9. y=-2(x-3)
10. 12x + 30 y = 10
11. y = -5x+2
12. y=6+36-1)
13. y-3 = 2x
14. y=-3-4(x+9)


intercept form

Answer:

[tex]-4y-1[/tex]

Step-by-step explanation:

[tex](5y+-y+-8y)+(8+-8+-1)[/tex]

[tex]-4y-1[/tex]

Answer:

5y + 8 - 1y - 8 - 8y - 1

variables = -4y

numbers = -1

Answer:

a) 1 and 7 = congruent

b) 2 and 5 = supplementary

c) 4 and 6 = congruent

d) 3 and 8 = supplementary

Step-by-step explanation:

Congruent angles are the same, but in different forms. So they might be flipped around, but they are still the same angle and they have the same number of degrees.

Supplementary angles are 2 angles that add up to 180 degrees.

For example, you know that 2 + 3 = 180 degrees, because its sitting on a straight line, and so they are supplementary. They have been cut unevenly which makes 2>3. Same goes for all the other pairs of angles. Using this, you can determine which ones are supplementary and congruent.

So, even though they haven't given you exact values for each of the angles, just by looking at the shape, you can often tell very easily what kind they are:

*acute angles = angles that are less than 90 degrees

*obtuse angles = angles more than 90 degrees, but less than 180 degrees.

a) 1 and 7 have the same shape. Both are acute angles, just flipped upside down.

b) 2 and 5 are complementary. 5 is an acute angle, like 1 and 7. 2 is an obtuse angle, like 6 and 8. If you look at it closely, you can tell that they add up to 180 degrees.

c) 4 and 6 are congruent. They are both obtuse angles.

d) 3 and 8 are supplementary. 3 is an acute angle and 8 is obtuse.

Hope this helped : )

Answer:

Step-by-step explanation:

When the question comes with answer choices, please share them.   In this case it sounds like there were four graphs from which to choose.

f(x) = |x^2 − x − 2| is always zero or greater, due to the absolute value function.

x^2 − x − 2 = 0 factors to (x - 2)(x + 1) = 0, so the zeros of f(x) are {-1, 2}.

Plot x-intercepts {-1, 2}.  The axis of symmetry is the vertical line x = 1/2, which is precisely halfway between the x-intercepts.  If we now choose the test number x = 0, we find the value of f(0) to be |-2}, which tells us that the y-intercept is (0, |-2|), or (0, 2), so we have a parabolic curve opening down between x = -1 and x = 2 and touching (but not crossing) the x-axis at those x-values. To the left of x = -1 the curve increases steadily from y = 0 in Quadrant II; to the right of x = 2, the curve increases steadily from y = 0 in Quadrant I.

The graph for the given function is plotted below.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=|x²-x-2|.

Graph the absolute value using the vertex and a few selected points.

Put x= -2, -1, 0 and 1 in the given function, we get

When x=0

y= |0-0-2|

y=0

When x=1

y=|1-1-2|

y=2

When x=-2

y=|4+2-2|

y=2

Now, plot points (-2, 4), (-1, 0), (0, 2) and (1, 2) on graph

Therefore, the graph for the given function is plotted below.

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Answer:

258 cm

Step-by-step explanation:

Given:

Distance from the base of the pole to the base of a tent guy line is [tex]2\frac{1}{2}[/tex]

Length of a tent guy line is 359 cm

To find: Height of the upright tent pole

Solution:

Let AB denotes the pole and AC denotes a tent guy line.

According to Pythagoras theorem, in a right angled triangle, square of hypotenuse is equal to sum of squares of other two sides.

[tex]AC^2=AB^2+BC^2[/tex]

[tex]AC=359 cm\\AB=x\\BC=2\frac{1}{2}\,m=\frac{5}{2}\,m=\frac{5}{2}\times 100=250\,cm[/tex]

Therefore,

[tex](359)^2=x^2+(250)^2\\128881=x^2+62500\\128881-62500=x^2\\66381=x^2\\x=257.6\,cm\approx 258\,cm[/tex]

Answer: t = 7.85seconds

Step-by-step explanation:

Given that :

Height of tower = 986 Feets

Function s(t) = 16t^2

To find the time t 8 in Seconds taken for an object to fall to the ground from the top of the​ building

16t^2 = 986

t^2 = 986/16

t ^2 = 61.625

Take the square root of both sides

t = sqrt(61.625)

t = 7.85seconds

Answer:

7.85sec

Step-by-step explanation:

Given that,

s(t)=16t squared​, where t is time in seconds. The height of a certain tower is 986 feet.

s(t) = 16t²

so when s = 986feet

16t² = 986 feet

t² = 986 /  16

t² = 61.625

t = √61.625

t= 7.85 seconds

Answer:

y = 8x +4

Step-by-step explanation:

Answer:

0.6206

Step-by-step explanation:

We would be using the Z score probability to answer this question

The formula to find the is given as :

is z = (x-μ)/σ,

x = observed value

μ = mean or average value

σ = Standard deviation

To find the probability that between 3,000 and 4,800 acres will be burned in any given year

Step 1

Find the probability that that between 3,000 will be burned in any given year

z = (x-μ)/σ,

x = observed value = 3000

μ = mean or average value = 4500

σ = Standard deviation = 780

z = (3000- 4500)/780

z = -1.92308

Step 2

Find the probability that that between 4,800 will be burned in any given year

z = (x-μ)/σ,

x = observed value = 4800

μ = mean or average value = 4500

σ = Standard deviation = 780

z = (4800- 4500)/780

z =0.38462

Step 3

Using the Z score normal distribution table:

= P(Z <0.38462) - P(Z < - 1.92308)

= P(-1.92308 < Z < 0.38462)

Using the Z score normal distribution table:

P(z) -1.92308 = 0.02743

P(z) 0.38462 = 0.64803

Therefore, the probability that between 3,000 and 4,800 acres will be burned in any given year

0.64803 - 0.02743

= 0.6206

Answer: 0.6225

Step-by-step explanation:

$P\left(3,000<X<4,800\right)=0.6225

The mean is μ=4500 and the standard deviation is σ=780. Because the probability between two values is to be calculated, subtract the probability of the lower value from the higher value. In this case, you have to use the NORMDIST function twice.

1. Open Excel and click on any empty cell. Click Insert function, fx.

2. Search for NORMDIST in the search for a function dialog box and click GO.

3. Make sure NORMDIST is on top in select a function. Then click OK.

4. In the function arguments of the NORMDIST function, enter 4800 for X, 4500 for mean, 780 for Standard_dev, and TRUE for Cumulative, all for the higher value of X. Thus, the answer, rounded to four decimal places, is 0.6497.

5. Click on any other empty cell. Click Insert function, fx.

6. Search for NORMDIST in the search for a function dialog box and click GO.

7. Make sure NORMDIST is on top in select a function. Then click OK.

8. In the function arguments of the NORMDIST function, enter 3000 for X, 4500 for mean, 780 for Standard_dev, and TRUE for Cumulative, all for the lower value of X. Thus, the answer, rounded to four decimal places, is 0.0272.

Now subtract: 0.6497−0.0272=0.6225. Thus, the probability that between 3,000 and 4,800 acres will be burned in any given year is 0.6225.

Answer:

Step-by-step explanation:

1)Since he can lose 5 pounds per week, this is a linear rate. The weight is decreasing in arithmetic progression. The formula for determining the nth term of an arithmetic progression is expressed as

Tn = a + (n - 1)d

n = number of terms(weeks)

d = common difference(5 pounds)

a= first term(300 pounds)

The equation that could be used to find how many weeks, w, it would take for him to weigh 150 pounds would be

150 = 300 + (w - 1)5

150 - 300 = 5w - 5

- 150 + 5 = 5w

w = 145/5 = 29 weeks

2) t represents the number of hours used to fix the car. The cost of t hours is 52t. Total amount paid is 210 + 52t. The equation that could be used to find, t, the length of time it took to fix the car is

210 + 52t = 527.23

3) 52t = 527.23 - 210 = 317.23

t = 317.23/52

t = 6 hours

3) Let x represent the time it will take before you and your sister have the same amount of money. The amount that you would have in x weeks is 60 + 7x

The amount that you sister will have in x weeks is 120 + 5x. The equation would be

60 + 7x = 120 + 5x

7x - 5x = 120 - 60

2x = 60

x = 60/2 = 30 weeks

4) let L represent the length of the parking lot.

let W represent the width of the parking lot.

If the length of a rectangular parking lot is 3 times its width, it means that

L = 3W

Its perimeter is 840 yards. It means that

2(L + W) = 840

L + W = 840/2 = 420

Substituting, it becomes

3W + W = 420

4W = 420

W = 420/4 = 105

L = 3 × 105 = 315

Length = 315 yards

Answer:

[tex]-0.36a^5x^6b^6[/tex]

Step-by-step explanation:

Ok first multiply the first two monomials:

[tex]-0.6a^3x^6b^3[/tex]

Then multiply THAT with the OTHER monomial:

[tex]-0.36a^5x^6b^6[/tex]

This should be the answer. Let me know if it's wrong.

Answer:

2

Step-by-step explanation:

10a² : 5a² = 10 : 5 = 2

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

Explanation:

Let x and y be the two integers where x > y.

The two integers have a sum of x+y and this is equal to 2, so x+y = 2. Solve for y to get y = -x+2

The two integers also have a difference of 12, so x-y = 12. Plug in y = -x+2 and solve for x

x-y = 12

x - ( y ) = 12

x - ( -x+2 )  = 12 ... replace y with -x+2

x + x - 2 = 12

2x - 2 = 12

2x - 2+2 = 12+2 .... adding 2 to both sides

2x = 14

2x/2 = 14/2 .... divide both sides by 2

x = 7

Use this x value to find y

y = -x+2

y = -7+2

y = -5

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

As a check,

x+y = 7+(-5) = 7-5 = 2 ... we get a sum of 2

x-y = 7-(-5) = 7+5 = 12 ... and get a difference of 12

the answers have been confirmed

Answer:

10.50+10.50+7.95=$28.95

Answer:

54 plants

Step-by-step explanation:

3rows of tomatoes with 8 plants each

=3×8=24

5 rows of zucchini plants with 6 plants each

=5×6

=30

Total number of plants in Francesca garden

=24 tomatoes+30 zucchini

=54 plants

Answer:

x = -4

Step-by-step explanation:

6 -x = 5x + 30

6 - 30 = 5x + x

-24 = 6x

divide both sides by 6 to get x = -4

Answer:

[tex]=-4[/tex]

Step-by-step explanation:

[tex]6-x=5x+30\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\6-x-6=5x+30-6\\\mathrm{Simplify}\\-x=5x+24\\\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}\\-x-5x=5x+24-5x\\Simplify\\-6x=24\\\mathrm{Divide\:both\:sides\:by\:}-6\\\frac{-6x}{-6}=\frac{24}{-6}\\Simplify\\\frac{-6x}{-6}=\frac{24}{-6}\\\mathrm{Simplify\:}\frac{-6x}{-6}:\quad x\\\frac{-6x}{-6}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{6x}{6}\\\mathrm{Divide\:the\:numbers:}\:\frac{6}{6}=1\\=x[/tex]

[tex]\mathrm{Simplify\:}\frac{24}{-6}:\quad -4\\\frac{24}{-6}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{6}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{6}=4\\=-4\\[/tex]

Answer: V=1008π units³

Step-by-step explanation:

The formula for volume is [tex]V=\pi r^2h[/tex]. We can plug in our values to find volume.

[tex]V=\pi (12)^2(7)[/tex]

[tex]V=1008\pi[/tex]

Answer:

b

Step-by-step explanation:

i did the test and I got the answer right here after being corrected so yah.

Answer:

All real numbers

Step-by-step explanation:

Answer: The above answer is correct.

1. C

2. B

Step-by-step explanation: I got this right on Edmentum.

The vertices of the hyperbola will be (–20, 41) and (–20, 1). Then the correct option is C. The foci of the hyperbola will be (–20, 50) and (–20, –8). Then the correct option is B.

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

The equation of the hyperbola is given below.

[tex]\rm \dfrac{(y-21)^2}{20^2}-\dfrac{(x+20)^2}{21^2}=1[/tex]

The vertices (h, k + a), (h, k – a) are the two bending points of the hyperbola with center (h, k).

The center of the hyperbola will be at (-20, 21).

The value of a and b will be 20 and 21, respectively.

Then the vertices of the hyperbola will be

(–20, 21 + 20) and (–20, 21 – 20)

(–20, 41) and (–20, 1)

Then the correct option is C.

The foci (h, k + c), (h, k – c) are the two bending points of the hyperbola with center (h, k).

c² = a² + b²

c² = 20² + 21²

c = 29

Then the foci of the hyperbola will be

(–20, 21 + 29) and (–20, 21 – 29)

(–20, 50) and (–20, –8)

Then the correct option is B.

More about the hyperbola link is given below.

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Answer:

[tex]\frac{3y+4}{2-6y} = -\frac{2}{5} \\y=-8[/tex]

Answer:

y = -8

Step-by-step explanation:

[tex]\frac{3y+4}{2-6y} = \frac{-2}{5}[/tex]

5 ( 3y + 4) = -2 ( 2 - 6y)

15y + 20 = -4 + 12y

15y - 12y + 20 = -4 + 12y -12y

3y + 20 = -4

3y + 20 - 20 = -4 -20

3y = -24

y = -8

Hope this helps ^-^

Answer:

60 cubic meters will be the volume of such cone.

Step-by-step explanation:

Formula for volume of a cylinder:

[tex]V = \pi r^{2} h ...... (1)[/tex]

Where [tex]r[/tex] is the radius of base of cylinder

and [tex]h[/tex] is the height of cylinder

V = 180 cubic meters

Formula for volume of a cone:

[tex]V' = \dfrac{1}{3}\pi R^{2} H ...... (2)[/tex]

Where [tex]R[/tex] is the radius of base of cone

and [tex]H[/tex] is the height of cone

Now, it is given that height and radius of cone are equal.

[tex]r = R\\h =H[/tex]

Putting the values in equation (2):

[tex]V' = \dfrac{1}{3}\pi r^{2} h[/tex]

Using equation (1):

[tex]V' = \dfrac{1}{3} \times V[/tex]

Putting V = 180 cubic meters

[tex]\Rightarrow V' = \dfrac{1}{3} \times 180\\\Rightarrow V'=60 \text { cubic meters}[/tex]

Hence, 60 cubic meters will be the volume of such cone.

Answer:

-4

Step-by-step explanation:

i just did it..

Answer:

The correct answer is -4

Step-by-step explanation:

I hope this helps you.

Answer:

rational

irrational

  irrational

 rational

rational

irrational  

Step-by-step explanation:

sqrt(16) +  (-21/5) = 4 + (-21/5) = 4+(-4 1/5)= rational both can be written as fractions

pi +24  irrational  pi is irrational

sqrt(8) + pi = 2 sqrt(2) + pi   irrational because  both are irrational

sqrt(4) +5 = 2+5 = 7  rational

sqrt(36) + cuberoot(27) =6+3 = 9  rational

3/4+ sqrt(27) = 3/4 + 3sqrt(3) = irrational   sqrt(3) is irrational  

Answer:

rational

irrational

irrational

rational

rational

irrational  

Step-by-step explanation:

√16 = 4 is rational.

-21/5 is rational it can be expressed as a fraction.

[tex]\pi[/tex] is irrational.

√4 = 2 is rational.

5 is a rational number.

√36 = 6 is rational.

∛27 = 3 is rational.

3/4 is rational.

√27 is irrational.

Answer:

P = 30

A = 22

Step-by-step explanation:

Find perimeter first

P = 5 + 5 + 2 + 2 + 2 + 2 + 2 + 2 + 4 + 4

P = 10 + 12 + 8

P = 30

Now area

A = 2(5 * 2) + (2 * 1)

A = 2(10) + (2)

A = 20 + 2

A = 22

Answer:

Perimeter: 34

Area: 22

Step-by-step explanation:

You can split this diagram into 3 rectangles and then find the area and perimeter of each using the formula P=2l+2w and A=lw. Then add each answer up.

Answer:

2/5

Step-by-step explanation:

0.4 = 4/10 which in simplest form is 2/5

Answer:

2/5

Step-by-step explanation:

Answer:

..........................

Answer:

60 degrees.

Step-by-step explanation:

We know that we can rotate the image by a total of 360 degrees until we reach the original point again.

To rotate the image to a point where the image looks the same, we need to take a look at how we can do this. We want to line up the image with the gap between the two white semicircles. There are a total of 6 of these gaps:

360/6 = 60 degree rotations will make the image the same.

I hope this helps!

Answer:

C

Step-by-step explanation:

9.16 meters

The length of sandbox 2 is 9.16 meters.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

Given Two sandboxes with the same area,

area of sand box 1 = 25 m²

area of sand box 2 = w(3w+1) = 25

25 = w(3w + 1)

3w² + w - 25 = 0

w = 2.7248 (round to 2.72 m)

length is (3w + 1) = 3(2.72) + 1 = 9.16 m

Hence the length is 9.16 meters.

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the complete Question is,

Two sandboxes with the same area are shown. The equation w(3w+1)=5^2 represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter. and area of sandbox 1 ia 25 m².

Answer:

(-1, 4)

Step-by-step explanation:

In the figure attached,

Ordered pair representing point P is (3, 4) [parallel to y-axis]

If this point has been reflected across a line x = 1

New point after reflection across x = 1 will be,

P(3, 4) → P'(-1, 4)

Since point P and P' will be equidistant from the line (x = 1), so the x ordinate of P' will be = 3 - 4 = -1

And y-ordinates of point P' will be same as y = 4

Answer:

8km

Step-by-step explanation:

1:100000

8 : x

x = the distance travelled in cm = 8 x 100000 = 800000cm

convert cm to km = 800000/100000 = 8km

Hope this helps.

Good Luck

Answer:

[tex]\frac{1}{5x-5}[/tex]

Step-by-step explanation:

=> [tex]\frac{x-1}{5(x-1)^2}[/tex]

=> [tex]\frac{x-1}{5(x-1)(x-1)}[/tex]

Cancelling (x-1)

=> [tex]\frac{1}{5(x-1)}[/tex]

=> [tex]\frac{1}{5x-5}[/tex]

The simplified form of the expression (x-1)/5(x-1)² is 1/(5x-5).

The given expression is (x-1)/5(x-1)²

To simplify the expression (x-1)/5(x-1)², we can first cancel out the common factor of (x-1) in the numerator and denominator:

(x-1)/(5(x-1)²) = 1/[5(x-1)]

The expression simplifies to 1 divided by 5 times (x-1), which can be written as:

1/(5x-5)

So, the simplified form of (x-1)/[5(x-1)²] is 1/(5x-5).

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