Given the equation 2x² - 5x + 7 = 0. Find the discriminant. Describe the roots and explain your reasoning.

Answer:

Option D.

Step-by-step explanation:

The given expression is

[tex]\dfrac{(5ab)^3}{30a^{-6}b^{-7}}[/tex]

We need to find the expression, which is equivalent to the given expression.

The given expression can be rewritten as

[tex]\dfrac{5^3a^3b^3}{30a^{-6}b^{-7}}[/tex]     [tex][\because (ab)^m=a^mb^m][/tex]

[tex]\dfrac{125}{30}\times \dfrac{a^3}{a^{-6}}\times \dfrac{b^3}{b^{-7}}[/tex]

[tex]\dfrac{25}{6}\times a^{3-(-6)}\times b^{3-(-7)}[/tex]    [tex][\because \dfrac{a^m}{a^n}=a^{m-n}][/tex]

[tex]\dfrac{25}{6}\times a^{3+6}\times b^{3+7}[/tex]

[tex]\dfrac{25a^9b^{10}}{6}[/tex]

Therefore, the correct option is D.

Answer:

The correct option is D

Step-by-step explanation:

Answer: OA) (4, -2), (-2, 2), (2, -2), (4, 2)

Step-by-step explanation:

Answer:

Erica has 51 action figures and Ricardo has 17 action figures.

Step-by-step explanation:

First, label your variables.

x=the number of action figures Erica has

y=the number of action figures Ricardo has

You know that they have 68 total action figures so x+y=68.

Erica has 3 times as many as Ricardo so 3y=x. Then solve for x and y.

x+y=68    3y=x   (Substitue 3y for x)

3y+y=68   (Then combine like terms)

4y=68  (Divide each side by 4)

y= 17

Now that you know that Ricardo has 17 action figures, you can plug 17 in for y in either equation to find x.

3(17)=x

x=51

To check your answers, you can plug them back into the original equations.

Answer:

Erica:51 action figures; Ricardo: 17 action figures

Reason:

68/4=17

17*3=51<- this is the amount of action figures that Erica has.

17 <-this is the amount of action figures that Ricardo has.

17 (Ricardo) + 51 (Erica) = 68 (total amount)

Answer:

see below

Step-by-step explanation:

3 ^ ( 6/5)

The base a is 3

The power is 6 which is b

the root is 5 which is c

[tex]\sqrt[5]{3^6}[/tex]

Answer:

The dimensions of the rectangular room is 48 ft by 20 ft

Step-by-step explanation:

Drawing a Diagonal line in a rectangle forms two right angle triangles

The diagonal line will represent the hypotenuse

In a right angle triangle:

Hypotenuse^2= adjacent^2+opposite^3

One wall measures 28 ft longer than the adjacent wall.

Let the adjacent=x ft

Opposite=28+x ft

Hypotenuse=52 ft

Hypotenuse^2= adjacent^2+opposite^3

52^2 = x^2 + (28+x)^2

2704 =x^2 + 784 + 56x + x^2

2704=2x^2+784+56x

2x^2+56x+784-2704=0

2x^2+56x-1920=0

Solve the quadratic equation using the quadratic formula

x= -b +or- √b^2-4ac / 2a

a=2

b=56

c=-1920

x= -b +or- √b^2-4ac / 2a

= -56 +or- √56^2 - (4)(2)(-1920) / (2)(2)

= -56 +or- √3136 - (-15,360) / 4

= -56 +or- √3136+15,360) / 4

= -56 +or - √ 18496/ 4

= -56 +or- 136 / 4

x= -56 + 136 / 4

=- 56/4 + 136/4

= -14+34

=20

OR

x= -56 - 136/4

= -56/4 - 136/4

= -14 - 34

= -48

The value of x can't be negative, so will use the positive value of x which is 20

Recall,

Adjacent=x

=20 ft

Opposite=28+x ft

=28+20

=48 ft

The dimensions of the rectangular room is 48 ft by 20 ft

Answer:

The fourth one

Step-by-step explanation:

Only the first one x and y interval 1, 2. The rest aren't linear.

