Add the two equations 2x+6 and 6x-1

3/10 = 30/100 after multiplying top and bottom by 10

so we have 30/100 + 62/100 = (30+62)/100 = 92/100

Reduce this fraction

92/100 = (23*4)/(25*4) = 23/25

Therefore, 3/10+62/100 = 23/25

The solutions of the polynomial are  [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex]  ,  [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]

Step-by-step explanation:

The solutions of a polynomial is the value of x when the polynomial equal to zero

The formula of quadratic polynomial is [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}[/tex] , where

∵ The polynomial is 4x² - 4x + 10

- Equate it by zero to find its solutions

∴ 4x² - 4x + 10 = 0

∵ The coefficient of x² is 4

∴ a = 4

∵ The coefficient of x is -4

∴ b = -4

∵ The numerical term is 10

∴ c = 10

- Use the formula to find the values of x

∵ [tex]x=\frac{(-4)(+/-)\sqrt{(-4)^{2}-4(4)(10)}}{2(4)}[/tex]

∴ [tex]x=\frac{-4(+/-)\sqrt{16-160}}{8}[/tex]

∴ [tex]x=\frac{-4(+/-)\sqrt{-144}}{8}[/tex]

∵ [tex]\sqrt{-144}=12\sqrt{-1}[/tex]

- Substitute  [tex]\sqrt{-1}[/tex]  by i

∴ [tex]12\sqrt{-1}=12i[/tex]

∴ [tex]x=\frac{-4(+/-)12i}{8}[/tex]

- Divide up and down by 4 to simplify the fraction

∴ [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex]   ,   [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]

The solutions of the polynomial are  [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex]  ,  [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]

Learn more:

You can learn more about the quadratic formula in brainly.com/question/8196933

#LearnwithBrainly

The core of calculus in mathematics are functions. The unique varieties of relations are the functions.

The cost of 1 salad exists $3.

A function is a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Let, the cost of 1 sandwich be 'x' and the cost of 1 salad is 'y'.

4 sandwiches = 4x

3 salads = 3y

total spent = $24

From the given equation, we get

4x + 3y = 24

If each sandwich costs $3.75,

⇒ 4(3.75) + 3y = 24

simplifying the above equation, we get

⇒ 15 + 3y = 24

⇒ 3y = 24 - 15

⇒ 3y = 9

⇒ y = 9/3

⇒ y = 3

Therefore, the cost of 1 salad exists $3.

To learn more about function, refer to:

https://brainly.com/question/20688364

#SPJ2

Answer:

Karen had 45 m and m's candy.

Step-by-step explanation:

Let the number of m and m's candy be 'x'.

Now given:

Karen gave an equal amount of m and m's to herself and four friends.

So we can say that;

Number of people m and m's candy distributed equally = 5

Also Given:

Each person receives m and m's equivalent to the largest one digit number.

Now we know that;

Largest one digit number is 9.

So we can say that;

Each person receives m and m's = 9

We need to find number of m and m's Karen have.

Solution:

So we can say that;

Total number of m and m's Karen have is equal to Number of people m and m's candy distributed equally multiplied by number of m and m's can each person receives.

framing in equation form we get;

Total number of m and m's Karen had = [tex]9\times5 = 45[/tex]

Hence Karen had 45 m and m's candy.

Apply the product rule by raising each term by the power outside powers.

Then divide and simplify to get the second choice:

Answer:

[tex]y+2=(x+2)[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(-2,-2) and (2,2)

substitute the values

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

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=1\\(x1,y1)=(-2,-2)[/tex]

substitute

[tex]y-(-2)=(1)(x-(-2))[/tex]

[tex]y+2=(x+2)[/tex]

Answer:

{(3, 4), (4, 8), (6, 6), (7, 10)}

Step-by-step explanation:

Only the first one is a function because the others have repeated x values in some of the ordered pairs.

For example,  {-1, 4), (0, 3), (0, -2)}   has a repeated x = 0.

Answer:

1.5

Step-by-step explanation:

y2 - y1 ÷ x2 - x1

(3,4) (8, -3)

(x1,y1) (x2,y2)

Answer: Interest rate = 0.065

Step-by-step explanation:

I=PRT

3250=5000r*10

Divide by 10 on both sides

325=5000r

r=0.065

Answer:

34

Step-by-step explanation:

when n=4.

n^2+6n-6 = (4)^2+6(4)-6 = 16 + 24 - 6 = 10 + 24 = 34

Answer:

Step-by-step explanation:

d = rt....and just so you know, speed is the same as rate

since we are looking for r, I am gonna change the equation

d = rt......r = d / t

d = 400

t = 10

now sub

r = d / t

r = 400/10

r = 40 ft per minute <=====

Answer: 40 per minute

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]a \times b = 0.24\\b = \frac{0.24}{a} or, a = \frac{0.24}{b}[/tex].

