if measure 1 = x+70 and measure 2 = 5x -54 what is measure 3.Write an equation and solve

For quadratics, these formulas are used mainly for factoring.

Your equation can be written as ...

... 2(x² +2x -3) = 0

You factor this by looking for factors of -3 (c=x1·x2) that add to give +2 (b=-(x1+x2)). These are {-1, +3}, so the factorization is ...

... 2(x -1)(x +3) = 0

The roots are then 1 and -3, which sum to -b = -2.

(You will note that the numbers used in the binomial factors are the opposites of the roots x1 and x2 in the Viete's Formulas. That is how we can look for them to sum to "b", rather than "-b".)

y + 3 = [tex]\frac{2}{3}[/tex] (x - 5)

the equation of a line in point- slope form is

y - b = m ( x - a )

where m is the slope and (a, b) a point on the line

here m =[tex]\frac{2}{3}[/tex] and (a,b) = (5 , - 3 )

y + 3 = [tex]\frac{2}{3}[/tex] (x - 5 ) ← in point-slope form

The equation of the line that passes through the point (5, -3) and has a slope of 2/3 is y = 2/3x - 19/3, using the point-slope form for the equation of a line.

The line that you're looking for can be represented using the point-slope form of a linear equation. This form is written as y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and 'm' is the slope of the line. For a line that passes through the point (5, -3) and has a slope of 2/3, you replace x1 with 5, y1 with -3, and m with 2/3. So, the equation of the line becomes y - (-3) = 2/3(x - 5), which simplifies to y + 3 = 2/3x - 10/3. Further simplifying, we get y = 2/3x - 10/3 - 3, or y = 2/3x - 19/3.

https://brainly.com/question/29054476

#SPJ3

given a linear equation in slope- intercept form y = mx + c

where m is the slope and c the y -intercept

the slope of a line perpendicular to it is - [tex]\frac{1}{m}[/tex]

If equation is y = 2x + 3 ( with slope m = 2 )

then the perpendicular slope = - [tex]\frac{1}{2}[/tex]

The closet area is 1/9 of the bedroom area, so is (1/9)·(90 ft²) = 10 ft².

The width of the closet multiplied by the length is the area.

... length×(2 ft) = 10 ft²

... length = (10 ft²)/(2 ft) = 5 ft

The length of Jackson's closet is 5 ft.

we have

[tex]f(x)=\frac{1}{2}x+2[/tex]

To graph the line find the x and y intercepts

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

so

Find the y-intercept

For [tex]x=0[/tex]

[tex]f(0)=\frac{1}{2}*0+2=2[/tex]

the y-intercept is the point [tex](0,2)[/tex]

Find the x-intercept

For [tex]y=0[/tex]

[tex]0=\frac{1}{2}x+2\\x=-4[/tex]

the y-intercept is the point [tex](-4,0)[/tex]

Using a graphing tool

Plot the points to graph the line

therefore

the answer in the attached figure

The graph of the linear function f(x) = 12x + 2 is attached below

The graph of a linear equation is a straight line when plotted on a coordinate plane. A linear equation can be written in the form:

y = mx + b

Where:

"y" represents the dependent variable (usually plotted on the vertical axis).

"x" represents the independent variable (usually plotted on the horizontal axis).

"m" is the slope of the line, which determines its steepness.

"b" is the y-intercept, which is the point where the line crosses the y-axis.

The graph of the linear equation f(x) = 12x + 2 is attached below;

Learn more on graph of linear function here;

https://brainly.com/question/4025726

#SPJ4

If you actually do what the problem statement tells you to do, the answer falls into your lap.

The attachment shows the triangle reflected across the y-axis (blue), then across the x-axis (red). The red triangle is clearly equivalent to the original being rotated 180° about the origin.

The appropriate choice is ...

... a 180° rotation about the origin

_____

Algebraically, reflection across the y-axis negates the x-coordinate:

... (x, y) ⇒ (-x, y)

and reflection across the x-axis negates the y-coordinate:

... (x, y) ⇒ (x, -y)

Then, reflection across first one axis then the other will result in both coordinates being negated:

... (x, y) ⇒ (-x, -y)

This is precisely what happens when a figure is rotated 180° about the origin.

Answer:

A 180 rotation about the origin

The x-coordinate of the intersection point of two perpendicular lines, one with equation y = mx + b and the other with equation y = -x/m - b, is given by x = 2b/(m + 1/m).

Given two perpendicular lines, one has the equation y = mx + b. The y-intercept of this line is b, and the slope is m. The equation of the second line, which is perpendicular to the first, will have a negative reciprocal slope, -1/m, and for opposite y-intercepts, we'll assume its y-intercept to be -b. Thus the equation of the second line is y = -x/m - b.

