Fiona and Diana are sisters. They each baked cookies. Fiona baked 15 more cookies than Diana. They baked a total of 75 cookies. How many cookies did each girl bake?

Answer:

x = 3.5

Step-by-step explanation:

[tex] \triangle DEF \sim \triangle XYZ\\\\

\therefore \frac{DE}{XY} =\frac{DF}{XZ} \\\\

\therefore \frac{5}{7.5} =\frac{7}{3x} \\\\

\therefore 3x = \frac{7.5\times 7}{5} \\\\

\therefore x = \frac{7.5\times 7}{3\times 5} \\\\

\therefore x = \frac{52.5\times 7}{15} \\\\

\therefore x = 3.5[/tex]

Step-by-step explanation:

If [tex]\triangle[/tex]DEF~[tex]\triangle[/tex]XYZ

[tex]\tt{\dfrac{DE}{XY}=\dfrac{EF}{ZY}=\dfrac{DF}{XZ} }[/tex]

According to the question

[tex]\tt{\dfrac{5}{7.5}=\dfrac{3}{4.5}=\dfrac{7}{3x} }[/tex]

[tex]\tt{\dfrac{3}{4.5}=\dfrac{7}{3x} }[/tex]

[tex]\tt{ 9x=4.5×7}[/tex]

[tex]\tt{ 9x=31.5 }[/tex]

[tex]\tt{ x=\dfrac{22.5}{9} }[/tex]

[tex]\tt{x=3.5 }[/tex]

Answer:

$9

Step-by-step explanation:

In this circumstance, 20% off is the original number (40) divided by 5, and that's the answer. I hope this helps!

Answer: They saved $8

Step-by-step explanation:

0.20 × $40 = $8.00

Answer:

12

Step-by-step explanation:

The required equation of the line that is parallel to the given line is 4y - 10x = 12. Option B is correct.

Given that,
Which equation represents a line parallel to the line whose equation is 2y - 5x = 10 is to be determined.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The property of the parallel line state that the slope of the parallel line are always equal.
So the slope of line given in B 4y - 10x = 12 is m = 5 and slope of the given line is m = 5 which are equal.

Thus, the required equation of the line that is parallel to the given line is 4y - 10x = 12. Option B is correct.

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Answer:

142

Step-by-step explanation:

opposite angle theorem

Answer:

D. 142

Step-by-step explanation:

They are vertical angles which are always equal

Answer:

45495

Step-by-step explanation:

Answer:

10077

Step-by-step explanation:

A culture of bacteria has an initial population of 5400 bacteria and doubles every 10 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P

t

​

=P

0

​

⋅2

d

t

​

, where P_tP

t

​

 is the population after t hours, P_0P

0

​

 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 9 hours, to the nearest whole number?

P_0=5400

P

0

​

=5400

The initial population

t=9

t=9

Time elapsed

d=10

d=10

The doubling time

P_t = P_0\cdot 2^{\frac{t}{d}}

P

t

​

=P

0

​

⋅2

d

t

​

P_t=5400\cdot 2^\frac{9}{10}

P

t

​

=5400⋅2

10

9

​

Plug in

P_t=10076.7563\approx10077

P

t

​

=10076.7563≈10077

Use parenthesis in the calculator for the exponent

Answer:

4 and 1/2 miles (or 9/2 miles)

Step-by-step explanation:

I would set this up as a proportion

3/4          x

10          60

Cross multiply

60 x 3/4 = 45

Divide

45/10 = 4.5

4.5 = 4 and 1/2 miles

Answer:

[tex]b_2 = \frac{2A}{h} -b_1[/tex]

Step-by-step explanation:

Given

[tex]A = \frac{1}{2}h(b_1 + b_2)[/tex]

Required

Select equivalent expressions

Multiply through by 2

[tex]2*A = 2*\frac{1}{2}h(b_1 + b_2)[/tex]

[tex]2*A = h(b_1 + b_2)[/tex]

[tex]2A = h(b_1 + b_2)[/tex]

Divide through by h

[tex]\frac{2A}{h} = \frac{h(b_1 + b_2)}{h}[/tex]

[tex]\frac{2A}{h} = b_1 + b_2[/tex]

Subtract b1 from both sides

[tex]\frac{2A}{h} -b_1= -b_1 + b_1 + b_2[/tex]

[tex]\frac{2A}{h} -b_1= b_2[/tex]

[tex]b_2 = \frac{2A}{h} -b_1[/tex]

From the list of options, there is only one answer

Answer:

Area = 18 Sq.units

Step-by-step explanation:

From the given dimensions we have, we can say that the total length of the base = 6 + 4 = 10 units

Now,since we know that all sides of the red square are 6 units, we can use pythagoras theorem to get the length of the long diagonal that serves as the base of the blue colored area.

