Point I is on line segment HJ. Given H I = x, H J = 3x – 9, and
IJ = x + 5, determine the numerical length of HJ.

Answer:

The dolphin speed in miles per hour is 6

Step-by-step explanation:

we know that

1 mi=1,609.34 m ------> 1 m=1/ 1,609.34 mi

1 h= 3,600 sec ----> 1 sec=1/3,600 h

we have

[tex]2.68\frac{m}{sec}[/tex]

Convert to mi/h

[tex]2.68\frac{m}{sec}=2.68\frac{(1/1,609.34)}{(1/3,600)}=6\frac{mi}{h}[/tex]

Answer:

6

Step-by-step explanation:

Step-by-step explanation:

given

[tex](1.5 \times {10}^{4} )(8 \times {10}^{8} )[/tex]

in order to make multiplication easier we need to change the 1.5 into a whole number form.

thus

[tex](15 \times {10}^{ - 1} \times {10}^{4} )(8 \times {10}^{8} )[/tex]

[tex] = (15 \times {10}^{4 - 1} )(8 \times {10}^{8} )[/tex]

First law of indices applied there

=(15×10^3)(8×10^8)

=(15×8)(10^3×10^8)

=120×10^3+8 ( first law of indices, which states that , numbers of the same base multiplying each other, take one of the base and add the exponent. and clearly both 15 and 8 are in base 10

=120×10^11

=1.20×10^2 ×10^11

=1.20×10^11+2

=1.20×10^13

so the answer is alt B

(1.5 x 10^4)(8 x 10^8) written in scientific notation will be  1.2×10¹³.

We write standard numbers in scientific form as it can be written in more compact way.Think of writing a billion in copy and writing it in scientific notation.

Given (1.5×10⁴)(8×10⁸) and we have to write it in scientific form.

Let us first multiply the bases which are (8×1.5) = 12 and 10⁴×10⁸ is 10⁴⁺⁸ = 10¹².

∴ (1.5×10⁴)(8×10⁸) = 12×10¹² but is scientific natation base should be less than 10 so we'll a decimal one digit before 12 like dividing it by 10 so to balance it out we also have to multiply by 10 we'll multiply that 10 to the 10¹² which will make it 10¹³.

∴ 12×10¹² = 1.2×10¹³.

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Answer:r

Step-by-step explanation:

let x and y this numbers : x +y = -103 and x = y +59

so : y+59 +y = -103

2y +59 = -103

2y +59-59 = -103-59

2y = -162

y = -162/2

y = -81  but  x = y +59

so : x = -81+59

x = -22

The two numbers satisfying the given condition is -22 and -81.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have sum of two numbers is -103. One number is 59 less than the other.

Assume that the first number is [x]. Then, another number would be (x - 59).

We can write -

x + (x - 59) = - 103

2x - 59 = - 103

2x = - 103 + 59

2x = - 444

x = - 22

Another number would be -

x - 59 = - 22 - 59 = - 81

Therefore, the two numbers satisfying the given condition is -22 and -81.

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Answer:The volcano has a height of nearly 22 km (13.6 mi or 72,000 ft) as measured by the Mars Orbiter Laser Altimeter (MOLA). Olympus Mons is about two and a half times Mount Everest's height above sea level.

Olympus Mons - Wikipedia

Step-by-step explanation:

Olympus Mons on Mars is the tallest mountain in the solar system, standing over 20 kilometers above its surroundings and nearly 30 kilometers above the lowest points on Mars.

The height of Olympus Mons, which is the tallest mountain in the solar system, located on Mars, is incredibly impressive in comparison to mountains on Earth. Olympus Mons towers more than 20 kilometers above its surroundings, reaching nearly 30 kilometers above the lowest elevation areas on Mars. When converted to more familiar units, this equals approximately 22 miles in height, a figure that dwarfs the height of Mount Everest, which stands at 29,029 feet or about 8.848 kilometers.

Hey!

