What is the sum of two intergers with different sighs is 8. Give two possible intergers

Answers

Answer 1

Answer: You can use positive 10 and -2 and you'll get a positive 8

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Using the slope formula for the points (1, 5) and (2, -2), what would the denominator be?-2 - 5
-2 - 1
2 - 1
2 - 5

Answers

Answer:

2-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Moving from (1, 5) to (2, -2), x increases by 1 and y decreases by 7. The slope of the line connecting these two points has the slope m = rise / run = -7 / 1, or just -7.

Alternatively, using the slope formula,

5-[-2] 7

m = ------------ = -------- = (-7/1). The denominator would be 1.

1 - 2 -1

Which does not show a direct variation between x and y?  A.y = x/9  B.y = 2x  C.y = 0.5x  D.y = 9/x

If f(x) varies directly with x, and f(x) = 8 when x = 6, write the direct linear variation equation.
A. f(x) = 3/4x  B.f(x) = 6x  C.f(x) = 8x  D.f(x) = 4/3x

Find the constant of variation for the relationship f(x)= 30x.  A.10  B.30  C.x  D.f(x)

If f(x) varies directly with x, and f(x) = 56 when x = 8, find the value of f(x) when x = 2  A.4  B.7  C.8  D.14

Answers

$(1)\ndirect\ variation\ between\ x\ and\ y:\ \ \ y=k\cdot x\ \ \ and\ \ \ k\in\ R\n\nAns.\ NOT\ direct\ is\ D\n\n(2)\nf(x) = m\cdot x\ \ \ and\ \ \ f(6)=8\n\n \Rightarrow\ \ \ m\cdot 6=8\ \ \ \Rightarrow\ \ \ m= (8)/(6) = (4)/(3) \ \ \ \ \Rightarrow\ \ \ \ Ans.\ D\n\n(3)\nf(x)=30x\ \ \ \Leftrightarrow\ \ \ (f(x))/(x) =30\ \ \ \ \ \ \Rightarrow\ \ \ \ constans=30\ \ \ \ Ans.\ B.$

$\n\n(4)\nf(x)=m\cdot x\ \ and\ \ f(8)=56\n\nm\cdot8=56\ \ \Leftrightarrow\ \ m= (56)/(8) =7\ \ \Rightarrow\ \ \ f(x)=7x\ \ \ \Rightarrow\ \ \ f(2)=7\cdot2=14\n\nAns.\ D.$

Write a expression that is equivalent to 7/10

Answers

An expression that is equivalent to 7/10 is .70, 70/10. Those are just a few examples. There are many more! I hope this helped.

50 POINTS! Vectors u, v, and w are shown in the graph. What are the magnitude and direction of u + v + w? Round the magnitude to the thousandths place and the direction to the nearest degree.

Answers

Answer:

C) 48.786, 152°

Step-by-step explanation:

To add the vectors u, v and w, we first need to rewrite each vector in component form (where vectors are represented using the unit vectors i and j along the x and y axes).

The (x, y) components of a vector, given its magnitude (r) and direction (θ), are (r cos θ, r sin θ), where θ is measured in the anticlockwise direction from the positive x-axis.

Every vector in two dimensions is made up of horizontal and vertical components, so any vector can be expressed as a sum of i and j unit vectors. Therefore, the i + y form of a vector is:

(r cos θ) i + (r sin θ) j

So, the component form of the given vectors are:

$\mathbf{u}=80 \cos 230^(\circ)\textbf{i}+80 \sin 230^\circ}\textbf{j}$

$\mathbf{v}=60 \cos 120^(\circ)\textbf{i}+60 \sin 120^\circ}\textbf{j}$

$\mathbf{w}=50 \cos 40^(\circ)\textbf{i}+50 \sin 40^\circ}\textbf{j}$

Sum the vectors:

$\mathbf{R}=\mathbf{u}+\mathbf{v}+\mathbf{w}\n\n\mathbf{R}=(80 \cos 230^(\circ)+60 \cos 120^(\circ)+50 \cos 40^(\circ))\textbf{i}+(80 \sin 230^\circ}+60 \sin 120^\circ}+50 \sin 40^\circ})\:\textbf{j}\n\n\mathbf{R}=-43.1207866\:\textbf{i}+22.8173493\:\textbf{j}$

$\textsf{For a vector\;\;$\mathbf{a} = x\mathbf{i} + y\mathbf{j}$, its magnitude is\;\;$||\mathbf{a}|| = √(x^2+y^2)$.}$

Calculate the magnitude of the resultant vector ||R||:

$\mathbf{||R||}=√((-43.1207866)^2+(22.8173493)^2)\n\n\mathbf{||R||}=48.7855887...\n\n\mathbf{||R||}=48.786$

The direction θ can be found by finding the angle with the horizontal, which is given by:

$\boxed{\theta=\tan^(-1)\left((y)/(x)\right)}$

As the resultant vector is in quadrant II (since the i component is negative and the j component is positive), we need to add 180° to the value of tan⁻¹(y/x). Therefore:

$\theta=\tan^(-1)\left((22.8173493)/(-43.1207866)\right)+180^(\circ)$

$\theta=-27.8855396+180^(\circ)$

$\theta=152.114460^(\circ)$

$\theta=152^(\circ)\; \sf (nearest\;degree)$

Therefore:

Magnitude = 48.786
Direction = 152°

The answer is c :48.786; 152°

Use the intercepts to graph the equation 4x-2y=8 please help me solve and graph

Answers

$4x-2y=8 \n \n the \ slope \ intercept \ form \ is : \n \n y= mx +b \n \n2y=4x-8 \ \ / :2\n\ny=2x-4$

Today, a bicycle rider rode her bike 5 1/2 miles. Yesterday, she rode 6 1/4 miles. The difference in length between the two rides is what fraction of the longer ride?

Answers

Answer

$(3)/(25)$

Explanation

First we need to find the difference of the tow fractions. But to find it, we need to convert the mixed fraction to improper fraction so we can ease our calculation.

Remember that to convert a mixed fraction to an improper fraction, we just need to multiply the denominator of the fraction part by the whole number and add the result to the numerator of the fraction part; the denominator of the improper fraction will be the same denominator of the fraction part of the mixed fraction:

$5(1)/(2) =((5*2)+1)/(2) =(10+1)/(2)=(11)/(2)$

$6(1)/(4) =((4*6)+1)/(4) =(24+1)/(4) =(25)/(4)$

Now we can find the difference:

$(25)/(4) -(11)/(2)$

Remember that to add or subtract fractions, both fraction must have the same denominator, so we are multiplying both numerator and denominator of our second fraction by 2:

$(25)/(4) -(11)/(2)*(2)/(2)$

$(25)/(4) -(22)/(4)=(25-22)/(4) =(3)/(4)$

Now to find what fraction of our difference is to the longer ride, we just need to divide our difference by the longer ride:

$((3)/(4))/(6(1)/(4) ) =((3)/(4))/((25)/(4) ) =(3)/(4) *(4)/(25) =(3)/(25)$

We ca conclude the difference in length between the two rides is $(3)/(25)$ of the longer ride.

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