Which subset(s) of numbers does 8 2/3
belong to?

Answer:

x=4, x=3

B is correct.

Step-by-step explanation:

Given: [tex]x^2-7x+12=0[/tex]

Using middle term splitting factor the left side equation.

[tex]x^2-4x-3x+12=0[/tex]

[tex](x-4)(x-3)=0[/tex]

Equate each factor to 0 and solve for x

x-4=0    or     x-3=0

x=4 and x=3

Hence, The solution of the equation is 4 or 3

43.2/16= 2.7

Answer: 2.7

Your answer would be 2.7

Answer:4 months

Step-by-step explanation:

if you go by members for each group. group A has 450 but adds in 15 members each month. group B has 25 members each month. not take 25 and multiply it by 4 it equals to 100. and multiply 15 by 4 equals 50. which makes group B 500. and group A 500.

After 5 months, Fitness Club A and Fitness Club B will have the same number of members.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have.
We can solve this problem by setting up an equation to represent the number of members at each club after a certain number of months and then solving for the number of months that makes the number of members equal.

Let's use "m" to represent the number of months:

Number of members at Club A after m months = 450 + 15m

Number of members at Club B after m months = 400 + 25m

To find when the two clubs will have the same number of members, we can set these two expressions equal to each other and solve for m:

450 + 15m = 400 + 25m

Subtracting 400 from both sides:

50 + 15m = 25m

Subtracting 15m from both sides:

50 = 10m

Dividing both sides by 10:

m = 5

Therefore,

After 5 months, Fitness Club A and Fitness Club B will have the same number of members.

Learn more about expressions here:

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Answer:

The value of x is -3

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of a line that passes through points (x1 , y1) and (x2 , y2) is

  [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

* Lets solve the problem

∵ The points (4 , 1) and (x , -6) lie on the same line

∵ The slope of the line is 1

- Let the point (4 , 1) is (x1 , y1) and the point (x , -6) ix (x2 , y2)

∵ x1 = 4 , x2 = x and y1 = 1 , y2 = -6

∴ [tex]m=\frac{x-4}{-6-1}[/tex]

∴ [tex]m=\frac{x-4}{-7}[/tex]

∵ The slope of the line is m = 1

∴ [tex]\frac{x-4}{-7}=1[/tex]

- By using cross multiplication

∴ x - 4 = -7 ⇒ add 4 to both sides

∴ x = -3

* The value of x is -3

the value of x for the point on the line is -3.

The student is asking how to find the value of x for a point on a line with a given slope. Since the slope of the line is 1, we can use the slope formula, which is (y2 - y1) / (x2 - x1) = slope, to find the value of x. Here, we have two points, (4, 1) and (x, -6), and a slope of 1.

Using the formula, we get (-6 - 1) / (x - 4) = 1. Simplifying, we get -7 / (x - 4) = 1. To find the value of x, we solve the equation -7 = x - 4, which gives us x = -3. So, the value of x for the point on the line is -3.

Yes, they're similar.

Step-by-step explanation:

Triangles are similar when they have the same shape but vary in sizes. This is our case here. We have two equilateral ∆s which makes them similar but what differs them is the length. One is 6 and the other is 10. Although that doesn't affect anything in the triangle. If you drew a height to any base (in either triangle) it would still be a bisector, median, and perp bisector. Their angles are alsp equal.

Answer:

4

Step-by-step explanation:

Answer:

y=15t

t is time

By using the counting principle in mathematics, the student can know that there are 128 possible sandwiches that can be made with one type of each ingredient.

The question you're asking is related to the counting principle in mathematics. The counting principle suggests that if you can choose one item from 4 different types of bread, one from 8 types of meat, and one from 4 different types of cheese, the number of different sandwiches you could make is the product of these choices.

To calculate it, simply multiply the choices together like this: 4 (types of bread) * 8 (types of meat) * 4 (types of cheese) = 128. So, there are 128 different sandwiches that could be created with one type of each ingredient.

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Answer:

x = 5/3    or   x = -5/2

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

Step-by-step explanation:

Given in the question an equation

6x²+5x- 25

here a = 6

        b = 5

        c = -25

To solve the polynomial equation we will use quadratic equation

x = -b ±√(b²-4ac) / 2a

Plug values in the equation

-5±√(5²-4(6)(-25)) / 2(6)

-5±√(25 + 600) / 2(6)

-5±√(625) / 2(6)

-5± 25 / 2(6)

-5 + 25 / 2(6)  or -5 - 25 / 2(6)

x = 5/3    or   x = -5/2

Answer:

The rate of sales tax is 6%.

Step-by-step explanation:

First you must subtract 12.50 from 13.25

This brings you to .75

Then, divide .75/12.50 to get 0.06 which is equivalent to 6 percent.

I don't know if you still need this but here you go

Answer: Equation for the line of best fit is given by

f(x)=-4.28402x+0.0875

Step-by-step explanation:

Long Course Season       Recorded Best time

2005                          2:33.42

2006                          2:24.81

2007                          2:10.93

2008                          2:03.45

2009                          1:58.67

2010                          1:59.17

2011                          1:55.06

2012                          1:55.82

2013                          1:54.81

2014                          2:00.03

Since we can see from the scatter plot that it has negative correlation.

Equation for the line of best fit is given by

f(x)=-4.28402x+0.0875

Carolyn wants to deposit a check into her savings account. She should sign the back of the check , complete a deposit slip, and visit the teller at the bank.

Answer:

Step-by-step explanation:

4(3-2x)=15

Distribute 4:

12-8x= 15

Subtract 12:

-8x= 3

Divide

X= -3/8 or -0.375

ANSWER

[tex]x = - \frac{3}{8} [/tex]

EXPLANATION

The given equation is:

4(3 - 2x) = 15

Expand the parenthesis to obtain:

12-8x=15

Group similar terms to get;

-8x=15-12

Combine similar terms to get:

-8x=3

Divide both sides by -8

[tex]x = - \frac{3}{8} [/tex]

Final answer:

The normal form of x + 5y - 2 = 0 is (1/√26)x + (5/√26)y - (2/√26) = 0. The length of the normal is 1, and the angle it makes with the positive x-axis can be calculated using tan θ = 5, which gives the angle as tan-1(5).

Explanation:

To rewrite the equation x + 5y - 2 = 0 in normal form, we need to express it in the form Ax + By + C = 0, where A2 + B2 = 1. The equation is already in this form, but we must divide each term by the square root of (12 + 52) to satisfy the condition for A2 + B2. After the division, the normal form becomes (1/√26)x + (5/√26)y - (2/√26) = 0.

The length of the normal is the magnitude of the vector (A, B), which in this case, is 1 due to the normalization. To find the angle θ that the normal makes with the positive x-axis, we use the relationship tan θ = B/A. For our equation, tan θ = 5/1, so θ = tan-1(5).

The analytical method of vector addition involves identifying the x- and y-components of vectors and merging them to calculate the resultant vector's magnitude and direction.

Answer: its the one under the first one i think good luck adriana lol

Step-by-step explanation:

Answer:

The correct answer is X²/³

Step-by-step explanation:

Points to remember

Identity

Xᵃ/Xᵇ = X⁽ ᵃ⁻ ᵇ ⁾

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

(Xᵃ)ᵇ = Xᵃᵇ

To find the equivalent expression

We have, (X⁴/³ X²/³)¹/³

Using identities we can write,

(X⁴/³ X²/³)¹/³ = (X⁴/³  * X²/³)¹/³

 = (X⁴/³ ⁺ ²/³)¹/³

 = ( X⁽⁴⁺²⁾/³)¹/³

 = (X⁶/³)¹/³

= (X²)¹/³

= X²/³

Therefore the correct answer is X²/³

Answer:

P = 0.332

Step-by-step explanation:

The probability of having the disease is 0.08

The probability that the test predicts with accuracy is 0.7.

We need to find the probability that the test positive for the disease.

Several cases may occur.

Case 1.

You have the disease and the test predicts it accurately

[tex]P_1 = 0.08(0.7) = 0.056[/tex]

Case 2

You do not have the disease and the test predicts that you have it

[tex]P_2 = 0.92(0.3) = 0.276[/tex]

Then the probability that the test predicts that you have the disease is the union of both probabilities P1 and P2

[tex]P = P_1 + P_2\\\\P = 0.056 + 0.276\\\\P = 0.332[/tex]

Answer:

The ball was dropped from 150 feet.

It will take the ball 3.06 seconds to reach the ground.

Step-by-step explanation:

A story is 10 feet.

You want to find the number of seconds for the ball to reach the ground, which is a height of 0.  So you can put 0 in for h(t), and then solve that.  If you need more help than that, let me know.

Answer:

78

Step-by-step explanation:

78 is the answer because if you count inwards then you get 78

Answer:

D

Step-by-step explanation:

add them all except 50 divide by 9 because only used 9.

The formula for finding the circumference of the circle is 2 pi r or pi d. R stand for radius and D stand for diameter. The problem gave you the length of the diameter so can either put it in form of pi as in 30pi or multiply it by pi (3.14) which will give you the result of 94.2

Answer:

- 30pi

- 94.2

Answer:

A.) 30

Step-by-step explanation:

The entire figure consists of two angles supplementary to each other, which means that ∠YWZ + ∠ZWX = 180°. Since ∠ZWX is 20°, we know that ∠YWZ is 160°.

So now we have an equation to solve:

5x + 10 = 160

     - 10     - 10

5x = 150

÷ 5   ÷ 5

x = 30

Check the picture below.

let's notice that the angle at K is an inscribed angle with an intercepted arc

[tex]\bf \stackrel{\textit{using the inscribed angle theorem}}{K=\cfrac{\widehat{LI}+\widehat{IJ}}{2}}\implies 9x+1=\cfrac{(10x-1)+59}{2} \\\\\\ 9x+1=\cfrac{10x+58}{2}\implies 18x+2=10x+58\implies 8x+2=58 \\\\\\ 8x=56\implies x=\cfrac{56}{8}\implies x=7 \\\\[-0.35em] ~\dotfill\\\\ K=9x+1\implies K=9(7)+1\implies \boxed{K=64}[/tex]

now, let's notice something again, the angle at L is also an inscribed angle, intercepting and arc of 97 + 59 = 156, so then, by the inscribed angle theorem,

∡L is half that, or 78°.

now, let's take a look at the picture down below, to the inscribed quadrilateral conjecture, since ∡J and ∡I are both supplementary angles, then

∡I = 180 - 64 = 116°.

∡J = 180 - 78 = 102°.

The measure of all the angle of KLIJ which is inscribed in circle k(O) are, 64, 78, 116, 102 degrees.

Inscribed angle theorem is the theorem, which state that the angle inscribed in a circle will be half of the angle which delimits the same arc on the circle.

The quadrilateral KLIJ is inscribed in circle k(O). In this the measure of the angle are given as,

[tex]m\angle K = (9x+1)^o[/tex]

m (arc) LI = (10x−1)°

m (arc) IJ = 59°,

m (arc) KJ =97°

All angles of the quadrilateral KLIJ has to be found out. By the inscribed angle theorem,

[tex]K=\dfrac{LI+IJ}{2}\\9x+1=\dfrac {10x-1+59}{2}\\18x+2=10x+58\\8x=56\\x=7[/tex]

Therefore, the value of the angle k is,

[tex]m\angle K = (9(7)+1)^o\\m\angle K = 64^o[/tex]

Similarly, the measure of the angle L is,

[tex]m\angle L=\dfrac{KJ+IJ}{2}\\m\angle L=\dfrac {97+59}{2}\\m\angle L=\dfrac{156}{2}\\m\angle L=78^o[/tex]

Now the angles I and J are the supplementary angles of the angle K and angle L respectively. Therefore,

[tex]m\angle I=180-m\angle K=180-64=116^o\\ m\angle J=180-m\angle L=180-78=102^o[/tex]

Hence, the measure of all the angle of KLIJ which is inscribed in circle k(O) are, 64, 78, 116, 102 degrees.

Learn more about the inscribed angle theorem here;

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Answer:

The correct answer is A.

Answer:

The answer is .800

To round .796 to the nearest hundredth, we observe the third decimal place (6) and round up the second decimal place from 9 to 10, which effectively turns .796 into .80.

The question asks us to round .796 to the nearest hundredth. To do this, we look at the third decimal place, which is 6. Since 6 is greater than 5, we round up the second decimal place from 9 to 10. However, since the second place cannot literally take the value of 10, it effectively rolls over and adds 1 to the first decimal place, changing .796 to .80. Therefore, the answer is .80 when rounded to the nearest hundredth.

Answer:

[tex](4,-\frac{\pi}{3}+2n\pi)[/tex] And [tex](-4,-\frac{\pi}{3}+(2n+1)\pi).[/tex]

Hope this helps you out!

Answer:

All the polar coordinates of point P are [tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex] and [tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex], where n is any integer and θ is in radian.

