Graph the system of
equations on the graph
and determine the
solution.
Y = -4x +2
Y =X +3

Answer: Commutative property

Vector v can be written as the sum of two vector components, \(v_x = -5i\)  and \(v_y = 6j\)

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)

The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)

Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)

Now, we can write vector v as the sum of its components:

\(v = v_x + v_y = -5i + 6j\)

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

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Answer:

x<-11 or x>7

Step-by-step explanation:

First, we get the right side to be 0.

\(x^2+4x-77 > 0\)

Then we factor the left side.

\((x+11)(x-7) > 0\)

Using the Snake Method, we determine the intervals as x<-11 or x>7

Answer:

10.81665

Step-by-step explanation:

In order to solve this we can use pythagorean theorem, or \(a^{2} + b^{2} = c^{2}\)

C represents the hypotenuse and a and b represent the two other sides.

We have the hypotenuse, 21 feet. We also have a side, 18 feet. We can plug these in and solve for a.

\(a^{2} + 18^{2} = 21^{2}\)

\(a^{2} + 324 = 441\)

Subtract 324 from both sides.

\(a^{2} =117\)

Square root both side to remove the square.

\(\sqrt{a^{2} } =\sqrt{117}\)

\(a=10.81665\)

Hope this helps!

This  question is based on the Pythagorean theorem.  Therefore, 10.81665 feet  far from the base of the mast should he attach the end of the light string.

Given:

Randy wants to attach a 21 foot string of lights to the top of the 18 foot mast of his sailboat.

We need to determined the base of the mast should he attach the end of the light string.

According to the question,

By using Pythagorean theorem,

\(a^2 + b^2 = c^2\)

Here, it is given that, b = 18 and c = 21.

Putting this value in above formula.

We get,

\(a^2 + 18^2 = 21^2\)

\(a^2 = 441 - 324\\\\a^2 = 117\)

Square root both sides. We get,

\(\sqrt{a^2} = \sqrt{117}\)

a = 10.81665.

Therefore, 10.81665 feet  far from the base of the mast should he attach the end of the light string.

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Answer:

The area of the parallelogram in square centimeters is 2.4.

Step-by-step explanation:

The area of a paralellogram is given by the following formula:

A = B*H

In which B is the length of the base, and H is the height.

In this question:

B = 2.4, H = 1. So

A = B*H = 2.4*1 = 2.4

The area of the parallelogram in square centimeters is 2.4.

The domain of (boa)(x) is [1, ∞].

In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.

Based on the information provided above, we have the following functions:

a(x) = 3x+1

\(b(x) = \sqrt{x-4}\)

Therefore, the composite function (boa)(x) is given by;

\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)

By critically observing the graph shown in the image attached below, we can logically deduce the following domain:

Domain = [1, ∞] or {x|x ≥ 1}.

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Answer:

Sure, here are the answers to your questions:

**A) The value of $f(-5)$ is $-2$.**

To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:

$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$

**B) The vertex of the parabola is $(2,6)$.**

To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:

$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$

Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:

$$f(x)=-2(x+2)^2-20$$

The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.

[Image of a parabola with vertex at (-2, -20)]

**C) The $y$-intercept is the point $(0,14)$.**

The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:

$$f(0)=-2(0)^2-8(0)+14=14$$

Therefore, the $y$-intercept is the point $(0,14)$.

**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**

To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:

$$-2x^2-8x+14=0$$

We can factor the left-hand side of the equation as follows:

$$-2(x-2)(x-3)=0$$

This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:

$$x=2\text{ or }x=3$$

However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:

$$x=2.5\text{ and }x=-3.5$$

Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.

The problem ask us to find C, which is the total cost of the rental and the insurance.

Then, to find C in terms of M, we need to add the functions S and I:

Standard charge:

S(M) = 16.15 + 0.6M

Insurance Fee:

I(M) = 4.9 + 0.15M

Then the function C(M) that represents the total charge for a rental with insurance, after driving M miles is:

Then write:

The answer is:

The surface area for each of the cylinders is given as follows:

13. 126 yd².

14. 490 m².

15. 283 mm².

16. 297 cm².

The surface area of a cylinder of radius r and height h is given by the equation presented as follows, which combines the base area with the lateral area:

S = 2πrh + 2πr²

S = 2πr(h + r)

Item 13:

r = 2 yd and h = 8 yd, hence the surface area is given as follows:

S = 2π x 2(2 + 8)

S = 126 yd².

Item 14:

r = 6 m and h = 7 m, hence the surface area is given as follows:

S = 2π x 6(6 + 7)

S = 490 m².

Item 15:

r = 3 mm and h = 12 mm, hence the surface area is given as follows:

S = 2π x 3(3 + 12)

S = 283 mm².

Item 16:

r = 3.5 mm and h = 10 mm, hence the surface area is given as follows:

S = 2π x 3.5(3.5 + 10)

S = 297 cm².

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Answer:

So when u do (-4)-(-6) it equals 2.

But when u do (-7)*(-8) it equals 56

Therefore saying that (-7)*(-8)=56 is the greatest product.

