Find the slope-intercept form of the equation of the line that passes through the points

(2, -1) and (-3, 4)

Answer:

x = 8 and x = 2 are both valid solutions.

There are no extraneous answers.

Step-by-step explanation:

Given absolute value function:

[tex]|2(x-5)|+11=17[/tex]

To solve an equation containing an absolute value, isolate the absolute value on one side of the equation:

[tex]\implies |2(x-5)|+11=17[/tex]

[tex]\implies |2(x-5)|+11-11=17-11[/tex]

[tex]\implies |2(x-5)|=6[/tex]

Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations.

Equation 1 (positive)

[tex]\implies 2(x-5)=6[/tex]

[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{6}{2}[/tex]

[tex]\implies x-5=3[/tex]

[tex]\implies x-5+5=3+5[/tex]

[tex]\implies x=8[/tex]

Equation 2 (negative)

[tex]\implies 2(x-5)=-6[/tex]

[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{-6}{2}[/tex]

[tex]\implies x-5=-3[/tex]

[tex]\implies x-5+5=-3+5[/tex]

[tex]\implies x=2[/tex]

Therefore, the solutions are x = 8 and x = 2.

Check if the solutions are valid by substituting them into the original equation:

[tex]\begin{aligned}x=8 \implies |2(8-5)|+11 & =17\\|2(3)|+11 & =17\\|6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies |2(2-5)|+11 & =17\\|2(-3)|+11 & =17\\|-6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]

Therefore, both solutions are valid and there are no extraneous answers.

Note:  An extraneous solution is a solution that is produced by solving the problem, but is not a valid solution to the problem.

The vertex (the common end point for the two rays) in the angle SRQ is the point R as it is in the middle and common.

The angle is SRQ with sides SR and RQ. The common point is R.

A vertex of an angle is the endpoint where two line or rays come together. The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place.

Here two sides are SR and RQ the end point to both the sides is common which is R. So the vertex to the angle SRQ is R.

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Answer: its 56

Step-by-step explanation:

plug #'s in

t=72-8x2

t=56

The guarantee period of the electronic components by Accrotime manufactures is 38 months.

mean = μ = 24 months

standard deviation = σ = 5 months

2 years = 24 months

a) P(x < 24)

= P[(x - μ ) / σ < (24 - 28) / 5]

= P[(x - μ ) / σ < -0.8

= P(z < -0.8 )

Using z table,

= 0.212

Percentage = 21.2%

b) Use standard normal table,

Refund percentage = 12%

P(Z > z) = 12%

= 1 - P(Z < z) = 0.12

= P(Z < z) = 1 - 0.12

= P(Z < z ) = 0.88

= P(Z < 0.174 ) = 0.94  

z = 0.174

Using z-score formula,

x = z ×σ  + μ

x = 1.74 × 5 + 28

x = 36.7

The guarantee period = 38 month

Thus, the guarantee period of the electronic components by Accrotime manufactures is 38 months.

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Answer: i feel like all of them but dont go by my word

Step-by-step explanation:

The measure of the missing angle is 112°.

When you need to find some interior angle of polygons, you can apply the  formula for the sum of interior angle. This formula relate the number of sides of the polygon with the sum of interior angle. The formula is presented below.

S = (n – 2 )*180º, where:

S= sum of interior angles

n= number of sides of the given polygon

The given figure shows:

Applying the formula, S = (n – 2 )*180º, you find:

S=(5-2) * 180

S=3*180

S=540°

Now  that you know the sum of the interior angles for the given polygon, thus:

x+105+118+75+130=540

x+428=540

x=540-428

x=112°

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Ian got a discount of 3.4 and percent discount is 10% after buying the items he wants in the local grocery store

Given data

price before tax and discount = $34

price after discount = $30.60

solving for discount

$34  -  $30.60 =  $3.4

percent discount

= 3.4 / 34 * 100 / 1

= 0.1 * 100

= 10%

Therefore we can say that Ian got a discount of 3.4 and percent discount is 10% after buying the items he wants in the local grocery store

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Answer:

3n+5

Step-by-step explanation:

you don’t know the official age, all you know is that his age is 3 times whatever number

Answer:

6

Step-by-step explanation:

Terms are what is separated by addition and subtraction.

