Dan Stocked up on batteries.
He Brought 10 packages of AA and AAA batteries for a total of 72 batteries.
The AA batteries are sold in packages of 6, and the AAA batteries are sold in packages of 8. Write a system of equations that can be solved to find how many packages of each type of battery Dan bought. Remember to define your variables.
1. C+D=10
2.6c+8D=72

Answer:

17.3

Step-by-step explanation:

The following data were obtained from the question:

Angle T = 87°

Side T = t

Side V = 14

Side U = 11

The value of t can be obtained by using cosine rule as show below:

t² = u² + v² – 2uv cosT

t² = 11² + 14² – 2×11×14 cos 87°

t² = 121 + 196 – 308 × Cos 87°

t² = 300.88

Take the square root of both side

t = √300.88

t = 17.3

Therefore, the value of t is 17.3

[tex]

5-6x=8x+17 \\

-14x=12\implies x=-\frac{6}{7}

[/tex]

Hope this helps.

Answer: -6/7

Step-by-step explanation: 5 - 6x = 8x + 17

                                             5 + - 6x = 8x + 17

                                            -6x + 5 = 8x + 17

                                            -6x + 5 - 8x = 8x + 17 - 8x

                                            -14x + 5 = 17

                                            -14x + 5 - 5 = 17 - 5

                                           -14x = 12

                                            -14x/-14 = 12/-14

                                             x = -6/7

Answer:

 90°

Step-by-step explanation:

∆GFD is an isosceles right triangle, so angle FDG is 45°. Segment DF bisects angle EDG, so that angle is 90°.

Arc AG is the other half of the semicircle AGE that includes 90° arc GE.

So, arc AG is 90°.

__

Comment on the problem

"a" and "b" are irrelevant to arc AG. They come into play for arc CE.

Answer:

Angles 1 and 2 are supplementary.

Step-by-step explanation:

<BAC is equal to <FGE, because BC and DE are parallel. So <DGF would be 180° minus angle 1. So, they are supplementary.

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Answer:

Step-by-step explanation:

8c2×6c2=((8×7)/2)×((6×5)/2)=28×15=420

Answer:

[tex]\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }[/tex]

Step-by-step explanation:

Hello,

a and b are the zeros, we can say that

[tex]f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)[/tex]

So we can say that

[tex]a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}[/tex]

Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b

for instance we can write

[tex](x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab[/tex]

and we can notice that

[tex]a^2+b^2=(a+b)^2-2ab[/tex] so

[tex](x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab[/tex]

it comes

[tex]x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}[/tex]

multiply by 3

[tex]3x^2-20x+2*16+5=3x^2-20x+37[/tex]

Answer:

11, 17, and 28.

Step-by-step explanation:

[tex]x, y, z\\[/tex]

Lowest number is [tex]x[/tex]

Median is [tex]y[/tex]

Highest number is [tex]z[/tex]

[tex]x=11\\y=17\\\\z-x=17\\z-11=17\\z-11+11=17+11\\z=28\\\\x=11\\y=17\\z=28\\\\11, 17, 28[/tex]

The three numbers are 11 , 17 and 24

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first number be = a

Let the second number be = b

Let the third number be = c

And , the lowest number is 11

So , the value of a = 11

The median is 17

So , the value of the middle number b = 17

Now , the range of the three numbers = 13

So , the maximum value - minimum value = 13

Substituting the values in the equation for range , we get

c - a = 13

c - 11 = 13

Adding 11 on both sides , we get

c = 11 + 13

c = 24

Therefore , the value of a = 11 , b = 17 and c = 24

Hence , The three numbers are 11 , 17 and 24

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Answer:

-4<n≤5

If you are using another variable just replace it in.

The information in the number line is an interval (-4,5]

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5 and it is represented as (1,5)

Given here, the line extends to -4 and ends at 5 but the it is open on the LHS and closed on the RHS and thus the interval notation is (-4,5]

Hence the interval represented in the number line is  (-4,5]

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Answer:

2 cm.

Step-by-step explanation:

The entire base is 10 cm and the top is 8 cm, so b is 10 - 8 = 2 cm.

Hope this helps!

I hope this helps you

b+8=10

b=2

Answer:

44664.59503

Step-by-step explanation:

Hello,

In this question, you're asked to find the radical of a number. However in mathematics, the radical of a number simply means "√" and not directly square root of that number, its could be the cube root "³√" or even the fourth root "⁴√".

In this case, we're asked to find the 3 radical of p/q which means 3√(p/q)

P = 2.78×10¹¹

Q = 3.12×10⁻³

p / q = 2.78×10¹¹ / 3.12×10⁻³

p / q = 8.91×10¹³

The 3 radical = 3√(8.91×10¹³)

3√(p/q) = 44664.59503

Answer:

12.5

Step-by-step explanation:

y varies inversely as x.

y = k/x

10 = k/20

200 = k

The constant proportion k is 200.

16 = 200/x

Cross multiply.

200 = 16x

200/16 = x

x = 12.5

Answer:

324.5m^2

Step-by-step explanation:

To find the area of the composite shape, divide the shape into 3 known shapes and calculate their areas.

SO, here we divide the shape into 2 triangles and 1 rectangle.

Area of rectangle = 15 x 8 = 120m^2

Area of triangle 1 = 1/2 x 7 x 15 = 52.5m^2

Area of triangle 2 = 1/2 x 9 x 8 = 4 x 9 = 32cm^2

Now, the sum of these areas = area of composite shape = 32 + 52.5 + 120 = 204.5m^2

Hope this helps.

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Good Luck

Answer: 52.5 + 36 + 120 = 208.5

208.5 m is your answer.

Step-by-step explanation: To come to this, first you have to break the composite shape into the three different shapes that you see. 2 rectangles and a triangle. From there, you simply solve the area for each individual shape and then add them together as shown in the answer.

Answer:

0.7

if you multiply 0.7 with 0.7 you get 0.49 so 0.7 is the square root

Hope this helps

Step-by-step explanation:

Answer:

0.7

Step-by-step explanation:

0.49 = 49/100

√(49/100)

√49/√100

7/10

= 0.7

Answer:

1.  A. No

2. A. Yes

Step-by-step explanation:

1. B.   Because the numbers to the left of 7 are smaller than the numbers to the right of 7 on the number line.

2. B. Because to the right side has more numbers than the left side so amber is correct

Answer:

The measure of angle XYZ will be 120° because the included arc of an inscribed angle will always be twice the measure of the inscribed angle

Answer:wrong. Its 249 degrees

Step-by-step explanation:

Just got it right on the quiz

Answer:

588 units^2

Step-by-step explanation:

To find the area of the enlarged rectangle, first find the length and width of the enlarged rectangle.

This is 3.5 multiplied by their original measures:

Length = 3.5 x 8 = 28

Width = 3.5 x 6 = 21

Now, area =. LxW = 588 units^2

Hope this helps

Answer:

588 units squared

Step-by-step explanation:

We have a rectangle that has dimensions 8 units by 6 units.

From the problem, we know that this rectangle has been enlarged by a scale of 3.5. Essentially, to obtain the dimensions of the new, bigger rectangle, we multiply the current length (8 units) by 3.5 and the current width (6 units) by 3.5:

new length = 8 * 3.5 = 28 units

new width = 6 * 3.5 = 21 units

Given this, we can now calculate the area.

The area of a rectangle is denoted by A = lw, where l is the length and w is the width.

Here, the length is l = 28 and the width is w = 21. Plug these in:

A = lw

A = 28 * 21 = 588

The answer is thus 588 units squared.

~ an aesthetics lover

Answer:  B) y = 2 · 3ˣ

Step-by-step explanation:

We can see that (2, 18) is a point on the graph.

Plug it into the equations to see which one make a true statement.

        A) y = 1 · 3ˣ

            18 = 1 · 3²

            18 = 1 · 9

             18 ≠ 9

       B) y = 2 · 3ˣ

          18 = 2 · 3²

           18 = 2 · 9

           18 = 18             This works!

       C) y = 3 · 2ˣ

          18 = 3 · 2²

           18 = 3 · 4

           18 ≠ 12

       D) y = 4 · 3ˣ

          18 = 4 · 3²

           18 = 4 · 9

           18 ≠ 36

Replace m with 12 and simplify.

m-8 = 12-8 = 4

Answer:

work is shown and pictured

Answer:

answer is 1

Step-by-step explanation:

The scale factor of triangle ABC to triangle DEF is 1. Therefore, the correct answer is option D.

In the given triangle ABC, AB=5 units, BC=5 units and AC=5 units and in triangle DEF, DE=5 units, DF=5 units and EF=5 units.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

So, the scale factor of ABC to DEF is

AB/DE = BC/EF = AC/DF = 5/5 = 1

Therefore, the correct answer is option D.

