find the square by multiplying the polynomial
(4c + 4)²

Given

[tex]25x^{-4} - 99x^{-2} - 4 = 0[/tex]

consider substituting [tex]y=x^{-2}[/tex] to get a proper quadratic equation,

[tex]25y^2 - 99y - 4 = 0[/tex]

Solve for [tex]y[/tex] ; we can factorize to get

[tex](25y + 1) (y - 4) = 0[/tex]

[tex]25y+1 = 0 \text{ or } y - 4 = 0[/tex]

[tex]y = -\dfrac1{25} \text{ or }y = 4[/tex]

Solve for [tex]x[/tex] :

[tex]x^{-2} = -\dfrac1{25} \text{ or }x^{-2} = 4[/tex]

The first equation has no real solution, since [tex]x^{-2} = \frac1{x^2} > 0[/tex] for all non-zero [tex]x[/tex]. Proceeding with the second equation, we get

[tex]x^{-2} = 4 \implies x^2 = \dfrac14 \implies x = \pm\sqrt{\dfrac14} = \boxed{\pm \dfrac12}[/tex]

If we want to find all complex solutions, we take [tex]i=\sqrt{-1}[/tex] so that the first equation above would have led us to

[tex]x^{-2} = -\dfrac1{25} \implies x^2 = -25 \implies x = \pm\sqrt{-25} = \pm5i[/tex]

Answer:

d.)

Plot these inequalities:

Graphed below (shaded yellow region):

where all the inequalities meet or touches each other.

No solutions exist to this system of equations

A system of equations is said to be inconsistent if the two equations do not agree, meaning that there is no set of values that can simultaneously satisfy each equation. For example, the most basic inconsistent system of equations could be x = 4 a nd x = 5 at same time which is not possible.

A single equation in three unknowns can be interpreted geometrically in 3-dimensional space. If we look at a system of such linear equations, the solution set is the set of all points lying in all of the corresponding planes.

Systems of equations in three variables that are inconsistent could result from three parallel planes, two parallel planes and one intersecting plane, or three planes that intersect the other two but not at the same location.

Hence, No solutions exist to this system of equations

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Answer:

a

Step-by-step explanation:

Answer:

14.52% are unicyclists

Step-by-step explanation:

First, we can use proportions to find the number of unicyclists at the convention. Since we know that the ratio of unicyclists to aerial artists is 9:11, and there are 88 aerial artists, we can set up the following equation:

[tex]\frac{9}{11}=\frac{x}{88}[/tex]

If we cross multiply, we get that 11x = (88)(9). After we divide through by 11 to isolate x, we get that x = (8)(9) = 72

Second, we have to figure out the number of mimes at the convention to figure out the total number of people there. We know that the ratio of unicyclists to mimes is 3:14, and the number of unicyclists is 72. So, we can set up the following proportion:

[tex]\frac{3}{14}=\frac{72}{y}[/tex]

If we cross multiply, we get that 3y = 1008, or y = 336 mimes

The total number of people at the convention is 336 mimes + 72 unicyclists + 88 unicyclists = 496. Now we have to figure out what percent of 496 is 72 (the number of unicyclists). If we let z = the percentage, we can simply set up an equation that says that 72 is z% of 496:

[tex]72=0.01z*496\\0.01z=0.14516\\z=14.52[/tex]

This means that approximately 14.52% of the performers are unicyclists.

Answer:

14.52%

Step-by-step explanation:

U/A = 9/11       and   A = 88      multiply by  8/8   ( to get A=88 as given)

9/11 * 8/8 = 72/88  = U / A       so U = 72

Then U/M = 3/14    multiply by  24/24   ( to get U = 72 as found above)

  then  U/M=    72 / 336     M = 336

U / ( A + U + M )  x  100% = 14.52 %

The statement which is true about the given graph is  that f(x)<0 in the interval (-∞,3) which is option 3.

Given Graph of a function

We have to choose a statement which is correct about the function whose graph is given.

