*2. For each of the following discriminant state what it indicates about the number ofoots of the quadratic equation.a. b²-4ac=5b. b² - 4ac = 0c. b²-4ac = -10

Answer:

x = -2

Step-by-step explanation:

-3x + 4 = x + 12

Subtracting 4 from both sides:

-3x = x + 8

Subtracting x from both sides:

-4x = 8

Diving both sides by -4:

x = 8 / -4 = - (8/4) = -2

x = -2

Answer:

We conclude that:

csc (U) = 26 / 24        

Step-by-step explanation:

Given

To determine

csc (U) = ?

Using the trigonometric ration

sin Ф = opposite / hypotenuse

substituting Ф = U, opposite = 24, hypotenuse = 26

sin (U) = 24/26

We know that: csc (U) = [1 ] / [sin(U)]

Therefore,

csc (U) = [1 ] / [sin(U)]

            = 26 / 24

Therefore, we conclude that:

csc (U) = 26 / 24        

Answer:

c=2

Step-by-step explanation:

(4x^2 y^2 + 8x^3 y^5) / (2x y^2) = 4x^2 y^2 / 2x y^2 + 8x^3 y^5 / 2x y^2 = 2x + 4x^2 y^3

Therefore, a = 1, b = 0, c = 2 and d = 3

Answer:

Step-by-step explanation:

c=2

Answer:

we conclude that:

\(\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}=81\)

Step-by-step explanation:

Given the expression

\(\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}\)

\(\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}=\left(\frac{2}{54}\right)^{-\frac{4}{3}}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\)

         \(=\frac{1}{\left(\frac{2}{54}\right)^{\frac{4}{3}}}\)

        \(=\left(\frac{1}{27}\right)^{-\frac{4}{3}}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}\)

        \(=\frac{1}{\frac{1^{\frac{4}{3}}}{27^{\frac{4}{3}}}}\)

         \(=\frac{1}{\frac{1^{\frac{4}{3}}}{81}}\)      ∵ \(27^{\frac{4}{3}}=81\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}\)

         \(=\frac{81}{1^{\frac{1}{3}}}\)              

\(\mathrm{Apply\:rule}\:1^a=1\)

         \(=\frac{81}{1}\)

          \(=81\)

Therefore, we conclude that:

\(\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}=81\)

The volume of the rectangular pyramid is 64 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

V = (l)(b)(h) / 3

V = (6)(8)(4) / 3

V = 192 / 3

V = 64 cubic feet.

Hence, the volume of the rectangular pyramid is 64 cubic feet.

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The correct question is:

Answer:

the correct answer is A. 25 sandwiches.

Step-by-step explanation:

Assuming you have plenty of bread and jelly, you can make 25 sandwiches from the jar of peanut butter.

Each sandwich typically requires 2 tablespoons of peanut butter, one slice of bread with peanut butter and one slice of bread with jelly.

So, if you have 50 tablespoons of peanut butter, you can make 25 sandwiches with it, because 50 / 2 = 25.

Therefore, the correct answer is A. 25 sandwiches.

Answer: 25

Step-by-step explanation:

We have 50 tablespoons of peanut butter and we know that it requires 2 tablespoons to make a single sandwich. In order to find how many sandwiches we can make with our 50 tablespoons, we would have to do 50 divided by 2.

2+2...=50

Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

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Answer:

I think you want to us 7/9=x/21

cross multiply to get 9x =174

divide both sides by 9

x=16.3?

x being the perimeter

Step-by-step explanation:

Answer:

The greatest number of t-shirts that the Sports Committee can purchase is 232.

Step-by-step explanation:

The student council raised $2,790 during its annual fundraiser.

Each t-shirt costs $12.

The total cost of buying x t-shirts is given by:

\(T(x) = 12x\)

What is the greatest number of t-shirts the Sports Committee can purchase?

The total cost has to be lesser, or equal, to 2790. So

\(T(x) \leq 2790\)

\(12x \leq 2790\)

\(x \leq \frac{2790}{12}\)

\(x \leq 232.5\)

Since you cant buy half a shirt.

The greatest number of t-shirts that the Sports Committee can purchase is 232.

Answer:

1/2 yard of fabric

Step-by-step explanation:

To find how much fabric Madison used, all you have to do is 5/6 * 2/5 which is 1/3.

