Whatis the value of the expression
4(x + y)
when x= 6 and y= 24?

[tex](f-g)(x)=3x+10-(2x-4)=3x+10-2x+4=x+14[/tex]

Answer:

Step-by-step explanation:

y=-x+3

x+y=-1

y=-x+3

y=-x-1

-x+3=-x-1

add x to both sides

3=-1

no solutions

Answer:

X = 14

Step-by-step explanation:

The given figure is a quadrilateral  .In a Quadrilateral sum of angles is 360 degrees.

The given four angles in the quadrilateral are 70°,110°,110° and 5x °.

Applying angle sum property of quadrilateral:

70+110+110+5x=360°

Adding ,

290+5x=360

Subtracting both sides by 290 so that  x term can be isolated,

290-290+5x=360-290.

5x=70

Dividing both sides by 5

x=14.

Value of x is 1

Answer:

x=14

Step-by-step explanation:

Answer:

(5,0) and (5,-2)

Step-by-step explanation:

we know that

If two points are on the line x=5, then the x-coordinates of the points must be equal to 5

therefore

The coordinates of two points that are on the line x=5 are

(5,0) and (5,-2)

Answer:

The angular velocity of Earth is π/12 radians per hour.

The angular velocity of Earth is 2π radians per day.

Step-by-step explanation:

A full circumference of a circle (as the Equator line on Earth) is 2π radians.

Since the planet does a full revolution in 24 hours... that means it makes a full turn in a day.

So, we can see that in a day, the planet rotates 360 degrees... or 2π radians per day!

Now, if you want to find the angular velocity per HOUR... you divide that by 24... so  2π/24 = π/12 radians

So, we can also say it does π/12 radians per hour.

Answer:

a and d on ed

Step-by-step explanation:

The solution of the system of equations is a = 4 and b = 5.

A system of equations is a set of two or more equations that you deal with at one time.

The given system of equations are;

8a + 12b = 92

6a – 4b = 4

From equation 1

[tex]\rm 8a + 12b = 92\\\\ 8a=92-12b\\\\a=\dfrac{92-12b}{8}[/tex]

Substitute the value of a in the equation 2

[tex]\rm 6a-4b=4\\\\6\times \dfrac{92-12b}{8}-4b=4\\\\3\times \dfrac{92-12b}{4}-4b=4\\\\ 276-36b-16b=16\\\\-52b=16-276\\\\-52b=-260\\\\b=\dfrac{-260}{-52}\\\\b=5[/tex]

Substitute the value of b in the equation 2

[tex]\rm 6a – 4b = 4\\\\6a-4\times 5=4\\\\6a-20=4\\\\6a=4+20\\\\6a=24\\\\a=\dfrac{24}{6}\\\\a=4[/tex]

Hence, the solution of the system of equations is a = 4 and b = 5.

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Answer:

a

Step-by-step explanation:

thanks

Answer:

B: Permutation;  Number of ways are 60

Step-by-step explanation:

At a competition with 5 runners, medals are awarded for first, second, and third places.

Each of the 3 medals is different.

This is a case of Permutation and the Number of ways are 60.

We have to award 3 medals among 5 runners.

This can be done in 5P3 ways.

= [tex]\frac{5!}{(5-3)!}[/tex]

= [tex]\frac{5\times4\times3\times2\times1}{2\times1}[/tex]

= [tex]5\times4\times3=60[/tex]

Therefore, the answer is option A.

Answer: C. 30 degrees

Step-by-step explanation:

By definition, an hexagon is a polygon with six sides.

The sum of the interior angles of an hexagon is 720 degrees.

Based on this, the measure of eac interior angle is:

[tex]interior\ angle=\frac{720\°}{6}=120\°[/tex]

Therefore, the measure of ∠1 is:

 [tex]\angle 1=\frac{120\°}{2}\\\\ \angle 1=60\°[/tex]

So, to find the angle ∠2, you can divide ∠1 by 2:

[tex]\angle 2=\frac{60\°}{2}\\\\ \angle 2=30\°[/tex]

Answer:

C≈37.7 or 36

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

2x3.14x6=36

Step-by-step explanation:

Answer:  The correct options are

(A) DEF.

(C) FED.

Choices:

A. DEF B. DFE C. FED D. EFD

Answer:

FED and DEF

Step-by-step explanation:

vertex is the middle letter

Answer:

general, factored, and vertex form.

general: y=ax^2+b^2+c

Factored: y=(x+a)(x+b)

Vertex: y=a(x-h)^2+k

Step-by-step explanation:

Answer:

The perimeter of the rectangle is 10 + 2x.

Step-by-step explanation:

The formula for the perimeter of a rectangle is 2(l + w) where l = length and w = width because you add up the length of all the sides.

So we can plug in our givens into the formula and simplify:

2(5 + x)

So the perimeter is: 10 + 2x

Notice that we cannot simplify the expression further because there is an unknown (the length).

Answer:

2x + 10

Step-by-step explanation:

A rectangle has opposite sides equal

2(5 + x)

2x + 10

Since the numbers are not consecutive natural numbers, how about if I let the 4 numbers be a, b, c, and d?

The sum is given to be 1320.

a + b + c + d =1320...I will call this the first equation.

Can I then say that the second equation is b + c + d = 0.4a + a? Yes, I can do this.

Simplifying my second equation,

I get b + c + d = 1.4a.

Plugging this into my first equation, I get

a +1.4a =1320

2.4a =1320

So, a =1320/(2.4) =550.

Answer: 550

Answer:

550

Step-by-step explanation:

We aren't given that they are consecutive so lets just pretend the numbers are x, y, z , and r.

We are given x+y+z+r=1320

We are also given that y+z+r=.4x+x

Simplifying my second equation gives us y+z+r=1.4x. I'm going to plug this into first equation giving me

x+1.4x=1320

2.4x=1320

So x=1320/2.4=550

Answer: Infinitely Many Solutions

Step-by-step explanation:

Substitute y into the second equation:

2(-2x-6)=-4x-12

Then you get -4x-12=-4x=-12. Since this is 0=0 it would make it infinitely many solutions.

There are infinitely many solutions to the given system. The equations in the system are y = -2x - 6 and 2y = -4x - 12.

For a system of linear equations, there are three types of solutions. They are,

Infinitely many solutions are there for a system if they both are equal on both sides while solving. (their graphs intersect at all the points)

Given the system of equations as

y = -2x - 6

2y = -4x - 12

Using substitution method, substituting first equation into the second equation,

2( -2x -6) = -4x - 12

⇒ -4x -12 = -4x - 12

Thus, both sides are equal, and the given system has infinitely many solutions.

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Answer:

Step-by-step explanation:

Two lines that are parallel have the same slope but different y intercepts.

So you could have any equation that satisfies y = 8x + b. The only value that b cannot have is 7. All other values including 0 are fine.

So here are a couple of examples.

y = 8x     b = 0

y = 8x + 92

y = 8x + 1/2

y = 8x + pi

y = 8x - 13

7 = 8x - pi

Answer:

38.68        

Step-by-step explanation:

First we need to find the markdown

markdown = original price * markdown rate

               = 45.50 * 15%

               = 45.50 * .15

               = 6.825

Then we need to find the sale price  

sale price = original price- markdown

                = 45.50 - 6.825

                =38.675

Rounding to the nearest cent

               = 38.68

The sale price is 38.68          

Answer: 2:1

Step-by-step explanation:

Volume of a pyramid (V) = [tex]\dfrac{1}{3}\times l\times w\times h\bigg[/tex]

For simplicity, let's assume that l = w = h, then [tex]V = \dfrac{1}{3}s^3[/tex]

Pyramid 1 has a volume of 64:

[tex]64=\dfrac{1}{3}s^3\\\\3\times 64=s^3\\\\\sqrt[3]{3\times 64}=\sqrt[3]{s^3}  \\\\4\sqrt[3]{3} =s[/tex]

Pyramid 2 has a volume of 8:

[tex]8=\dfrac{1}{3}s^3\\\\3\times 8=s^3\\\\\sqrt[3]{3\times 8}=\sqrt[3]{s^3}  \\\\2\sqrt[3]{3} =s[/tex]

Comparing the sides of Pyramid 1 to the sides of Pyramid 2:

[tex]\dfrac{4\sqrt[3]{3}}{2\sqrt[3]{3}}=\dfrac{2}{1}\implies \text{scale factor of }2:1[/tex]

The scale factor of two similar pyramids with volumes of 64 cubic feet and 8 cubic feet is 2.

Understanding the Scale Factor of Similar Pyramids

To find the scale factor between two similar pyramids, we need to understand the relationship between their volumes and their corresponding dimensions. The volumes of the two pyramids given are 64 cubic feet and 8 cubic feet.

The formula for the volume of similar shapes indicates that the volume varies as the cube of the scale factor. This can be mathematically expressed as:

If V1 and V2 are the volumes of two similar figures with a scale factor of k, then: V1 / V2 = k3

For this problem:

64 ÷ 8 = k3

Simplifying:

8 = k3

Taking the cube root of both sides:

k = 2

So, the scale factor of the two similar pyramids is 2.

Use two pints on the graph to find the slope:

(0,0) and (5,1)

Slope = Change in Y over the change in x.

Slope = (1-0) / (5-0) = 1/5 = 0.20

The slope of the given equation is 0.25 which is greater than 0.20.

The unit rate is greater in the equation.

Answer:

[tex]\text{The slope:}\ m=-\dfrac{7}{8}\\\\\text{The point-slope form:}\ y+4=-\dfrac{7}{8}(x-7)\\\\\text{The slope-intercept form:}\ y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

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

We have two points (7, -4) amd (-1, 3).

Calculate the slope:

[tex]m=\dfrac{3-(-4)}{-1-7}=\dfrac{7}{-8}=-\dfrac{7}{8}[/tex]

The point-slope form of an equation of a line:

[tex]y-(-4)=-\dfrac{7}{8}(x-7)\\\\y+4=-\dfrac{7}{8}(x-7)[/tex]

Convert to the slope-intercept form:

[tex]y+4=-\dfrac{7}{8}(x-7)[/tex]        use the distributive property

[tex]y+4=-\dfrac{7}{8}x+\dfrac{49}{8}[/tex]     subtract 4 = 32/8 from both sides

[tex]y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]

The equation of the line passing through (7,-4) and (-1,3) has a slope of -7/8, the point-slope form is y + 4 = -7/8(x - 7), and the slope-intercept form is y = -7/8x + 17/8.

To write the equation of the line that passes through the points (7,-4) and (-1,3), we first need to calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1).

Applying this to our points, we get m = (3 - (-4)) / (-1 - 7), which simplifies to m = 7 / -8 = -7/8. Now, using the point-slope form y - y1 = m(x - x1), and the point (7, -4), we can write the equation as y - (-4) = -7/8(x - 7).

Next, to convert this to slope-intercept form, we simplify the point-slope equation to solve for y: y + 4 = -7/8x + 49/8, and then subtract 4 (or 32/8) from both sides to get y = -7/8x + 17/8. This is our slope-intercept form, where -7/8 is the slope, and 17/8 is the y-intercept.

Answer:

Marcus practiced for 4 hours and Donnell practiced for 7 hours

Step-by-step explanation:

We can set up this problem as a system of linear functions

We'll use d to represent Donnell and m to represent Marcus

Since Donnell practiced 3 hours more than Marcus, we can represent this as an equation:

d=m+3

And since they both practiced for a combined total of 11 hours, we can represent this an an equation:

d+m=11

We can substitute d=m+3 into d+m=11 and we get:

m+3+m=11

2m+3=11

2m=8

m=4

Now we can substitute m=4 into d+m=11

d+4=11

d=7

Therefore, Donnell practiced for 7 hours and Marcus practiced for 4 hours

Answer:

a=1, b=-6, c=2, d=1

Step-by-step explanation:

You are given the function

[tex]y=x^4+ax^3+bx^2+cx+d[/tex]

Find the derivative:

[tex]y'=4x^3+3ax^2+2bx+c[/tex]

The curve has a tangent line when x = 0 with equation y = 2x + 1, so

[tex]y'(0)=2\\ \\y(0)=1[/tex]

Hence,

[tex]y'(0)=4\cdot 0^3+3a\cdot 0^2+2b\cdot 0+c=2\Rightarrow c=2\\ \\y(0)=0^4+a\cdot 0^3+b\cdot 0^2+2\cdot 0+d=1\Rightarrow d=1[/tex]

The curve has a tangent line when x = 1 with equation y = -3x + 2, so

[tex]y'(1)=-3\\ \\y(1)=-3+2=-1[/tex]

So,

[tex]y'(1)=4\cdot 1^3+3a\cdot 1^2+2b\cdot 1+c=4+3a+2b+2=-3\Rightarrow 3a+2b=-9\\ \\y(1)=1^4+a\cdot 1^3+b\cdot 1^2+2\cdot 1+d=1+a+b+2+1=-1\Rightarrow a+b=-5[/tex]

From the second equation, a=-5-b, substitute it into the first one:

[tex]3(-5-b)+2b=-9\\ \\-15-3b+2b=-9\\ \\-b=-9+15\\ \\-b=6\\ \\b=-6\\ \\a=-5-b=-5-(-6)=-5+6=1[/tex]

Answer:

y=4x+48

Step-by-step explanation:

ANSWER

Option C is correct.

