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3 years ago

Simplify the product using the distributive property. (-4h +2)(3h +7)

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

3 0

Answer:

A. -12h² - 22h + 14

Step-by-step explanation:

(-4h +2)(3h +7) = -4h(3h +7) +2(3h +7) . . . . . . . (a +b)c = ac +bc

= (-4h)(3h) + (-4h)(7) + (2)(3h) + (2)(7) . . . . . . . a(b +c) = ab +ac . . . (twice)

= -12h² -28h +6h +14

= -12h² -22h +14 . . . . . . . . collect terms

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-2 (4x-9) = -18 ×=___

Dahasolnce [82]

Answer:

x = 9/2 or 4 1/2 or 4.5

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve. Hope this helped :)!

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2 years ago

P is inversely proportional to the cube of (q-2) p=6 when q=3 find the value of p when q is 5

sveticcg [70]

$\bf \begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
\\
&&y=\cfrac{{{ k}}}{x}
\end{array}\\\\
-----------------------------\\\\
\textit{p is inversely proportional to the cube of (q-2)}\implies p=\cfrac{k}{(q-2)^3}
\\\\\\
now \quad 
\begin{cases}
p=6\\
q=3
\end{cases}\implies 6=\cfrac{k}{(3-2)^3}$

solve for "k", to find k or the "constant of variation"

then plug k's value back to $\bf p=\cfrac{k}{(q-2)^3}$

now.... what is "p" when q = 5? well, just set "q" to 5 on the right-hand-side, and simplify, to see what "p" is

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2 years ago

A restaurant is offering a dinner special that includes one starter and one entree. The choices are listed below. Starter: bread

artcher [175]

Answer:

There are 15 combinations.

Step-by-step explanation:

A restaurant is offering a dinner special that includes one starter and one entree.

Starter: bread-sticks, soup, salad

Entree: beef, fish, chicken, shrimp, pork

So, we have 3 starters and 5 entrees.

To know the possible dinner special combinations we will simply multiply the two.

$3\times5=15$

Therefore, there are 15 combinations.

8 0

2 years ago

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Two solid metal spheres have masses of 5 kg and 135 kg respectively. If the radius of the smaller one is 4 cm, find the radius o

Cerrena [4.2K]

Answer: 12 cm

Step-by-step explanation:

The masses of the spheres are proportional to their volums, and the cube of the ratio is k^3=135/5=27 ==> k=3

The greater radius is 3*4=12 (cm)

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2 years ago

Measure the lengths of the sides of ∆ABC in GeoGebra, and compute the sine and the cosine of ∠A and ∠B. Verify your calculations

marusya05 [52]

Answer:

$Sin \angle A =0.80$

$Cos \angle A=0.60$

$Sin \angle B =0.60$

$Cos \angle B=0.80$

Step-by-step explanation:

Given

I will answer this question using the attached triangle

Solving (a): Sine and Cosine A

In trigonometry:

$Sin \theta =\frac{Opposite}{Hypotenuse}$ and

$Cos \theta =\frac{Adjacent}{Hypotenuse}$

So:

$Sin \angle A =\frac{BC}{BA}$

Substitute values for BC and BA

$Sin \angle A =\frac{8cm}{10cm}$

$Sin \angle A =\frac{8}{10}$

$Sin \angle A =0.80$

$Cos \angle A=\frac{AC}{BA}$

Substitute values for AC and BA

$Cos \angle A=\frac{6cm}{10cm}$

$Cos \angle A=\frac{6}{10}$

$Cos \angle A=0.60$

Solving (b): Sine and Cosine B

In trigonometry:

$Sin \theta =\frac{Opposite}{Hypotenuse}$ and

$Cos \theta =\frac{Adjacent}{Hypotenuse}$

So:

$Sin \angle B =\frac{AC}{BA}$

Substitute values for AC and BA

$Sin \angle B =\frac{6cm}{10cm}$

$Sin \angle B =\frac{6}{10}$

$Sin \angle B =0.60$

$Cos \angle B=\frac{BC}{BA}$

Substitute values for BC and BA

$Cos \angle B=\frac{8cm}{10cm}$

$Cos \angle B=\frac{8}{10}$

$Cos \angle B=0.80$

Using a calculator:

$A = 53^{\circ}$

So:

$Sin(53^{\circ}) =0.7986$

$Sin(53^{\circ}) =0.80$ -- approximated

$Cos(53^{\circ}) = 0.6018$

$Cos(53^{\circ}) = 0.60$ -- approximated

$B = 37^{\circ}$

So:

$Sin(37^{\circ}) = 0.6018$

$Sin(37^{\circ}) = 0.60$ --- approximated

$Cos(37^{\circ}) = 0.7986$

$Cos(37^{\circ}) = 0.80$ --- approximated

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2 years ago

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