The value of logarithmic equation log₂ (x+3) + lox₂ (3) = log₂(27) which is taken as an example is x = 6.

Step 1: Isolate a logarithmic expression (with the same base) on both sides of the equation using exponentiation rules.

Step 2: equalize the arguments.

Step 3: Solve the resultant equation.

Step 4: Verify your responses.

Let us consider an example -

log₂ (x+3) + lox₂ (3) = log₂(27)

using logₐ(m.n) = logₐ(m) + logₐ(n)

log₂(3(x+3)) = log₂(27)

log₂(3x + 9) = log₂(27)

3x+9 = 27

x = 27 - 9 / 3

x = 6

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Step-by-step explanation:

To find a line perpendicular to one another and passing through the point we take the slope of the original line and apply its reciprocal in point slope form.

Reciprocal of [tex]\frac{1}{4}[/tex] is [tex]\frac{-4}{1}=-4[/tex]

Now plug the slope into point-slope form with the known x and y values:

[tex]x-(-2)=-4(y-4)\\x+2=-4(y-4)\\x+2=-4y+16\\x+2+4y=16\\4y=16-x-2\\y=4-\frac{x}{4}-\frac{2}{4}\\y=3.5-\frac{x}{4}[/tex]

Answer:

Steps below.

Step-by-step explanation:

Unit Conversion is definitely needed in this question. Therefote, we will do some conversions first.

[tex]1m = 1000 mm \\ 1 {m}^{2} = {(1000)}^{2} {mm}^{2} \\ 1 {m}^{2} = 1000000 {mm}^{2} [/tex]

Now we can use the above converted unit to solve for the question.

[tex]32 {m}^{2} = 32 \times 1000000 \\ = 32000000 {mm}^{2} [/tex]

Answer:

- 3b + 21

Step-by-step explanation:

- 3(b - 7) ← multiply each term in the parenthesis by - 3

= - 3b + 21

Answer:

[tex]x\leq 25[/tex]

Step-by-step explanation:

Since x can equal anything 25 and lower, here are some of the possibilities x can be.

x = 25, 24, 23, 22, 21, 20, etc.

X could also be a decimal and doesn't have to be an integer.

x = 24.7, -20.4, 24 5/7

So to put these numbers in one equation, we can use the [tex]\leq[/tex] symbol.

Therefore, [tex]x\leq 25[/tex].

Hope this helped! Have a great day!

The height of the street light is approx. 3.5m.

Angle of depression is defined as the angle formed between the horizontal line and the line of sight when the observer looks down .

In the given question  

let h be the height of the street light

let d be the distance from the base of building to the street light .

form the figure given below.

In ΔADE

[tex]tan(57.8)=\frac{AD}{DE}[/tex]

Substituting the value of AD and DE from the figure

[tex]tan (57.8)=\frac{35}{d} \\ \\ d=\frac{35}{tan(57.8)} \\ \\ d=\frac{35}{1.5879}[/tex]....substituting the value of tan (57.8)

d=22.04 m      ...(i)

In ΔABC

[tex]tan(55)=\frac{AB}{BC}[/tex]

Substituting the value of AB and BC from the figure

since AD=AB+BD

35=AB+h

AB=35-h

[tex]tan (55)=\frac{35-h}{d}[/tex]

Substituting the value of d from (i)

[tex]tan (55)=\frac{35-h}{22.04}\\ \\ 35-h=tan(55)*22.04\\ \\ 35-h=1.428*22.04[/tex]( substituting the value of tan(55)  )

[tex]35-h=31.47[/tex]

[tex]h=35-31.47\\h=3.53\\[/tex]

h≅3.5

Therefore , the height of the streetlight is approx. 3.5m  .

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The solutions of the expression are;

a. - 5 - 2 = -7

b. 6 - (-5) = 11

What is Addition?

A process of combining two or more numbers are called Addition.

