what substitution should be used to rewrite 6(x+5)^2+5(x+5)-4=0 as a quadratic equation

Answer:

Step-by-step explanation:

Find the discriminant, b^2-4ac:  Here a = 1, b = -5 and c = 5.

Then the discriminant is (-5)^2-4(1)(5) = 5, and so there are 2 real, different roots.  The roots are:

      -(-5) ±√5

x = ----------------,   which correspond to answers A and C.

           2(1)

The roots of the equation will be (5 - √5) / 2 and (5 + √5) / 2. Then the correct options are A and C.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The quadratic equation is given below.

x² - 5x + 5 = 0

Then the root of the equation is given as

[tex]\rm x = \dfrac{ - (-5) \pm \sqrt{(-5)^2 - 4*1*5}}{2*1}\\\\x = \dfrac{5 \pm \sqrt{25-20}}{2}\\\\x = \dfrac{5 \pm \sqrt5}{2}\\\\x = \dfrac{5 - \sqrt5}{2}, \dfrac{5 + \sqrt5}{2}[/tex]

Thus, the correct options are A and C.

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Answer:

Solve the equation

[tex]\displaystyle \frac{8.8 + 9.5 + 9.2 + x}{4} \ge 9.1[/tex],

where [tex]x[/tex] is the minimum score of the fourth judge.

At least 8.9 points.

Step-by-step explanation:

Let the score of the fourth judge be [tex]x[/tex].

The average score is the sum of the four judges' score divided by the number of scores. That is:

[tex]\displaystyle \text{Average Score} = \frac{8.8 + 9.5 + 9.2 + x}{4}[/tex].

The minimum average score needs to be greater than or equal to [tex]9.1[/tex]. In other words,

[tex]\displaystyle \frac{8.8 + 9.5 + 9.2 + x}{4} \ge 9.1[/tex].

Multiply both sides of by four.

[tex]8.8 + 9.5 + 9.2 + x = 4\times 9.1[/tex].

Subtract [tex]8.8 + 9.5 + 9.2[/tex] from both sides of the equation:

[tex]x = 4\times 9.1 - (8.8 + 9.5 + 9.2) = 8.9[/tex].

In other words, the minimum score of the last judge is [tex]8.9[/tex] for Julie to move on.

Answer:

Multiply 5π/6 by 180/π, you will get answer 150°.

Answer: [tex]150^{\circ}[/tex]

Step-by-step explanation:

To convert a radian measure to degrees , we generally multiply it by 180° and divide it by [tex]\pi[/tex].

Given : [tex]m. \overarc{XYZ}=\dfrac{5\pi}{6}\text{radian}[/tex]

Then, In degrees it should be

[tex]m. \overarc{XYZ}=\dfrac{5\pi}{6}\times\dfrac{180^{\circ}}{\pi}\\\\\Rightarrow m.\overarc{XYZ}=150^{\circ}[/tex]

Hence, the correct answer is [tex]150^{\circ}[/tex].

The x-intercepts of the parabola are [tex]\(x = -3 + \sqrt{\frac{14}{3}}\) and \(x = -3 - \sqrt{\frac{14}{3}}\).[/tex]

To find the x-intercepts of the parabola, we need to set y=0 in the equation of the parabola and solve for x.

Given that the vertex of the parabola is [tex]\((-3, -14)\),[/tex] the equation of the parabola can be expressed in the form [tex]\(y = a(x - h)^2 + k\)[/tex], where [tex]\((h, k)\)[/tex]represents the vertex and a is the coefficient determining the direction and width of the parabola.

Using the vertex form, we have:

[tex]\[ y = a(x + 3)^2 - 14 \][/tex]

We know that the y-intercept is (0,13) so when x=0, y=13:

[tex]\[ 13 = a(0 + 3)^2 - 14 \]\[ 13 = a(9) - 14 \]\[ 13 = 9a - 14 \]\[ 9a = 13 + 14 \][/tex]

[tex]\[ 9a = 27 \]\[ a = \frac{27}{9} \]\[ a = 3 \][/tex]

So, the equation of the parabola is:

[tex]\[ y = 3(x + 3)^2 - 14 \][/tex]

Now, to find the x-intercepts, we set y=0:

[tex]\[ 0 = 3(x + 3)^2 - 14 \]\[ 3(x + 3)^2 = 14 \]\[ (x + 3)^2 = \frac{14}{3} \][/tex]

Now, we take the square root of both sides:

[tex]\[ x + 3 = \pm \sqrt{\frac{14}{3}} \][/tex]

Answer:

see explanation

Step-by-step explanation:

The error is in Step 1, by not adding 2 on the left side, that is

Given

7.7 = w - 2 ( add 2 to both sides )

7.7 + 2 = w - 2 + 2

9.7 = w

Answer:

B

Step-by-step explanation:

it is a simple exchange for goods and services because, is stores value for later use.

