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3 years ago

Solve for x. −12x+13>35 Drag and drop a number or symbol into each box to correctly complete the solution.

Mathematics

1 answer:

Katen [24]3 years ago

7 0

Answer:

x < -11/6.

Step-by-step explanation:

−12x + 13 > 35

-12x > 35 - 13

-12x > 22

Divide both sides by -12 and invert the inequality sign:

x < -22/12

x < -11/6.

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In parallelogram ABCD, base AD is 15 and side AB is 8. What are the height and area of paralelogram ABCD if mDAB is 20?

Goshia [24]

Step-by-step explanation:

✰ $\underline{ \underline{ \large{ \tt{G\: I \: V \: E \: N}}}} :$

AD = 15 , AB = 8 , $\angle$ DAB

✰ $\underline{ \underline{ \large{ \tt{T \: O \: \: F\: I \: N \: D}}}} :$

Height & Area of the given parallelogram

✰ $\underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T\: I\: O \: N}}}} :$

In right angled triangle ABE :

Hypotenuse ( h ) = 8
Perpendicular ( p ) = h [ height ]
$\theta$ = 20°

Now , Using trigonometric ratio :

$\large{ \tt{Sin \theta \: = \: \frac{Perpendicular}{Hypotenuse} }}$

Plug the known values :

⟶ $\large{ \tt{ Sin(20) = \frac{h}{8} }}$

⟶ $\large{ \tt{0.34 = \frac{h}{8}}}$

⟶ $\large{ \tt{h = 0.34 \times 8}}$

⟶ $\large{ \tt{h = 2.72}}$

Now , We have :

Base ( b ) = 15
Height ( h ) = 2.72

Finding the area of a parallelogram whose base and height are 15 and 2.72 respectively :

❀ $\underline{ \underline{ \text{Area \: of \: parallelogram = \tt{b *\: h}}}}$

⟶ $\large{ \tt{A = 15 *2.72}}$

⟶ $\large{ \tt{A = 40.8 \: {units}^{2} }}$

Hence , Our final answer :

$\large{ \boxed{ \sf{Height \: ( \: h \: ) = 2.72 \: units}}}$

$\large{ \boxed{ \sf{Area \: of \: parallelogram \: ( \:A \: ) = \: 40.8 \: {units}^{2} }}}$

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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3 years ago

Number 10Please just show the math and not the sentence explanations, I just want to use this problem as an example :)

Morgarella [4.7K]

Explanation

We are given the following right-angled triangle:

We are required to determine the indicated angle in the given figure.

This is achieved thus:

According to the image, we have:

$\begin{gathered} Opposite=9 \\ Adjacent=21 \end{gathered}$

Therefore, we have:

$\begin{gathered} \tan\theta=\frac{opposite}{adjacent} \\ \tan\theta=\frac{9}{21} \\ \theta=\tan^{-1}(\frac{9}{21}) \\ \theta\approx23\degree \end{gathered}$

Hence, the answer is:

$23\degree$

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1 year ago

Put the linear inequality into slope-intercept form.

Ugo [173]

Answer:

y ≤ $\frac{7}{4}x - 5$

Step-by-step explanation:

We are to put the linear inequality;

7x - 4y ≥ 20

in slope intercept form.

We can rearrange the inequality as;

-4y ≥ - 7x + 20

Dividing throughout by -4 we get;

y ≤ $\frac{7}{4} x$ - 5

Note that the inequality sign '≥' changes to '≤' since we divided all through with a negative number.

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3 years ago

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xxMikexx [17]

Answer:

3 h(x) = 4 sin(2x + π) + 3

Step-by-step explanation:

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3 years ago

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A bag contains 4 red marbles, 16 yellow marbles, 5 purple marbles, 16 blue marbles, and 10 green marbles. What is the probabilit

Evgen [1.6K]

4 red marbles
16 yellow marbles
5 purple marbles
16 blue marbles
10 green marbles

Total marbles 51 marbles

16 blue marbles or 4 red marbles

(16+4)/51= 20/51

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3 years ago