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2 years ago

Two system of equations 2y =14-2x and y=-x + 7 is graphed. What is the solution to the system of equations

Mathematics

2 answers:

Molodets [167]2 years ago

7 0

Answer:

Infinitely many solutions

Step-by-step explanation:

<u>Given equations</u>

2y =14-2x and
y= -x + 7

<u>Rewriting the first equation</u>

2y = 14 - 2x
2y = -2x + 14
y = -x + 7

As we see it is same as the second equation. So same two lines, overlapping when graphed and the system has infinitely many solutions

Trava [24]2 years ago

6 0

<h2>Answer:</h2>

To solve this system, we will use the graphing method.

Based on the graph shown below, we can conclude that this system has infinite solutions, because they are the same line.

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Your answer is 110. You take 10 and divide it by 750. = 75 then you take 75. Divided 8250. = 110

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2 years ago

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Klio2033 [76]

Answer:

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21√2

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Step-by-step explanation:

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2 years ago

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2 years ago

Read 2 more answers

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

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2 years ago

Carlo and Helen spend the same amount of money on art supplies. Carlo buys 4 glue sticks and spends $3 on glitter. Helen buys 2

Veseljchak [2.6K]

<u>Answer:4.75</u>

<u>Since we don't have a total cost we will write an equation that will allow us to find the cost of x. The equation is 4x= 2x + $3 + $3.75 + $2.75. Now that we have our equation we are going to start by adding 3, 3.75, and 2.75. When added together, they come out with a total of 9.5. Now the equation becomes 4x= 2x + $9.50. Since we have our new equation we are going to subtract 2x from both sides of the equation. We now have the equation 2x= $9.50. Finally, you will divide both sides by 2. This leaves us with the final outcome x= $4.75. This means that one glues stick cost $4.75. Let's check by substituting $4.75 as the value of x in the expressions 4x is Carlo's total and 2x + $3 + $3.75 + $2.75 is Helen's total. First we do 4x, 4 multiplied by 4.75 equals 19, so Carlo spent $19 on art supplies. Now we do 2x + $3 + $3.75 + $2.75, which is 9.5 added to 9.5 and equals 19. So Helen spent $19 on art supplies. This proves that the cost of one glue stick, x, is equal $4.75.</u>

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1 year ago