There are 142 laptops and desktop computers in a lab. There are 6 more laptops than desktops. What is the total number of laptops in the lab

Answer:

y = -3x + 3

Step-by-step explanation:

Parallel lines have the same slope.

The given line has a slope of -3, its parallel line will also have a slope of -3... m = -3

y = -3x + c

When x = 1, y = 0

0 = -3(1) + c

c = 3

y = -3x + 3

(a) 10^5/10^2 = 1000
(b) x^2/x^6 = 1/(x^4)
(c) x^4y/xy^8 = x^3/y^7

a) To rewrite the expression 10^5/10^2 as the product of two fractions, we can write it as (10^5)/(10^2) = (10 * 10 * 10 * 10 * 10) / (10 * 10).

Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have 10 as a common factor, we can simplify further to get (10 * 10 * 10 * 10 * 10) / (10 * 10) = 10 * 10 * 10 = 1000.

Therefore, the equivalent and simpler expression for 10^5/10^2 is 1000.

(b) For the expression x^2/x^6, we can rewrite it as (x * x) / (x * x * x * x * x * x).

Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have x as a common factor, we can simplify further to get (x * x) / (x * x * x * x * x * x) = 1 / (x * x * x * x).

Therefore, the equivalent and simpler expression for x^2/x^6 is 1/(x^4).

(c) To rewrite the expression x^4y/xy^8 as the product of two fractions, we can write it as (x * x * x * x * y) / (x * y * y * y * y * y * y * y).

Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have x and y as common factors, we can simplify further to get (x * x * x * x * y) / (x * y * y * y * y * y * y * y) = (x^3) / (y^7).

Therefore, the equivalent and simpler expression for x^4y/xy^8 is x^3/y^7.

Complete question :-

Rewrite each expression as the product of two fractions, one of which is equal to . Then, write it as an equivalent, but simpler, expression.. (a) 10^5/10^2 (b) x^2/x^6 (c) x^4y/xy^8

x - 2y = -4 is the standard form of equation

Solution:

Given equation is:

[tex]y = \frac{1}{2}x + 2[/tex]

We have to write the equation in standard form

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

From given,

[tex]y = \frac{1}{2}x + 2[/tex]

Simplify the above equation

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

Shift the variable terms to the left side of the equation and everything else to the right side

[tex]x - 2y = -4[/tex]

Thus the standard form of equation is found

Answer:

48

Step-by-step explanation:

i just did it

For the given graph  y = 3x²:

The value of y at x = 4 is 48.

Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.

The given function is,

y = 3x²

And x = 4

To find the value of y,

Put x = 4 in the given fucntion we get,

y = 3(4²)

Simplifying we get,

y = 48

A graph is also attached to illustrate these points.

Hence,

At x = 4 the value of y is 48.

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Answer:

Therefore,

There are Four i.e 4 terms in the expression,

[tex]-7+12x^{4}-5y^{8}+x[/tex]

Step-by-step explanation:

Algebraic Expression:

An algebraic expression is a mathematical expression that consists of variables, numbers and operations.

Here the Expression is

[tex]-7+12x^{4}-5y^{8}+x[/tex]

So,

[tex]-7 = One\ Term\\12x^{4}=Second\ Term\\-5y^{8}=Third\ Term\\x=Fourth\ Term[/tex]

In all there are Four i.e 4 terms in the given expressions.

Therefore,

There are Four i.e 4 terms in the expression,

[tex]-7+12x^{4}-5y^{8}+x[/tex]

4 is the answer and no explanation

hope this helps and on edgenuity it is D

Answer:

-1, -3/4, -5/8, -1/20, 0

Step-by-step explanation:

-1/20 = -2/40

-5/8 = -25/40

-3/4 = -30/40

0 = 0/40

-1 = -40/40

Answer:

Step-by-step explanation:

4 A + 7K= $83

5 A + 7 K= +7= $90

It means one adult ticket costs 7 more than a kid ticket. If I replace A with K+7 in equation one,  it'll look like

4(K+7) + 7 K= $83

=> 4 K +28+ 7 K= $83

=> 11 K= 83-28= 55

K=5

A= 12

Answer:

12 = x

Step-by-step explanation:

The | | mean absolute value.  Pretty much making every number within the sign a positive.

|-7| + 5 = x

7 + 5 = x

12 = x

Hope this helps.

Whenever you see this " | | "  character, it means that whatever negative number in between those characters are always positive.

It converts -7 to just 7.  This makes the question 7+5.

Giving you the answer 12.

Answer:

-4/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(20-(-4))/(-4-14)

m=(20+4)/-18

m=24/-18

simplify

m=-4/3

The number of viruses was 4000 times greater than number of protozoa.

Step-by-step explanation:

Given,

Number of protozoa = [tex]5*10^5[/tex]

Number of viruses = [tex]2*10^9[/tex]

Let,

x be the number of times number of viruses is greater than number of protozoa.

Number of viruses = Number of time * Number of protozoa

[tex]2*10^9=(5*10^5)x[/tex]

Dividing both sides by [tex]5*10^5[/tex]

[tex]\frac{2*10^9}{5*10^5}=\frac{(5*10^5)x}{5*10^5}\\\\4*10^3= x\\x=4*10^3 \\x=4000[/tex]

The number of viruses was 4000 times greater than number of protozoa.

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Answer:

  B.  T<-4, -2>, r(90°, O)

Step-by-step explanation:

Point A' is 4 units left and 2 units down from point A, so the translation is T<-4, -2>.

Segment C"D" is on the -x axis, 90° counterclockwise from segment C'D' on the +y axis. Since rotation angles are measured the same way other angles are measured (positive is CCW), the rotation is +90° about the origin.

The congruence transformation that maps the quadrilateral ABCD to A''B''C''D'' is [tex]T_{ < -4, \, -2 > } \circ T_{90^{\circ}}, origin > (ABCD)[/tex] which corresponds with the option B.

B. [tex]T_{ < -4, \, -2 > } \circ T_{90^{\circ}}, origin > (ABCD)[/tex]

A congruent transformation, which is also a rigid transformation is one in which the size and shape of the original figure is preserved.

The coordinates of the vertices of the quadrilaterals ABCD and A'B'C'D' indicates that the transformation from the quadrilateral ABCD to the quadrilateral A'B'C'D' is a translation of 4 units to the left and 2 units downwards, which can be expressed as T<-4, -2>

The side D'C' in the quadrilateral A'B'C'D' is vertical while the side D''C'' in the quadrilateral A''B''C''D'' is horizontal and due to the order of the letters D'' and C'' in D''C'' arranged from left to right suggesting a 90° counterclockwise rotation about the origin, which is a T90°, origin

The congruence transformation that maps ABCD to A''B''C''D'' therefore is the option B, [tex]T_{ < -4, \, -2 > }\circ T_{90^{\circ}}, origin > (ABCDE)[/tex]

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Answer:

[tex]9x^{5}y^{5}[/tex] yards.

Step-by-step explanation:

Given that the area of a rectangle (A) is [tex]45x^{8}y^{9}[/tex] square yards.

If the length of the rectangle (L) is given to be [tex]5x^{3}y^{4}[/tex] yards, then we have to find the width (W) of the rectangle in yards.

Now, A = L × W

⇒ [tex]W = \frac{A}{L} = \frac{45x^{8}y^{9}}{5x^{3}y^{4}} = (\frac{45}{5})\times (\frac{x^{8}}{x^{3}}) \times (\frac{y^{9}}{y^{4}}) = 9x^{8 - 3}y^{9 - 4} = 9x^{5}y^{5}[/tex] yards. (Answer)

Answer:

1 3/5

Step-by-step explanation:

Answer:

1161/100

Step-by-step explanation:

Answer:

no graphs r shown...

Step-by-step explanation:

up 1 on y axis then up one for every 3 xs

Step-by-step explanation:

[tex]cos \: x = sin \: (2x + 57) \\ \\ \therefore \: sin(90 \degree - \: x) = sin \: (2x + 57) \\ \\ \therefore \:90 - \: x = 2x + 57 \\ \\ 90 + 57 \: = 2x + 3 \\ \\ \therefore \:3x = 147 \\ \\ \therefore \: x = \frac{147}{3} \\ \\ \huge \orange{ \boxed{\therefore \: x = 49 \degree}}[/tex]

When you subtract the y values you find that each increase in x decreases y by 4.

X is going from 4 to 82 which is 78 units.

78 x 4 = 312

Subtract 312 from the last y value:

209 - 312 = -103

The answer is -103

Answer:

When x = 82, y = -103

Step-by-step explanation:

So an arithmetic sequence is a sequence whose terms differ by a constant value. To find the value of the [tex]n^{th}[/tex] term we need to form an equation for the sequence.

