A system of equations is given below. y = 2x + 1/4 and 2x - 1/4

Which of the following statements best describes the two lines?

They have the same slope but different y-intercepts, so they have no solution.
They have the same slope but different y-intercepts, so they have one solution. They have different slopes but the same y-intercept, so they have no solution.
They have different slopes but the same y-intercept, so they have one solution.

Answer:

D.

Step-by-step explanation:

To find this area, we can break it up into two rectangles, one with dimensions of 4x19 and another of 24x11. All we have to do is find the areas of both rectangles and add them together!

Since 4*19=76 and 11*24=264, we get D. 340 square units as our answer.

For this case we have that the area of the figure is given by the sum of the areas of two rectangles. The area of a rectangle is given by:

[tex]A = a * b[/tex]

Where:

a, b: They are the sides of the rectangle

[tex]A_ {1} = 24 * 11\\A_ {1} = 264[/tex]

On the other hand:

[tex]A_{2} = 4 * (4 + 11 + 4) = 4 * 19 = 76[/tex]

Thus, the total area is:

[tex]A_ {t} = 264 + 76\\A_ {t} = 340[/tex]

The total area is 340 square units

Answer:

Option D

Answer:

[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]

Step-by-step explanation:

The equation of a quadratic function in vertex form is given by:

[tex]f(x)=a(x-h)^2+k[/tex]

Where (h,k) is the vertex.

It was given in the question that the vertex of the parabola is (-1,4).

When we substitute the vertex into the formula we get:

[tex]f(x)=a(x+1)^2+4[/tex]

The parabola also passes through (4,19) hence it must satisfy its equation.

[tex]19=a(4+1)^2+4[/tex]

[tex]19-4=a(5)^2[/tex]

[tex]15=25a[/tex]

We divide both sides by 25 to get:

[tex]a=\frac{15}{25}= \frac{3}{5}[/tex]

Hence the quadratic function is:

[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]

Answer:

Third option.

Step-by-step explanation:

You need to cube both sides of the equation. Remember the Power of a power property:

[tex](a^m)^n=a^{mn[/tex]

[tex]\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d[/tex]

According to the Product of powers property:

[tex](a^m)(a^n)=a^{(m+n)[/tex]

Then. simplifying you get:

[tex]162x^cy^5=162x^6y^{(3+d)}[/tex]

Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6,  then the exponent of "x" on the left side must be 6. Therefore:

[tex]c=6[/tex]

You can notice that the exponent of "y" on the left side is 5,  then the exponent of "x" on the left side must be 5 too. Therefore "d" is:

[tex]3+d=5\\d=5-3\\d=2[/tex]

Answer:

D. Vertex (1, -25); intercepts x = -4, 6

Step-by-step explanation:

Vertex

x = -b/2a

x = - (-2)/2(1)

x = 2/2

x = 1

y = 1^2 - 2(1) - 24

y = 1 - 2 - 24

y = -25

Vertex (1, -25)

x-intercepts when y = 0

x^2 - 2x - 24 = 0

(x - 6)(x + 4) = 0

x - 6 = 0; x = 6

x + 4 = 0;x = -4

Answer

D. Vertex (1, -25); intercepts x = -4, 6

Answer:

d

Step-by-step explanation:

im very smart (def did not get it wrong and it showed me the answer)

Answer:300 cm2(in the case of rectangle)

Step-by-step explanation:

The question is ambiguous.Something is missing.what is the shape of the object is not told here.

But if you consider it a "rectangle",the angles will be right angles.

area of a rectangle=length×breadth

=20cm×15cm

=300 centimetre2

Answer: square centimeters

Step-by-step explanation:

Hi, the answer to the question is square centimeters.

The lengths of the picture are in centimeters. So, when you calculate the area of the picture that is a triangle you obtain square centimeters.

Mathematically speaking:

20cm x 15 cm =  300 square centimeters

By multiplying the same unit you obtain the square unit.

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

The answer I believe is 4.

