mr ramos thumb measures 4 cm. Express this length in meters

Steps:

[tex]x=\frac{-8+\sqrt{8^2-4\cdot \:1\cdot \:20}}{2\cdot \:1}: -4+2i[/tex]

[tex]x=\frac{-8-\sqrt{8^2-4\cdot \:1\cdot \:20}}{2\cdot \:1} -4-2i[/tex]

=\frac{-8-\sqrt{16}i}{2\cdot \:1}[tex]=-8-\sqrt{16}i[/tex]

[tex]=\frac{-8-\sqrt{16}i}{2}[/tex]

[tex]=\frac{-8-4i}{2}[/tex]

[tex]=-2\left(2+i\right)[/tex]

[tex]=-4-2i[/tex]

[tex]x=-4+2i,\:x=-4-2i[/tex]

Answer:you can use the quadratic formula but if you have to factor do the following:

x^2+8x+20=0

add -4 to both sides of the equation to complete the square

x^2+8x+20+(-4)=0+(-4)

x^2+8x+16=-4

(x+4)^2=-4

take the square root of both sides

x+4=+sqrt(-4)

x+4=+sqrt[(4)(-1)]

x+4=+2sqrt(-1) where sqrt(-1)=i, a complex number

x+4=+2i

x=-4+2i

x=-4+2i and x=-4-2i

you would get the same answer using the quadratic formula

Step-by-step explanation:

We are given the  volume of a spherical tank =  790.272 π cubic feet.

We need to find the diameter of the container .

We know formula for volume of a sphere.

[tex]V=\frac{3}{4}(r^{3}\pi)[/tex]

Where r is the radius.

Plugging V= 790.272 π  in the above formula, we get

[tex]790.272\pi =\frac{3}{4}(r^{3}\pi)[/tex]

Dividing both sides by π, we get

790.272 =[tex]\frac{4}{3}(r^{3})[/tex]

Multiplying both sides by 3, we get

2370.816 = [tex]4r^3[/tex]

Dividing both sides by 4, we get

592.704 = [tex]r^3[/tex]

Taking cube root on both sides, we get

r=8.4.

Diamater is 2 times of radius, that is 2 × 8.4 = 16.8

Therefore, the diameter of the container = 16.8 feet.

To represent 8.2 using base 10 blocks, you need 8 one blocks and 2 tenth blocks, where one blocks represent 1 and tenth blocks represent 0.1. This method is effective for visualizing numbers in base 10.

To represent the number 8.2 using base 10 blocks, we use different sizes of blocks to represent different place values in base 10.

Each size block is worth a different value based on its place in the number.

To represent 8.2, we would need:

This method of representation helps in visualizing and understanding the value of numbers in the base 10 system. It's particularly useful in educational settings for explaining the concept of place values and decimals.

Answer:

2 student who want to jump are measured

3/5(30) = 18.

60% of the days in April it rained.

It rained 18 days in April.

Best of luck.

60% of it rained cause 3/5 is equaled to 60% so 18 Yeah.

Answer:

$82.5

Step-by-step explanation:

We can calculate it with a direct rule of 3. As it has a 30% off, the remaining price is the 70% and we want to know how much is the 100%

[tex]70\% -\!\!\!-\!\!\!- \$57.75\\ 100\% -\!\!\!-\!\!\!- \$ x[/tex]

We use the formula of the direct rule of 3:

[tex]x = \frac {100/100*57.75}{70/100} \\ \\ x = \frac {57.75}{70/100}\\ x = 57.75 * 100/70[/tex]

x = 82.5

The original price of the stereo was $82.5

The original price of the stereo is 82.5

Since the car stereo system was on sale for 30% off, this means that it was sold for 100% - 30% = 70% of the original price.

Let the original price be represented by x

Therefore, 70% of x will be 57.75

70/100 × x = 57.75

0.7 × x = 57.75

0.7x = 57.75

Divide both side by 0.7

0.7x/0.7 = 57.75/0.7

x = 82.5

The original price of the stereo is 82.5

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Since one piece is four time the length x, we can represent that as 4x.

Thus making the equation:

4x+x=275

5x=275

x=55

4(55)=220

220+55=275

So, the length of the longer piece is 220 inches, and the length of the shorter piece is 55 inches.

In order to find the length of the shorter piece of pipe, we can set up and solve the equation x + 4x = 275. When simplified, we get 5x = 275, and by dividing both sides of the equation by 5, we find that x = 55. This tells us that the length of the shorter piece is 55 inches.

To solve this problem, let's denote the shorter piece as x. Because the other piece is four times the length of the shorter one, it can be denoted as 4x. We know that these two pieces put together make the total length of the initial pipe, which is 275 inches. Therefore, we can set up the equation: x + 4x = 275.

Simplifying this equation, we get 5x = 275. To get the value of x, we need to divide both sides of this equation by 5, resulting in x = 55. Hence, the length of the shorter piece is 55 inches.

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Let cost of Emma's phone = x

Given that cost of Sophie's phone = 640

Then ratio of their phones cost will be x:640 or x/640

Given that ratio of their phones cost is 7:8 or 7/8

So both ratios will be equal.

[tex]\frac{x}{640}=\frac{7}{8}[/tex]

[tex]x=\frac{7}{8}*640[/tex]

x=560

So the new ratio of the cost of their phones will be 560:640

Now we have to find about how much should the prices of their phones decrease in order to have a ratio of 9:11.

So let that decreased amount is k then we will get equation :

[tex]\frac{560-k}{640-k}=\frac{9}{11}[/tex]

11(560-k)=9(640-k)

6160-11k=5760-9k

6160-5760=11k-9k

400=2k

200=k

Hence final answer is prices of their phones should decrease by 200 in order to have a ratio of 9:11.

Answer:

For the ratio between the price of the phones to be 9:11, the price of Emma's phone must decrease from $ 560 to $ 523.66. That is, the price of Emma's phone should decrease $ 36,364

Step-by-step explanation:

To answer this question, call x on Emma's phone and z on Sophie's phone.

We know that the price relationship between x and z is 7: 8

This means that:

[tex]\frac{7}{8} =\frac{x}{z}[/tex]

We know that the price of Sophie's phone is $ 640

Entoces z = 640  

Now we clear x

[tex]\frac{7}{8} =\frac{x}{640}\\ x =640}\frac{7}{8}=560\\ x = 560[/tex]

Then, if the new relationship is 9:11 then:

[tex]\frac{9}{11} =\frac{x}{640}[/tex]

x = $523,636

For the ratio between the price of the phones to be 9:11, the price of Emma's phone must decrease from $ 560 to $ 523.66. That is, the price of Emma's phone should decrease $ 36,364

15 and 45 becuase bith 3 and 8 can go into them.

Answer-

The coordinates of the solution to the system of equations is (4, -3)

Solution-

According to the graph the equations are,

[tex]y=-\frac{1}{2}x-1\\\\y=\frac{1}{4}x-4[/tex]

We can get the coordinates of the solution to the system of equations, by substitution.

[tex]\Rightarrow y=\frac{1}{4}x-4[/tex]

Putting the value of y in first equation,

[tex]\Rightarrow \frac{1}{4}x-4=-\frac{1}{2}x-1[/tex]

[tex]\Rightarrow \frac{1}{4}x+\frac{1}{2}x=-1+4[/tex]

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

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

[tex]\Rightarrow x=4[/tex]

Putting the value of x in the first equation,

[tex]y=-\frac{1}{2}\times 4-1=-2-1=-3[/tex]

Therefore, the coordinates of the solution to the system of equations is (4, -3)

Answer: Option B. exponential decay

Solution:

If initially the number of competitors is n

If the number of round is "r" and the number of competitors after "r" rounds is N(r)

1) After the first round (r=1), the number of competitors is:

N(r)=N(1) = n * 50% = n * 50/100 →N(r)=N(1)=n*0.5=n*0.5^1

2) After the second round (r=2), the number of competitors is:

N(r)=N(2) = N(1) * 50% = (0.5 n)*(50/100)=(0.5n)*(0.5)→N(r)=N(2)=n*0.5^2

3) After the third round (r=3), the number of competitors is:

N(r)=N(3)=N(2)*50%=(n*0.5^2)*(50/100)=(n*0.5^2)*(0.5)→N(r)=N(3)=n*0.5^3

Then:

For r=1→N(r)=N(1)=n*0.5^1

For r=2→N(r)=N(2)=n*0.5^2

For r=3→N(r)=N(3)=n*0.5^3

In general: N(r)=n*0.5^r

This is an exponential function because the independent variable "r" is in the exponent, and because the number of competitors (funcion N(r) )decrease with the number of rounds the type of relationship most appropiately models this situation is an exponential decay

The reduction by 50% of competitors each round in a chess tournament is modeled by an exponential decay relationship, not a linear decrease, as it depends on the current number of competitors.

The chess tournament with the number of competitors decreasing by 50% each round is best modeled by a exponential decay relationship. This is because with each round, the number of competitors is halved, which is a rate that depends on the current number of competitors. (A) linear decrease would imply a constant decrease irrespective of the current number of competitors, which is not the case here.

Exponential relationships can be represented by mathematical functions where the rate of change is proportional to the current value. In contrast to exponential growth, where the quantity increases at a rate proportional to its current value, exponential decay describes a situation where the quantity is reduced by a certain factor over equal successive periods.

Answer:

3

Step-by-step explanation:

Its the number immediately before x

Answer:

What is the coefficient in the expression 3x13+4?

               3/13

Step-by-step explanation:

g(x):

flip f(x) over x-axist and next translate 2 units down.

Look at the picture.

Translations

y = f (x) + m up m units

y = f (x) - m down m units

y = f (x + m) left m units

y = f (x - m) right m units

Stretches/Shrinks

y = n · f (x) stretch vertically by a factor of n

y = 1/n · f (x) shrink vertically by a factor of m (stretch by 1/n)

y = f (1/n x) stretch horizonally by a factor of n

y = f (nx) shrink horizontally by a factor of n (stretch by 1/n)

Reflections

y = - f (x) reflect over x-axis (over line y = 0)

y = f (- x) reflect over y-axis (over line x = 0)

x = f (y) reflect over line y = x

8 + 5n = -27

5n = -35

n = -7

Answer,

- 1 1/4

Hope this helps :-)

Answer:

A) y=mx+b

Step-by-step explanation:

The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called y = mx + b form.

1) The solution of expression is, x = - 6

2) The solution is, - 26

We have to give that,

1) An expression is,

3x - 6 = 7x + 18

2) An expression,

65 - 4² (10 - 2) + 37

Now, Simplify the expressions as,

1) 3x - 6 = 7x + 18

Add 6 on both sides,

3x - 6 + 6 = 7x + 18 + 6

3x = 7x + 24

Subtract 7x on both sides,

3x - 7x = 24

- 4x = 24

Divide both sides by - 4,

x = - 24/4

x = - 6

Hence, Solution is, x = - 6

2) 65 - 4² (10 - 2) + 37

Apply the BODMAS rule,

65 - 16 (8) + 37

65 - 128 + 37

65 + 37 - 128

102 - 128

- 26

Therefore, the Solution is, - 26

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x + x+6 +x+12+x+18+ x+24 = 930

5x + 90 = 930

5x = 930 - 60

5x = 870

x = 174 (which is the smallest consec multiple of 6)

174 is answer.

Given that sum of 5 consecutive multiples of 6 is 930

To find the smallest multiple

The consecutive multiples of 6 would be of the form

6(k-2), 6(k-1), 6k, 6(k+1), 6(k+2) for some natural number k.

The sum would be

6(k-2)+ 6(k-1)+ 6k+ 6(k+1)+ 6(k+2)= 6(5k) = 930

Divide by 30

k = 930/30 = 31

Smallest number = 6(k-2) = 6(31-2)

= 6(29) = 174

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

Verify:

174+180+186+192+198 = 930

Hence verified

To find the X and Y intercepts from a slope intercept equation, first understand the equation structure (y = mx + b). The 'm' signifies the slope, and the 'b' indicates the y-intercept. To find the x-intercept, set y to zero and solve for x. To find the y-intercept, look at the 'b' value.

In a slope intercept equation written in the form y = mx + b, the x-intercept and y-intercept are determined by values of y and x when they equal zero respectively. The 'm' signifies the slope of the line, indicating the rise over run on the graph, and the 'b' indicates the y-intercept, which is the point at which the line intersects the y axis.

To find the y-intercept from a slope-intercept equation, you consider the 'b' in the equation. For instance, in the line graph, the y-intercept is 9, meaning the line crosses the y-axis at the point (0,9).

To find the x-intercept (the point where the line crosses the x-axis), you set y equal to zero and solve for x. If 'y' is equal to '0', then the equation becomes 0 = mx + b. Solving for 'x' in this equation will give the x-intercept.

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2 11/32 / 1 1/2 = 25/16 hope this helps you

[tex]6\cdot32=6(30+2)=(6)(30)+(6)(2)=180+12=192\\\\7\cdot29=7(30-1)=(7)(30)-(7)(1)=210-7=203[/tex]

Answer:

Step-by-step explanation:

You would first try to round the numbers to the nearest 10 and then multiply for a reasonable estimate. In other words, 40x70=2800

t<-3 should be the answer. I hope this helps

3 3/4 miles as a decimal is 3.75 miles. He rode for one hour. Average speed within an interval is (distance made) / (interval duration). So the average speed = 3.75 miles / 1 hour, or 3.75 mph.

Henrieta's work is incorrect. The correct answer is 0.04.

No, Henrieta's work is not correct. To divide 0.80 by 20, we need to divide the numerator (0.80) by the denominator (20).

Dividing 0.80 by 20, we get 0.04.

Therefore, the correct answer is 0.04.

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-2(x + 9)  = -8

Distributive property.

-2x - 18 = -8

Add 18 to both sides.

-2x = 10

Divide both sides by -2.

x = -5