The graph of a function tells us about the domain and range of the function. The values on y axis are the codomain of the function and the values on x axis are the values of domain.

When we see the graph we can find that x=-∞ to x=3 the values are negative means when we put the values of x less than 0 we will get negative number. For example if we put the value of x=-1, we will get -20 which is a negative number.

Hence the third statement is true for the given graph which is that it has values less than zero in the interval (-∞,3).

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Answer:A

Step-by-step explanation:125 miles divided by 5 gallons would equal 25, meaning 25 gallons per mile

Answer:

C

Step-by-step explanation:

Solution

There are 8 apples in the bowl

There are 8 + 14 = 22 total fruits in the bowl.

Ratio apples / total = 8 / 22. But that is not the answer. You can divide top and bottom of the ratio by 2.

When you do that, you get 4/11 which is C

Answer: 4/11 or C

Answer:

Here is your answer

Step-by-step explanation:

Step -1: Forming equations.

                  Let, present age of son = x

                  And, present age of father = 3x+3

                  3 years later, age of son = x+3

                  age of father = 3x+3+3=3x+6                                  ...(i)

                  According to the given condition, age of father = 10+2(x+3)        ...(ii)

Step -2: Solving for x

                  From (i) and (ii)

                  ∴3x+6=10+2(x+3)

                  ⇒3x+6=10+2x+6

                  ⇒3x−2x=10+6−6

                  ⇒x=10

                  ∴Present age of son = 10 

                  and present age of father = 3x+3=3×10+3=33

Hence, son’s present age is 10 years and father’s 

Answer:

6(2)x = 384

12x = 384

12x/12 = 384/12

x = 32

Step-by-step explanation:

The ladder reaches 19.938 foot high from the ground on the wall.

A right angled triangle is a triangle that has one of its angle measure as 90  degree.

It is given that

Ladder Length = 22 foot

The angle between the ladder and the ground is 65 degree.

When the ladder leans on a wall , the wall makes 90 degree with the ground and the ladder is the hypotenuse of the right angled triangle formed.

The figure is attached with the answer.

sin 65 = Height of the wall / Hypotenuse

0.9063 = Height of the wall / 22

Height of the wall = 19.938 foot

Therefore the ladder reaches 19.938 foot high from the ground on the wall.

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Answer:

19.94

Step-by-step explanation:

The point-slope equation of the line is y-2=-2(x-7)

How will we find the equation of line?

First, we will find the slope of line using the given points then put slope and point in the formula to get equation of line.

We can find the equation as shown below:

Given points (6,4) and (7,2)

slope(m)= (2-4)/ (7-6)

m=-2/1

m=-2

The point slope form:

(y-y1) = m(x-x1)

y1=2, x1=7

putting in formula

(y-2) = -2(x-7)

y-2=-2(x-7)

Hence, the point-slope equation of the line is y-2=-2(x-7)

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Answer:

Step-by-step explanation:

Angles EBA and DBC are congruent. The three angles EBA, EBD, and DBC are together supplementary, so their measures sum to 180°. This means

x + (4x + 11°) + x = 180°

6x + 11° = 180°

6x = 169°

x = (169/6)°

Then the measure of angle D is

2x + 8° = 2 (169/6)° + 8° = (193/3)°

The interior angles of any triangle sum to 180°, so if y is the measure of angle C, we have

(169/6)° + (193/3)° + y = 180°

y = (175/2)° = 87.5°

Answer:

x = -3/2, -2

Step-by-step explanation:

2x^2 + 7x + 6 = 0

(2x + 3)(x + 2) = 0

(2x + 3)

2x = -3

x = -3/2

(x + 2)

x = -2

Answer:

[tex]\large {\textsf{A and C}}\ \implies x_1=-2,\ x_2=-\dfrac{3}{2}}[/tex]

Step-by-step explanation:

In this problem, we can use two methods to solve for the values of x (roots) of the given equation. Those methods are: using the quadratic formula and factoring.

Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0

Given equation: 2x² + 7x + 6 = 0

⇒ a = 2, b = 7, c = 6

Method 1: Using the Quadratic Formula

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Step 1: Substitute the values of a, b, and c into the quadratic formula.

[tex]\implies x=\dfrac{-7\pm\sqrt{7^2-4(2)(6)}}{2(2)}\\\\[/tex]

Step 2: Simplify

[tex]\implies x=\dfrac{-7\pm\sqrt{\bold{7^2}-4(2)(6)}}{\bold{2(2)}}\\\\\implies x=\dfrac{-7\pm\sqrt{49-4\bold{(2)(6)}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{49\bold{-4(12)}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{\bold{49-48}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{\bold{1}}}{4}\\\\\implies x=\dfrac{-7\pm1}{4}[/tex]

Step 3: Separate into two possible cases and solve for the values of x.

[tex]\implies x_1=\dfrac{-7-1}{4}\implies \dfrac{-8}{4}\implies \boxed{-2}\\\\\implies x_2=\dfrac{-7+1}{4}\implies \dfrac{-6}{4}\implies\boxed{-\dfrac{3}{2}}[/tex]

Method 2: Solve by Factoring

In order to be able to solve this equation by factoring, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = 12) and give us the sum of the middle term (b = 7).

Factors that give a product of a • c: 4 • 3 = 12

Factors that give a sum of b: 4 + 3 = 7

Step 1: Rewrite the given equation with those factors.

2x² + 7x + 6 = 0

⇒ 2x² + 4x + 3x + 6 = 0

Step 2: Factor out 2x and 3.

(2x² + 4x) + (3x + 6) = 0

⇒ 2x(x + 2) + 3(x + 2) = 0 [ Factor out the the common factor. ]

⇒ (2x + 3)(x + 2) = 0

Step 3: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0).

a) 2x + 3 = 0 ⇒ 2x = -3 ⇒ x = -³⁄₂

b) x + 2 = 0 ⇒ x = -2

Therefore, the two roots of this equation are x = -³⁄₂ and x = -2.

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Answer:

No

Step-by-step explanation:

Let's assume that x=2 and y=3.

1/2+1/3≠1/5

Also, when adding fractions, you cannot simply add the denominator. You have to make the denominators of all fractions the same and then add.

So, if you are given 1/x +1/y, you should get (y+x)/xy, not 1/(x+y)

The probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

μρ=ρ

The standard deviation of this sampling distribution of sample proportion is:

σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]

The information provided is:

n = 533

p = 0.09

As the sample size is quite large, i.e. n = 533 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by a Normal distribution.

The mean and standard deviation are:

μρ=ρ=0.09

σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]=[tex]\sqrt\frac{0.09(1-0.09)}{533}=0.01239[/tex]

Compute the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% as follows:

[tex]p(p^-p > 0.03)=P(p^ > 0.12) \\=P(z > \frac{0.12-0.9}{0.012}) \\= P(Z > 2.5) \\= 1-P(Z > 2.5) \\ = 1- 0.993 \\ = 0.00621[/tex]

Thus, the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.

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The total amount you have paid from May 2014 to July 2022 is $75,319.86

= 96 + 2

= 98 months

Total amount paid from May 2014 to July 2022 = $768.57 × 98 months

= $75,319.86

The total amount paid so far from May 2014 to July 2022 is $75,319.86

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Answer:

SR and RZ

Step-by-step explanation:

A perpendicular bisector is a line segment that passes through the midpoint of a side of a triangle. In other words, If it goes through a side, it should split the segment in half perfectly. Furthermore, it must be perpendicular to the side it passes through (it should form a ninety-degree angle with the side). Given these two rules, one can say that one of the perpendicular bisectors is SR. SR forms a right angle with (and is thus perpendicular to) side AB. Furthermore, AS is congruent to (has the same length as) SB, which means SR cuts AB in half exactly. Another bisector would be RZ (for similar reasoning). Let me know if that doesn't make sense.

The force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N

A tangible body's mass is the amount of matter it possesses. It's also a metric of inertial or the resistance to velocity when a net force is exerted.

