Distance = Speed x Time

= 102.08 x 4.06

= 414.44 Feet

Hence, charlotte traveled in 414.44 feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

To learn more about Speed, here

https://brainly.com/question/7359669

#SPJ4

The required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given the trigonometry identity;

d=94 secθ.

If the object is sighted at an angle of  25°, then;

d=94 sec25

d = 94 × 1/cos25

d = 94 × 1.1033

d = 103.71feet

If the object is sighted at an angle of  55°, then;

d=94 sec55

d = 94 × 1/cos55

d = 94 × 1.7434

d = 163.88feet

Hence the required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

Learn more on functions and values here: https://brainly.com/question/2284360

#SPJ1

When the cool rock that is rolling down the side of the volcano is compared to the mass of hot lava that is slowly flowing, the rock has 2. less thermal energy and more mechanical energy.

The mechanical energy that an object has refers to the combination of kinetic and potential energy. The rock will have more mechanical energy than the hot lava as it is moving faster.

Thermal energy on the other hand refers to how much heat/ energy is in an object. The rock is cool as opposed to the hot lava which would have more thermal energy as a result of its heat.

Find out more on mechanical energy at https://brainly.com/question/28351693

#SPJ1

The equation that represent the statement "quotient of a number x and five is half the difference of the number and four" is x / 5 = 4 - 1/2x

x / 5 = 4 - 1/2x

x/5 + 1/2x = 4

(2x+5x) / 10 = 4

7/10x = 4

x = 4 ÷ 7/10

= 4 × 10/7

= 40/7

= 5.714285714285714

Approximately,

x = 5.7

Therefore, the value of x in the equation is approximately 5.7

Learn more about equation:

https://brainly.com/question/24334139

#SPJ1

Answer:

Area: 6[tex]x^{2}[/tex] - 8x

Perimeter: 10x - 8

Step-by-step explanation:

Area:

Multiple the 2 sides together

2x(3x -4)  Distribute the 2x

2x(3x)- 2x(4)

6[tex]x^{2}[/tex] -8x

Perimeter:

Add the four sides together

3x -4 + 3x -4 +2x + 2x  Combine like terms

10x - 8

 We write the expression in its simplest form and we are left with.

y²√3 + y - 6

  Before proceeding let's define an algebraic expression.

    An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

     The first thing we will do is to write the expression:

(√y-√3)(√y+2√3)

  Then we perform the multiplication, with the distributive property, which gives as a result

(y + 2√3y - √3y - 6)

y²√3 + y - 6

Learn more about algebraic expression in:

https://brainly.com/question/21856579

#SPJ4

Step-by-step explanation:

the first suspicion we get from the first terms is that the creation algorithm is a multiplication by 3.

-1/3 × 3 = -1

-1 × 3 = -3

-3 × 3 = -9

then the next term would be

-9 × 3 = -27

and the next

-27 × 3 = -81

and the 7th term, that we have already defined, would be

-81 × 3 = -243

we are correct !

so, the missing terms are

-27, -81

It follows that the least integer greater than log√₇ √50 is 3.

We have a logarithm function that is given to us.

Let x = log√₇ √50

We get that:√ 7 ˣ = √ 50

So, we must find an integer x, such that √ 7 ˣ > √ 50.

We know that √ 49 = 7

√ 7 ˣ > 7

7 ⁰°⁵ˣ  > √ 7

x / 2 > 1

x > 2

In this case, x = 3 will be the least integer to satisfy this inequality.

Therefore, it follows that the least integer greater than log√₇ √50 is 3.

Learn more about logarithm here:

https://brainly.com/question/25710806

#SPJ4

The factors for given equation are -2/3 and -2.

Rewriting the equation firstly -

3x² + 8x + 4 = 0

ax² + bx + c = 0

Factorizing the equation as per mentioned two rules -

6 and 2 are the suitable factors for given expression -

3x² + 6x + 2x + 4 = 0

3x (x + 2) + 2(x + 2) = 0

(3x + 2) (x + 2) = 0

3x + 2 = 0

3x = -2

x = -2/3

x + 2 = 0

x = -2

So, the two factors of equation are -2/3 and -2.

To check the factors, we will keep the value of x in equation -

When x = -2/3

3x² + 8x + 4 = 0

3(-2/3)² + 8(-2/3) + 4 = 0

3(4/9) - 16/3 + 4 = 0

4/3 - 16/3 + 4 = 0

Multiplying the equation with 3/4

1 - 4 + 3 = 0

- 3 + 3 = 0

0 = 0

When x = -2

3x² + 8x + 4 = 0

3(-2)² + 8(-2) + 4 = 0

12 - 16 + 4 = 0

- 4 + 4 = 0

0 = 0

Since for both values of x, Left hand Side and Right Hand Side of equation is same, the two resultant factors are correct.

Learn more about factorizing -

https://brainly.com/question/25829061

#SPJ4