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Answer:

0

Step-by-step explanation:

It is a horizontal line.

Answer:

undefined

Step-by-step explanation:

The slope of a line is found by

m = (y2-y1)/(x2-x1)

   = (-9 -10)/(-9 - -9)

   = -19/ (-9+9)

   = -19/0

We cannot divide by zero so the slope is undefined

Answer:

The number of ways she can choose four albums for display with at least two from Diana Kroll is from the sixteen albums is 665 ways

Step-by-step explanation:

1) The number of ways she can choose 2 albums of Diana from the 5 Diana Kroll  albums is 5!/(2!(5 - 2)!) = 10 ways

Choosing the other 2 albums from the remaining 11 albums gives;

11!/(2!(11 - 2)!) = 55 ways

Total number of ways is then 10 × 55 = 550 ways

Choosing 3 from the 5 Diana Kroll  albums is 5!/(3!(5 - 3)!) = 10 ways

Choosing the other 1 album from the remaining 11 albums gives;

11!/(1!(11 - 1)!) = 11 ways

Total number of ways is then 10 × 11 = 110 ways

Choosing 4 from the 5 Diana Kroll  albums is 5!/(4!(5 - 4)!) = 5 ways

Choosing the other 0 album from the remaining 11 albums gives;

11!/(0!(11 - 0)!) = 1 way

Total number of ways is then 5 × 1 = 5 ways

Total number of ways = 550 + 110 + 5 = 665 ways

2) In the indirect method, we first find the number of ways to choose 4 albums out of the 16 albums, then we subtract the number of cases where there are  1 and 0 Diana Kroll albums as follows;

16!/(4!(16 - 4)!) = 1820 ways

With 1 Diana Kroll album gives

5!/(1!(5 - 1)!)×11!(3!(11 - 3)!) = 825 ways

With 0 Diana Kroll album gives

5!/(0!(5 - 0)!)×11!(4!(11 - 4)!) = 330 ways

Total number of ways with at least 2 Diana Kroll albums = 1820 - 825 - 330

Total number of ways with at least 2 Diana Kroll albums = 665 ways.

Answer:

independent events

Step-by-step explanation:

dependent is when the previous event affects the outcome of the next event.

Ex: When I draw a card without replacement at first I will have 52 cards. Once I draw the card, I will have only 51 cards to choose from.

Independent event is when the outcome is not related.

Example like the problem given to you

Answer:

Step-by-step explanation:

3/4 t = 2/3

Multiply both sides of the equation by 4/3

4/3 * 3/4 t = 4/3 * 2/3

Reduce the numbers with G.C.F 4

1/3 * 3t = 4/3 * 2/3

Reduce the numbers with G.C.F 3

t = 4/3 * 2/3

Multiply the fractions

t = 8/9

Hope this helps...

Good luck on your assignment...

Answer:

[tex]t= \frac{8}{9} \\ [/tex]

Step-by-step explanation:

[tex]3/4t=2/3 \\ \frac{3}{4} t = \frac{2}{3} \\ cross - multiply \\ 3t \times 3 = 4 \times 2[/tex]

[tex]9t = 8 \\ divide \: both \: sides \\ of \: the \: equation \: by \: 9 \\ \frac{9t}{9} = \frac{8}{9} [/tex]

[tex]t = \frac{8}{9} [/tex]

Answer:

-721 is greater than -723.

Step-by-step explanation:

Answer:

x < - 721

Step-by-step explanation:

x < - 721 is the one according to the pictured line

Answer:

  cosine

Step-by-step explanation:

"Cos" is the abbreviation usually applied to the name of the cosine function. That function gives the x-coordinate of the point on a unit circle that is at some angle measured counterclockwise from the x-axis. A unit circle is a circle with a radius of 1 unit, centered at the origin.

Hey there! :)

Answer:

C. x = 6.

Step-by-step explanation:

Given:

4(8 - x) = 8

Solve for x. Distribute:

32 - 4x = 8

Subtract 32 from both sides:

-4x = -24

Divide both sides by -4:

-4x/(-4) = -24/(-4)

x = 6.

Lynda previous best time was 52.9 second.

Given that, Lynda runs the 400 meter for her school's track team.

She beat her best time by 3.6 seconds in the meet today with a time of 49.3 seconds.

It means that, previous best time of Lynda was 3.6 second more than as compared to todays time.

So that,

Previous best time is, [tex]=49.3+3.6=52.9seconds[/tex]

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