MA 912. G.1.4
60. What is the slope of a line that passes through the point (-1, 1) and is parallel to a line that passes through
(3.6) and (1, -2)?

Answer:

It cannot be simplified any further.

The simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15 is (y-4)/(y-5) .

(y^2-y+12)/(y^2-2y-15)  factor both the numerator and denominator...

(y^2-4y-3y+12)/(y^2-5y+3y-15)

(y(y-4)-3(y-4))/(y(y-5)+3(y-5))

((y-4)(y-3))/((y-5)(y+3))  so the (y+3) and (y-3) cancel leaving

(y-4)/(y-5)

(y-4)/(y-5) the simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15.

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Answer:

The custodian can make 128 pails.

Step-by-step explanation:

first, you convert 1/8 to 0.125.

then, you divide 16 by 0.125 to get 128.

Answer:

112560

Step-by-step explanation:

The total profit is the sale price of the helmet is $ 60 is:

                        $ 27,600

p denote the total profit and s denote the sale price.

The total profit in terms of the sale price is given by the function :

        [tex]p(s)=-24s^2+2200s-18000[/tex]

Now we are asked to find the value of p when the s=60

when s=60 we have:

[tex]p(60)=-24\times (60)^2+2200\times 60-18000\\\\\\p(60)=-24\times 3600+132000-18000\\\\\\p(60)=-86400+132000-18000\\\\\\p(60)=27600[/tex]

          Hence, the total profit when sale price is $ 60 is:

                              $ 27,600

Answer:

Add the five terms.

Use the formula for the fifth partial sum.

The fifth partial sum represents the total amount of money the athlete earns over the first five years.

Step-by-step explanation:

Add the five terms.

Use the formula for the fifth partial sum.

The fifth partial sum represents the total amount of money the athlete earns over the first five years.

Answer:  The fifth partial sum = 2210

The fifth partial sum represent the sum of the first 5 terms in the sequence.

Step-by-step explanation:

We know that he partial sum of a sequence gives the sum of the first n terms in the sequence.

Thus, the fifth partial sum represent the sum of the first 5 terms in the sequence.

The given geometric sequence : $400, $420, $441, $463, and $486.

Now, the fifth partial sum of the above sequence will be :

[tex]S_5=\$400+ \$420+ \$441+ \$463+\$486=\$2210[/tex]

Answer:

[tex]\large\boxed{2\sqrt7}[/tex]

Step-by-step explanation:

Look at the picture.

ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:

[tex]\dfrac{AC}{AD}=\dfrac{AB}{AC}[/tex]

We have

[tex]AC=x,\ AD=2,\ AB=2+12=14[/tex]

Substitute:

[tex]\dfrac{x}{2}=\dfrac{14}{x}[/tex]           cross multiply

[tex]x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7[/tex]

For this case we have the following functions:

[tex]f (x) = 3x\\g (x) = x ^ 2 + 1[/tex]

We must find (f + g) (x). By definition of operations with functions we have to:

(f + g) (x) = f (x) + g (x)

So we have to:

[tex](f + g) (x) = 3x + (x ^ 2 + 1)\\(f + g) (x) = x ^ 2 + 3x + 1[/tex]

Answer:

[tex](f + g) (x) = x ^ 2 + 3x + 1[/tex]

Option B

We have three similar triangles, because each has a right angle and shares an angle.   Let's write the angles in order: opposite to short leg, long leg, hypotenuse.

CAB similar to BAD similar to CBD

Or as ratios,

CA:AB:CB = BA:AD:BD = CB:BD:CD

We also know

AC = AD + CD

(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD

(AD+CD)/CB=CB/CD

We have CB=6, AD=5 and seek x=CD.

[tex](5 + x)/6 = 6/x[/tex]

[tex]x(x+5) = 36[/tex]

[tex]x^2 +5x - 36 = 0[/tex]

[tex](x+9)(x-4) = 0[/tex]

We reject the negative root and conclude x=4

Answer: 4

From opposite to the short leg, long leg, and hypotenuse DC is A) 4

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Because each triangle has a right angle and shares an angle, we have three comparable triangles. The angles should be written from opposite to the short leg, long leg, and hypotenuse.

