True ot false? K = 3 over 5 is a solution to the inequality 15k + 3

zloy xaker [14]

X= # of miles
.55x+1.75 is greater than or equal to 10

So if she has to go more than 2 miles we will put 2 in for X

.55(2)+1.75 is greater than or equal to 10
.55×2= 1.10+1.75= 2.85
2.85 is greater than 10 is false so now we know she has to go more than 2 miles.

Let's guess and check. Now let's say 15 miles
.55×15= 8.25+1.75= 10
10=10 So she needs to drive at least 15 miles

x is greater than or equal to 15

Please don't solely rely on my answer I don't know if it's correct

3 0

3 years ago

To find how high school students feel about hot lunches, Adam walks to the nearest high When a=6 and b=22, c=33. If c varies dir

Delvig [45]

Answer:The equation that models the solution will be

33 = 22k / 6

Step-by-step explanation:

The two types of variation involved in this problem are direct variation and inverse variation.

In direct variation, when one item changes in the positive or negative direction, the other item also changes in the positive or negative direction.

In inverse variation, when one item changes in the positive or negative direction, the other item also changes in the negative or positive direction.

From the information given,

c varies directly with b

If we introduce a direct proportionality constant, k, then,

c = kb

c also varies inversely with a

If we introduce an inverse proportionality constant, k, then,

c = k/b

Therefore, c = kb / a

When a=6 , b=22 and c=33.

The equation that models the solution will be

33 = 22k / 6

8 0

3 years ago

Li transformed rectangle ABCD. The image is shown. Does Li’s transformation represent a translation? Yes, the image represents a

iris [78.8K]

Answer:

C. No, the image does not have the same orientation.

Step-by-step explanation:

Just took the quiz.

6 0

3 years ago

Read 2 more answers

Ryan has 3/4 of tank of gas in his car. it takes 1/6 of a tank of gas to drive to socccer practice and back home. with the gas i

marishachu [46]

I don’t know if this is correct but about 4 times because

3/4 -> 18/24 and 1/6 -> 4/24

7 0

3 years ago

1. Consider the right triangle ABC given below.

lbvjy [14]

#1)
A) b = 10.57
B) a = 22.66; the different methods are shown below.
#2)
A) Let a = the side opposite the 15° angle; a = 1.35.
Let B = the angle opposite the side marked 4; m∠B = 50.07°.
Let C = the angle opposite the side marked 3; m∠C = 114.93°.
B) b = 10.77
m∠A = 83°
a = 15.11

Explanation
#1)
A) We know that the sine ratio is opposite/hypotenuse. The side opposite the 25° angle is b, and the hypotenuse is 25:
sin 25 = b/25

Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b

B) The first way we can find a is using the Pythagorean theorem. In Part A above, we found the length of b, the other leg of the triangle, and we know the measure of the hypotenuse:
a²+(10.57)² = 25²
a²+111.7249 = 625

Subtract 111.7249 from both sides:
a²+111.7249 - 111.7249 = 625 - 111.7249
a² = 513.2751

Take the square root of both sides:
√a² = √513.2751
a = 22.66

The second way is using the cosine ratio, adjacent/hypotenuse. Side a is adjacent to the 25° angle, and the hypotenuse is 25:
cos 25 = a/25

Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a

The third way is using the other angle. First, find the measure of angle A by subtracting the other two angles from 180:
m∠A = 180-(90+25) = 180-115 = 65°

Side a is opposite ∠A; opposite/hypotenuse is the sine ratio:
a/25 = sin 65

Multiply both sides by 25:
(a/25)*25 = 25*sin 65
a = 25*sin 65
a = 22.66

#2)
A) Let side a be the one across from the 15° angle. This would make the 15° angle ∠A. We will define b as the side marked 4 and c as the side marked 3. We will use the law of cosines:
a² = b²+c²-2bc cos A
a² = 4²+3²-2(4)(3)cos 15
a² = 16+9-24cos 15
a² = 25-24cos 15
a² = 1.82

Take the square root of both sides:
√a² = √1.82
a = 1.35

Use the law of sines to find m∠B:
sin A/a = sin B/b
sin 15/1.35 = sin B/4

Cross multiply:
4*sin 15 = 1.35*sin B

Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin B)/1.35
(4*sin 15)/1.35 = sin B

Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin B)
50.07 = B

Subtract both known angles from 180 to find m∠C:
180-(15+50.07) = 180-65.07 = 114.93°

B) Use the law of sines to find side b:
sin C/c = sin B/b
sin 52/12 = sin 45/b

Cross multiply:
b*sin 52 = 12*sin 45

Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77

Find m∠A by subtracting both known angles from 180:
180-(52+45) = 180-97 = 83°

Use the law of sines to find side a:
sin C/c = sin A/a
sin 52/12 = sin 83/a

Cross multiply:
a*sin 52 = 12*sin 83

Divide both sides by sin 52:
(a*sin 52)/(sin 52) = (12*sin 83)/(sin 52)
a = 15.11

3 0

2 years ago

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True ot false? K = 3 over 5 is a solution to the inequality 15k + 3 < 15.