In the above equation the proper values can not be found only when the denominator will be 0.

As for example, if a = 2, then b = 0.12.

If a = 0.12, then b = 2.

If a = 1, b = 0.24 or b = 1, a = 0.24.

Thus, a or b can be any real number rather than 0.

Answer:

x = 76°

Step-by-step explanation:

At point I

to get angle JID

angle JID + 107° = 180°. (angle on a straight line)

angle JID = 180° - 107°

angle JID = 73°

for Triangle JiD

angle DJI + 31° + 73° = 180° (Sum of angles in a triangle)

angle DJI = 180 - 104 = 76°

angle FJI = 31 + 73 =104°. ( Sum of two interior angles in a triangle is equal to one exterior angle)

Hence,

x° + 104° = 180° (angle on a straight line)

x = 76°

The algebraic expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)

Solution:

Given the statement:

Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen

Let us first understand the given statement,

Let the number be "x"

" sum of a number and four" means x + 4

"Three sets of a sum of a number and four" translated to 3(x + 4)

"sum of seven times the same number and thirteen" means 7x + 13

Thus the algebraic expression for given statement is:

[tex]3(x+4)+(7x + 13)[/tex]

Using distributive property in above expression

[tex]a(b+c) = ab + bc[/tex]

Therefore,

[tex]3(x+4)+(7x + 13) = 3x + 12 + 7x + 13[/tex]

Combine the like terms

[tex]3(x+4)+(7x + 13) = 10x+25[/tex]

Thus the required expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)

Answer: w = 15

Original Question: 40w + (1.5)(8)(w) =780

Step-by-step explanation:

1) 40w + 1.5 x 8w = 780

2) 40w + 12w = 780

3) 52w = 780

4) 52w/52 = 780/52

w = 15

Answer:

A. x=13

Step-by-step explanation:

[tex]x + 11 = 24 \\ x = 24 - 11 \\ x = 13[/tex]

Answer:

Amount in 4% account: $550

Step-by-step explanation:

Use simple interest formula [tex]I=P\cdot r\cdot t,[/tex] where

I = interest

P = principal

r = rate (as decimal)

t = time.

4% account:

[tex]P_1=x\\ \\r_1=0.04\\ \\t_1=1,[/tex]

then

[tex]I_1=x\cdot 0.04\cdot 1=0.04x[/tex]

5% account:

[tex]P_2=1,500-x\\ \\r_2=0.05\\ \\t_2=1,[/tex]

then

[tex]I_2=(1,500-x)\cdot 0.05\cdot 1=0.05(1,500-x)[/tex]

You have earned $69.50 in total, so

[tex]I_1+I_2=69.50\\ \\0.04x+0.05(1,500-x)=69.50\\ \\4x+5(1,500-x)=6,950\\ \\4x+7,500-5x=6,950\\ \\4x-5x=6,950-7,500\\ \\-x=-550\\ \\x=550\\ \\1,500-x=1,500-550=950[/tex]

Amount in 4% account: $550

Amount in 5% account: $950

Answer:

y=3 x -4

Step-by-step explanation:

yes

Answer:

The straight-line distance (in paces) from the tree to the treasure is 80.62 paces

Step-by-step explanation:

Given:

Distance walked towards the north = 70 Paces

Distance walked towards the East = 40 Paces

To Find:

The straight line distance  from the tree to the treasure =?

Solution:

We we track the trail we can find a right triangle formed where the two sides are 70 pace and 40 pace each. The straight line distance is the hypotenuse of the triangle(Refer the figure below

Now we can find the length of the hypotenuse by Pythagorean theorem

[tex]a^2 =b^2 +c^2[/tex]

where b and c are the sides of the triangle

and a is the hypotenuse

[tex]a^2 = 70^2 +40^2[/tex]

[tex]a^2 =4900 + 1600[/tex]

[tex]a = \sqrt{4900 + 1600}[/tex]

[tex]a =\sqrt{6500}[/tex]

a =  80.62

Final answer:

The additive inverse of – 4 is 4 because when – 4 is added to 4, the result is 0. This demonstrates the concept of additive inverses in algebra, where each number has a counterpart that sums to zero.

