The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.

let's use those two endpoints in the line of (-5 , 2) and (5 , -1)

[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-2}{5-(-5)}\implies \cfrac{-3}{5+5}\implies -\cfrac{3}{10}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{3}{10}[x-(-5)]\implies y-2=-\cfrac{3}{10}(x+5) \\\\\\ y-2=-\cfrac{3}{10}x-\cfrac{3}{2}\implies y=-\cfrac{3}{10}x-\cfrac{3}{2}+2\implies y=-\cfrac{3}{10}x+\cfrac{1}{2}[/tex]

Answer:

y=-(3/10)x+(1/2)

Step-by-step explanation:

Let

A(-5,2),B(5,-1)

step 1

Find the slope m

m=(-1-2)/(5+5)

m=-3/10

step 2

Find the equation of the line into slope point form

we have

m=-3/10

point A(-5,2)

y-2=(-3/10)(x+5) ----> equation of the line into slope point form

Convert to slope intercept form -----> isolate the variable y

y=-(3/10)x-(15/10)+2

y=-(3/10)x+(5/10)

simplify

y=-(3/10)x+(1/2)

1. The angles DCA and BCA are the same.

2. Angles DCA and BCA are not supplementary. Since the both of them add up to 90° (we know that angle c is equal to 90° because in a right square all angles are 90°) the angles would be complementary, not supplementary. Supplementary angles add up to 180°

The angle relationship between ∠DCA and ∠BCA are equal and they are complementary angles.

A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.

Given that, ABCD is a square.

Here, a straight line from point A to C.

1) AC is diagonal, ∠DCA and ∠BCA are equal.

2) ∠DCA and ∠BCA are equal and added to 90°.

Therefore, the angle relationship between ∠DCA and ∠BCA are equal and they are complementary angles.

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Answer:

9

Step-by-step explanation:

When the leading coefficient (the coefficient of the x² term) is 1, we can complete the square by taking the b coefficient (coefficient of the x term), dividing it by 2, squaring the result, and adding it to both sides.

b = -6

b/2 = -3

(b/2)² = 9

Add 9 to both sides to make the left side a perfect-square trinomial.

To form a perfect square trinomial from the equation x²-6x, add 9 to both sides. This is achieved by halving the coefficient of x and squaring the result.

Amira can make the left side of the equation, x² - 6x, a perfect-square trinomial by adding 9 to both sides. The process for this involves completing the square. Half of the coefficient of x, which is -6, is -3. Squaring -3 gives 9. Therefore, Amira should add 9 to both sides of the equation to get x² - 6x + 9 = 1 + 9, simplifying to (x-3)² = 10. This results in a perfect-square trinomial on the left.

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Answer:

B. Systematic Random Sampling

Step-by-step explanation:

The process of systemic random sampling involves randomly selecting the starting point but the succeeding points will be based on the interval in between each point. The interval is computed by dividing the population by the sample size.

Answer:

B. Systematic Random Sampling

Step-by-step explanation:

none that i can explain

Answer: W=-1.8

Step-by-step explanation:

Divide both sides by 2.02 and you are left with W=-1.8.

Hope this helps!

Answer:

W = -1.8

Step-by-step explanation:

Step 1: Divide 2.02 on both sides.

W = -1.8

Answer: x = 239

Step-by-step explanation:

You need to get rid of everything else except the x = #

So, to do that you need to take the -47 and add 47 on each side.

That would get you x = 239

Answer:

239

Step-by-step explanation:

X - 47 = 192

       X = 192 + 47

       X = 239

Answer:

A = 42 cm^2

Step-by-step explanation:

To find the area of a rectangle , multiply the length and the width

A = lw

A = 7cm * 6 cm

A = 42 cm^2

ANSWER=5

EXPLANATION

The Mode is known as the number that occurs most often in a set of data, so the data being 5,5,5,5,5 only has fives in it so the answer must be 5.

Hello There!

The mode is the number that occurs the most in a set of numbers. In this case, there is only 5 numbers but they are all the same so the mode of the data set shown would be 5.

Answer: OPTION A.

Step-by-step explanation:

You can observe that in the figure CDEF the vertices are:

[tex]C(-2,-1),\ D(-2,0),\ E(2,2)\ and\ F(2,1)[/tex]

And in the figure C'D'E'F'  the vertices are:

[tex]C'(-8,-4),\ D'(-8,0),\ E'(8,8)\ and\ F'(8,4)[/tex]

For this case, you can divide any coordinate of any vertex of the figure C'D'E'F' by any coordinate of any vertex of the figure CDEF:

For C'(-8,-4) and C(-2,-1):

[tex]\frac{-8}{-2}=4\\\\\frac{-4}{-1}=4[/tex]

Let's choose another vertex. For E'(8,8) and E(2,2):

[tex]\frac{8}{2}=4\\\\\frac{8}{2}=4[/tex]

You can observe that the coordinates of C' are obtained by multiplying each coordinate of C by 4 and the the coordinates of E' are also obtained by multiplying each coordinate of E by 4.

Therefore, the rule that yields the dilation of the figure CDEF centered at the origin is:

[tex](x, y)[/tex]→[tex](4x, 4y)[/tex]

Answer:

A. (x, y) => (4x, 4y) this will help you out ;-)

Answer:

f(x) = x² + 2x - 3  ..….equation1

The graph of function will be a parabola

Standard form of parabola:

y=ax²+bx+c

x-coordinate of the vertex can be found using

x = [tex]\frac{−b}{2a}[/tex]

from equation 1 find values for a, b, and c.

a = 1, b = 2, c = -3    ⇒  x=−2/2(1) ⇒  x = -1

substitute the value of x into equation 1 for y-coordinate

f(-1) = (-1)² + 2(-1) – 3 ⇒ −4

vertex =(-1,−4)

Axis of symmetry = x = -1,  

Axis of symmetry is vertical and passes through the vertex with equation

x = -1

For x-intercept, put y = 0

x² + 2x - 3=0   ⇒   x² + 3x -x - 3=0     ⇒  x( x + 3 ) -1 ( x + 3 )  ⇒ ( x − 1 )( x + 3 ) = 0

equate each factor to zero and solve for x

x − 1 = 0  ⇒  x = 1,         x + 3 = 0  ⇒  x = -3

x-intercept = { 1, -3 }

For y-intercepts put x = 0

y = (0)² + 2(x) - 3

y = -3

y-intercept = ( 0 , -3 )

The points for the vertex, x-intercepts, and y-intercept and axis of symmetry are plotted on the graph.  

Answer: $0.12 per pound

Step-by-step explanation:

divide $360.00 by 3, then divide it by 1000, because 1000 lbs is 1 ton

Final answer:

To calculate the price per pound of dirt, divide the total cost of $360.00 by the total weight of 6000 pounds, resulting in a cost of $0.06 per pound.

Explanation:

The student asked how much it would cost per pound if 3 tons of dirt cost $360.00. First, it's essential to know how many pounds are in a ton. There are 2000 pounds in one ton. So for 3 tons, there would be 6000 pounds (3 tons x 2000 pounds/ton).

Next, to find the price per pound, you would divide the total cost by the total weight in pounds. That's $360.00 divided by 6000 pounds, which equals $0.06 per pound.

Therefore, the price per pound of dirt is $0.06.

Answer:

It is cryptic

Step-by-step explanation:

It is cryptic bc it means secretive and with hidden meaning

Answer:

Cryptic

Step-by-step explanation:

Cryptic means "having a meaning that is mysterious or obscure," so this would be the right answer

Why the others aren't correct:

Boisterous- Noisy, energetic, cheerful, rowdy [This doesn't fit the sentence]

Petulant- Childishly sulky [pouty] or bad tempered [This doesn't fit the sentence]

Jovial- Cheerful and friendly [This doesn't fit the answer]

Thus, the answer is cryptic.

I hope this helps!

Replace x in the equation with the x value from the ordered pair and see if the y value meets the inequality.

y ≤ 2(-9) -7

y ≤ -18 - 7

y ≤ -25

The y value in the ordered pair is 1, so replace y with 1 and see if the inequality is true:

1 ≤ -25

1 is a positive value and the equation equals a negative value, so this is not true, because 1 is greater than -25.

Answer:

100

Step-by-step explanation:

1=ad=100

and I need more characters so don't mind me.

Answer:

The correct option is 3. The measure of arc AD is 100°

Step-by-step explanation:

Given information: BD is a diameter, ∠1 = 100°  and arc BC=30°.

The central angle of an arc is the measure of arc.

From the given figure it is clear that the central angle of arc AD is equal to the angle 1.

[tex]Arc(AD)=\angle 1[/tex]

It is given that ∠1 = 100°

[tex]Arc(AD)=100^{\circ}[/tex]

The measure of arc AD is 100°, therefore the correct option is 3.

let's bear in mind that the cylinder and the cone both have the same volume of 112 cm³, and the same radius, but different heights.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} V=112\\ h=7 \end{cases}\implies 112=\pi r^2(7)\implies \cfrac{112}{7\pi }=r^2\implies \cfrac{16}{\pi }=r^2 \\\\\\ \sqrt{\cfrac{16}{\pi }}=r\implies \cfrac{\sqrt{16}}{\sqrt{\pi }}=r\implies \cfrac{4}{\sqrt{\pi }}=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\qquad \qquad \begin{cases} r=\frac{4}{\sqrt{\pi }}\\ V=112 \end{cases}\implies 112=\cfrac{\pi \left( \frac{4}{\sqrt{\pi }} \right)^2(h)}{3} \\\\\\ 336=\pi \left( \cfrac{4^2}{(\sqrt{\pi })^2} \right)h\implies 336=\pi \cdot \cfrac{16h}{\pi }\implies 336=16h \\\\\\ \cfrac{336}{16}=h\implies \blacktriangleright 21=h \blacktriangleleft[/tex]

Calculate the radius of the cup using its volume and height. Determine the cone's height by applying the cup's height to the volume formula for a cone after elimination.

The volume of the cup:

The formula for the volume of a cylinder: V = πr²h.

The formula for the volume of a cone: V = (π/3)r²h.

(πr²h)cylinder = ((π/3)r²h)cone

Since the cone has the same radius as the cylindrical cup and given h = 7 cm

Finding the height of the cone by eliminating:

[tex]h_{cylinder}[/tex] = [tex]h_{cone}[/tex]×(1/3)

[tex]h_{cone}[/tex] = 3 × 7 = 21

Therefore, height of cone is 21 cm.

ANSWER

p

[tex]{f}^{ - 1} (x) = 3x + 4[/tex]

EXPLANATION

The line r has equation,

[tex]f(x) = \frac{x - 4}{3} [/tex]

The line that represents

[tex] {f}^{ - 1} [/tex]

is p.

To find the equation of p, we let

[tex]y = \frac{x - 4}{3} [/tex]

We now interchange x and y.

[tex]x= \frac{y - 4}{3} [/tex]

We solve for y,

[tex]3x=y - 4[/tex]

[tex]y = 3x + 4[/tex]

Therefore

[tex] {f}^{ - 1} (x) = 3x + 4[/tex]

Answer:

x² + 11x + 30

Step-by-step explanation:

Solve using the FOIL method. The FOIL method is:

FOIL =

First

Outside

Inside

Last

, and is the order in which you do the problem.

(x + 5)(x + 6)

Follow FOIL. First, solve First (multiply x with x)

(x)(x) = x²

Next, multiply Outside (multiply x with 6)

(x)(6) = 6x

Then, multiply Inside (multiply 5 with x)

(5)(x) = 5x

Finally, multiply Last (multiply 5 with 6)

(5)(6) = 30

Combine like terms (terms with the same amount of variables, and the same variables)

x² + 6x + 5x + 30

x² + (6x + 5x) + 30

x² + 11x + 30

x² + 11x + 30 is your answer.

~

ANSWER

[tex]y= log_{x}(p)[/tex]

EXPLANATION

The given expression is

[tex] {x}^{y} = p[/tex]

We take logarithm of both sides to base x.

[tex] log_{x}( {x}^{y} ) = log_{x}(p) [/tex]

Apply the power rule of logarithms to get:

[tex]ylog_{x}( {x}) = log_{x}(p)[/tex]

Logarithm of the base is 1.

This implies that,

[tex]y( 1) = log_{x}(p)[/tex]

[tex]y= log_{x}(p)[/tex]

Sorry this took awhile.

So for Friday, it would be $550

Saturday, $895

Sunday, 1,095

So the total is $2540 if you add the numbers up. Hope this helps!

Answer:

The option on the top left

Step-by-step explanation:

As the equation is [tex]x^2+(y-4)^2=16[/tex]

We know that the circle will have a radius of 4 and will be shifted 4 units up

The center and radius of given circle equation are (0, 4) and 6√6 units respectively.

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²

The given circle equation is x²+(y-4)²=216.

Find the properties of the conic section

Center: (0,4)

Radius: 6√6

Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain:

[−6√6,6√6],{x∣∣−6√6≤x≤6√6}

Range: [4−6√6,4+6√6],{y∣∣4−6√6≤y≤4+6√6}

Therefore, the center and radius of given circle equation are (0, 4) and 6√6 units respectively.