For the intersection point, equal the y-values of the two equations: mx + b = -x/m - b. Simplify to obtain the x-coordinate of the intersection point:

mx + x/m = 2b or x(m + 1/m) = 2b. Therefore, the x-coordinate of the intersection point is x = 2b/(m + 1/m).

https://brainly.com/question/27476927

#SPJ12

To find the x-coordinate of the intersection point of two perpendicular lines with opposite y-intercepts, set the equations of the lines equal to each other and solve for x.

To find the x-coordinate of the intersection point of two perpendicular lines with opposite y-intercepts, we need to find the equations of both lines. Let's assume the equation of one line is y = mx + b. Since the lines are perpendicular, the slope of the other line will be the negative reciprocal of m. Let's call the slope of the other line n. Therefore, the equation of the other line will be y = -nx + c, where c is the y-intercept of the second line. To find the x-coordinate of the intersection point, we can set the two equations equal to each other and solve for x:

mx + b = -nx + c

x(m + n) = c - b

x = (c - b)/(m + n)

https://brainly.com/question/18271653

#SPJ12

The slope of y = -x is m = -1.  Thus, starting with the slope-intercept form y = mx + b, we substitute -1 for m, 8 for x and 2 for y, to determine the vaue of b:

2 = -1(8) + b, or 10 = b.  Then the equation of the line parallel to y = -x and passing thru (8,2) is:

y = -x + 10.

Answer:

The answer will be 3.55

Step-by-step explanation:

Answer:

3.55

Step-by-step explanation:

26.30 - 22.75 = 3.55

So, you got it right.

[tex]Echy[/tex]

Drop all the minus signs (change them to +) to get your answers:

37, 2.987, 54, 2/3, 45

Answer:

Yes. (See below for explanation.)

Step-by-step explanation:

The number of servings is found by dividing the quantity available by the size of a serving. The quantity of punch is the sum of the quantities of the juices that go into the punch. The serving size of 3/4 cup is the same as 6 ounces, since a cup is 8 ounces. (3/4 × 8 oz = 6 oz)

The quantity available is (64 oz + 28 oz + 76 oz). The serving size is 6 oz. Since the units of numerator and denominator are the same, they cancel, leaving ...

... number of servings = (quantity available)/(serving size)

... = (64 +28 +76)/6 . . . . as shown in the problem statement

_____

It might not be obvious that the above ratio gives the number of servings. However, if you look at the real units, you see how it happens.

[tex]\dfrac{oz}{(\frac{oz}{serving})}= oz\dfrac{serving}{oz}=\dfrac{oz}{oz}serving=serving[/tex]

First you had to switch sides of equation form.

[tex]\frac{x}{100}= \frac{7}{10}[/tex]

Then you multiply by one-hundred from both sides of equation form.

[tex]\frac{x}{100}*100= \frac{7}{10}*100[/tex]

And finally, simplify by equation.

[tex]\frac{x}{100}*100=x[/tex]

[tex]\frac{7}{10}*100=70[/tex]

[tex]70*1=70[/tex]

[tex]x=70[/tex]

Final answer: [tex]\boxed{x=70}[/tex]

[tex]70/10=7[/tex]

[tex]70/7=10[/tex]

[tex]10*7=70[/tex]

[tex]7*10=70[/tex]

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

x = 70

given [tex]\frac{7}{10}[/tex] = [tex]\frac{x}{100}[/tex] ( cross-multiply )

10x = 7 × 100 = 700 ( divide both sides by 10 )

x = [tex]\frac{700}{10}[/tex] = 70

Answer:

Erica

Step-by-step explanation:

Two lines with the same (defined) slope will only have infinite solutions if their y-intercepts are the same. Otherwise, the number of solutions (points on both lines) is zero.

Since the 2 lines have the same slope, then the lines are parallel and never intersect. Thus there is no solution to the system of equations

Neither Jake nor Erica are correct.

- 3, - 9.6 and - 22.8

to generate the first, fourth and tenth term substitute n = 1, 4, 10 into the rule

a(1) = - 3 + 0 = - 3

a(4) = - 3 - 6.6 = - 9.6

a(10) = - 3 - 19.8 = - 22.8

Adam will be 14, and it is 8 more than 6.

We have given that,

Adam is three years younger than twice bobs age. in 5 years Adams's age will be 8 years more than bobs age.

We have to determine the what are their 2 ages.

The age of majority is the age when children legally become adults.

Adam is 9 years old and Bob is 6.