Explanation:

The question is asking to find the additive inverse or opposite of – 4. The additive inverse of a number is the number that, when added to the original number, results in a sum of zero. This is a fundamental concept in algebra and mathematics in general. To find the additive inverse of – 4, you simply need to find a number that, when added to – 4, equals 0.

The additive inverse of – 4 is 4. This is because – 4 + 4 = 0. When you add – 4 and its additive inverse together, their sum is 0, which means 4 is the correct answer. The concept of the additive inverse is crucial in equations solving and other algebraic manipulations, assisting in understanding how to balance equations and solve for unknowns.

Answer:

11 x^2 + 4x -6

Step-by-step explanation:

combine like terms but be careful with the minus sign in front of the second set of parentheses.

4x^2 + 9x -7 + 7x^2 -5x +1

Answer: [tex]-3x^2+4x-6\\[/tex]

Step-by-step explanation:

4x^2 +9x-7 does not need distributive propery

-(7x^2+5x-1) does with that negitive in front of parentheses

It then becomes -7x^2-5x+1

Add it all together

[tex]-3x^2+4x-6[/tex]

Answer:

x is 1 or -7

Step-by-step explanation:

x^2-7x+6=0 //we must find two numbers with multiple as -7 and sum as +6. numbers are -1 and 7.

(x-1)(x+7)=0

x-1=0 -»x=1

x+7=0 -»x= -7

Answer:

The answer is A 160% and E [tex]\frac{160}{100}[/tex].

Step-by-step explanation:

To find what percentage 40 is of 25, you first need to find what 1% of 25 is. To solve you do 25 ÷ 100 which is equal to 0.25. You then need to divide 40 by 0.25, which would be the same as multiplying 40 by 4. 40 ÷ 0.25 = 160. Therefore, 40 is 160% of 25. 160% is the same as saying [tex]\frac{160}{100}[/tex] or 160 out of 100 or you could say 160 ÷ 100 = 1.6, which would mean 25 × 1.6 = 40.

40 as a percentage of 25 can be applied such that the percentage would be:

To find what percent 40 is of 25, you would use the formula:

= (Part / Whole) * 100%

So here, 40 is the part and 25 is the whole:

= (40 / 25) * 100%

= 160%

40 is 160 % of 25.

160 / 100 is also 160 %. The rest of the options are incorrect leaving options A and E.

Find out more on percentages at https://brainly.com/question/24304697

#SPJ6

Answer:

100

Step-by-step explanation:

We know that if we convert 1/4 into a decimal it becomes 0.25 so,

0.25

x

400

____________________

100

Hope this helps!

Answer:

4.4 cubic inches

Step-by-step explanation:

From the question;

We are required to determine the volume of a cone;

Volume of a cone is given by the formula;

V=1/3πr²h

Therefore; taking π to be 3.142

Volume =1/3 × 3.142 × 1.2² × 2.9

             = 4.373664

             = 4.4 cubic inches (to the nearest tenth)

Thus, the volume of a cone is 4.4 cubic inches

The height of the house, given the angle of elevation and the distance of the point is 25. 98 meters.

How to find the height ?

You can use the tangent function because it relates the angle of elevation to the opposite side and the adjacent side (the horizontal distance).

The tangent of the angle of elevation is equal to the ratio of the height to the horizontal distance:

tan(30 degrees) = h / 45 meters

Solve for "h" by multiplying both sides by 45 meters:

h = 45 meters x tan(30 degrees)

You can calculate the value of tan(30 degrees):

tan(30 degrees) = 0.5774

Multiply:

h = 45 meters x 0.5774

= 25.98 meters

Answer:

84 cases

Step-by-step explanation:

The amount of money need to be raised = $ 500

Selling price of each ball = $2

1 Tennis case = 3 balls.

Earnings = Selling Price of each ball x Number of balls sold

Quantity sold = Earnings / Selling Price of each ball

Quantity sold = $ 500 / $ 2 = 250 balls

Using direct proportions

1 case = 3 balls

? cases = 250 balls

No.cases = 250 balls / 3 balls = 83.333

Note: Minimum number of cases required are 83.3333 to earn $ 500; however, we can not sell 0.3333 number of cases, hence, we will sell atleast 84 cases.