What describes the number and type of the roots of the equation 4x+7=0

a. 1 imaginary root
b. 1 real root and 1 imaginary root
c. 2 real roots
d. 1 real root

Answer:

13 / 204; No, they are dependent events

Step-by-step explanation:

Total number of cards in the deck = 52

Total number of spades in the deck = 13

Total number of hearts in the deck = 13

Part 1: Calculating the Probability

Picking up the first card:

When picking the first card i.e spade, we have the option to pick 13 cards out of 52. So the probability will be 13/52

When first card is picked, the total number of cards will be reduced to 51 because we are not placing the card back in the deck

Picking up the second card:

When picking up the second card i.e. heart, we have the option to pick 13 cards out of 51. So the probability will be 13/51

The probability of picking a spade and then a heart is = 13/52 x 13/51 = 13/204

Part 2: Independent or Not

Note that, picking up a spade and not replacing it back is changing the probability of picking up a heart. In normal cases, picking up a heart from a deck will have the probability of 13/52, but since the we are not placing the card back the probability is changed to 13/51

Since, the probability of picking a heart is being changed by the previous event, we say that the two events are dependent.

Therefore, the correct answer will be final option: 13 / 204; No, they are dependent events

Answer:

Step-by-step explanation: If w is hours at Westside, then (18-w) is the number of hours taken at Pinewood.

Cost to westside = 98w. Cost to Pinewood = 115(18-w).

Total cost = 98w + 115(18 - w) = 2070 - 17w.

[I guess there should be some constraints like 0 > w > 18]

I put it as "greater than" rather than "greater than or equal" because the problem states he takes classes at both schools, hence he has to take at least something at Westside, and similarly he has to take something at Pinewood so he would not take all 18 hours at Westside.

Answer:

98 × w + $115(19-w)

Step-by-step explanation:

We are given that Alan takes classes at both Westside Community College, where class fees are $98 per credit hour, and Pinewood Community College, where class fees are $115 per credit hour.

If Alan is taking a total of 19 credit hours at the two mentioned schools, we are to write an expression for the combined total dollar amount he paid for his class fees.

Considering the fees per credit hour mentioned for each school, we can write the total payed fees as:

[tex]98 \times w + $115(19-w)[/tex]

1<x<6 or its x>1 and x>6

The solution to the compound inequality is given by:

                       [tex]1\leq x<6[/tex]

The compound inequality is given by:

[tex]3x-8\geq -5[/tex] and

[tex]2x-7<5[/tex]

[tex]3x-8\geq -5[/tex]

on adding both side of the inequality by 8 we get:

[tex]3x\geq -5+8\\\\i.e.\\\\3x\geq 3[/tex]

Now on dividing both side of the inequality by 3 we get:

[tex]x\geq 1[/tex]

[tex]2x-7<5[/tex]

On adding both side of the inequality by 7 we get:

[tex]2x<5+7\\\\i.e.\\\\2x<12[/tex]

on dividing both side of the inequality by 2 we get:

[tex]x<6[/tex]

Hence, the solution of the compound inequality is:

                    [tex]1\leq x<6[/tex]

Answer: option c

Step-by-step explanation:

By definition, you can calculate the slope of  line by applying the formula shown below:

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

Then:

You can see that in the option C the equation of the slope is applied correctly:

[tex]\frac{9-(-3)}{1-(-2)}[/tex]

Where:

[tex]y_2=9\\y_1=-3\\\\x_2=1\\x_1=-2[/tex]

Then, you obtain the following value of the slope of the line:

[tex]m=\frac{9-(-3)}{1-(-2)}=4[/tex]

Answer: Your correct answer should be C, [tex]\frac{(9 - (-3))}{(1 - (-2))}[/tex]

Step-by-step explanation:

Recall the slope equation is: (y2 - y1)/(x2 - x1) or [tex]\frac{(y2 - y1)}{(x2 - x1)}[/tex]. You need two points: point one (x1, y1) and point two (x2, y2).

* The first answer choice is flawed because not only is it in a different formula (xs are in the numerator instead of the denominator area), but it says 1 - 2 when it should be 1 - (-2) or 1 + 2.

* The second answer choice is flawed because it is in a different formula (this time, x1 - x2/y3 - y2) and 2 - 1 is suppose to be -2 - 1.

* The last answer is flawed because it should be -3 - (-) 11 and -2 - (-)4, or -3 + 11 and -2 + 4.