Step-by-step explanation:

Answer: the answer is 4

Step-by-step explanation:

;)

Answer:

θ = 240

and

cos(θ) = -0.5

Step-by-step explanation:

Theta is in the third quadrant, that meansit goes from 180 to 270 degrees

Then,

cos^2 (θ) =1/4

cos (θ) = ± 1/2

θ = arccos(0.5)

θ = 60

But in the third quadrant

θ = 180 + 60  = 240

θ = 240

and

cos(θ) = -0.5

Answer:

The output is 23

Step-by-step explanation:

we know that

f(x) ----> is the output

x ----> is the input

we have that

f(x)=3x-1

For x=8 (input)

Find the value of f(x) (output)

f(8)=3(8)-1=23

The output is 23

Answer:

63 % for cats and 37 % for dogs

Step-by-step explanation:

Answer:

13 is your answer

Step-by-step explanation:

x - 8.1 = 5.3

  +8.1    +8.1         Add 8.1 to both sides

x     =     13.4

Which if you want the whole number i'd be 13, Because if your rounding the 3, 4 won't bump the 3 up any because 4 isn't greater than 5.

Hope my answer has helped you!

Answer:

x=13

Step-by-step explanation:

A quick rough estimate could be obtained by adding 8 to both sides:

x = 5.3 + 8, or x = 13 (approx.)

The exact solution is x = 8.1 + 5.3 = 13.4 (which rounds down to 13).

The x-intercepts of the parabola are [tex]\( x = -3 \) and \( x = 1 \)[/tex].

To find the x-intercepts of the parabola defined by the equation [tex]\( y = -3x^2 - 6x + 9 \)[/tex], we need to set y=0 and solve for x.

So, we have:

[tex]\[ -3x^2 - 6x + 9 = 0 \][/tex]

Now, let's solve this quadratic equation using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]where \( a = -3 \), \( b = -6 \), and \( c = 9 \).\[ x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(-3)(9)}}{2(-3)} \]\[ x = \frac{6 \pm \sqrt{36 + 108}}{-6} \]\[ x = \frac{6 \pm \sqrt{144}}{-6} \][/tex]

[tex]\[ x = \frac{6 \pm 12}{-6} \][/tex]

Now, we have two possible values for x:

1. When [tex]\( x = \frac{6 + 12}{-6} = \frac{18}{-6} = -3 \)[/tex]

2. When [tex]\( x = \frac{6 - 12}{-6} = \frac{-6}{-6} = 1 \)[/tex]

Answer:

B just took it.

Step-by-step explanation:

The fact that all right angles can be bisected is not a postulate of Euclidean geometry.

Euclidean geometry is the classical form of geometry first described by Euclid in his work Elements. He gathered all the mathematical knowledge known to the Greeks at the time, today his work presents itself as the first known axiomatization in the history of mathematics.

Originally, it was only cultivated on a plane and in three-dimensional space, at the same time linking it with the physical world that it was supposed to describe, thus preventing the possibility of studying other varieties of geometry.

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Answer:

1 solution

Step-by-step explanation:

This is a linear equation and has one solution

6x - 4 = x + 6 ( subtract x from both sides )

5x - 4 = 6 ( add 4 to both sides )

5x = 10 ( divide both sides by 5 )

x = 10 ← only 1 solution

Answer:

(2,1)

Step-by-step explanation:

So the first thing you want to do is substitute. You want to plug in the equation for y in for the y value above.

So you would do 3x+4(x-1)=10. As you can see we took the bottom equation and put it in for the top equation. We did this so we only have x s and no y s.

Now you would solve. You would distribute first. You would get 3x+4x-4=10. Now combine like terms. 3+4 is 7 so you would get 7x-4=10.The next thing you want to do is get the 7x by itself so move the 4.You would get 7x=14. Now divided both sides by 7 because you want to get the x by itself.

You would get x=2. Now for the y value just plug it in for an equation above. The easier one would be y=x-1. y=(2)-1 will equal 1. You write your final answer in (x,y) style. Your final answer will then be (2,1)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x+4y=10&(1)\\y=x-1&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\\\3x+4(x-1)=10\qquad\text{use the distributive property}\\3x+4x-4=10\qquad\text{add 4 to both sides}\\7x=14\qquad\text{divide both sides by 7}\\x=2\\\\\text{put the value of x to (2):}\\\\y=2-1\\y=1[/tex]

Answer:

Step-by-step explanation:

This is not a linear function. This is actually an exponential function.

Answer:

A

Step-by-step explanation:

trust me bro

Answer:

An equation to have no solution means that the system of equations do not intersect at all and therefore will not have any solutions. If an equation has indefinite many solutions then the system of equations will have the same line since they are intersecting each other

Step-by-step explanation:

Answer:

A pentagon is a 5 sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably a math equipment.

Step-by-step explanation:

A pentagon is a 5-sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably math equipment.

A pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape.

In geometry, it is considered as a is a five-sided polygon with five straight sides and five interior angles, which add up to 540°.

A pentagon shape is a plane figure, or a flat (two-dimensional) 5-sided geometric shape.

The measure of each angle of a regular pentagon is given by the below formula. The measure of the central angle a regular pentagon makes a circle, i.e. total measure is 360°.

Hence, a pentagon is a 5-sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably math equipment.

Learn more about the pentagon here;

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Answer:

B.) 83.7758

Step-by-step explanation:

Answer:

83.75 cubic inches

Step-by-step explanation:

We are given the diameter of a cone 8 inches, and height 5 inches and we are to find the volume of this cone.

(diameter is 8 inches so radius will be 4 inch)

We know that the volume of a cone is given by:

Volume of cone = [tex] \pi r ^ 2 \frac { h } { 3 } [/tex]

Substituting the given values in the above formula:

Volume of cone = [tex] \pi \times 4 ^ 2 \times \frac { 5 } { 3 } [/tex] = 83.75 cubic inches

(diameter is 8 inches so radius will be 4 inches)

Answer:

The value of x is 20°

Step-by-step explanation:

we know that

m∠ 9 and m∠ 11 are corresponding angles

If line c is parallel to line d

then

m∠ 9 = m∠ 11

Substitute

6x=120°

x=20°

Answer:

20

Step-by-step explanation:

:))

We're looking for a model of the form

[tex]y=a\cos(b(x-c))+d[/tex]

[tex]a[/tex] is the amplitude, equal to half the difference between the maximum and minimum hours of daylight:

[tex]a=\dfrac{15.3-9.1}2=3.1[/tex]

[tex]b[/tex] determines the period of the cosine function. The period itself is [tex]\dfrac{2\pi}b[/tex], which we want equal to 365, so that

[tex]365=\dfrac{2\pi}b\implies b=\dfrac{2\pi}{365}[/tex]

(so that the value in the second box should be 365)

[tex]c[/tex] determines the horizontal shift of the cosine function. We'll come back to this in a moment.

[tex]d[/tex] represents the vertical shift of the function. The standard function is bounded between -1 and 1:

[tex]-1\le\cos x\le1[/tex]

Our new function has an amplitude of 3.1, so that

[tex]-3.1\le3.1\cos x\le3.1[/tex]

We want the range of values to fall between 15.3 and 9.1, so we want to pick [tex]d[/tex] such that

[tex]\begin{cases}-3.1+d=9.1\\3.1+d=15.3\end{cases}\implies d=12.2[/tex]

So the current model is

[tex]y=3.1\cos\left(\dfrac{2\pi}{365}x\right)+12.2[/tex]

[tex]c[/tex] represents the horizontal shift of the function. [tex]x=0[/tex] represents the first day of the year, which according to the current model tells us we should expect [tex]3.1\cos0+12.2=15.3[/tex] hours of daylight on the first day of the year. But this conflicts with the data. We want this maximum to occur on the 172nd day of the year, so we shift the model by this amount, and the model is

[tex]y=\boxed{3.1}\cos\left(\dfrac{2\pi}{\boxed{365}}}(x-\boxed{172})\right)+\boxed{12.2}[/tex]

First, you must find the total number of people. Add together 32, 54, 78, 112, and 96 to get 372. Next, add the number of diabetic patients with the number of patients with eye problems (54 + 112 = 166).

Your fraction is now 116/372. Simplify this to get your answer, 29/93 or 0.31.

Answer:

The length of the rectangular park is [tex]1.2\ mi[/tex] and the width of the rectangular park is [tex]0.3\ mi[/tex]

Step-by-step explanation:

Let

x ----> the length of the rectangular park

y ---> the width of the rectangular park

we know that

The perimeter is equal to

[tex]P=2(x+y)[/tex]

[tex]P=3\ mi[/tex]

so

[tex]3=2(x+y)[/tex] -----> equation A

[tex]x=4y[/tex] ----> equation B

substitute equation B in equation A and solve for y

[tex]3=2(4y+y)[/tex]

[tex]3=10y[/tex]

[tex]y=0.3\ mi[/tex]

Find the value of x

[tex]x=4(0.3)=1.2\ mi[/tex]

therefore

The length of the rectangular park is [tex]1.2\ mi[/tex] and the width of the rectangular park is [tex]0.3\ mi[/tex]

Final answer:

To determine the dimensions of a park with a 3-mile perimeter where the length is 4 times the width, we set up the equation 3 = 2l + 2w, substitute l = 4w into it, and solve for width and length. The calculations show the park is 1.2 miles long and 0.3 miles wide.

