Solve the system of equations.
4x+3y+6z=3
5x+5y+6z=5
6x+3y+6z=3

ANSWER

[tex]3= a( - 1 +6)( - 1 - 5)[/tex]

EXPLANATION

The equation of a parabola in factored form is

[tex]y = a(x + m)(x + n)[/tex]

where 'a' is the leading coefficient and 'm' and 'n' are the zeros.

From the question, the zeros of the parabola are 6 and −5.

This implies that,

[tex]m = 6 \: \: and \: \: n = - 5[/tex]

We plug in these zeros to get:

[tex]y= a(x +6)(x - 5)[/tex]

If (-1, 3) is a point on the graph of this parabola,then it must satisfy its equation.

We substitute x=-1 and y=3 to obtain:

[tex]3= a( - 1 +6)( - 1 - 5)[/tex]

The first choice is correct.

Final answer:

To solve the equation 4x = 8x - 1, isolate the variable x by subtracting 4x from both sides, then add 1 to both sides, and finally divide both sides by 4. The solution is x = 1/4.

Explanation:

To solve the equation 4x = 8x - 1, we need to isolate the variable x. We can do this by subtracting 4x from both sides of the equation:

4x - 4x = 8x - 4x - 1

0 = 4x - 1

Next, we can add 1 to both sides of the equation:

1 = 4x - 1 + 1

1 = 4x

Finally, we can divide both sides of the equation by 4 to solve for x:

1/4 = 4x/4

x = 1/4

The solution to the equation 4x = 8x - 1 is x = 1/4. We solve the equation by isolating x through standard algebraic steps. Checking our solution, we substitute it back into the original equation and confirm it is correct by verifying the equality.

The equation given by the student is 4x = 8x − 1. To find the value of x, we need to solve the equation. We start by subtracting 4x from both sides of the equation to get 0 = 4x − 1. We then add 1 to both sides which gives us 1 = 4x. Finally, we divide both sides by 4 to isolate x, which results in x = 1/4. This is the solution to the equation.

As a check, substituting x = 1/4 back into the original equation yields 4(1/4) = 8(1/4) − 1, simplifying to 1 = 2 − 1, which is a true statement and confirms our solution is correct.

Using the same technique, we can also solve different algebraic equations or systems of equations by manipulating the equations algebraically before substituting numerical values. This is illustrated in the given set of equations where variables are systematically eliminated until we end up with a single variable.

Therefore the by solving the equation 4x = 8x - 1 we get x = 1/4

For a given trapezium ABCD, measure of angle [tex]D = 52\°[/tex].

" An angle is defined as when two rays meet at a common point known as vertex."

According to the question,

Given trapezium ABCD,

Measure of angle [tex]BAD= 128\°[/tex]

Measure of angle [tex]ABC= 126\°[/tex]

Measure of angle [tex]BCD= 54\°[/tex]

Sum of all the interior angles in a trapezium is equal to [tex]360\°[/tex].

Therefore,

[tex]\angle ABC + \angle BCD +\angle CDA + \angle DAB = 360\°\\\\\implies 126\°+54\°+ \angle CDA + 128\°=360\°\\\\\implies \angle CDA = 360\° - 308\°\\\\\implies \angle CDA = 52\°[/tex]

Hence, Option (A) is the correct answer.

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Answer:

15

Step-by-step explanation:

Because x=y÷7

i.e,105÷7=15

Answer:

B.) -19

Step-by-step explanation:

-37 + n = -56

Add 37 to each side

-37 +37+ n = -56+37

n = -19

Answer: b) -19

Step-by-step explanation:

-37 + n=-56

use inverse operations and subtract -56 by 37 to get your answer

Answer:

See below in bold.

Step-by-step explanation:

a. The vertex is at (2, -1) in both functions.

b. Function A : Rate of increase = (change in y values)/ (change in x values)

= (0 - (-1)) / (3-2)

= 1.

c.  Function  B : Rate of change =

(0.5 - (-1)) / (3-2)

= 1.5.

d.  Function B increases faster between x = 2 and x = 3.