Note: If you had a negative operation and a negative number behind it, you can either formulate the equation like x - (-) y or drop the negative sign from said number and change the minus operation sign to the plus one (x + y).

The only answer choice that checks out and is not flawed is C.

Answer:

38.4

Step-by-step explanation:

1. Pythagorean Theorem: 4.5²+ x²= 12²→  20.25 + x² = 144→ 144-20.25= 123.75

2. Square root 123.75, number wont be perfect, just round. (11.1)

3. Use inverse cos, sin, or tan. Answer will be the same.

360 is the answer for sure

Answer:

Choice B is correct

Step-by-step explanation:

The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.

Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;

[tex]r=\frac{k}{1-4sin(theta)}[/tex]

The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;

k= 4*6 = 24

The polar equation is thus given by alternative B

Answer:

B

Step-by-step explanation:

edge

did you mean to put. y= -1/2x+2 for choice b? because that's what I got as a solution

Answer:

B) A rectangle with a length of 15 cm and a width of 9 cm

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

Verify each cases

case A) A rectangle with a length of 9 cm and a width of 6 cm

[tex]\frac{10}{9}\neq \frac{6}{6}[/tex]

therefore

The rectangle case A) is not similar to rectangle A

case B) A rectangle with a length of 15 cm and a width of 9 cm

[tex]\frac{10}{15}=\frac{6}{9}[/tex]

[tex]\frac{2}{3}=\frac{2}{3}[/tex]

therefore

The rectangle case B) is  similar to rectangle A

case C) A rectangle with a length of 14 cm and a width of 7 cm

[tex]\frac{10}{14}\neq \frac{6}{7}[/tex]

therefore

The rectangle case C) is not similar to rectangle A

case D) A rectangle with a length of 12 cm and a width of 8 cm

[tex]\frac{10}{12}\neq \frac{6}{8}[/tex]

therefore

The rectangle case D) is not similar to rectangle A

Answer:

A rectangle with a length of 15 cm and a width of 9 cm.

Step-by-step explanation:

In similar rectangles, the ratios of the corresponding sides are equal.In similar rectangles, the ratios of the corresponding sides are equal.

[tex]\frac{length}{width}[/tex] → [tex]\frac{10}{6}[/tex] = [tex]\frac{5}{3}[/tex]  and [tex]\frac{15}{9}[/tex] = [tex]\frac{5}{3}[/tex]

Answer:

p:a

Step-by-step explanation:

given: AB=c, BC=a, CA=b

          PQ=r, QP=p, PR=q

  also , ∠CAB ≅ ∠RPQ,--------- (1)

          , ∠ABC ≅ ∠RQP,---------(2)

    and, ∠ACB ≅ ∠QRP,---------(3)

FROM (1), (2) AND (3),

we can say that a=p, b=q, c=r

therefore, the triangles are congruent (S.S.S congruence criteria),

also then, r:c=1

then the ratio equal to r:c, will be p:a ( since p=a and p:a would be =1)    

Answer:

i believe that the answer is P:A if it is not I'm sorry

Step-by-step explanation:

Answer:

y = -3

Step-by-step explanation:

First, subtract 44 from both sides of the equation to set it equal to 0. This will give you 6 + 2y = 0. Then, subtract 6 from both sides, leaving you with 2y = -6. Then just divide both sides by 2 to isolate the y and give you your answer. -6 divided by 2 is -3. y = -3

Answer:

[tex]I=\frac{13xr}{1,200}[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Simple interest Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal form

t is Number of Time Periods in years

in this problem we have

[tex]t=(13/12)\ years\\ P=\$x\\r=(r/100)[/tex]

substitute in the formula above

[tex]I=x(r/100)(13/12)[/tex]

[tex]I=\frac{13xr}{1,200}[/tex]

Final answer:

To calculate simple interest for x dollars at an rate of r percent over 13 months, convert r percent to a decimal and time to years, then use the formula I = x × (r/100) × (13/12). For example, $100 at 5% interest for 13 months would earn approximately $5.42 in simple interest.

Explanation:

The calculation of simple interest for a principal of x dollars at a rate of r percent over 13 months involves a few straight-forward steps. The formula for the simple interest is given by:

I = P × r × t

Where I represents interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time the money is invested or borrowed for, in years.

To convert the rate r percent to a decimal, divide by 100. Then, convert the time of 13 months to years by dividing by 12.

