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inessss [21]
3 years ago
7

Simplify the expression 7(8g+ 9f – 6h)

Mathematics
2 answers:
zzz [600]3 years ago
7 0

Answer:

below

Step-by-step explanation:

7 ( 8g + 9f - 6h) \\7*8g + 7*9f - 7*6h \\56g + 63g - 42h

Lubov Fominskaja [6]3 years ago
5 0

63f + 56g - 42h

you distribute the 7 to all of the numbers

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Given that f(x)=x2-1 and g(x)=2x+8 find (g-f)(10)
irga5000 [103]

Answer:

<h2>(g-f)(10) = - 71</h2>

Step-by-step explanation:

f(x) = x² - 1

g(x) = 2x + 8

To find (g-f)(10) first find ( g - f)(x)

To find ( g - f)(x) subtract f(x) from g(x)

That's

( g - f)(x) = 2x + 8 - ( x² - 1)

Remove the bracket

( g - f)(x) = 2x + 8 - x² + 1

Simplify

( g - f)(x) = - x² + 2x + 9

To find (g-f)(10) substitute the value in the bracket that's 10 into ( g - f)(x)

That is

(g-f)(10) = -(10)² + 2(10) + 9

= - 100 + 20 + 9

= - 100 + 29

= - 71

Hope this helps you

7 0
3 years ago
Write and evaluate the expression. Then, complete the statements. Ten less than the quotient of thirty and a number Evaluate whe
Artyom0805 [142]

Answer:

expression:  (30/t) - 10

evaluation:  30/2 - 10 = 5

Step-by-step explanation:

8 0
3 years ago
Ella ran 3.6 kilometers. How many meters did she run?
Helga [31]

Answer:3600 Step-by-step explanation:

5 0
3 years ago
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The scale for a map to actual distance is 2 cm to 100 miles. The driving distance on the map between Los Angeles and Las Vegas i
pantera1 [17]

Answer:

225 miles

Step-by-step explanation:

We start by converting it into a fraction, then multiply by the quantity

\frac{100 miles}{2 cm} *4.5 cm =225 miles

3 0
3 years ago
Write the given expression in terms of x and y only.<br> sin(sin−1(x) + cos−1(y))
yan [13]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2308127

_______________


Write the expression below in terms of x and y only:

(I'm going to call it "E")

\mathsf{E=sin\!\left[sin^{-1}(x)+cos^{-1}(y)\right]\qquad\quad(i)}


Let

\begin{array}{lcl} \mathsf{\alpha=sin^{-1}(x)}&\qquad&\mathsf{then~-\,\dfrac{\pi}{2}\le \alpha\le \dfrac{\pi}{2}}\\\\\\ \mathsf{\beta=cos^{-1}(x)}&\qquad&\mathsf{then~0\le \beta\le \pi.} \end{array}


so the expression becomes

\mathsf{E=sin(\alpha+\beta)}\\\\ \mathsf{E=sin\,\alpha\,cos\,\beta+sin\,\beta\,cos\,\alpha\qquad\quad(ii)}


•   Finding \mathsf{sin\,\alpha:}

\mathsf{sin\,\alpha=sin\!\left[sin^{-1}(x)\right]}\\\\ \mathsf{sin\,\alpha=x\qquad\quad\checkmark}


•   Finding \mathsf{cos\,\alpha:}

\mathsf{sin^2\,\alpha=x^2}\\\\ \mathsf{1-cos^2\,\alpha=x^2}\\\\ \mathsf{cos^2\,\alpha=1-x^2}\\\\ \mathsf{cos\,\alpha=\sqrt{1-x^2}\qquad\quad\checkmark}


because \mathsf{cos\,\alpha} is positive for \mathsf{\alpha\in \left[-\frac{\pi}{2},\,\frac{\pi}{2}\right].}


•   Finding \mathsf{cos\,\beta:}

\mathsf{cos\,\beta=cos\!\left[cos^{-1}(y)\right]}\\\\ \mathsf{cos\,\beta=y\qquad\quad\checkmark}


•   Finding \mathsf{sin\,\beta:}

\mathsf{cos^2\,\alpha=y^2}\\\\&#10; \mathsf{1-sin^2\,\beta=y^2}\\\\ \mathsf{sin^2\,\beta=1-y^2}\\\\ &#10;\mathsf{sin\,\beta=\sqrt{1-y^2}\qquad\quad\checkmark}


because \mathsf{sin\,\beta} is positive for \mathsf{\beta\in [0,\,\pi].}


Finally, you get

\mathsf{E=x\cdot y +\sqrt{1-y^2}\cdot \sqrt{1-x^2}}\\\\\\ \therefore~~\mathsf{sin\!\left[sin^{-1}(x)+cos^{-1}(y)\right]=x\cdot y +\sqrt{1-y^2}\cdot \sqrt{1-x^2}\qquad\quad\checkmark}


I hope this helps. =)


Tags:   <em>inverse trigonometric trig function sine cosine sin cos arcsin arccos sum angles trigonometry</em>

6 0
3 years ago
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