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

[tex]\large\boxed{0.65~rotations~per~foot}[/tex]

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Solution:

speed = rotations / distance

speed = 65 / 100

speed = 0.65

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Hope This Helped! Good Luck!

A trapezoid has exactly one pair of parallel sides.

I hope I was helpful! :)

Answer:

x=9

Step-by-step explanation:

-2(-5x - 4) + 2x - 2 = 114

-2(-5x - 4) + 2x = 116

10x + 8 + 2x = 116

12x + 8 = 116

12x = 108

x = 9

Answer:

Option D. 1

Option E. 1/2

Step-by-step explanation:

we know that

Looking at the graph

The domain is the interval ----> [-1,1]

[tex]-1\leq x\leq 1[/tex]

The domain is all real numbers greater than or equal to -1 and less than or equal to 1

The range is the interval ----> [0,1]

[tex]0\leq y\leq 1[/tex]

The range is all real numbers greater than or equal to 0 and less than or equal to 1

therefore

The values that are in the range are

1 and 1/2

Answer:

D.1

E.[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We have to find the values lie in the range of function in given graph.

Let f(x) be given function

Domain takes along x- axis and range takes along y- axis.

From given graph , we can see that

Domain of function =[-1,1]

It means

[tex]-1\leq x\leq 1[/tex]

Range of function:[0,1]

It means

[tex]0\leq y \leq 1[/tex]

The value of range of given function  from 0 to 1.

Hence, option D and E are correct.

D.1

E.[tex]\frac{1}{2}[/tex]

For this case we must solve the following equation:

[tex]\frac {2} {5} + p = \frac {4} {5} + \frac {3} {5}[/tex]

Since the denominators on the right side of the equation are equal, then we add the fractions:

[tex]\frac {2} {5} + p = \frac {4 + 3} {5}\\\frac {2} {5} + p = \frac {7} {5}[/tex]

We subtract [tex]\frac {2} {5}[/tex]on both sides of the equation:

[tex]p = \frac {7} {5} - \frac {2} {5}\\p = \frac {7-2} {5}\\p = \frac {5} {5}\\p = 1[/tex]

Thus, the value of p is 1.

Answer:

[tex]p = 1[/tex]

The solution to the linear equation is; p= 1.

The equation given in the task content is;

On this note, By isolating the unknown variable, p, we have;

By taking the LCM, we have; p = (4+3-2)/5

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Answer:

840,000 / 306,000 = 2.7450980392

So, Greenland is about 2 and 3/4 times larger than New Guinea.

Step-by-step explanation:

Greenland, the largest island in the world, is 534,000 square miles larger than New Guinea.

Greenland is 840,000 square miles and New Guinea is 306,000 square miles. To find out how much larger Greenland is than New Guinea, we subtract the area of New Guinea from the area of Greenland:

840,000 - 306,000 = 534,000 square miles

Therefore, Greenland is 534,000 square miles larger than New Guinea.

To determine how much larger Greenland is than New Guinea, one must subtract the size of New Guinea from the size of Greenland. Given that Greenland, the largest island in the world, is 840,000 square miles and New Guinea is 306,000 square miles, you would perform the following calculation:

840,000 - 306,000 = 534,000 square miles

Therefore, Greenland is 534,000 square miles larger than New Guinea.

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Answer:

(x + 4) × (2x - 5)

Step-by-step explanation:

Hope this helps!!

Answer:

Answer:

(2x−5)(x+4)

Step-by-step explanation:

Factor 2x2+3x−20

2x2+3x−20

=(2x−5)(x+4)

Answer:

(2x−5)(x+4)

Hey!

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Steps To Solve:

~Follow PEMDAS

6.4 − 2.4 ÷ 0.1

~Divide

6.4 − (2.4 ÷ 0.1)

~Simplify

6.4 - 24

~Subtract

(6.4 - 24)

~Simplify

-17.6

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Answer:

[tex]\large\boxed{-17.6}[/tex]

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Hope This Helped! Good Luck!