The given expression are;

a. -5 - 2

b. 6 - (-5)

Now, Solve the expression as;

-5 - 2 = - 7

And, 6 - (-5) = 6 + 5 = 11

So, The solutions of the expression are;

- 5 - 2 = -7

6 - (-5) = 11

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There is 0.329 probability or chance that the software really has a virus.

The calculation will be based on Bayes' theorem which relates the probability and statistics, as is mentioned in the given question. The values provided are True positive = 97%, False positive = 2% and Prevalence = 1%.

Probability = (True positive × user) ÷ (True positive × user) + (false positive × non user)

Keep the values in formula to find the probability

Probability = (0.97 × 0.01) ÷ (0.97 × 0.01) + (0.02 × 0.99)

Probability = 0.0097 ÷ (0.0097 + 0.0198)

Probability = 0.0097 ÷ 0.0295

Probability = 0.329

Thus, there is 0.329 chance that the software really has a virus.

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The inequality represented by the given number line is; -4 ≥ x ≥ 5

From the given number line we can find the inequality. Some of the rules are that;

For a shaded circle pointing to the left means less than or equal to (≤)

For a shaded circle pointing to the right means greater than or equal to (≥).

For an unshaded circle pointing to the left means less than (<)

For a shaded circle pointing to the right means greater than (>)

Thus, applying the above to the inequality line gives;

-4 ≥ x ≥ 5

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Answer:

[tex] \dfrac{x^{5}}{y^{8}} [/tex]

Step-by-step explanation:

[tex] \dfrac{y^{-8}}{x^{-5}} = [/tex]

[tex] = \dfrac{x^{5}}{y^{8}} [/tex]

The expression is simplified to give y⁻⁸x⁵

First, it is important to note that index forms are described as mathematical forms that are used to represent numbers of variables that are too large or that are too small in more convenient forms.

These index forms are also known as scientific notations or standard forms

From the information given, we have that;

y to the negative eighth power over x to the negative fifth power

This is represented as;

y⁻⁸/x⁻⁵

Since the forms are not of the same bases, we cannot add the exponents

y⁻⁸x⁵

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Answer:

109.

Step-by-step explanation:

62+41+(2)+(4)       we can remove the brackets:

= 62 + 41 + 2 + 4

= 109.

The total number of cupcakes sold by the bakery on that day were 200.

Here, we are given that a bakery sold 26 vanilla cupcakes in a day.

This was 13% of the total number of cupcakes sold that day.

Let the total number of cupcakes sold that day be x

Then 13% of x is given to be 26. Mathematically this can be represented as-

(13/100)x = 26

solving the equation to find the value of x, we get-

x = 26 × 100/ 13

x = 26/13 × 100

x = 2 × 100

x = 200

Thus, the total number of cupcakes sold by the bakery on that day were 200.

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Answer: “The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.”

      - https://www.mathplanet.com

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Angles DBF and EBF form a linear pair, so:

[tex]5x+6+3x-2=180 \\ \\ 8x+4=180 \\ \\ 8x=176 \\ \\ x=22 \\ \\ \implies m\angle DBF=116^{\circ}[/tex]

Similarly, because angles DBF and DBC form a linear pair, the answer is 64°.

Answer:

A) "If q, then p."

B) "If not p, then (not) q."

C) "If (not) q, then not p."

Answer: $96.27

Step-by-step explanation: 15x5=75, 75+21.27=96.27

Answer: $96.27

Step-by-step explanation:

If five of Carries' family members donated $15 we would have 15x5.

15+15+15+15+15=$75.

Carrie, herself, donated $21.27.

$75+$21.27

75+21=96

Add the .27 to 96.

Answer= $96.27 in total

Answer:

The measure of angle 3 is 30 (C).

Step-by-step explanation:

m<1, m<2, and m<3 have a sum of 180        Linear Pair Postulate

So 2x + 3x - 20 + x - 4 = 180

6x - 24 = 180

6x = 204

x = 34

Then you substitute and get 34 - 4 for angle 3 which = 4

Hope this helps!

Answer:  4 players can play and still have 8 cards each.

39÷8=4.875

Answer:

4 people

Step-by-step explanation:

39 cards / 8 cards = 4.87500

each person must have 8 cards, so only 4 people can play