Thus, the simple interest formula for this question becomes:

I = x × (r/100) × (13/12)

For example, if you deposit $100 into a savings account with a simple interest rate of 5% for 13 months, the interest earned would be calculated as follows:

I = 100 × (5/100) × (13/12)

This results in:

I = 100 × 0.05 × 1.08333

I = $5.42 (approximately)

The simple interest earned, in this case, would be approximately $5.42.

Answer:

The correct answer option is P (both green) = 91 / 435

Step-by-step explanation:

We are given that in a jar containing 30 marbles, 10 are red, 6 are black and 14 are green.

Two marbles are drawn and the second one is drawn without returning the first marble and we are to find the probability of getting green marbles both time.

P (both green) = [tex] \frac { 1 4 } { 3 0 } \times \frac { 1 3 } { 2 9 } [/tex] = 91 / 435

ANSWER

D. 25 feet

EXPLANATION

The height of the wall,h, the taut wire and the distance from the base of the pole to the point on the ground, formed a right triangle.

According to the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.

Let the hypotenuse ( the length of the ) taught wire be,l.

Then

[tex] {l}^{2} = {h}^{2} + {b}^{2} [/tex]

[tex]{l}^{2} = {20}^{2} + {15}^{2} [/tex]

[tex]{l}^{2} = 400 + 225[/tex]

[tex]{l}^{2} = 625[/tex]

[tex]l= \sqrt{625} = 25ft[/tex]

Answer:

25

Step-by-step explanation:

Answer:

In repeated sampling, 95% of the intervals constructed would contain the population mean.

Answer:

B. -12

Step-by-step explanation:

The given limit are;

[tex]\lim_{x \to -11} f(x)=-3[/tex] and [tex]\lim_{x \to -11} g(x)=4[/tex]

We want to find;

[tex]\lim_{x \to -11} (fg)(x)=\lim_{x \to -11} f(x)\times \lim_{x \to -11} g(x)[/tex]

We substitute the given limits to obtain;

[tex]\lim_{x \to -11} (fg)(x)=-3\times 4[/tex]

[tex]\lim_{x \to -11} (fg)(x)=-12[/tex]

Answer:

B

Step-by-step explanation: EDGE 2020

ANSWER

y=7

EXPLANATION

The horizontal asymptote of an exponential function

[tex]f(x)= a {(b)}^{x} + c[/tex]

is y=c.

The given exponential function is

[tex]f(x)= 4 {(52)}^{x} + 7[/tex]

When we compare to

[tex]f(x)= a {(b)}^{x} + c[/tex]

c=7, therefore the horizontal asymptote is y=7.

Answer:

The answer is d

Step-by-step explanation:

A line segment is a portion of an infinite line separated by two end points

To create 16.25 gallons of a certain shade of blue paint, based on a ratio of 1.5 quarts of blue to 5 quarts of white, one would need to mix 15 quarts of blue paint with 50 quarts of white paint.

The student is asking how to scale a recipe for paint, which involves a ratio of blue paint to white paint, to create a specific amount of a new shade of blue. Given that the original ratio is 1.5 quarts of blue paint to 5 quarts of white paint, and the goal is to mix up 16.25 gallons of this shade, we need to calculate the amount of each color needed.

Step-by-Step Explanation:

First, identify the total number of quarts needed since the question includes quarts and gallons. Since there are 4 quarts in a gallon, multiply 16.25 gallons by 4 to convert to quarts.
16.25 gallons  imes 4 = 65 quarts

Next, calculate the ratio of blue to total quarts, and white to total quarts. The original recipe has 1.5 quarts of blue paint out of a total of 6.5 quarts, as 1.5 quarts of blue plus 5 quarts of white equals 6.5 quarts.

Determine the proportions: Blue Paint = (1.5 / 6.5) times Total Quarts and White Paint = (5 / 6.5) times Total Quarts.

Calculate the required amounts: Blue Paint = (1.5 / 6.5) times 65 quarts = 15 quarts and White Paint = (5 / 6.5) times 65 quarts = 50 quarts.

In conclusion, to mix 16.25 gallons of the shade of blue paint, 15 quarts of blue paint and 50 quarts of white paint are required.

You would need 19.5 quarts of blue paint and 65 - 19.5 = 45.5 quarts of white paint to make a total of 16.25 gallons of the shade of blue paint.

To find out how much of each color should be mixed, we first need to convert the total amount needed into quarts.

