The sum of four consecutive integers is -10. What are the integer

Answer:

39 ft^2

Step-by-step explanation:

Find the area of the triangle and subtract the area of the square.

area of triangle = bh/2

area of square = s^2

shaded area = bh/2 - s^2

shaded area = (20 ft)(16 ft)/2 - (11 ft)^2

shaded area = 160 ft^2 - 121 ft^2

shaded area = 39 ft^2

Answer:

20 cents

Step-by-step explanation:

Possible coins in grandfather's pocket include : nickel, dime, quarter

A nickel = 5 cents

A dime = 10 cents

A quarter = 25 cents

First combination= nickel+dime+quarter+quarter

Second combination=nickel+quarter+quarter+quarter=

Third combination= dime+quarter+quarter+quarter

Third combination=quarter+quarter+quarter+quarter

4th combination = nickel + nickel+dime+quarter

5th combination= nickel +nickel+nickel+dime

6th combination =nickel+nickel+nickel+quarter

7th combination= nickel + nickel + nickel +nickel

8th combination = dime + dime +quarter +nickel

9th combination = dime +dime+dime+quarter

10th combination =dime+dime+dime+nickel

11th combination=dime+dime+dime+dime

If Grandpa offers to give you the coins if you are able to guess the amount within ten cents, then all coins are below ten cents and all coins are nickels = 4 nickels ×5 = 20 cents

The length of the second trial will be equal to 2(⁵/₈) miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.

The length of the second trial will be calculated as,

Length =  3/4 x ( 3¹/₂ )

Length = 2(⁵/₈)

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Answer:

C.  5x(-x + 2)

Step-by-step explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

\(\hrulefill\)

Additional notes:

If we expand the expressions in the given answer options, we get:

  A.  −5x(x + 2) = -5x² - 10x

  B.  5(−x² + 10x) = -5x² + 50x

  C.  5x(−x + 2) = -5x² + 10x

  D.  x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):

We can check our answer by distributing \(-5x\) to the expression inside the parentheses:

\(\therefore\) The answer is \(-5x(x-2)\).

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Answer:

The set M of all square numbers less than 80 is:

M = {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set N of all non-negative even numbers that are under 30 is:

N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Answer:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Step-by-step explanation:

A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.

The square numbers less than 80 are:

An even number is an integer that is divisible by 2 without leaving a remainder.

The non-negative even numbers that are under 30 are:

Therefore:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Answer:

slope is 1/2

Step-by-step explanation:

rise over run.

Answer:

1/2

Step-by-step explanation:

to find the slope, think of it as rise/run. find two points on the line that pass exactly thorugh the intersection of two coordinates, in this case 2,1 and 4,2. then count the rise (1) and run (2)

Step 1: Pick any two points

The points are represented as (x1,y1), (x2,y2).

where x1= -4, y1= -8, x2= 0, y2= 4

Step 2: Write out the formula of the equation to use

Step 3: Substituting the values and to get the equation

The equation that represents the graph is y= 3x+4.

Option A is the correct answer.

Steps to solve:

b + 4.22 = 7.08

~Subtract 4.22 to both sides

b = 2.86

Best of Luck!

Answer:

6.6 is the answer

Step-by-step explanation:

Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)

Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).

The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,

 A' = 2A

 A'(8, -12) = 2×A(4, -6)

These facts are all you need to know to choose the correct answer (shown above).

Answer: 1/2

Step-by-step explanation:

I took the quiz!

Answer:

1100

Step-by-step explanation:

8 = 1000

9 = 1001

10 = 1010

11 = 1011

12 = 1100

hope this helps :)

The regression equation is y = 28.0 + 0.0510x.

The best predicted temperature at a time when the cricket chirps 3000 times in 1 minute, based on the regression equation is 181°F.

What is wrong with this predicted temperature: B. It is unrealistically high. The value 3000 is far outside of the range of observed values.

In this scenario, the chirps in 1 min would be plotted on the x-axis (x-coordinate) of the scatter plot while the temperature would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the chirps in 1 min and the temperature, a regression equation or an equation for the line of best fit is given by:

y = 28.0 + 0.0510x

When x = 3000, the temperature can be calculated as follows;

y = 28.0 + 0.0510(3000)

y = 181°F

In conclusion, a temperature of 181°F is unrealistically too high because a chirps of 3000 times in 1 min is an outlier.

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Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Answer:

D

Step-by-step explanation:

1 + 4x and 57° are corresponding angles and are congruent , so

1 + 4x = 57 ( subtract 1 from both sides )

4x = 56 ( divide both sides by 4 )

x = 14

1) Two different functions that could represent Davis' gross wages, where h is the number of hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and d(h) is his gross wages from walking dogs are:

Function A: a(h) = 16.25h - 7.50

Function B: d(h) = 12.50h

2) If Davis works 1 hour, his gross pay at each job is:

    1 Hour      6 Hours

a) $16.25      $97.50

b) $12.50      $75

3) To find Davis' net pay after tax, the modified functions in question 1 are as follows:

Function A: a(h) = (16.25h - 7.50)(1 - 0.105)

Function B: d(h) = 12.50h(1 - 0.18)

4) The domain and range for each of these new functions are:

                          Domain                     Range

a) Function A    [1, 2, ... 7]           [7.83, 15.66, ... 54.81]

b) Function B    [1, 2, ... 12]         [10.25, 20.5, ... 123]

The domain refers to all the possible values of the independent (input) variables.