Answer:

Step-by-step explanation:

it is the fourth one

Hello there! :)

Answer:

y = -4x.

Step-by-step explanation:

Begin by finding the slope of the line using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in two points on the graph. We can use the points (-1, 4) and (0, 0):

[tex]m = \frac{0 - 4}{0 - (-1)}[/tex]

Simplify:

m = -4.

Therefore, the equation of this line in slope-intercept form (y = mx + b) is:

y = -4x.

Answer:

a) P(X=x) = p× (1-p)^(x-1)

b) P(X=3) = 0.081

c) P(X≤5) = 0.40951

d) Mean of X= 10

e) Var(X)= 90

Step-by-step explanation:

This is a question on geometric distribution.

In geometric distribution, we have two possible outcomes for each trial (success or failure) for independent number of binomials series trial. Also the probability of success is constant for each trial.

This discrete probability distribution is represented by the probability density function: f(x) = p× (1-p)^(x-1)

For a random variable with a geometric distribution, we do not know the number of trials we will have = {1, 2, 3, ...}

We stop the trials when we get a success.

From the question, there are 10 numbers

The probability of success = p = 1/10

For the solutions of the question from (a-e), See attachment below.

f(x) = P(X= x)

Where P(X= x) is the probability of X taking on a value x

Answer:

A. -259

B. inverse function is 1/2 √(-x-3)

Step-by-step explanation:

Here, we want to find f(8)

Simply substitute x = 8 in the equation.

The equation is

f(x) = -4x^2 -3

So f(8) = -4(8)^2-3

f(8) = -256-3

f(8) = -259

Inverse of f(x) = -4x^2 -3

Simply equate this to m

m = -4x^2-3

-4x^2 = m + 3

x^2 = (m + 3)/-4

x^2 = -m/4 -3/4

x = √(-m-3)/4

x = 1/2√(-m-3)

Put back the value of x for m

x = 1/2 √(-x-3)

Answer:

38/21 or 1.80952381

Step-by-step explanation:

Answer:

(76/3) / 14 OR AROUND 9/5

Step-by-step explanation:

So I'm assuming this equation is (76/9) / (14/3)

We can solve this in a simple way instead of a hard way -->

9 and 3 can cancel out to 3 and 1 so we have (76/3) / (14)

76/3 = 25 1/3 --> 25 1/3 / 14 If you simplify this it's around 1 4/5 or 9/5

Hope this helps!

Answer:

1) To calculate length of fringe, we need to find the perimeter

The question does not clearly say how much is length and width

Assuming length = 245 and width = 234 inches

P = 2(length + width)

P = 2 ( 245 + 234)

P = 2 (479)

P = 958 inches

2) To calculate length of fringe, when length is increased by 33 inches

P = 2 ( l + w)

P = 2 (278 + 234)

P = 2 x 512

P = 1024 inches

Answer:

D.(-4,-8) and(2,4)

Step-by-step explanation:

y=-2x

y=x²-8

this means that the two equations are equal because they both add up to y

thus; x²-8=-2x

formulae=Ax²+bx+c=0

x²+2x-8=0

find two numbers which multiplied will give you x² and when added will give you 2x that is x and x

x²+x+x-8=0

x(x+1)+1(x-8)=0

(x+1)(x-8)=0

1)x+1=0. x= -1

1)y=-2x

y=-2(-1)=2

y=2

2)y=x²-8

y=1²-8= -8

y= -8

note*this means that the answer should have both 2 and -8 thus d is the answer

Answer:

Y= -9, -4, 1, and 11

Step-by-step explanation:

You substitute in the numbers on the left (under x) into the equation to find y.

6% of $14.00=$0.84 so the total cost of shorts=$14.84

6% of $25.00=$1.50 so the total cost for soccer ball=$26.50

6% of $10.00=$0.60 so the total cost of shin guards=$10.60

$60.00+$104.94+$109.94+$115.54+$120.54=$510.96

36% of $510.96=$183.95 so the total cost of cleats=$694.91

694.91+$10.60+$26.50+$14.84=$746.85

$746.85+$5=$751.85

Answer:

its option d $120.54

Step-by-step explanation:

ALSOOOO a braddison shipper :)

Answer:

x≤7.8  ⇒(-∞;7.8]

x<7.8  ⇒ (-∞;7.8)

x>7.8  ⇒ (7.8; ∞)

x≥7.8  ⇒ [7.8; ∞)

Step-by-step explanation:

Hi, to answer this question we have to analyze each expression:

• x≤7.8

The solution is all the numbers less or equal to 7.8, since it can be equal to 7.8, it includes 7.8 , we have to use closed brackets

(-∞;7.8]

• x<7.8

All the numbers less than 7.8 , it excludes the endpoint , it's an open interval (parenthesis)

(-∞;7.8)

• x>7.8

All the numbers higher than 7.8, open interval (parenthesis)

(7.8; ∞)

• x≥7.8

All the numbers higher or equal to 7.8, closed interval (closed brackets for the endpoint)

[7.8; ∞)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of a sphere is

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

Where r is the radius

diameter = radius × 2

To find the diameter we must first find the radius

Volume = 34cm³

That's

[tex]34 = \frac{4}{3} \pi {r}^{3} \\ \\ 34 \times 3 = 4\pi {r}^{3} \\ \\ 102 = 4\pi {r}^{3} \\ {r}^{3} = \frac{102}{4} \pi \\ \\ r = \sqrt[3]{ \frac{51}{2\pi}} \\ \\ r = 2.01 \\ \\ r = 2.0 cm[/tex]

Diameter = 2 × 2cm

Hope this helps you

Answer:

The answer is 4

Step-by-step explanation:

Answer:

-4 points

Step-by-step explanation:

Since each incorrect answer is worth the same amount of negative points, use the equation below.

3x = -12      DIvide both sides by 3

x = -4 points  

Step-by-step explanation:

The expression:

[tex]\frac{1}{1+a} + b^{-1} + \frac{1}{1+b} + c^{-1} + \frac{1}{1+c} + a^{-1}[/tex]

It is possible that there are values for a, b, and c, but are omitted. If this is not the case, then the expression can be rewritten in another form. These are about all that can be done.

The second case is more plausible, given there are no values given for a, b, and c.

The expression can be rewritten as:

[tex]a^{-1}+b^{-1}+c^{-1} + \frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c}[/tex]

When a number has an index of -1, it is the same as taking the reciprocal of the number.

That is;

[tex]a^{-1} = \frac{1}{a}[/tex]

Therefore, the whole expression gives:

[tex]\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c}[/tex]

Taking the common denominator in the first three expressions, we have

[tex]\frac{a+b+c}{abc} + \frac{1}{1+a} +\frac{1}{1+b} + \frac{1}{1+c} \\[/tex]

It is also possible to take the common denominator of the whole whole expression, this will however, make the expression look more tedious, rather than simple.

The expression:

It is possible that there are values for a, b, and c, but are omitted. If this is not the case, then the expression can be rewritten in another form. These are about all that can be done.

The second case is more plausible, given there are no values given for a, b, and c.

The expression can be rewritten as:

When a number has an index of -1, it is the same as taking the reciprocal of the number.

That is;

Therefore, the whole expression gives:

Taking the common denominator in the first three expressions, we have

It is also possible to take the common denominator of the whole whole expression, this will however, make the expression look more tedious, rather than simple.

Answer:

number 1

Step-by-step explanation:

Answer:

The growth rate is 7.2%

Step-by-step explanation:

First thing we need to do here is to set up an exponential equation;

This can be written as follows;

F = I(1 + r)^t

where F is the future value = 20,000

I is the initial value = 10,000

r is the rate in percent which we want to calculate

t is time in years = 10 years

Substituting the values in the question into the exponential equation, we have;

20,000 = 10,000(1 + r)^10

divide both side by 10,000

2 = (1+r)^10

Find the 10th root of both sides

1+ r = 2^(1/10)

1 + r = 1.07177346254

r = 1.07177346254-1 = 0.07177346253

Let’s approximate r as 0.072

Now this to percentage?

