In 2010, the national debt of the United States was about 14 trillion dollars. In 2003 it was about 7 x 10 to the 12 dollars. About how many times larger was the national debt in 2010 than 2003? THIS IS SCIENTIFIC NOTATION

The length of the larger piece lies in the interval [102.85 , 180) and the length of the smaller piece lies in the interval [0 , 77.15]

In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between.

Given here, that 3 times the larger piece is greater than 4 times the smaller piece. let the length of the larger piece be x and length of the smaller piece be 180-x,  then we get the following inequality-

3x >  4(180-x)

3x>720-4x

7x>720

x>102.85

therefore 102.85≤ x <180

Hence, the larger piece lies in the interval [102.85 , 180) and the length of the smaller piece lies in the interval [0 , 77.15]

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Answer:ANSWER

The correct answer is C

EXPLANATION

is just the y-value of the point where

That is, the image of 1.

If we were given the function

,we would have plug in 1 to find

Since the function is not given, we were given the graph so that we trace

from it.

So we read from the grid to find that y-value .

Each grid is one unit. So moving one unit on the x-axis and two units on the y-axis will give us the point

This means that,

ANSWER The correct answer is C EXPLANATION [tex]B(1)[/tex] is just - 1

Step-by-step explanation:

Answer:

1. Using your straightedge, draw a reference line, if one is not provided.

2. Copy the side of the square onto the reference line, starting at a point labeled A'.

3. Construct a perpendicular at point B' to the line through ab2.

4. Place your compass point at B', and copy the side of the square onto the perpendicular b'g. Label the end of the segment copy as point C.

5. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.

6. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.

7. Connect points A' to D, D to C, and C to B' to form a square.

Step-by-step explanation:

abcdefghijklmnopqrstuvwxyz

The graph of y = x⁴ is also a parabola that opens upward and it is an even function.

The blue graph represents a quadratic function and the red graph represents a biquadratic function.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We also know that graph of a quadratic function y = x² is a parabola,

Now, the graph of y = x⁴ will also be a parabola,

and it is more steeper or has a greater slope than the graph y = x² as the independent variable has a larger exponent value it is also an even function that is symmetric about the y-axis.

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EDMENTUM QUESTION:

Kayla set up an outdoor digital thermometer to record the temperature overnight as part of her science fair project. She began recording the temperature, in degrees Fahrenheit, at 10:00 p.m. Kayla modeled the overnight temperature with function t, where h represents the number of hours since 10:00 p.m. t(h) = 0.5h2 − 5h + 27.5

Answer: 15°F at 3:00 a.m.

Step-by-step explanation:

Number of days Julia took to learn 145 word is 21 days.

Given that, Julia knows 19 latin words. Each day, she learns 6 new words.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of days be x.

Here, 145-19=126

Number of days = 126/6

= 21

Therefore, number of days Julia took to learn 145 word is 21 days.

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Answer: C) mC > mA > mB is correct regarding the angles of the  triangle ABC.

Step-by-step explanation:

Given: In Δ ABC, the side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.

AB=4p-1 , AC=p+4 , BC=3p

where p+4 < 3p        [as p≥3]

3p < 4p-1          [as p≥3]

⇒  4p-1> 3p > p+4

⇒AB>BC>AC

Angle opposite to AB ,BC and AC is m∠C ,m∠A and m∠B.

Therefore mC > mB > mA    [∵Angle opposite to greater side is greater]

Thus , mC > mA > mB is correct regarding the angles of the  triangle ABC.

Answer:

C

Step-by-step explanation:

The unit rate for almonds is approximately $2.58 per pound.

To find the unit rate, we divide the total cost by the total quantity.

In this case, the total cost is $15.50 and the total quantity is 6 pounds.

So, the unit rate is:

[tex]\[ \text{Unit rate} = \frac{\text{Total cost}}{\text{Total quantity}} \][/tex]

[tex]\[ \text{Unit rate} = \frac{15.50}{6} \][/tex]

[tex]\[ \text{Unit rate} \approx \$2.58 \][/tex]

Rounding to the nearest cent, the unit rate is approximately $2.58 per pound.

Answer:

x = 1/2

Step-by-step explanation:

-3x +1 +10x = x + 4

7x + 1 = x + 4

6x + 1 =4

6x = 3

x = 3/6

x = 1/2

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of x in the equation -3x + 1 + 10x = x + 4 is 1/2.

x = 1/2

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 6 is an equation.

3x + 4 = 6 is an equation.

x + 5 is an equation.

3x + 4x + 5 is an equation.

We have,

The equation:

-3x + 1 + 10x = x + 4

We will solve for x.

Add 3x on both sides.

1 + 10x = x + 4 + 3x

1 + 10x = 4x + 4

Subtract 4x on both sides.

1 + 10x - 4x = 4

1 + 6x = 4

Subtract 1 on both sides.

6x = 4 - 1

6x = 3

Divide 6 on both sides.

x = 3/6

x = 1/2

Thus,

The value of x in the equation -3x + 1 + 10x = x + 4 is 1/2.

x = 1/2

Option A is the correct answer.

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Option: B is the correct answer.

B.  The number of excluded values of a rational expression cannot exceed the degree of the denominator.

We know that a rational expression is a expression of the form:

[tex]\dfrac{p(x)}{q(x)}[/tex]

where p(x) and q(x) are polynomials.

Excluded value--

The excluded value of a rational expression are the values where the denominator of the expression is zero.

Also, the number of zeros of a polynomial is always less than or equal to degree of the polynomial.

Hence, the  number of excluded values of a rational expression cannot exceed the degree of the denominator.

         The answer is:

            Option: B

Option: A is the correct answer.

              The axis of symmetry is:

                      A.    x=3/2      

We are given a graph as:

[tex]y+3x-6=-3(x-2)^2+4[/tex]

and

[tex]y=-3(x-2)^2+4+6-3x[/tex]

and

[tex]y=-3[(x-2)^2+x]+10\\\\i.e.\\\\y=-3[x^2+4-4x+x]+10\\\\i.e.\\\\y=-3[x^2-3x+4]+10[/tex]

This equation could also be written in the form:

[tex]y=-3[x^2-3x+4-\dfrac{9}{4}+\dfrac{9}{4}]+10\\\\i.e.\\\\y=-3[(x-\dfrac{3}{2})^2+4-\dfrac{9}{4}]+10\\\\i.e.\\\\y=-3[(x-\dfrac{3}{2})^2+\dfrac{7}{4}]+10\\\\i.e.\\\\y=-3(x-\dfrac{3}{2})^2-3\times \dfrac{7}{4}+10\\\\i.e.\\\\y=-3(x-\dfrac{3}{2})^2+\dfrac{19}{4}[/tex]

Now, we know that for any general equation of the type:

[tex]y=a(x-h)^2+k[/tex]

The axis of symmetry of the graph of the equation is:

[tex]x=h[/tex]

Here we have:

[tex]h=\dfrac{3}{2}[/tex]

            Hence, the answer is: Option: A

this was correct on my test, hope it helps! ;)

(Brainliest would help a lot btw)

To solve the problem, set up and solve an algebraic equation. Find the value of x, then use it to determine the number of years it will take for you to be twice as old as your brother.

To solve this problem, we can use algebraic equations. Let's assume the age of your brother is x. Since you are four times as old as your brother, your age would be 4x. In two years, your age would be 4x + 2, and your brother's age would be x + 2. According to the problem, 4x + 2 = 3(x + 2). We can solve this equation to find x, and then determine the number of years it will take for you to be twice as old as your brother.

By simplifying the equation, we get 4x + 2 = 3x + 6. Subtracted 3x from both sides, we get x + 2 = 6. Subtracting 2 from both sides, we get x = 4.

So, your brother's age is currently 4 and your age is currently 16. To determine the number of years it will take for you to be twice as old as your brother, we need to find the value of y that satisfies the equation 2(4 + y) = 16 + y. By solving this equation, we'll find that it will take 8 years for you to be twice as old as your brother.

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Answer:

[tex]r>\frac{4 +\sqrt{23732} }{154} \approx1.03\\[/tex]

Step-by-step explanation:

The area of the rectangular rug is given by this equation:

[tex]77r^2-4r-77[/tex]

The area must be a number greater than 0 since a negative area, or an area equal to 0 wouldn't have much sense. So:

[tex]77r^2-4r-77>0[/tex]

Let's find the roots of this equation using the quadratic formula:

[tex]r=\frac{-b\pm \sqrt{b^2-4ac} }{2a} =\frac{-(-4)\pm\sqrt{(-4)^2-(4)(77)(-77)} }{2(77)} \\\\r=\frac{4 \pm \sqrt{23732} }{154} \\\\r_1=\frac{4 +\sqrt{23732} }{154} \approx1.03\\\\r_2=\frac{4 - \sqrt{23732} }{154} \approx-0.97[/tex]

Now, let's evaluate the area for [tex]r>r_1[/tex] for example r=1.05:

[tex]A=77(1.05)^2-4(1.05)-77=3.6925>0[/tex]

The result is greater than zero, so for [tex]r>r_1[/tex] the values make sense.

Now let's evaluate the area for [tex]r_2<r<r_1[/tex] for example r=0.5 and r=-0.7:

[tex]A=77(0.5)^2-4(0.5)-77=-59.75<0\\\\A=77(-0.7)^2-4(-0.7)-77=-36.47<0[/tex]

The result is less than zero, so for [tex]r_2<r<r_1[/tex] the values don't make sense.

Now, let's evaluate the area for [tex]r<r_2[/tex] for example r=-1:

[tex]A=77(-1)^2-4(-1)-77=4>0[/tex]

The result is greater than zero, so for [tex]r<r_2[/tex] the values make sense

However, since negative values of r wouldn't make much sense (I never heard about of -8 inches for example) the possible dimensions of the​ rug are just:

[tex]r>\frac{4 +\sqrt{23732} }{154} \approx1.03\\[/tex]

The total cost of the power tools set if Jackson must pay off the tools within two years after the deferment period is  $2,644.82.

To find the total cost of the power tools set after the deferred payment period, we need to consider both the initial cost of the tools and the interest accrued during the deferment period and the subsequent payment period.

First, let's calculate the interest accrued during the deferment period:

Interest = Principal × Rate × Time

Interest = $1,543 × 23.76% × (6/12)   (since the deferment period is 6 months)

Interest = $1,543 × 0.2376 × 0.5

Interest = $183.78

Now, add this interest to the initial cost of the power tools:

Total cost after deferment = Initial cost + Interest

Total cost after deferment = $1,543 + $183.78

Total cost after deferment = $1,726.78

Next, we need to calculate the total amount Jackson must pay off within two years after the deferment period. This includes the principal amount and the interest accrued during the payment period. We'll use the formula for calculating the total payment for a loan with compound interest:

[tex]\[A = P(1 + r/n)^{nt}\][/tex]

Where:

A = Total amount to be paid

P = Principal amount (initial cost after deferment)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Time in years

In this case, we'll compound interest annually, so (n = 1), and (t = 2) years.

[tex]\[A = $1,726.78(1 + 0.2376/1)^{1*2}\][/tex]

[tex]\[A = $1,726.78(1 + 0.2376)^2\][/tex]

[tex]\[A = $1,726.78(1.2376)^2\][/tex]

[tex]\[A = $2,644.82\][/tex]

So, the total cost of the power tools set if Jackson must pay off the tools within two years after the deferment period is  $2,644.82.

Answer:

C. [tex]x\leq 5[/tex]; Lisa can buy 5 pounds or less of tomatoes.

Step-by-step explanation:

We have been given an inequality [tex]1.20x+1.80\leq 7.80[/tex], where x is the number of pounds of tomatoes. The inequality represents amount spend by Lisa on tomatoes and loaf. We are asked to find number of pounds that Lisa can buy.

First of all, we will subtract 1.80 from both sides of our inequality.

[tex]1.20x+1.80-1.80\leq 7.80-1.80[/tex]

[tex]1.20x\leq 6.00[/tex]

Now, we will divide both sides of our inequality by 1.20.

[tex]\frac{1.20x}{1.20}\leq \frac{6.00}{1.20}[/tex]

[tex]x\leq 5[/tex]

Therefore, Lisa can buy 5 pounds or less of tomatoes and option C is the correct choice.

If a regular polygon has interior angles each measuring 165 degrees, the polygon has 24 sides. This is calculated by using the formula to find the number of sides in a regular polygon, given the angle size.

To find out how many sides a regular polygon has, based on the size of its interior angles, you can use the formula to calculate the sum of the interior angles of a polygon:

n

= 180(

n

- 2), where

n

is the number of sides.

However, this formula gives the sum of the interior angles as a whole. Since, in a regular polygon, all angles are equal, you can then divide this sum by the known size of each angle.

So the specific formula to calculate the number of sides of a regular polygon, given the angle size, is:

n

= 360 / (180 -

angle size

).

In this case, you can substitute the angle size of 165 degrees into this formula:

n

= 360 / (180 - 165) = 360 / 15 = 24.

So a regular polygon with interior angles each measuring 165 degrees has 24 sides.

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To find the total amount of money in nickels, quarters, and dimes, we need to add the value of each coin together. In this case, the total amount of money is represented by the expression 60x + 50 cents.

To find the total amount of money, we need to determine the value of each coin in cents. A nickel is worth 5 cents, a quarter is worth 25 cents, and a dime is worth 10 cents.

The total amount of money in x nickels is 5x cents. The total amount of money in (x+2) quarters is 25(x+2) cents. The total amount of money in 3x dimes is 30x cents.

Adding these values together, we can find the total amount of money:

Total amount of money = 5x + 25(x+2) + 30x cents Now, simplify the expression:

Total amount of money = 5x + 25x + 50 + 30x cents

Total amount of money = 60x + 50 cents

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Answer:

62.1371 miles/hr

Step-by-step explanation:

The posted speed limit in many parts in Europe = 100 kilometers per hour

We have to convert the speed limit into miles per hour.

As we know, 1 kilometer = 0.621371 miles

Therefore, 100 kilometers = 100 × 0.621371

                                           = 62.1371 miles

The equivalent speed of 100 km/hr is 62.1371 miles/hr.

The fish swims 264 yards per minute faster than the boy.

To find out how much faster the fish swims than the boy in yards per minute, we first need to convert both speeds to yards per minute. Since 3 feet is equal to 1 yard, we can convert the fish's speed of 4.4 feet per second to yards per minute by multiplying it by (3 feet/1 yard) × (60 seconds/1 minute) = 4.4 × 3 × 60 yards per minute = 792 yards per minute. Similarly, the boy's speed of 12 miles per hour can be converted to yards per minute by multiplying it by (5280 feet/1 mile) × (1 yard/3 feet) × (1 hour/60 minutes) = 12 × 5280/3/60 yards per minute = 1056 yards per minute.

To find out how much faster the fish swims than the boy, we subtract the boy's speed from the fish's speed: 792 - 1056 = -264 yards per minute. Therefore, the fish swims 264 yards per minute faster than the boy.