Find the solutions of the given equation.

25x^2+64=289

The easiest way to do this is to start with the power of 5 that is just under 219.

125 would be the closest power of  5

Now subtract 125 from 219 = 94

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

The highest power of 5 closest to 94 is 25. You have to multiply 25 * 3 to get a number close enough to 94 that leaves a remainder under 25

94 - 75 = 19

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

19 - 3 * 5 = 4 Same argument as above.

Answer

219_10 = 1334_5

Answer:

1334/5

Step-by-step explanation:

We are given

edge of cube =x

we know that formula for volume of cube

[tex]V=x^3[/tex]

we are given

[tex]V=\frac{1}{8} cm^3[/tex]

we can plug value

[tex]x^3=\frac{1}{8} cm^3[/tex]

now, we can solve for x

[tex]\sqrt[3]{x^3} =\sqrt[3]{\frac{1}{8} cm^3 }[/tex]

[tex]x=\frac{1}{2} cm[/tex]............Answer

Answer:

1/2 cm

Step-by-step explanation:

We are given

initial population is 5891

so, [tex]P_i=5891[/tex]

Population after 50 years is 5178

so, [tex]P_f=5178[/tex]

now, we can find percent error

so, we can use formula

[tex]error=\frac{P_i-P_f}{P_i}\times 100[/tex]

now, we can plug values

[tex]error=\frac{5891-5178}{5891}\times 100[/tex]

now, we can simplify it

so, we get

The percent decrease is 12.1032%.........Answer

First: work out the difference (decrease) between the two numbers you are comparing by the formula

Decrease = Original Number - New Number

In your case,

[tex]\text{Decrease}=5891-5178=713.[/tex]

Second: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100

In your case,

[tex]\%\text{Decrease}=\dfrac{713}{5891}\cdot 100\%=12.1\%.[/tex]

Answer: The percent decrease is approximately  12.1%.

3. AB≅CE

4.CE≅AC

5.transitive property of congruence

6. definition of a isosceles triangle

First of all, we need to do the expression in parenthesis first.

(4% - 2.25%) = 1.75%

Now, we convert the percent into an integer.

1.75% = 0.0175

Then, we multiply 44.5 by 0.0175

and we get 0.77875.

We have to round the number to the nearest cent.

0.77875 is roughly 0.78

So the answer is $0.78.

Answer:

Option a

Step-by-step explanation:

Given that temperature originally was t.

It was decreasing continuously overnight.

finally the temperature reading was -12.8 degree C

Given that it decreased by 15.2 degree C

This means original temperature -15.2 = new temperature -12.8

i.e. t-15.2 = -12.8 is the correct equation.

Option a is right.

Verify:

Solve to get t = 15.2-12.8 = 2.4

Hence when 2.4 decreases by 15.2 we get new temperature

= 2.4-15.2 = -12.8

First take note he only has $20 and the bag he must buy is $12.55. Also the loose seeds are $1.49 per pound.

To solve subtract 12.55 from 20

20-12.55=7.45

So after buying the 10 lb bag he has $7.45 left now divide that by 1.49

7.45/1.49=5

So after buying the 10 lb bag he can also buy 5 lb of the loose seeds!

Total number of baseball cards Jessica has = 1368 cards.

Total number of baseball cards Thomas has = 1633 cards.

We need to find who has more baseball cards.

We can see 1633 is greater than 1368, because we have hundreds digit in 1633 is 6 and hundreds digit in 1368 is 3.

6 is greater than 3.  Therefore 1633 is greater than 1368.

Answer:Thomas

Step-by-step explanation:

1633 > 1368

t + 23 > 1     subtract 23 from both sides

t + 23 - 23 > 1 - 23

t > -22

Let x represent the amount of savings

[tex]\frac{3}{4}[/tex] of savings minus tv equals zero

[tex]\frac{3}{4}x[/tex] - 200 = 0

[tex]\frac{3}{4}x[/tex] = 200

3x = 4(200)

[tex]x = \frac{4(200)}{3}[/tex]

x = 266.67

Answer: $266.67

We are given that initially there were 40 people in the audience.

And an up-and-coming band has seen a 50% monthly increase in the the number of audience members at their concerts.

The number of audience members is represented by y variable and

Number of months is represented by x variable.

So, the exponential function would be

y= a(b)^x

Where a is the initial value, b is the growth factors.

a= 40 and b= 1+ 0.50 = 1.50.

Therefore,

y= 40(1.50)^x is the exponential function situation.

Let us check some point on the graph.

If we plug x=0, we get initial value 40.

If we pug x=2, we get

y=40(1.50)^2 = 40(2.25) = 90.

Graph C represents y=40 at x=0 and y=90 at x=2.

If you're on Plato the answer would be C

Answer:  Yolanda's mistake is that she is assuming 105 is same as 10 x 5 .

Explanation:Here 105 represents a three digit number where 1 is at hundreds place,0 is at tens place and 5 is at once place and it can be written as the product  of its factors 5 and 21 i.e 105=5×21 =21+21+21+21+21+21=105(by adding once place and tens place), where as 10×5 represents 5 times number 10 i.e.10+10+10+10+10=50(by adding once place and tens place)

So ,assuming 105 is same as 10 x 5 is her mistake.

Answer:

y = 44+22m

Step-by-step explanation:

Given that a taxi has a minimum charge of 44 dollar upto 1 mile and adds 22 for every additional 1 mile.

If a person travels 1 miles his charges are 44 dollar

If he travels >1 miles charges are 4 dollar +22(extra miles )

Let y be the charges and m be the no of miles.

Then the equation for y in terms of m would be

y =44+22m

is the correct answer.

1) Given

2) m∠1 + m∠2 = 90°

3) BD bisects ∠ADC

4) definition of angle bisector

5) definition of congruency

6) m∠1 + m∠3 = 90°

7) ∠1 is complementary to ∠3          (7) definition of complementary

If there is a drop down box, and my answer is not an option, type in the options in the comment box and I will let you know which theorems (or definitions) are the same as my answer.

how did you gett such a hard question (yes im asking in an awnser box)

Answer: 12.6

Step-by-step explanation:

  (0 + 11 + 13 + 2 + 20 + 3 + 40 + 4 + 40 + 5 + 13 + 6 + 7)/13

= 164/13

= 12.6

To divide the polynomial [tex]6x^2+11x-3[/tex] by the polynomial [tex]2x-1,[/tex] you have to do such steps:

1 step. Multiply the polynomial [tex]2x-1[/tex] by [tex]3x[/tex]. You get the polynomial [tex]6x^2-3x.[/tex]

2 step. Subtract the polynomial  [tex]6x^2-3x[/tex] fro mthe polynomial [tex]6x^2+11x-3:[/tex]

[tex]6x^2+11x-3-(6x^2-3x)=6x^2+11x-3-6x^2+3x=14x-3.[/tex]

Step 3. Multiply the polynomial [tex]2x-1[/tex] by [tex]7[/tex] to get the polynomial [tex]14x-7.[/tex]

Step 4. Subtract the polynomial  [tex]14x-7[/tex] from the polynomial [tex]14x-3:[/tex]

[tex]14x-3-(14x-7)=14x-3-14x+7=4.[/tex]

Step 5. Write the division result:

[tex]6x^2+11x-3=(2x-1)(3x+7)+4.[/tex]

Here the quotient is the polynomial [tex]3x+7[/tex] and the remainder is the polynomial [tex]4.[/tex]

Answer: the remainder is 4.

Answer:

-1

Step-by-step explanation:

Just took the test

Answer:

The ferry can travel [tex]\frac{7}{18}[/tex] of the distance between the two ports in one hour.

Step-by-step explanation:

A ferry traveled [tex]\frac{1}{6}[/tex] of the distance between two ports in [tex]\frac{3}{7}[/tex] hour.

Suppose, the ferry traveled [tex]x[/tex] of the distance between the two ports in one hour.

So, the equation according to the ratio of "distance" to "time" will be.......

[tex]\frac{\frac{1}{6}}{\frac{3}{7}} =\frac{x}{1} \\ \\ x=\frac{1}{6}\times \frac{7}{3}= \frac{7}{18}[/tex]

Thus, the ferry can travel [tex]\frac{7}{18}[/tex] of the distance between the two ports in one hour.

Answer:

14.64 cm

Step-by-step explanation:

this problem is finding radius of a circle from the circumference given.

Circumference of a circle = 2(3.14) r

Using the above we can find one if we know the other.  In our case we know circumference and calculate radius.

Circumference = 2(3.14)r= 92 cm

Hence r = 92/2(3.14) = 14.6497cm

apprxoximately 14.64 cm is close to the answer

Hence answer is 14.64 cm.

Answer:

14.64 cm

Step-by-step explanation:

The circumference of a planting pot = 92 cm

To find the measurement of the plant which is planted directly planted in the middle of the pot, we need to find the radius of the planting pot.

We know that the formula of the circumference of a circle is:

Circumference = [tex]2\pi r[/tex]

Therefore, putting the value of the circumference in the formula to get:

92 = 2 x 3.14 x r

r = 92 / (3.12 x 2) = 14.64 cm

Therefore the plant is 14.64 cm long.

Answer:

False.

Step-by-step explanation:

[tex] \dfrac{1}{x^{-3}} = x^3 [/tex]

[tex] x^3 [/tex] is a simplified expression. The given expression is not simplified.

For this case, we have the expression given by:

[tex]a + b = c\\[/tex]

This expression turns out to be generic.

The commutative property of the addition states that the order of the addends does not alter the sum. Thus it is concluded that the previous expression above can be written as:

[tex]b + a = c\\[/tex]

In this way [tex]7 + 4 = 11[/tex], applying the commutative property of the addition, it can be written as:

[tex]4 + 7 = 11\\[/tex]

Answer:

Option A

Answer: 4,398,200

Step-by-step explanation:

4, 398, 202    

the underlined 2 is in the 100's place.  look at the number to the right of it.  If that number is greater than or equal to 5, then the 2 is rounded up.  Otherwise, the 2 remains the same.

The number to the right of the underlined 2 is 0, so the 2 remains the same.  All digits to the right will become 0s.

Answer: Option D. 1,778

Solution:

Standard brick:

Width: w=3.625 in

Height: h=2.25 in

Length: l=7.625 in

Volumen of one standard brick: v

v=w*h*l

v=(3.625 in)*(2.25 in)*(7.625 in)

v=62.19140625 in^3

Pallet of bricks:

Side: s=4 feet

s=(4 feet)*(12 in / 1 feet)→s=48 in

Volume of a pallet of bricks: V=s^3

V=(48 in)^3

V=110,592 in^3

Number of bricks could be in  a pallet: n

n=V/v

n=(110,592 in^3) / (62.19140625 in^3)

n=1,778.252119

n=1,778

Can someone confirm if this is the answer or not?

we are given

[tex]\frac{2x^5-x^4+3x^2-x+5}{x-1}[/tex]

Here , we have

[tex]dividend=2x^5-x^4+3x^2-x+5[/tex]

[tex]divisor=x-1[/tex]

now, we can use synthetic division

so, we get

[tex]Quotient=2x^4+x^3+x^2+4x+3[/tex]

[tex]Remainder=8[/tex]

now, we can write in fraction form

[tex]\frac{2x^5+x^4+3x^2-x+5}{x-1}=(2x^4+x^3+x^2+4x+3)+\frac{8}{x-1}[/tex]............Answer

To divide using synthetic division, arrange the polynomial in descending order, set up the synthetic division table, find the root of the divisor, perform the synthetic division, and read the coefficients of the quotient. In this case, the quotient is 2x^3 + x^2 + 4x + 3 with a remainder of -1.

To divide using synthetic division, you need to follow these steps:

In this case, the polynomial is 2x5 - x4 + 3x2 - x + 5, and the divisor is x - 1. Using synthetic division, we divide the coefficients:

The coefficients in the bottom row of the synthetic division table are 2, 1, 4, 3. Therefore, the quotient is 2x3 + x2 + 4x + 3, and the remainder is -1.

Answer:

t = 3.5 sec

Step-by-step explanation:

The equation that represents the position of the ball as a function of time is the following:

[tex]h(t) =P_{o} + V_{o}t+\frac{1}{2}2at^2[/tex]

Where:

[tex]P_{o}[/tex] = Initial position of the ball (4 feet tall)

[tex]V_{0}[/tex] = Initial speed of the ball (55feet / s)

a = acceleration (9.8 [tex]\frac{m}{s^2}[/tex], or in this case 32.16[tex]\frac{ft}{s^2}[/tex])

t = time in seconds

Then we want to know how long it takes to get to the ground, for this we equal h (t) = 0 and clear t.

So:

[tex]0 = 4 + 55t -16.08t ^ 2[/tex]

Solving the second degree equation we have:

[tex]\frac{-b+\sqrt{b ^ 2-4ac}}{2a} \\ \frac{-b-\sqrt{b ^ 2-4ac}}{2a}[/tex]

[tex]\frac{-55+\sqrt{55^2-4 (-16.08) 4}}{2 (-16.08)}= -0.0712\\\frac{-55-\sqrt{55^2-4 (-16.08) 4}}{2 (-16.08)} = 3.492[/tex]

t = -0.071 sec

t = 3.5 sec

We must take the positive solution.

So:

t = 3.5 sec

Answer:

4 tickets were sold

Step-by-step explanation:if you have 100 of anything. 5 sets of 20=100

Answer:

Answer: x = 100

Step-by-step explanation:

(20)(x) = (5)(x) = 20/5 = 5x/5 = 100

I just answered and got it correct.

Answer:

Jenni spent 44

Step-by-step explanation:

Let the amount spent by Jenni be x

Let the amount spent by Sara be  2x which also equals 88

2x = 88

x = ?

Cross multiplying gives:

x/2x × 88 = 44

Jenni therefore spent 44

Answer: 93 grams Zinc

Step-by-step explanation:

3 Zinc : 13 Copper

x 31       x 31            

93 Zinc,     403 Copper

or

set up a proportion, cross multiply, and solve for the variable:

[tex]\frac{Zinc}{Copper}: \frac{3}{13} = \frac{x}{403}[/tex]

3(403) = 13(x)

[tex]\frac{3(403)}{13} = x[/tex]

3(31) = x

93 = x

The amount of zinc in the chemical is determined by using the given ratio of zinc to copper and applying it to the given amount of copper. Step-by-step calculations reveal the quantity of zinc to be 93 grams.

The question is asking for the amount of zinc in a chemical where the ratio of zinc to copper is 3:13. To find out this, we need to solve for zinc in terms of the given amount of copper.

First, understand that the ratio means for every 3 grams of zinc, there are 13 grams of copper. Now, simply set up a proportion where 3/13 = x/403. Here x is the amount of zinc in grams we are trying to find. 3/13 is the zinc to copper ratio and 403 is the known amount of copper in grams.

When you cross multiply and solve for x, you'll find that x = 3 * 403 / 13 = 93 grams. This means, if there are 403 grams of copper, then there must be "93 grams of zinc".

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