MATHEMATICS HIGH SCHOOL

What happens when h is a negative number?

Answers

Answer 1

Answer:

Answer: -h

Step-by-step explanation:

If h is a negative number, h would be -h.

For example, if h had a value of 1, 1 as a negative number would be -1.

Related Questions

Frank and Gertrude mow lawns for extra money over the summer. Frank's income is determined by f(x) = 5x + 15, where x is the number of hours. Gertrude's income is g(x) = 4x + 20. If Frank and Gertrude were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Frank works 4 hours. Create the function h(x) and indicate if Frank will make more money working alone or by teaming with Gertrude.
What is the equation of the line that passes through the point (-3, 5) with a slope of 4?y=4-7O y-4x+17O y= 4x+12O y=47-17o y = 4x+2
If the area of the base of a rectangular solid is tripled, what is the percent increase in itsvolume?
What 3 consecutive numbers add up to 237?
What is the value of a in the equation 3a+b=54, when b=9

Match each fraction with its equivalent decimal number.1.2/5
2.7/20
3.3/25
4.7/10

A.0.35
B.0.7
C.0.12
D.0.4

Answers

Changing a fraction to its decimal form can be done by long division method. Dividing the denominator by its numerator will change the fraction into decimal form. Alternatively, you can use a calculator to do that for you. Below are the fractions with their decimal forms listed:

1.) 2/5 = 0.4 (D)
2.) 7/20 = 0.35 (A)
3.) 3/25 = 0.12 (C)
4.) 7/10 = 0.7 (B)

Answer:

Answer:

68 km/hr,3 hrs

Step-by-step explanation:

340/5 km=68 km

204 km/68 km=3 hrs

Step-by-step explanation:

Find the student’s error in solving the following inequality.2 < –3x –4 < 5
6 < –3x < 5
–2 > x > –5/3

a.The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.

b.The student divided 6/–3 incorrectly.

c.The student should not have switched the direction of the sign in the final step.

Answers

The second step is wrong because he did not add 4 to the number 5. Then the correct option is A.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The solution to inequality is given below.

Step 1 ⇒ 2 < –3x –4 < 5

Step 2 ⇒ 6 < –3x < 5

Step 3 ⇒ –2 > x > –5/3

The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.

The second step is wrong because he did not add 4 to the number 5. Then the correct option is A.

More about the inequality link is given below.

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the answer is a, the students should have added 4 to all parts

Two towns are 1,100 miles apart. A group of hikers Starts from each town and walks down the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels 2 1/2 mile per hour slower than the other group, find the rate of each group.

Answers

Answer:

3.54 and 1.04

Step-by-step explanation:

Given:

Two towns are 1,100 miles apart.

A group of hikers Starts from each town and walks down the trail toward each other..

They meet after a total hiking time of 240 hours.

If one group travels 2 1/2 mile per hour slower than the other group.

Question asked:

Find the rate of each group.

Solution:

Let speed of faster hiker = $x\ mph$

Speed of slower hiker = $x-(5)/(2)\ mph$

As we know:

$Distance=speed* time$

Total distance between two town = Total combined speed of both hikers $*$ Total combined time taken

$1100=(x+x-(5)/(2) )*240\n \n Dividing\ both\ sides\ by\ 240\n \n 4.58=(x+x-(5)/(2) )\n \n 4.58=2x-(5)/(2) \n \nAdding\ both\ sides\ by\ (5)/(2) \n \n 4.58+ (5)/(2)=2x- (5)/(2)+ (5)/(2)\n \n (2*4.58+5)/(2) =2x\n \n (14.16)/(2) =2x\n \n By \ cross\ multiplication\n \n 2*2x=14.16\n \n 4x=14.16$

$By\ dividing\ both\ sides\ by \ 4\n \n x=3.54\ miles\ per\ hour$

Speed of faster hiker = $x\ mph$ = 3.54 miles per hour.

Speed of slower hiker = $x-(5)/(2)\ mph$ =

$3.54-(5)/(2) =3.54-2.5=1.04\ miles\ per\ hour$

Therefore, speed of faster hiker is 3.54 miles per hour and speed of slower hiker is 1.04 miles per hour.