First we need to find the difference between the values of the sequence. In this case the difference is -4:

217 - 221 = -4,  209 - 213 = -4

So the equation is:

[tex]n^{th}[/tex] term = -4n + c

Now we need to find the c, so we substitute the [tex]n^{th}[/tex] term and the term number and solve the equation:

221 = (-4 x 1) + c

221 = -4 + c

c = 225

So the final equation is:

[tex]n^{th}[/tex] term = -4n +225

Now all we need to do is substitute into the equation and find the answer:

[tex]n^{th}[/tex] term = (-4 x 82) + 225

[tex]n^{th}[/tex] term = -328 +225

[tex]n^{th}[/tex] term = -103

The probability of selecting either a multiple of 4 or a multiple of 5 is [tex]\frac{11}{25}[/tex] or 0.44

Solution:

Given that, A number is chosen at random from 1 to 50

selecting either a multiple of 4 or a multiple of 5

Sample space is given as:

{ 1, 2, 3, ................, 50 }

Muliples of 4 = 4, 8, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52

Favorable outcomes = 12

Muliples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Favorable outcomes = 10

The probability is given as:

[tex]Probability = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}[/tex]

[tex]probability = \frac{12}{50} + \frac{10}{50}\\\\probability = \frac{12+10}{50}\\\\probability = \frac{22}{50}\\\\probability = \frac{11}{25} \text{ or } 0.44[/tex]

Thus probability of selecting either a multiple of 4 or a multiple of 5 is [tex]\frac{11}{25}[/tex] or 0.44

The probability of selecting either a multiple of 4 or a multiple of 5 is 11/25.

A multiple of a number is the product of an integer and that number.

The first step is to determine the numbers that are a multiple of 4. They are  4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.  There are 12 numbers.

The second step is to determine the numbers that are a multiple of 5. They are : 5, 10 15, 20, 25, 30, 35, 40, 45, 50. There are 10 numbers.

Probability of picking a multiple of 4 or 5 = 12/50 + 10/50 = 22/50 = 11/25

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Answer: [tex]62.92 \frac{mi}{h}[/tex]

Step-by-step explanation:

If we are asked about how fast a car is going, this means we are asked about its velocity [tex]v[/tex], which is defined by the relation between the traveled distance [tex]d[/tex] and time [tex]t[/tex]:

[tex]v=\frac{d}{t}[/tex]

Where:

[tex]d=(330+\frac{1}{3}) mi=330.33 mi[/tex] is the traveled distance

[tex]t=(5+\frac{1}{4}) h=5.25 h[/tex] is the time

Solving the equation with the given information:

[tex]v=\frac{330.33 mi}{5.25 h}[/tex]

Finally:

[tex]V=62.92 \frac{mi}{h}[/tex] This is the car's velocity

Answer:

The speed of the car is 77.72 miles per hour

Step-by-step explanation:

To find out how fast is a car travelling when it traveled 330 and 1/3 miles in 4 and 1/4 hours following formula will be used

     Speed=  [tex]\frac{Distance}{Time}[/tex]

Total distance = 330 and 1/3

                        = 330+ 0.33

                        =  330.33 miles

Total time = 4 and 1/4

                 =  4 + 0.25

                 =  4.25 hrs

putting the values in equation we get speed of car

Speed= [tex]\frac{330.33}{4.25}[/tex]

Speed   = 77.72 miles per hour

So the speed of the car is 77.72 miles per hour

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Answer:

5.65685424949 or 5.66

Step-by-step explanation:

In a right-angled triangle, the longest side/leg is called the hypotenuse.

The formula to solve for the hypotenuse is:

hyp^2= side^2+side^2

If the hypotenuse of the triangle is already given then we have to solve for a side.

The formula to solve for the side is:

side^2= hyp^2-side^2

This formula to solve for the side is the opposite of solving for the hypotenuse which is the longest side/leg of the right-angled triangle.

In this question we have to solve for the side.

