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Komok [63]
3 years ago
15

The product of 15 and the sum of a number and 5 is 90.

Mathematics
1 answer:
finlep [7]3 years ago
6 0
Fifteen times six is ninty so if we add one in five we get fifteen times six which gives the product ninty

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Quadrilateral EFGH has coordinates E(2a, 2a), F(3a, a), G(2a, 0), and H(0, 0). Find the midpoint of he
Gre4nikov [31]
The formula of the midpoint of HE:
\left(\dfrac{x_H+x_E}{2};\ \dfrac{y_H+y_E}{2}\right)

We have H(0; 0) and E(2a; 2a). Substitute:
\left(\dfrac{0+2a}{2};\ \dfrac{0+2a}{2}\right)=(a;\ a)

4 0
3 years ago
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In the base-ten number system, ten digits {0, 1, 2, 3, 4, 5, 7, 8, 9) are used for number
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6 0
2 years ago
A high school drama club is putting on their annual theater production. There is a maximum of 800 tickets for the show. The cost
astra-53 [7]
<span>a.) Let x be the number of tickets sold before the event and y the number of tickets sold on the day of the event. Then x + y =< 800 and 6x + 9y >= 5000. (b.) Suppose the club sold 440 tickets before the event, i.e. x = 440, maximum number of tickets remaining to be sold = 800 - 440 = 360. Maximum amount realized from the sales supposing all tickets were sold = 6(440) + 9(360) = 2640 + 3240 = $5880 which is greater than $5000. Therefore, it is possible for the club to sell enough additional tickets on the day of the show to meet the expenses of the show.</span>
3 0
2 years ago
Chord AC intersects chord BD at point P in circle Z.
Sliva [168]
1. To solve this exercise, you must use the "Intersecting chords theorem".

2. You have that:

AP=3.5 in
PC=6 in
DP=4 in

3. Then, by applying the "Intersecting chord theorem", you have:

(AP)(PC)=(BP)(DP)

4. When you substitute the values into (AP)(PC)=(BP)(DP), you obtain:

(3.5 in)(6 in)/BP(4 in)

5. Now, you must clear BP. Then:

(3.5 in)(6 in)/4 in=BP
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BP=5.25 in
7 0
3 years ago
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A camera is mounted at a point 4000 feet away from a geyser. If the water is rising vertically at 900 ft/s when it is 3000 feet
Leno4ka [110]

Answer:

\dot \theta = 0.144\,\frac{rad}{s}, \dot \theta = 8.251\,\frac{deg}{s} (Option B)

Step-by-step explanation:

The trigonometric diagram is included herein as attachment. The expression is presented below:

\tan \theta = \frac{y}{x}

Where:

x - Horizontal distance between the geyser and the camera.

y - Vertical distance between the geyser and the camera.

The rate of change in terms of time is:

\dot \theta \cdot \sec^{2}\theta = \frac{\dot y\cdot x-y\cdot \dot x}{x^{2}}

\dot \theta  \cdot \left(\frac{1}{\cos^{2}\theta} \right) = \frac{\dot y \cdot x - y\cdot \dot x}{x^{2}}

\dot \theta = \left(\frac{\dot y \cdot x - y \cdot \dot x}{x^{2}} \right)\cdot \cos^{2}\theta

\dot \theta = \left(\frac{\dot y \cdot x - y\cdot \dot x}{x^{2}} \right)\cdot \left(\frac{x^{2}}{x^{2}+y^{2}} \right)

\dot \theta = \frac{\dot y \cdot x - y\cdot \dot x}{x^{2}+y^{2}}

Finally,

\dot \theta = \frac{\left(900\,\frac{ft}{s} \right)\cdot (4000\,ft)-(3000\,ft)\cdot \left(0\,\frac{ft}{s} \right)}{(4000\,ft)^{2}+(3000\,ft)^{2}}

\dot \theta = 0.144\,\frac{rad}{s}

\dot \theta = 8.251\,\frac{deg}{s}

3 0
2 years ago
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