16.25 gallons * 4 quarts/gallon = 65 quarts

Now, since the ratio of blue paint to white paint is 1.5:5, we can set up a proportion to find out how much of each color should be used:

1.5/5 = x/65

Cross multiplying:

5x = 1.5 * 65

5x = 97.5

x = 97.5 / 5

x = 19.5

So, you would need 19.5 quarts of blue paint and 65 - 19.5 = 45.5 quarts of white paint to make a total of 16.25 gallons of the shade of blue paint.

Answer:

see attachment.  

Step-by-step explanation

see attachment

1 yard = 3 feet.

Multiply the length of the truck by 3 to get total feet:

6 x 3 = 18 feet.

Subtract the length of the truck from the length of the parking space:

20 - 18 = 2 feet

1 foot = 12 inches.

Multiply 2 feet by 12:

2 x 12 = 24 inches longer.

Answer:

The value of x = -0.46

Step-by-step explanation:

∵ [tex]4e^{5x}-e^{-x}=-3e^{2x}[/tex] ÷ [tex]e^{-x}[/tex]

∴ [tex]\frac{4e^{5x}}{e^{-x}}-\frac{e^{-x}}{e^{-x}}=\frac{-3e^{2x}}{e^{-x}}[/tex]

* Subtract the power of the same bases

∴ [tex]4e^{6x}-1=-3e^{3x}[/tex]

* Let [tex]e^{3x}=y[/tex]

∴ [tex]e^{6x}=y^{2}[/tex]

∴ 4y² - 1 = -3y

∴ 4y² + 3y - 1 = 0 ⇒ factorize

∴ (4y - 1)(y + 1) = 0

∴ y + 1 = 0 ⇒ y = -1

∴ 4y - 1 = 0 ⇒ 4y = 1 ⇒ y = 1/4

∵ [tex]y=e^{3x}[/tex]

∴ y = -1 refused ([tex]e^{ax}[/tex] never gives -ve value)

∴ [tex]e^{3x}=1/4[/tex] ⇒ insert ln in both sides

∵ [tex]lne^{ax}=axln(e)=ax[/tex] ⇒ ln(e) = 1

∴ 3xln(e) = ln(1/4)

∴ 3x = ln(1/4)

∴ x = [ln(1/4)] ÷ 3 = -0.46

Answer:

Step-by-step explanation:

[tex]sin (\frac{\pi}{2} - x) = cos x \\\\ sin (a - b) = sin a.cos b - sin b.cos a \\\\ sin (\frac{\pi}{2} - x) = sin \frac{\pi}{2}.cos x - sin x.cos \frac{\pi}{2} \\\\ sin \frac{\pi}{2} = 1; cos \frac{\pi}{2} = 0 \\\\ sin (\frac{\pi}{2} - x) = 1.cos x - sin x.0 \\\\ sin (\frac{\pi}{2} - x) = cos x[/tex]

I hope I helped you.

By substituting a = π/2 and b = x into the trigonometric subtraction formula and considering that sin(π / 2) equals 1 and cos(π / 2) equals 0, we can verify the identity sin((π / 2) – x) = cos x

The question asks us to use the trigonometric subtraction formula for sine to verify the identity: sin((π / 2) – x) = cos x. From the trigonometric subtraction formulas, we know that sin(a - b) = sin a cos b - cos a sin b.

In this case, a = π/2 and b = x. Substituting these values into the formula, we ge: sin((π / 2) - x) = sin(π / 2) cos x - cos(π / 2) sin x.

Since sin(π / 2) equals 1 and cos(π / 2) equals 0 (from the Unit Circle in trigonometry), our equation simplifies to:  sin((π / 2) - x) = 1 * cos x - 0 * sin x, which further simplifies to sin((π / 2) - x) = cos x.

https://brainly.com/question/31837053

#SPJ11

Answer:

See below  

Step-by-step explanation:

14)

 14² =   8² + TV²

196 = 64  + TV²

TV² = 132

TV =√132 = √(4 × 33) = 2√33

sinA = TV/AT   = (2√33)/14 = √33/7

cosA = AV /AT = 8/14          = 2/7

tanA = TV/AV   = (2√33)/8  = √33)/4

sinT = AV/AT   = 8/14          = 4/7

cosT = TV/AT   = (2√33)/14 = √33/7

tanT = AV/TV   = 8/(2√33)   = (4√33)/33

16)

