Can you use mechanical pencils on the PSAT?

The ball hits the ground at 0 seconds or 2.5 seconds.

h represents the height of the golf ball after x seconds. The height is given by:

h(x)=-4.8x(x-2.5)

h(x) = -4.8x² + 12x

The time taken for the ball to reach the ground is at h(x) = 0, hence:

0 = -4.8x² + 12x

4.8x² - 12x = 0

x(4.8x - 12) = 0

hence x = 0; or 4.8x - 12 = 0

x = 0; or x = 2.5

Therefore the ball hits the ground at 0 seconds or 2.5 seconds.

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Answer:

X=-2.4

Step-by-step explanation:

3x+4=8x+16

-5x+4=16

-5x=12

x=-2.4

$224

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Answer:

y= -2x+1

Step-by-step explanation:

y=mx+b

y= -2x +b

3= -2(1) +b

3= -2 +b

b=1

y= -2x+1

Answer:

In two right-angled triangles,If the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are said to be congruent.

Step-by-step explanation:

Thank you!!!!

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Explanation:

The RHS congruence theorem states that, if the hypotenuse and side of one right triangle are equal to the hypotenuse and the corresponding side of another right triangle, the two triangles are congruent.

This is also known as the HL (hypotenuse-leg) congruence theorem for right triangles.

__

The four theorems generally available for showing congruence of triangles are abbreviated ...

  SSS, ASA, SAS, AAS . . . . A=angle, S=side; order is important

These list the sides/angles that must be identified as corresponding congruent parts.

Notable for its absence from this list is an SSA theorem. The reason is that SSA congruence can only be shown under the specific circumstance that the angle is opposite the longest of the two sides. That can only be guaranteed if the angle is a right angle or obtuse angle.

If the triangle is a right triangle, and the hypotenuse (longest side) is one of the two corresponding sides involved in the congruence statement, then the conditions required for RHS, or SSA, or HL congruence are established.

_____

Additional comment

In general, a triangle can be "solved" (all sides and angles determined) if at least one side and any two of the remaining angles or sides are specified. That is, the triangle will be uniquely specified.

The exception is described above, where two sides and an angle are given, but the side opposite the angle is the shorter of the two. In that case, if the triangle is not a right triangle, there are always two possible solutions. This is why, in general, congruence cannot be shown between two triangles with the same SSA specification.

Answer:

if

A= 3

B= 4

C= 2

so

A x B - C

iis

3 x 4 - 2

=12 - 2

=10 ✓

Answer:

if

A= 3

B= 4

C= 2

so

A x B - C

iis

3 x 4 - 2

=12 - 2

=10 ✓

Problem 1

I'm assuming your teacher means "list all the possible rational roots".

If so, then we use the rational root theorem. This is the idea where we'll divide the factors of the last term over the factors of the first coefficient.

If we divide said factors in the order mentioned, then we get this list of possible positive rational roots:

1/1, 1/3, 5/1, 5/3

That list simplifies to

1, 1/3, 5, 5/3

That takes care of the positive possible rational roots. We double the list to incorporate the negative possible rational roots as well

-1, -1/3, -5, -5/3

Note: We can rewrite that list in bold into [tex]\pm 1, \pm\frac{1}{3}, \pm 5, \pm \frac{5}{3}[/tex] to shorten it.

============================================================

Problem 2

We'll follow the same idea as the previous problem

Factors of 36:  1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 4:  1, 2, 4

To keep track of everything, I made a spreadsheet table. Refer to the diagram below. The factors of 36 are laid across the top while the factors of 4 are along the left side. Each inner cell represents dividing the headers.

For example, 36/4 = 9 is in the bottom right corner. The first table is before the fractions are reduced, and the second table after the fractions are reduced.

As the second table shows, we have a few repeats. The unique items here are:

1,2,3,4,6,9,12,18,36,1/2,3/2,9/2,1/4,3/4,9/4

We'll then mirror this set to include negative values as well to write the full list of all possible rational roots.

============================================================

Problem 3

Divide the factors of 15 over the factors of 5 to get

1/1, 1/5, 3/1, 3/5, 5/1, 5/5, 15/1, 15/5

That list reduces to

1, 1/5, 3, 3/5, 5, 1, 15, 3

we can then toss out the duplicates to get

1, 3, 5, 15, 1/5, 3/5

Don't forget to include the negative values as well

============================================================

Problem 4

The steps will be effectively the same as before. You can write out the factors like done in problem 3, or make a table like done in problem 2. I'll skip the steps shown here unless you need me to go over them.

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Problem 5

There's not really much new here, except for the fact that the first term has coefficient of 1. This is a special case where all we have to do is list the factors of the last term -40 to generate all the roots we need. This is because each time we're dividing over +1 or -1 which doesn't really change the overall result (except for the sign part).

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

Don't forget the negative values as well

Answer:

f(x)=-6*(x+1)^2+-7

Step-by-step explanation:

This is because the vertex is at (-1|-7)

f(x)=-6*x^2+-12*x+-13

f(x)=-6*(x^2+2*x+13/6) ( Factor out )

f(x)=-6*(x^2+2*x+(1)^2+-1*(1)^2+13/6) ( Complete the square )

f(x)=-6*((x+1)^2+-1*(1)^2+13/6) ( Use the binomial formula )

f(x)=-6*((x+1)^2+1*7/6) ( simplify )

f(x)=-6*(x+1)^2+-7 ( expand )

Hope this Helps

Answer:

Step-by-step explanation:

Is there a question to it?