Answer:

A). (2, -1)

B). Average rate of change of function A = 1

C). Average rate of change of function B = 1.5

D). Graph of function B increases faster than function A.

Step-by-step explanation:

A). vertex of the function A will be (2, -1)

and vertex of the function B will be same as function A, (2, -1)

B). Average rate of change in function A between x = 2 and x = 3 will be

[tex]\frac{f(3)-f(2)}{x-x'}[/tex]

Equation of the function A will be f(x) = (x - 2)²-(-1)

f(x) = (x - 2)² + 1

f(3) = (3 -2)² + 1

     = 1² + 1 = 2

f(2) = 0 + 1 = 1

Therefore, rate of change = [tex]\frac{2-1}{3-2}[/tex]=1

C). Average rate of change of function B will be

=[tex]\frac{f(3)-f(2)}{x-x'}[/tex]

=[tex]\frac{0.5+1}{3-2}[/tex] [ from the given table]

= 1.5

D).Since rate of change of graph B is greater than graph A therefore, function B will increase faster than function A.

Answer:

22

Step-by-step explanation:

substitute:

5(7) - 3(8) + 11=0

35 - 24 + 11 = 0

=22

[tex]

5\times7-3\times8+11= \\

35-24+11= \\

11+11=22

[/tex]

Hope this helps.

r3t40

Answer:

[tex]\large\boxed{(x-h)^2+(y-v)^2=r^2-\bold{Standard\ form}}\\\boxed{x^2+y^2-2hx-2vy+h^2+v^2-r^2=0-\bold{General\ form}}[/tex]

Step-by-step explanation:

[tex](x-h)^2+(y-v)^2=r^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\x^2-2hx+h^2+y^2-2vy+v^2=r^2\qquad\text{subtract}\ r^2\ \text{from both sides}\\\\x^2+y^2-2hx-2vy+h^2+v^2-r^2=0[/tex]

Answer:

x = 9

x = 3

Step-by-step explanation:

find the roots of x² - 6x - 27 = 0

by factorization (or use any of your favorite methods for solving quadratic equations):

x² - 6x - 27 = 0

(x-9)(x+3) = 0

Hence,

(x-9) = 0  --------> x = 9

or

(x+3) = 0  --------> x = -3

The intercepts of the quadratic function is 9 and 3.

A function can be defined as a mathematical expression which explains the relationship between dependent variable and independent variable.

It always comes with a defined  range and domain.

The function given in the question is

f (x) = x² - 6x - 27

To find the intercept means to find the roots of the equation

roots can be determined by

x² - 9x + 3x -27 = 0

x(x-9) -3(x-9) = 0

x= 9 , 3

Therefore the intercepts of the quadratic function is 9 and 3 .

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Final answer:

The y-intercept in the equation y=0.10x+9.50 represents an initial financial value of $9.50, such as a fixed charge or baseline cost, before any variable amounts are factored in.

Explanation:

In everyday English, the financial meaning of the y-intercept in the equation y=0.10x+9.50 refers to the initial amount or fixed cost that does not depend on the quantity represented by x. In other words, when x, which might represent the quantity of goods sold or the number of hours worked, is zero, the y-intercept indicates a starting value of $9.50. This could be a baseline charge, a fixed fee, or some kind of initial cost before any additional variables are added to the equation.

Answer

The answer to this question is not one of your answer choices, but the answer is 240.1413932 square centimeters.

Step-by-step explanation:

A=πr(r+√h² + r²) [radical wrapped around h² + r²]

Answer:

The slope of this line is 3.

Step-by-step explanation:

Solve 12x - 4y = 3 for y to obtain the equation in slope-intercept form:

Add 4y to both sides, obtaining 12x = 3 + 4y

Subtract 3 from both sides:  12x - 3 = 4y

Finally, divide all terms by 4:  y = 3x - 3/4

The slope of this line is 3.

Answer:  The slope of the graph is 3.

Step-by-step explanation:

The equation of a line in slope intercept for is given by :-

[tex]y=mx+c[/tex], where m is the slope of the line.

