Please help me out with 3 questions..

Exact Distance:   [tex]\sqrt{130}[/tex] units

Approximate Distance:  11.4018 units

===================================================

Explanation:

Use the distance formula to have the following steps

[tex](x_1,y_1) = (3,-2) \text{ and } (x_2, y_2) = (-4,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-4))^2 + (-2-7)^2}\\\\d = \sqrt{(3+4)^2 + (-2-7)^2}\\\\d = \sqrt{(7)^2 + (-9)^2}\\\\d = \sqrt{49 + 81}\\\\d = \sqrt{130}\\\\d \approx 11.4018\\\\[/tex]

The exact distance is [tex]\sqrt{130}[/tex] units

This approximates to about 11.4018 units.

Answer:

B

Step-by-step explanation:

Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

Length of the house = 35 feet

width of the house = 28 feet

Height of the house = 6 feet

Total surface area = 2 l b + 2 b h + 2 h l

A = 2 (35) (28) + 2 (28) (6) + 2 (6) (35)

A = 1960 + 336 + 420

A = 2716 feet²

If he uses 2 coats of stain, the area he need to cover = 2 (2716) = 5432 feet²

Gallon of paint required = 5432 / 225 = 24.14 gallons.

Therefore, Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

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Jack spends 300 minutes in two weeks riding his skateboard to and from his friend's house Monday through Friday.

Time taken by Jack to ride his skateboard down the hill to his friend's house = 10 minutes

Time taken by Jack to ride his skateboard up the hill to his friend's house = 20 minutes

Total time combined = 30 minutes

Total days in a week Monday through Friday= 5 days

Total days in 2 weeks = 10 days

Therefore, time spent by jack riding his skateboard up and down the hill to his friend's house in two weeks Monday through Friday  = 10*30 = 300 minutes

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If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be  3  and the constant term would be 12 .

What is  polynomial function?

f(x)=(x+1)(x+3)9x-4)

f(x ) = 3x³ + 36x² + 27x - 4x² - 16x - 12

f(x) =  3x³ + 32 x² + 11x - 12

in above function highest degree would be 3 and constant -12 .

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.

Answer: 80 degrees because a line is 180°.

So if you subtract

180 - 100 = 80°

Answer:

x=80°

Step-by-step explanation:

The measures of angle x and the 100° angle form a straight angle.

This straight angle is 180°.

You can subtract the measure of one angle from the whole to find the measure of the other angle.

180°-100°=80°

This means angle x is 80°.

Answer: f(-7)=41

Step-by-step explanation:

f(x) = x² + 2x + 6

f(-7)=(-7)² + 2(-7) + 6

f(-7)=49-14 + 6

f(-7)=35 + 6

f(-7)=41

Answer:

f(-7) = 41

Step-by-step explanation:

f(x) = x² + 2x + 6

In order to find f(-7) ,we just need to substitute x in the expression of the function f by -7.

Then

f(-7) = (-7)² + 2(-7) + 6

      = 49 - 14 + 6

      = 35 + 6

      = 41

Answer:

At the 3rd day 160 students caught flu.

Step-by-step explanation:

Consider the provided model P = − t ² + 13t + 130 where 1 ≤ t ≤ 6

The total number of students is represents by P.

We need to find the day that 160 students had the flu.

Substitute the value of P=160 in above formula.

Hence the value of t=10 or t=3

But it is given that 1 ≤ t ≤ 6, Therefore select t=3

Hence, at the 3rd day 160 students caught flu.

The total number of notebooks on Sasha's notebook is 2c - 6.

Unitary method:

The unitary method is used to solve problems by first determining the value of a single unit and then multiplying that value by the required value.

So, this method is basically used to find the value of a unit and then the value of a required number of units.

Given,

Sasha has c green notebooks.

She has 6 fewer red notebooks then green notebooks.

So, here we need to find how many notebooks does Sasha have in all.

We know that.

Sasha has c green notebooks.

The number of red notebooks on her is  

=> c − 6.

Here Sasha has either green or red notebooks.

The total number of notebooks on Sasha's notebook is  

=> c + c − 6

=> 2c - 6

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The cost of Robert purchase of books after the paid tax is $32.66.

For the given question;

The original cost of the book purchased by the Robet = $30.45.

The tax of 7.25% is applied on the original cost of the book.

7.25% of $30.45 = (7.25×30.45)/100

7.25% of $30.45 = $2.21

The final cost of the book = original cost + tax

The final cost of the book = $30.45 + %2.21

The final cost of the book = 32.66

Therefore, the total price paid by the Robert for the book after 7.5% of the tax is applied is $36.66.

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The complete question is-

Robert spends $30.45 before tax at the bookstore. If the sales tax rate in his city is 7.25%, what is the total cost of his purchase?

Answer:

£124

Step-by-step explanation:

first of all, you're meant to add all the figures given on the pie chart, which is 29+137+58+62+74 and that will give you a total of 360 degrees

so, you say 360 degrees is equal to the total amount of money he spent, which is £720, what about 62 degrees

therefore, you just do (62×720)÷360

that will give you £124

The volume of the box in terms of x will be :   [tex]\frac{50x-x^{3} }{2} cm^{3}[/tex]

We know, Total surface area of a cuboid is: 2(l*b + b*h + h*l)

and it is given that TSA is 100cm^2, the length of the base which is in a square shape is x. So, length l = breadth b = x, and taking height h = y

We need to find out the value of y for finding out the volume of the box.

Putting these values in the formula for TSA,

             => 2(x*x + x*y + x*y) = 100

             => 2(x^2 + 2xy) = 100    =>  y = (50-x^2)/2x

Put this value of y in the formula for volume.

The volume of Cuboid is : l*b*h

            =>  x*x*{(50-x^2)/2}       =>  x^2{(50-x^2)/2x}

             =>   (50x - x^3)/2

Hence, the volume for the box is   [tex]\frac{50x-x^{3} }{2} cm^{3}[/tex]

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The distance from the left side of the stage to the first trap door is 24 3/4.

given;

total lenght of the stage is 76 feet.

Anna is 26 feet high on a rock-climbing.

here we have to substract 76-26 1/2.

   =76-26 1/2

  =49 1/2/2

  =24 3/4

Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km.the space between the two points are called distance

Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km..

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Answer: A=32 B=19

Step-by-step explanation:

Answer:

y=16

Step-by-step explanation:

11 = −5+y

Solve for Y

Add 5 to each side

11+5 = -5+y+5

16 = y

y=16

Answer:

==================================

We see the exterior angle measures given with one unknown.

Recall the sum all exterior angles of a polygon is 360°.

Set up equation and find the unknown value:

Answer:

9.6*10^-12

Step-by-step explanation:

To calculate this, you will do the mass of 2 times 10^(-12) gram. So, 2*(10)^-12. Then we know 30 hours = 480,000,000 bacteria.

So now now you calculate the mass, 480,000,000 * 2(10)^-12 which gives you 9.6*10^-4.

Sorry if it sounds confusing! I hope this helps, have a good day! :D

Answer:

The first and fourth statement.

Step-by-step explanation:

1. - 3 - 12/3 + 5

= - 3 - 4 + 5

= - 7 + 5

= - 2

- 2 < 0

4. 4 - 2 - 3/2

= 2 - 3 / 2

= 1 / 2

1 / 2 > 0

Hope this helped! ^^

Sidenote: If you need me to explain for 2, 3 and 5, comment below this and I'll explain.

Answer: -1536

Step-by-step explanation:

1: 4(3+3) (3+1) (3+5) (3-5)

2: 4(6) (4) (8) (-2)

3: 24 (4) (8) (-2)

4: 96 (8) (-2)

5: 768 (-2)

= -1536

Step-by-step explanation:

I assume these are all angles.

4x is the arc angle (at the center of the circle) between the 2 endpoints of the short triangle side (baseline).

the trials itself is isoceles, so both legs have the same length, bedclothes the arc angles between their endpoints are equal.

now, when we move the reference point of an arc angle back, back, back to the circle arc, the angle is cut in half.

so, the inner top angle of the triangle is therefore 4x/2 = 2x.

because of the isoceles nature, the second triangle inner angle at the baseline is also x.

the sum of the triangle angles is therefore

2x + x + x = 4x

and we know the sum of all angles in a triangle is always 180°.

so,

4x = 180

x = 180/4 = 45°

4x is then again 180°, and 2× 8y are then the remaining 180° of the full circle 360°.

2× 8y = 180

8y = 90

y = 90/8 = 11.25

x = 45

y = 11.25

Answer:

x = 1 and x = -3.5

Step-by-step explanation:

y = -2x² -5x + 2

-2x² -5x + 2 = -5

which means y = -5

Draw the line on y = -5 like the green line in the attached file

and see where this line intersects with the graph

the values are:

x = 1 and x = -3.5

Answer:

Draw a line at y = -5.

x ≈ -3.5

x ≈ 1

Step-by-step explanation:

Given equation:

[tex]y = -2x^2 - 5x + 2[/tex]

This is the equation of the graphed parabola.

To solve the equation  [tex]-2x^2 - 5x + 2 = -5[/tex]  draw a line at y = -5 and find the points of intersection of the two graphed equations.

From inspection of the graph, the x-values of the points of intersection are:

Solving algebraically

Add 5 to both sides of the equation:

[tex]\implies -2x^2-5x+2+5=-5+5[/tex]

[tex]\implies -2x^2-5x+7=0[/tex]

Factor out -1 from the left side:

[tex]\implies -1(2x^2+5x-7)=0[/tex]

Divide both sides by -1:

[tex]\implies 2x^2+5x-7=0[/tex]

Find two numbers that multiply to -14 and sum to 5:  7 and -2

Rewrite b as the sum of these two numbers:

[tex]\implies 2x^2+7x-2x-7=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x+7)-1(2x+7)=0[/tex]

Factor out the common term (2x + 7):

[tex]\implies (x-1)(2x+7)=0[/tex]

Apply the zero-product property:

[tex](x-1)=0 \implies x=1[/tex]

[tex](2x+7)=0 \implies x=-\dfrac{7}{2}=-3.5[/tex]

Answer:

-1/5

y=-1/5 x-8

-1/5 is the slope

Step-by-step explanation:

-1/5

Formula-    y=mx+b

The slope-intercept form is

y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Rewrite in slope-intercept form.

Simplify the left side

Simplify each term.

Combine 1/8 and x.

x/9+5y/8=-5

Subtract x/8 from both sides of the equation.

5y/8=-5-x/8

Multiply both sides of the equation by8/5.

8/5.5y/8=8/5(-5-x/8)

Simplify both sides of the equation.

Simplify the left side.

Simplify 8/5.5y/8

y=-x/5-8

y=-1/5 x-8

Step-by-step explanation:

Given equation:

1/8x + 5/8y =-5

Now write it in standard form like ax+by+c=0

1/8x + 5/8y + 5= 0

Now,slope of line (m) = -a/b

here value of a is 1/8 and value of b is 5/8

now by formula..

-(1/8)÷(5/8) = m(slope)

-1/8 × 8/5 = m

-1/5 = m

here ia your answer

A point is the solution of the inequality expression given as: -2x + 3y > 1 - 5x + 6y is (0, -2/3)

The inequality expression is given as:

-2x + 3y > 1 - 5x + 6y

Collect the like terms in the above expression

So, we have:

3y - 6y > 1 + 2x - 5x

Evaluate the like terms in the above expression

So, we have:

-3y > 1 - 3x

Divide both sides by -3

y < -1/3 + x

Let x = 0

So, we have

y < -1/3

This means that a point in the solution is

(x, y) = (0, < -1/3)

-2/3 < -1/3

So, we have

(x, y) = (0, -2/3)

Hence, a point is the solution of the inequality expression given as: -2x + 3y > 1 - 5x + 6y is (0, -2/3)

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Step-by-step explanation:

I think the answer is just no solution to begin with since the value of an absolute value will never be a negative number or in this case less than -2. therefore the equation is false

A number raised to a power represents a product where the same number is used as a repeated factor. The number is called the base and the power is given by the exponent. The base is the repeated factor and the exponent counts the number of factors. An exponent is that we are dealing with products and multiplication.

In the expression bn, b is the base and n is the exponent.

The Power Rule for Exponents: (am)n = am*n.

To raise a number with an exponent to a power, multiply the exponent times the power.

Negative Exponent Rule: x–n = 1/xn.

Invert the base to change a negative exponent into a positive.

Zero Exponent Rule: x0 = 1, for .

Any non-zero number raised to the zeroth power is 1.

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z + 16.2 ≤ 30

z ≤ 13.8

Answer:

5 year

3 inches every year 48 minus 32 equals 16 3 Inches divided into 16 equal 5.333333 round it equals 5 years y = 5 years

Step-by-step explanation:

completing the square means finding an expression

(x + a)² = b²

or

(x - a)² = b²

(x + a)² = x² + 2ax + a²

(x - a)² = x² - 2ax + a²

because of the "+ 18x" in the original equation we know that we are looking for (x + a)².

now, let's compare the different terms :

x² = x²

18x = 2ax

18 = 2a

a = 9

so, the complete square would look like

(x + 9)² = x² + 18x + 81

but we have only "+ 79" in the original equation.

so, we add the missing 2 (to both sides to keep the equation true)

x² + 18x + 79 + 2 = 0 + 2

x² + 18x + 81 = 2

(x + 9)² = 2

x + 9 = ±sqrt(2)

x1 = sqrt(2) - 9

x2 = -sqrt(2) - 9

x = sqrt(2) - 9, -sqrt(2) - 9

yes, every quadratic equation has 2 solutions.

as every cubic equation has 3 solutions.

and so on.