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3 years ago

Find the area of the composite figure. A=36cmA=40cmA=48cmA=64cm

Mathematics

1 answer:

MissTica3 years ago

8 0

Check the picture below.

so the shape is really 4 triangles with a base of 2 and a height of 4 each, and 2 squares tha are 4x4.

$\bf \stackrel{\textit{area of the 4 triangles}}{4\left[\cfrac{1}{2}(2)(4) \right]}~~+~~\stackrel{\textit{area of the two squares}}{2(4\cdot 4)}\implies 16+32\implies 48$

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Evan collected 45 trading cards. Jessica collected 3 times as many trading cards as Evan. How many trading cards did Jessica col

Anuta_ua [19.1K]

Answer: Jessica collected 135 trading cards.

Step-by-step explanation:

you just multiply 45 by 3 to get 135

5 0

3 years ago

Need help please!

Paul [167]

Answer:

$a=\frac{m}{(q+r^2)}$

Step-by-step explanation:

We begin with the equation $qa+r^2a=m$ for which we need to solve for a.

The first thing that we can do is to factor out the a from both terms on the left side of the equation

$qa+r^2a=m\\\\a(q+r^2)=m$

Then we can divide each side by $(q+r^2)$ to isolate a

$a(q+r^2)=m\\\\a=\frac{m}{(q+r^2)}$

8 0

3 years ago

Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph

Dennis_Churaev [7]

ANSWER TO QUESTION 1

$f(x)=(x-2)(x+3)(x-1)^2$ .

EXPLANATION

The function given to us is,

$f(x)=x^4-x^3-7x^2+13x-6$

According to rational roots theorem,

$\pm1,\pm2,\pm3,\pm6$ are possible rational zeros of

$f(x)=x^4-x^3-7x^2+13x-6$ .

We find out that,

$f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6$

$f(-3)=81+27-63-39-6$

$f(-3)=6-6$

$f(-3)=0$

Also

$f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6$

$f(2)=16-8-28+26-6$

$f(2)=6-6$

$f(2)=0$

This implies that

$x-2 and x+3$ are factors of

$f(x)=x^4-x^3-7x^2+13x-6$ and hence $(x-2)(x+3)=x^2+x-6$ is also a factor.

We perform the long division as shown in the diagram.

Hence,

$f(x)=(x-2)(x+3)(x-1)^2$ .

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots

$x=2$ and $x=-3$ have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root $x=1$ has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

$x\le -3$

$f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6$

$f(-4)=150\:>0$

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

$f(3)=24\:>0$

We can now use these information to sketch the function as shown in diagram

4 0

3 years ago

The deciles of any distribution are the points that mark off the lowest 10% and the highest 10% of the distribution. the deciles

Levart [38]

(a) We need to figure out the deciles for a normal distribution curve in this part.

In order to do so, we need to find the z score corresponding to probability 0.10 and 0.90 on the normal distribution curve.

Upon looking at the normal distribution table, we can see that the probability P = 0.10 corresponds to a z score of -1.28 and probability P = 0.90 corresponds to a z score of 1.28.

Therefore, deciles are -1.28 and 1.28 for a normal distribution curve.

(b) In this part, we are given that mean height is 69.5 inches and standard deviation in height is 2.7 inches. Therefore, we can find the deciles using the z score formula as shown below:

$z=\frac{x-\mu}{\sigma }\Rightarrow \pm 1.28=\frac{x-69.5}{2.7}\\
x-69.5 = \pm 3.456\Rightarrow x=69.5\pm 3.456\Rightarrow \\
x=66.044,72.956$

Therefore, the required deciles are 66.044 and 72.956

7 0

3 years ago

Plz help in a rush!!!!!!!!!!

Bogdan [553]

Your answer is 4.7

Using the Pythagorean Theorem, you can find the length of the missing side:

$a^{2}+b^{2}=c^{2}\\(3)^{2}+b^{2}=(5.6)^{2}\\9+b^{2}=31.36\\b^{2}=22.36\\b=\pm \sqrt{22.36}$
Length cannot be negative, so your answer is:
$b=\sqrt{22.36}=4.728636...\\\\b=4.7$

5 0

3 years ago

Read 2 more answers

Find the area of the composite figure. A=36cmA=40cmA=48cmA=64cm​

Find the area of the composite figure. A=36cmA=40cmA=48cmA=64cm