how do you solve a quadratic function using x^2+bx+c?

Answer:

$6

Step-by-step explanation:

9 tubes of paint costs

$70 - $16 = $54

1 tube of paint cost

$54 : 9 = $6

f(x) = 3x - 1 is the linear function for the line represented by the point-slope equation

Solution:

Given point slope equation is:

[tex]y - 5 = 3(x-2)[/tex]

We have to find the linear function for the line

The formula y = mx + b is said to be a linear function

Rearrange the given equation

[tex]y - 5 = 3(x-2)\\\\y - 5 = 3x - 6\\\\Move\ the\ varibale\ y\ to\ one\ side\ and\ constants\ and\ x\ to\ other\ side\\\\y = 3x - 6 + 5\\\\y = 3x - 1[/tex]

Let y = f(x)

Then we get,

f(x) = 3x - 1

Thus the linear function is found

Answer:

the answer will be B. f(x)=3x-1

Question:

Which equation can be solved by using this system of equations?

y = 3x^3 - 7x^2 + 5

y = 7x^4 + 2x

A.) 3x^3 - 7x^2 +5 = 0

B.) 3x^3 - 7x^2 + 5 = 7x^4 +2x

C.) 7x^4 +2x = 0

D.) 7x^4 +3x^3 -7x^2 +2x + 5 = 0

Answer:

Option B: [tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex] is used to solve this system of equations.

Explanation:

The two equations are [tex]y=$3 x^{3}-7 x^{2}+5$[/tex] and [tex]y=$7 x^{4}+2 x$[/tex]

Using substitution method, let us substitute [tex]y=$7 x^{4}+2 x$[/tex] in the equation [tex]y=$3 x^{3}-7 x^{2}+5$[/tex], we get,

[tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex]

Thus,  [tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex] is used to solve this system of equations.

Hence, Option B is the correct answer.

Answer:

Answer is B. 3x^3-7x^2+5 = 7x^4+2x

Step-by-step explanation:

got it right!

hope this helps

Answer: x= -1 y= 4

Step-by-step explanation:

We are going to solve this using substitution.

Here is the work...

5x+3(4)=7

That is what it woud look like because y is equal to 4.

3 times 4 is 12.

So now we have...

5x+12=7

Now we want to get All the common factors together...

To do this we will subtract 12 from 7 and we get -5.

Here is our equation now...

5x=-5

Now we divide x by 5 to get x alone, but we also divide -5 by 5.

x=-1

Now all we have to do to solve for y is put x in an equation.

In this case here is what we will do...

5(-1)+3y=7

Multiply...

-5+3y=7

Now we need to get the common factors together so lets add 5 to 7.

3y=12

3y/3=y

12/3=y

y=4

But that is already in your problem...OOF.Dont worry its still correct.

To solve the system, substitute y=4 into the first equation, leading to x=-1. Thus, the solution is x=-1 and y=4.

To solve the system of equations 5x + 3y = 7 and y = 4, we can start by substituting the value of y from the second equation into the first equation. We are given y directly, so the substitution is straightforward.

Substituting y = 4 into the first equation:

So, the solution to the system of equations is x = -1 and y = 4. We can say that x and y are variables, and in this case, y is dependent on x in other linear equations but is given directly here.

Answer:

7D

Step-by-step explanation:

2D + 5D

Add the figures

Answer: 10

Step-by-step explanation:

2 * 4 = 8

8/2 = 4

2 * 2 = 4

4/2 = 2

4 + 2 = 6

2 * 2 = 4

4 + 6 = 10

Answer:

18 minutes

Step-by-step explanation:

the beaver is 18 minutes so multiply that by 3 which equals 54 then add those two together then you get 72 then add 23 qhich then you end up with 95 minutes total.

To solve the problem, we create an equation representing the total time all three animals can hold their breath. Solving it reveals that a beaver can hold its breath for 18 minutes.

Let's denote the time a beaver can hold its breath as 'x' minutes. According to the problem, a Greenland whale can hold its breath three times as long as a beaver, so that's '3x' minutes. A hippopotamus can hold its breath for five minutes more than a beaver, making it 'x+5' minutes.

The combined time for all three animals is given as 95 minutes, so we can set up the following equation:

x (beaver) + 3x (Greenland whale) + x + 5 (hippopotamus) = 95

Simplified, it becomes:

5x + 5 = 95

Next, you subtract 5 from both sides:

5x = 90

Finally, divide by 5:

x = 18

So, a beaver can hold its breath for 18 minutes.

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Answer:

Step-by-step explanation:

hello :

-6(w+1) < 2(w+5)

-6w-6< 2w+10

-6w-2w< 6+10

-8w < 16

8w > -16

w > -2

Answer:

Step-by-step explanation:

Answer:

  15 inches

Step-by-step explanation:

The space diagonal of a rectangular prism is the root of the sum of the squares of the edge lengths. The longest straight part that will fit in the box will be at most ...

  l = √(4² +4² +14²) = √228 ≈ 15.10 . . . . inches

The greatest length the part could have been is 15 inches.

Answer:

A

Step-by-step explanation:

3,-12,15,-21

The product 3 x [1 -4 5 -7] of [ -3  12  -15  21 ]

In mathematics, when we multiply a scalar (a single number) by a vector, the result is a new vector where each element of the original vector is multiplied by that scalar.

In this case, we have the scalar 3 and the vector [1  -4  5  -7].

1. Multiply each element of the vector by the scalar 3:

  3 x 1 = 3  

  3 x (-4) = -12  

  3 x 5 = 15  

  3 x (-7) = -21

2. Arrange the results in order:

  -3  12  -15  21

So, the product of 3 and the vector [1  -4  5  -7] is the new vector [-3  12  -15  21].

In this process, we essentially scaled each component of the original vector by a factor of 3, either increasing or decreasing the magnitude based on the sign of the original component.

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Answer:

look at the picture shown

The first number is 8

Solution:

Let the first number be "x"

The second number is 6 times the first

Second number = 6x

The third number is 15 less than the second

Third number = second number - 15

Third number = 6x - 15

The sum of three numbers is 89

Therefore,

First number + second number + third number = 89

[tex]x + 6x + 6x - 15 = 89\\\\13x - 15 = 89\\\\13x = 89+15\\\\13x = 104\\\\Divide\ both\ sides\ by\ 13\\\\x = 8[/tex]

Thus the first number is 8

Answer:

1/8, 1/4, 3/8, 9/16, 3/4, 1

Step-by-step explanation:

The fractions have been arranged in order from smallest to largest as 1/8< 1/4< 3/8< 9/16< 3/4< 1.

Fractions with different denominators can be compared by making the denominators the same. For example, take 1/4 and 1/2. The LCM of these fractions is 4. Now we can alter the fractions so that they have the same denominators as follows:

1/4 and 2/4

We can see that 2/4 is greater than 1/4.

The given fractions are: 3/4, 1/8, 9/16, 1, 1/4, 3/8

The lowest common multiple of these fractions is 16.

We can convert the fractions as shown below:

12/16< 2/16< 9/16< 16/16< 4/16< 6/16

Now we can arrange them in ascending order easily as shown below:

2/16, 4/16, 6/16, 9/16, 12/16, 16/16

or 1/8< 1/4< 3/8< 9/16< 3/4< 1

Therefore, we have arranged the fractions in order from smallest to largest as 1/8< 1/4< 3/8< 9/16< 3/4< 1.

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We can start off by making 12 1/2 to an improper fraction:

12 1/2 = 25/2

Divide the large jar of salsa by the small jar of salsa: 75 /  25/2.

Reciprocal of second and turn divide to multiply:

75 * 2/25.

150/25 =  6.

So 6 jars of small salsa = 1 large jar of salsa.

