Solve the following equation by factoring
8x²-9x-14=0

Answer:

[tex]2sin(x)cos^2(x)[/tex]

Step-by-step explanation:

To solve the problem, you must expand the trigonometric expression using the information given.

[tex]sin(2x)cosx\\sin(2x)\\=2sin(x)\\=2sin(x)cos^2(x)[/tex]

The system of inequalities that represents the graph are y >  -x + 3 and y ≤  2x - 2

A line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b

For the broken line, the coordinate points will be(0, 3) and (3, 0)

m = -3/3

m = -1

The equation of the line will be y >  -x + 3

For the solid line, the coordinate points will be(0, -2) and (1, 0)

m = 2/1

m = 2

The equation of the line will be y ≤  2x - 2

Hence the system of inequalities that represents the graph are y >  -x + 3 and y ≤  2x - 2

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The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

Scaling is the way of enlarging or reducing the image of an object.

Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;

Convert both measures to same units

Since 1 feet. = 12 in

90 feet = 90/12 in = 7.5 in

Take the ratio

3 : 7.5 = 30: 75

Reduce to lowest term

30: 75 = 2 : 5

Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

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Answer:

Step-by-step explanation:

Area A(t) = πR² = π x 400 (t + 2) = 400π (t + 2)

A(2) = 400π (2 + 2) = 1600π = 5026.5 in²

A function assigns the values. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

If we plot the function, y = 4x⁴ - 8x² + 4, then it can be observed that the lists all of the turning points of the graphs are (–1, 0), (0, 4), and (1, 0).

Hence, the correct option is C.

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A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of objects. The coordinates of the translated line segment will be A' (3,6) and B' (5,6).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Since AB is a line segment the changes will occur on both the coordinates, therefore, if the line segment is translated 2 units down and 2 units left, the coordinates will be,

A = (5,8) → 2 units down ⇒ (5, 8-2) → 2 units left ⇒ (5-2, 8-2) = (3, 6)

B = (7,8) → 2 units down ⇒ (7, 8-2) → 2 units left ⇒ (7-2, 8-2) = (5, 6)

Hence, the coordinates of the translated line segment will be A' (3,6) and B' (5,6).

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Step-by-step explanation:

this is very easy u can do urself

I apologize for the handwriting it's not the best :)

The number of children and adults who bought the tickets at the circus was 500 and 900 respectively.

let

x + y = 1400

22x + 46y = 52,400

From equation (1)

x = 1400 - y

Substitute into (2)

22(1400 - y) + 46y = 52,400

30,800 - 22y + 46y = 52,400

- 22y + 46y = 52,400 - 30,800

24y = 21,600

y = 21,600 / 24

y = 900

substitute y into

x + y = 1400

x + 900 = 1400

x = 1400 - 900

x = 500

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The number of children's ticket that was bought is 500.

The number of adult's ticket that was bought is 900.

a + b = 1400 equation 1

22a + 46b = 52,400 equation 2

Where:

Multiply equation 1 by 22

22a + 22b = 30800 equation 3

Subtract equation 3 from equation 2

21,600 = 24b

b = 21,600 / 24

b = 900

Subtract 900 from 1400

1400 - 900 = 500

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Answer: X = 6

Step-by-step explanation:

Substitute the x’s in the equation for the answer options that are provided.

Solutions of quadratic equation x = √(-2x + 48) are x = -8 and x = 6.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given, quadratic equation;

x = √(-2x + 48)

Squaring on both sides,

x² = -2x + 48

x² + 2x - 48 = 0

Now, we have to solve for x.

Simplifying,

x² + 8x - 6x - 48 = 0

(x + 8)(x -6) = 0

(x + 8) = 0 and (x -6) = 0

x = -8 and x = 6

After eliminating the extraneous solutions;

we have,

x = -8 and x = 6.

Therefore, the solutions are x = -8 and x = 6.

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Answer:

yes

Step-by-step explanation:

independence means the object or so are completely unreliant of eachother or does not have order.

for example a dependent situation would be sports players getting picked because there is order.

Answer:

Find the area land of each town.

Let x be the area of town D

then, x+ 30000 is the area of town C

we know that,

the total area of town C and town D is 120,000 square miles.

x+x+30000=120000

2x= 90000

x=45000

Area of town D= 45000 square miles

Area of town C= 45000+30000= 75000 square miles.

Step-by-step explanation:

if the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle

bbc

10 squared = 100

13 squared = 169

17 squared = 289

100 + 169 = 269 NOT 289 so

there is no right angle and so its not a right triangle

answer:

c

step by step explanation:

I did it on edge.

Interpretation 1:

[tex]5x = 15 \\ [/tex]

Divide both sides by 5:

[tex]\implies \boxed{x = 3}[/tex]

(Which is the final answer.)

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

Interpretation 2:

[tex] 5^{x}=15[/tex]

Take logarithm to the base 5 on both sides:

[tex]\implies log_5(5^{x})=log_5(15)\\\implies x=log_5 (15) \\\implies x= \frac{ln(15)}{ln(5)} \\\implies \boxed{x≈1.683} [/tex]

(Which is a thing too!)