Answer:

Step-by-step explanation:

For obects already in motion, the distance travelled, s, is:

s = vi*t + (1/2)at^2

where vi is the initial velocity, a is the acceleration, and t is the time in seconds.

We want the time, t, to reach 1000 meters.

1000 m = (3 m/s)*t + (1/2)*(0.1m/s^2)*(t^2)

(1/2)*(0.1m/s^2)*(t^2) = 0.05t^2

0.05t^2 + 3t -1000 = 0

Solve quadratic equation:

t = 114.6 seconds

Answer:

-8

Step-by-step explanation:

I’ll substitute x for the blank space:

-2 = x + 6

-2 - 6 = x

x = -8

-8 + 6 = -2 ✅

Answer:

Step-by-step explanation:

The lowest common denominator of 10 and 6 is 30.

9/10 = 3*9/10*9 = 27/30

1/6 = 5/1/(6 * 5) = 5/30

6 27/30 - 5/30 = 6 22/30 = 6 11/15

Answer 6 11/15

41

Step-by-step explanation:

3(8)+11+6=24+17=41

Answer:

b) m = 1/2

c) m = 3

d) m = 1/3

Step-by-step explanation:

b) rise = 1, run = 2; m = rise/run, so m = 1/2

c) rise = 3, run = 1; m = rise/run, so m = 3

d) rise = 1, run = 3; m = rise/run, so m = 1/3

Answer:

√10−√14+√15−√21

Step-by-step explanation:

Answer:

√10−√14+√15−√21

Step-by-step explanation:

Correct on Edge 2022

Answer:

(0,4) and (5,-3)

Step-by-step explanation:

Answer:

Step-by-step explanation: -3(m-2)=-9

                                           -3m + 6 = -9

                                           -3m = -15

                                                 m=5

Answer:

[tex]m=5[/tex]

Step-by-step explanation:

[tex]-3(m-2)=-9~(Given)\\\\-3m+6=-9~(Distributive~Property)\\\\-3m+6-6=-9-6~(Addition~Property~of~Equality)\\\\-3m=-15~(Simplify)\\\\\frac{-3m}{-3}=\frac{-15}{-3}~(Division~Property~of~Equality)\\\\m=5~(Simplify)[/tex]

Answer:

coordinate is 3rd or -;- coordinates

Answer:

15*4=60;60*3.5=210

Step-by-step explanation:

60 is the number of baskets Lucy makes in an hour,210 is her 3.5 hours of baskets

Answer:

answer is 1/4 × 3 1/2 =

3 1/8

Answer:

Rational

Step-by-step explanation:

Its rational because it has the same numbers/pattern

You can find the answer in the image above.

Answer:

Michael's daily income is $96

Step-by-step explanation:

Given

john's income=$120

by question

John's income is 20%more than Micheal's

so,. Micheal's income= John's income - 20%of John's income

=$120 - 20%of $120

=$120 -20/100*$120

=$120 - $24

=$96

Answer:

100

Step-by-step explanation:

[tex]x + \frac{20x}{100} = 120 \\ x + \frac{x}{5} = 120 \\ 5x + x = 600 \\ 6x = 600 \\ x = 100[/tex]

Answer:

12 * 1.07 = 12.84

Step-by-step explanation:

You an can pick any number to express another number in this example we find  0.84 = 7% and 12 = 1 as 12 represents 1 whole.

Answer:

K=3r-s

K+s=3r

K/3+s/3=r

Step-by-step explanation:

k=3r-s

k+s=3r

k+s/3 = r

r = k+s/3

Answer:

The third one

Step-by-step explanation:

y=>x+1

y=<x-1

removing y

x-1 => x+1

removing x

we have no solution

Answer:

x²(x - y)

Step-by-step explanation:

x³ - x²y ( x² is common to both terms so factor it out )

= x²(x - y)

Step-by-step explanation:

using set notation

domain [-3,3]

range[-1,3]

Answer:

EF ║ CD and AB ║ CD are the parallel segments.

Step-by-step explanation:

The given question is incomplete without picture; here is the picture attached with the answer.

Since m∠A = m∠D = 42°

Therefore, AB ║ CD and segment AD is the transverse.

Now ∠AEF + ∠IEF = 180° [Supplementary angles]

138° + ∠IEF = 180°

∠IEF = 180 - 138

       = 42°

∠IHG + ∠DHG = 180° [ Supplementary angles ]

∠IHG + 122 = 180

∠IHG = 180 - 122

∠IHG = 58°

But ∠IEF ≠ ∠IHG

Therefore, EF and GH are not parallel.

If the segments AB and GH are parallel then ∠IHG = ∠IAB (By the property of alternate angles)

But ∠IHG ≠ ∠IAB

Therefore, AB and GH are not parallel.

Now ∠IEF ≅ ∠IDC ≅ 42° [alternate angles]

which reveals that EF ║ CD

Therefore, EF ║ CD and AB ║ CD