The given equation of  the line graphed by Helaine = [tex]12x - 4y = 3[/tex]

Now, rewrite the above equation in slope-intercept form by adding 4y  and  subtracting 3 from both sides , we get

[tex]4y=12x-3[/tex]

Divide 4 on both sides , we get

[tex]y=3x-\dfrac{3}{4}[/tex] which is the slope-intercept form.

[tex]\Rightarrow\text{Slope}=3[/tex]

Hence, the slope of Helaine's line =3

Answer: OPTION C.

Step-by-step explanation:

It is important to know the following:

Dilation:

Translation:

Therefore, since the Square T was translated and then dilated to create Square T'', we can conclude that the statement that explains why  they are similar is:

Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.

Answer:

C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Next he marks the circumference of the circle with 6 equal marks that also equal the radius.

He numbers the points consecutively.

He joins points 2 4 6 2  or 1 3 5 1 (The last point gets him back to where he started.

That's his equilateral triangle using just a straight edge and compass.

Answer:

B = 58.9

Step-by-step explanation:

We are given that a triangle ABC has two side lengths of 28 ft. and 24 ft. with angle C measuring 91°. We are to find the measure of angle B.

AB = 28 ft

AC = 24 ft

For this, we will use the sine formula:

[tex]\frac{sin B}{24} = \frac{sin91}{28}[/tex]

[tex]sin B = \frac{sin91 \times 24}{28}[/tex]

[tex] sin B = 0 . 8 5 7 [/tex]

[tex] B = sin' 0 . 8 5 7 [/tex]

B = 58.9

the answer is C, all sides must be proportional to a specific factor, or the dilation

Similar shapes may or may not be congruent.

The true statement is: (c) Verify corresponding pairs of sides are proportional by dilation.

From the question, we understand that:

QRST and WXYZ are similar

The possible scenarios are:

The best way to determine their similarities is to assume that they are not congruent

This means that, the trapezoids are dilated, and they must have proportional corresponding sides.

The above highlight means that:

Option (c) is true

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Answer:

25

Step-by-step explanation:

Because they cost $25 to make so in order to cover the cost they would need to charge at least 25, but out of those choices if they wanted to make a profit they'd need to charge the $50

Answer:

A. x^2 + y^2 = 36

Step-by-step explanation:

The equation of a circle is usually written in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

The center is at the origin so (h,k) = (0,0) and  the radius is 6 so r=6

x^2 + y^2 = 6^2

or x^2 +y^2 = 36

Answer:

A. [tex]x^2+y^2=36[/tex]

Step-by-step explanation:

An equation of a circle form is: [tex](x-h)^2+(y-k)^2=r^2[/tex]

Details:

[tex](h, k)[/tex] is the center of a circle, [tex]r[/tex] which means radius.

The origin is the center of the circle. [tex](h,k)=(0,0)[/tex] and the radius is [tex]6[/tex] so that means [tex]r=6[/tex]. [tex]x^2+y^2=6^2[/tex], and or [tex]x^2+y^2=36[/tex].

Note: I hope this helps anyone. Sorry about the wait for another answer but should help you and others in the meantime. And if you could please give either me, or the other person brainliest.

And enjoy the rest of your day. :)

Answer:

(-0.84, 0) and (-5.16, 0).

Step-by-step explanation:

Step-by-step explanation:

y = 2/27 x² − 4/3 x

a) The leading coefficient (the coefficient of the x² term) is positive, so that means the parabola points up.  So the vertex is at the bottom of the parabola, making it a minimum.

b) For a parabola y = ax² + bx + c, the x coordinate of the vertex can be found at x = -b / (2a).  Here, a = 2/27 and b = -4/3.

x = -(-4/3) / (2 × 2/27)

x = (4/3) / (4/27)

x = (4/3) × (27/4)

x = 9

c) To find the y coordinate of the vertex, we simply evaluate the function at x=9:

y = 2/27 x² − 4/3 x

y = 2/27 (9)² − 4/3 (9)

y = 6 − 12

y = -6

d) The ordered pair is (9, -6).  This means that at the lowest point of the dish, the dish is 6 inches deep.  Also, since the dish is symmetrical, and the lowest point is 9 inches from the end, then the total width is double that, or 18 inches.