EXPLANATION

The given function is

[tex]y = \sqrt[3]{x - 1} + 3[/tex]

The base function is

[tex]y = \sqrt[3]{x} [/tex]

The given function has the same domain as its base function which is all real numbers.

Any real number you plug into this function is defined.

Since the function has no restriction, the domain is all real numbers.

[tex]x | x \: is \: real \: number[/tex]

Answer:

Step-by-step explanation:

[tex]\text{If}\ A(n)\ \text{represents a geometric sequence, then}\ \dfrac{A(n)}{A(n-1)}=\bold{constant}.\\\\A.\\\\A(n)=P(1+i)^{n-1}\\\\A(n-1)=P(1+i)^{n-1-1}=P(1+i)^{n-2}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{P(1+i)^{n-1}}{P(1+i)^{n-2}}\\\\=(1+i)^{(n-1)-(n-2)}=(1+i)^{n-1-n+2}=(1+i)^1=1+i=\bold{constant}[/tex]

[tex]B.\\\\A(n)=(n-1)(P+i)^n\\\\A(n-1)=(n-1-1)(P+i)^{n-1}=(n-2)(P+i)^{n-1}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{(n-1)(P+i)^n}{(n-2)(P+i)^{n-1}}=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-(n-1)}\\\\=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-n+1}=\left(\dfrac{n-1}{n-2}\right)(P+i)^1\neq\bold{constant}[/tex]

others the same

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant. This is different from a quadratic function which does not represent a geometric sequence.

In mathematics, a function represents a geometric sequence when each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The general form of a geometric sequence can be written as a, ar, ar^2, ar^3, ... where 'a' is the first term, and 'r' is the common ratio.

The important factor in a geometric sequence is the multiplication by a constant. For example, let's say we have a sequence 2, 4, 8, 16. This is a geometric sequence because each term is multiplied by 2 to get the next term.

In contrast, a quadratic function, for instance, does not represent a geometric sequence as it's formed by the equation ax^2 + bx + c where a, b, and c are constants.

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Answer:

Remote Interior Angle

Step-by-step explanation:

The name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle is Remote Interior Angle.

If you take a look at the picture attached, you will find three angles: ∠A, ∠C and ∠D. In this case, we have that ∠A comes to be the exterior angle while ∠C and ∠D are the remote interior angle given that they are not adjacent to ∠A

Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= - 4x² - 6x - 1 + (- x² - 5x + 3) ← remove parenthesis

= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms

= - 5x² - 11x + 2 → C

The conversion from 2000 Swiss francs to Dutch guilders requires a historical exchange rate which is not provided. The Dutch guilder is obsolete since 2002, and precise conversions cannot be made without the rate from the time period when both currencies were in use.

To convert 2000 Swiss francs to Dutch guilders, you would need to know the specific exchange rate between the Swiss franc and the Dutch guilder at the time of the conversion. Unfortunately, as of today, the Dutch guilder is no longer in use, as the Netherlands adopted the euro as its currency in 2002. However, if you were to convert currencies similar to how holders of dollars are willing to exchange $2,500 for euros or vice versa, you would need the specific exchange rate from Swiss francs (CHF) to Dutch guilders (NLG) during the time when both currencies were in use.

Without historical exchange rate data, it is impossible to provide an exact number of Dutch guilders you would receive for 2000 Swiss francs. If you have a specific date in mind, you could find the historical exchange rate for that date and then calculate the conversion using this formula:

Amount in Swiss francs * Exchange rate (CHF to NLG) = Amount in Dutch guilders

Remember, when performing historical currency conversions, it's essential to use the correct exchange rate from the time period in question.

Answer:

y = - 5x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = - 5 and b = - 7, hence

y = - 5x - 7 ← equation of line

Since b equals the y-intercept, we automatically know that the answer will be in slope-intercept form which is y = mx + b where m equals slope and b equals the y-intercept.

Given.

m = –5, b = –7

Slope intercept formula.

y = mx + b

Plug in m = -5 and b = -7.

y = -5x - 7 ← Choice C

Answer:

[tex]\large\boxed{f(x)-g(x)=x^2-4x+13}[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2-4x-3\\\\g(x)=(x-4)(x+4)=x^2-4^2=x^2-16\qquad\text{used}\ a^2-b^2=(a-b)(a+b)\\\\f(x)-g(x)=(2x^2-4x-3)-(x^2-16)\\\\=2x^2-4x-3-x^2-(-16)\\\\=2x^2-4x-3-x^2+16\qquad\text{combine like terms}\\\\=(2x^2-x^2)-4x+(-3+16)\\\\=x^2-4x+13[/tex]