solve 5x^2-2=-12 by taking the square root

Answer:

m = 4

n = 5

Step-by-step explanation:

[tex]m + 8 = 3m\\\\m - 3m = - 8\\\\-2m = - 8\\\\m = 4[/tex]

[tex]2n - 1 = 9 \\\\2n = 9 + 1\\\\2n = 10\\\\n = 5[/tex]

Hello!

3(x + 2) - 4x = 8 <=>

<=> 3x + 6 - 4x = 8 <=>

<=> -x + 6 = 8 <=>

<=> -x = 8 - 6 <=>

<=> -x = 2 <=>

<=> x = -2

Good luck! :)

Answer:

The correct answer is 3x-2

Step-by-step explanation:

It gives you the expression for JM and LM, and it asks for JL. Therefore, if you take away LM from JM, you are left with JL. You must subtract 2x-6 from 5x-8.

∴5x-8-(2x-6)

Do not forget to distribute the negative since you are subtracting, so instead of subtracting 6 from 8, you will be adding 6 to 8 because two negatives make a positive.

Answer:

Step-by-step explanation:

volume of cone=1/3 πr²h

=1/3×π×5²×11

=275/3 ×3.14

≈287.33 in³

Answer:

The second number is 100.

Step-by-step explanation:

Let the first integer be x.

Then since the five integers are consecutive, the second integer will be (x + 1), the third (x + 2), fourth (x + 3), and the fifth (x + 4).

They total 505. Hence:

[tex]\displaystyle x+(x+1)+(x+2)+(x+3)+(x+4)=505[/tex]

Solve for x. Combine like terms:

[tex]5x+10=505[/tex]

Subtract 10 from both sides:

[tex]5x=495[/tex]

And divide both sides by five. Hence:

[tex]x=99[/tex]

Thus, our sequence is 99, 100, 101, 102, and 103.

The second number is 100.

Answer:

After 10 years, Julie's account balance will be $ 363.88 and Leah's account balance will be $ 411.75, thus Leah will have more money in her account.

Step-by-step explanation:

Since Julie invests $ 200 per month in an account that earns 6% interest per year, compounded monthly, and Leah invests $ 250 per month in an account that earns 5% interest per year, compounded monthly, to determine the amount of each after 10 years, the following calculations must be performed:

200 x (1 + 0.06 / 12) ^ 10x12 = X

200 x 1.005 ^ 120 = X

200 x 1.8193 = X

363.88 = X

250 x (1 + 0.05 / 12) ^ 10x12 = X

250 x 1.00416 ^ 120 = X

250 x 1.647 = X

411.75 = X

Therefore, after 10 years, Julie's account balance will be $ 363.88 and Leah's account balance will be $ 411.75, thus Leah will have more money in her account.

Answer:

The dimensions are 45 feet by 40 feet.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

[tex]\displaystyle A=w\ell[/tex]

Where w is the width and l is the length.

The length is five feet longer than the width. Thus, we can write that:

[tex]\ell = w+5[/tex]

The total area is 1800 square feet. Substitute:

[tex]1800=w(w+5)[/tex]

Solve for w. Distribute:

[tex]w^2+5w=1800[/tex]

Subtract 1800 from both sides:

[tex]w^2+5w-1800=0[/tex]

Factor. We can use 45 and -40. Hence:

[tex]\displaystyle (w+45)(w-40)=0[/tex]

Zero Product Property:

[tex]w+45=0\text{ or } w-40=0[/tex]

Solve for each case:

[tex]\displaystyle w=-45\text{ or } w=40[/tex]

Since the width cannot be negative, we can ignore the first solution.

So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.

The dimensions are 45 feet by 40 feet.

Answer:

C

Step-by-step explanation:

here in the question it is given that it is four times as long as wide and its area is 36 square inches

now as we onow 3×4 =12

therefore here the side becomes four time

now area of rectangle is equal to 12 ×3 =36

Answer:

D, E, and F

Step-by-step explanation:

✔️Statement D is true:

Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2

✔️Statement E is true:

Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1

✔️Statement F is true:

Rationale:

m<4 is an external angle of the triangle.

m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,

m<4 = m<1 + m<2

Answer: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]

Step-by-step explanation:

[tex]f(x)=10x^{3}\\y=10x^{3}[/tex]

switch the x and y:

[tex]x=10y^{3}[/tex]

Now solve for y:

[tex]x=10y^{3} \\\frac{x}{10} =y^{3} \\\sqrt[3]{\frac{x}{10} } =y\\[/tex]

Therefore, the inverse of that function is: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]

Answer:

Problem 1 has a greater answer.

Step-by-step explanation:

Solve problem 1 using the order of operatiobs PEMDAS (Parentheses, Exponents, multiplication/division, and addition/subtraction):

Multiplication/division depends from left to right of the expression, the same goes to addition/subtraction.

(2 + 3) (5 + 5)

= (5)(10)

= 50

SOLVE problem 2 using PEMDAS:

2 + 3 x 5 + 5

= 2 + 15 + 5

= 17 + 5

= 22

Answer 1 (50) compared to Answer 2 (22):

50 > 22

HOPE THIS HELPS!

Answer:

yes , This is an example of the associative property.

Step-by-step explanation:

Answer:

Hello dude

[tex] - 1 \frac{21}{24} + 1 \frac{22}{24} = + \frac{1}{24} [/tex]

so it's positive

HAVE A NİCE DAY

Step-by-step explanation:

GREETİNGS FROM TURKEY ツ

Answer:

i think the mistake was in step 1

Step-by-step explanation:

Answer:

[tex]P(win) = 0.4722[/tex]

Step-by-step explanation:

Given

[tex]n = 36[/tex] --- slots

[tex]Even = 17[/tex] i.e. even numbers between 1 and 34 (inclusive)

Required

[tex]P(win)[/tex]

The probabiity of winning is the number of even numbers divided by the total slot;

i.e.

[tex]P(win) = \frac{Even}{n}[/tex]

So, we have:

[tex]P(win) = \frac{17}{36}[/tex]

[tex]P(win) = 0.4722[/tex]

(C)

Step-by-step explanation:

The sum of angles a and b is 180°, which make the two supplementary angles.

Answer:

(a) 74553

(b) 172120

(c) 234802

Step-by-step explanation:

Given

[tex]y = \frac{340110}{1 + 377e^{-0.259t}}[/tex]

Solving (a): 1998

Year 1998 means that:

[tex]t =1998 - 1980[/tex]

[tex]t =18[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*18}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-4.662}}[/tex]

[tex]y = \frac{340110}{1 + 3.562}[/tex]

[tex]y = \frac{340110}{4.562}[/tex]

[tex]y = 74553[/tex] --- approximated

Solving (b): 2003

Year 2003 means that:

[tex]t = 2003 - 1980[/tex]

[tex]t =23[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*23}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-5.957}}[/tex]

[tex]y = \frac{340110}{1 + 0.976}[/tex]

[tex]y = \frac{340110}{1.976}[/tex]

[tex]y = 172120[/tex] --- approximated

Solving (c): 2006

Year 2006 means that:

[tex]t = 2006 - 1980[/tex]

[tex]t =26[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*26}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-6.734}}[/tex]

[tex]y = \frac{340110}{1 + 0.4485}[/tex]

[tex]y = \frac{340110}{1.4485}[/tex]

[tex]y = 234802[/tex] --- approximated

Answer:

Orange

Step-by-step explanation:

As the chance of choosing orange is 18% which is the least.

Answer:

6.8

Step-by-step explanation:

The number is already rounded to the nearest tenth and hundredth.

Answer:

Both give remainder 0 for the polynomial

Step-by-step explanation:

p(-2) = (-2)² - (-2) - 6

= 6 - 6 = 0

p(3) = (3)² - 3 - 6

= 9 - 9 = 0

Answer:

The 3rd

Step-by-step explanation:

If x goes to infinity, f(x) goes to infinity too:

[tex]lim \: \frac{2 {x}^{2} }{3x - 1} = lim \frac{2x}{3 - \frac{1}{x} } = \frac{ 2 \times \infty }{3 - 0} = \infty [/tex]

Actual data table :

X __ y

2 15

6 13

7 9

8 8

12 5

Answer:

0.953

Step-by-step explanation:

The question isnt well formatted :

The actual data:

X __ y

2 15

6 13

7 9

8 8

12 5

Using a correlation Coefficient calculator, the correlation Coefficient obtained by fitting the data is 0.953 which depicts a strong linear correlation between the x and y variable. This shows that the value of y increases with a corresponding increase in x values and vice versa.

Answer:

C

Step-by-step explanation:

In ∆DEG, we are given that all the three angles are congruent.

This means that all the three angles have equal measure. Thus,

<D = <E = <F

An equilateral triangle has equal angle measure. ∆DEF is an equilateral triangle.

Since the sum of a triangle is 180°, therefore, each angle in ∆DEF = 60°

m<D = 60°

Answer:

My answer is 78.55

Step-by-step explanation:

I've given the steps. Hope it really helps

Answer: 78.5 inches

Step-by-step explanation:

Area = Pi x r x r

Diameter = 10 in

Radius = 5 in

314/100 x 5 x 5 = 314/4

314/4 = 78.5

= 78.5 inches

Answer:

Table B

Step-by-step explanation:

correct on edge :)

9514 1404 393

Answer:

  3.  y = 3·4^x

  4.  y = 24·0.5^x

  5.  y = 45·0.9^x

Step-by-step explanation:

Each table appears to represent an exponential function. Such a function can be written in the form ...

  y = a·b^x

where 'a' is the value of y when x=0, and 'b' is the ratio of the values of y when x=1 and x=0.

__

3. a = 3. b = 12/3 = 4

  y = 3·4^x

__

4. a = 24. b = 12/24 = 0.5

  y = 24·0.5^x

__

5. a = 45. b = 40.5/45 = 0.9

  y = 45·0.9^x

Answer:

55.75 cents per ounce

Step-by-step explanation:

Take the cost and divide by the number of ounces

We want cents per ounce so change dollars to cents

446 / 8

55.75 cents per ounce

9514 1404 393

Answer:

  1604 m

Step-by-step explanation:

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

Here, the "opposite" is the elevation of point B above point A, and the "hypotenuse" is the length of the railway. Then the total height of point B is ...

  B = 856 + 864·sin(120°)

  B = 856 +864(√3)/2 = 856 +432√3 ≈ 1604.246

The height of the train at point B is about 1604 m above sea level.

Answer:

8

Step-by-step explanation:

By taking the number "3" and plus together with the number 5