Answer:

15.7

Step-by-step explanation:

8 1/5= 8.2

4 2/5= 4.4

3 3/10= 3.1

4.4 + 3.1 = 7.5

7.5 + 8.2 = 15.7

Answer:

Step-by-step explanation:

Combine fractions with similar denominators

81/5 + 42/5 + 33/10

Add 81 and 42

123/5 + 33/10

To write 123/5 as a fraction with a common denominator, multiply by 2/2

123/5 >2/2 + 33/10

Write each expression witha common denominator of 10

123 . 2/10 + 33/10

Common numerator over denominator

123 . 2 + 33/10

Simplify

279/10

Thus answer = 279/10 0r 27.9

Eva has $20.00, Justin has $27.50 and Emma has $15.50

Step-by-step explanation:

The given is:

We need to find how much money each person has

Assume that Eva has $x

∵ Eva has $x

∵ Justin has $7.50 more than Eva

- Add 7.50 to x

∴ Justin has = x + 7.50

∵ Emma has $12 less than Justin

- Subtract 12 from (x + 7.50)

∴ Emma has = x + 7.50 - 12 = x - 4.50

∵ Together, they have a total of $63.00

- Add x , (x + 7.50) and (x -4.50), then equate the sum by 63.00

∴ x + (x + 7.50) + (x - 4.5) = 63.00

- Add like terms

∴ (x + x + x) + (7.5 - 4.5) = 63.00

∴ 3x + 3 = 63.00

- Subtract 3 from both sides

∴ 3x = 60.00

- Divide both sides by 3

∴ x = 20.00

Substitute x by 20.00 in each expression above

∴ Eva has = $20.00

∴ Justin has = 20.00 + 7.50 = $27.50

∴ Emma has = 20.00 - 4.50 = $15.50

Eva has $20.00, Justin has $27.50 and Emma has $15.50

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Answer:1 8/45

Step-by-step explanation:73-20/45

53/45

1 8/45

Answer:

4 29/45

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Consider Δ JKL and Δ GDF

If the ratios of corresponding sides are equal then the triangles are similar.

[tex]\frac{JK}{GD}[/tex] = [tex]\frac{24}{20}[/tex] = [tex]\frac{6}{5}[/tex]

[tex]\frac{xJL}{GF}[/tex] = [tex]\frac{18}{15}[/tex] = [tex]\frac{6}{5}[/tex]

[tex]\frac{KL}{DF}[/tex] = [tex]\frac{12}{10}[/tex] = [tex]\frac{6}{5}[/tex]

Since the ratios are equal then Δ JKL and Δ GDF are similar by SSS postulate.

36 teaspoons. since the number of quarts is multiplied by 3, multiply the number of teaspoons as well. 12 × 3 = 36

The solution set is (7,3).

Step-by-step explanation:

Given system of equations is;

3x−2y=15     Eqn 1

y=2x−11        Eqn 2

Substituting value of y from Eqn 2 in Eqn 1

[tex]3x-2(2x-11)=15\\3x-4x+22=15\\-x+22-15=0\\7=x\\x=7[/tex]

Putting x=7 in Eqn 2

[tex]y=2(7)-11\\y=14-11\\y=3[/tex]

The solution set is (7,3).

Keywords: linear equation, substitution method

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Answer:

Yes, you can

Step-by-step explanation:

The standard form of the equation of a parabola is [tex]y=ax^2+bx+c[/tex]

When given three points, you substitute each point into the equation to obtain 3 simultaneous linear equations.

You then solve the three equations simultaneously to find the values of the constants a,b, and c.

You then substitute these constants into [tex]y=ax^2+bx+c[/tex]

Answer:

[tex]m=\frac{1}{ab}[/tex]

Step-by-step explanation:

we know that

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

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

we have the points

(a,1/b) and (b,1/a)

substitute

[tex]m=\frac{1/a-1/b}{b-a}[/tex]

[tex]m=\frac{\frac{b-a}{ab}}{b-a}[/tex]

[tex]m=\frac{1}{ab}[/tex]

The slope of the line joining the points (a,1/b) and (b,1/a) is calculated using the slope formula and is found to be 1 divided by the product of a and b, assuming a and b are not equal and neither is zero.

To find the slope of the line joining the points with coordinates (a,1/b) and (b,1/a), we use the slope formula, which is the change in y divided by the change in x. We can write the formula as:

slope (m) = (y2 - y1) / (x2 - x1)

Substituting the given points into the formula gives us:

slope (m) = (1/a - 1/b) / (b - a)

If we assume that a does not equal b and neither a nor b is zero, the slope can be calculated by simplifying the numerator and the denominator:

slope (m) = ((b - a) / (ab)) / (b - a)

The (b - a) terms cancel out, leaving us with:

slope (m) = 1 / (ab)

Therefore, the slope of the line is the reciprocal of the product of a and b.