The vertex of the function is a minimum point. The x and y-coordinates of the vertex are 27 and -54 respectively, representing the deepest point in the dish where signals are concentrated.

a) The vertex of a parabolic function y = ax^2 + bx + c is a maximum point if 'a' is negative and a minimum point if 'a' is positive. In this case, we have a = 2/27, which is positive, so the vertex of the function is a minimum point.

b) The x-coordinate of the vertex can be found using the formula -b/2a. For the quadratic function y = 2/27x^2 - 4/3x, b = -4/3, and a = 2/27. So the x-coordinate of the vertex is -(-4/3)/(2*2/27) = 27.

c) The y-coordinate of the vertex can be obtained by substituting the x-coordinate of the vertex into the equation. Therefore, y = 2/27*(27)^2 - 4/3*27 = -54

d) So the vertex, as an ordered pair (x, y), is (27, -54). The vertex represents the shallowest point in the parabola, which in the case of a satellite dish, equates to the deepest point of the dish, where signals are most concentrated or focused.

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Answer:

six tenths cupcake

Step-by-step explanation:

6/1 ÷ 10/1

6/1 × 1/10 = 6/10

The fraction of a cupcake does each person receive will be [tex]\frac{6}{10}[/tex] i.e. option A, i.e. six tenths of cupcake.

The fraction is numerical representation of the numbers in the form of numerator and denominator.

We have,

Total cupcakes = 6

Total people = 10

So,

To get equal share of the cupcake divide it by total number of people,

i.e.

Equal share  [tex]=\frac{Total\ cupcake}{Total\ people}[/tex]

So,

Equal share for 10 people [tex]=\frac{6}{10}[/tex]

So,

Everyone gets six tenths of cupcake.

Hence, we can say that the fraction of a cupcake does each person receive will be [tex]\frac{6}{10}[/tex] i.e. option A, i.e. six tenths of cupcake.

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Answer:

Plain still in air = 240

Air current = 28

Step-by-step explanation:

To find the speed of the jet in still air and the speed of the wind, we can set up a system of equations using the given information. Solving these equations, we find that the speed of the jet in still air is 88 mph and the speed of the wind is 180 mph.

To find the speed of the jet in still air and the speed of the wind, we can set up a system of equations using the given information. Let's say the speed of the jet in still air is x mph and the speed of the wind is y mph. When the jet is flying with a tailwind, the speed of the jet relative to the ground is x + y mph. We can write the equation as 1,072 = (x + y) * 4. Similarly, when the jet is flying into a headwind, the speed of the jet relative to the ground is x - y mph. We can write the equation as 848 = (x - y) * 4. Now, we can solve these two equations to find the values of x and y.

Multiplying the first equation by 4, we get 4,288 = 4x + 4y. Subtracting the second equation from this, we get 1,440 = 8y. Dividing both sides by 8, we find that y = 180. Substituting this value back into the first equation, we get 1,072 = 4x + 4 * 180. Simplifying, we get 1,072 = 4x + 720. Subtracting 720 from both sides, we find that 4x = 352. Dividing both sides by 4, we find that x = 88.

Therefore, the speed of the jet in still air is 88 mph and the speed of the wind is 180 mph.

Answer:

Option D) 15 3/4 cups

Step-by-step explanation:

we know that

using proportion

Let

x ----> the cups of flour needed

[tex]4\frac{1}{2}=\frac{4*2+1}{2}=\frac{9}{2}\ cups\ flour[/tex]

[tex]\frac{(9/2)}{2}=\frac{x}{7} \\ \\x=(9/2)*7/2\\ \\x=63/4\ cups\ flour[/tex]

convert to mixed number

[tex]63/4\ cups=15.75=15\frac{3}{4}\ cups[/tex]

Answer:

283cm³

Step-by-step explanation:

The linear scale factor= Height of larger/Height of smaller cylinder.