Hope this helps :)

Answer:

slope = 2 / 3

Step-by-step explanation:

slope = rise / run

rise = 2

run = 3

slope = 2 / 3

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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\(g(x) > -6\)

Graphically, we can see from the graph that \(g(x)\) is will not go less than or equal to \(-6\).

Answer:

g(x)>-6

Step-by-step explanation:

Answer:

the numbers r switched

Step-by-step explanation:

Answer:

its opposites y=1/2x+4 would be more because its adding on the other on is decreasing

Step-by-step explanation:

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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Answer:

Step-by-step explanation:

use SOH CAH TOA to remember sin cos and tan functions

Sin = oppostive/hypotenuse
Cos = adjacent/hypotenuse
Tan = opposite/adjacent

22. cos(x) = b/c
24. sin(x) = 2/2sqrt(17) = 1/sqrt(17)
26. tan(x) = 2/8 = 1/4

28. cos(y) = 2/2sqrt(17) = 1/sqrt(17)
30. sin(30)
in a 30 60 90 triangle, the side opposite 30 is 1, the side opposite 60 is sqrt(3), the side opposite 90 is 2.
sin(30) = opposite/hypotenuse = 1/2/1 = 1/2
32.
in a 45 45 90 triangle, the side opposite 45 is 1, the side opposite 45 is 1, the side opposite 90 is sqrt2.

sin = opposite/hypotenuse = 1/sqrt(2)
34. cos(30) = sqrt(3)/2

36. tan(31) = AC/9 --> AC = 9tan(31) = 5.408

Answer:

22.  \(\dfrac{b}{c}\)

24.  \(\dfrac{\sqrt{17} }{17}\)

26.  \(\dfrac14\)

28.  \(\dfrac{\sqrt{17} }{17}\)

30.  \(\dfrac12\)

32.  \(\dfrac{\sqrt{2} }{2}\)

34.  \(\dfrac{\sqrt{3} }{2}\)

36. AC = 5.41 (nearest hundredth)

Step-by-step explanation:

Using trig ratios:

\(sin(\theta)=\dfrac{O}{H}\\\\\\cos(\theta)=\dfrac{A}{H}\\\\\\tan(\theta)=\dfrac{O}{A}\)

where \(\theta\) is the angle, O is the side opposite the angle, A is the side adjacent the angle, H is the hypotenuse of a right angle

22. \(cos(x)=\dfrac{b}{c}\)

24.  \(sin(x)=\dfrac{2}{2\sqrt{17} }=\dfrac{\sqrt{17} }{17}\)

26. \(tan(x)=\dfrac{2}{8}=\dfrac14\)

28. \(cos(y)=\dfrac{2}{2\sqrt{17} }=\dfrac{\sqrt{17} }{17}\dfrac{}{}\)

30. \(sin(30)=\dfrac12\)

32. \(sin(45)=\dfrac{\sqrt{2} }{2}\)

34. \(cos(30)=\dfrac{\sqrt{3} }{2}\)

36. \(tan(31)=\dfrac{AC}{9}\)

\(\implies AC=9tan(31)=5.41\) (nearest hundredth)

Answer:

no picture i cant see

Step-by-step explanation:

rip

Answer:

there's no attachment

Step-by-step explanation:

For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.

What is function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.

A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).

Four orders of functions live functions with return values and arguments.

This function accepts arguments and gives back a result.

functions that take arguments but have no return values.

functions with return values and no arguments.

functions that have no arguments or return values.

we are given two function f( x) and g( x);

f( x) = 3x- 2 and

g( x) = x2

So, for fg( x), we've to put value of g( x) into f( x);

Hence, the equation will be;

fg( x) = 3x2- 2.

thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.

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Without knowing the total number of coins or the ratio between one dollar and two dollar coins in the jar, we cannot accurately determine the number of two dollar coins.

Amadi has a jar with both one dollar and two dollar coins. The question is asking how many of the coins in the jar are two dollar coins.
To determine the number of two dollar coins, we need more information. The question does not provide any details about the total number of coins or the ratio between one dollar and two dollar coins in the jar. Without this information, it is not possible to give an accurate answer.
If we assume that the jar contains a total of 100 coins, we can use algebra to solve for the number of two dollar coins.

