Write an equation of the line passing through point P that is perpendicular to the given line. P(4,−3), y=−x−5

Answer:

x = 1

Step-by-step explanation:

Given

- | x + 2 | + 1 = 4x - 6 ( subtract 1 from both sides )

- | x + 2 | = 4x - 7 ( multiply both sides by - 1 )

| x + 2 | = - 4x + 7

The absolute value always returns a positive value, but the expression inside can be positive or negative, thus

x + 2 = - 4x + 7 ( add 4x to both sides )

5x + 2 = 7 ( subtract 2 from both sides )

5x = 5 ( divide both sides by 5 )

x = 1

OR

- (x + 2) = - 4x + 7, that is

- x - 2 = - 4x + 7 ( add 4x to both sides )

3x - 2 = 7 ( add 2 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

As a check substitute these values into both sides of the equation and if both sides are equal then they are the solutions.

x = 1 : - |1 + 2| + 1 = - | 3 | + 1 = - 3 + 1 = - 2

right side = 4(1) - 6 = 4 - 6 = - 2 ← True

x = 3 : - |3 + 2| + 1 = - |5| + 1 = - 5 + 1 = - 4

right side = 4(3) - 6 = 12 - 6 = 6 ← False

Thus x = 3 is an extraneous solution and

x = 1 is the solution

Answer:

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right\\\\|x+2|=\left\{\begin{array}{ccc}x+2&for&x+2\geq0\to x\geq-2\\-(x+2)&for&x<-2\end{array}\right[/tex]

[tex](1)\ x<-2\\\\-\bigg(-(x+2)\bigg)+1=4x-6\\\\+(x+2)+1=4x-6\qquad\text{combine like terms}\\\\x+(2+1)=4x-6\\\\x+3=4x-6\qquad\text{subtract 3 from both sides}\\\\x+3-3=4x-6-3\\\\x=4x-9\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\x-4x=4x-4x-9\\\\-3x=-9\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{-9}{-3}\\\\x=3\notin(1)[/tex]

[tex](2)\ x\geq-2\\\\-(x+2)+1=4x-6\\\\-x-2+1=4x-6\\\\-x+(-2+1)=4x-6\\\\-x-1=4x-6\qquad\text{add 1 to both sides}\\\\-x-1+1=4x-6+1\\\\-x=4x-5\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\-x-4x=4x-4x-5\\\\-5x=-5\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5x}{-5}=\dfrac{-5}{-5}\\\\x=1\in(2)[/tex]

Answer:

Step-by-step explanation:

Sec B

1) 5p⁻³ = 8*5⁻²      

p⁻³  = 2³*5⁻²/5            

p⁻³ =2³*5⁻³             { 1/a^m = a^-m}

p⁻³ = 5⁻³ /2⁻³            {a^m = 1/a^-m}

p⁻³ = (5/2)⁻³

p= 5/2

2) 4x²  = 81

x²  = 81/4

x²  = 9² /2²

x²  =(9/2)²

x = 9/2

3) 9^x/3 =81

9^x/3 = 9^2

Comparing the powers, x/3 = 2

                                         x = 2*3 =6

  x = 6

Answer:

7/3

Step-by-step explanation:

7 1/3=22/3

22/3-5=22/3-15/3=7/3

Answer: 2 and 1/3

Step-by-step explanation: In this problem, we begin by subtracting the fractions. Since 5 has no fraction, imagine the fraction 0/3 so 1/3 - 0/3 is 1/3.

Next, subtract the whole numbers. 7 - 5 is 2 so 7 and 1/3 - 5 = 2 and 1/3.

Answer:

Gianna makes $18 per hour.

Step-by-step explanation:

Given Gianna makes 90$ for 5 hours. That means she should make [tex]$ \frac{90}{5} $[/tex] $  = 18$ every hour.

Therefore we have:

a.

HOURS                    DOLLARS

  1                                   18

  2                                  36

  3                                  54

  4                                   72

  5                                   90

  6                                   108

  7                                   126

b.

For the tabular column mark Hours on the x - axis and Dollars on the Y - axis. It can be plotted from the above table easily.

c.

If Gianna works for 8 hours she would have made 8 X 18 = 144$.

So, she will earn 144$ in 8 hours.

d.

To make 60$ she would have to work [tex]$ \frac{60}{18} $[/tex] hours = 3.33 hours.

Answer:

[tex]\frac{3}{8}[/tex] yards of fabric.

Step-by-step explanation:

Jessica has [tex]\frac{9}{10}[/tex] yards of fabric and she cut [tex]\frac{5}{12}[/tex] of the length.

Therefore, Jessica has cut fabric of the length [tex]\frac{9}{10} \times \frac{5}{12} = \frac{3}{8}[/tex] yards.

This is the answer as a fraction in simplest form.

