All categories

3 years ago

I am having trouble with this 6th grade math problem. Can someone please help me?

Mathematics

2 answers:

fomenos3 years ago

3 0

The dimensions ofthesquare forms a 6 x 6=36 and the triangle is 1/2(4x6)=12,
36+12=48 so the answer is B.

Archy [21]3 years ago

3 0

The answer is B! 48 is the area of both square and triangle. Enjoy!

You might be interested in

How do you find the area of a compound figure?

Reika [66]

Divide the figure into known figures like rectangle and semi-circle
Calculate the area of the whole figure by adding the area of the separate figures

8 0

3 years ago

If Seth used 4 ounces of black beans, how many beans did he use altogether?

musickatia [10]

Answer: 4 Ounces.

Step-by-step Explanation: I don't know the full context of the problem, but if Seth used 4 ounces, that means that he used 4 ounces all together.

6 0

2 years ago

Complete the steps to solve the polynomial equation x3 – 21x = –20. According to the rational root theorem, which number is a po

jeka94

Answer:

Zeroes : 1, 4 and -5.

Potential roots: $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

Step-by-step explanation:

The given equation is

$x^3-21x=-20$

It can be written as

$x^3+0x^2-21x+20=0$

Splitting the middle terms, we get

$x^3-x^2+x^2-x-20x+20=0$

$x^2(x-1)+x(x-1)-20(x-1)=0$

$(x-1)(x^2+x-20)=0$

Splitting the middle terms, we get

$(x-1)(x^2+5x-4x-20)=0$

$(x-1)(x(x+5)-4(x+5))=0$

$(x-1)(x+5)(x-4)=0$

Using zero product property, we get

$x-1=0\Rightarrow x=1$

$x-4=0\Rightarrow x=4$

$x+5=0\Rightarrow x=-5$

Therefore, the zeroes of the equation are 1, 4 and -5.

According to rational root theorem, the potential root of the polynomial are

$x=\dfrac{\text{Factor of constant}}{\text{Factor of leading coefficient}}$

Constant = 20

Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.

Leading coefficient= 1

Factors of leading coefficient ±1.

Therefore, the potential root of the polynomial are $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

3 0

3 years ago

Which expression is equivalent to...

olga_2 [115]

Answer:

$8m^5$

Step-by-step explanation:

Well we can simplify the numerator, by multiplying the 4 by the 6 and the m^3 and m^4 (add the exponents, explained in one of my previous answers I think)

This gives us the fraction: $\frac{24m^7}{3m^2}$

We can now divide the m^7 by m^2 by subtracting the exponents, and the reason why this works, is you're simply cancelling out the m's, If we express this in expanded form we have the following fraction: $\frac{24 * m * m * m * m * m * m * m}{3 * m * m}$

Since there is two m's in the denominator and there is also two (more than two) m's in the numerator, we can cancel those two m's out, and we get the fraction:

$\frac{24 * m * m * m * m * m}{3}$ which can be simplified in exponent form as: $\frac{24m^5}{3}$ , now all we have to do is divide the 24 by the 3, to get 8

This gives us the answer: $8m^5$

6 0

1 year ago

Find the vertex of the graph of the function.

lapo4ka [179]

Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) $y=(x+2)^2+3$ , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

$f(x)=a(x-h)^2+k$ .....(1)

Where, (h,k) is the vertex of the parabola.

(1)

The given equation is,

$f(x)=(x-5)^2+10$

Comparing this equation with equation (1),we get,

$h=5$ and $k=10$

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

$f(x)=3x^2-18x+24$

$f(x)=3(x^2-6x)+24$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $9$ . Since there is factor 3 outside the parentheses, so subtract three times of 9.

$f(x)=3(x^2-6x+9)+24-3\times 9$

$f(x)=3(x-3)^2-3$

Comparing this equation with equation (1),we get,

$h=3$ and $k=-3$

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

$f(x)=4x^2+8x+7$

$f(x)=4(x^2+2x)+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $1$ . Since there is factor 4 outside the parentheses, so subtract three times of 1.

$f(x)=4(x^2+2x+1)+7-4$

$f(x)=4(x+1)^2+3$

Comparing this equation with equation (1),we get,

$h=-1$ and $k=3$

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

$y=x^2+4x+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $2^2$ .

$f(x)=x^2+4x+4+7-4$

$f(x)=(x+2)^2+3$

Therefore, the correct option is 4.

(5)

The given equation is,

$h=-16t^2+672t$

It can be written as,

$h=-16(t^2-42t)$

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

$x=\frac{b}{2a}$

$x=\frac{42}{2}$

$x=21$

Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

$f(x)=3x^3-12x^2-15x$

$f(x)=3x(x^2-4x-5)$

Use factoring method to find the factors of the equation.

$f(x)=3x(x^2-5x+x-5)$

$f(x)=3x(x(x-5)+1(x-5))$

$f(x)=3x(x-5)(x+1)$

Equate each factor equal to 0.

$x=0,-1,5$

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0

3 years ago