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Answer:

a) If order matters, choices the player have = 5040

b) If order does not matter, choices the player have = 210

Step-by-step explanation:

n = 10, r = 4

When the order matters, its permutation.

permutation without repetition = P(n, r) =  [tex]\frac{n!}{(n - r)!}[/tex]

= [tex]\frac{10!}{(10 - 4)!}[/tex]

= [tex]\frac{10!}{6!}[/tex]

= 5040

When the order doesn't matter, its combination.

combination without repetition= C(n, r) = [tex]\frac{n!}{r!(n - r)!}[/tex]

= [tex]\frac{10!}{4!(10 - 4)!}[/tex]

= [tex]\frac{10!}{4! × 6!}[/tex]

= 210

If order matters, there are 5,040 different choices. If order does not matter, there are 210 different choices.

a) If order matters, the player has 10 choices for the first number, 9 choices for the second number (since it cannot be the same as the first), 8 choices for the third number, and 7 choices for the fourth number. Therefore, the total number of different choices is 10 * 9 * 8 * 7 = 5,040.

b) If order does not matter, the player is selecting a combination rather than a permutation. The number of combinations of four numbers chosen from a set of ten is given by the formula nCr = n! / (r!(n-r)!). In this case, n = 10 and r = 4, so the number of different choices is 10! / (4!(10-4)!) = 210.

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Answer:

[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]

Step-by-step explanation:

The terms of the sequence are:

[tex]5,-1,-7,-13,-19[/tex]

The first term of this sequence is [tex]f(1)=5[/tex].

There is a constant difference among the terms.

This constant difference can determined by subtracting a previous term from a subsequent term.

[tex]d=-1-5=-6[/tex]

The general term of this arithmetic sequence is given  recursively by [tex]f(n)=f(n-1)+d[/tex]

We substitute the necessary values to obtain:

[tex]f(n)=f(n-1)+-6[/tex]

Or

[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Instead of x substitute (x + 4) to f(x) = x² - 12

f(x + 4) = (x + 4)² - 12        use (a + b)² = a² + 2ab + b²

f(x + 4) = x² + 2(x)(4) + 4² - 12

f(x + 4) = x² + 8x + 16 - 12

f(x + 4) = x² + 8x + 4

Answer:

Part A)AT=16x^2

Part B)AT=4b^2 +12x^2

Step-by-step explanation:

Part A:

length of each side of square in tile=x

length of each small base side of trapezoid in tile=x

length of each large base side of trapezoid in tile=2x

height of each trapezoid in tile=x

Area of each square in tile= x^2

Area of each trapezoid in tile= x(x+2x)/2

                                               = (3x^2)/2

area of squares inside tile= 4(x^2)

area of trapezoids inside tile= 8[(3x^2)/2]

Area of tile, AT= area of squares inside tile+area of trapezoids in tile

AT= 4(x^2) + 8[(3x^2)/2]

     = 4x^2 + 12x^2

      = 16x^2

Part B)

if If the tile is a square with a length of b centimeters then AT

= 4b^2 +12x^2 !

Carlos is 15 years old and Andre is 30 years old.

Let's represent Carlos' age as 'x', and Andre's age as 'y'.

We are given that Carlos is half as old as Andre, so we can write the equation:

x = (1/2)y

We are also told that Andre is 15 years older than Carlos, so we can write the equation:

y = x + 15

Substituting the value of y from the second equation into the first equation, we get:

x = (1/2)(x + 15)

Now, we can solve for x:

2x = x + 15

x = 15

Therefore, Carlos is 15 years old. Andre's age can be found by substituting the value of x into the second equation:

y = 15 + 15

y = 30

So, Andre is 30 years old.

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Answer:

Step-by-step explanation:

y=kx

4=k(-2)

k=-2

y=-2x

when x=30

y=-2*30=-60

The top line has 4x^-2, they needed to move the x^-2 to the denominator using the negative exponent rule, so in line 1 instead of 1/y^-2, it should be 1/x^-2

Then the answer would become 4y^3 / x^3

Answer:

Step-by-step explanation:

Base x width x height

For this case we have by definition that the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where we have to:

A: It is the radius of the cylinder

h: It is the height of the cylinder

To find the volume of a cylinder we must have the radius and the height. In an equivalent way we can have the diameter, the radius is obtained by dividing the diameter by 2.

Answer:

[tex]V = \pi * r ^ 2 * h[/tex]

She could've subtracted 19 from both sides of the equation in the second step to find the value of [tex]x[/tex] immediately, rather then add 19 to both sides.

[tex]34=x+19 \\ \\ 34-19=x+19-19 \\ \\ x=15[/tex]

Answer:

19  should have been subtracted from, not added to, both sides of the equation.

Step-by-step explanation:

Answer:

Option B. [tex]11.78\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3} \pi r^{2}h[/tex]

we have

[tex]r=1.5\ in[/tex]

[tex]h=5\ in[/tex]

substitute

[tex]V=\frac{1}{3} \pi (1.5)^{2}(5)[/tex]

[tex]V=3.75\pi\ in^{3}[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]V=3.75(3.14)=11.78\ in^{3}[/tex]