Now, Jessica used the expression to find the amount of fabric she cut as [tex] \frac{9}{10} \times \frac{5}{12}[/tex] was correct. ( Answer )

Answer:

see explanation

Step-by-step explanation:

(A) Given

4(2x - 3) = 4 ( divide both sides by 4 )

2x - 3 = 1 ( add 3 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

(B)

As a check substitute x = 2 into the left side of the equation and if equal to the right side then it is the solution.

4(2(2) - 3) = 4(4 - 3) = 4(1) = 4 = right side

Hence x = 2 is the solution

Answer:

The solution of the given equation is x = 2.

Step-by-step explanation:

The given linear equation is,

[tex]4(2x-3)=4[/tex]

At first, we will eliminate '4' from the LHS by dividing both sides i.e., LHS and RHS by 4 because '4' is present in multiplication with the term containing unknown in LHS.

So, dividing both sides by '4', we get

[tex]\frac{4(2x-3)}{4} = \frac{4}{4}[/tex]

[tex]\implies 2x - 3 = 1[/tex]

Our next step will be to eliminate '3' from the LHS that is being subtracted from the term containg unknown variable. For this, we will add '3' on both sides of the above obtained equation.

So, adding '3' on both sides, we get

[tex]2x - 3 + 3 = 1 + 3[/tex]

[tex]\implies 2x = 4[/tex]

Now, we will eliminate '2' from the LHS that is in multiplication with the unknown variable 'x'.

For this, we will divide both sides of the above obtained equation by '2'.

So, dividing both sides by '2', we get

[tex]\frac{2x}{2}=\frac{4}{2}[/tex]

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

CHECKING :

For this, we will substitute x = 2 in the LHS of the given equation and then check whether it is equal to RHS or not.

LHS = 4(2x - 3)

= 4(2 × 2 - 3)

= 4(4 - 3)

= 4 × 1

= 4

= RHS

So, the solution of the given equation is x = 2.

50 miles per hour  is the rate (speed) of the wind.

Step-by-step explanation:

Let consider the variable ‘x’ for speed of wind.  

Below we write two values of the speed of the airplane in the air in terms of ‘x’:

1. Subtract wind speed from airplane speed: 250 - x.

2. Add wind speed to the airplane speed against the wind: 150 + x.

And now, set these above two expressions equal to each other to find x (wind speed),

                                      250 – x = 150 + x

                                      2x = 100

                                     x = 50 miles per hour

Answer:

False

Step-by-step explanation:

1x= y

Step-by-step explanation:

x being the weight and y being the cost

Answer:

y=9

Step-by-step explanation:

substitution x=2 in equation

y= 3^2

y=9

Final answer:

To evaluate y=3^x for x=2, substitute x=2 into the expression y=3^x to find that y=9.

Explanation:

The given expression is y = 3^x. To evaluate y for x = 2, substitute x = 2 into the expression:

y = 3^2

y = 9

Therefore, y = 9 when x = 2.

Answer:

$176.40

Step-by-step explanation:

Lets assume the order of events to be:

20 dollars discount first,

2% coupon discount, next

So, original cost is 200

Discount of 20 dollars, means that it now costs:

200 - 20 = $180

Now, we have a 2% discount coupon on it. We have to find 2% of 180 and subtract that from 180.

Note: 2% is 2/100 = 0.02

So,

180 * 0.02 = 3.6

So, final price would be:  180 - 3.6 = $176.40

Mark paid $176.40 for the shoes

Answer:

7/2

Step-by-step explanation:

Answer:

The value of x is 2[tex]\sqrt{29}[/tex] .

Step-by-step explanation:

Given as :

The area of Trapezoid = x² unit²

The measure of base 1 = [tex]b_1[/tex] = - 19 unit

The measure of base 2 = [tex]b_2[/tex] = 10 unit

The height of the mid segment = 8 unit

Now, From the Area of Trapezoid

i.e Area = [tex]\dfrac{1}{2}[/tex] × (sum of opposite base) × height

Or, x² = [tex]\dfrac{1}{2}[/tex] × (19 + 10) × 8

Or,  x² = [tex]\dfrac{8}{2}[/tex] × (29)

Or, x² = 4 × (29)

Or,  x² = 116

∴ x = [tex]\sqrt{116}[/tex]

I.e x = 2[tex]\sqrt{29}[/tex]

Hence, The value of x is 2[tex]\sqrt{29}[/tex] . Answer

Final answer:

Using the properties of a trapezoid's midsegment being the average length of the bases, the equation (10 + (x² - 19))/2 = 8 was solved to find that x equals 5.

Explanation:

The question revolves around the properties of a trapezoid and its midsegment. In a trapezoid, the midsegment (also called the median) is the segment that joins the midpoints of the non-parallel sides and is parallel to both bases.

The length of the midsegment is the average of the length of the two bases, which can be expressed as (base1 + base2) / 2.

Given that the midsegment is 8 units long, and one base is given as 10 units, let the other base be expressed as x² − 19 units. The formula for the midsegment becomes:

(10 + (x² − 19))/2 = 8

Now we solve for x:

10 + x² − 19 = 16

x² − 9 = 16

x² = 25

x = ± 5

Since the measure of a base cannot be negative, the positive root is the realistic solution:

x = 5

Answer:

The value of x is 17°.

Step-by-step explanation:

The two exterior angles on the same side of the transversal are always supplementary.

Therefore, if the measure of two exterior angles on the same side of the transversal are 3x and 7x+10, then we can write  

3x + (7x + 10) = 180°

⇒ 10x = 180° - 10° = 170°

⇒ x = 17°  

Therefore, the value of x is 17°. (Answer)

Answer:

Probability that a student chosen randomly from the class plays basketball or baseball is  [tex]\frac{23}{30}[/tex] or 0.76

Step-by-step explanation:

Given:

Total number of students in the class = 30

Number of students who plays basket ball = 19

Number of students who plays base ball = 12

Number of students who plays base both the games = 8

To find:

Probability that a student chosen randomly from the class plays basketball or baseball=?

Solution:

[tex]P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]---------------(1)

where

P(A) = Probability of choosing  a student playing basket ball

P(B) =  Probability of choosing  a student playing base ball

P(A \cap B) =  Probability of choosing  a student playing both the games

Finding  P(A)

P(A) = [tex]\frac{\text { Number of students playing basket ball }}{\text{Total number of students}}[/tex]

P(A) = [tex]\frac{19}{30}[/tex]--------------------------(2)

Finding  P(B)

P(B) = [tex]\frac{\text { Number of students playing baseball }}{\text{Total number of students}}[/tex]

P(B) = [tex]\frac{12}{30}[/tex]---------------------------(3)

Finding [tex]P(A \cap B)[/tex]

P(A) = [tex]\frac{\text { Number of students playing both games }}{\text{Total number of students}}[/tex]

P(A) = [tex]\frac{8}{30}[/tex]-----------------------------(4)

Now substituting (2), (3) , (4) in (1), we get

[tex]P(A \cup B)= \frac{19}{30} + \frac{12}{30} -\frac{8}{30} [/tex]

[tex]P(A \cup B)= \frac{31}{30} -\frac{8}{30} [/tex]

[tex]P(A \cup B)= \frac{23}{30}[/tex]

Answer:

4x^2+20x+24

Step-by-step explanation:

(4x+8)(x+3)=4x^2+8x+12x+24=4x^2+20x+24

The value of f(x) * g(x) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3

We have two functions -

f(x) = 4x + 8

g(x) = x + 3

We have to determine f(x)*g(x).

A function in mathematics is an expression with a independent variable (x) in it. The variable is called independent because it is not dependent on any value to get its value. Function also has a dependent variable (y) whose value depend on x. Ex -

y = f(x) = ax + d

According to the question, we have -

f(x) = 4x + 8

g(x) = x + 3

Therefore -

f(x) * g(x) = (4x + 8)(x + 3) = 4x(x + 3) + 8(x + 3) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3

Hence, the value of f(x) * g(x) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3

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[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}}\implies \cfrac{-3+1}{3}\implies -\cfrac{2}{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{0}) \\\\\\ y+1=-\cfrac{2}{3}x\implies y=-\cfrac{2}{3}x-1[/tex]

Answer:

Step-by-step explanation:

 13x+2y=1

+ 5x-2y=-19

-------------------

18x=18

x=1

5x1-2y=-19

5-2y=-19

-2y=-19-5

-2y=14

-y=7

y=-7

x=1

y=-7

To solve the system, eliminate variables, find [tex]\( x = -1 \)[/tex], then substitute into an equation to get [tex]\( y = 7 \)[/tex].

To solve the system of equations [tex]\(13x + 2y = 1\)[/tex] and [tex]\(5x - 2y = -19\)[/tex], you can use the method of elimination.

First, let's eliminate one of the variables. We can eliminate [tex]\(y\)[/tex] by adding the two equations together:

[tex]\[ (13x + 2y) + (5x - 2y) = 1 + (-19) \][/tex]

This simplifies to:

[tex]\[ 13x + 5x = -18 \][/tex]

[tex]\[ 18x = -18 \][/tex]

Now, divide both sides by 18:

[tex]\[ x = \frac{-18}{18} \][/tex]

[tex]\[ x = -1 \][/tex]

Now that we have found [tex]\(x\)[/tex], we can substitute it into one of the original equations to find [tex]\(y\)[/tex]. Let's use the first equation:

[tex]\[ 13(-1) + 2y = 1 \][/tex]

[tex]\[ -13 + 2y = 1 \][/tex]

Add 13 to both sides:

[tex]\[ 2y = 1 + 13 \][/tex]

[tex]\[ 2y = 14 \][/tex]

Divide both sides by 2:

[tex]\[ y = \frac{14}{2} \][/tex]

[tex]\[ y = 7 \][/tex]

So, the solution to the system of equations is [tex]\(x = -1\)[/tex] and [tex]\(y = 7\)[/tex].

Answer:

i think its km.

Step-by-step explanation:

(please correct me if im wrong)

Final answer:

Greg's unit rate is  [tex]1\frac{5}{7}[/tex]  walls per hour, which is found by dividing 1/7 of a wall by 1/12 of an hour. The correct answer is option C: [tex]1\frac{5}{7}[/tex].

Explanation:

If Greg can build 1/7 of a brick wall in 1/12 of an hour, we want to find his unit rate, which is the amount of wall he can build per hour. To find Greg's unit rate, we divide the fraction of the wall built by the fraction of the hour spent building it. This calculation gives us:

Unit rate = (1/7) ÷ (1/12) = (1×12)/(7×1) = 12/7 = [tex]1\frac{5}{7}[/tex] walls per hour.

Therefore, the correct option is C: [tex]1\frac{5}{7}[/tex].

Final answer:

The equation representing the sentence is 'R *4 = 72', where R is Rita's height. Dividing both sides by 4 yields Rita's height as R = 18 units.

Explanation:

The sentence' 72 is the product of Rita’s height and 4' can be translated into the equation R *4 = 72, where R represents Rita's height in the appropriate unit (e.g., meters or feet).

To find Rita's height, you would divide both sides of the equation by 4, simplifying to R = 72 / 4. Therefore, Rita's height would be 18 units. In the context of the given examples, the algebraic representation involves setting up equations and solving for an unknown variable through techniques like cross multiplication and proportion.

Answer:

No.

Step-by-step explanation:

Answer: 37 1/3

Step-by-step explanation:

14/1÷3/8=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

14/1 × 8/3=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

14×8/1×3 = 112/3

This fraction cannot be reduced.

The fraction

112/3

is the same as

112÷3

Convert to a mixed number using

long division so

112/3=37 1/3

Therefore:

14/1 ÷ 3/8=37 1/3

They are left with 0.51 pounds of clay.

Step-by-step explanation:

Given,

Amount of clay bought = 3.8 pounds

Amount used by Martha = [tex]\frac{1}{4}\ of\ clay[/tex]

Amount used by Martha = [tex]\frac{1}{4}*3.8=0.95\ pounds[/tex]

Amount left after Martha's use= Total amount - amount used by Martha

Amount left = 3.8 - 0.95 = 2.85 pounds

Amount used by Scott = [tex]\frac{2}{5}\ of\ amount\ left[/tex]

Amount used by Scott = [tex]\frac{2}{5}*2.85=\frac{5.70}{5}[/tex]

Amount used by Scott = 1.14 pounds

Amount left after Scott's use = Amount left after Martha's - Amount used by Scott

Amount left after Scott's use = 2.85 - 1.14 = 1.71 pounds

Amount used by Alison = 1.2 pounds

Amount left = Amount left after Scott's use - Amount used by Alison

Amount left = 1.71 - 1.2 = 0.51 pounds

They are left with 0.51 pounds of clay.

Keywords: subtraction, fraction

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Answer:

x=4

Step-by-step explanation:

Missing picture is attached.

As we can see in the picture drawn, there are two cord insecting outside the circle.

∴ we will use Intersecting secant theorem.

When two secant lines intersect each other outside a circle then the product of the length of the chord and the length of the part outside the circle are equal.  

Now, using the value in theoram as given in the picture.

⇒[tex]x\times 6= 3\times 8[/tex]

Dividing both side by 6

⇒ [tex]x= \frac{3\times 8}{6}[/tex]

∴x= 4

The fraction 9/5 can be expressed as the sum of 1 (whole number) and 4/5 (fraction).

The fraction 9/5 can be expressed as a sum of a whole number and a fraction. First, divide 9 by 5 which will result in 1 with a remainder of 4. The 1 forms the whole number, and 4/5 forms the fraction. So, 9/5 is equivalent to 1 4/5, which means 1 (whole number) plus 4/5 (fraction) is equal to 9/5.

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Answer:

(-2 i) * (-3 i) = -6

Step-by-step explanation:

This is a product between imaginary numbers, so have in mind how the imaginary unit multiplies by itself: [tex]i\,*\,i = i^2=-1[/tex]

So let's work on the product:

[tex]-2\,i\,*\,(-3\,i)= (-2)\,*\,(-3)\,*\,i\,*\,i =(6)\,* i^2\,=(6)\,*\,(-1)= -6[/tex]

Answer:

its A 280

Step-by-step explanation: