Gloria pays her insurance in three installments each year. The first payment is 40% of the annual premium, and each of the next two payments is 30% of annual premium. If the annual premium is $924. Find the amounts of the three payments

Answer:

The slope is 1/2

Step-by-step explanation:

Slope Formula: m = y2 – y1

                                  x2 – x1

(-3 , -2) (5 , 2)

m = 2 – (-2) = 4 = 1

      5 – (-3) = 8 = 2

Answer:

24/30-5/30=19/30

this is the answer

Answer:

It's 24/30 and 5/30 and it's 19/30

Step-by-step explanation:

Given:

m || QR

To find:

The measure of ∠QPR.

Solution:

Since m || QR and a transversal line intersect them, therefore the alternate interior angles are equal.

Let points S and T lie on the line m. S is on the right and T is on the left side of point P.

[tex]m\angle RPS=m\angle PRQ[/tex]

[tex]m\angle RPS=45^\circ[/tex]

Now, angles TPQ, QPR and RPS lie on the one side of a straight line. It means, their sum is 180 degrees.

[tex]m\angle TPQ+m\angle QPR+m\angle RPS=180^\circ[/tex]

[tex]50^\circ+m\angle QPR+45^\circ=180^\circ[/tex]

[tex]m\angle QPR+95^\circ=180^\circ[/tex]

[tex]m\angle QPR=180^\circ-95^\circ[/tex]

[tex]m\angle QPR=85^\circ[/tex]

Therefore, the measure of angle QPR is 85 degrees.

Answer:

I think it is 10 km/hr

Step-by-step explanation:

5 hrs = 40 more with 2 km/hr current

2 hrs= less 40 no current

40-2x5=30

30 without current for three hours

30/3=10 km/hr no current

CHECK

10x2=20

10x5=50+2x5=60

The speed of the motorboat in still water is 10 km/hr

A motorboat travels downstream on a river for 5 hours.      

The speed of the current = 2 km/h

The river flows into a still lake and the motorboat continues for two more hours.

The distance covered by the boat on the river was 40 km more than the distance that was covered on the lake.

We have to determine the speed of the motorboat in still water

Let the speed of motorboat in still water = m km/h

Given that

The speed of river current = 2 km/hr

The river runs into a still lake

The motorboat continues to travel for 2  more hours

The distance traveled by the motorboat in two more hours in the lake  = 2m km

The distance covered by the boat in the river = (40 +2m)   km

Net speed of the boat in the river = (m +2 ) km/hr

Let t  be the time spent by motorboat into the river.

[tex]\rm Time = \dfrac{Distance}{Speed}[/tex]

[tex]\rm t = \dfrac{40+2m }{m +2}..........(1)[/tex]

Given that the motorboat travels downstream of the river for 5 hrs

so on putting t = 5 in equation (1).

[tex]\rm 5 = \dfrac{40 +2m }{m+2}\\\\5m +10 = 40 +2m\\5m -2m = 40-10\\3m = 30\\m = 10 km/h[/tex]

So the speed of the motorboat in still water is 10 km/hr

For more information please refer to the link given below

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Answer:

m∠ABG = 20 degrees

m∠BCA = 22 degrees

m∠BAC = 118 degrees

m∠BAG = 59 degrees

DG = 4

BE = 12.4

BG = 11.7

GC = 20.4

Step-by-step explanation:

The given parameters are;

m∠CBG = 20°, m∠BCG = 11°

The incenter of a triangle is the point where the three bisectors of ΔABC meets

m∠ABG = m∠CBG = 20° by definition of angle bisector

m∠ABG = 20°

m∠ACG = m∠BCG = 11° by definition of angle bisector

m∠BCA = m∠ACG + m∠BCG = 11° + 11° = 22°

m∠ABC = m∠ABG + m∠CBG = 20° + 20° = 40°

m∠BAC = 180° - (m∠BCA+m∠ABC) = 180° - (40° + 22°) = 118°

m∠BAG = m∠CAG by definition of angle bisector

m∠BAC = 118° = m∠BAG + m∠CAG = m∠BAG + m∠BAG = 2 × m∠BAG

2 × mBAG = 118°

m∠BAG = 118°/2 = 59°

m∠BAG = 59°

Given that "G" is the incenter of the triangle ABC, we have;

GF = GE = DG = The radius of the incircle of the triangle = 4

Therefore, by Pythagoras' theorem, we have;

BG = √(11² + 4²) = √137 ≈ 11.7

BE = √((BG)² + 4²) = √(137 + 4²) = √153 ≈ 12.4

GC = √(20² + 4²) = √416= 4·√26 ≈ 20.4

Applying the definition of the incenter of a triangle, the measures in triangle ABC where G is the incenter are:

Recall the following facts about the incenter of a triangle:

The incenter of a triangle is the point where the three angle bisectors that divides each angle vertex into two intersect each other.

The incenter also, is a point equidistant to all three sides of the triangle at right angle.

Applying the properties above, the measures in the image can be calculated as shown below.

[tex]m \angle EBG = 20^{\circ}\\\\m \angle ECG = 11^{\circ}\\\\CF = 20\\\\EG = 4\\\\BD = 11[/tex]

Find [tex]m \angle ABG[/tex]:

[tex]m \angle ABG = m \angle EBG[/tex] (angle bisector definition)

[tex]\mathbf{m \angle ABG = 20^{\circ}}[/tex]

Find [tex]m \angle BCA[/tex]:

[tex]m \angle BCA = 2(m \angle ECG)[/tex] (angle bisector definition)

[tex]m \angle BCA = 2(11)\\\\\mathbf{m \angle BCA = 22^{\circ}}[/tex]

Find [tex]m \angle BAC[/tex]:

[tex]m \angle BAC = 180 - (m \angle CBA + m \angle BCA)[/tex] (sum of triangle definition)

[tex]m \angle BAC = 180 - (40 + 22)\\\\\mathbf{m \angle BAC = 118^{\circ}}[/tex]

Find [tex]m \angle BAG[/tex]:

[tex]m \angle BAG = \frac{1}{2} (m \angle BAC)[/tex] (angle bisector definition)

[tex]m \angle BAG = \frac{1}{2} (118)\\\\\mathbf{m \angle BAG = 59^{\circ}}[/tex]

Find DG:

[tex]DG = EG[/tex] (Perpendicular bisectors of the sides of a the triangle are equal in length from the incenter of a triangle)

[tex]\mathbf{DG = 4}[/tex]

Find BG:

[tex]BG = \sqrt{BD^2 + DG^2}[/tex] (Pythagorean Theorem)

[tex]BG = \sqrt{11^2 + 4^2} \\\\BG = \sqrt{137} \\\\\mathbf{BG = 11.7}[/tex]

Find BE:

[tex]BE = \sqrt{BG^2 - EG^2}[/tex] (Pythagorean Theorem)

[tex]BE = \sqrt{11.7^2 - 4^2} \\\\BE = \sqrt{120.89} \\\\\mathbf{BE = 10.99}[/tex]

Find GC:

[tex]GC = \sqrt{CF^2 + FG^2}[/tex] (Pythagorean Theorem)

[tex]GC = \sqrt{20^2 + 4^2} \\\\GC = \sqrt{416} \\\\\mathbf{GC = 20.4}[/tex]

In summary, applying the definition of the incenter of a triangle, the measures in triangle ABC where G is the incenter are:

Learn more here:

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Answer:

11

Step-by-step explanation:

90-35=55

55=5x

x=11

good luck

Answer:

40

Step-by-step explanation:

I hope this helps!

Answer:

40

Explanation:

Multiply -4 by 5

Then, Multiply -20 by -2

Which equals 40

Hope this helps:)

Answer:

x value

Step-by-step explanation:

Answer:

1/5. d

Step-by-step explanation:

sorry if I'm wrong

Answer:

(-8*6)

Step-by-step explanation:

hope I helped

Answer:

22.5% increase.

Step-by-step explanation:

Because her collection grows by 9, that means it increases by 9/40 total. As a decimal, this would be 0.225. Then, as a percent you multiply that by 100 to get 22.5%. Pilar's collection increased by 22.5%

Answer:

hahaha is

easy hmm..........

Answer:

this is an iscoceles triangle.

I know this because 2 of the sides are equal in length

Therefore,

AB=AC

3x-5=-2x+15

x-5=15

x=20

if x=20 then BC=2(20)

BC=40

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Answer:

QS = 8x - 2

Step-by-step explanation:

QS = QR + RS

QS = 6x - 11 + 2x + 9

QS = 8x - 2

Answer: She should sell her artwork for $39.60 or almost $40.

Step-by-step explanation:

First you need to find out what 80% of 22 is, which is 17.6, then you add that price to the price of her supplies.

22+17.6=$39.60

Answer:

B

Step-by-step explanation:

Answer:

What is the LCM of 60 and 108? The LCM of 60 and 108 is 540.

Step-by-step explanation:

What is the LCM of 60 and 108? The LCM of 60 and 108 is 540.

The HCF of 60 and 108 is 540.

For given question,

We have been given the HCF of 60 and 108 is 12.

We know, the product of LCM and HCF of numbers is equivalent to the product of the given numbers.

⇒ LCM × 12 = 60 × 108

⇒ LCM = 540

Therefore, the HCF of 60 and 108 is 540.

Learn more about LCM and HCF here:

https://brainly.com/question/17437347

#SPJ3

Answer:

Step-by-step explanation:

16 divided by $3.50 = 4.5

Answer:

0.286 pounds

Step-by-step explanation:

one pound=$3.50

x pounds=$1.00

then

1/3.5=0.286 pounds

check:

0.285 pounds per dollar x $3.50=1 pound

Answer:

A

Step-by-step explanation:

Not much of a reason but thats what i g ot

Answer:

a

Step-by-step explanation:

Answer:

Yes, it is

Step-by-step explanation:

For the first part is 10 per people = y = 10x

And the second part is 2 per people = y = 2x

So the two equations are

y = 10x

and

y = 2x

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:

15.83 servings

Answer:

I think answer is

D. X=4

:-))

Answer:

(1, 6)

Step-by-step explanation:

Use elimination or substitution (elimination is easier)

Answer:

your answer,

you can answer 15 math problems in 12 minutes

Answer: 3

Step-by-step explanation:

From the question, we are informed that Johnny has 30 marbles while Mark has m marbles.

Since Johnny has 10 times as many marbles as Mark, it means that Johnny has: = 10 × m = 10m

Therefore, 10m = 30

m = 30/10

m = 3

Mark has 3 marbles