Find the solution of the system of equations.
- 2x - 5y=-12
10x - 4y = 2

Answer:

Find the roots of (2x+6)(3x−9)=0(2x+6)(3x-9)=0 by solving for x. x=-3,3 or A

Answer: y = (x - 1)² - 3

Step-by-step explanation:

y = (1-1)²-3
y=0-3
y=-3

Answer:

7cm

14cm

dπ or 2r π

14π or 2(7π)

Step-by-step explanation:

Radius = 7cm

Diameter = 7 x 2 = 14cm

Circumference = 2 x π x r = dπ

Circumference Value = 2 x π x 7 = 14π

Answer:

Radius: 7 cm

Diameter: 14 cm

Circumference Formula: c = dπ or c = 2rπ

Circumference Value: c = 14π or c = 2(7π)

Step-by-step explanation:

We are given that the radius of the circle is 7 cm. The diameter will always be twice as large as the radius so that will lead us to 14 cm as the diameter of the circle. The formula is quite simple. There are two different types of formulas for finding the circumference of a circle. If only the diameter is given, then we use the formula c = dπ, where d is for diameter and π is for pi or 3.14159. If only the radius is given, then we use the formula c = 2rπ, where r is for radius and π is for pi or 3.14159. In this case, we are going to use the formula for radius since only the radius is given. Simply plug in the value for radius then multiply the radius to π or 3.14159 and multiply the product by 2 to get the circumference of the circle. If I am wrong, please let me know. I hope this helps! :D

The amount of cups of lemonade sold by Abbie is 6 x 8 = a.

Hence, option A is correct.

Use the concept of multiplication defined as:

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that,

Number of lemonade cups sold by Lust = 8

Number of lemonade cups sold by Abbie =  6 times of lust

Let 'a' represents the number of cups sold by Abbie,

Therefore,

6 x 8 = a

Hence,

The correct expression is 6 x 8 = a which is option A.

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The complete question is:

Luct sold 8 cups of lemonade Abbie sold 6 times as many cups of lemonade. Which equation helps us find how many cups Abbie sold if the number of cups sold by Abbie is 'a'.

A. 6x8 = a

B. 8xa = 6

C. 6xa = 8

When a distribution has three or more peaks then it is said to be a multimodal distribution .

In histograms, there are often three types of distributions which are classified according to the number of peaks that they have . A unimodal distribution would be a histogram that has a single peak in its distribution .

Then there are binomial distributions which boast of having two peaks , Then finally, there is the multimodal distribution which is for all distributions with either three peaks, or more than that .

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Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the formula is:

A = 0.5yh.

Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.

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Answer:

If 10 men dig a ditch in 12 days .

Total man-days required to dig the ditch

= 10 men × 12 days

= 120 man-days

how long would 15 men take to dig it?

No of days required to finish the job by 15 men

= 120 men-days / 15 men

= 8 days

Answer: 8 days will be required to finish the job by 15 men

Step-by-step explanation:

Hope this helps u

Crown me as brainliest:)

Based on simple interest, the solution to the question is that his friend will ultimately owe Darrel $2,875.

A loan or investment's interest can be calculated using simple interest using the principal, interest rate, and duration of the transaction. Because it just considers the original principal and does not account for any compounded interest, it is known as "simple" interest.

Darrel will be indebted to his friend for the following sum if he lends him $2,500 and receives repayment with 15% simple interest after a year:

Interest = Principal x Rate x Time

Interest = $2,500 x 0.15 x 1

Interest = $375

Thus, the total sum his friend will be required to pay Darrel is:

Total amount = Principal + Interest

Total amount = $2,500 + $375

Total amount = $2,875

Thus, the total amount his friend owes Darrel is $2,875.

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Answer: Sunflower

Step-by-step explanation: Hope this helps

Answer:

10340000000 in standard form is

Hope this helps you

Answer:

y + 4 = -6 (x - 8)

Step-by-step explanation:

Change the equation to the slope intercept form for a line

x - 6y 5 = 0  Add 5 to both sides

x - 6y = 5  Subtract x from both sides

-6y = -x + 5  Divide both sides by -6

y = \(\frac{1}{6}\) c  - \(\frac{5}{-6}\)  Your slope is \(\frac{1}{6}\)

A perpendicular slope is the opposite reciprocal of \(\frac{1}{6}\), that would be -6

y - \(y_{1}\) = m( x - \(x_{1}\))  Plug is -4 for \(y_{1}\) and 8 for \(y_{1}\)

y - -4) -6(x-8)

y + 4= -6 (x -8)

Answer:

Risheeta: The sticks won’t form any triangle.

Step-by-step explanation:

Risheeta is correct.  Since 2+3=5, the three sticks put together would form a line, not a triangle.  The sum of the two smaller legs HAVE TO equal more than the third leg in order to make a triangle.

(It won’t let me spell her name correctly because it “contains a swear word”!

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

x = 35.537677791974°

y = 63.434948822922°

Step-by-step explanation:

let x be the measure of the angle of elevation of the sun.

tan(x) = 10/14

Then

x = tan⁻¹ (10÷14) = 35.537677791974°

………………………………………………

let y be the measure of the angle of elevation of the sun

where the shadow decreases to 5m.

tan(y) = 10/5 = 2

Then

y = tan⁻¹ (2) = 63.434948822922°

Answer:

a) 35.54°

b) 63.43°

Given following:

Determining, the shadow is adjacent side and length of the pole is the opposite side. Hence, use the tan rule. Let the angle be x.