Let's say the number of two dollar coins is x. Then, the number of one dollar coins would be 100 - x.
Since the value of the two dollar coins is double the value of the one dollar coins, we can set up the equation 2x + 1(100 - x) = total value of coins.
Simplifying the equation, we get 2x + 100 - x = total value of coins.
Combining like terms, we have x + 100 = total value of coins.
Since we don't know the total value of coins, we cannot solve for x. Therefore, we cannot determine the number of two dollar coins without additional information.

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Answer:

Diameter- 60.42^2

Answer:

$935.76

Step-by-step explanation:

BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?​

Step 1

We find the Present value factor of sum

The formula =

(1 + i)^n

Where

i = maturity rate = 9% = 0.09

n = number of years = 10 years

Present Value = ( 1 + 0.09)^-10

= 0.4224

Step 2

We find the present value factor of annuity

The formula is given as:

1 - (1+i)^-n / i

i = maturity rate = 9% = 0.09

n = number of years = 10 years

= 1 - (1 + 0.09)^-10 /0.09

= 1 - 0.4224 /0.09

= 0.5775 /0.09

= 6.417

Step 3

The bond's current market price is calculated as:

= PV factor of Sum × Par Value + PV factor of annuity × coupon payment

Coupon payment is calculated as:

= Coupon interest × par value

= 8% × 1000

= 80

Hence,

= 0.4224 × 1,000 + 6.417 × 80

= 422.4 + 513.36

= 935.76

In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:

\(\$935.76\)

We find the Present value factor of sum, by the formula of:

\((1 + i)^n\)

Where:

Substituting the values ​​in the formula as;

\(Present \ Value = ( 1 + 0.09)^{-10} = 0.4224\)

We find the present value factor of annuity, by the formula as:

\(1 - (1+i)^{-n} / i\)

Where:

Substituting the values ​​in the formula as;

\(= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417\)

The bond's current market price is calculated as:

\(= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment\)

Coupon payment is calculated as:

\(= Coupon\ interest * par\ value\\= 8\% * 1000= 80\)

So continue the calcule;

\(= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76\)

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Answer:

The answer is 27.

Step-by-step explanation:

When you put it in PEMDAS formation it will look like 9/3x7+6.

9/3 is equivalent to 3 so your formation will now look like 3x7+6. Next step will be 3x7 which equals 21. Your equation will now look like 21+6. And the final step is adding the 21+6, which will give you 21!

Answer:

27

Step-by-step explanation:

PEMDAS

9 divided by 3 = 3

3 x 7 = 21

21 + 6 = 27

Yes, based on the 99% confidence interval (0.297, 0.503), there is convincing evidence of a difference in the proportion of "big" bank customers who bank with more than one bank compared to the "small" customers who bank with more than one bank.

The confidence interval (0.297, 0.503) represents the range of values within which the true difference in proportions between the two customer groups is likely to fall with 99% confidence. Since the interval does not include zero (0), we can conclude that there is a statistically significant difference between the proportions.

To further explain, the confidence interval was constructed using the sample proportions and the standard error. The sample proportion for the "big" customers who bank with other banks is 160/200 = 0.8, and for the "small" customers, it is 120/300 = 0.4. The standard error takes into account the sample sizes and proportions, and it measures the uncertainty in the estimation.

Since the confidence interval does not include zero, it indicates that the true difference in proportions is unlikely to be zero. In other words, there is strong evidence that the proportion of "big" bank customers who bank with more than one bank is higher than the proportion of "small" customers who do the same.

Therefore, based on the provided data and the confidence interval, we can conclude that there is convincing evidence of a difference in the proportion of "big" bank customers who bank with more than one bank compared to the "small" customers who bank with more than one bank.

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we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.

How to solve the problem ?

The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.

To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.

Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.

Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.

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The perimeter and area of a rectangle are (5,6) and (6,5).

The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.

A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.

The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.

The perimeter of the rectangle:

P=2l+2w=22

divide 2 into both sides

l+w=11 -------------> (1)

w=11-l

Area of the rectangle:

l*w=30

l(11-l)=30

11l-l^2-30=0

l^2-11l+30=0

By factor method,

(l-5)(l-6)=0

l=5,6.

Substitute this value in w,

l=5 implies w=6

l=6 implies w=5

There we have two solutions.

The length and breadth of the rectangle is

(5,6) and (6,5).

