A hiker is climbing down a valley. He stops for a water break 4 times. Between each break, he descends 15 meters. How many meters did he descend?

Ju Chan answered the question by writing the following:

4(−15) meters = −60 meters.

Which word in the problem indicates that a negative number should be used?

Part (a)

[tex]247 \approx 200\\\\201 \approx 200\\\\\implies 247 \times 201 \approx 200 \times 200=\boxed{40000}[/tex]

Part (b)

[tex]756 \approx 800\\\\8674 \approx 9000\\\\\implies 756 \times 8674 \approx 800 \times 9000 =\boxed{7200000}[/tex]

Part (c)

[tex]3025 \approx 3000\\\\2007 \approx 2000\\\\\implies 3025 \times 2007 \approx 3000 \times 2000=\boxed{6000000}[/tex]

Answer:

bx=-3

Step-by-step explanation:

-2(bx-5)=16

Use distributive property.

-2bx+10=16

Now, subtract 10 from both sides.

-2bx=6

Divide -2 from both sides.

bx=-3

Hope this helps!

If not, I am sorry.

Solving a system of equations, it is found that the value of a is of -191.75 and the value of b is of 278.25.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

Multiplying the first equations by 17 and the second by -5, we have that the system is:

Then, adding them:

4a = -767

a = -767/4

a = -191.75

Then:

[tex]b = \frac{49 - 7a}{5} = \frac{49 - 7(-191.75)}{5} = 278.25[/tex]

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Answer:

$ 164.68   markup

Step-by-step explanation:

22 3/8 % = 22.375 %    which is .22375 in decimal

  .22375 * $ 736 =  $ 164.68

In a regular polygon, all interior angles have equal measures because the polygon has congruent sides and angles. The sum of all interior angles in a polygon can be found using the formula:

(n-2) * 180°,

where n represents the number of sides of the polygon.

Based on this, we can determine which angles cannot be interior angles in a regular polygon.

24°: This angle can be an interior angle in a regular polygon because it is smaller than the interior angles of any polygon with more than 6 sides.

72°: This angle can be an interior angle in a regular pentagon (5 sides) or any polygon with more sides, as it satisfies the requirement for interior angles.

135°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 8 sides.

164°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 9 sides.

179°: This angle cannot be an interior angle in any regular polygon because it is larger than the maximum measure of interior angles in any polygon.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: f = \cfrac{9}{a}+7[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \:a = \cfrac{9}{f - 7} [/tex]

[tex]\qquad \tt \rightarrow \:a(f - 7) = 9[/tex]

[tex]\qquad \tt \rightarrow \:(f - 7) = \cfrac{9}{a}[/tex]

[tex]\qquad \tt \rightarrow \:f = \cfrac{9}{a} + 7[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The factored form of the expression is 2(g-h)(12g+5h)

A quadratic Expression is what can be written in the form of

ax²+bx +c

The given quadratic expression is

24g² -gh -10h²

10g² - 10h² +14g² -gh

10(g+h)(g-h) +14 g(g -h)

(g-h)(10 g +10h +14g)

2(g-h)(12g+5h)

Therefore the factored form of the expression is 2(g-h)(12g+5h).

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Answer:

2 hours

Step-by-step explanation:

you can write two linear equations and then set them equal to each other to see when they intersect. so for the first equation which will be representing the junior space cadets distance from his house. this can be written as

d = 50t + 50

where t represents time and d represents distance. there is 50 being added to the equation since he had already been traveling for an hour

the second equation which will represent his sister Gwen can be represented as

d = 75t

Now we set them equal to each other

50t + 50 = 75t

50 = 25t

2 = t

The attached graph represents the piecewise function h(x)

Which of the following is the graph of the piecewise function

[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]

The function is given as:

[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]

The above means that the piecewise function has 3 domains

Next, we plot the graph using a graphing tool

See attachment for the graph of the piecewise function h(x)

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Answer:

y^3

Step-by-step explanation:

x^3 y^3     and    y^4  

y^3 * x^3     and y^3  * y

Answer:

3

Step-by-step explanation:

3 is an odd number and obviously the only odd (same) three digit that add up to 9

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Answer:

23

Step-by-step explanation:

seen it before

The value of the coefficient of xy is 0.

It is an expression made of numbers and letters where the numbers are called coefficient.

Analysis:

(ax+by)(cx-dy)

ac[tex]x^{2}[/tex] -adxy +bcxy -bd[tex]y^{2}[/tex]

But, ac = 18, ad=bc, bd = 50

18[tex]x^{2}[/tex] -xy(bc -ad) - 50[tex]y^{2}[/tex]

since bc = ad, the coefficient of xy = 0

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

Expression in scientific notation :

[tex]\qquad \tt \rightarrow \:3.45 × {10}^{-4} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 0.000345[/tex]

[tex]\qquad \tt \rightarrow \: 0.000345 \times \cfrac{10000}{10000} [/tex]

[tex]\qquad \tt \rightarrow \: (0.000345 \times 10000) \times \cfrac{1}{10000} [/tex]

[tex]\qquad \tt \rightarrow \: 3.45 \times \cfrac{1}{10 {}^{4} } [/tex]

[tex]\qquad \tt \rightarrow \: 3.45 \times{10 {}^{ - 4} } [/tex]

[tex] \textsf{Correct option - D} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

3.45 x 10-4

Step-by-step explanation:

The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, option A is the correct answer.

Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.

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The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.

An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, option A is the correct answer.

Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.

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Answer:

$305.9022863 or $305.90 (rounded to 2 decimal places)

Step-by-step explanation:

It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula  

A= P(1+R)^n

A= the total amount P=Initial amount       R= rate  n=time period

P=$100 R=15% or 0.15(decimal)  n=8 (years)  

A= 100 (1.15)^8

A= 100(3.059022863)

A=305.9022863

The amount you will have after 8 years is $220

The formula for calculating simple interest is expressed as:

SI =PRT

P is the principal = $100

T is the time = 8 years

R is the rate. = 15%

SI = 100 * 8 * 0.15
SI = $120

Amount after 8years = $100 + $120
Amount after 8years = $220

Hence the amount you will have after 8 years is $220

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Answer:

A

Step-by-step explanation:

Set the equation equal to bx.

[tex](3x + 3)(ax - 2) - {x}^{2} + 6 = bx[/tex]

[tex]3a {x}^{2} - 6x + 3ax - 6 - {x}^{2} + 6 = bx[/tex]

Cancel out the constants

[tex]3 {ax}^{2} - 6x + 3ax - x {}^{2} = bx[/tex]

In order to cancel out the quadratics, we must solve for a.

[tex]3 {ax}^{2} - {x}^{2} = 0[/tex]

[tex]3 {ax}^{2} = {x}^{2} [/tex]

[tex]3a = 1[/tex]

[tex]a = \frac{1}{3} [/tex]

So plug in 1/3 for a.

[tex]3( \frac{1}{3} ) {x}^{2} - 6x + 3( \frac{1}{3} )x - {x}^{2} = bx[/tex]

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

[tex] - 5x = bx[/tex]

[tex]b = - 5[/tex]

The conditional probability values are 0.57 and 0.43

               Has Eaten before   Have not           Total

Snack A     144                               108                252

Snack B      92                               228                320

Total          236                              336                572

Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person.

The required probabilities are conditional probabilities, and they are calculated using:

P(A | B) = P(A and B)/P(B)

Using the above formula, we have:

The probability that a customer eats snack A given that the customer has eaten snack A before, to be:

P = n(Have eaten snack A)/n(Snack A)

This gives

P = 144/252

Evaluate

P = 0.57

Also, we have:

The probability that a customer eats snack A given that the customer has not eaten snack A before, to be:

P = n(Have not eaten snack A)/n(Snack A)

This gives

P = 108/252

Evaluate

P = 0.43

Hence, the probabilities are 0.57 and 0.43

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Answer:

tan theta - cot theta

Step-by-step explanation:

sin/cos = tan

cos/sin = cot

Answer:

C

Step-by-step explanation:

The contrapositive is always logically equivalent to the original statement.

Answer:

C

Step-by-step explanation:

Hi!

I am not completely sure what you mean but if you are looking for the slope of a line here is the best way to find it.

Y=Mx+b

it look difficult but really it's quite easy and once you get it it's super memorable. Y will always be Y that doesn't change. The M is the slope of the line (don't let equations confuse you with different letters! the M might be different but it is always the letter next to x) and b is the y intercept (where the line crosses y). All you need to find the slope of a line is 3 points. I see here you have a graph. So what you do is count how much it's moving up each block on the graph. I would say your slope is about 1/3. Y is really easy! just find the point it crosses the y axis(horizontal axis or the one going up and down) for yours it's 0. So your answer is y=1/3x+0

Answer: [tex]8\sqrt{5}[/tex]

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]

Thus, by the Pythagorean thoerem,

[tex]8^2 +16^2=x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]

It will take 5 seconds for the waste to hit the ground.

We know that the bird releases the waste from a height of 400ft, so the height equation is:

[tex]h(t) = -16t^2 + 400[/tex]

The waste will hit the ground when its height is equal to zero, so we just need to solve the quadratic equation:

[tex]h(t) = 0 = -16t^2 + 400\\\\16t^2 = 400\\\\t^2 = 400/16 = 25\\\\[/tex]

Now we can apply the square root in both sides:

[tex]t = \sqrt{25} = 5[/tex]

It will take 5 seconds for the waste to hit the ground.

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Answer:

1.19

Step-by-step explanation:

1) Shift the decimals of both 0.8449 and 0.71 to the right by 2 decimal places. (This is needed to convert 0.71 to 71, since long division must divide by a whole number.)

84.49 ÷ 71

2)  Use the algorithm method.

1 . 1 9

7 1 | 8 4 . 4 9

7     1 .  

1 3 . 4

7 . 1

6 . 3 9

6 . 3 9

3) Therefore,  0.8449 ÷ 0.71 = 1.19.

1.19

The midpoint of the class interval 80-89 is 84.5.

The mid point of a class interval is also called the class mark of the class interval.

The midpoint is defined as the average of the upper and lower class limits.

Therefore, the midpoint of the class interval 80-89 can be calculated as follows:

mid point = 80 + 89 / 2

mid point = 169 / 2

mid point = 84.5

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The simplified expression of (-2 - c)(-1) is 2 + c

We have:

(-2 - c)(-1)

Express as product

(-2 - c) * (-1)

Evaluate the product

2 + c

Hence, the simplified expression of (-2 - c)(-1) is 2 + c

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Answer:

Step-by-step explanation:

Do you have any options or a graph?