(a)

\(\sf tan(x) = \dfrac{opposite}{adjacent}\)

\(\sf tan(x) = \dfrac{10}{14}\)

\(\sf x = tan^{-1}(\dfrac{10}{14} )\)

\(\sf x = 35.54^{\circ \:} \quad (rounded \ to \ nearest \ hundredth )\)

(b) If the shadow decreases to 5 meter.

\(\sf tan(x) = \dfrac{opposite}{adjacent}\)

\(\sf tan(x) = \dfrac{10}{5}\)

\(\sf x = tan^{-1} (\dfrac{10}{5})\)

\(\sf x = 63.43 ^\circ \quad (rounded \ to \ nearest \ hundredth)\)

Answer:

2

Step-by-step explanation:

2*3+3*4 x 1/3 power 2

6+12 x 1/9

18 x 1/9

2 x 1 (because 9 and 18 are cutted by each other)

2

2

To evaluate the expression (2b+3a)×(c^2) when a=4, b=3, and c=1/3, we substitute the given values into the expression and perform the indicated arithmetic operations:

(2b + 3a) × (c^2)

= (2(3) + 3(4)) × ((1/3)^2) (substitute a=4, b=3, c=1/3)

= (6 + 12) × (1/9) (evaluate 2(3) + 3(4) and (1/3)^2)

= 18/9

= 2

Therefore, when a=4, b=3, and c=1/3, the expression (2b+3a)×(c^2) equals 2.

Answer:

(x,y)->(x+4,y-5)

Step-by-step explanation:

Find a set of common points first, for example, A and A', or B and B'
Then, find the coordinates of the two points. I'm choosing B and B'.
B: (1,8) x = 1, y = 8
B':(5,3) x = 5, y = 3
from B to B', we see that the x increases by 4 and the y decreases by 5. So, the third option, (x,y)->(x+4,y-5) is correct

Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

The surface area of the sphere is 1810 cm²

A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of sphere is expressed as;

A = 4πr². where r is the radius.

A = 4 × 3.14 × 12²

A = 1809.7 cm²

approximately to the nearest whole number

A = 1810 cm²

Therefore the surface area of the sphere to the nearest whole number is 1810 cm².

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Using the uniform distribution, there is a 0.6667 = 66.67% probability that it takes a randomly selected customer more than 30 seconds to connect to the internet.

It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

The probability of finding a value above x is:

\(P(X > x) = \frac{b - x}{b - a}\)

For this problem, the connection time has parameters a = 20 sec and b = 50 sec, as stated in the problem.

The probability that it takes a randomly selected customer more than 30 seconds to connect to is P(X > 30).

Hence, applying the formula, with the bounds, we have that:

P(X > 30) = (50 - 30)/(50 - 20) = 2/3 = 0.6667.

The measure above is the desired probability.

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Answer:

C: the x-coordinates of the intersection points of the graphs of y = 2x2 and y = –x2 – 5x – 1

Step-by-step explanation: The answer was correct.

The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.

To solve the given equations, we need to find the value of the function f(x) for specific values of x.

"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"

To find f(2), we can substitute x = 2 into the equation and solve for f(2).

Plugging in x = 2, we get:

f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)

Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.

"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"

To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).

Plugging in x = -3, we get:

f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2

Simplifying, we have:

f(-3) / 0 = 3(9) + 12 + 2

f(-3) / 0 = 27 + 12 + 2

f(-3) / 0 = 41

Additional information or context is needed to solve for f(-3).

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Answer:

so for the table X= 6 y=2

Answer:

Option A is the right answer mate...

Answer:

$20,285.51

Step-by-step explanation:

A = P + I where

P (principal) = $12,000.00

I (interest) = $8,285.51

A = Pe^(r*t)

A = 12,000.00(2.71828)^((0.075)*(7))

A = $20,285.51

e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828

e here helps to show continously compounded interest

calculatorsoup

wikipedia

Answer:

The answer is "\(\bold{(7.1-8.3) \pm 1.665 \sqrt{\frac{(1.7)^2}{50}+\frac{(1.9)^2}{39}} }\\\\\)"

Step-by-step explanation:

Given values:

\(\bar{x_1}=7.1\\\\\bar{x_2}=8.3\\\\s_1=1.7\\\\s_2=1.9\\\\n_1=50\\\\n_2=39\)

Using formula:

\(\to (\bar{x_1} -\bar{x_2}) \pm t \sqrt{\frac{(s_1)^2}{n_1}+\frac{(s_1)^2}{n_2}} \\\\\)

Put the values in the above formula:

\(\to (7.1-8.3) \pm 1.665 \sqrt{\frac{(1.7)^2}{50}+\frac{(1.9)^2}{39}} \\\\\)

Answer:

T1=-12

T2=-19

T3=-26

Step-by-step explanation:

Determine which term will have a value of -6998

-7n-5=-6998

-7n=-6998+5

-7n=-6993

-7n/-7=-6993/-7

n=999

Answer:

Step-by-step explanation: 462 Divided by 24 = 19.25$

Proof: 19.25 x 24 = 462

Answer: 19.25$

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

Answer:

x = -3

Step-by-step explanation:

to solve this equation you should first find the LCD or least common denominator for 2 and 6

the LCD is 6

so you should multiply each side by six

\(6 * \frac{x + 5}{2} + 6 * -\frac{x + 3}{6} = 6 * 1\)

3x + 15 - x - 3 = 6

now combine like terms

2x + 12 = 6

now subtract both sides by 12

2x = -6

lastly divide everything by 2

x = -3

that is your answer