Write an inequality for each description.

1) Thirty subtracted from four times a number is greater than the opposite of ten.


And the 2nd one in the picture

3n - 4

substitute t = 5 - n into f(t)

f(5 - n) = 11- 3(5 - n) = 11- 15 + 3n = 3n - 4

[tex]h(t)=11-3(5-n)[/tex]                 Substitute [tex]5-n[/tex] to [tex]t[/tex] in this equation

[tex]h(t)=11-15+3n[/tex]                 Use Distributive property

[tex]h(t)=3n-4[/tex]                        Combine Like Terms

*(Answer)*= [tex]h(t)=3n-4[/tex]

s = 6 + e

s + e = 28

We can use this system of equations to find the exact values of s and e.

We have a current value of s, so we can find the exact value of e now.

e + e + 6 = 28

Combine like terms.

2e + 6 = 28

Subtract both sides by 6.

2e = 22

Divide both sides by 2.

e = 11

Now we have an exact value of e, and can solve for the value of s.

s = 6 + 11

s = 17

Sophia is 17 years old, and Eric is 11 years old.

The age of Sophia is 17 years and Eric is 11 years.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Sophia is 6 years older than her brother eric.

The sum of their ages is 28.

let the age of Eric be x.

So, Sophia's age will be x+ 6

Then, x+ x +6 = 28

2x + 6= 28

2x= 22

x= 11

Hence, the age of Sophia is 17 years and Eric is 11 years.

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The answer you want is going to be 164+3.28

Answer:

Step 3 is [tex]=164 + 3.28[/tex]            

Step-by-step explanation:

Given : Yuuma applied the steps below to find the product of (–10.2)(–16.4).

To find : Which expression correctly fills in the blank in Step 3?

Solution :

The given expression is  [tex](-10.2)(-16.4)[/tex]

Step 1 : Write the expression,

[tex](-10.2)(-16.4) = (-16.4)(-10.2)[/tex]

Step 2: Distribute 10.2 into two parts 10+0.2

[tex]=(-16.4)(-10) + (-16.4)(-0.2)[/tex]

Step 3: Simplify the multiplication,

[tex]=164 + 3.28[/tex]

Step 4: Add the terms

[tex]=167.28[/tex]

Therefore, Step 3 is [tex]=164 + 3.28[/tex]

Yes because 10 to the power of 2 is 100 and if she runs 15 minutes a day for 7 days that would = 105 minutes

The way I would solve this problem is by first finding the unit rate, or the rate that the jet plane travels in one minute. Then I would multiply the rate by the number of minutes I want to know how far the jet plane flies; in this case it would be multiplied by 18 minutes.

Let's start by finding the unit rate. To find the unit rate we would divide the ratio, 450 miles:60 minutes (one hour) by 60 minutes to make the 60 minutes become one minute and 450 miles become 7.5 miles.

450 miles:60 minutes ÷ 60/60

7.5 miles:1 minute

The unit rate is 7.5 miles per minute. Since we know the jet plane flies 7.5 miles every one minute, we can multiply this amount by 18 minutes to find how many miles the place can fly in 18 minutes.

7.5 miles * 18 minutes = 135 miles

The answer to your question is the jet plane travels 135 miles in 18 minutes.

We are given that there is a plane which flies at 450 miles per hour. ("A jet plane flies at 450 miles per hour.)

We can also see that the question is how far it would travel in 18 minutes most likely assuming it to be going the same speed. ("How far does it travel in 18 minutes?")

First: How can we answer the question with the information given?

To answer this question, we can break it down into smaller questions. Here is one to start off with.

One of the most important things to note for this is one hour = 60 minutes. Therefore, we can see these two are related as you can convert either mph or minutes to miles per minute or hours (respectively).

Now I'm going to do just that by converting 18 minutes to an hour:

If you know one hour = 60 minutes, what would you do to make the right side 18 minutes? I would personally multiply both sides by 18/60, making the left side 3/10 (18/60 simplified is 3/10) of an hour, and the right 18 minutes (because 18/60 * 60 = 18)

Alright. So now we know that 18 minutes is equal to 3/10th of an hour. Since the units now match (450 miles per hour and 3/10th of an hour), we can relate them.

