A pair of linear equations is shown
y=-3x5
y=x+2
Which of the following statements best explains the steps to solve the pair of equations graphically?
on a graph, find the point of intersection stwo lines; the first line has y-intercept - 5 and slope - -3, and the second line has y-intercept = 2 and slope - 1.
On a graph, find the point of intersection of two lines, the first line has y-intercept -3 and slope - 5, and the second line has y-intercept - 1 and slope - 2.
On a graph, find the point of intersection of two lines, the first line has y-intercept -- and slope - 3, and the second line has y-intercept = -2 and slope --1
On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope -5, and the second line has y-intercept -1 and slope --2.

Answer:  D) 8

Work Shown:

32/24 = 2x/12

32*12 = 24*2x

384 = 48x

48x = 384

x = 384/48

x = 8

The correct option is Option D: the value of x is 8

The triangles whose corresponding angles are equal and the corresponding sides are in equal proportiion are called similar triangles.

If two triangles are similar

then a₁/a₂=b₁/b₂=c₁/c₂

where a₁, b₁, and c₁ are the sides of one triangle

a₂, b₂, and c₂ are the sides of another triangle

Here it is given that

triangles ΔJLK and ΔRJS are similar.

so by the property of similar triangles,

JR/JL = JS/JK = RS/KL

Given that JR=24

JL=32

JS=12

JK=2x

By using the property

JR/JL = JS/JK

⇒ 24/32 = 12/2x

⇒2x= 12*32/24

⇒2x=16

⇒x=16/2

⇒x=8

Therefore the value of x is 8.

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Answer:

r=8

Step-by-step explanation:

45=6r-3

48=6r

r=8

Answer:

The simplified form of r^-7 + s^-12 is ----> 1/r^7 + 1/s^12

Step-by-step explanation:

Answer:m

Step-by-step explanation:m

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

A. (16 - 12)² = 4² = 4 · 4 = 16

B. -|-4| = -4

C. (96 : 8) - 2³ = 12 - 8 = 4

D. 24 - 42 = -(42 - 24) = -18

or 2⁴ - 4² = 16 - 16 = 0

The correct answer is C

Answer:

$203

Step-by-step explanation:

15x8=$120

120+83=$203

Answer:

8

Step-by-step explanation:

-2 xy

Let x = -4 and y = 1

-2 (-4)*(1)

8(1)

8

you can go for option g cause ans is 14:5

Answer:

9 times 20 is equally to 180 minutes

Answer:

f=-1/20t+12

Step-by-step explanation:

khan

The base angles of an isosceles trapezoid are equal; For EFGI to be a parallelogram, the measure of [tex]\angle HGI[/tex] is: 108 degrees

Given that:

[tex]\angle IEF = 36^o[/tex]

IEF and GHI are the base angles of the trapezoid.

So:

[tex]\angle GHI = \angle IEF = 36^o[/tex]

Also:

[tex]\triangle GHI[/tex] is an isosceles triangle.

This means that:

[tex]\angle GHI = \angle HIG = 36^o[/tex] --- base angles of an isosceles triangle

So:

[tex]\angle GHI + \angle HIG + \angle HGI = 180[/tex] --- sum of angles in a triangle

Substitute known values

[tex]36 + 36+ \angle HGI = 180[/tex]

[tex]72 + \angle HGI = 180[/tex]

Collect like terms

[tex]\angle HGI = 180-72[/tex]

[tex]\angle HGI = 108[/tex]

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This is a point, so it has x- and y-coordinates. Both of these coordinates are positive, therefore the point must be in the first quadrant.

The pattern for the points on a unit circle is 3 - 2 - 1 starting at 0 and up to pi/2. The pattern for the radian denominators on a unit circle is 6 - 4 - 3 starting at 0 and up to pi/2.

(sqrt(3) / 2, 1/2) = pi / 6 radians

Hope this helps!

Answer:

A. pi/6 radians

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1/2 : sqrt(3/2) : 1

sin theta = opp/hyp

tan theta = 1/2 / 1

tan theta = 1/2

theta = pi/6 radians

Answer: A. pi/6 radians

Answer:

unless this is a stats question and you are suggesting that you have bad sampling techniques being used

117/484 is about 24% that is 100% under the "about 50%" stated in the article

Step-by-step explanation:

Answer:

Hello,

a=0.5

Step-by-step explanation:

[tex]\left \{ \begin{array}{ccc}ax+2y&=&12\\8x+32y&=&144\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}ax+2y&=&12\\x+4y&=&18\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}(1-2a)x&=&-6\\x+4y&=&18\\\end{array}\right.\\\\if\ 1-2a\neq 0\ (or\ a\neq \dfrac{1}{2} )\ then\\\left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{18-\dfrac{6}{2a-1}}{4} \\\end{array}\right.\\\\[/tex]

[tex]\Longleftrightarrow\ \left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{ 3(3a-2)}{2a-1} \\\end{array}\right.\\\\[/tex]

else\

[tex]a=\dfrac{1}{2} \\\Longleftrightarrow\ \left \{ \begin{array}{ccc}\dfrac{1}{2} x+2y&=&12\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}x+4y&=&24\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}0=6\ !!!!!\\\end{array}\right.\\\\Syetem\ has\ no\ solution\\[/tex]

Answer:

10

Step-by-step explanation:

4 * 2.5  = 10

Answer:

1 and 3 are congruent

Answer:

Angle 1 and angle 3 are congruent

Answer:

Step-by-step explanation:

.007  = 7 x [tex]10^{-3}[/tex]

.07    = 7 x [tex]10^{-2}[/tex]

7      = 7 x [tex]10^{0}[/tex]

