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Vika [28.1K]
3 years ago
13

Which statements must be true?

Mathematics
1 answer:
slamgirl [31]3 years ago
7 0

Answer:

The options 2,3 and 5 are correct.

Step-by-step explanation:

From the figure it is noticed that the points U,V and W are midpoint of JK,KL and JL respectively.

Midpoints theorem of triangle states that the line connecting the midpoints of two sides is parallel to third side and its length is half of the third side.

The points U and W are midpoint of JK and JL. Using midpoint theorem, we get

UW=\frac{1}{2}KL

UW\parallel KL

The points U and V are midpoint of JK and KL. Using midpoint theorem, we get

UV=\frac{1}{2}JL

UV\parallel JL

The points V and W are midpoint of KL and JL. Using midpoint theorem, we get

VW=\frac{1}{2}JK

2VW=JK

VW\parallel JK

Therefore options 2, 3 and 5 are correct.

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Use the formula h(t)=−16t2+v0t+h0 , where v0 is the initial velocity and h0 is the initial height. How long will it take for the
Rama09 [41]

<em><u>Question:</u></em>

Britney throws an object straight up into the air with an initial velocity of 27 ft/s from a platform that is 10 ft above the ground. Use the formula h(t)=−16t2+v0t+h0 , where v0 is the initial velocity and h0 is the initial height. How long will it take for the object to hit the ground?

1s   2s   3s   4s

<em><u>Answer:</u></em>

It takes 2 seconds for object to hit the ground

<em><u>Solution:</u></em>

<em><u>The given equation is:</u></em>

h(t) = -16t^2 + v_0t+h_0

Initial velocity = 27 feet/sec

h_0 = 10\ feet

Therefore,

h(t) = -16t^2 +27t+10

At the point the object hits the ground, h(t) = 0

-16t^2 +27t+10 = 0\\\\16t^2-27t-10=0

Solve by quadratic formula,

\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=16,\:b=-27,\:c=-10:\quad \\\\t=\frac{-\left(-27\right)\pm \sqrt{\left(-27\right)^2-4\cdot \:16\left(-10\right)}}{2\cdot \:16}\\\\t = \frac{27 \pm \sqrt{1369}}{32}\\\\t = \frac{27 \pm 37}{32}\\\\We\ have\ two\ solutions\\\\t = \frac{27+37}{32}\\\\t = \frac{64}{32}\\\\t = 2\\\\And\\\\t = \frac{27-37}{32}\\\\t = -0.3125

Ignore, negative value

Thus, it takes 2 seconds for object to hit the ground

7 0
3 years ago
Recent studies indicate that the average surface temperature of the
andreev551 [17]

Answer:

Slope : The rate of increase of temperature on the earth's surface is 0.02°C per year since 1900.

T-intercept : 8.5 represents the temperature in °C of the earth's surface in the year 1900.

Step-by-step explanation:

The average surface temperature of Earth rising steadily. Scientists have modeled the temperature by the equation, T = 0.02t + 8.50 where t represents years since 1900 and T is the temperature in ◦C.

Now, the slope of the model equation is 0.02 which means the rate of increase of temperature on the earth's surface is 0.02°C per year since 1900.

Again, the T-intercept i.e. 8.5 represents the temperature in °C of the earth's surface in the year 1900. (Answer)

7 0
3 years ago
I need help with this practice problem
Norma-Jean [14]

Answer:

Step-by-step explanation:

V of a sphere is (4/3)*pi*r³, and because we have 3 scoops

V = 3* (4/3) * 3.14 * 4³ = 4* 3.14 * 4³ = 803.84 cm³

3 0
3 years ago
I need help! I don't understand!
Tcecarenko [31]
Lawd i’m confused too
4 0
3 years ago
What goes where. JdhshshHshxjancixd
valentina_108 [34]

Answer:

\boxed { \frac{7}{5}y } \to \: \boxed {y+ \frac{2}{5}y }

\boxed { \frac{3}{5}y } \to \: \boxed {y -  \frac{2}{5}y }

Step-by-step explanation:

We need to simplify

y +  \frac{2}{5}y

We collect LCM to get;

\frac{5y + 2y}{5}  =  \frac{7y}{5}

Therefore:

\boxed { \frac{7}{5}y } \to \: \boxed {y+ \frac{2}{5}y }

Also we need to simplify:

y -  \frac{2}{5}y

We collect LCM to get;

y -  \frac{2}{5}y =  \frac{5y - 2y}{5}  =  \frac{3}{5} y

Therefore

\boxed { \frac{3}{5}y } \to \: \boxed {y -  \frac{2}{5}y }

5 0
3 years ago
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