  6² = 3² + GT²

 36 = 9   + GT ²

GT² = 27

GT  = √27 = √(9 × 3) = 3√3

sinA = GT/AT  = (3√3)/6 = √3/2

cosA = AG/AT = 3/6        = ½

tanA = GT/AG = (3√3)/3 = √3

sinT = AG/AT = 3/6        = ½

cosT = GT/AT = (3√3)/6 = √3/2

tanT = AG/GT = 6/(3√3) = (2√3)/3

18)

 13² =   8² + TX²

169 = 64  + TX²

TX² = 105

TX  = √105

sinA = TX/AT  = (√105)/13

cosA = AX/AT = 8/13

tanA = TX/AX  = (√105)/8

sinT = AX/AT  = 8/13

cosT = TX/AT  = (√105)/13

tanT = AX/TX  = 8/(√105) = (8√105)/105

Answer:

It's A.

Step-by-step explanation:

5x2 + 60x = 0

5x is the GCF so:

5x(x + 12 ) = 0

5x = 0, x + 12 = 0

x =0, x = -12.

Answer:

The correct option is 1.

Step-by-step explanation:

The given quadratic equation is

[tex]5x^2+60x=0[/tex]

Taking out the common factors.

[tex]5x(x+12)=0[/tex]

Using zero product property, equate each factor equal to 0.

[tex]5x=0\Rightarrow x=0[/tex]

[tex]x+12=0\Rightarrow x=-12[/tex]

The solutions of the given equations are x=0 and x=-12.

Therefore the correct option is 1.

Answer: first option

Step-by-step explanation:

To form an arithmetic sequence, you have that for the sequence [tex]7,6k,22[/tex]:

[tex]6k-7=22-6k[/tex]

Therefore, to calculate the value of k to form an arithmetic sequence, you must solve for k, as following:

- Add like terms:

[tex]6k+6k=22+7\\12k=29[/tex]

- Divide both sides by 12. Then you obtain;

[tex]k=\frac{29}{12}[/tex]

Answer:

[tex]k=\frac{29}{12}[/tex]

Step-by-step explanation:

The given sequence is 7, 6k, 22.

For this to be an arithmetic sequence, there must be a common difference.

[tex]6k-7=22-6k[/tex]

Group similar terms;

[tex]6k+6k=22+7[/tex]

Simplify;

[tex]12k=29[/tex]

Divide by 12

[tex]k=\frac{29}{12}[/tex]

[tex]f'(x)\ge0[/tex] for all [tex]x[/tex] in [-3, 0], so [tex]f(x)[/tex] is non-decreasing over this interval, and in particular we know right away that its minimum value must occur at [tex]x=-3[/tex].

From the plot, it's clear that on [-3, 0] we have [tex]f'(x)=-x[/tex]. So

[tex]f(x)=\displaystyle\int(-x)\,\mathrm dx=-\dfrac{x^2}2+C[/tex]

for some constant [tex]C[/tex]. Given that [tex]f(0)=7[/tex], we find that

[tex]7=-\dfrac{0^2}2+C\implies C=7[/tex]

so that on [-3, 0] we have

[tex]f(x)=-\dfrac{x^2}2+7[/tex]

and

[tex]f(-3)=\dfrac52=2.5[/tex]

Answer:The Time (period) is 0.003 s

Step-by-step explanation:

The period is equal to Time.

the formula for calculating Time (period) is:

Time (period)= 1/frequency

frequency= 293 hz

Time (period) = 1/293

                      = 0.003 s

Answer:

Period = 0.0034 seconds

Step-by-step explanation:

It is given that,

The d string on a violin has a frequency of 293 Hz when it is in tune. We have to find its period. The relationship between the time period and the frequency is given by :

[tex]T=\dfrac{1}{\nu}[/tex]

Here, [tex]\nu=293\ Hz[/tex]

So,

[tex]T=\dfrac{1}{293\ Hz}[/tex]  

T = 0.0034 seconds

Hence, the period of the d string on a violin is 0.0034 seconds.

Answer:

60

Step-by-step explanation:

Since it turns 30 degrees each hour, it is simply 2 * 30 which is 60.

Answer:

6.63 cm

Step-by-step explanation:

The segments within the circle form a right angle. Triangle CRS as a right triangle must follow the Pythagorean theorem which says the square of each leg adds to the square of the hypotenuse.

a² + b² = c²

Here a is unknown, b = 10 and c = 12.

a² + 10² = 12²

a² + 100 = 144

a² = 44

a = √44 = 6.63