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Answer:

c

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

This option is correct because it starts with an initial intercept of 5, and rapidly heads up, then slows down and reaches 50. Options B and C are incorrect because they are going down, which is incorrect. Option D is incorrect because the graph is constant.

Hope it helps!

Answer:

$12,938.26

Step-by-step explanation:

The equation for solving this is:

A = P(1+r/n)^nt

P = 4600

^ initial amount/principal

R = 0.09

^ rate (9% converted to a decimal)

n = 1

^ how often it is compounded (yearly, so it is 1)

t = 12

^ how long the investment is for (in years)

A = 4600(1.09)^12

A = 12,938.26

^ rounded to the nearest hundred, because when dealing with money it has to be rounded to the nearest hundred. Un-rounded the answer is 12938.2579962.

The investment will be worth $12,938.26 after 12 years.

Answer:

The area of this circle is \((\frac{\pi}{2} )\)  the area of the square.

For the uniform electric field normal to the surface, the flux through the surface is electric field multiplied by the area of this surface.

Therefore, Φsquare is \((\frac{2}{\pi} )\) ϕcircle

Step-by-step explanation:

Area of the circle is given by;

\(A_c = \frac{\pi d^2}{4}\)

Area of the square is given by;

\(A_s = L^2\)

relationship between the edge length of the square, d, and length of its side, L,

\(d = \sqrt{L^2 + L^2} \\\\d = \sqrt{2L^2}\)

But area of the square , \(A_s = L^2\)

\(d = \sqrt{2A_s}\)

Then, the area of the square in terms of the edge length is given by;

\(A_s = \frac{d^2}{2}\)

Area of the circle in terms of area of the square is given by;

\(A_c = \frac{\pi d^2}{4} = \frac{\pi}{2}(\frac{d^2}{2} )\\\\But \ A_s = \frac{d^2}{2} \\\\A_c = \frac{\pi}{2}(\frac{d^2}{2} )\\\\A_c = \frac{\pi}{2}(A_s )\)

For the uniform electric field normal to the surface, the flux through the surface is electric field multiplied by the area of this surface.

Ф = E.A

Flux through the surface of the circle is given by;

\(\phi _{circle} = E.(\frac{\pi d^2}{4})\)

Flux through the surface of the square is given by;

\(\phi _{square} = E.(\frac{d^2}{2} )\\\\\phi _{square} =E.(\frac{d^2}{2} ).(\frac{\pi}{2} ).(\frac{2}{\pi} )\\\\\phi _{square} =E.(\frac{\pi d^2}{4} ).(\frac{2}{\pi} )\\\\\phi _{square} =(\phi _{circle}).(\frac{2}{\pi} )\)

Therefore, Φsquare is \((\frac{2}{\pi} )\) ϕcircle

If the circle has the same diameter as the edge length of the square, then the area of this circle is \(\rm \dfrac{\pi }{2}\) the area of the square

The uniform electric field is normal to the surface, the flux through the surface is the electric field multiplied by the area of this surface.

Φsquare is \(\dfrac{2}{\pi}\)  ϕcircle

If the circle has the same diameter as the edge length of the square, then the area of this circle is ___________the area of the square

For the uniform electric field normal to the surface, the flux through the surface is____________the area of this surface.

Therefore, Φsquare is ________ ϕcircle .

1. If the circle has the same diameter as the edge length of the square, then the area of this circle is ___________the area of the square.

The area of the circle is;

\(\rm Area \ of \ circle = \dfrac{\pi d^2}{4}\)

The area of the square is;

\(\rm Area \ of \ square = a^2\)

The relationship between the edge length of the square, d, and length of its side a is;

\(\rm d = \sqrt{a^2+a^2}\\\\d = \sqrt{2a^2}\\\\d = \sqrt{2} a\)
The area of the circle in terms of the area of the square is;

\(\rm Area \ of \ circle = \dfrac{\pi }{2} \ Area \ of \ square\)

If the circle has the same diameter as the edge length of the square, then the area of this circle is \(\rm \dfrac{\pi }{2}\) the area of the square.

2. The uniform electric field is normal to the surface, the flux through the surface is the electric field multiplied by the area of this surface.

Ф = E.A

3. Flux through the surface of the circle is given by;

\(= \rm E\dfrac{\pi d^2}{4}\\\\=\dfrac{2}{\pi }\)

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