Answer:

-17.6

Step-by-step explanation:

6.4 - 2.4 ÷ 0.1

6.4 - 24 *Order of operations tells you

to divide first

-17.6 *Subtract

Answer:

I am not sure but the answer might be: $1688.1816

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The base angles of an isosceles triangle are equal.

The sum of the 3 angles in a triangle = 180°, thus

vertex angle = 180° - (55 + 55)° = 180° - 110° = 70°

Answer:

1

Step-by-step explanation:

It would be 1 because it is the least number there

Answer:

Step-by-step explanation:

It's highly advisable to find and use the LCD in problems like this.

21/32 has the denominator 32; if we multiply numerator and denominator each of 3/4, we get the equivalent fraction 24/32.

Now, compare 21/32 and 24/32.  It's pretty obvious that "21/32 greater than 3/4" is false; 24/32 is greater than 21/32, so 3/4 is greater than 21/32.

Answer:

x = y + 8

Step-by-step explanation:

Given

y = x - 8 ( add 8 to both sides )

y + 8 = x

Final answer:

To make x the subject of the equation y = x - 8, simply add 8 to both sides of the equation to get x = y + 8, which is the rearranged equation.

Explanation:

To rearrange the equation y = x - 8 to make x the subject, you need to isolate x on one side of the equation. Here are the steps to do so:

Add 8 to both sides of the equation to get y + 8 = x.

Once you have done that, the equation is already solved for x, and the new equation with x as the subject is x = y + 8.

This process is common in algebra when solving linear equations or finding the equation of a line, similar to when you want to determine the line of best fit in a set of data points. For example, in the equation y = 9 + 3x, rearranging to solve for x would involve subtracting 9 from both sides and then dividing by 3.

A rectangle with sides 15 and w has perimeter

[tex]2p = 2(15+w) = 2w+30[/tex]

We want this quantity to be at most 50, so it must be less than or equal to 50:

[tex]2w+30\leq 50[/tex]

For the record, this implies that

[tex]2w\leq 20 \iff w \leq 10[/tex]

So, the width can be at most 10.

Answer:

2x+30< 50   ...answer : A

Step-by-step explanation:

the perimeter is :  P = 2(L+W)

let : L= x   given : L=15

P= 2(x+15)

The perimeter of the rectangle is, at most, 50:   P<50

2(x+15) < 50

2x+30< 50   ...answer : A

Answer:  (a) 3     (b) -4      (c) 8      (d) 8i        (e) 11

Step-by-step explanation:

For a cubed root, you need three like terms on the inside to make one on the outside.

[tex]a)\quad \sqrt[3]{27}\quad = \sqrt[3]{3\cdot3\cdot3}\quad =\large\boxed{3}\\\\b)\quad \sqrt[3]{-64}\quad = \sqrt[3]{-4\cdot-4\cdot-4}\quad =\large\boxed{-4}[/tex]

For a square root, you need two like terms on the inside to make one on the outside. Reminder that √-1 = i

[tex]c)\quad \sqrt{64}\quad = \sqrt{8\cdot8}\quad =\large\boxed{8}\\\\d)\quad \sqrt{-64}\quad = \sqrt{-1\cdot8\cdot8}\quad =\large\boxed{8i}\\\\e)\quad \sqrt{121}\quad = \sqrt{11\cdot11}\quad =\large\boxed{11}[/tex]

Answer:

-1

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

[tex] \frac{0 + 8}{ - 2 - 6} = - \frac{8}{8} = - 1[/tex]

I am joyous to assist you anytime.

we can alsoways find the slope by simply using two points off the table, bearing in mind  that slope goes by different names

rate of change

average rate of change

delta difference

rise over run

however is the same cat disguised in different costumes.

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} time&distance\\ \cline{1-2} 15&2\\ 30&4\\ 45&5\\ 60&6\\ \cline{1-2} \end{array} \begin{array}{llll} \\[1em] \leftarrow \\\\ \leftarrow \end{array}\qquad \qquad (\stackrel{x_1}{30}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{60}~,~\stackrel{y_2}{6})[/tex]

[tex]\bf \stackrel{\textit{\large average rate of change}}{\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{60}-\underset{x_1}{30}}}\implies \cfrac{2}{30}\implies \cfrac{1}{15}}[/tex]

2/3x=36

multiply by 3 both sides

2x=108

divide by 2

x=54

The value of the number whose two thirds part is equal to the number 36 is number 54.

A fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

[tex]\dfrac{a}{b}[/tex]

Here (a) is the numerator and (b) is the denominator.

Two thirds of a number is 36. Let suppose the number is x. As it is given that the two third of this number x is equal to the 36.

Thus, we have to multiply the fraction 2/3 to x and equate it to 36.

[tex]x\times\dfrac{2}{3}=36\\x=\dfrac{36\times3}{2}\\x=54[/tex]

Hence, the value of the number whose two thirds part is equal to the number 36 is number 54.

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Just divide one by another and you'll get the ratio

4000/15 = 800/3 ≈ 266,67

So 4000 is 266,67 times greater than 15

Answer:

266.666 or 266.67

Step-by-step explanation:

You´d divide 4000 by 15 and you get 266.666, which can be simplified to 266.67.

Answer:

B. x^4+2x^2+2

Step-by-step explanation:

(x^2+1)^2+1

=(x^2+1)(x^2+1)+1

=(x^4+x^2+x^2+1)+1

=x^4+2x^2+2

Answer: 5b = 15

Step-by-step explanation:

5b + 2 = 17

     - 2     -2

5b = 15

The two steps are:

step 1  : 5b = 17 - 2

step 2 : b = 15/5

Given,

5b + 2= 17

Now,

The equation given two us is in linear form with one variable .

So,

Simplifying the equation,

5b + 2= 17

Take 2 from LHS to RHS

5b = 17 - 2

5b = 15

b = 15/5

b = 3

Thus the value of b is 3 .

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Answer:

[tex]8x[/tex]

Step-by-step explanation:

Let us suppose that items carried by one hiker is [tex]x[/tex]

We know that everyone will carry same number of items

hence for a group of [tex]8[/tex] hikers, total number of items will be [tex]8x[/tex]

Answer:

(a). $20,000

(b). The estimate will be lower than the actual amount.

Step-by-step explanation:

We have been given that Michael saves $423 dollars a month for college.

(a). We know that 1 year equals 12 months.

4 years = 4*12 months = 48 months.

[tex]\text{Actual amount saved}=\$423\times 48[/tex]

Since we are asked to find the estimated amount of money Michael will save in 4 years, so we will estimate both quantities as:

[tex]423\approx 400\\\\48\approx 50[/tex]

[tex]\text{Actual amount saved}=\$400\times 50[/tex]

[tex]\text{Actual amount saved}=\$20,000[/tex]

Therefore, Michael will save approximately $20,000 in 4 years.

(b).

The estimate will be lower than the actual amount as we rounded $423 down $23 to nearest hundred that is $400 and rounded 48 up 2 to nearest ten that is 40.

Therefore, the estimate will be lower than the actual amount.

The required expression would be -2(y+7) represents which is negative two times the sum of y and 7.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

We have been given that y represents a number.

To determine the expression for negative two times the sum of y and 7.

As per the given statement,

So the expression would be -2(y+7).

Hence, the required expression would be -2(y+7) represents which is negative two times the sum of y and 7.

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Answer:

$5.20 x 20 = $104.00

$104.00 ×8= $832.00

Using the given number line, the plotted number is 1000 when rounded to the nearest thousand.

How to round a number to the nearest thousand?

To round a number to the nearest thousand, you need to identify the digit in the thousands place and then decide whether to round up or down based on the digit in the hundreds place.

Now, the nearest number too the plotted dot is 1000.

Thus, we can clearly conclude that the using the given number line, the plotted number is 1000 when rounded to the nearest thousand.