=8cm/4cm=2

VOLUME scale factor = linear scale factor³

=2³=8

Therefore we divide the volume of the larger cylinder by  the volume scale factor.

volume of small cylinder=2264cm³÷8

=283cm³

Answer: first option.

Step-by-step explanation:

 You know that the height of the smaller cylinder is 4 cm and the height of the  larger cylinder is 8 cm, then you can find the volume ratio. This  is:

[tex]Volume\ ratio=(\frac{4\ cm}{8\ cm})^3\\\\Volume\ ratio=\frac{1}{8}[/tex]

Knowing that the volume of the larger cylinder is 2,264 cubic centimeters, you need to multiply it by the volume ratio to find the volume of the smaller cylinder.

Therefore:

[tex]V_{smaller}=\frac{1}{8}(2264\ cm^3)\\\\V_{smaller}=283\ cm^3[/tex]

Answer:

17/20

Step-by-step explanation:

To find the simplest form of 0.85 you need to turn it into a fraction.

To turn it into a fraction you put 85 over 100 since 0.85 is in the hundredths place.

85/100 can be simplified to 17/20 because 85/5 is 17 and 100/5 is 20

Answer:

17/20

Step-by-step explanation:

The simplest form of a number is a fraction. .85 as a fraction is 85/100. Simplifying this into 17/20 puts it into its simplest form.

Step-by-step explanation:

The second one, of course. Because the inequality means that x must be smaller than -3. So in negative numbers, numbers are getting smaller when they go far from 0. So [tex]-8\frac{2}{3},-6,-4, -3,5[/tex] are smaller than -3 because the distance between 0 and these numbers are more than he distance between zero and -3. Good luck :)

Answer:

(0,∞)

Step-by-step explanation:

The problems tells us to find the range of the function

f(x)=2*(1/4)^x

after it has been reflected over the y-axis

This means

g(x) = 2*(1/4)^(-x)

To quickly find the answer, we can plot the equation and examine the range in the graph.

The range of both functions is the same

(0,∞)

See attached picture

Answer:  (0, -1 [tex]\frac{2}{3}[/tex]), (1, -1), (2, 1)

Step-by-step explanation:

Set the exponent equal to zero - that is your anchor point.

Then choose an x-value less than and greater than the anchor point.

[tex]\left\begin{array}{c|c|l}&\underline{\quad x\quad }&\underline{\qquad \qquad f(x)\qquad \qquad \qquad \quad }\\\text{less than anchor}&0&3^{0-1}-2=3^{-1}-2=\frac{1}{3}-2 = -1\frac{2}{3}}\\\\anchor\ point&1&3^{1-1}-2=3^{0}-2=1-2 = -1}\\\\\text{greater than anchor}&2&3^{2-1}-2=3^{1}-2=3-2 = 1}\end{array}\right[/tex]

Answer:

x6 − x3 − 20 = (x3)2 − x3 − 20 = (x3 + 4)(x3 − 5)

Step-by-step explanation:

In this trinomial, the exponent of the first term, 6, is double the exponent in the second term, 3. And, the third term contains no variables. So, we can factor the expression as we would a quadratic, but treating x3 as if it were x:

Answer:

(x³ - 5)(x³ + 4)

Step-by-step explanation:

Consider the factors of the constant term (- 20) which sum to give the coefficient of the x³ term (- 1)

The factors are - 5 and + 4, since

- 5 × 4 = - 20 and - 5 + 4 = - 1, hence

[tex]x^{6}[/tex] - x³ - 20 = (x³ - 5)(x³ + 4)

Answer:

D

Step-by-step explanation:

The line x originates from the center of the circle and forms a perpendicular line with line RS, which means that the line is bisected.

That means that line RT is half of line RS, or 7.

Then we can use the Pythagorean Theorem to find the measure of x.

[tex]7^2+b^2=9^2[/tex]

[tex]49+b^2=81[/tex]

[tex]b^2=32[/tex]

b = √32

b ≈ 5.66