Chris has a collection of 20 baseball cards and Kyle has collection of 40 baseball cards. Chris is adding 3 baseball cards per month to his collection while Kyle is adding one baseball card per month to his collection. After how many months will Chris and Kyle have the same number of baseball cards?

Answers

Answer:

11 months

Step-by-step explanation:

The initial number of baseball cards that Chris has is 20.

This is like the first term of a sequence.

If Chris is adding 3 baseball cards per month, then there will be a constant difference of 3.

The number of baseball cards after $n$ months is given by the formula;

$C_n=20+(n-1)3$

$\Rightarrow C_n=20+3n-3$

$\Rightarrow C_n=3n+17$ where $n\ge1$

Similarly, Kyle initially has 40 baseball cards and adds one base ball card per month to his collection;

The number of his baseball cards after $n$ months is given by the formula;

$K_n=40+(n-1)1$

$K_n=40+n-1$

$\Rightarrow K_n=n+39$

To determine the number of months that will pass before Kyle and Chris have the same number of base ball cards, we equate both equations to get;

$\Rightarrow 3n+17=n+39$

We group like terms to get;

$3n-n=39-17$

$\Rightarrow 2n=22$

$\Rightarrow n=11$

Therefore Chris and Kyle will have the same number of baseball cards after 11 months.

Final answer:

By setting equal the linear expressions for how many baseball cards Chris and Kyle have after a given number of months, we find that it will take 10 months for them to have the same number.

Explanation:

The question is essentially asking how long it will take for Chris and Kyle to have the same number of baseball cards. It's a problem about linear expressions, rooted in mathematics. Chris starts with 20 baseball cards and adds 3 per month. We can express this as C = 20 + 3m, where m is the number of months. Kyle starts with 40 baseball cards and adds 1 per month. We express this as K = 40 + m.

We want to find out when Chris and Kyle will have the same number of cards, so we set C = K, which results in 20 + 3m = 40 + m. By solving this equation, we can condense it to 2m = 20 or m = 10. Therefore, it will take 10 months for Chris and Kyle to have the same number of baseball cards.

Learn more about Linear Equations here:

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Express 56 million in scientific notation

Answers

5.6000000 × 107 is in scientific notation

Y = 10 + 16x − x^2y = 3x + 50
If (x1, y1) and (x2, y2) are distinct solutions to the system of equations shown above, what is the sum of the y1 and y2?

Answers

Solving the system we can see that the sum of the y-values of the two solutions is 139.

How to get the sum of y₁ and y₂?

Let's solve the system of equations.

y = 10 + 16x − x²

y = 3x + 50

We can write this as a single quadratic equation:

10 + 16x - x² = 3x + 50

10 + 16x - x² - 3x - 50 = 0

-x² + 13x - 40 = 0

Using the quadratic formula we will get the two solutions for x:

$x = (-13 \pm √(13^2 - 4*-1*-40) )/(-2) \n\nx = (-13 \pm 3 )/(-2)$

So the two solutions are:

x = (-13 + 3)/-2 = 5

x = (-13 - 3)/-2 = 8

Evaluating the linear equation in these two values we will get y1 and y2.

if x = 5

y₁ = 3*5 + 50 = 65

if x= 8

y₂ = 3*8 + 50 = 74

The sum is:

65 + 74 =139

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Final answer:

The distinct solutions to the system of equations are (5, 65) and (8, 74), and the sum of the y-values is 139.

Explanation:

To find the sum of y-values of the distinct solutions to this system of equations, first, you need to set the two equations equal to each other to find the x-values of the solutions:

10 + 16x − x^2 = 3x + 50.

Then, solve the resulting equation for x:

x^2 - 13x + 40 = 0.

This is a quadratic equation, and it can be solved either by factoring or using the quadratic formula. The solutions for x result in:

x = 5 and x = 8.

These are the two distinct x-values for the intersections of the graphs of the two equations. To find the corresponding y-values, plug these x-values into either of the original equations. We'll use the simpler equation, y = 3x + 50:

For x = 5, y = 65 and for x = 8, y = 74.

Therefore, the distinct solutions to the system of equations are (5, 65) and (8, 74). Finally, the sum of y1 and y2 is 65 + 74 = 139.

Learn more about System of Equations here:

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