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sweet-ann [11.9K]

3 years ago

7

Formulate Alisha has a number in mind. If she adds three to her number the result is less than five. Use this information to wri

te and solve an inequality about Alisha's number. Then graph the solution set.

1 answer:

inessss [21]3 years ago

3 0

The inequality would be x (Alisha’s number)+ 3 > 5. The set can be graphed open circle on 5 with a line going down all the way through negatives.

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At homecoming, 125 tickets where sold. Tickets purchased for homecoming cost $20.5 without an activity card, and $15.75 with an

ale4655 [162]

Answer:

Nearly 83 students did not had activity card.

Nearly 42 students had an activity card.

Step-by-step explanation:

Total number of tickets sold at homecoming = 125

Cost of each ticket without activity card = $20.5

Cost of each ticket with activity card = $15.75

Total amount earned = $2365

Let, the number of tickets sold without activity car d = k

So, the number of tickets sold without card = (Total sold - k)

= 125 - k

Now, according to the question:

$20.5(k) + $15.75(125 - k) = $2365

or, 20.5 k + 1968.5 - 15.75 k = 2365

⇒ 4.75 k = 2365 - 1968.5 = 396.5

⇒ $k = \frac{396.5}{4.75 } = 83.47$

Hence, nearly 83 students did not had activity card.

So,the number of students that had activity card = 125 - 83.47 = 41.53 ~ 42

Hence, nearly 42 students had an activity card.

4 0

2 years ago

RS has a midpoint at M(7, 10). Point R is at (8, 10). Find the coordinates of point s.

Elena L [17]

Answer:

S(6, 10)

Step-by-step explanation:

1. The Midpoint (in this case, M) will always be halfway between both R and S (or other characters in some cases).

2. As M is only one X value away from R, it is only 1 X value from S as well, but in the other direction.

3. (7, 10) - (1, 0) = (6, 10)

The (7, 10) is the Midpoint Coordinates.

The (1, 0) is the distance from M to R.

The (6, 10) is the coordinates of S.

5 0

3 years ago

If (x+2) is a factor of x^3-6x^2+kx+10, k=

Alja [10]

If a binomial $(x-a)$ is a factor of a polynomial, then $a$ is a root of this polynomial.

$(x+2)=(x-(-2)) \Rightarrow a=-2\\\\
(-2)^3-6\cdot(-2)^2+k\cdot(-2)+10=0\\
-8-24-2k+10=0\\
-2k=22\\\
\boxed{k=-11}
$

3 0

2 years ago

Fine length of BC on the following photo.

MrMuchimi

Answer:

$BC=4\sqrt{5}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

$AC^2=320$

$AC=\sqrt{320}\ units$

simplify

$AC=8\sqrt{5}\ units$

step 2

In the right triangle ACD

Find the cosine of angle CAD

$cos(\angle CAD)=\frac{AD}{AC}$

substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

$cos(\angle CAD)=\frac{2}{\sqrt{5}}$ ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

so

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

$BC=4\sqrt{5}\ units$

7 0

2 years ago

Please help me with this

Alexxandr [17]

If the perimeter is 98 cm, the sum of the lengths of two adjacent sides is 49 cm.

... (2x -1) + (3x +5) = 49 . . . . use the given information and relation

... 5x +4 = 49 . . . . . . . . . . . simplify

... 5x = 45 . . . . . . . . . . . . . . . subtract 4

... x = 9 . . . . . . . . . . . . . . . . . divide by 5

The left side dimension is then

... 2x -1 = 2·9 -1 = 17 . . . . cm

The top dimension is

... 3x +5 = 3·9 +5 = 32 . . . . cm

The rectangle is 17 cm by 32 cm.

5 0

2 years ago