The correct answer is option d) ( y = -x + 2 ).

Let's analyze each option to determine which equation does not represent the line passing through the points (1, 1) and (5, 5).

a) ( y = x ): This equation represents a line with a slope of 1 and passes through the origin. To check if it passes through (1, 1) and (5, 5), we substitute the coordinates into the equation:

- For (1, 1): ( 1 = 1 ) (True)

- For (5, 5): ( 5 = 5 ) (True)

The equation ( y = x ) is consistent with the given points.

b) ( y = 2x - 1 ): This equation represents a line with a slope of 2 and a y-intercept of -1. Checking with the given points:

- For (1, 1): ( 1 = 2(1) - 1 ) (True)

- For (5, 5): ( 5 = 2(5) - 1 ) (True)

The equation ( y = 2x - 1 ) is consistent with the given points.

c) ( 2y = 2x ): This equation can be simplified to ( y = x ), which we have already determined is consistent with the points.

d) ( y = -x + 2 ): Checking with the given points:

- For (1, 1): ( 1 = -1 + 2 ) (True)

- For (5, 5): ( 5 = -5 + 2 ) (False)

The equation ( y = -x + 2 ) does not pass through the point (5, 5).

QUESTION

Which of the following equations does not represent the line passing through the points (1, 1) and (5, 5)?

a) ( y = x )

b) ( y = 2x - 1 )

c) ( 2y = 2x )

d) ( y = -x + 2 )

Answer:

Number of Large Pizzas: 30

Number of Medium Pizzas: 8

Number of Small Pizzas: 27

Step-by-step explanation:

L = # of large Pizzas

M = # of medium Pizzas

S = # of small Pizzas

Amount:

L = 4M - 2

S = 3M + 3

Cost:

21L + (I'm assuming you meant 14) 14M + 7S = 931

Plus in the Amounts to the Cost:

21(4M - 2) + 14M + 7(3M + 3) = 931

84M - 42 + 14M + 21M +21 = 931

Combine like terms:

119M - 21 = 931

Isolate the Variable:

119M - 21 + 21 = 931 + 21

119M = 952

119M/119 = 952/119

M = 8

Plug it into the Amount equations:

Large: L = 4(8) - 2

L = 32 - 2

L = 30

Small: S = 3M + 3

S = 3(8) + 3

S = 24 + 3

S = 27

Check your work (plug the values into Cost.):

21(30) + 14(8) + 7(27) = 931

630 + 112 + 189 = 931

931 = 931

The number of medium pizzas ordered was 10. Hence, based on the given relationships, the number of large pizzas was 38 and the number of small pizzas was 33.

To solve this problem, really, we are using three algebraic expressions that represent the total cost, the relationship between the large and medium pizzas, and the relationship between the small and medium pizzas.

We can define M as the number of medium pizzas, L as the number of large pizzas, and S as the number of small pizzas. We can then set up the following equations based on the problem:

We can substitute equations 2 and 3 into equation 1 to get a single equation in terms of M:

$21(4M-2) + $14M + $7(3M+3) = $931

Which simplifies to:

93M = 931

Then, M=10, hence, the number of medium pizzas is 10, number of large pizzas (4M-2) is 38, and the number of small pizzas (3M+3) is 33.

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Answer:

P 1 red) = 1/3

Step-by-step explanation:

We have 12 marbles (3+4+5)

P(red) = red marbles/ total marbles

          = 4/12 = 1/3

Answer:

4 / 12 or 1/3

Step-by-step explanation:

The total is 3 blue, 4 red and 5 green marbles which is 12 marbles altogether.

There is exactly 4 marbles out of the 12 marbles that are red so the probability of choosing a red is 4 / 12 or 1/3

Answer:

D

Step-by-step explanation:

because we know that angle EOD is less the 90 so that means that it is complementary. For AOB it is  the same but we can check by adding 35 plus x plus 90 =180 degrees  so 35+90=125  x=180-125=55 so x=55 and 55 is less then 90  so it is a complementary angle.

Answer:

x=1

Step-by-step explanation:

We distribute the negative 5 to x minus three to get 8x-5x+15=18. Then, we cancel out the 15 by subtracting it from both sides. This leaves us with 8x-5x=3. When we subtract, we get 3x=3, and when we divide both sides by 3, we get x=1. Hope this helps :)

Answer:

your answer would be A -9 9/14

ANSWER

The diameter is 8 units.

EXPLANATION

A portion of the y-axis is serving as the diameter of the circle.

The portion of the y-axis that intersects the circle at two points.

We can use these intercepts to find the diameter.

There is a y-intercept at y=2 and y=-6.

The distance between the two intercepts is the diameter of the circle.

[tex] |2 - - 6| = |2 + 6| = 8[/tex]

Therefore the radius is 8 units.

Answer: [tex]diameter=8\ units[/tex]

Step-by-step explanation:

By definition, the radius of a circle is the distance from its center to its edge.

We need to remember that diameter of a circle is twice the radius:

[tex]diameter=2(radius)[/tex]

Then, you can observe in the figure that there are 4 units between the center of this circle and its edge, therefore the radius is:

[tex]radius=4\ units[/tex]

Finally, you need to substitute the radius calculated into the formula  [tex]diameter=2*radius[/tex] to find the value of the diameter of this circle. Then, this is:

 [tex]diameter=2(4\ units)[/tex]

 [tex]diameter=8\ units[/tex]

Answer:

B: Directly; $5.10

Step-by-step explanation:

1 pound of apples = $1.50

so

3.4 pounds of apples = $1.50 x 3.4

                                    =$5.10

Answer:

4x2−25

Step-by-step explanation:

yes

Answer:

4x^2-25

Step-by-step explanation:

Answer:

Explanation:

The pattern of the game consists on 7 congruent (necessary assumption) rectangles.

The dimensions of such congruent rectangles are given for the rectangle number 6: lenght = t + 3 (a binomial) and width = t (a monomial).

So, the area of each rectangle is found as the product of a monomial and a binomial:

Apply distributive property:

Since that is the area on one rectangle, you have to mulply by the number of reactangles (7):

Answer:

Step-by-step explanation:

Given is a form of hopscotch called Jumby.

The pattern consists of 7 identical rectangles with length t+3 and width 5

To find area it is necessary to add the totals of all 7 rectangles

OR area = 7 * area of one rectangle

Area of one rectangle [tex]= lw \\= t(t+3)\\= t^2+3t[/tex]

Hence area of whole figure = [tex]7(t^2+3t)\\=7t^2+21t[/tex]

Answer:

    -9/7

Step-by-step explanation:

To find the slope given 2 points, we use the formula

m = (y2-y1)/(x2-x1)

 where (x1,y2) and (x2,y2) are the two points

m = (-3-6)/(5--2)

m = (-3-6)/(5+2)

   = -9/7

Answer:

y=-1.3x+3.4

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

x + 4y = 36

To find the x- intercept, let y = 0 in the equation and solve for x

x + 0 = 36 ⇒ x = 36 ← x- intercept

To find the y- intercept let x = 0 in the equation and solve for y

0 + 4y = 36 ⇒ y = 9 ← y- intercept

Answer:

x-intercept is 36; y-intercept is 9.

Step-by-step explanation:

Given equation of the line,

[tex]x+4y=36[/tex]

For x-intercept ( the point at which the line intersects the x-axis ),

y = 0,

[tex]\implies x+4(0) = 36[/tex]

[tex]x=36[/tex]

⇒ The value of x-intercept is 36,

Now, for y-intercept( the point at which the line interests the y-axis )

x = 0,

0 + 4y = 36

⇒ y = 9

⇒ The value of y-intercept is 9.

Hence, first option is correct.

Answer:

Option D

Step-by-step explanation:

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

In plain English, the definition means:

The range is the resulting y-values we get after substituting all the possible x-values.

