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4 years ago

Will you help me?

Mathematics

1 answer:

Volgvan4 years ago

8 0

Answer:

The length side of the original square banner was 9 ft

Step-by-step explanation:

Let

x-----> the length side of the original square banner

we know that

The new area of the banner is equal to

$91=(x+4)(x-2)$

Solve for x

$91=(x+4)(x-2)\\ \\91=x^{2}-2x+4x-8\\ \\x^{2}+2x-99=0$

Solve the quadratic equation by graphing

The solution is x=9 ft

see the attached figure

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Use long division or synthetic division to find the quotient of 2x^3+x^2+1 / x+1

gogolik [260]

Answer:

The quotient is 2x^2 - x + 1.

Step-by-step explanation:

If x + 1 is the divisor in long division, then -1 is the divisor in synthetic division:

-1 / 2 1 0 1

-2 1 -1

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

2 -1 1 0

The quotient is 2x^2 - x + 1. The coefficients were obtained through synthetic division.

7 0

3 years ago

(Anderson, 1.14) Assume that P(A) = 0.4 and P(B) = 0.7. Making no further assumptions on A and B, show that P(A ∩ B) satisfies 0

Goshia [24]

Answer with Step-by-step explanation:

We are given that

P(A)=0.4 and P(B)=0.7

We know that

$P(A)+P(B)+P(A\cap B)=P(A\cup B)$

We know that

Maximum value of $P(A\cup B)$ =1 and minimum value of $P(A\cup B)$ =0

$0\leq P(A\cup B )\leq 1$

$0\leq P(A)+P(B)-P(A\cap B)\leq 1$

$0\leq 0.4+0.7-P(A\cap B)\leq 1$

$0\leq 1.1-P(A\cap B)\leq 1$

$0\leq 1.1-P(A\cap B)$

$P(A\cap B)\leq 1.1$

It is not possible that $P(A\cap B)$ is equal to 1.1

$1.1-P(A\cap B)\leq 1$

$-P(A\cap B)\leq 1-1.1=-0.1$

Multiply by (-1) on both sides

$P(A\cap B)\geq 0.1$

Again, $P(A\cup B)\geq P(B)$

$0.4+0.7-P(A\cap B)\geq 0.7$

$1.1-P(A\cap B)\geq 0.7$

$-P(A\cap B)\geq -1.1+0.7=-0.4$

Multiply by (-1) on both sides

$P(A\cap B)\leq 0.4$

Hence, $0.1\leq P(A\cap B)\leq 0.4$

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3 years ago

At the beginning of summer, the water level on a pond is 2 feet below its normal level. After an unusually dry summer, the water

Scilla [17]

Answer:

Step-by-step explanation:

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3 years ago

In the given figure, C is the midpoint of AB and M is the midpoint of AC . Find the length of NB if MC = 4 and AN = 14.

Elina [12.6K]

Answer:

Given MC = 4

AN = 14

To Find, the length of NB

Step-by-step explanation:

AB is a line which has midpoint “C”. Now the line is divided into two equal portion AC and CB.

The AC has midpoint “M” and MC is 4, so AM will also be 4.

N is the midpoint of CB. So, CB = CN + NB

Now we know AC = AM + MC = 4 + 4 =8

Given, AN = 14

AN = AC + CN

14 = 8 + CN

CN = 6

Since N is the midpoint of CB then, CN = NB

Therefore, the NB is 6

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4 years ago

The number 75 can be written as the sum of the squares of 3 different positive integers. what is the sum of these 3 integers? 17

ioda

$75=7^2+5^2+1^1\\\\ 7+5+1=13$

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3 years ago