Donations to an annual fundraiser are 15% greater this year than last year. Last year, donations were 10% greater than the year before. The amount raised this year is $10,120. How much was raised two years ago?

Answer:

Answer by josgarithmetic(37226) (Show Source): You can put this solution on YOUR website!

system%2810b%2B6p=17000%2C3b%2B20p=17000%29

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

Let +a+ = the cost of 1 pencil

Let +b+ = the cost of 1 book

---------------------------

(1) +6b+%2B+10a+=+17000+

(2) +3b+%2B+22a+=+17000+

----------------------

Multiply both sides of (2) by +2+

and subtract (1) from (2)

(2) +6b+%2B+44a+=+34000+

(1) +-6b+-+10a+=+-17000+

-------------------------

+34a+=+17000+

+a+=+500+

and

(1) +6b+%2B+10a+=+17000+

(1) +3b+%2B+5a+=+8500+

(1) +3b+%2B+5%2A500+=+8500+

(1) +3b+=+8500+-+2500+

(1) +3b+=+6000+

(1) +b+=+2000+

------------------

Step-by-step explanation:

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Answer:

b. x = 123

Step-by-step explanation:

Answer:

b; [5]

Step-by-step explanation:

i took the quiz

The number of the blue cubes is 35 and the number of the red cubes is 20.

The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times the other number.

Given that:-

The number of the blue cubes are calculated as:-

The two equations will be formed by the given data in the question.

[tex]\dfrac{r}{b}=\dfrac{4}{7}[/tex]

7r = 4b

[tex]\dfrac{r+10}{b}=\dfrac{6}{7}[/tex]

7r + 70 = 6b

Solving the above equation we will get the value of b.

4b + 70 = 6b

6b - 4b = 70

2b = 70

b = 35

7r = 4b

7r = 4 x 35

r = 20

Therefore the number of the blue cubes is 35 and the number of the red cubes is 20.

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Answer:

same thing for the rest, you just change the value of the radius according to the question

Step-by-step explanation:

area = pi * radius²

1)

a = pi * 10²

a = ~3.14 * 100

a = 314 mi²

Answer:

63 units

Step-by-step explanation:

d = √(x2-x1)^2 + (y2-y1)^2

Meaning it would look like this

d = √(15+48)^2 + (23-23)^2

we changed the subtraction sign in the first one to an addition sign because it was a double negative

hope this helped

Answer:

RIght triangle

Step-by-step explanation:

Based on the relationship of special angles, the values of x are:

1. x = 34

2. x = 9

3. x = 6

Alternate interior angles are equals and corresponding angles are also equal.

Linear pair angles are supplementary.

1. Angles j and a are linear pair angles, therefore:

3x + 15 + 2x - 5 = 180

5x + 10 = 180

5x = 180 - 10

5x = 170

x = 170/5

x = 34

2. Angles m and g are corresponding angles, therefore:

4x + 12 = 2x + 30

4x - 2x = -12 + 30

2x = 18

x = 9

3. Angles c and v are alternate interior angles, therefore:

6x + 9 = 3x + 27

6x - 3x = -9 + 27

3x = 18

x = 6

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The statement that proves that quadrilateral JKLM is a kite is (b) LM = JM = 3 and JK = LK = √17

See attachment for the complete question, the graph and the options

The coordinates of the quadrilateral are:

J = (4,5)

K = (5,1)

L = (1,2)

M = (1,5)

Calculate the lengths of the kite using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]JK = \sqrt{(4 -5)^2 + (5 -1)^2} = \sqrt{17[/tex]

[tex]LK = \sqrt{(1 -5)^2 + (2 -1)^2} = \sqrt{17[/tex]

[tex]LM = \sqrt{(1 -1)^2 + (5 -2)^2} = 3[/tex]

[tex]JM = \sqrt{(1 -4)^2 + (5 -5)^2} = 3[/tex]

On a kite, the adjacent sides are of equal lengths

Because LM = JM = 3 and JK = LK = √17, we can conclude that the quadrilateral JKLM is a kite

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total no of marbles = 10

no. of marbles which are not yellow = 9

9/10

hope it helps...!!!

Answer:

Q=8

Step-by-step explanation:

Just multiply the entire first function by 2

therfore

(x-3y=4) * 2

therefore

=2x-6y=8

This is the same as the second function and in it, the coefficient of x is 2, therefore

Q=8

Answer:

Step-by-step explanation:

(-5, 3) and (-5, -3)

(-3 - 3)/(-5 + 5) = -6/0 = UNDEFINED

That is also the CORRECT ANSWER

Answer:

[tex]\tan 2 x = \dfrac{24}7[/tex]

Step by step explanation:

[tex]\textbf{2)}\\\\\text{Given that,} \\\\~~~~~\cos x = -\dfrac 45\\\\\implies \cos^2 x = \dfrac{16}{25}~~~~~~~~~~;[\text{Square both sides}]\\\\\implies 1- \sin^2 x= \dfrac{16}{25}\\\\\implies \sin^2 x = 1- \dfrac{16}{25}\\\\\implies \sin^2 x = \dfrac{9}{25}\\\\\implies \sin x =\pm\sqrt{\dfrac{9}{25}}\\\\\implies \sin x = \pm \dfrac 35\\\\[/tex]

[tex]\text{Since,}~ \pi \leq x \leq \dfrac{3\pi}{2}, ~ \text{the angle lies in the 3rd quadrant, where}~ \sin x ~ \text{is negative.}\\\\\text{So,}~ \sin x = -\dfrac 35[/tex]

[tex]\text{Now,}~\\\\\tan x = \dfrac{\sin x }{\cos x} = \dfrac{-\tfrac 35}{-\tfrac 45} = \dfrac 35 \times \dfrac 54 = \dfrac 34\\\\\\\tan 2x =\dfrac{2 \tan x }{ 1- \tan^2 x}\\\\\\~~~~~~~~~=\dfrac{2 \left( \tfrac 34 \right)}{1- \left( \tfrac 34 \right)^2}\\\\~~~~~~~~~=\dfrac{\tfrac 64}{1-\tfrac {9}{16}}\\\\\\~~~~~~~~~=\dfrac{\tfrac 32 }{\tfrac 7{16}}\\\\\\~~~~~~~~~=\dfrac 32 \times \dfrac{16}7\\\\\\~~~~~~~~~=\dfrac{24}7[/tex]

Using the distance formula, the perimeter of triangle ABC is approximately 40.5 units.

Perimeter = sum of all three sides.

Use the distance formula, [tex]d = \sqrt{(y_2 - y_1)^2 - (x_2 - x_1)^2}[/tex] to find the distance between each of the vertices of the triangle.

The given vertices are:

AB = √[(8−(−6))² + (−1−4)²]

AB = √221

AB ≈ 14.9 units

BC = √[(8−0)² + (−1−(−9))²]

BC = √128

BC ≈ 11.3 units

AC = √[(−6−0)² + (4−(−9))²

AC = √205

AC ≈ 14.3 units

Perimeter of △ABC = 14.9 + 11.3 + 14.3

Perimeter of △ABC ≈ 40.5 units

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Answer:

2nd option

Step-by-step explanation:

(5x² - 4x - 1) - (- 4x² - 4)

remove first set of parenthesis and distribute second set by - 1

= 5x² - 4x - 1 + 4x² + 4 ← collect like terms

= 9x² - 4x + 3

Answer:

141/1.95 km/hr, or 72.308 km/hr

Step-by-step explanation:

To find the average speed, we need to know the total distance traveled / time (hours).
The total distance is 72 km + 69 km =  141 km.
The total time is 48 minutes / 60 (because we want this in hours, not minutes) + 69/60 = 1.95 hours
141/1.95 =  72.3 km/hr

