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2 years ago

Which number line best represents the solution to the inequality 7x ≤ 49 ?

Mathematics

2 answers:

user100 [1]2 years ago

6 0

Answer:

Step-by-step explanation:

im not 100 % sure hope i am correct

Oliga [24]2 years ago

5 0

Step-by-step explanation:

uedhhhjdjdhdhdddjjdhvdhddbdbddbb

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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.60 and the co

erik [133]

<h2>Explanations:</h2>

From the given question, we have the following parameters

Cost of a small greeting card = $1.60

The cost of a large greeting card = $4.05.

Cost of 5 small greeting cards = 5(1.60)

Cost of 5 small greeting cards = $8.00

Cost of 4 large greeting cards = 4(4.05)

Cost of 4 large greeting cards = $16.2

Cost of 5 small and 4 large = $8.00 + $16.2

Cost of 5 small and 4 large $24.2

Hence it would cost $24.2 to get 5 small greeting cards and 4 large greeting cards

Similarly;

Cost of x small greeting cards = 1.60x

Cost of y large greeting cards = 4.05y

Cost of small greeting cards and y large greeting cards = 1.60x + 4.05y

Hence it would cost $(1.60x + 4.05y) to get x small greeting cards and y large greeting cards

5 0

1 year ago

Find the equation of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit.

leonid [27]

<u>Answer-</u>

The equations of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit are

$12x-5y+14=0 \\ 12x-5y-14=0$

<u>Solution-</u>

Let a point which is 1 unit away from the line 12x-5y-1=0 is (h, k)

The applying the distance formula,

$\Rightarrow \left | \frac{12h-5k-1}{\sqrt{12^2+5^2}} \right |=1$

$\Rightarrow \left | \frac{12h-5k-1}{\sqrt{169}} \right |=1$

$\Rightarrow \left | \frac{12h-5k-1}{13} \right |=1$

$\Rightarrow 12h-5k-1=\pm 13$

$\Rightarrow 12h-5k=\pm 14$

$\Rightarrow 12h-5k=14,\ 12h-5k=-14$

$\Rightarrow 12h-5k-14=0,\ 12h-5k+14=0$

$\Rightarrow 12x-5y-14=0,\ 12x-5y+14=0$

Two equations are formed because one will be upper from the the given line and other will be below it.

4 0

2 years ago

Round 9.58507409207 to the nearest whole number

Sholpan [36]

The answer would be 10

8 0

3 years ago

Read 2 more answers

Where should the point P be chosen on line segment AB so as to maximize the angle θ? (Assume a = 4 units, b = 5 units, and c = 9

taurus [48]

From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.

Using pythagoras theorem,
$\tan M= \frac{a}{b-x} \\ \\ M=\tan^{-1}\left(\frac{a}{b-x}\right)$
and
$\tan N= \frac{c}{x} \\ \\ N=\tan^{-1}\left(\frac{c}{x}\right)$

Angle θ is given by
$\theta=180-M-N \\ \\ =180-\tan^{-1}\left(\frac{a}{b-x}\right)-\tan^{-1}\left(\frac{c}{x}\right)$

Given that a = 4 units, b = 5 units, and c = 9 units, thus
$\theta=180-\tan^{-1}\left(\frac{4}{5-x}\right)-\tan^{-1}\left(\frac{9}{x}\right)$

To maximixe angle θ, the differentiation of <span>θ with respect to x must be equal to zero.
i.e.
$\frac{d\theta}{dx} = -\frac{4}{x^2-10x+41} + \frac{9}{x^2+81} =0 \\ \\ -4(x^2+81)+9(x^2-10x+41)=0 \\ \\ -4x^2-324+9x^2-90x+369=0 \\ \\ 5x^2-90x+45=0 \\ \\ x^2-18x+9=0 \\ \\ x=9\pm6 \sqrt{2}$

Given that x is a point on line segment AB, this means that x is a positive number less than 5.

Thus
$x=9-6 \sqrt{2}=0.5147$

Therefore, The distance from A of point P, so that </span>angle θ is maximum is 0.51 to two decimal places.

6 0

3 years ago

Miss Cowboys classroom has 6 rolls of desk each row has 4 desk explain how to use skip counting to find how many deaths there ar

andrew-mc [135]

Answer:

Simply count 4 × 6 =28

Step-by-step explanation:

7 0

3 years ago