How to find the range

1.The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)

2. Substitute different x-values into the expression for y to see what is happening. (Ask yourself: Is y always positive? Always negative? Or maybe not equal to certain values?)

3. Make sure you look for minimum and maximum values of y.

4. Draw a sketch! In math, it's very true that a picture is worth a thousand words.

Answer:

2767550

Step-by-step explanation:

looking at the number 2767545

reading number from right to left

the most right number is 0 there that is the ones digit

next right number is 4 that is the tens digit (that is what we are rounding to. we use the one right of the ten's digit to decide to round up or not. You round up if is 5 or more. So since the ones digit is 5, that is 5 or more. so we round the 4 in the ten's to a 5 and make one's 0.

---

If someone side round to nearest hundreds: it would be 2767500 because the digit directly to the right of it was a 4

Answer:

2767550.

Step-by-step explanation:

Th ten's digit is 4 and as the units digit is 5 we round up. That gives us

2767550.

ANSWER

[tex]y = - 4 {x}^{2} + 4x - 3[/tex]

EXPLANATION

Let the quadratic function be

[tex]y = a {x}^{2} + bx + c[/tex]

We substitute each point to find the constants, a,b, and c.

Substitute: (x=0,y=-3)

[tex] - 3 = a {(0)}^{2} + b(0) + c[/tex]

[tex] \implies \: c = - 3...(1)[/tex]

Substitute: (x=-1,y=-11) and c=-3

[tex] - 11 = a {( - 1)}^{2} + b( - 1) + - 3[/tex]

[tex] \implies \: - 11 = a - b - 3[/tex]

[tex] \implies \: a - b = - 8...(2)[/tex]

Substitute: (x=3,y=-27) and c=-3

[tex] -27= a {( 3)}^{2} + b( 3) + - 3[/tex]

[tex] \implies \: - 27 = 9a + 3b - 3[/tex]

[tex]\implies \: 3a + b = - 8...(3)[/tex]

Add equations (3) and (2)

[tex]3a + a = - 8 + - 8[/tex]

[tex]4a = - 16[/tex]

[tex]a = - 4[/tex]

Put a=-4 in equation (2)

[tex] - 4 - b = - 8[/tex]

[tex] - b = - 8 + 4 [/tex]

[tex] - b = - 4[/tex]

[tex]b = 4[/tex]

The quadratic equation is

[tex]y = - 4 {x}^{2} + 4x - 3[/tex]

Final answer:

To fit a quadratic function to the three given points, we use the general form y = ax² + bx + c and set up a system of equations. Solving the system yields the function y = -2x² + 6x - 3.

Explanation:

To fit a quadratic function to the points (-1, -11), (0, -3), and (3, -27), we need to find a function of the form y = ax² + bx + c where a, b, and c are constants. We will set up three equations based on the given points:

Solving these equations gives us a system:

From the second equation, we have c = -3. Inserting that into the first and third equations:

Solving this system gives us a = -2 and b = 6.

Therefore, the quadratic function fitting the points is y = -2x² + 6x - 3.

Answer:

x=93

Step-by-step explanation:

The exterior angles of a triangle add to 360 degrees

133+134+x = 360

267+x =360

Subtract 267 from each side

267+x-267 = 360-267

x =93

Answer:

4x - 3y -18 = 0 or y = 4x/3 - 6

Step-by-step explanation:

We will have to find the slope of the line first

The formula for slope:

[tex]m =\frac{y_{2}- y_{1} }{x_{2} -x_{1} } \\m= \frac{-2-2}{3-6}\\ =\frac{-4}{-3}\\ =\frac{4}{3}[/tex]

The standard form of equation of a line is:

y = mx + b

We know m,

So the equation will be:

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

We have to find the value of b, for that we will put any one of the point in the equation

So, putting (6,2)

2 = 4/3 * 6 + b

2 = 8 +b

b = -6

Putting the value of m and b in the standard form of equation of line,

[tex]y = mx + b\\y = \frac{4}{3}x+(-6)\\y = \frac{4}{3} x - 6\\Multiplying\ both\ sides\ by\ 3\\3y = 4x - 18\\4x - 3y -18 = 0[/tex] ..

[tex]12=2\cdot7+1\\12=15[/tex]

[tex]LHS\not=RHS[/tex] so no, it isn't on the line.

Answer:

[tex]-3,\ -1,\ 1[/tex]

Step-by-step explanation:

You are given the relation

[tex]R=\{(-3,-2),\ (-3,0),\ (-1,2),\ (1,2)\}[/tex]

The domain of the relation are all possible inputs and the range of the relation are all possible outputs. In your case,

So,

Answer:

-3, -1, and 1

Step-by-step explanation:

hope that helps :)

Answer:

10*7+ 18x *7 =2590

or 70 + 18x*7  =2590

Step-by-step explanation:

10*7 to find out how much the shipping costs for the 7 teams altogether

18*x  because you need to find how much the jerseys cost for all the soccer teams

then multiply it by 7 to find how many players on each team

when you solve for x you get 20

there are 20 players on each on team.

Final answer:

To determine the number of players on each soccer team, given the total jersey order cost for all teams, the equation 7(18x) + 7(10) = 2590 can be used, where x represents the number of players.

Explanation:

The question asks which equation can be used to determine x, the number of players on each team, given that the total cost to order jerseys for all the teams is $2,590, the cost per jersey is $18, and the shipping per team is $10, with 7 teams ordering. To find the equation, we first outline the total costs involved: the cost of the jerseys plus the shipping cost for all teams.

Let's denote x as the number of players on each team.

The cost for jerseys for one team would be 18x (since each jersey costs $18), and the cost to outfit all 7 teams would be 7 times that amount, plus the total shipping cost for all teams (7 teams times $10 per team).

So, the equation can be represented as:

7(18x) + 7(10) = 2590

This equation accounts for both the per-jersey cost and the fixed shipping fee for each team, totaling up to the overall cost reported.

Answer:

Step-by-step explanation:

[tex]s(x)=x-7,\ t(x)=4x^2-x+3\\\\(t\circ s)(x)=t\bigg(s(x)\bigg)-\text{exchange x to }\ s(x)=x-7:\\\\(t\circ s)(x)=4(x-7)^2-(x-7)+3[/tex]

Answer:

B

Step-by-step explanation:

The volume (V) of a pyramid is calculated as

V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)

area of square base = 12 × 12 = 144 units² and h = 8, hence

V = [tex]\frac{1}{3}[/tex] × 144 × 8 = [tex]\frac{1152}{3}[/tex] = 384 units³ → B

Volume of the pyramid is equal to [tex]384 \ unit^{3}[/tex].

" Volume is defined as the total space occupied by any three- dimensional object enclosed in it."

Formula used

Volume of a pyramid [tex]= \frac{1}{3} \times Area \ of \ the \ base \times height[/tex]

Area of a square [tex]= s^{2}[/tex]

[tex]s=[/tex] Side length

According to the question,

Given dimensions of pyramid,

Height of the pyramid [tex]= 8 \ units[/tex]

Base of the pyramid is square in shape

Side length of a square [tex]= 12 \ units[/tex]

Substitute the value in the formula to get the area of the base,

Area of the base [tex]= 12 \times 12[/tex]

                            [tex]= 144 \ units^{2}[/tex]

Substitute the value to get the volume of the pyramid,

Volume of the pyramid [tex]= \frac{1}{3} \times 144 \times 8[/tex]

                                       [tex]= 48 \times 8\\\\= 384 \ units^{3}[/tex]

Hence, Option(B) is the correct answer.

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Answer:

a. 64 tickets.

b. $11.

Step-by-step explanation:

[tex]y[/tex] is given as [tex]37[/tex], and the question is asking for the value of [tex]x[/tex].

Solve this equation with respect to [tex]x[/tex].

[tex]0.50x + 5.00 = 37[/tex].

Subtract 5.00 from both sides of this equation:

[tex]0.50x = 32[/tex].

[tex]\displaystyle x= \frac{32}{0.50} = 64[/tex].

In other words, 64 tickets were purchased.

[tex]x = 12[/tex], and the question is asking for the value of [tex]y[/tex].

Replace [tex]x[/tex] with 12 and evaluate the expression [tex]y = 0.50x + 5.00[/tex] for [tex]y[/tex].

[tex]y = 0.50\times 12 + 5.00 = 11.00[/tex].

In other words, $11.00 were spent.