Find the solutions of the quadratic equation –9x2 + 49 = 0.
Question 8 options:

A)

x = 9∕7, – 9∕7

B)

x = 3∕7, –7∕3

C)

x = 7∕3, –7∕3

D)

x = 7∕9, –7∕9

Answer: I just points so rate this a 10

Step-by-step explanation:

Answer:

owi4w85e963696w95witote5iw47e

Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail

We are told in the question that

Linda walked 3/4 of the length of the Tremont Trail before stopping for a rest.

From the question, the length of the Tremont Trail = 3 1/2 miles

Hence, the distance (how far )Linda has walked =

3/4 of 3 1/2 miles

= 3/4 × 3 1/2 miles

= 3/4 × 7/2 miles

= 21/8 miles

= 2 5/8 miles or 2.625 miles

Therefore, Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail.

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Answer:

31 and 59

Step-by-step explanation:

We can figure this out by putting the words into an equation

"three degrees less than twice the measure of the smaller angle"

we know the smaller angle = x, so:

twice the smaller angle=2x

3 degrees less=-3

you then put those into an equation where they all add up to equal 90 and simplify

x+2x-3=90

3x-3=90

3x=93

x=31

you then plug that into the equation we would have for the second angle:

2x-3

2(31)-3

62-3

59

the first angle would be 31 and the second angle would be 59

:D

Answer:

Step-by-step explanation:

Given function:

[tex]y=\sqrt{x-2}[/tex]

The domain is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken, the domain of the given function is restricted.

[tex]x-2\geq 0 \implies x\geq 2[/tex]

Therefore, the domain of the given function is [2, ∞).

The range is the set of all possible output values (y-values).

As the square root of a negative number cannot be taken, the range of the given function is restricted.  

Therefore, the range of the given function is [0, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Therefore, the function is continuous on its domain [2, ∞).

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}[/tex]

Therefore, there are no stationary points.

As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}[/tex]

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: [2, ∞)

Range: [0, ∞)

Continuity: Function is continuous on its domain [2, ∞).

Minimum point at (2, 0).

Increasing function: (2, ∞)

Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.

Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:

1.) 3.075 gallons.

To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.

We have that:

Hence the remaining amount is:

15 - 11.925 = 3.075 gallons.

Which means that option 1 is correct.

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Answer: 3.075 gallons

Step-by-step explanation:

Start by dividing both sides by G, giving us

[tex]\frac{F}{G}=\frac{m_{1} m_{2} }{d^{2} } }[/tex]. Multiply both sides by d^2. [tex]\frac{F}{G}(d^{2})=m_{1} m_{2}[/tex].

Finally, divide both sides by m2.

[tex](\frac{F}{G}\div{m_{2}}) (\frac{d^{2} }{m_{2} } )=m_{1}[/tex]

Hope this helps! This was a tough problem for me too.

4 x 10¹¹

Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.

400 billion in scientific notation = 4 x 10¹¹

We can complete the sentence as,

My new music player has a capacity of 4 x 10¹¹

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Answer:

$243 is his profit

Step-by-step explanation:

Answer: $4100

Step-by-step explanation:

discount = [tex]\frac{1800}{90}[/tex]×100 = 2000

profit = [tex]\frac{115}{100}[/tex]×2000 = 2300

market price = 2300 + 1800 = 4100

The length of the rectangle is 12 meters and its width is 4 meters.

A rectangle is a four sided figure, whose opposite sides are equal and the angle formed by any two adjacent sides is 90 degrees.

Here, we are given that the perimeter of the rectangle is 32 meters.

Let the length of the rectangle be L and breadth or width be B

We known that perimeter of a rectangle = 2(L + B)

Now, it is given that the length is 4 m more than two times the width

⇒ L = 4 + 2B

Thus, the area of the perimeter will be-

Perimeter = 2(4 + 2B + B)

⇒ 32 = 2(4 + 2B + B)

32/2 = 4 + 2B + B

16 = 4 + 3B

16 - 4 = 3B

12 = 3B

or 3B = 12

B = 12/3

B = 4

Thus, the width of the rectangle is 4 meters.

Therefore, L = 4 + 2(4)

L = 4 + 8

L = 12

Thus, the length of the rectangle is 12 meters.

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the answer to your question is Ettwice is 45 years old and Mavis is 15 years old. hope this helps

Step-by-step explanation:

15 * 3 = 45

45 + 15 = 60

Answer:

the answer is 42

Step-by-step explanation:

you add 217+153+88=458

500-458=42

[tex] \Large {\mathbb {SOLUTION: }}[/tex]

[tex] \: \: \text{L = 3w - 1}[/tex]

[tex] \: \: \text{P=46}[/tex]

[tex] \: \: \text{2(3w-1) + 2w = 46}[/tex]

[tex] \: \: \text{6w - 2 + 2w = 46}[/tex]

[tex] \: \: \text{8w = 48}[/tex]

[tex] \: \: \text {W = 6 }[/tex]

[tex] \: \: \text{L = 17}[/tex]

[tex] \: \: \text{Applying the inequalities:}[/tex]

[tex] \: \: \text{L>=17 and w=6}[/tex]

[tex] \: \: \text{The perimeter is at least 46.}[/tex]

Answer: Your computer will be worth $1,171.12

Step-by-step explanation:

[tex]a_n = 1500(0.94)^4\\a_n=\boxed{1171.12}[/tex]

Answer:

 I think the answer is 9.920 please be careful with your answer I think it 9.920 because it says nine hundred and ninety two thousands so therefor the decimal need to be in between 9 and 9 I hope you get this correct!

step-by-step explanation:

The length and width of rectangle is 10 feet and 4.5 feet.

This problem is related to the area and perimeter of plane figures. We have to find the dimensions of the rectangle using the data given.

Given, the length is 1 feet more than twice the width.

Let the width be a feet.

So, length = (2a+1) feet

Now according to question,

   [tex](2a+1)(a)=45\\[/tex]

⇒ [tex]2a^{2} +a-45=0[/tex]

On solving the above quadratic equation we get a=4.5 feet.

So, length = 10 feet.

The dimension of rectangle is 10 feet × 4.5 feet.

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Answer:

$10.8

Step-by-step explanation:

First, to determine the price of one cake divide 6.30/7

You will determine one cake costs 90 cents.

So, multiply 0.90 by 12, and you get $10.8

Answer:

Step-by-step explanation:

Answer:

a) $168,760

b) $119,275

Step-by-step explanation:

For this, I believe you do $288,035 - $49,485. This equals $238,550.

Then divide this by 2 to get the salary for state B, which is $119,275 .

$168,760 remains, so it's the salary for state A.

Answer:

Governor of state A = 168,760

Governor of state B = 119,275

Step-by-step explanation:

A = 49485 + B         Eq. 1

A + B = 288035       Eq. 2

A = Earns  of governor of state A

B = Earns of governor of state B

Replacing Eq. 1 in Eq. 2:

(49485+B) + B =288035

2B + 49485 = 288035

2B = 288035  - 49485

2B = 238550

B = 238550/2

B = 119275

From eq. 1

A = 49485 + 119275

A = 168760

Check:

from eq. 2:

A + B = 288035

168760 + 119275 = 288035

The linear equation would be y = 18 - 4x which represents the distance Jordan still has to walk after x hours.

The y-intercept represents the total distance Jordan has to walk.

Distance is defined as the product of speed and time.

We have to determine the distance.

So distance = speed× time

Given that his speed is 4 mph and x hours of walking, then:

So distance = 4 × x

Let it Start of the trail: 0 miles

And the end of the trail: 18 miles​

The trail length is 18 miles, so if he walked 1 mile, 18 - 1 = 17 miles are left, in general:

⇒ y = 17 - 4(x)

Here y would be the distance Jordan still has to walk.

The y-intercept would be if substitute x = 0, then:

⇒ y = 17- 4(0)

⇒ y = 17

This represents the total distance Jordan has to walk

Hence, the linear equation would be y = 18 - 4x which represents the distance Jordan still has to walk after x hours.

The y-intercept represents the total distance Jordan has to walk.

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For the linear function x - y = 3, three ordered pairs are given as follows:

Using points (3,0) and (0,-3), the graph of the function is given at the end of the problem.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the function is:

x - y = 3.

In standard notation:

y = x - 3.

Hence three pairs of points are given as follows, replacing the value of x in the equation to find y.

The graph of the function is given at the end of the answer.

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The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.

What is probability?

These generalities have been given a self-evident fine formalization in probability proposition, which is used extensively in areas of study similar to statistics, mathematics, wisdom, finance, gambling, artificial intelligence, etc.

P(sugar | oatmeal) = (7/25)(6/24) = 0.07

The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.

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The set notation of the numbers is {x | x < 50 ∪ x > 50}

The set is given as

The set of all real numbers less than 50 or greater than 50

Let the number be represented by x

So, we have

x less than 50 or x greater than 50

When represented as an inequality, we have

x < 50 or x > 50

Using set notation, we have

{x | x < 50 ∪ x > 50}

Hence, the set notation of the numbers is {x | x < 50 ∪ x > 50}

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Answer:

[tex]8^{20}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](8^5)^{4}[/tex] = [tex]8^{5(4)}[/tex] = [tex]8^{20}[/tex]

The sentence "5 is subtracted from the square of a number" represented as an algebraic expression is x² -5.

Algebraic expressions: what are they?

Given,

Let the number be x and 3 is subtracted from a number.

Represent it in expression.

Step 2

3 is subtracted from a number means 3 is subtracted from x.

Here we have to subtract 3 from x. It can be represented as = x - 3

Let the number be x.

In this exercise, you're required to write an algebraic expression to represent the word problem (sentence). Also, the number would be denoted by the letter x and no need for further simplification of the algebraic expression.

Translating the word problem (sentence) into an algebraic expression, we have;

Square of a number (x) = x²

Subtracting 5 from the the square of x, we have  x² -5 .

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Answer:

x=11

Step-by-step explanation:

9x=7x+22

9x-7x=22

2x=22

2x/2=22/2

x=11

(1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7

From the question, we are to determine the factor by which 1.143 × 10¹ is larger than 9 × 10⁻¹

To determine how many times larger the number is, we will divide 1.143 × 10¹ by 9 × 10⁻¹

Carrying out the division operation

(1.143 × 10¹) ÷ (9 × 10⁻¹)

= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)

= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)

= 0.127 × (10¹ ⁻ ⁽⁻¹⁾)

= 0.127 × (10¹ ⁺ ¹)

= 0.127 × (10²)

= 0.127 × 10²

= 12.7

Hence, (1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7

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Answer:

44

Step-by-step explanation:

because if u pit it together 44 is what u get

Answer:

Add all like terms

12s = 0

s = 0

Step-by-step explanation:

8s + 6 + 4s = 6

12s + 6 = 6

       -6   -6

12s = 0

÷12   ÷12

s = 0

I hope this helps!

The interval notation is { 5/ 2 < x > 0 }

Given the inequalities;

To determine the value of x, we have;

2x - 1 < 4

collect like terms

2x < 4 + 1

2x < 5

Make 'x' the subject

x < 5/ 2

−5x −3 > −3

collect like terms

-5x > -3 + 3

-5x > 0

x > 0

Thus, the interval notation is { 5/ 2 < x > 0 }

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