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3 years ago

Which expression is equivalent to |b|>2 ?

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

6 0

Answer:

b < –2 or b > 2

Step-by-step explanation:

The given expresion is

$|b| \: > \: 2$

By the definition of absolute value function.

|x|=x, if x>0

|x|=-x, if x<0

This implies that:

$b \: > \: 2 \: or \: - b \: > \: 2$

Divide the second inequality by -2 and reverse the sign

$b \: > \: 2 \: or \: b \: < \: - 2$

Option B is correct

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Use the coordinate plane to help you identify the length of each leg then use the Pythagorean Theorem to find the length of CD

Nitella [24]

Answer:

CE= 9cm, DE= 5cm, CD= 10.2956cm

Step-by-step explanation:

Let E be the point of the other triangle.

Using Pythagoras' Theorem,

CD= square root symbol (CE^2 + DE^2)

= square root symbol (9^2+5^2)

= 10.2956cm (6 sf)

7 0

2 years ago

The rug in Alan's room has an area of 18 square feet. He is planning to buy another rug that is twice as long and twice as wide.

Dennis_Churaev [7]

Yeah its gonna be 18 square feet in wide and length and the area is gonna be 36 square feet

5 0

2 years ago

Newberg City Cafe recently introduced a new flavor of coffee. They served 23 grande cups and 51 jumbo cups of the new coffee tod

yuradex [85]

Answer:

Grand coffee cup = 1469 gm

Jumbo coffee cup = 60 gm

Step-by-step explanation:

Let x be the grande coffee cup and y be the jumbo coffee cup.

Solution:

From the first statement. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equal a total of 36,846 grams.

So, the equation is.

$23x+51y = 36846$ ---------(1)

From the second statement. They served 58 grande cups and 68 jumbo cups of the new coffee tomorrow, which equal a total of 59460 grams.

$58x+68y=59460$ ----------(2)

Solve the equation 1 for x.

$23x = 36846-51y$

$x=\frac{36846}{23}-\frac{51}{23}y$

$x=1602-\frac{51}{23}y$ ---------(3)

Substitute $x=1602-\frac{51}{23}y$ in equation 2.

$58(1602-\frac{51}{23}y)+68y=59460$

$92916-\frac{51\times 58}{23}y+68y=59460$

$-\frac{2958}{23}y+68y=59460-92916$

$\frac{-2958+1564}{23}y=-33456$

$\frac{-1394}{23}y=-33456$

Using cross multiplication.

$y=\frac{-23\times 33456}{-1394}$

$y = 55.99$

y ≅ 60 gram

Substitute y = 60 in equation 3.

$x=1602-\frac{51}{23}\times 60$

$x=1602-\frac{3060}{23}$

$x=1602-133.04$

$x = 1469$ grams

Therefore, grand coffee cup = 1469 gm and jumbo coffee cup = 60 gm

7 0

2 years ago

What’s the answer to this equation?

Tresset [83]

Answer:

Part A) The graph in the attached figure

Part B) see the explanation

Step-by-step explanation:

Part A) Graph the function

we have the quadratic function

$y=3x^2-12x-36$

This is a vertical parabola open upward

The vertex is a minimum

using a graphing tool

The graph in the attached figure

Part B) What are the values of a, b and c?

we know that

The values of a and b represent the x-intercepts of the quadratic equation

The x-intercepts are

(-2,0) and (6,0)

$a=-2\\b=6$

Find the value of c

we know that

The x-coordinate of the vertex in a vertical parabola is equal to the midpoint of the roots

The value of c is equal to

$c=\frac{a+b}{2}$

substitute the given values

$c=\frac{-2+6}{2}=2$

see the attached figure

7 0

2 years ago

If Marlene can type 157 words per minute how many words can she type in 25 minute

Nitella [24]

Answer:

3925

Step-by-step explanation:

25x

25*157

5 0

2 years ago