Mph is miles per hour, so how many miles traveled in an hour. In an hour. Does that sound familiar? We do have a number with the unit of an hour, 3/10th of an hour.

From that, we can get the question of, how far does a jet plane travel going at the rate of 450 mph for 3/10th of an hour?

Since we have defined what MPH is (how many miles traveled in an hour), we can therefore figure out how to calculate that question with math.

The correct method to calculate would be to multiply 3/10 and 450 together. Why?

Multiplication is essentially adding something a certain number of times. For example, multiplying 2 by 3 is adding 2 three times, to get 6.

Now, if you want to find 3/10th of 450, you would multiply it as that would result in 3/10th of 450, as you're adding 3/10th of 450. (as for lack of better phrasing.)

(Very vague explanation as to why, if it interests you you can think about it more personally.)

3/10 * 450 = 135 miles

Final answer:

To find the measure of angle KNL, we need to add the given upward-left obtuse angle and the downward-right acute angle. Simplify the expression to find the measure of angle KNL.

Explanation:

The question is asking for the measure of angle KNL. We are given that lines MK and JL intersect at their midpoint N. We are also given that the upward-left obtuse angle is labeled as (5x+2) degrees and the downward-right acute angle is labeled as [3(x+14)] degrees.

To find the measure of angle KNL, we need to add the two given angles together since angle KNL is formed by the intersection of these two lines. So, we have:

m angle KNL = (5x+2) + [3(x+14)]

Simplifying the expression, we get:

m angle KNL = 5x + 2 + 3x + 42

m angle KNL = 8x + 44

Therefore, the measure of angle KNL is 8x + 44 degrees.

Final answer:

The measure of angle m∠KNL is 136°.

Explanation:

The question asks for the measure of the angle m∠KNL. It provides some information about the angles formed by the line segments MK and JL. The upward-left obtuse angle is labeled as (5x+2)° and the downward-right acute angle is labeled as [3(x+14)]°. To find m∠KNL, we need to solve for x and substitute it into one of the angle expressions.

We know that the sum of the measures of the angles in a triangle is 180°. Since m∠KNL is opposite the obtuse angle (5x+2)°, we can write the equation as: (5x+2)° + [3(x+14)]° + m∠KNL = 180°.

Simplifying the equation by expanding the brackets and combining like terms, we get: 5x + 2 + 3x + 42 + m∠KNL = 180. Combining like terms further, the equation becomes: 8x + m∠KNL + 44 = 180. To isolate m∠KNL, we subtract 44 from both sides, resulting in: 8x + m∠KNL = 136. Therefore, the measure of angle m∠KNL is 136°.

Question: The area of triangle MNP is how many times the area of triangle JKL?

Answer: The answer you want would be 9... The area of triangle MNP is 9 times larger than the area of triangle JKL.

Explanation: It would be 9 times larger because it says the base and height which means multiply the base and the height so it would be 3*3=9

Hope It Helps!!

The area of triangle MNP is 9 times the area of triangle JKL.

The area of a triangle is equal to half the product of its base and height. Let's say the base and height of triangle JKL are represented by b and h respectively. According to the question, the base and height of triangle MNP are 3 times as long as triangle JKL, so the base and height of triangle MNP would be 3b and 3h respectively.

Now, let's calculate the area of triangle MNP:

Area of MNP = 1/2 * (3b) * (3h) = 9/2 * b * h

Similarly, the area of triangle JKL would be:

Area of JKL = 1/2 * b * h

To find the ratio of the areas, divide the area of MNP by the area of JKL:

Area of MNP / Area of JKL = (9/2 * b * h) / (1/2 * b * h) = (9/2) / (1/2) = 9

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the complete question is given below:

The base and height of triangle MNP are 3 times as long as the base and height of triangle JKL. The area of triangle MNP is how many times the area of triangle JKL?