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Answer:

14.2 squared units

Step-by-step explanation:

Always draw a diagram for the question. Capital letters are usually angles, and their opposite side is the same letter as a lowercase. (See diagram) The opposite side of angle B is side b.

The formula for area of a triangle is A = bh/2

"A" is for area.

"b" is for base (usually bottom side)

"h" is for height (perpendicular to base).

We know the measurement for the base c = 7.1. We need to find the height.

Notice when you draw in the height, it form two right triangles. We can use trigonometric ratios for right triangles.

Remember the trigonometric ratios using SohCahToa:

sinθ = opposite/hypotenuse;

cosθ = adjacent/hypotenuse and;

tanθ = opposite/adjacent, where θ means the angle of reference.

Focus on the triangle on the left side. We know one angle (∠B = 80°) and one side (a = 4.1). We can find "h", the missing side.

Since ∠B is our angle of reference, "h" is opposite. Since "a" is a longest side, it's the hypotenuse. Use the sine ratio because it uses the opposite and hypotenuse sides.

sinθ = opp/hyp             General sine ratio formula

sinB = h/a                  Variables you use in this problem

sin80° = h/4.1               Isolate "h". Multiply both sides by 4.1

h = 4.1(sin80°)                 Multiply with calculator

h = 4.1(0.98480775...)         Unrounded sin80

h = 4.03771178...                 Round this number

Note the number of decimal places given in the question.

h ≈ 4.0                Round to one decimal place

Now we can use the formula for the area of a triangle.

A = bh/2           Don't confuse side "b" with the base in this question

A = (7.1)(4.0)/2           Simplify the division

A = (7.1)(2.0)                   Multiply

A = 14.2                     Final answer for area

Since we don't know what the units are, you can say the answer is:

A = 14.2u²  or  14.2 squared units

Answer:

z ÷ 3 + z

Step-by-step explanation:

Answer:

8x-6

Step-by-step explanation:

[tex]21+7.50p\leq 52[/tex]

For inequalities, "a is no more than b" can be written as:

[tex]a\leq b[/tex]

Here we know Candace that can spend no more than $52 before tax. She can spend a certain amount of money in both Dark Roast coffee and Morning Blend coffee. So she spends:

Therefore:

Amount of money for Morning Blend coffee:

[tex]2\times 10.50=\$21[/tex]

Amount of money for Dark Roast coffee:

[tex]p\times 7.50=\$7.50p[/tex]

So the total amount of money:

[tex]21+7.50p[/tex]

Finally, the inequality becomes:

[tex]21+7.50p\leq 52[/tex]

Besides, in order to know how many pounds she can spend let's solve for p:

[tex]7.50p\leq 52-21 \\ \\ 7.50p\leq 31 \\ \\ p\leq 4.13[/tex]

So she can spend less that 4.13 pounds.

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Final answer:

The correct inequality to determine the possible values for the number of pounds of Dark Roast coffee, p, along with 2 pounds of Morning Blend coffee for $52 or less is 9p + 15.10 ≤ 52. This inequality can be used to solve for p, the number of pounds of Dark Roast coffee Candace can buy which is p ≤ 4.1.

Explanation:

Calculator Candace wants to determine the number of pounds of Dark Roast coffee, represented as p, she can buy if she purchases 2 pounds of Morning Blend coffee for a total of $52 or less. The price of the Morning Blend coffee is $7.55 per pound. To calculate this, we need to create an inequality that represents the scenario:

Now, the inequality will consider the total price of the Morning Blend coffee and add the price of the Dark Roast coffee (which is $9.00 per pound). So the inequality should look like this:

9p + 15.10 ≤ 52

This inequality can be used to solve for p, the number of pounds of Dark Roast coffee Candace can buy which is p≤4.1.

The expression '6a + 3' consists of two terms: '6a' and '3'. In mathematical expressions, terms are separated by addition or subtraction operations.

The expression given, 6a + 3, is a mathematical expression that involves operations of addition and multiplication. In this expression, there are two terms separated by a plus sign. To clarify, a term refers to the separated parts of an expression when it is written as a sum or difference. This expression contains one numerical value (3) and one algebraic term (6a).

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