Find the expression for the area of the figure. Give your answer as a simplified radical.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Area of rectangle= length × breadth

Area of figure

$= ( √(15x)) ( √(10x) ) \n = √((10x)(15x)) \n = \sqrt{150 {x}^(2) } \n = \sqrt{6(25 {x}^(2)) } \n = (√(6) )( \sqrt{( {5x})^(2) } ) \n = ( √(6) )(5x) \n = 5x √(6)$

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what is an equation of the line that passes through the point (4,5) and is parallel to the line whose is equation is y=2/3x-4

Answers

Answer:

y = 2/3x + 7/3

Step-by-step explanation:

We know

The line pass through the point (4,5)

The equation is: y = 2/3x - 4

m = 2/3

To solve this, we can use the fact that parallel lines have the same slope. Since the parallel line we're looking for has the same slope, we can use the point-slope form of a linear equation to find its equation:

y - y1 = m(x - x1)

y - 5 = 2/3(x - 4)

y - 5 = 2/3x - 8/3

y = 2/3x + 7/3

So, the answer is y = 2/3x + 7/3

How do you solve the following exponential equation by expressing each power of the same base and then equating the exponents?6^x-3/4= square rot of 6

Answers

Start by switching everything into exponent form: 6^(x-3/4)=6^(1/2). In this equation, we're trying to find the value of x that will make each side equal. Because the base (6) is the same on either side of the equal sign, all we need to worry about is the exponents, because this equation can only be true if the exponents are the same (i.e. 6^(1/2)=6^(1/2)). Thus, you can actually ignore the 6's entirely and only focus on the exponents: x-3/4=1/2. Then, this has just become a simple algebraic expression. x-3/4+3/4=1/2+3/4. x=1/2(2/2)+3/4. x=2/4+3/4. x=5/4

$6^{x-\tfrac{3}{4}}=√(6)\n6^{x-\tfrac{3}{4}}=6^{\tfrac{1}{2}}\nx-(3)/(4)=(1)/(2)\nx=(1)/(2)+(3)/(4)\nx=(2)/(4)+(3)/(4)\nx=(5)/(4)$

Write an inequality to model the situation. Thomas earned $44 or more.A. t ≥ 44

B. t ≤ 44

C. t > 44

D. t < 44

Answers

Answer

A. t ≥ 44

Explanation

Remember the sing ≥ (greater or equal than), means that Thomas earned $44 or more.

Let $t$ represent the mount of money that Thomas earned.

Since the sing ≥ (greater or equal than), means that Thomas earned $44 or more, the inequality that model the situation is:

$t\geq 44$

Hello,

Answer A
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Solve 2/3 (6x+30)=x+5(x+4)–2x

Answers

expand the left hand side of the equation first. this is easy since two thirds of six is four and two thirds or thirty is twenty.
4x + 20 = x + 5(x+4) - 2x
expand the right hand side :
4x + 20 = x + 5x + 20 -2x

Collect up all the x terms on the right hand side: 4x + 20 = x + 5x - 2x + 20
So the total number of "x" 's on the right hand side is 1 + 5 -2 = 4
4x + 20 = 4x + 20
Hey ! look at that ! you've got the same thing on both sides of the equation ! this means that it doesn't matter what value x is, the equation works for ALL values of x . ( ANSWER)

What is the numerical coefficient of '-3z'?

Answers

Answer: -3

Step-by-step explanation:

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:f(t) = −16t2 + 32t + 90

The average rate of change of f(t) from t = 4 seconds to t = 6 seconds is :blank: feet per second.

Answers

f ( 6 ) = -16·6²+32·6+90= -576 + 192 + 90 = -294
f ( 4 ) = -16· 4³+32·4+90=-256+128+90= -38
The average rate of change: [f(t2)-f(t1)]/ t2-t1=
[-294-(-38)] / (6-4) = -256 : 2 = -128 feet/s

The value of the average rate of change of f(t) is -128feet/s.

We have given that,

f(t) = −16t^2 + 32t + 90

f ( 6 ) = -16·6²+32·6+90= -576 + 192 + 90

f ( 6 ) = -294

f ( 4 ) = -16· 4³+32·4+90=-256+128+90

f ( 4 )= -38