Twice Bob’s age is 12, and three years younger than that is 9.

If Adam is 9 now then in five years, Adam will be 14, which is 8 more than 6.

To learn more about the age visit:

https://brainly.com/question/26423521

#SPJ2

m∠3 + m<6 = 180

Given: m∠6 = 75°

so

m<3 + 75°= 180°

m<3 = 105°

Answer:

Here is the answer! Hope I helped! Have a nice day! Really helpful for k12 users! And sorry I am late!!!!

Step-by-step explanation:

Answer:

(-2.5, ∞)

Step-by-step explanation:

You can add the opposite of the right side.

5.1(3 +2.2x) +14.25 +6(1.7x +4) > 0

15.3 +11.22x +14.25 + 10.2x +24 > 0 . . . eliminate parentheses

21.42x +53.55 > 0 . . . . . . . . . . . . . . . . . . collect terms

x + 2.5 > 0 . . . . . . . . . . . . . . . . . . . . . . . . .divide by the coefficient of x

x > -2.5 . . . . . . add the opposite of the constant

(- 2.5, ∞ )

distribute parenthesis on both sides of inequality and simplify

15.3 + 11.2x > - 14.25 - 10.2x - 24

15.3 + 11.2x > - 38.25 - 10.2x ( add 10.2x to both sides )

15.3 + 21.42x > - 38.25 ( subtract 15.3 from both sides )

21.42x > - 53.55 ( divide both sides by 21.42 )

x > - 2.5

solution x ∈ (- 2.5, ∞ )

Answer:

1/8

Step-by-step explanation:

The relations can be written as ...

... blue = (3/5)×shirt

... sale = (5/8)×blue

... medium = (1/3)×sale

Substituting, we get

... medium = (1/3)×((5/8)×((3/5)×shirt)) = (1·5·3)/(3·8·5) × shirt = (1/8)×shirt

_____

1/8 of the shirts in the shop are medium blue T-shirts on sale.

Answer:

B. 120

Step-by-step explanation:

2cos x + 1 = 0

2 cos x = -1

cos x = -1/2

x = cos^1(-1/2)

(cos inverse (-1/2))

x = 120°

The only factorial expression that is shown properly evaluated is that of selection A.

_____

If you number the terms starting from 0 on the left, you find that 20 is term #3 on the row that has 6 as term #1. In combination notation, this would be

... 6C3 or C(6, 3)

It is computed as

... 6!/(3!·(6-3)!) = 6·5·4/(3·2·1) = 20

Answer: The answer is 40

Step-by-step explanation:

In the attachment, the original parallelogram is shown in red. Its image is shown in blue. The purple parallelogram is the original reflected across the y-axis. You can see that it becomes the blue parallelogram if rotated 90° clockwise around the origin.

The appropriate choice is ...

... a reflection over the y-axis and then a 90 degree clockwise rotation about the origin

Answer:

B. a reflection over the y-axis and then a 90degree clockwise rotation about the origin

Step-by-step explanation:

I just did it, and all was well! :) :) :)

Short answer: you don't.

The linear term in the numerator of the integral means the form shown is not applicable. Rather, you perform the integration using partial fraction expansion.

[tex]\displaystyle\int{\frac{5x+1}{25x^2+60x-13}}\,dx=\int{\frac{5x+1}{(5x-1)(5x+13)}}\,dx\\\\=\frac{1}{35}\int{\frac{5}{5x-1}}\,dx+\frac{6}{35}\int{\frac{5}{5x+13}}\,dx[/tex]

The integral is ...

... (1/35)ln|5x-1| +(6/35)ln|5x+13| +C

_____

If the numerator of your integral were a constant, then the fractions multiplying the separate partial fraction integrals would have the same magnitude and opposite signs. You would end with the difference of logarithms, which could be expressed as the log of a ratio as shown in your problem statement.

The median on any box plot is the little dot in the middle of the box so the answer is C)42. So where the line is in the middle of the box it is always going to be the median. The median is in the middle. You can also remember it like this Hey Diddle diddle the medians the middle you add and divide for the mean and the mode is the most.

Answer:  

B) 38  

Step-by-step explanation:

38 is the first (lower) quartile of the box-and-whisker plot.

The median is the middle number in order of the set of values:

2, 4, 8, 10, 12

8 is the median in the set of values!

Answer:

its 8

Step-by-step explanation:

No

The equation of a parallel line will have the same x-term, but a different constant (y-intercept). The required value can be found by putting the given point values in to the equation to see what it needs to be.

... y = 5x + ___

... 8 = 5·4 + ___

... 8 - 20 = -12 = ___

Your equation is ...

... y = 5x -12