If a=3 and b=5, what is the value of 3a + b to the power of 2?

Answers

Answer 1

Answer: 3a+b²=3(3)+5²=34

therefore 34 is the answer

Answer 2

Answer: $3a+b^2=3\cdot3+5^2=9+25=34$

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Solve x2 + 5x + 6 = 0

Answers

Answer:

Use the quadratic formula

=−±2−4√2

x=−b±b2−4ac2ax=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}x=2a−b±b2−4ac

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

2+5+6=0

x2+5x+6=0x^{2}+5x+6=0x2+5x+6=0

a=1a={\color{#c92786}{1}}a=1

b=5b={\color{#e8710a}{5}}b=5

c=6c={\color{#129eaf}{6}}c=6

=−5±52−4⋅1⋅6√2⋅1

Simplify

Separate the equations

Solve

Solution

=−2=−3

Step-by-step explanation:

Answer:

x= - 2 or x = - 3

Step-by-step explanation:

$x^(2) +5x+6=0\nFactorise\n(x^(2) +3x)(+2x+6)=0\nx(x+3)+2(x+3)=0\n(x+2)(x+3)=0\nx+2 = 0 or x+3=0\nx=-2 or x=-3$

$log(x+3) = log 8 - log 2$
agree or disagree and justify

Answers

Answer:

Step-by-step explanation:

log (x+3)=log8-log2

log(x+3)=log(8/2)=log4

x+3=4

x=4-3=1

How many unit tiles need to be added to the expressionx2 + 4x + 3 in order to form a perfect square trinomial

Answers

In the question "How many unit tiles need to be added to the expression x2 + 4x + 3 in order to form a perfect square trinomial" the correct answer is 1 unit tile. Because, to make the expression x^2 + 4x + 3 a perfecr square trinomial we have x^2 + 4x + 3 + 1 = x^2 + 4x + 4 = (x + 2)^2

Answer:

A) 1

Step-by-step explanation:

A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of? a. 6 in3
b. 24 in3
c. 36 in3
d. 48 in3

Answers

To find the volume of a cylinder that the cone fits exactly inside, we can use the formula for the volume of a cone. By solving for the radius and height of the cone, we can then substitute those values into the formula for the volume of a cylinder to obtain the volume.The correct option is C.

To find the volume of a cylinder that the cone fits exactly inside, we need to understand the relationship between the cone and the cylinder. The volume of a cone can be found using the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height of the cone. The volume of the cylinder is equal to the volume of the cone, so the volume of the cylinder can also be calculated using the formula V = π * r^2 * h. In this case, the volume of the cone is given as 12 cubic inches. We can set up an equation to find the radius and height of the cone using this volume, and then use those values to find the volume of the cylinder.

Let's solve for the radius and height of the cone:

1.Start with the formula for the volume of a cone: V = (1/3) * π * r^2 * h

2.Substitute the given volume of the cone as 12 cubic inches: 12 = (1/3) * π * r^2 * h

3.Cancel out the 1/3 by multiplying both sides of the equation by 3: 36 = π * r^2 * h

4.Divide both sides of the equation by π to isolate r^2 * h: r^2 * h = 36/π

5.Since we don't have enough information to solve for both r and h, we will express the height h in terms of the radius r.

6.Substitute r^2 * h with 36/π: r^2 * (36/π) = 36/π

7.Simplify the equation by canceling out the π: r^2 * (36/π) = 36/π

8.Multiply both sides of the equation by π/36: r^2 = 1/π

9.Take the square root of both sides to find the radius r: r = 1/√π

10.Now that we have the radius, we can find the height using the equation r^2 * h = 36/π: (1/√π)^2 * h = 36/π

11.Simplify the equation: h = 36

So, the radius of the cone is 1/√π and the height is 36. Using these values, we can calculate the volume of the cylinder:

1. Start with the formula for the volume of a cylinder: V = π * r^2 * h

2. Substitute the values we found for the cone into the formula: V = π * (1/ √π)^2 * 36

3. Simplify the equation: V = 36 cubic inches

the volume of the cylinder that the cone fits exactly inside is 36 cubic inches.

Therefor the correct option is C.

Learn more about volume of a cone and cylinder here:

brainly.com/question/35498382

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Volume of a cone = 1/3 r² π h
Volume of a cylinder = r² π h = 3 · V ( cone ) = 3 · 12 = 36 in³
Answer: C )

8 is what percent of 75?

Answers

8/75 = 0.1066666.....

Therefore 8 is roughly 11% of 75.

Or you could figure it out this way...

$\frac { n }{ 100 } \cdot 75=8\n \n 75n=800\n \n n=\frac { 800 }{ 75 } \n \n \therefore \quad n=10.67\quad \left( 2\quad dp \right)$

Therefore, more precisely, 8 is roughly 10.67% of 75.

In one day, Annie traveled 5 times the sum of the number of hours brian traveled and 2. Together they traveled 20 hours. Find the number of hours each person traveled

Answers

Brian traveled 1 2/3 hours while Annie traveled 18 1/3 hours.

Explanation:
Let b be the number of hours Brian travels. Annie travles 5 times the sum of Brian's hours and 2, or 5(b+2). Together they travel 20 hours:
5(b+2)+b=20.

Use the distributive property:
5*b+5*2+b=20
5b+10+b=20.

Combine like terms:
6b+10=20.

Subtract 10 from both sides:
6b+10-10=20-10
6b=10.

Divide both sides by 6:
6b/6=10/6
b=5/3=1 2/3.

Brian travels 1 2/3 hours. This means Annie travels
5(1 2/3+2)=5(3 2/3)=5(11/3)=55/3=18 1/3 hours.

Annie and Brian traveled 18.3 hours and 1.7 hours respectively