There are two sides in this triangle. Let's name those sides side a and side b. Side a is already given.

hyp= 9

side a = 7

side^2 = hyp^2-side^2

side b = 9^2 - 7^2

side b = 81 - 49

side b = 32

side b = √32

side b= 5.65685424949. to 2 decimal places -> 5.66

The ball reaches the ground after 7.76 s

Step-by-step explanation:

The motion of the ball along the vertical direction is a free fall motion, which is affected by the force of gravity only; therefore it is a uniformly accelerated motion (=constant acceleration), so we can use the following suvat equation:

[tex]s=ut-\frac{1}{2}gt^2[/tex]

where

s is the displacement

u is the initial vertical velocity

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

t is the time

In this problem,

u = 38 m/s

Also, we want to find the time t at which the ball hits the ground again: so, when the displacement becomes zero again,

s = 0

Therefore the equation becomes:

[tex]0=38t-\frac{1}{2}9.8t^2\\0=38t-4.9t^2[/tex]

And solving for t,

[tex]t(38-4.9t)=0[/tex]

we have two solutions:

t = 0 (instant at which the ball is kicked)

[tex]38-4.9t=0\\t=\frac{38}{4.9}=7.76 s[/tex]

which is the solution to the problem.

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The correct inequality among the given options is -a > -c. Thus, option A is correct.

To determine the correct inequality among the given options, we need to compare the values of the variables a, b, and c in the number line.

Given: a = -4, b = 1, and c = 7

Let's evaluate each option:

A. -a > -c:

Substituting the values, we have -(-4) > -(7), which simplifies to 4 > -7.

This is true.

B. -a < -b:

Substituting the values, we have -(-4) < -(1), which simplifies to 4 < -1.

This is false.

C. a > 0:

Substituting the value, we have -4 > 0. This is false since -4 is not greater than 0.

Based on the comparisons, the correct inequality is A. -a > -c.

Therefore, the correct answer is A. -a > -c.

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Answer:

d

Step-by-step explanation:

We know that the length of the garden is 4 - (-3) = 7 feet, the answer is (Negative 3, 5) and (4, 5).

A vertex is a point in geometry where two or more curves, lines, or edges intersect.

As a result of this definition, vertices are the points where two lines intersect to form an angle, as well as the corners of polygons and polyhedra.

Let's assume that the other two vertices are at points (a, b) and (c, d). The area of the garden can be calculated as follows:

Area = Length × Width

35 = 7 × (b - (-1)) [since the width is the distance between the y-coordinates of the vertices]

Simplifying the above equation, we get:

b - (-1) = 5

b = 4

So, one of the vertices should be at (a, 4) and the other at (c, 4). Since the garden is symmetrical about the x-axis, the y-coordinate of the missing vertices is 1 more than the y-coordinate of the given vertices. Hence, the other two vertices should be at (−3, 5) and (4, 5).

Therefore, the answer is (Negative 3, 5) and (4, 5).

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Answer:

50%

Step-by-step explanation:

50% is half. Half of 6 is 3. 3 dollars.

Answer:

  all non-negative real numbers, [0, ∞)

Step-by-step explanation:

Replacing x in the parent function √x with (x+5) shifts the graph horizontally, but has no effect on the vertical extent of the graph. It still ranges from 0 to +∞.

The range of √(x+5) is [0, ∞).

Answer:

i think it is 68

Step-by-step explanation:

12 x 3 = 36

8 x 4 = 32

36 + 32 = 68

Answer:

The graph that shows the dilation of the rectangle in the attached figure

Step-by-step explanation:

we know that

A dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem we have that the scale factor is equal to 2

Remember that

If a scale factor is greater than 1, then the dilation is a enlargement

To find out the dimensions of the dilated figure multiply the original dimensions by the scale factor

The original dimensions of rectangle are

[tex]b=2 units\\h=4\ units[/tex]

The dimensions of the dilated rectangle are

[tex]b=(2)2=4\ units\\h=(2)4=8\ units[/tex]

therefore

The graph that shows the dilation of the rectangle in the attached figure

Answer:

the answer is the last graph  

Step-by-step explanation:

you just have to add 2 squares to each one square

i did the test and got 100%

Answer:

12

Step-by-step explanation:

11.5 rounds the .5 to 12

Another one got MATHED

12

Step-by-step explanation:

anything below five is rounded down

Answer:

98

Step-by-step explanation:

  0 0 9 8. 0 0 0

3 9 3 8 2 2. 0 0 0

 − 0            

   3 8          

 −   0          

   3 8 2        

 − 3 5 1        

     3 1 2      

   − 3 1 2      

         0 0    

       −   0    

           0 0  

         −   0  

             0 0

           −   0

               0

Answer: 98

Step-by-step explanation:

Answer:

p < 0

Step-by-step explanation:

Given

- 3(p - 7) > 21

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

p - 7 < - 7 ( add 7 to both sides )

p < 0