CAB is similar to BAD similar to CBD

CA : AB : CB = BA : AD : BD = CB : BD : CD

We also know

AC = AD + CD

(AD + CD) : AB : CB = BA : AD : BD = CB : BD : CD

(AD + CD)/CB = CB/CD

We have CB = 6, AD = 5, and x = CD.

∴ (5 + x)/6 = 6/x.

x(5 + x) = 36.

5x + x² = 36.

x² + 5x - 36 = 0.

x² + 9x - 4x - 36 = 0.

x(x + 9) - 4(x + 9) = 0.

(x + 9)(x - 4) = 0.

x = - 9 Or x = 4.   (length can not be negative).

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Answer:

Perimeter = 32.44 units

Area = 30 square units

Step-by-step explanation:

Given

Vertices

A(2,8), B(16,2) and C(6,2)

WE have to determine the lengths of all sides before finding the perimeter and area.

The formula of modulus is:

[tex]d = \sqrt{(x_{2}- x_{1})^{2} +(y_{2}-y_{1})^{2}}\\AB=\sqrt{(16-2)^{2} +(2-8)^{2}}\\=\sqrt{(14)^{2} +(-6)^{2}}\\=\sqrt{196+36}\\ =\sqrt{232}\\=15.23\\\\BC=\sqrt{(6-16)^{2} +(2-2)^{2}}\\=\sqrt{(-10)^{2} +(0)^{2}}\\=\sqrt{100+0}\\ =\sqrt{100}\\=10\\\\AC=\sqrt{(6-2)^{2} +(2-8)^{2}}\\=\sqrt{(4)^{2} +(-6)^{2}}\\=\sqrt{16+36}\\ =\sqrt{52}\\=7.21\\\\[/tex]

So the perimeter is:

[tex]Perimeter=AB+BC+AC\\=15.23+10+7.21\\=32.44\ units[/tex]

Using hero's formula,

[tex]s=\frac{perimeter}{2}\\s=\frac{32.44}{2}\\ s=16.22\\Area=\sqrt{s(s-a)(s-b)(s-c)}\\=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}\\=\sqrt{(16.22)(0.99)(6.22)(9.01)}\\=\sqrt{899.91}\\=29.99\ square\ units[/tex]

Rounding off will give us 30 square units ..

Answer:

30 square units

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

2 || 1   -   4     6    -   4

              2    -4       4

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

     1       -2    2

x^2 - 2x + 2 with no remainder.

Looks like the answer is B

Note: Note that the two in x - 2 changes sign. That always happens when using synthetic division as long the number in front of the x is positive.

Answer:

Step-by-step explanation:

Area of a circle is ...

  A = πr² . . . r is the radius

Area of a sphere is ...

  A = 4πr²

Lateral area of a cylinder is ...

  A = πdh = 2πrh . . . h is the height

Volume of a cylinder is ...

  V = πr²h

Volume of a sphere is ...

  V = (4/3)πr³

___

The area of the composite figure is the sum of the areas ...

  total area = base circle area + cylinder lateral area + 1/2 sphere area

  = πr² + 2πrh + (1/2)4πr² = (πr)(r +2h +2r)

  = πr(3r +2h)

For the given dimensions, r=3 in, h = 13 in, this is ...

  total area = π(3 in)((3·3 +2·13) in) = 105π in²

___

The volume of the composite figure is the sum of the volumes ...

  total volume = cylinder volume + 1/2 sphere volume

  = πr²h + (1/2)(4/3)πr³ = πr²(h + 2/3r)

  = π(3 in)²((13 +2/3·3) in) = 135π in³

Answer:

(x - 4)² + (y + 7)² = 53

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (4, - 7), so

(x - 4)² + (y + 7)² = r²

The radius is the distance from the centre to a point on the circle.

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (4, - 7) and (x₂, y₂ ) = (- 3, - 5)

r = [tex]\sqrt{(-3-4)^2+(-5+7)^2}[/tex]

  = [tex]\sqrt{(-7)^2+2^2}[/tex] = [tex]\sqrt{49+4}[/tex] = [tex]\sqrt{53}[/tex]

Hence r² = ([tex]\sqrt{53}[/tex] )² = 53

(x - 4)² + (y + 7)² = 53 ← equation of circle

After 5 weeks, Brian will have completed 445 sit-ups, and Christina will have completed 425 sit-ups.

To calculate the total number of sit-ups Brian and Christina will have done after 5 weeks, we can use arithmetic progressions since the number of sit-ups increases by the same amount each week after the first.

For Brian:

For Christina:

Therefore, after 5 weeks, Brian will have done 445 sit-ups and Christina will have done 425 sit-ups.

Answer:

Step-by-step explanation:

4 miles = 1hour

5miles = 1hour and 25 minutes

10miles = 2 hours and 50 min

15miles = 4hours and 15min

x miles = 5 hours

20 miles = 5 hours

tell me if i got it wrong sry

Answer:

The box of 32oz is cheaper by 2 cents per ounce.

Step-by-step explanation:

1. 3.84/24 ($0.16/oz)

2. 4.48/32 ($0.14/oz)

___

Hope this helps you! :)

Step-by-step explanation:

h = -490t² + 1470t

When h = 980:

980 = -490t² + 1470t

Simplifying:

0 = -490t² + 1470t - 980

0 = t² - 3t + 2

Factoring:

0 = (t - 1) (t - 2)

t = 1, 2

There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.

The rocket reaches a height of 980 cm at 1 second and 2 seconds. The equation is factored to find these solutions, symbolizing the ascent and descent of the rocket.

To find when the height of the rocket is 980 cm, we set the height formula equal to 980 cm:

h = -490t² + 1470t = 980.

We then solve the equation by factoring:

-490t² + 1470t - 980 = 0
Divide by -10:
t²- 3t + 2 = 0
Factor:
(t - 1)(t - 2) = 0

Setting each factor to zero gives us the solutions:

t = 1 second

t = 2 seconds

There are two solutions because the rocket reaches 980 cm twice: once on its way up and once on its way down. This is demonstrated by the positive and negative components of the parabolic trajectory represented by the quadratic equation.

Answer:

tallest man height is more extreme.

Step-by-step explanation:

Given:

Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm.

Concept used:

Convert height into z scores for comparison of deviation from the mean.

Solution:

Tallest man height = 265 cm

[tex]Z_{tall} =\frac{265-173.73}{8.65} \\=10.55[/tex]

Shortest man height = 109.1 cm

[tex]Z_{short} =\frac{109.1-173.73}{8.65} \\=-7.47[/tex]

Thus we find that tallest man is 10.55 std deviations from the mean to the right and shortest man is 7.47 std deviations from the mean to the left.

Hence tallest man height is more extreme.

The tallest living man at one time had a more extreme height compared to the shortest living man at that time.

In this question, we are given the heights of the tallest and shortest living men at a specific time, as well as the mean and standard deviation of heights at that time. To determine which man had a more extreme height, we need to compare their heights to the mean and see how many standard deviations away they are.

The tallest man had a height of 265 cm, which is 265 - 173.73 = 91.27 cm above the mean.

The shortest man had a height of 109.1 cm, which is 173.73 - 109.1 = 64.63 cm below the mean.

Since the tallest man's height is significantly farther away from the mean compared to the shortest man's height, we can conclude that the tallest man had a more extreme height.

Hello there! The answer is B. (3, 21).

So you want to be able to substitute one of the equations into the other. We can't do this right now since both of the equations are y = something, so we need to change the second equation to x = something so we can plug it in to the value of x in the first equation.

y = x + 18 can translate to x = y - 18. Now, plug "y - 18" into x in the first equation.

y = 10(y-18) - 9 and solve.

y = 10y - 180 - 9

-9y = - 180 - 9

-9y = -189

y = 21.

Now we have our y value, but we need our x value. Well, remember that y = x + 18? So, since y is 21, what plus 18 is equal to 21? The answer is 3, making our x value 3.

If x = 3 and y = 21, the ordered pair is (3, 21) or option B. I hope this was helpful and have a great day! :)

Hello

10x-9=x+18

10x-x=18+9

9x=27

x=3

=30-9=21

(3,21)

Good Luck

Goodbye ♥

Final answer:

A number that can be expressed as a ratio of two integers is called a fraction. Ratios compare quantities and can be written in various forms, like fractions or with a colon. Proportions represent the equivalence of two ratios and are widely used in both mathematics and science.

Explanation:

Any number that can be written as a ratio of two integers is known as a fraction. A fraction is a type of ratio where one integer, the numerator, is divided by another integer, the denominator. For instance, 5/8 is a fraction because it represents 5 parts out of a total of 8.

A ratio can compare any two quantities, not just parts of a whole. These can be written as fractions, with a colon, or with the word 'to'. Examples include 2/3, 2:3, . Ratios are often used to compare dimensions, such as on a map where a unit scale is provided. For example, a map might state that 1 inch represents 100 feet, which is a ratio written as 1 inch/100 ft. Ratios are also essential in the health sciences, for instance, when describing solutions with a certain proportion like 1:1000.

In more complex applications, proportions are used to express equivalences between two ratios. For example, 1/2 is equivalent to 3/6, and this relationship forms a proportion. Proportions are useful in various fields, for setting up equivalencies and solving for unknown quantities.

[tex](-\infty, +\infty)[/tex]

Hope this helps.

r3t40

Answer:

[tex]\frac{32m^{15}}{x^3-x^2}[/tex]

Step-by-step explanation:

The given expression is: [tex]\frac{4m^{12}}{x-1}\div \frac{x^2}{8m^3}[/tex]

We multiply by the reciprocal of the second fraction:

[tex]\frac{4m^{12}}{x-1}\times \frac{8m^3}{x^2}[/tex]

We cancel out the common factors to get;

[tex]\frac{32m^{12+3}}{x^2(x-1)}[/tex], where [tex]x\ne0[/tex] and [tex]m\ne0[/tex]

We simplify to get:

[tex]\frac{32m^{15}}{x^3-x^2}[/tex]

Answer:

To simplify all that its D

Step-by-step explanation:

The option that shows a two-way conditional frequency table is option B as shown in the image attached.

A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:

Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.

The correct option is option B because it meets the following requirements:

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Answer:

Do you prefer dancing or playing sports?

 Playing sports Dancing Row totals

Male students 0.48 0.52 1

Female students 0.35 0.65 1

Step-by-step explanation:

This is the answer

Answer:

-10

Step-by-step explanation:

Velocity is the derivative of position.  Derivative is defined as:

f'(x) = lim(h->0) [ f(x+h) - f(x) ] / h

s(t) = 1 - 10t

s(t+h) = 1 - 10(t+h)

Plugging in:

s'(t) = lim(h->0) [ 1 - 10(t+h) - (1 - 10t) ] / h

s'(t) = lim(h->0) (1 - 10t - 10h - 1 + 10t) / h

s'(t) = lim(h->0) (-10h) / h

s'(t) = lim(h->0) -10

s'(t) = -10

v(t) = -10

So at t=0, v(0) = -10.

The instantaneous velocity at [tex]t = 10[/tex] is 10.

The instantaneous Velocity of the object at a time [tex]t[/tex] is determined by mathematical concept of Derivative, whose description is shown below:

[tex]v = \lim_{h \to 0} \frac{s(t+h) - s(t)}{h}[/tex] (1)

Where:

[tex]h[/tex] - Time difference.

[tex]s(t)[/tex] - Function position evaluated at time [tex]t[/tex].

If we know that [tex]s(t) = 1 - 10\cdot t[/tex], then the instantaneous Velocity of the object is:

[tex]v = \lim_{h \to 0} \frac{1-10\cdot (t+h)-1+10\cdot t}{h}[/tex]

[tex]v = \lim_{h \to 0} \frac{10\cdot h}{h}[/tex]

[tex]v = \lim_{h \to 0} 10[/tex]

[tex]v = 10[/tex]

As instantaneous velocity is a constant function, it means that objects travels at constant velocity. Hence, we conclude that the instantaneous velocity at [tex]t = 10[/tex] is 10.

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Answer:

A box of 50 stickers would cost $13

Explanation:

1- getting the equation representing the price:

We have two variables; the number of stickers and the price of the box

We can note that the price is the dependent variable (y) while the number of stickers is the independent one (x)

We are given that:

A box of 15 stickers cost $6..........> first point is (15,6)

A box of 25 stickers cost $8 ........> second point is (25,8)

The general equation of the linear line is:

y = mx + c

where m is the slope and c is the y-intercept

i. getting the slope:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{25-15}=0.2[/tex]

The equation now became: y = 0.2x + c

ii. getting the y-intercept:

To get the y-intercept, use any of the given points and substitute in the equation we got in part i. I will use the point (15,6)

y = 0.2x + c

6 = 0.2(15) + c

c = 6 - 0.2(15) = 3

The final equation is:

y = 0.2x + 3

where y is the price of the box and x is the number of stickers it contains

2- getting the price of a box with 50 stickers:

To get the price of a box of 50 stickers, simply substitute with x = 50 in the equation we got from part 1

This is done as follows:

y = 0.2(50) + 3 = 13

Therefore, a box of 50 stickers will cost $13

Hope this helps :)

Answer:

  D)  If Jack drives 200 miles, it will cost anywhere between $30 and $42

Step-by-step explanation:

The cost is said to be a range of possibilities. The first three answer choices seem to assume the cost is at one extreme or the other. They incorrectly interpret the statement of cost.

Recall that the area of an equilateral triangle with side length [tex]s[/tex] is [tex]\dfrac{\sqrt3}4s^2[/tex].

In the [tex]x-y[/tex] plane, the base is given by two equations:

[tex]x^2+y^2=9\implies y=\pm\sqrt{9-x^2}[/tex]

so that for any given [tex]x[/tex], the vertical distance between the two sides of the circle is

[tex]\sqrt{9-x^2}-\left(-\sqrt{9-x^2}\right)=2\sqrt{9-x^2}[/tex]

and this is the side of length of each triangular cross-section for each [tex]x[/tex]. Then the area of each cross-section is

[tex]\dfrac{\sqrt3}4(2\sqrt{9-x^2})^2=\sqrt3(9-x^2)[/tex]

and the volume of the solid is

[tex]\displaystyle\int_{-3}^3\sqrt3(9-x^2)\,\mathrm dx=\boxed{36\sqrt3}[/tex]

Answer:

jnd8663393765422345678

Step-by-step explanation:

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Answer:

i am assuming 2 and 5 because they are the only ones that are not like the others

Step-by-step explanation:

Answer:

Angles 2 and 5

Step-by-step explanation:

Supplement angles are the angles which up to 180 degrees.

And all the angles shown are Vertically opposite angles and these angles are always the same.

Vertically opposite angles:

Angles  2 and 5

Angles 1 and 3

Angles 6 and 4

As shown in the picture, Angle 2 is 90 degrees and angle 5 being a vertically opposite angle, angle 5 is 90 degrees too.

90 + 90 = 180 degrees.

1.63

4.89 divided by 3 = 1.63

1.63 just divided the total by 3

Answer:

5x-(3x+1) or 2x-1

Step-by-step explanation:

The difference (subtraction) between five times x (5x) and one more (+1) than three times x (3x.) 5x-(3x+1)

Simplified, 5x-3x-1=2x-1.

These 5 numbers can be written as [tex]x,x+2,x+4,x+6,x+8[/tex], so their sum is

[tex]x+(x+2)+(x+4)+(x+6)+(x+8)=5x+20=310[/tex]

[tex]\implies5x=290[/tex]

[tex]\implies x=58[/tex]

Then the numbers are 58, 60, 62, 64, and 66.