The range refers to the possible values of the dependent (output) values.

                                            Arena       Dog Walking

Pay rate per hour              $16.25           $12.50

Travel expense                  $7.50            $0

Maximum hours worked    7 hours          10 hours

Gross pay for one hour     $16.25        $12.50

Gross pay for 6 hours       $97.50         $75

After

Tax                                      10.5%           18%

After-tax factor                (1 - 0.105)       (1 - 0.18)

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The 70 meters by 50 meters rectangular field having a path with an area of 104 m² around it indicates that the width of the path, found using the quadratic formula is about 0.43 meters.

The quadratic formula is a formula that is used to find the values of x that are the solutions to the the the quadratic equation of the form, a·x² + b·x + c = 0.

The length of the rectangular field = 70 meters

The width of the rectangular field = 50 meters

The width of the path around the field = Uniform width

Area of the path around the field = 104 m²

Let x represent the width of the path, we get;

(70 + 2·x) × (50 + 2·x) - 70 × 50 = 104

4·x² + 240·x = 104

4·x² + 240·x - 104 = 0

The quadratic formula which can be used to find the value of x in the equation a·x² + b·x + c = 0, is presented as follows;

\(x = \dfrac{-b\pm \sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

Comparing the equation 4·x² + 240·x - 104 = 0 to the quadratic equation for the quadratic formula; a·x² + b·x + c = 0, we get;

a = 4, b = 240, c = -104

Therefore;

\(x = \dfrac{-240\pm \sqrt{240^2-4\times 4 \times (-104)} }{2\times 4}\)

x ≈ 0.430 or x ≈ -60.4

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Vector v can be written as the sum of two vector components, \(v_x = -5i\)  and \(v_y = 6j\)

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)

The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)

Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)

Now, we can write vector v as the sum of its components:

\(v = v_x + v_y = -5i + 6j\)

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

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The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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The linear function parallel to the line represented by y = 3x/4 - 1/2 is given as follows:

y = 3x/4 + 1/2.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

When two lines are parallel, they have the same slope.

The slope of the line y = 3x/4 - 1/2 is given as follows:

m = 3/4.

Hence the equation of the parallel line is given as follows:

y = 3x/4 + 1/2.

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The width cannot be negative, the width of the walkway is 6 feet. The total area of the garden and the walkway is given as 648 square feet. We know the area of the garden is length multiplied by width, which in this case is 12 feet by 15 feet, so the garden area is\(12 \times 15 = 180\) square feet.

To find the area of the walkway, we subtract the garden area from the total area. Therefore, the area of the walkway is 648 - 180 = 468 square feet.

The walkway surrounds the garden on all sides, so its length and width will be greater than the corresponding dimensions of the garden.

To calculate the width of the walkway, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 + 2x (twice the width of the walkway) and the width is 15 + 2x.

So, we have the equation\((12 + 2x) \times (15 + 2x) = 468\).

Expanding and rearranging the equation, we get\(4x^2 + 54x - 228 = 0.\)

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that x = 6 or x = -9/2.

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Answer:

Step-by-step explanation:

The value of the expression; 6 × 10 + 4³ as given in the task content is; 124.

It follows from the task content that the value of the expression given in the task content; 6 × 10 + 4³ is to be determined.

Hence, the value of the expression can be evaluated using PEMDAS guidelines as follows;

Since the given expression is;

6 × 10 + 4³

Since the exponent, so that we have;

6 × 10 + 64

Next, solve the multiplication, so that we have;

60 + 64

= 124.

On this note, the value of the expression is; 124.

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The actual selling price of the camera after the 25% discount is $345.

The amount received by the buyer is the selling price of a product or service. Although the seller sets the price, a number of variables affect how the seller arrives at that particular figure. Depending on the seller's discretion, different customers may pay different prices for the same good or service.

If the normal price of the camera is $460, a 25% reduction in price would be:

25% of $460 = 0.25 x $460 = $115

This means the reduction in price when buying the camera duty-free is $115.

So the actual selling price of the camera after the discount is:

$460 - $115 = $345

Therefore, the actual selling price of the camera after the 25% discount is $345.

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Step-by-step explanation:

198×202=39,996

200×200=40,000

hence,

39,9996 < 40,000

hope it helps

Answer:

9/10

Step-by-step explanation:

8.6-4x2+3/10- multiply first 4x2=8

8.6-8+3/10 - subtract 8.6-8+.6

.6+3/10= 9/10

Answer:

3 2/25 = 3.08

Step-by-step explanation:

Answer:

\(1216 = 64 \times 19\)

64 is 4 cubed, and 19 is a prime number between 10 and 20.

Step-by-step explanation: