2/3 - 5bx = bx + 1/3 In the equation shown above, b is a constant. For what value of b = NO SOLUTIONS? A. 5 B. 0 C. -5 D. 2/5

Answer:

2 rays: Two examples of rays are AB and AC, both emanating from a common endpoint A and extending infinitely in opposite directions.

2 line segments: Two examples of line segments are AB and CD, both of which have two endpoints and a finite length.

2 lines (not including the parallel lines): Two examples of lines are AB and CD, which intersect at a point E.

2 sets of parallel lines: Two examples of sets of parallel lines are AB and CD, and EF and GH, where AB and CD are parallel to each other, and EF and GH are parallel to each other.

2 acute angles (not incl. the ones in the As): Two examples of acute angles are ∠BAC and ∠EFG, both of which measure less than 90 degrees.

2 obtuse angles (not incl. the ones in the As): Two examples of obtuse angles are ∠PQR and ∠XYZ, both of which measure greater than 90 degrees.

2 right angles (not incl. the ones in the As): Two examples of right angles are ∠ABC and ∠EFG, both of which measure 90 degrees.

2 clear examples of supplementary angles: Two examples of supplementary angles are ∠ABC and ∠DEF, and ∠PQR and ∠RST, where the sum of the angles in each pair is 180 degrees.

2 clear examples of complementary angles: Two examples of complementary angles are ∠ABC and ∠PQR, and ∠DEF and ∠RST, where the sum of the angles in each pair is 90 degrees.

2 clear examples of more than two angles on a line that add up to 180°: Two examples of sets of angles on a line that add up to 180 degrees are ∠ABC, ∠BCD, and ∠CDE, and ∠PQR, ∠QRS, and ∠RST.

2 right triangles: Two examples of right triangles are ΔABC and ΔPQR, where ∠CAB and ∠QRP are right angles.

2 acute triangles: Two examples of acute triangles are ΔDEF and ΔGHI, where all angles are acute.

The sum of the measures of angles within each triangle:

In ΔABC, the sum of the measures of the angles is 180 degrees, where ∠A measures 90 degrees, and ∠B and ∠C measure 45 degrees each.

In ΔPQR, the sum of the measures of the angles is 180 degrees, where ∠P and ∠R measure 90 degrees each, and ∠Q measures 0 degrees.

In ΔDEF, the sum of the measures of the angles is 180 degrees, where all angles are acute, and ∠D, ∠E, and ∠F measure 60 degrees each.

In ΔGHI, the sum of the measures of the angles is 180 degrees, where all angles are acute, and ∠G, ∠H, and ∠I measure 40 degrees each.

In ΔJKL, the sum of the measures of the angles is 180 degrees, where ∠K measures 90 degrees, and ∠J and ∠L measure 45 degrees each.

In ΔMNO, the sum of the measures of the angles is 180 degrees, where ∠O measures 90 degrees, and ∠M and ∠N measure 45 degrees each.

Answer:

63

Step-by-step explanation:

60% of $100 is just %60 and 5% of 60 is 3 so, 60 + 3 = $63

Answer:

$45

Step-by-step explanation:

So, first we would find 60% of the $100

100 x .60 = 60

(When finding the amount of a percentage we move the decimal over twice)

then subtract what we got from the original price to find what he paid before tax:

100 - 60 = 40

Now we find 5% of $100:

100 x .05 = 5

Finally, we add this to what he was paying before taxes:

40 + 5 = 45, so $45

Hope this helps!! :)

If you are on the surface of a sphere and cannot leave that surface, you can move in two dimensions. The surface of a sphere is a two-dimensional space.

To understand this, imagine yourself standing on a globe. You can move along the surface by walking in any direction, such as east-west or north-south. These movements are described by two coordinates, typically latitude and longitude, which define your position on the sphere.

However, you cannot move in the third dimension, which would involve going up or down from the surface of the sphere.

The concept of dimensions in this context refers to the number of independent directions in which you can move. In the case of a sphere, the surface is curved and can be represented using two coordinates, giving you the ability to move in two dimensions.

Adding a third dimension would involve moving away from the surface, which is not possible within the constraints of being confined to the sphere's surface.

Therefore, you can move in two dimensions but not in three or four dimensions while on the surface of a sphere.

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Answer:

that would be 60 yards

Step-by-step explanation:

3 feet in 1 yard, so divide 180 by 3 and you get 60 yards

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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Step-by-step explanation:

Just plugging into the equation given

BC^2 = 30^2 + 21^2 - 2 (30)(21) cos 123

BC^2 = 900 + 441 + 1260 cos (123)

   BC = 45 units

Answer:

Step-by-step explanation:

we assume that we starts with n=1

a(1)=3*1+7=10

a(2)=6+7=13

a(3)=9+7=16

a(4) will be 19, a(5)=22 and so on

By calculating the given expression , we get 5 as a final resultant.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers the use of letters or alphabets without specifying their real values. The basics of algebra taught us the way to express an unknown fee the use of letters consisting of x, y, z, and so on. those letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any fee that is placed earlier than and improved with the aid of a variable is a coefficient.

Given expression ,

32- (3^2 -1 ) + 20 / 2

So by using the BODMAS rule ,

32 - (3*3  -  1 ) + 20 / 2

23 - (9 - 1 ) + 10

23 - (8) + 10

23 - 18

23 - 18

= 5

Hence, By calculating the given expression , we get 5 as a final resultant.

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Answer:

6.25

Step-by-step explanation:

17.50/2=8.75

8.75+2.50=11.25

17.50-11.25=6.25

Answer:

Toni has $7.50

Step-by-step explanation:

Tobi = x

Sabi = x + 2.5

x + x +  2.5 = 17.5

2x + 2.5 = 17.5

2x = 15

x = 7.5

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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(V.O.A) means vertically opposite angle.

The level of significance in hypothesis testing is the probability of: c. rejecting a true null hypothesis. In hypothesis testing, the critical value is:
a. a number that establishes the boundary of the rejection region.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research. In statistics , a null hypothesis is a statement that one seeks to nullify with evidence to contrary most commonly it is a statement that the phenomenon being studied produces no effect on makes no difference.

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Step-by-step explanation:

Using Trigonometry,

tan33° = Opposite/Adjacent = GF/DF.

Therefore GF = DF * tan33°

= 235tan33° = 152.6.

Angle GEF = Angle EDG + Angle DGE

= 33° + 34° = 67°. (Exterior Angle Theorem)

Using Trigonometry,

sin67° = Opposite/Hypotenuse = GF/EF.

Therefore EF = GF / sin67°

= 152.6 / sin67° = 165.8.

Hence the answer is the 1st option.

Answer:

the answer is A. GF =152.6 and EG=165.8

GF= 235*(tan(33))

EG= 152.6/(sin(67))

Answer:

7/20

Step-by-step explanation:

\(\frac{3}{5}\div \frac{12}{7}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\)

\(=\frac{3}{5}\times \frac{7}{12}\)

\(Cancel\;common\;factor\)

\(=\frac{1}{5}\times \frac{7}{4}\)

\(\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\)

\(=\frac{7}{5\times \:4}\)

\(\mathrm{Multiply\:the\:numbers:}\:5\times \:4=20\)

\(=\frac{7}{20}\)

Answer = 7/20

~Learn with Lenvy~

Answer:

5? i think i got it wrong

Step-by-step explanation:

Answer:

21.333

Step-by-step explanation:

Answer:

tje answer is (2,-1) to this

The surface area of the triangular prism is 924 cm².

What is the triangular prism?

When a prism has three rectangular sides and two triangular bases, the prism is said to be triangular. A pentahedron, that is.

Volume is calculated using the formula volume = 0.5 * b * h * length, where b is the triangle's base length, h is its height, and length is the prism length.

                                         Area is defined as length * (a + b + c) + (2 * base area), where a, b, and c are the triangle's sides and base area is the triangle's base area.

The surface area is equal to the area of the two triangles + area of the three rectangles.

Area of two triangles:

12 × (9+5) × 1/2

= 84

84(2) = 168

Area of the three rectangles:

15 × 20 + 13 × 20 + 14 × 20

= 840

840 + 84

The surface area of the triangular prism is 924 cm².

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To solve graphically this set of equations, we should first draw both lines and see the value of x at which the lines crosses

Both graphs can be drawn as follows

We can see that both graphs intersect at a negative value of x. With a more accurate graph, we can determine that both lines intersect at x=-2.

So the solution for this system of equation is x=-2.

The surface area equation simplifies to 4πa².

The surface area of the part of the cylinder y² + z² = a² that lies inside the cylinder x² y² = a² can be calculated using the equation 4πa². This equation considers the two-dimensional curved surface area of a cylinder and uses the variable a as the radius of the cylinder.

To explain this in more detail, first, consider the definition of a cylinder as a three-dimensional solid figure with two circular faces whose perpendicular line segments are equal in length.

Then, the formula for the surface area of a cylinder is the sum of the area of its two circular faces, each equal to πr², plus the area of its curved surface, equal to 2πrh, where r is the radius and h is the height of the cylinder. In this case, the cylinder has the same radius and height,

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ANSWER:

The surface area of the figure is 574 in^2

STEP-BY-STEP EXPLANATION:

We have that the surface area of a rectangular prism is given by the following formula

replacing:

A.

a number that can be written as a fraction but not as a decimal I think

Answer:

uhm the x would be the -7 since she's going to be taking that off and it says she will be paying 224 so its y=-7x+224 (harder to explain than i thought, im sorry if this don't help:(..)

Answer:

y = -7x + 224

Step-by-step explanation:

First off, the m-value.

The m-value is the constant rate at which something changes. For example, if I had 43 bananas and I subtracted 7 each week, the constant rate at which it changed would be -7. Another way to think about it is the amount of something you subtract per period. According to my last example, you subtract 7 each period, which would be a week. This is also called the slope, which is the rate of change, but I'm assuming you won't analyze these graphs until later. Using the situation presented in the problem, the constant rate at which the gym subtracts from Lucy's account is -$7 per period, which is each time Lucy goes to the gym.

Secondly, the b-value, also known as the y-intercept. This is your starting point. Using my last example, I am starting at 43 bananas. Using the example from the problem, Lucy pays $224 dollars in advance to the gym. So, her starting point is $224.

(you don't need to read this if you don't want to, but it might be helpful!) The reason we use this equation is to be able to find the value of x or y at a given point. X is usually time, which is an independent variable, and y is dependent on the situation. In this one, it is how much money Lucy has spent at the gym. So, for example, if you wanted to find out how many trips to the gym it would take for Lucy to run out of her initial amount, $224, you would plug in 0 for y and solve for x.

0 = -7x + 224      *add 7x to the other side, in order to reverse the negative*

7x = 224        *divide by 7 on both sides*

x = 32 trips to the gym

Another way you could use it is if you wanted to find out how much money Lucy had left after she went to the gym 4 times. You would plug in 4 for x.

y = -7*(4) + 224    

y = -28 + 224         *multiply -7 by 4*

y = 224- 28             *adding a negative is like subtracting a positive*

y = $196                  

Hope this helps!

The sum of an arithmetic sequence given a partial sum is 35532.

Firstly, we need to identify the common difference of the arithmetic sequence. This can be done by finding the difference between any two consecutive terms. In this case, subtracting 9 from 3 gives us a common difference of 6.

Next, we determine the number of terms in the sequence. To do this, subtract the first term from the given partial sum and divide the result by the common difference. In this case, subtracting 3 from 639 and dividing by 6 gives us 106 terms.

Finally, we can calculate the sum using the arithmetic series formula: Sn = (n/2)(2a + (n-1)d), where Sn represents the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we have Sn = (106/2)(2*3 + (106-1)*6). Simplifying this expression, we find that the sum of the arithmetic sequence is 35532.

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Answer:

\(volume = 2304\pi \ mm^3\\\\volume = 7234.56 \ mm^3\)

Step-by-step explanation:

Radius , r = 12mm

\(Volume = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (12^3)\\\\\)

                      \(=\frac{4}{3} \pi \times 1728\\\\= 4\pi \times 576\\\\= 2304 \pi \ mm^3\\\\or \\\\= 7234.56 \ mm^3\)

Answer:I don’t understand too

Step-by-step explanation:

Sorry I can’t help you

Answer:

44%

Step-by-step explanation:

Total number of students = 100

Number of girls = 49

So,

Number of boys = Total number of students - Number of girls = 100 - 49 = 51

Number of girls liking biology the best = 22

Number of girls liking chemistry = 21

Total number of students liking chemistry = 35

So,

Number of boys liking chemistry = 35 - 21 = 14

Number of boys liking Physics = 15

Number of boys liking biology = Total number of boys - Number of boys liking Physics - Number of boys liking Chemistry = 51 - 14 -15 = 22

Total number of students (girls and boys) liking biology the best =  Number of boys liking Biology +  Number of girls liking Biology = 22 + 22 = 44

Percentage of students who prefer bio = \(\frac{44}{100} \times 100 = \bold{44\%}\)