Question 4
Solve the equation x² - 4x+6=0 by completing the square.
BIUX² X₂ 15px help!!

Here's the solution,

we know,

[tex] \large \boxed{Sn = \frac{n}{2}[ 2a _1 + (n - 1)d ] }[/tex]

=》

[tex]Sn = \dfrac{17}{2} [ (2 \times 8 )+ (17 - 1) \times ( - 9) ][/tex]

=》

[tex]Sn = \dfrac{17}{2} [16 + (16 \times - 9)][/tex]

=》

[tex]Sn = \dfrac{17}{2} [16 + ( - 144)][/tex]

=》

[tex]Sn = \dfrac{17}{2} \times (- 128)[/tex]

=》

[tex]Sn = 17 \times ( - 64)[/tex]

=》

[tex]\huge\boxed{Sn = - 1088}[/tex]

The graph's X-intercepts are ((9+55)/2,0) and ((955)/2,0), and its Y-intercept is (0,13).

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

Axis of symmetry:

x=9 /2

Vertex (minimum point): (9/2,−55/2)

X-intercepts: ((9+√55)/2,0) and ((9−√55)/2,0)

Y-intercept: (0,13)

The graph's X-intercepts are ((9+55)/2,0) and ((955)/2,0), and its Y-intercept is (0,13).

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Answer: The answer is 29,446,941,856

Step-by-step explanation:

Answer:

0.2 recurring I the same as 2/9

Step-by-step explanation:

x=0.2222

10x=2.2222

10x-x=9x

9x=2

divide both sides by 9

9x÷9=x

2÷9=2/9

Hope it helps:)

Answer:

C.

Step-by-step explanation:

A flowerpot is basically a circle, so you are looking for the circumference of a circle.

Formula: 2 x π x Radius

Answer:

310 cm 2

Step-by-step explanation:

Answer:

A,D, and E

ur welcome

Step-by-step explanation:

B becuase it keeps the same orientation and have the same distance from each point and they both produce rigid motion.

A is a reflection.

C is a dilation.

D is a rotation.

Answer:

A = 38.5 units²

Step-by-step explanation:

the figure has one pair of parallel sides and is therefore a trapezium.

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

b₁ and b₂ are the parallel bases and h the perpendicular height between them.

here h = 7 , b₁ = 5 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 7 × (5 + 6) = 3.5 × 11 = 38.5 units²

Answer:

73

Step-by-step explanation:

48^2 + 55^2 = 5329

square root of 5329 is 73

Answer:73mi

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

Answer:

Hi.

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

7x+9= 9x-19

-2x= -28

x= 14

they are corresponding angles

Answer:

x = 14

Step-by-step explanation:

the angles are corresponding.

corresponding angles theorem states that when two parallel lines are cut by a transversal , the resulting corresponding angles are congruent.

therefore:

7x + 9 = 9x -19

9 = 2x - 19

28 = 2x

14 = x

Answer:

21.2058333333

Step-by-step explanation:

Answer:

Step-by-step explanation:

Circumference = 2 * pi * r

r = 9 inches

Circumference = 18 pi

If there are 12 pieces (all equal) then the length of the crust is

C_part = 18*pi/12

C_part = 3/2 * pi

C_part= 4.71 inches

Answer:

Corect Answer: A (5,5)

Step-by-step explanation:

5(5)+2(5)= 35, which is greater than 19

5+5= 10, which is greater than 5

therefore- (5,5) is correct & works for the system of inequalities

Answer:

88 is the correct answer.

please mark brainliest

Answer:

88

Step-by-step explanation:

since a straight line is 180

180-92=88

Answer:

A

Step-by-step explanation:

they are complementary, they add to 90

Here, we are required to apply ratios and proportions to help convert a recipe to serve more people.

The recipe for 30 people would be as follows:

The recipe in the question above only serves 8 persons.

However, we are required to convert the recipe into one that serves 30 persons.

To do that, it is important to first convert the recipe into one that serves one(1) person.

If the recipe serves 8 persons, therefore to serve 1 person, it requires dividing the quantity of each ingredient by 8.

The results are as follows:

The new recipe above is for serving 1 person Molten lava cake.

Therefore, to serve 30 persons with the Molten lava cake, the quantity of each ingredient required for 1 person's serving i multiplied by 30.

The results are as follows:

However, the question requires that the quantities be rounded off to the nearest half.

therefore we have,

4 c of sugar

22 ¹/2 squares of bittersweet chocolate

7 ¹/2 squares semisweet chocolate

4 ¹/2 stick butter

2 cup all-purpose flour

5 ¹/2cups confectioners’ sugar

11 ¹/2 large eggs

15 egg yolks

4 tsp vanilla extract

9 ¹/2 tablespoons orange liqueur.

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9514 1404 393

Answer:

  630 miles

Step-by-step explanation:

distance = speed × time

distance = (70 mi/h)(9 h) = 630 mi

Jennifer traveled 630 miles in 9 hours.

