Ask question

Ask question

All categories

3 years ago

5

Nadia's father bought a new camera,lens, and case. He rounded the cost of all the items to estimate how much money he would need

. He rounded the cost of the camera to $800,the cost of the lens to $500, and the cost of the case to $200. The actual cost of all three was 1,489. What could the actual cost of the item be?

2 answers:

valentina_108 [34]3 years ago

6 0

Doesn't it say the answer in that question...
It is asking for the actual cost of the item and it said $1,489
for his set.

ser-zykov [4K]3 years ago

6 0

The actual cost is 537

You might be interested in

Sam wants to build a wooden deck on his patio, which is in the shape of a parallelogram. The area of the patio is 280 ft 2. Find

Radda [10]

Answer: The base is 18.3ft

Sam wants to build a wooden deck on his patio, which is in the shape of a parallelogram. The area of the patio is 280 ft2. Find the base. Round your answer to the nearest foot. (height=5x)(base=6x)

Step-by-step explanation:

Given;

Area = 280ft^2

height = 5x

Base = 6x

The area of the parallelogram A can be written as;

Area = base × height

A = b×h

Substituting the values of Area, base and height.

280 = 5x × 6x

280 = 30x^2

x^2 = 280/30

x = √(280/30)

Since the base = 6x ;

Substituting the value of x.

Base = 6x = 6(√(280/30))

Base = 18.3ft

The base is 18.3ft

4 0

3 years ago

What is the justification for each step in solving the inequality?

Fed [463]

Step-by-step explanation:

$3x+\frac{5}{8}\geq 4x-\frac{1}{2}$

Subtract 5/8 on both sides

To subtract 5/8 we make the denominators same

$3x\geq 4x-\frac{1*4}{2*4}-\frac{5}{8}$

Addition or Subtraction property of order is used

$3x\geq 4x-\frac{9}{8}$

Subtract 4x on both sides

Addition or Subtraction property of order is used

$-x\geq -\frac{9}{8}$

Now divide both sides by -1

Multiplication or Division property of order is used

$\frac{-x}{-1} \geq \frac{-\frac{9}{8}}{-1}$

Multiplication or Division property of order is used

$x\leq \frac{9}{8}$

5 0

3 years ago

Evaluate the integral, show all steps please!

Aloiza [94]

Answer:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x$

Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:

$\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x$

<u>Integration by substitution</u>

<u />

<u /> $\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}$

$\textsf{Let }x=3 \sin \theta$

$\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}$

Find the derivative of x and rewrite it so that dx is on its own:

$\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta$

$\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta$

<u>Substitute</u> everything into the original integral:

$\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}$

Take out the constant:

$\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta$

$\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}$

$\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$

$\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}$

$\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}$

$\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}$

$\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:$

$\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}$

$\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:$

$\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Learn more about integration by substitution here:

brainly.com/question/28156101

brainly.com/question/28155016

4 0

2 years ago

Jimmy began deriving the quadratic formula as shown. ax² +bx +c = 0 x2+bax+ca=0 x2+bax=−ca x2+bax+(b2a)2=−ca+(b2a)2 What should

andrew11 [14]

Factor the trinomial

8 0

3 years ago

A family has an annual income of $30,600 Of this, 1/4 is spent for food, 1/5 for housing, 1/10 for clothing, 1/9 for savin

Ksenya-84 [330]

Answer:

$6,120

Step-by-step explanation:

1/5 (one-fifth) of the family's annual income ($30,600) is spent on housing- as the word problem states.

You have to find 1/5 (one-fifth) of* $30,600.

Write it out as an equation.

$\frac{1}{5} \times 30600$

*The <em>of</em><em> </em>in the word equation (1/5 of 30600) simply means multiplication.

4 0

2 years ago