700 = 7 x [tex]10^{2}[/tex]

Answer:

(f+g)(x)=5x+2x²-7x+4+3x-7 = 2x²+x-3

Step-by-step explanation:

Answer:

=6x^3-20x^2+26x-28

Step-by-step explanation:

Answer:

a) X=75°

y= 105°

b) b= 120°

a=45°

d) r=75°

q=37°

p= 37°

e) y=100°

X= 143°

Step-by-step explanation:

soln no. a

here,

X+50+55=180(sum of all angle of triangle)

or, X= 180-105

or, X= 75°

again,

X+y = 180 (straight angle)

or, y= 180-75

or, y= 105°

soln no b

here,

b+60=180(straight angle)

or, b = 180 - 60

or, b = 120°

again,

a+60+75=180(sum of all angle of triangle)

or, a = 180- 135

or, a = 45°

soln no. d

here,

r=70°( alternate angle)

again,

73°+q+r=180( sum of all angle of triangle)

or,q=180-143

or,q=37°

again,

p=q=37(alternate angle)

soln no. e

y+80=180(straight angle)

or,y= 180-80

or, y = 100°

again,

63+80+<RMB=180(sum of all angles of triangle)

or, 143+<RMB=180

or, <RMB=180-143

or,<RMB= 37°

again,

X+ <RMB= 180(straight angle)

or,X= 180°-37°

or, X = 143°

Answer:

8,1,-6

Step-by-step explanation:

8 + (-7)

= 8-7 = 1

1 + (-7) = 1 - 7 = -6

The first three terms are 8, 1,-6

Answered by Gauthmath

Answer: A): 15.90 ounces to 16.4 ounces.

Step-by-step explanation:

Considering the standard deviation is 0.25 ounces. The mean of the juice is 16.15 ounces. Additionally, 68% is one standard deviation away from the mean.

With that being said, you would do the following calculations:

[tex]16.15-0.25=15.90\\\\16.15+0.25=16.40[/tex]

This question relates to The Empirical Rule and understanding how it works. A brief summary is that within one standard deviation of the mean, that is where 68% of the data lies. Two standards deviations is 95%. And three standard deviations is 99.5%.

The formula: [tex]u\frac{+}{-} o[/tex]

the mean PLUS OR MINUS the standard deviation.

Answer:

A

Step-by-step explanation:

The function written in the rational form is, C. F(x) = (x - 5)/3x

Rational numbers are subsets of real numbers which can be written in the form of p/q, where q ≠ 0. As at q = 0 it is undefined.

Similarly, A rational expression is also written in the form of p/q, where p and q are algebraic expressions and q ≠ 0.

From the given options, F(x) is written in the form p/q,

Where, p = x - 5 and q = 3x.

Therefore, The rational function is, F(x) = (x - 5)/3x, where x ≠ 0.

As at x = 0 the function is undefined.

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Answer:

1/2

Step-by-step explanation:

2^ -1

We know that a^-b = 1/a^b

1 / 2^1

1/2

Answer:

The answer is A. [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex].

Step-by-step explanation:

To find the difference of this problem, start by simplifying the denominator, which will look like [tex]\frac{3}{x+7}-\frac{42}{(x+7)(x-7)}[/tex]. Next, multiply [tex]\frac{3}{x+7}[/tex] by [tex]\frac{x-7}{x-7}[/tex]  to create a fraction with a common denominator in order to subtract from [tex]\frac{42}{(x+7)(x-7)}[/tex]. The problem will now look like [tex]\frac{3}{x+7}*\frac{x-7}{x-7}-\frac{42}{(x+7)(x-7)}[/tex].  

Then, simplify the terms in the problem by first multiplying [tex]\frac{3}{x+7}[/tex] and [tex]\frac{x-7}{x-7}[/tex], which will look like [tex]\frac{3(x-7)}{(x+7)(x-7)}-\frac{42}{(x+7)(x-7)}[/tex]. The next step is to combine the numerators over the common denominator, which will look like [tex]\frac{3(x-7)-42}{(x+7)(x-7)}[/tex].

Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of [tex]3(x-7)-42[/tex], which will look like [tex]\frac{3(x-7-14)}{(x+7)(x-7)}[/tex]. Then, subtract 14 from -7, which will look like [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex]. The final answer will be [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex].    

Given a function g(x), its derivative, if it exists, is equal to the limit

[tex]g'(x) = \displaystyle\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]

The limit is some expression that is itself a function of x. Then the derivative of g(x) at x = 1 is obtained by just plugging x = 1. In other words, find g'(x) - and this can be done with or without taking a limit - then evaluate g' (1).

Alternatively, you can directly find the derivative at a point by computing the limit

[tex]g'(1) = \displaystyle\lim_{h\to0}\frac{g(1+h)-g(1)}h[/tex]

But this is essentially the same as the first method, we're just replacing x with 1.

Yet another way is to compute the limit

[tex]g'(1) = \displaystyle\lim_{x\to1}\frac{g(x)-g(1)}{x-1}[/tex]

but this is really the same limit with h = x - 1.

You do not compute g (1) first, because as you say, that's just a constant, so its derivative is zero. But you're not concerned with the derivative of some number, you care about the derivative of a function that depends on a variable.

Answer:

1. h

2. b

3. a

4. d

5. c

Step-by-step explanation:

all answers are straight forward. only the last (5) is phrased a bit strangely. I would have said "reflect across a horizontal line".

Answer:

76

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin ? = 32/33

Taking the inverse sin of each side

sin ^-1( sin ?) = sin^-1 (32/33)

? =75.85888

To the nearest degree

? = 76

Answer:

rational

Step-by-step explanation:

it can be written as a fraction