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s344n2d4d5 [400]

4 years ago

8

Write the following phrase as a variable expression. Use X to represent “a number.” The sum of eleven, a number, and the product

of nineteen and the number.
Please help I’m having trouble understanding

1 answer:

melamori03 [73]4 years ago

6 0

Answer:

11 + x + 19*x

Step-by-step explanation:

The sum of eleven, a number, and the product of nineteen and the number.

we have to read carefully and understand how to interpret

when he says the sum of separates into 3 parts because there is a "comma" and an "and"

Now let's separate the 3 parts of the sum

1 part

says eleven so we just put 11

eleven = 11

2 part

in the text it says that we replace "a number" with x

a number = x

3 part

In this case we simply make the product between the given values

the product of nineteen and the number

19 * x

Now we can accommodate everything and we finish

11 + x + 19*x

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3 years ago

kenny6666 [7]

Answer:

The value of the constant $k$ so that $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{2}$ is $\frac{7}{10}$ .

Step-by-step explanation:

Let be $\vec u_{1} = [2,3,1]$ , $\vec u_{2} = [4,1,0]$ and $\vec u_{3} = [1, 2,k]$ , $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{3}$ if and only if:

$\alpha_{1} \cdot \vec u_{1} + \alpha_{2} \cdot \vec u_{2} +\alpha_{3}\cdot \vec u_{3} = \vec O$ (Eq. 1)

Where:

$\alpha_{1}$ , $\alpha_{2}$ , $\alpha_{3}$ - Scalar coefficients of linear combination, dimensionless.

By dividing each term by $\alpha_{3}$ :

$\lambda_{1}\cdot \vec u_{1} + \lambda_{2}\cdot \vec u_{3} = -\vec u_{3}$

$\vec u_{3}=-\lambda_{1}\cdot \vec u_{1}-\lambda_{2}\cdot \vec u_{2}$ (Eq. 2)

$\vec O$ - Zero vector, dimensionless.

And all vectors are linearly independent, meaning that at least one coefficient must be different from zero. Now we expand (Eq. 2) by direct substitution and simplify the resulting expression:

$[1,2,k] = -\lambda_{1}\cdot [2,3,1]-\lambda_{2}\cdot [4,1,0]$

$[1,2,k] = [-2\cdot\lambda_{1},-3\cdot \lambda_{1},-\lambda_{1}]+[-4\cdot \lambda_{2},-\lambda_{2},0]$

$[0,0,0] = [-2\cdot \lambda_{1},-3\cdot \lambda_{1},-\lambda_{1}]+[-4\cdot \lambda_{2},-\lambda_{2},0]+[-1,-2,-k]$

$[-2\cdot \lambda_{1}-4\cdot \lambda_{2}-1,-3\cdot \lambda_{1}-\lambda_{2}-2,-\lambda_{1}-k] =[0,0,0]$

The following system of linear equations is obtained:

$-2\cdot \lambda_{1}-4\cdot \lambda_{2}= 1$ (Eq. 3)

$-3\cdot \lambda_{1}-\lambda_{2}= 2$ (Eq. 4)

$-\lambda_{1}-k = 0$ (Eq. 5)

The solution of this system is:

$\lambda_{1} = -\frac{7}{10}$ , $\lambda_{2} = \frac{1}{10}$ , $k = \frac{7}{10}$

The value of the constant $k$ so that $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{2}$ is $\frac{7}{10}$ .

4 0

4 years ago

The sum of 7 times a number and 23 is equal to 79.

AlladinOne [14]

<h2>ANSWER:</h2>

LET THE NUMBER BE "X"

7x-12=5(x+2)

7x-12=5x+10

7x-5x=10+12

2x=22

x=22÷2

x=11

<h2 />

3 0

3 years ago

Read 2 more answers

The weights of Twinkies are Normally distributed with a mean of 1.5 ounces and a standard deviation of 0.1 ounces. a) The middle

tensa zangetsu [6.8K]

Answer:

The middle 99.7% of Twinkies weigh between approximately 1.2 and 1.8 ounces.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 1.5

Standard deviation = 0.1

middle 99.7%

Within 3 standard deviations of the mean, so

1.5 - 3*0.1 = 1.2

1.5 + 3*0.1 = 1.8

So the answer is:

The middle 99.7% of Twinkies weigh between approximately 1.2 and 1.8 ounces.

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3 years ago

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ra1l [238]

Total surface area = 2(pi)(r^2) + 2(pi)(r)(h)

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3 years ago