Answer:

y=2x-5

explanation

m is gradient so rise over run and b is the y intercept which is -5

Answer: y = 2x - 5

Step-by-step explanation:

Method I:

▪︎ Slope: m = (y2 - y1) / (x2 - x1)

▪︎ b is where the graph crosses the y-axis

▪︎ Points: (1, -3), (2, -1)

▪︎ m = (-1 - (-3)) / (2 - 1) = (3 - 1) / (1) = 2

▪︎ b = -5

▪︎ => y = 2x - 5

Method II:

▪︎ y = mx + b

▪︎ Points: (1, -3), (2, -1)

▪︎ System of equations:

-3 = m*1 + b,

-1 = m*2 + b

-3 = m + b,

-1 = 2m + b

m = -b - 3,

-1 = 2(-b - 3) + b

m = -b - 3,

-1 = -2b - 6 + b

m = -b - 3,

-1 + 6 = -2b + b

m = -b - 3,

5 = -b

m = -(-5) - 3,

b = -5

m = 2,

b = -5

▪︎ => y = 2x - 5

Answer:

7 6 5 5

Step-by-step explanation:

the highest numbers should go in the leftmost digits place, as these are worth more

here, we put 7 in the thousands place, which is 2 thousand higher than if we put 5 in the thousands place

Using proportions, it is found that 96,734 more obese people were there in evansville than in boulder.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For Evansville, the proportion of obese people is given by:

189/(311+189) = 189/500.

Hence, out of 358,676 people:

oE = 189/500 x 358676 = 135580.

For Boulder, the proportion is given by:

16/(16 + 109) = 16/125

Hence, out of 303,482 people:

oB = 16/125 x 303482 = 38846.

Hence the difference is given by:

135580 - 38846 = 96734

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The graph third represents the provided situation first line increases and then constant then again increases and becomes constant.

A line graph is a graph made up of segments of straight lines that connect the depicted data points.

We have:

Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.

Based on the information given we can say graph third represents the situation.

First Keisha ran to swim practice so the line first increases and then she  but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes which means the line should be constant.

Again they both ran so line increases.

Then they both stayed for 1 hour, so the line should be constant.

Thus, the graph third represents the provided situation first line increases and then constant then again increases and becomes constant.

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Answer:

I don't understand what the means

Answer:

No

Step-by-step explanation:

The defining property of a rhombus is that it has equal side lengths.

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

Finding all side lengths :

AB

⇒ √(-4 + 6)² + (5 - 4)²

⇒ √2² + 1²

⇒ √5 units

BC

⇒ √(-3 + 4)² + (3 - 5)²

⇒ √1² + (-2)²

⇒ √5 units

CD

⇒ √(-5 + 3)² + (1 - 3)²

⇒ √(-2)² + (-2)²

⇒ √8 units

DA

⇒ √(-6 + 5)² + (4 - 1)²

⇒ √(-1)² + 3²

⇒ √10 units

As all side lengths of the quadrilateral are not equal, ABCD is not a rhombus.

Answer:

13/7

Step-by-step explanation:

Method 1 :

1/2*3/7-5/7*1/2+2​ = (3/14)- (5/14) + 2

                            = -2/14 + 2            

                            = -2/14 + 28/14

                            = 26/14

                            = 13/7

Method 2 :

1/2*3/7-5/7*1/2+2​ = (1/2) [3/7 - 5/7] + 2

                            = (1/2)(-2/7) + 2            

                            = (-1/7) + 14/7

                            = 13/7

The ratio of ab to bc to the nearest hundredth is gotten as; 0.84

From the attached image showing the circle geometry, we will first connect point A to point B.

After connecting point A to point B, we will draw a perpendicular line to AB through B to terminate at C.

Thus, we can have the ratio of trigonometry at;

tan ∠ABC = AB/BC

Thus;

AB/BC = tan 40

AB/BC = 0.84

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