Step-by-step explanation:

Answer:

1/8 more hours on her history assignment.

It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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I think that car travelled 128 km in one hour and 384km in 3 hours

Answer: 384 km

Step-by-step explanation:

Convert m/ph to k/ph by multiplying the equivalent of 1 mile in kilometers    

 (1m = about  1.6km) by the total number of miles.

 80  x  1.6 =  128

 You now have the distance traveled per hour in m/ph converted to k/ph.

 All you do now is multiply it by the time traveled:

 (128 kilometers per one hour for 3 hours)

 128 kph x 3 = 384km

Answer:

The correct answer is:

It is a discrete random variable. (A)

Step-by-step explanation:

Discrete Random Variables are variables that have distinct values. The number of variables that can be taken on can be counted. in this example, the variables to the question Did you smoke in the last week? is one of two possibilities; yes or no. Apart from these two values, there is no other possibility for the variables, hence it is a discrete random variable

Continuous Random Variables are values that can take on any value between distinct values, even up to infinity. The number of values that the variables can take on cannot be counted or listed. For example, is there are variables for the possible temperature that a particular city can take on in a day, the values are continuous random variables because the values do not have any distinct value, and the possibilities cannot be counted. the possibilities can be; anywhere between 20°C to 50°C. between these two, temperatures, you can have infinite possibilities; 20.1, 30.5, 40.8, etc. Hence the values cannot be counted, it is thus a continuous random variable.

Answer:

c not random variable

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 2-3)/(0-2)

   = -1/-2

  = 1/2

Answer:

Slope = 0.5

Step-by-step explanation:

Given: Line passes through (2, 3) and (0, 2)

\(\text{Slope formula} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_2 - y_1}{x_2 - x_1}\)

Substitute the coordinates in the formula and solve for the slope;

    \(\implies \text{Slope formula} = \dfrac{y_2 - y_1}{x_2 - x_1}\)

    \(\implies\text{Slope formula} = \dfrac{2 - 3}{0 - 2}\)

    \(\implies\text{Slope formula} = \dfrac{-1}{-2}\)

    \(\implies\text{Slope formula} = \dfrac{1}{2} = 0.5\)

Therefore, the slope of the line is 0.5.

Answer:(2x+7)+(2x+7)

Step-by-step explanation:

what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer

The expression in terms of x that represents the total amount that Jaxon paid is 1.3284x.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

To calculate the total amount that Jaxon paid, we need to add the tax and the tip to the subtotal.

The tax is calculated as 8% of the subtotal, which is 0.08 times x:

Tax = 0.08x

The tip is calculated as 23% of the total bill, which is the sum of the subtotal and the tax. So, the tip is 0.23 times (x + 0.08x):

Tip = 0.23(x + 0.08x)

Simplifying the expression for the tip, we get:

Tip = 0.23(1.08x) = 0.2484x

Therefore, the total amount that Jaxon paid is the sum of the subtotal, the tax, and the tip:

Total = x + Tax + Tip = x + 0.08x + 0.2484x

Simplifying the expression for the total, we get:

Total = 1.3284x

So, the required expression in terms of x is 1.3284x.

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When creating a budget, the importance of certain items can affect the process by influencing the allocation of funds. Essential items like housing, food, utilities, and transportation typically take priority over discretionary items like entertainment or hobbies. The importance of each item can help individuals determine how much money should be allocated to each category in their budget.

Fixed expenses are recurring expenses that remain the same from month to month, such as rent or mortgage payments. Variable expenses, on the other hand, fluctuate from month to month, such as groceries or utility bills.

Fixed expenses can be budgeted by simply allocating a specific amount of money towards that expense each month, while variable expenses may require more flexible budgeting strategies, such as estimating a monthly average or setting aside a certain amount of money for unexpected expenses.

Sorting needs and wants can have a significant impact on a personal budget. Needs are typically essential expenses required for daily living, such as housing, food, and healthcare. Wants, on the other hand, are non-essential expenses that are not required for basic survival, such as entertainment or hobbies.

By prioritizing needs over wants in their budget, individuals can ensure that they are meeting their basic living expenses before allocating money towards discretionary expenses. This can help individuals better manage their finances and avoid overspending on non-essential items.

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Answer:

YES, they are equal

Step-by-step explanation:

Given the expressions

h(x) = 2x – 3;j(x) = - 4x + 6; k(x) = – 2x + 3

h(x) + j(x) = 2x – 3 + (-4x + 6)

h(x) + j(x) =  2x - 3 -4x + 6

h(x) + j(x) = 2x - 4x -3 + 6

h(x) + j(x) = -2x + 3 = k(x)

This shows that h(x) + j(x) =  k(x)

Answer:

The value is  \(P(Z' | N )= 0.92\)

Step-by-step explanation:

From the question we are told that

   The proportion of defective widgets produced by older widget is  \(p = 23\% = 0.23\)

  The proportion of defective widgets produced by new  widget is  

\(q = 0.08\)

Generally since we are considering the new machine in this question it then mean that the probability that widget was defective given that it was produce by the new machine is

      \(P(Z | N ) = 0.08\)

Here Z  is the event that the widget was defective

         N  is the even that the widget was produced by the new machine

Also  the probability that the widget was defective given that it was not produced by the new machine is  

      \(P(Z | N') = 0.23\)

Generally  from the question the probability that the widget was produced by the new machine is mathematically represented as

      \(P( N) = \frac{3}{4}\)

=>   \(P( N) = 0.75\)

Generally the probability that the widget is defective  and that  it was produced by the new  is mathematically represented as

      \(P( Z\ n \ N) = P(Z | N ) * P(N)\)

=>   \(P( Z\ n \ N) = 0.08 * 0.75\)

=>   \(P( Z\ n \ N) = 0.06\)

Generally the probability that the widget is defective and that  it was not produced by the new machine is

     \(P(Z\ n \ N') = P( Z | N' ) * [1 -P(N)]\)

=>   \(P(Z\ n \ N') = 0.23 * [1 -0.75]\)

=>   \(P(Z\ n \ N') =0.0575\)

Generally the probability that the widget is defective is  

       \(P(Z) = P(Z \ n \ N) + P(Z \ n \ N')\)

=>     \(P(Z) = 0.06 + 0.0575\)

=>     \(P(Z) = 0.1175\)

Generally the probability that the widget is not defective and it produced by the new machine is mathematically represented as

      \(P(Z' \ n \ N ) = P(N ) - P(Z \ n \ N)\)

=>    \(P(Z' \ n \ N ) =0.75 - 0.06\)

=>    \(P(Z' \ n \ N ) =0.69\)

Generally the probability that the widget was produced by the new machine,given that a randomly chosen widget was tested and was found to be defective is mathematically represented as

       \(P(Z' | N ) =\frac{P(Z' \ n \ N)}{P(N)}\)

=>     \(P(Z' | N )= \frac{0.69}{0.75}\)

=>     \(P(Z' | N )= 0.92\)

Answer:

keep the car at a friends house untill you find a place to get it fixed at... or keep it at a trustworthy family members house.

If these don't help then im sorry.

Subtract the given score x from the mean µ and divide it by the standard deviation σ :

z = (x - µ) / σ = (302 - 300) / 20 = 0.1

Answer:

See below

Step-by-step explanation:

1. During which time period is Kelly's heart rate increasing? (1 point)

2. Using math, determine the exact rate of change for the increase (warm‐up). Explain how you got your answer. (3 points; 1 point for answering the question, 2 points for explaining your answer)

3. During which time period did Kelly's heart rate remain constant? (1 point)

4. Using math, determine the exact rate of change for this time period. Explain how you got your answer. (3 points; 1 point for answering the question, 2 points for explaining your answer)

5. During which time period did Kelly's heart rate decrease? (1 point)

6. Using math, determine the exact rate of change for the decrease (cool down). Explain how you got your answer. (3 points; 1 point for answering the question, 2 points for explaining your answer)

7. Explain why your rate of change for the cool down period was a negative value. (2 points)

Answer:

You should give the other guy brainliest

Step-by-step explanation:

1. During which time period is Kelly's heart rate increasing? (1 point)

0 to 15 minutes period

2. Using math, determine the exact rate of change for the increase (warm‐up). Explain how you got your answer. (3 points; 1 point for answering the question, 2 points for explaining your answer)

Rate of change = Change in y / change in x

(115 - 65)/(15-0) = 50/15 = 3.33

3. During which time period did Kelly's heart rate remain constant? (1 point)

15 to 35 minutes period

4. Using math, determine the exact rate of change for this time period. Explain how you got your answer. (3 points; 1 point for answering the question, 2 points for explaining your answer)

ROC = (115 - 115)/(35 - 15) = 0

5. During which time period did Kelly's heart rate decrease? (1 point)

35 to 45 minutes period

6. Using math, determine the exact rate of change for the decrease (cool down). Explain how you got your answer. (3 points; 1 point for answering the question, 2 points for explaining your answer)

ROC = (70 - 115)/(45 - 35) = - 45/10 = -4.5

7. Explain why your rate of change for the cool down period was a negative value. (2 points)

Negative rate indicates drop in heart rate during cool down

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer:

first one is right

Step-by-step explanation:

The line KD is transversal to line RJ, KR and JD as shown in the diagram.

option D.

Skew lines are a pair of lines that do not intersect and are not parallel to each other.

Also,  skew lines are defined as lines that are not parallel and do not intersect and are not contained within the same plane.

So from the given diagram, we can see that line RK and JD are not skew lines since they are parallel to each other. option A is wrong.

The angle at which line KD and JD intersects each other cannot be determined without further information. So it is not 90 degrees. Option B is wrong.

Line JD is not parallel to line RJ, so the option C is wrong as well.

So finally we are left with option D, and we can conclude that line KD is transversal to line RJ, KR and JD as shown in the diagram.

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\(\cos \angle B = \dfrac{2}{7}\\\\\implies \angle B = \cos^{-1} \left( \dfrac{2}{7} \right) = 1.28^{\circ}\)