Please help with steps:
converting a fraction to a termination decimal: basic

69
-----
20

Answer:

40,44,48,52,56,60,64,68...

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

Given: The sum of two digit number is 8

           Reversing the digit will get us number 18 less than the original.

Lets take x as tenth digit of our number and y as unit digit of our number.

As given sum of digit is 8

∴ [tex]x+y= 8[/tex]

∴ [tex]y= 8-x[/tex] -       equation 1

We also know that reversing the digit will get us number 18 less than the original.

∴ [tex]10y+x = 10x +y-18[/tex]

Now, lets put the value of y from equation 1

⇒ [tex]10(8-x) + x = 10x+ (8-x)- 18[/tex]

⇒ [tex]80-9x= 9x-10[/tex]

⇒ [tex]90= 18x[/tex]

∴ [tex]x= 5[/tex]

Next, substituting the value of x in equation 1

[tex]y= 8-x[/tex]

⇒ [tex]y= 8-5 = 3[/tex]

∴ [tex]y= 3[/tex]

∴ The original number is 53, sum of the digit is 8 and if we reverse the digit of the number, we get 35, which is 18 less than the original number.

Step-by-step explanation:

x² + 2ixy − y²

x² + 2ixy + i²y²

(x + iy)²

Answer:

(X+yi )(X+yi)

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

15 fish / 5 days = 3 fish per day

Answer:

3

Step-by-step explanation:

15 fish / 5 days = 3 fish per day

Answer:

45 cats 18 dogs

Step-by-step explanation:

63/7 = 9

9*5=45

9*2=18

45+18=63

The number of cats up for adoption is 45.

Given that, the ratio of cats to dogs=5:2.

The total number of cats and dogs up for adoption is 63.

In mathematics, a ratio indicates how many times one number contains another.

Now, 5+2=7

Number of cats=5/7×63=45

Therefore, the number of cats up for adoption is 45.

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Answer:

The number of green marbles are 36.

Step-by-step explanation:

Given:

Total number of marble bag contains is 42.

The number of green marbles is 6 more than 5 times the number of red marbles.

Let the number of red marbles be [tex]x[/tex].

So, the number of green marbles = [tex]6+5x[/tex]

Now, to get the number of green marbles.

According to question:

[tex]x+(6+5x)=42[/tex]

[tex]6x+6=42[/tex]

Subtracting 6 in both sides :

[tex]6x+6-6=42-6[/tex]

[tex]6x=36[/tex]

Now, by dividing 6 on both sides:

[tex]6x\div 6=36\div 6[/tex]

[tex]x=6[/tex]

The number of red marbles are 6.

And, the number of green marbles are [tex]6+5x[/tex]

                                                                 = [tex]6+5\times 6[/tex]

                                                                 =[tex]6+30[/tex]

                                                                 = [tex]36[/tex]

Therefore, the number of green marbles are 36.

In simple terms, absolute value makes a negative number positive. So, |ab| simplifies to -ab when a<0 and b>0, |2b| simplifies to -2b when b<0, and |c| simplifies to -c when c<0.

The expression |ab| simply represents the absolute value of the product of a and b. Absolute value is a mathematical function that determines the distance of a number from zero. In this case, as a is less than 0 (negative) and b is greater than 0 (positive), the product ab would be negative. But absolute value always returns a positive output or zero, so, |ab| would be -ab because absolute value would remove the negative sign.

The expression |2b|, where b is less than 0, would simplify to -2b, as b is negative so absolute value removes the negative sign.

Lastly, the expression |c|, when c is negative, simplifies to -c as the absolute value would remove the negative sign from c.

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Final answer:

To simplify expressions with absolute value signs, one must take into account the sign of the variables involved. If the result inside the absolute value sign is negative, then removing the absolute value signs will result in its positive counterpart.

Explanation:

When simplifying the expression |ab| given that a<0 and b>0, we consider that since a is negative and b is positive, their product ab will be negative. However, the absolute value signs indicate the positive magnitude of the result, thus |ab| = -ab.

For the expression |2b| where b<0, since b is negative, 2b will also be negative. Removing the absolute value sign should result in a positive number; thus |2b| = -2b.

Lastly, with |c| where c<0, the absolute value of a negative number c is the positive version of the number. Therefore, |c| = -c.

Answer:

Yes

Step-by-step explanation:

the total discount allowed will be 25% of the original price and futher 10% of the original price which will amount to 10%+25% and this equal 35%

Answer:

yes you can look below for details

Step-by-step explanation:

one reason is because opposite sides are congruent, which means that it is a parallelogram.

another way is to see if the two triangles created by an diagonal is congruent:

construct AC to get two triangles ABC and ADC

AC =CA because of reflection

BA=DC because its given

BC=DA because its also Given

so

triangle ABC= triangle CDA because of SSS(side side side)

Answer:

B-How many books have each of my classmates read this year?

Step-by-step explanation:

Every year the number of books each classmate read would be different

Answer:

b

Step-by-step explanation:

Answer:

Original Price = $500

Step-by-step explanation:

The discount is 36%

and the discount amount is $180

Thus,

we can say that 180 is 36% of what number?

We let that number be "x" (original price). So we can say:

180 is 36% of x

In equation that will be:

180=36%*x

180=(36/100)*x

180=0.36x

So,

x = 180/0.36

x = $500

This is the original price.

Answer:

A

Step-by-step explanation:

x^4=64

x^2= +- 8

x = +-sqrt2, x= +- i sqrt2

Answer:

A

Step-by-step explanation:

x^4-64=0

factor

(x^2+8)(x^2-8)=0

zero property

x^2+8=0, x^2-8=0

x^2=0-8-8,

x^2=-8,

x^2=0+8=8,

x^2=8,

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

sqrt(8) & sqrt(-8),

gives you 2*sqrt(2) and -2*sqrt(2),

also, the square root of a negative number contains the imaginary number, i. Because sqrt(-1)=i, don't forget this formula.

So sqrt(-8)=2i*sqrt(2) and -2i*sqrt(2).

Answer:(i)  84 cm.

(ii)  5635π cm^2

Step-by-step explanation:

(i)

The volume of the cone = 1/3 π r^2 h

= 1/3 π 35^2 h.

The volume of the hemisphere = 2/3 π 35^3.

As the volume of the cone is 1 1/5 ( = 6/5) times the volume of the hemisphere:

1/3 π 35^2 h =  2/3 π 35^3 * 6/5

h =  2/3 π 35^3 * 6/5 /   1/3 π 35^2

h =  84 cm (answer).

(ii)  Surface area of the hemisphere = 2 π * 35^2 =   2450π cm^2.

Surface area of the cone = π r l  where l = slant height.

l = √(35^2 + 84^2) =  91 cm.

So the surface area of the cone =  35*91 π = 3185π.

So the  total surface area of the solid is  3185π + 2450π

= 5635π cm^2.

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Answer:

4.23 * 10³ = 4.23 * 1000 = 4,230

Step-by-step explanation:

We should know that;

10³ = 10 * 10 * 10 = 1000

∴ 4.23 * 10³ = 4.23 * 1000 = [tex]\frac{423}{100}*1000[/tex] = 4,230

Answer:

4.23 * 10³ = 4.23 * 1000 = 4,230

Step-by-step explanation:

Answer:56

Step-by-step explanation:

difference between 36 and 18 is 18

difference between 96 and 72 is 24

so that means 18, 20, 22, 24

I HOPE THIS HELPS :)

Answer:

The debris will be at a height of 56 ft when time is 0.5 s and 7 s.

Step-by-step explanation:

Given:

Initial speed of debris is, [tex]s=120\ ft/s[/tex]

The height 'h' of the debris above the ground is given as:

[tex]h(t)=-16t^2+120t[/tex]

As per question, [tex]h(t)=56\ ft[/tex]. Therefore,

[tex]56=-16t^2+120t[/tex]

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

[tex]-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0[/tex]

Using quadratic formula to solve for 't', we get:

[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s[/tex]

Therefore, the debris will reach a height of 56 ft twice.

When time [tex]t=0.5\ s[/tex] during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at [tex]t=7\ s[/tex], the height is 56 ft.

Final answer:

To find when the debris will be 56 feet above the ground, we solve the quadratic equation -16t² + 120t = 56 using the quadratic formula. This will yield two possible solutions for t, which are the times at which the debris reaches 56 feet.

Explanation:

To determine when the debris will be 56 feet above the ground, we need to solve the given quadratic equation for t, which represents time in seconds. The equation provided is:

h = -16t² + 120t

Where h is the height in feet. To find the times when the debris is 56 feet above the ground, we set h to 56:

56 = -16t² + 120t

This equation can be solved by factoring or using the quadratic formula. To factor, we first set the equation to zero:

-16t² + 120t - 56 = 0

16t² - 120t + 56 = 0

Dividing by 4

4t² - 30t + 14 = 0

Again reducing by dividing by 2

2t² - 15t + 7 = 0

Now, we need two numbers which add to give 15 and multiply to give 14.

The two numbers are 1 and 14.

2t²- 14t - t + 7 = 0

2t (t - 7) - 1(t - 7) = 0

(t - 7)(2t - 1) = 0

t = 7 or 1/2

Since 1/2 second cannot be an answer, the required answer is 7 seconds

Answer:

12.5

Step-by-step explanation:

5/2*5=12.5

Answer:

Your answer is 12.5 meters long

Step-by-step explanation:

so you would want to see how long each 1/5 is so if 2/5 is 5 then 1/5 would be half of that so 2.5 then times that by 5 to get your answer which is 12.5.

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{5}}}\implies \cfrac{-6}{-7}\implies \cfrac{6}{7}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{6}{7}}(x-\stackrel{x_1}{5}) \implies y-3=\cfrac{6}{7}x-\cfrac{30}{7} \\\\\\ y=\cfrac{6}{7}x-\cfrac{30}{7}+3\implies y = \cfrac{6}{7}x+\cfrac{-30+21}{7}\implies y=\cfrac{6}{7}x-\cfrac{9}{7}[/tex]

Answer:

-6/7? I think I'm right but make sure to comment me to let me know!

Step-by-step explanation:

Okay so the equation for slope intercept form is y2-y1/x2-x1. So we can substitute -3-3=-6 and -2-5=-7 So I think you get -6/7

-viridiancat4, an 8th grader

Answer:

y = - 4x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and c the y- intercept )

Here m = - 4, thus

y = - 4x + b ← is the partial equation

To find b substitute (- 2, 5) into the partial equation

5 = 8 + b ⇒ b = 5 - 8 = - 3

y = - 4x - 3 ← equation of line

Answer:

y= -4x-3

Step-by-step explanation:

to find this, the first step is easy. We know the slope is -4 so we have y= -4x+b. Then we to find the y intersept, so we take the point that we have (-2,5) and make x (the first number) equal to 0. to do this we add two, which means to subtract 8 from give because the slope is -4. This gives the point (0,-3). So the equation is y= -4x-3.

ANSWER:

1/2 (x+3)(x+5)

= 1/2(x^2+8x+15)_This is the right answer

= x^2/2 + 8x/2 + 15/2

= x^2/2 + 4x + 15/2

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Answer:

4.  35 times larger

Step-by-step explanation:

Doing Question #4 Only

4.

Before we see this problem's solution. Lets get a background.

Suppose something has an area of "A" sq. meters.

and

Suppose another land has an area of "B" sq. meters.

and suppose A > B

If we want to know how many times A is larger than B, we simply have to divide the larger one (A) by the smaller one (B).

Now, onto our question:

We want to know how many times larger the national is than state park. So we divide the area of national by the area of state. That would be:

[tex]\frac{7*10^8}{2*10^7}[/tex]

Since the numbers are in scientific notation, we look at the rule below on how to divide scientific notation numbers:

[tex]\frac{a*10^b}{c*10^d}=(\frac{a}{c})*10^{b-d}[/tex]

Now, we apply the rule:

[tex]\frac{7*10^8}{2*10^7}\\=\frac{7}{2}*10^{8-7}\\=3.5*10^1\\=3.5*10\\=35[/tex]

So, the national park is 35 times larger than the state park.

The total number of tickets sold over these two days is 9,640.

Let's complete the table for Saturday:

For Saturday:

Adult Tickets: [tex]\(2 \times \text{Number of Adult Tickets on Friday}\)[/tex]

Children's Tickets: [tex]\(3 \times \text{Number of Children's Tickets on Friday}\)[/tex]

Using the information from Friday's sales:

Adult Tickets on Saturday: [tex]\(2 \times 976 = 1952\)[/tex]

Children's Tickets on Saturday: [tex]\(3 \times 1678 = 5034\)[/tex]

Now, we can complete the table:

[tex]\begin{array}{ccc}\text { Day } & \text { Adult Tickets } & \text { Children's Tickets } \\\text { Friday } & 976 & 1,678 \\\text { Saturday } & 1,952 & 5,034\end{array}[/tex]

To find the total number of tickets sold over these two days, add the tickets for Friday and Saturday:

Total Tickets Sold = Adult Tickets on Friday + Children's Tickets on Friday + Adult Tickets on Saturday + Children's Tickets on Saturday

[tex]\[ \text{Total Tickets Sold} = 976 + 1,678 + 1,952 + 5,034 \][/tex]

[tex]\[ \text{Total Tickets Sold} = 9,640 \][/tex]

Answer:

B

Step-by-step explanation:

For the arcs WX and YZ to be congruent.

The angles subtended at the centre of the circle must be congruent.

This is not the case here as arc WX subtends 80° and arc YZ subtends 35°

Thus arc WX and arc YZ are not congruent.

Step-by-step explanation:

x+6=0

x=(-6)

so if x =(-6) it will be undefined.

Answer:

x = −3

or

x = 6

Any number multiplied by 0 is 0. This means that either x+3 or x−6 can be 0.

(x+3)(x−6) to be 0. if x+3=0, then x=−3 if x−6=0,

then x=6 hence, x can either be −3

or 6.x= −3 or x=6

Answer:

ASA rule.

Step-by-step explanation:

See the diagram with the problem.

Given that Δ ABC and Δ ABD are congruent i.e. Δ ABC ≅ Δ ABD.

Now, we have to select the rule by which we can say that Δ ABC and Δ ABD are congruent.

Given in the figure that between Δ ABC and Δ ABD,

(i) ∠ CAB = ∠ BAD

(ii) AB is the common side, and  

(iii) ∠ ABC = ∠ ABD

Therefore, by Angle-Side-Angle i.e. ASA rule we can say that  Δ ABC ≅ Δ ABD.

Hence, option 2 is correct. (Answer)

Answer: B the second choice

Step-by-step explanation:

Answer:

Hey.

By what percentage was the price of the video games reduced ?

By 25%.

Step-by-step explanation:

$60 is the 100% price.

Now we have to find what percentage belongs to the reduced price, $45.

45×100/60 = 75.

75% is the percentage of the reduced price.

We can find the difference between them by doing a substraction.

100%-75% = 25%.

Hope I helped you !

Answer:

0.0322580645

Step-by-step explanation:

i feel like u meant 2418/78 but ok

Final answer:

To calculate 78 divided by 2418, you will get approximately 0.0322 when rounded to four significant figures.

Explanation:

The question asks for the result of the division 78 divided by 2418.

To find the answer, you need to perform the division either manually or by using a calculator. When you do so, you will find that the answer is a decimal. Taking the division to four significant figures, which is a common practice in mathematics to maintain precision without excessive digits, the calculation would look as follows:

78 ÷ 2418 = 0.0322

Thus, when dividing 78 by 2418, the result is approximately 0.0322 to four significant figures.

Answer:

The distance, D for the given expression is 70 miles

Step-by-step explanation:

Given as :

D = r t

r = 35 mi/ h

t = 2 h

Now, According to question

Distance = speed × Time

Where speed = r

Time = t

Distance = D

Now, from question

D = 35 miles per hour × 2 hours

So, D = 70 miles

Hence The distance, D for the given expression is 70 miles  . answer

Final answer:

The exact amount of the check is $5.

Explanation:

To solve this problem, we can set up an equation based on the given information. Let's assume that the amount of the check is x dollars. According to the problem, the man received the amount in cents instead of dollars, so he actually received x dollars and x cents. He then spent a nickel, which means he had x dollars and (x-5) cents left. It's stated that he had exactly twice the amount of the check after spending the nickel, so we can write the equation:

x + (x-5) = 2x

Simplifying the equation, we get:

2x - x = 5

x = 5

Therefore, the exact amount of the check is $5.

Abigail has eaten 3/8 of a pound of candy.

This is the answer because 3/4 is equivalent to 6/8, and if Abigail has eaten 3/8 of a pound of that 6/8 pound of candy, then there will be 3/8 remaining (6/8 - 3/8 = 3/8).

To find out how much candy Abigail has eaten, we subtract the amount of candy she has left (3/8 of a pound) from the original amount she bought (3/4 of a pound). The calculation shows that Abigail has eaten 3/8 of a pound of candy.

The student is asking how much candy Abigail has eaten if she originally bought 3/4 of a pound and now has 3/8 of a pound left. To calculate the amount of candy eaten, we subtract the amount left from the original amount. Since we are working with fractions, we ensure the denominators are the same before subtracting.

The steps to solve the problem are as follows:

Original amount of candy: 3/4 pound

Amount left: 3/8 pound

Calculate how much has been eaten: (3/4) - (3/8)

Convert the first fraction to have a denominator of 8: (6/8) - (3/8)

Subtract the second fraction from the first: (6/8) - (3/8) = 3/8

Abigail has eaten 3/8 of a pound of candy.