Let the diagonal be c. Thus;

c = √(10² + 6²)

c = √(100 + 36)

c = √136

Let length of the horizontal part of the blue area be "b". Thus, b = 6 units

Let the other part of the triangle be a. We can find a from pythagoras theorem.

a = √(4² + 6²)

a = √(16 + 36)

a = √52

Using hero's formula, we can find the area of the triangle;

Area = √(s(s − a)(s − b)(s − c))

Where s = (a + b + c)/2

s = (√52 + 6 + √136)/2

s = 12.4365

Area = √(12.4366(12.4365 −√52)(12.4365 − 6)(12.4365 − √136))

Area = 18 Sq.units

Pi is the ratio of the circumference of a circle to its diameter, D

Answer:

D.

Step-by-step explanation:

is the ratio of the circumference of any circle to the diameter of that circle

Step-by-step explanation:

I just need points sorry

Answer:

1296

Step-by-step explanation:

6 times 6 = 36 and 36 times 6=216 and 216 times 6 = 1296

Answer:

Step-by-step explanation:

conversion factors:

m:cm= 1:100

dm:km= 1,000,000:1

m:mm= 1:1000

hg:dg= 1:1000

g:cg= 1:100

kg:g=1000

so we plug in:

5m=500 cm

5246dm=0.5246km

5.246m=5246mm

3.7hg=3700dg

0.37g=37cg

370kg:370000

so the word is SPEAKUP

Answer:

350

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

[tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{75}{25}[/tex] = 3

[tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{225}{75}[/tex] = 3

[tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{675}{225}[/tex] = 3

This indicates the sequence is geometric with explicit formula

[tex]a_{n}[/tex]  = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 25 and r = 3 , then

a₆ = 25 × [tex]3^{5}[/tex] = 25 × 243 = 6075

Answer:

The answer is 1,785,815

1,785,815 their is your answer

Answer: 6.5 hours

Step-by-step explanation:

From the question, we are given the information that a truck has traveled 75 miles in 1.5 hours of driving. The miles pee hour travelled will be:

= 75 / 1.5

= 50 miles per hour

The number of hours that the truck will use to travel 325 miles will be:

= 325/50

= 6.5 hours

Answer:

Y = 40

X = 101

W = 20

Step-by-step explanation:

All of the triangles Angles should equal 180!

Answer:

4 times

Step-by-step explanation:

We known that 1 quart is equivalent to 32 fluid ounces

Suppose each eruption consumes 8 fluid of ounces, if we also assume that the amount of vinegar required per eruption is constant, then the number of times Adriana can make her volcano erupt is

n = 32 / 8

n = 4 times

Adriana can make her volcano erupt 4 times with 1 quart of vinegar

Answer:62.5

Hello

Step-by-step explanation:

1. 7.50 divided by 6 = 1.25 for 1 length of rope (Feet)

2.50x1.25=62.5

Hope this helped

Or I might be wrong Im not sure yet.

1.) 37

2.) -16

3.) 11

4.) 1

Step-by-step explanation:

Answer:

$400

Step-by-step explanation:

140 ÷ 35% = 400

Answer:

6; 8; 10

Step-by-step explanation:

First side: x

Second side: x+2

Third side: x+4

x + x + 2 + x + 4 = 24

3x + 6 = 24

3x = 18

x=6

First side: 6

Second side: 8

Third side: 10

Answer:

3 3/7 divided by 1 1/7 = 3

16/(-8) =  -2

2 2/5 divided by 4/5 = -3

-12.2/(-6.1) = 2

Step-by-step explanation:

Turn the mixed numbers into improper fractions and work from there. Then, make sure to find the reciprocal of the second fraction/number. For example,

3 3/7 = 24/7

1 1/7 = 8/7

24/7 (7/8) = 3

Hope this helped, but if you need more help then make sure to communicate with your teacher. This will help you out in the future.

Step 1: Simplify both sides of the equation.

5x−15−(2x+5)=3x−20

5x−15+−1(2x+5)=3x−20(Distribute the Negative Sign)

5x+−15+−1(2x)+(−1)(5)=3x−20

5x+−15+−2x+−5=3x−20

5x+−15+−2x+−5=3x+−20

(5x+−2x)+(−15+−5)=3x−20(Combine Like Terms)

3x+−20=3x−20

3x−20=3x−20

Step 2: Subtract 3x from both sides.

3x−20−3x=3x−20−3x

−20=−20

Step 3: Add 20 to both sides.

−20+20=−20+20

0=0

Answer:

All real numbers are solutions.

2x+5−(5x−15)=−3x+20

Answer:

All real numbers are solutions.

Answer:

Elena could tell without finishing by simplifying both sides. The next step would have been 30x +24x = 30x+24. This would have been simplified down to x=1

Step-by-step explanation:

She got to the last line 36x + 18 = 36x + 18 when she stopped and said the equation has infinitely many solutions.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given as,

12x +6(4x + 3) = 6(6x + 4) - 6

Simplify the equation, then we have

12x +6(4x + 3) = 6(6x + 4) - 6

12x + 24x + 18 = 36x + 24 - 6

36x + 18 = 36x + 18

She got to the last line 36x + 18 = 36x + 18 when she stopped and said the equation has infinitely many solutions.

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Answer:

b

Step-by-step explanation: