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3 years ago

Apply the distributive property to factor out the greatest common factor. 35 + 14 =

Mathematics

1 answer:

natka813 [3]3 years ago

3 0

Answer:

2(5+2)

Step-by-step explanation:

The greatest common factor would be 7. So now 35/7 is 5 and 14/7 is 2. Now put it in distributive property! GCF on the outside and the new numbers we just got in the inside. There's your answer! Have a great day! :)

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A ring is now reduced to £840. This is a saving of 40% of the original price.

gladu [14]

The original price of the ring is £1400

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3 years ago

Read 2 more answers

What is u equal to u=?

Jet001 [13]

Answer:

u= -449

Step-by-step explanation:

714=6(u+629)-366

+366 +366

1080=6u+3774

-3774 -3774

6u=-2694

÷6 ÷6

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3 years ago

The population of a town was 7652 in 2016. The population grows at a rate of 1.6% annually.

Serggg [28]

Answer:

(A) The population's growth rate in equation form is y = (0.016t * 7652) + 7652

(B) y = (0.016t * 7652) + 7652 =

y = (0.016(8) * 7652) + 7652 =

y = (0.128 * 7652) + 7652 =

y = 979.456 + 7652 =

y = 8631.456 (Or About) 8631

Step-by-step explanation:

(A) Y = the total population of the town. 0.016 is 1.6% just in its original form. T = the year in which were trying to find the town's total population. 7652 is the total population of the town in 2016. With this information, the equation reads, The total population of the town (Y) is equal to 16% (0.016) of the current year's population (T) added to 2016's population of 7652. (This last sentence can also be read what is 1.6% of the towns population in the year were trying to find. Because the population is always growing, 1.6% gets multiplied as to scale with the total population in year T)

(B) We just substitute (T) for 2024, or 8 years after 2016 (2024-2016) and simplify the equation we made.

7 0

3 years ago

Find the value of x pls help

bogdanovich [222]

Answer: 90 degrees

Step-by-step explanation:

It is a right angle which means it is 90 degrees. Plz mark me brainliest

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:

Fundamental Theorem of Calculus

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

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:

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

Integration by substitution

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

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

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

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

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

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

Substitute 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})$\end{minipage}}$