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

P. S.: Now please don't tell me that this is a PhD level question and this is referring to the Knuth's Up-Arrow Notation. Which translates the question into something like: [tex]^{5}x=15[/tex]

Answer:

Step-by-step explanation:

what would be the answer to this ?

Solve.

5x=15

x = 15 : 5

x = 3

--------------

check

5 * 3 = 15

the answer is good

Answer: the coordinates of D'

Step-by-step explanation:

Reflections are rigid motions, so area and perimeter are preserved.

However, the preimage of a point is only the same as the image of that same point if that point is the center of rotation. Since point D is not the center of rotation, the coordinates of D' will not be the same as those of D.

the answer would be 240 because wind speed is close to its median

Step-by-step explanation:

[tex] \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} [/tex]

[tex] \frac{3}{4} 36 = 27[/tex]

Answer:

x² - 25=(x-5)(X+5)

x²-3x -15=5.6 or. -2.6

Answer:  [tex]y^9[/tex]

This is the same as saying y^9

===================================================

Explanation:

When we apply the square root to the expression [tex]a^{2b}[/tex], we end up with [tex]a^b[/tex]

[tex]\sqrt{a^{2b}} = a^b[/tex]

The exponent 2b divides in half to get b

Based on that rule, we can then say:

[tex]\sqrt{y^{18}} = y^{18/2} = y^9[/tex]

Answer:

Step-by-step explanation:

if the volume of a cube is 27cm³ what are the dimensions of the cube​

Cube Volume = l³

we use the inverse formula

∛V = l

so

∛27 =

3 cm

The points on the line are points B and D

The equation is given as:

y = x + 4

The above means that the output value is 4 more than the input value

Using the above rule, the points that satisfy the equation are:

B) 2, 6 and D) 2, 4

This is so because:

6 = 2 + 4

4 = 2 + 2

Hence, the points on the line are points B and D

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Answer: 32

Step-by-step explanation:

Since [tex]\overline{FG} \parallel \overline{AC}[/tex], we know that by the corresponding angles theorem, [tex]\angle BFG \cong \angle BAC[/tex] and [tex]\angle BGF \cong \angle BCA[/tex].

Thus, [tex]\triangle BFG \sim \triangle BAC[/tex] by AA.

It follows that since corresponding sides of similar triangles are proportional,

[tex]\frac{36+90}{90}=\frac{CG+80}{80}\\ \\\frac{126}{90}=\frac{CG+80}{80}\\\left(\frac{126}{90} \right)(80)=CG+80\\112=CG+80\\CG=\boxed{32}[/tex]

Answer:

$8

Step-by-step explanation:

Let f = 1 kg of French Roast coffee

Let b = 1 kg of Boxer Blend coffee

Given:

⇒ f + b = 14

Given:

⇒ 2f + 3b = 36

Rewrite the first equation to make f the subject:

⇒ f + b = 14

⇒ f = 14 - b

Substitute this into the second equation and solve for b:

⇒ 2f + 3b = 36

⇒ 2(14 - b) + 3b = 36

⇒ 28 - 2b + 3b = 36

⇒ 28 + b = 36

⇒ 28 + b - 28 = 36 - 28

⇒ b = 8

Therefore, the price of 1 kg of Boxer Blend coffee is $8

Answer:

d

Step-by-step explanation:

the y- intercept is the point on the y- axis where the graph crosses

the graph crosses the y- axis at point (0, - 9 )

then y- intercept = (0, - 9 )

The first five terms of the sequence represented as an = 3(n -1) + 1 are 1,4, 7, 10 and 13

The formula of the sequence is given as:

an = 3(n -1) + 1

The above sequence is an arithmetic sequence, and the first five terms are the values of the sequence when the value of n is from 1 to 5

i.e. n = 1, 2, 3, 4 and 5

Next, we set n = 1, 2, 3, 4 and 5, and substitute these values for n in an = 3(n -1) + 1

So, we have the following equations

First term

a1 = 3(1 -1) + 1 = 1

Second term

a2 = 3(2 -1) + 1 = 4

Third term

a3 = 3(3 -1) + 1 = 7

Fourth term

a4 = 3(4 -1) + 1 = 10

Fifth term

a5 = 3(5 -1) + 1 = 13

Hence, the first five terms of the sequence represented as an = 3(n -1) + 1 are 1,4, 7, 10 and 13

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[tex]\left|\dfrac{2}{13}t-11\right|-10=-16\\\\\left|\dfrac{2}{13}t-11\right|=-6\\\\x\in\emptyset[/tex]

Keesha would say the ball is traveling at 7 km/h. The correct option is the second option 7 km/h

Relative velocity is defined as the velocity of an object with respect to another observer.

From the question, we are to determine how fast Keesha would say the ball is traveling. That is, the relative velocity

Relative velocity of the ball = 12 km/h - 5 km/h

Relative velocity of the ball = 7 km/h

Hence, Keesha would say the ball is traveling at 7 km/h. The correct option is the second option 7 km/h

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Answer:

7 km/h

Step-by-step explanation: