Which graph represents the equation y^2? = -4x?

Answer:

A.  Circle.

     [tex](x+15)^2+(y-0)^2=13^2[/tex]

B.  Parabola.

     [tex](x-15)^2=-16(y-20)[/tex]

C.  Maximum height of Tunnel A = 13 ft.

     Maximum height of Tunnel B = 20 ft.

     The truck can only pass through Tunnel B without damage.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3cm}\underline{General equation for any conic section}\\\\$Ax^2+Bxy+Cy^2+Dx+Ey+F = 0$\\\\where $A, B, C, D, E, F$ are constants.\\\end{minipage}}[/tex]

Circle:  A and C are non-zero and equal, and have the same sign.

Ellipse:  A and C are non-zero and unequal, and have the same sign.

Parabola:  A or C is zero.

Hyperbola:  A and C are non-zero and have different signs.

Tunnel A

[tex]x^2+y^2+30x+56=0[/tex]

As the coefficients of x² and y² are non-zero, equal and have the same sign, the conic section is a circle.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Rewrite the given equation for Tunnel A in the standard form of the equation of a circle:

[tex]\implies x^2+y^2+30x+56=0[/tex]

[tex]\implies x^2+30x+y^2-56[/tex]

[tex]\implies x^2+30x+\left(\dfrac{30}{2}\right)^2+y^2=-56+\left(\dfrac{30}{2}\right)^2[/tex]

[tex]\implies x^2+30x+225+y^2=-56+225[/tex]

[tex]\implies (x+15)^2+(y-0)^2=169[/tex]

[tex]\implies (x+15)^2+(y-0)^2=13^2[/tex]

Therefore, the center of the circle is (-15, 0) and the radius is 13.

Tunnel B

[tex]x^2-30x+16y-95=0[/tex]

There is no term in y² so the coefficient of y² is zero.  Therefore, the conic section is a parabola.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a parabola}\\(with a vertical axis of symmetry)\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$. \\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex.\\\end{minipage}}[/tex]

Rewrite the given equation for Tunnel B in the standard form a parabola:

[tex]\implies x^2-30x+16y-95=0[/tex]

[tex]\implies x^2-30x=-16y+95[/tex]

[tex]\implies x^2-30x+\left(\dfrac{30}{2}\right)^2=-16y+95+\left(\dfrac{30}{2}\right)^2[/tex]

[tex]\implies x^2-30x+225=-16y+95+225[/tex]

[tex]\implies (x-15)^2=-16(y-20)[/tex]

Therefore, the vertex is (15, 20).

Maximum height of Tunnel A

The maximum point of a circle is the sum of the y-value of its center and its radius:

Maximum height of Tunnel B

The maximum point of a downwards opening parabola is the y-value of its vertex:

As the truck is 13.5 feet high, it cannot pass through Tunnel A since the maximum height of Tunnel A is 13 feet.

The maximum height of Tunnel B is certainly adequate for the truck to pass through.  However, to determine if the truck can pass through Tunnel B safely, we also need to find the width of the tunnel when its height is 13.5 feet.  To do this, find the x-values of the parabola when y = 13.5.  If the difference in x-values is 8 or more, then the truck can pass through safely.

Substitute y = 13.5 into the equation for Tunnel B and solve for x:

[tex]\implies (x-15)^2=-16(13.5-20)[/tex]

[tex]\implies (x-15)^2=-16(-6.5)[/tex]

[tex]\implies (x-15)^2=104[/tex]

[tex]\implies \sqrt{(x-15)^2}=\sqrt{104}[/tex]

[tex]\implies x-15=\pm\sqrt{104}[/tex]

[tex]\implies x=15\pm\sqrt{104}[/tex]

Now find the difference between the two found values of x:

[tex]\implies (15+\sqrt{104})-(15-\sqrt{104})[/tex]

[tex]\implies 15+\sqrt{104}-15+\sqrt{104}[/tex]

[tex]\implies 2\sqrt{104}[/tex]

[tex]\implies 20.39607...[/tex]

Therefore, as the width of Tunnel B is 20.4 ft when its height is 13.5 ft, the 8 ft wide truck can easily pass through without damage since 20.4 ft is greater than the width of the truck.

Answer:

To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y)

Step-by-step explanation:

Thats basically it I think

The restriction of the given equation is [tex]cos^{2}x =cos^{2} x[/tex],  other than 0≤x≤2π.

What is restriction of equation?

Restriction of the equation is the value of domain where the value is limited.

Given,

[tex]sin^{2} xcos^{2}x +cos^4x =(1-sinx)(1+sinx)[/tex]

taking [tex]cos^2x[/tex] common, we get

[tex]cos^2x(sin^2x+cos^2x)=1+sinx-sinx-sin^2x[/tex]

we know

[tex]sin^2x+cos^2x=1\\cos^2x=1-sin^2x[/tex]

we get,

[tex]cos^2x=cos^2x[/tex]

and the restriction is 0≤x≤2π.

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The function to show the amount of tiles laid as a function of time is

The reasonable domain is 0 ≤ t ≤ 9.6

Information gotten from the question include

Jeremy and Travis are placing 1200 tiles in a building

hey have already place 200 tiles, and they are able to place 125 tiles every hour.

The relationship is expressed in the form.

y = mt + c

Definition of variables to suit the problem to be solved

y = Total number of tiles laid

m = tiles laid per hour = 125

t = number of time

c = tiles already placed

200 = 1200 - 125t

The reasonable domain is the range between zero tiles to laying up the 1200 tiles

0 = 1200 - 125t

1200 = 125t

t = 9.6

1200 = 1200 - 125t

0 = -125t

t = 0

the domain is 0 ≤ t ≤ 9.6

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Explanation:

We simplify the square root of 64 to get 8

[tex]\sqrt{64} = \sqrt{8^2} = 8[/tex]

Then we'll have the plus minus out front to say

[tex]x = \pm \sqrt{64} = \pm 8[/tex]

That breaks down into x = 8 or x = -8

As a check

x^2 = (8)^2 = 8*8 = 64

x^2 = (-8)^2 = (-8)*(-8) = 64

Both values lead to 64 when squaring.

Answer:

64

Step-by-step explanation:

the line BCD is a straight line, so angle BCA plus the angle ACD will add to 180. therefore 180 - 114 = 66.

all three angles in a triangle add to 180, so when angle A is 50 and angle C is 66, then 180 - 50 - 66 = 64

Answer:

m∠B = 64°

Step-by-step explanation:

We are told that m∠A = 50° and m∠ACD = 114°. We are then asked to find m∠B.

From the diagram, we can see the angles ACD and ACB lie on a straight line. Therefore, their measures add up to 180°. Hence:

∠ACD + ∠ACB = 180°

⇒ 114° + ∠ACB = 180°

⇒ ∠ACB = 180° - 114°

⇒ ∠ACB = 66°

∴ m∠C = 66°

We know that the angles inside a triangle add up to 180°.

Now that we know the measures of ∠A and ∠C, we can calculate m∠B:

∠A + ∠B + ∠C = 180°

⇒ 50° + ∠B + 66° = 180°

⇒ ∠B = 180° - 66° - 50°

⇒ ∠B = 64°

Answer:

E = mc²

Step-by-step explanation:

Answer:

E =mc^2

Step-by-step explanation:

This equation meant (E)energy equals mass (m) times the speed of light (c) squared. (^2).

Answer:

[tex]34532x = 5647\\\\x=\frac{5647}{34532} = 0.16352947[/tex]

set A is equal to set B which was found by comparing both the sets. So, you have to choose set A = set B.

Given sets are :

A = {4, 7, 10, 15}

B = {10, 4, 15,7}

The elements in set A and set B are 4,7,10 and 15. So, we can say that both the sets are equal.

Therefore, set A is equal to set B which was found by comparing both the sets. So, you have to choose set A = set B.