That would be 72/1000 * 100% = 7.2%

Answer:

50

Step-by-step explanation:

d-nr of ducks

g- nr of goats

2*d+4*g=260

d+g=80            /*(-2)

2d+4g=260

-2d-2g=-160

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

      2g=100

      g=100/2

     g=50

Answer:

Option D is the correct option

Solution,

Let no.of ducks be X

Let no.of goats be y.

Total heads= X+y=80 ➡️ equation (i)

Total legs= 2x+4y=260➡️ equation (ii)

X= 80-y

[tex]2(80 - y) + 4y = 260 \\ or \: 160 - 2y + 4y = 260 \\ or \: 160 + 2y = 260 \\ or \: 2y = 260 - 160 \\ or \: 2y = 100 \\ or \: y = \frac{100}{2} \\ y = 50[/tex]

Number of goats= 50

Hope this helps...

Good luck on your assignment...

Answer:

Periodic phenomena means that the phenomena has a (almost) constant time period or space period.

As you know, the trigonometric functions cos(x) and sin(x) also have a constant period of 2*pi, so these functions are really useful to model periodic phenomena.

Now, the problem may be that the trigonometric functions may be useful to describe the "periodic" part, but not to describe the actual phenomena.

An example of this can be a square alternating current.

While it has a constant period like a trigonometric function, the trigonometric functions can not really model the "square" part of this current (you know that the sinusoidal functions actually are curves and continuous)

Here comes something called the Fourier Series, that are series of the form:

F(x) = a₀ + ∑(aₙ*cos(nx) + bₙ*sin(nx))

That can be used to model almost any periodic phenomena, but the actual Fourier Series may be hard to construct.

Answer:

10 to the left I believe

Step-by-step explanation:

Step-by-step explanation:

a) $410 × £0.72 = £295.20

Answer:

The gradient is the same as the slope. To find the slope, let's convert this from standard form to slope-intercept form.

4x - 3y + 5 = 0

4x + 5 = 3y

4/3x + 5/3 = y therefore the answer is 4/3.

Answer:

a. No, because she will need money a year from now. Generally, stocks are long term investments. It is very unlikely that she will get a return on her investment in a year.

Step-by-step explanation:

Stocks are a riskier investment in comparison to bonds, and may pay higher interest rates, but still require the investment to "sit" for a long period of time. Like a 3 month (APY of about .50%), 6 month (APY of about .30%), 8 month (APY of about .10%), etc. bond, stocks will not grow considerably in a short amount of time.

Answer:  

Step-by-step explanation:

Concentration            Amount of             Amount

of Solution                   Solution (L)             of Acid

    15%                                x                         0.15x

    33%                               y                         0.33y

    21%                              40                      0.21•40      

x + y = 40    ⇒  x = 40 - y

0.15x + 0.33y = 0.21•40

0.15(40 - y) + 0.33y = 0.21•40

6 - 0.15y + 0.33y = 8.4

  0.18y = 2.4

        y = 13¹/₃

x = 40 -  13¹/₃ = 26²/₃

Answer:

13.6

Step-by-step explanation:

Since it is asking for 1 decimal place, we assume that it is the tenths decimal place. Since the hundredths decimal place is ≥5, we round up to 6.

There is no such thing as ones in decimals, so I am assuming you mean tenths. If you were to round this to the tenths place, the answer would be 13.6.

13.555 → 13.6 (4 and below, leave it alone. 5 and up, round it up)\

Hope this helps!

Answer:

Its B

Step-by-step explanation:

Answer:B 4(x – 7)2 – (x – 7) + 3Step-by-step explanation: got it ridgt on test