Explanation:

The student has asked for help to find the dimensions of a rectangular-shaped park with a 3-mile perimeter where the length is 4 times the width. To solve this, we will use the formula for the perimeter of a rectangle P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Since we know the perimeter is 3 miles, we can set up the equation 3 = 2l + 2w. Because the length is 4 times the width, we can also say that l = 4w. Substituting into the first equation, we get 3 = 2(4w) + 2w, which simplifies to 3 = 10w. To find the width, we divide both sides by 10, resulting in w = 0.3 miles. Then, using l = 4w, we find that the length l is 1.2 miles.

Therefore, the dimensions of the park are 1.2 miles long and 0.3 miles wide.

For this case we must solve the following linear equation:

[tex]- \frac {1} {4} x + 5 = \frac {3} {4}[/tex]

Subtracting 5 from both sides of the equation we have:

[tex]- \frac {1} {4} x = \frac {3} {4} -5\\- \frac {1} {4} x = \frac {3-20} {4}\\- \frac {1} {4} x = - \frac {17} {4}[/tex]

Multiplying by 4 on both sides of the equation:

[tex]-x = -17[/tex]

Multiplying by -1 on both sides of the equation we have:

[tex]x = 17[/tex]

Answer:

[tex]x = 17[/tex]

Answer: [tex]x=17[/tex]

Step-by-step explanation:

You need to solve for the variable "x":

The first step is to subtract 5 from both side of the equation, then:

[tex]-\frac{1}{4}x+5-5=\frac{3}{4}-5\\\\-\frac{1}{4}x=-\frac{17}{4}[/tex]

The final step is to multiply both sides of the equation by -4.

Therefore, the value of the variable "x" is the following:

[tex](-4)(-\frac{1}{4}x)=(-\frac{17}{4})(-4)\\\\x=17[/tex]

Answer:

Since, when a function f(x) is reflected across x-axis then resultant function is -f(x), and reflected across y-axis then resultant function is f(-x),

Also, In translation of f(x),

If the transformed function is,

g(x) = f(x+a)

If a is positive then function is shifted a unit left,

If a is negative then function is shifted a unit right,

While, if transformed function is,

g(x) = f(x) + a

If a is positive then function is shifted a unit up,

If a is negative then function is shifted a unit right,

Here, the given parent function is,

[tex]y=-x^2-1[/tex]

Hence, by the above explanation we can match the unction formula with the corresponding transformation, shown below,

1. [tex]y=-x^2-1[/tex]  : Reflected across the y-axis

2. [tex]y=-(x - 1)^2 - 1[/tex]  : Translated right by 1 unit

3. [tex]y= x^2 +1[/tex] : Reflected across the x-axis

4.[tex]y=-x^2[/tex]  : Translated up by 1 unit

5. [tex]y=-(x+ 1)^2 - 1[/tex]  : Translated left by 1 unit

6. [tex]y=-x2 - 2[/tex]  : Translated down by 1 unit

The simplified formula for calculating the monthly lease payment for a car is the sum of the depreciation fee and the finance fee. These are calculated based on the car's initial cost, residual value, and the lease factor.

In the context of car leasing, the simplified formula used to calculate the monthly lease payment is: depreciation fee + finance fee. The depreciation fee is calculated by subtracting the car's expected residual value at the end of the lease from its initial cost (MSRP) and then dividing this by the number of months in the lease. The finance fee is calculated as the sum of the MSRP and the residual value, multiplied by the lease factor or money factor which is essentially the interest rate.

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Answer:

see explanation

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x²(2x² + 3x - 1) + 3x(2x² + 3x - 1) + 2(2x² + 3x - 1)

Distribute all 3 parenthesis

= 2[tex]x^{4}[/tex] + 3x³ - x² + 6x³ + 9x² - 3x + 4x² + 6x - 2

Collect like terms

= 2[tex]x^{4}[/tex] +9x³ + 12x² + 3x - 2

Answer:

2x^4+9x^3-7x^2-6x-2

Step-by-step explanation:

=2x^4+3x^3-x^2+6x^3+9x^2-3x-x^2-3x-2

Simplify

=2x^4+9x^3-7x^2-6x-2

Answer:

Step-by-step explanation:

6|x| + 25 = 15

6|x| = 15 - 25

6|x| = -10

|x| = - [tex]\frac{10}{6}[/tex]

By definition, the absolute value of any number must be positive, hence  | x| can never be negative, there is no solution.