Step-by-step explanation:

It a polar coordinate is given as P(r,θ), then all the polar coordinates of point P  are defined as

[tex]P(r,\theta)=(r,2n\pi+\theta)[/tex]

[tex]P(r,\theta)=(-r,(2n+1)\pi+\theta)[/tex]

Where, n is any integer and θ is in radian.

The given point is

[tex]P(4,-\frac{\pi}{3})[/tex]

So, all the polar coordinates of point P  are defined as

[tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex]

[tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex]

Therefore all the polar coordinates of point P are [tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex] and [tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex], where n is any integer and θ is in radian.

Answer:

7x6x2= 84 ft cubed

Step-by-step explanation:

multiply length by width by height

Answer:

1. r=17

2. (-15,14) or (-15,-16)

Step-by-step explanation:

The radius of the circle is the distance from the center to the point on the circle, thus

[tex]r=\sqrt{(8-(-7))^2+(7-(-1))^2}=\sqrt{15^2+8^2}=\sqrt{225+64}=\sqrt{289}=17.[/tex]

The equation of the circle is

[tex](x-(-7))^2+(y-(-1))^2=r^2\\ \\(x+7)^2+(y+1)^2=289.[/tex]

If point lies on this circle, then its coordinates satisfy the circle's equation:

[tex](-15+7)^2+(y+1)^2=289\\ \\64+(y+1)^2=289\\ \\(y+1)^2=225\\ \\y+1=15\text{ or }y+1=-15\\ \\y=14\text{ or }y=-16[/tex]

the radius of the circle is 17 units.

the two possible points on the circle are (-15, 14) and (-15, -16).

The question requires calculating the radius of a circle given two points: the center of the circle and a point on the circumference. To find the radius, we will use the distance formula, which is derived from the Pythagorean theorem. The distance formula to find the distance between two points (x1, y1) and (x2, y2) is \\(
√{(x2 - x1)^2 + (y2 - y1)^2}\\).

Applying the distance formula with the center at (-7, -1) and a point on the circle being (8, 7), we get: \\(
√{(8 - (-7))^2 + (7 - (-1))^2}) = (√{(15)^2 + (8)^2}) = (√{225 + 64}) = (√{289}) = 17. Thus, the radius of the circle is 17 units.

To find the missing y-coordinate of the point (-15, ___) that lies on this circle, we use the circle's equation with its center at (-7, -1): ((x + 7)^2 + (y + 1)^2 = 17^2). Substituting x = -15, we solve for y.

((-15 + 7)^2 + (y + 1)^2 = 17^2)
((-8)^2 + (y + 1)^2 = 289)
64 + (y + 1)^2 = 289
(y + 1)^2 = 225
y + 1 = (√{225}) or y + 1 = -(√{225})
y = 14 or y = -16

Therefore, the two possible points on the circle are (-15, 14) and (-15, -16).

trapezoid: (25+19)/2 *20 (see formula for area of a trapezoid)

and the smaller parallelogram: (10*17) (see formula for parallelogram)

and subtract the parallelogram from the trapezoid and you're done!

so we have a trapezoid with a parallelogram inside.

now, if we just get the area of the trapezoid, which includes the parallelogram, and then  get the area of the parallelogram and subtract it from that of the trapezoid, what's leftover is the shaded region, because we'd be in effect making a "hole" in the trapezoid and the area leftover is the shaded part.

[tex]\bf \stackrel{\textit{area of a trapezoid}}{A=\cfrac{h(a+b)}{2}}~~ \begin{cases} a,b=\stackrel{bases}{parallel}\\ \qquad ~~ sides\\ h=height\\ \cline{1-1} a=19\\ b=25\\ h=20 \end{cases}\qquad \stackrel{\textit{area of a parallelogram}}{A=bh}~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=17\\ h=10 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{trapezoid}}{\cfrac{20(19+25)}{2}}~~-~~\stackrel{\textit{parallelogram}}{(17\cdot 10)}\implies 10(44)-170\implies 440-170\implies 270[/tex]

Answer:

18. 36.36%

22. 53.71

Step-by-step explanation:

Answer:

55 deg

Step-by-step explanation:

In triangle ABC, angle A is a right angle, so angles B and C are complementary; their measures add to 90 deg.

m<C + m<B = 90

m<C + 35 = 90

m<C = 90 - 35

m<C = 55

Angle Z corresponds to angle C, so angles Z and C are congruent.

m<Z = m<C = 55