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The value of the same input x is  -7

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1.A linear equation's graph will always be a straight line.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Let output A = A

And output B = B

According to the question,

5x - 4 = A

3x + 8 = B

And A = 3B

from the above equations,

5x - 4 = 3(3x + 8)

5x - 4 = 9x + 24

4x = -28

x = -7

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8x + 5y ≥ 50

This is from the inequality 16x + 10y ≥ 100.

The other three inequalities are:

x + y ≤ 8

x ≥ 1

y ≥ 3

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Total number of students = 100

Type A minibus = x

Type B minibus = y

Number of students type A carry = 16

Number of student type B carry = 10

We can write an inequality from the above situation as,

16x + 10y ≥ 100

Taking out the common factor.

2 (8x + 5y) ≥ 2 x 50

8x + 5y ≥ 50

The school wishes to use no more than eight minibusses.

This can be written as

x + y ≤ 8

The school wishes to use at least one type A minibus.

This can be written as

x ≥ 1

The school wishes to use at least three type B minibusses.

This can be written as

y ≥ 3

Thus,

8x + 5y ≥ 50

This is from the inequality 16x + 10y ≥ 100.

The other three inequalities are:

x + y ≤ 8

x ≥ 1

y ≥ 3

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Answer:

a.)

[tex]\left \{ {{y=4} \atop {y=x}} \right.[/tex]

See Image 1 for graph

b.)

[tex]\left \{ {{y=2x+2} \atop {y=2x-3}} \right.[/tex]

See Image 2 for graph

Step-by-step explanation:

A system that has exactly one solution is called a consistent independent system. These systems consist of 2 lines that intersect once. Here's an easy one to graph:

[tex]\left \{ {{y=4} \atop {y=x}} \right.[/tex]

See Image 1 for the graph of this system!

A system with no solutions is one where the lines of equalities never cross. They are parallel! Here's one that will impress your professor!

[tex]\left \{ {{y=2x+2} \atop {y=2x-3}} \right.[/tex]

See Image 2 for the graph of this system! Good luck!

Answer:

54°

Step-by-step explanation:

We know that the triangles are congruent by HL, meaning that [tex]m\angle QSR=m\angle QST[/tex].

[tex]9a+48=6a+50 \\ \\ 3a=2 \\ \\ \implies m\angle QST=2(2)+50=54^{\circ}[/tex]

Answer: 4 - 0.75x = 0.83333333333

Step-by-step explanation:

3/4 = 0.75

5/6 = 0.83333333

So 4 - 0.75x = 0.83333333

Check the picture below on the left side.

now, let's notice on that table when y = 0, namely the points in red in the table, those are "zeros", well obviously, or solutions of the quadratic, and those occur when x = -9 and when x = -3, now, let's use another point hmmmm we also know that the quadratic goes through (-7 , 8) so let's use those fellows

[tex]\begin{cases} x=-9\implies &x+9=0\\\\ x=-3\implies &x+3=0 \end{cases}\hspace{5em}a(x+9)(x+3)=\stackrel{0}{y} \\\\\\ \textit{we know that} \begin{cases} x=-7\\ y=8 \end{cases}\implies a(-7+9)(-7+3)=8\implies a(2)(-4)=8 \\\\\\ -8a=8\implies a=\cfrac{8}{-8}\implies \boxed{a=-1} \\\\\\ -(x+9)(x+3)=y\implies -(x^2+12x+27)=y\implies \boxed{-x^2-12x-27=y}[/tex]

Check the picture below on the right side.

Answer:

Step-by-step explanation:

8x2 = 16

8x4= 32 (since its the 2nd one meaning its in the tenth place add 1 Zero, 10) making it 320

8x3 =24 (since its hundredths place add 2 Zeros 100) making 2400

2400+ 320+ 16= 2736

The answer is 2737

Answer:

Step-by-step explanation:

15.

it was a sad day in the stock market for Rudo ;(  

All plus went down 2.5 the previous day and the next day it went down 0.25 of that or

2.5*.25=0.625

2.5+.625=3.125    or -$3.13

16.

-13.4 * .5 = -6.7

-13.4-6.7 = -20.1

at 5 am  it's -20.1° F

Answer:

  A: 8750(0.88^x)

  B: 9995(0.82^x)

Step-by-step explanation:

You want an exponential decay function for cars A and B given their cost and their "decay factor."