Answer:

2028

Step-by-step explanation:

156 x 13 = 2028

Answer:

24

Step-by-step explanation:

96 divided by 4 = 24

Answer:

[tex]C' =(5,3)[/tex]

Step-by-step explanation:

Given

[tex]A = (-3,5)[/tex]

[tex]B = (-2,3)[/tex]

[tex]C = (-5,3)[/tex]

Reflection across y-axis

Required

Find C'

For reflection across y-axis, the rule is:

[tex](x,y) \to (-x,y)[/tex]

So, the image of C is:

[tex](-5,3) \to (-(-5),3)[/tex]

[tex](-5,3) \to (5,3)[/tex]

Hence:

[tex]C' =(5,3)[/tex]

Given:

Measure of a cube = 1 unit on each side.

Dimensions of a space 2 units by 3 units by 4 units.

To find:

Number of cubes that can be fit into the given space.

Solution:

The volume of cube is:

[tex]V_1=a^3[/tex]

Where, a is the side length of cube.

[tex]V_1=(1)^3[/tex]

[tex]V_1=1[/tex]

So, the volume of the cube is 1 cubic units.

The volume of the cuboid is:

[tex]V_2=l\times b\times h[/tex]

Where, l is length, w is width and h is height.

Putting [tex]l=2,b=3,h=4[/tex], we get

[tex]V_2=2\times 3\times 4[/tex]

[tex]V_2=24[/tex]

So, the volume of the space is 24 cubic units.

We need to divide the volume of the space by the volume of the cube to find the number of cubes that can be fit into the given space.

[tex]n=\dfrac{V_2}{V_1}[/tex]

[tex]n=\dfrac{24}{1}[/tex]

[tex]n=24[/tex]

Therefore, 24 cubes can be fit into the given space.

Answer:

k = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

given variation equation

y = kx

to find k substitute y = 3 and x = 4 into the equation and solve for k

3 = 4k ( isolate k by dividing both sides by 4 )

[tex]\frac{3}{4}[/tex] = k

The area of the hot tub is 6079.04 in²

To determine the approximate area required for the installation of the hot tub. You can use the area of  a circle.

The area of  a circle is given by A = πr²

where r is the radius of the circle

Since the hot tub to have a diameter of 88 inches, the radius will be  88/2 = 44 inches. π = 3.14.

Thus, area of  the hot tub will be:

Area of hot tub = 3.14 × 44² = 6079.04 in²

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Answer: It is a reflection over the x axis!

Step-by-step explanation: The x axis is the horizontal line, so you reflect it over there. It is a reflection because you didn't rotate it, and you didn't translate it. You reflected the coordinates to the other side.

Answer:

this function model grows.

Step-by-step explanation:

The value of b, 1.56, is greater than 1.

Answer:

Step-by-step explanation:

If Colton makes a guaranteed salary of $500 per week, and he is paid a commission of 10% on top of that for a total of $1075 in sales, he would make an additional $107.50 in commission (1075 x .1 = 107.5). In total, Colton would make 500 + 107.5 = $607.50 in a week where he made $1075 in sales.

Answer:

209.25

Step-by-step explanation:

Calculate the areas of the triangle, rectangle, and half circle, then add them together:

triangle = 1/2bh = 1/2(6)(10) = 30

rectangle = bh = (14)(10) = 140

half circle = 1/2πr² = 1/2(3.14)(5)² = 39.25

radius = r = D/2 = 10/2 = 5

Total area = 30 + 140 + 39.25 = 209.25

Answer:

209.25 ft²

Step-by-step explanation:

To find the total area of the figure you have to add the areas of the triangle, rectangle and the semi circle.

Area of the triangle.

[tex] \sf \: A = \frac{1}{2} \times base \times height \\ \sf \: A = \frac{1}{2} \times 6 \: ft \times10 \: ft \\ \sf \: A = \frac{1}{2} \times 60 \: {ft}^{2} \\ \sf \: A =30 \: {ft}^{2} [/tex]

Area of the rectangle.

[tex]\sf \: A =length \times width \\ \sf \: A =14 \: ft \times 10 \: ft \\ \sf A =140 \: {ft}^{2} [/tex]

Area of the semi circle.

[tex] \sf \: A = \frac{1}{2} \pi {r}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times ( \frac{10}{2}) ^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times {5}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times 25 \\ \sf \: A = \frac{1}{2} \times 3.14 \times 25 \\ \sf \: A = \frac{1}{2} \times 78.5 \\ \sf \: A = 39.25 {ft}^{2} [/tex]

Add up all the areas to find the total area.

[tex] \sf \: Total \: Area = 30 {ft}^{2} + 140 {ft}^{2} + 39.25 {ft}^{2} \\ = 209.25 {ft}^{2} [/tex]