We have:

The mass of the body m = 0.8 kg

As we know,

F = mg

F is the force acting on the body and g is the acceleration due to gravity.

g = 9.8 m-s⁻²

F = (0.8)(9.8)

F = 7.84 kg-m-s⁻²

or

F = 7.84 N

Thus, the force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N

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There is a profit of $39.7.

It is given that there 100 tickets costing $10 per ticket.

You must look first for the probability of the 4 prizes which are $475, $195, $30, and no prize.

P ($475 prize) = 1/100 or 0.01

P ($95 prize) = 2/100 or 0.02

P ($30 prize) = 4/100 or 0.04

P (No prize) = 100/100 – 1+2+4/100 =93/100 .93

Expected gain or loss is computed by: (P(x)* n)

E= (475-10)*.01 + (95-10)*0.02 + (30-10)* 0.04 + (-10)*.93

= 46.5 + 1.70 + 0.8 – 9.3

E = 39.7

There is a profit of $39.7.

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Equations are written by equating the expressions to each other. The value of x is 7

Equations are written by Equating the expressions to each other.

Given the equation below:

10 - x = 3

Subtract 10 from both sides

10 - x - 10 = 3 - 10

-x = -7

Multiply both sides by -1

-(-x) = -(-7)

x = 7

Hence the value of x is 7

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At times, latitudes with values higher than 66.5  degrees can have ~ 24 hours of continuous sunshine.

Locations above the Arctic Circle (north of latitude 66.5 degrees, 90 degrees minus the tilt of the Earth's axis) are exposed to 24-hour sunlight. Below the Arctic Circle (latitude 66.5 degrees south), there is 24-hour darkness.

When at the equator, the sun is directly above – at the poles, the sun is on the horizon. However, regardless of the current location (from the pole to the equator), all parallels are bisected, so we have 12 hours a day and 12 hours a night in all locations.

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Answer: A

Step-by-step explanation:

The angle opposite the shortest side in a triangle has the smallest measure.

Answer:

x/2

Step-by-step explanation:

Madison didn't cancel the common factor of 2 and that 4 that is why she is wrong.

Hope this helps pls brainliest have a nice day :>

The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.

x + (2x - 3) = 15

x + 2x - 3 = 15

3x = 15 + 3

3x = 18

x = 18/3

x = 6

Therefore,

Number of boxes renita has unpacked = x

= 6 boxes

Number of boxes Vanessa has unpacked = 2x - 3

= 2(6) - 3

= 12 - 3

= 9 boxes

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Answer:

Step-by-step explanation:

The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.

Equation

Number of boxes renita has unpacked = x

Number of boxes Vanessa has unpacked = 2x - 3

Total boxes both unpacked = 15

x + (2x - 3) = 15

x + 2x - 3 = 15

3x = 15 + 3

3x = 18

x = 18/3

x = 6

Therefore,

Number of boxes renita has unpacked = x

= 6 boxes

Number of boxes Vanessa has unpacked = 2x - 3

= 2(6) - 3

= 12 - 3

= 9 boxes

Answer:

i think its c wouldve helped if i saw a pic of the triangle tho

Step-by-step explanation:

The length of side AB is 5√3.

Option B is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

We can use trigonometry to solve this problem.

Let's start by finding the length of BC.

sin(30°) = BC/AC

sin(30°) = BC/10

BC = 5

Now, we can use the Pythagorean theorem to find the length of AB.

AB² = AC² - BC²

AB² = 10² - 5²

AB² = 75

AB = 5√3

Therefore,

The length of side AB is 5√3.

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The original amount Sara has left is 172/209

The calculation can be done as follows

Let y represent the amount left

9/11 × 836

= 7524/11

= 110

Y  can be calculated as follows

Y + 38 +110= 836

148 + Y= 836

Y= 836 - 148

Y= 688

Therefore the fraction is

688/836

= 172/209

Hence the fraction of the original amount left is 172/209


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