In general, an exponential function has the form ...

  value = (initial value)·(growth factor)^x

The growth factor is usually defined as ...

  growth factor = 1 + growth rate

where the "growth rate" is often expressed as a percentage or a fraction.

Your form for f(x) has a=(initial value) and b=(growth factor).

The value of x will be zero at the point where the initial value applies. It will increase by 1 unit for each interval in which the growth factor applies.

Car A

The initial value is presumed to be the Cost. What is called the "growth rate" above is the opposite of what is called the "Decay Factor" in this problem. That is ...

The exponential function is then ...

  f(x) = 8750·(0.88^x)

Car B

For this car, we have ...

The exponential function is then ...

  f(x) = 9995·(0.82^x)

Answer: $290

Step-by-step explanation:

Cost per bracelet = $10

5 bracelets sold x $10/bracelet = $50 cash earned already

x = number of bracelets sold

Money made = (x )($10/bracelet)

Total money made if Autumn sells 24 more bracelets:

$50 + (24)($10) = $290

Answer:

  128°

Step-by-step explanation:

You want the missing angle in the octagon with interior angles x, 106°, 144°, 129°, and 70°; exterior acute angles of 45° and 31°; and exterior obtuse angle 141°.

The sum of angles in the n = 8-sided polygon will be 180°(n -2) = 1080°

The interior angles are the supplement of exterior acute angles. The interior reflex angle is the difference between 360° and the exterior obtuse angle. This means we have ...

  x +(180 -45) +106 +144 +(180 -31) +129 +(360 -141) +70 = 1080

  x -45 +106 +144 -31 +129 -141 +70 = 360 . . . . . . subtract 720

  x + 232 = 360

  x = 128

The missing angle is 128°.

Answer:

37500

Step-by-step explanation:

100-80 = 20 percent of original price

Therefore 20 percent of selling price = 7500

[tex]\frac{20x}{100}=7500\\ 20x = 750000\\x = 37500[/tex]

Answer:

20 percent * 37500 =

(20:100)* 37500 =

(20* 37500):100 =

750000:100 = 7500

The value is 10.81

From the question, we have

[tex]\sqrt{3^{4} +6^{2} } \\=\sqrt{81+36 }\\=\sqrt{117 }\\ = 10.81[/tex]

The value is 10.81

Addition:

When we say "the addition," we mean adding two or more numbers together. The plus sign (+) denotes addition of two numbers, therefore three is written as three plus three. You also have control over how often the plus sign (+) is used. such as 3 + 3 + 3 + 3. Mathematical addition is an essential part of children's education. Students learn basic addition sums in primary school, including one-digit facts, math addition sums, and double-digit math addition sums. Sums in addition are one of the most fundamental and fascinating Math concepts for elementary school students. Children first learn fundamental mathematical ideas like adding numbers in their early years because math is an enthralling subject.

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The equation of the straight line which makes intercepts 3 and "-4" on the axes is 4x - 3y =12 and the point (1, 2) not lie on the line.

When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. (0, b). The intercept form of a line's equation is written as [tex]\frac{x}{a} +\frac{y}{b} = 1[/tex], where a is the x- intercept and b is the y-intercepts, respectively. The x-intercept is the point on the x-axis that is closest to the origin where the line crosses the x-axis, and the y-intercept is the point on the y-axis that is closest to the origin where the line crosses the y-axis.

Now, finding the equation of line by putting the value of intercepts,

[tex]\frac{x}{a} +\frac{y}{b} = 1\\\frac{x}{3} +\frac{y}{-4} = 1\\-4x+3y=-12\\4x-3y=12[/tex]

so, the equation is 4x-3y=12.

Now, putting x=1 and y=2 to find whether (1,2) lie on the line or not,

4(1)-3(2)=12

4-6=12

-2≠12

So, the point (1, 2) not lie on the line.

Therefore, the equation of the straight line which makes intercepts 3 and "-4" on the axes is 4x - 3y =12 and the point (1, 2) not lie on the line.

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The probability of filling a cup between 22 and 33 ounces is 0.9371

The variable here is the machine's output which is normally distributed.

The normal distribution is defined by two parameters, namely, the mean and the standard deviation.  

The population mean for this normal distribution is μ = 25 ounces per cup, and a population standard deviation of σ = 4 ounces (per cup).

calculate the z-score using this formula:

z = x-μ/σ

z is the z-score.

x is the raw score.

μ is the population mean.

σ is the population standard deviation.

The probability of filling a cup between 18 and 33 ounces

z = 18-25/4

z = -7/4

z = -1.75

P(Z< - 1.75) = 1 - P(Z > -1.75)

                  = 1 - 0.9599

                  = 0.0400

We can proceed in the same way to obtain the z-score and the associated probability with the raw score x = 33. We can see that this value is above the mean (positive).

z = 33-25/4

z = 8/4

z = 2

P(z<2) = 0.9772

P(18<x<33) = 0.9772 - 0.0400

P(18<x<33) = 0.9371  

the probability of filling a cup between 22 and 33 ounces is 0.9371

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Answer: [tex]x > \frac{16}{3}[/tex]

Step-by-step explanation:

[tex]16(\frac{1}{4}x -\frac{1}{2} ) > 24-2x\\ 4x-8 > 24-2x\\6x > 32\\x > 32/6\\x > \frac{16}{3}[/tex]

The expression for double the product of 8 and a number is 16 + 2n.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Let the number be n.

Double the product of 8 and a number will be:

= 2(8 + n)

= 16 + 2n

The expression is 16 + 2n.

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Answer:Taylor is 28 and Julian is 26.

Step-by-step explanation: Because their ages are even integers, we know that Taylor is 2 years older than Julian. We can write this as an equation 132 = 4x + x + 2  where x is Julian's age.

Subtract 2 from both sides and you have 130 = 4x + x.

4x + x is the same as 5x, 130 = 5x

Divide both sides by 5 and you get 26, Julian's age.

Taylor is 28 years old and Julian is 26 years old.

An equation is made up of two algebraic expressions with the same value and the sign "=" in between.

Given, Taylor is older than Julian.

Their ages are consecutive even integers.

Let x be the age of Julian and x + 2 be the age of Taylor.

According to the question;

We have the equation,

x + 2 + 4x = 132

5x = 132 - 2

5x = 130

x = 130 / 5

x = 26

Julian's age is 26 and Taylor's age is 26+2 = 28.

Therefore, the Taylor is 28 years old and Julian is 26 years old.

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1. Everyone has a carrying capacity

     carrying capacity means is the total frequency of individuals within a    community a habitat can sustain.

2. Limiting factor are biotic or abiotic factors which limit the carrying capacity.

complete question:

When living conditions in an area are good, a population will generally grow. But eventually some environmental factors will cause the population to stop growing. A limiting factor is an environmental factor that causes a population to decrease. Some limiting factors for populations are food and water, space, and weather conditions.

1. Everyone has _____________

2.What is a limiting factor? please answer in a complete sentence by restating the question​

Answer:  

    1. Everyone has a carrying capacity

     carrying capacity means is the total frequency of individuals within a    community a habitat can sustain.

2. Limiting factor are biotic or abiotic factors which limit the carrying capacity.

The maximum population size that an ecosystem can support is called carrying capacity. Limiting factors determine carrying capacity. The availability of abiotic factors (such as water, oxygen, and space) and biotic factors (such as food) dictates how many organisms can live in an ecosystem. Carrying capacity is also impacted by the availability of decomposers. Decomposers breakdown and recycle dead organisms and organic matter. They prevent dead matter from accumulating and taking up space in an ecosystem.

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By making use of permutation, the number of possible orders for ways to get to school for three days is 6.

Permutation: An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.

On the 1st day, the child goes to school either by walking or biking,

So, the number of possible ways for day one is 2.

Similarly, for Day 2 and Day 3, the number of possible ways is 2 each.

Thus, the number of ways in which it can be ordered is 2 +2+2 = 6.

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