Let the necessary amount of water be x.  Then (1.00)(1 gallon antifreeze) = 0.40(x+1 gallon), or 1 = .40x + .40.  Combining like terms:  0.60 = 0.40x.

Then x = 0.60 / 0.40 = 1.5.

Adding 1.5 gallons of water to that 1 gallon of pure antifreeze results in 2.5 gallons of 40% antifreeze.

To create a solution that is 40% antifreeze, you would add .6 gallons of water to 1 gallon of pure antifreeze, using a ratio to determine this.

To find out how much water should be added to a gallon of pure antifreeze to create a solution that is 40% antifreeze, you would use a ratio. We find that 40% of a gallon of antifreeze is .4 gallons, as 1 gallon is equivalent to 100%. If this .4 gallons represents 40% of our final solution, that means the remaining 60% must be water.

Next, we set up a ratio. If .4 gallons is 40%, then x gallons is 60%. This gives us .4/40 = x/60. Simplifying that equation, we find that x equals .6 gallons.

In conclusion, to get a solution that is 40% antifreeze and 60% water, you need to add .6 gallons of water to 1 gallon of antifreeze.

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Set the first number as x.

Note that three consecutive integers are 3 numbers that are 1 greater than the previous.

(x) + (x + 1) + (x + 2) = 72

Simplify. Combine like terms

3x + 3 = 72

Isolate the x. Note the equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 3 from both sides

3x + 3 (-3) = 72 (-3)

3x = 69

Next, divide 3 from both sides

3x/3 = 69/3

x = 23

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

23 is your first answer

Plug in 23 for each x.

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

(x) + (x + 1) + (x + 2) = 72

(x) = 23

(x + 1) = 23 + 1 = 24

(x + 2) = 23 + 2 = 25

23, 24, 25 are your answers

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

~Rise Above the Ordinary

Three consecutive integers have a sum of 72.

So They will: x, x+1, x+2

x + (x +1) + (x+ 2) = 72

= 3x + 3 = 72

= 3x = 72 - 3

= 3x = 69

= x = 33

By putting value of x in: x, x+1, x+2

Hence the integers will be: 33, 34,35

3a + 2b = 13   ⇒   -1(3a + 2b = 13)   ⇒   -3a - 2b = -13

3a + 6b = 33   ⇒   1(3a + 6b = 33)   ⇒   3a + 6b = 33

                                                                         4b = 20

                                                                           b = 5

3a +  2b = 13

3a + 2(5) = 13

3a +  10  =  13

3a           = 3

  a          = 1

Answer: a = 1, b = 5  

gcf(84,96) = 12

I hope this helps :))

GCF is 12

Example Simplified Fraction:  84/96 => 7/8

The correct answer is 12

Hope This Helps!!!

Answer:

The voltage across resistor is [tex]E_{R}=96V[/tex]

Step-by-step explanation:

We are given with Voltage across terminals of a series RL circuit, [tex]E_{T}=120V[/tex]

And Resistance R=40Ω

And inductor reactance [tex]X_{L}=30[/tex]Ω

Since Resistor and inductor are in series, same current flows through both.

And that current, I = [tex]\frac{E_{T}} {Z}[/tex]

                             [tex]=\frac{120}{\sqrt{40^{2}+30^{2}}}= \frac{120}{\sqrt{2500}}[/tex]

                            = [tex]\frac{120}{50}=2.4A[/tex]

Therefore voltage across resistor, [tex]E_{R}=IR=2.4X40=96V[/tex]

The voltage across the resistor in the RL circuit, given the total voltage, resistance, and inductive reactance, can be calculated using Ohm's Law and the principles of Kirchhoff's voltage law. The final calculated voltage is 96 volts.

In this RL circuit, we're given the total voltage (ET), the resistance (R), and the inductive reactance (XL). Here, we need to calculate the voltage across the resistor, or ER. In a series RL circuit, the sum of the voltages across the resistor and the inductor equal the total voltage, according to Kirchhoff's voltage law. This is written as:

ET = ER + EL

Where ET is the total circuit voltage, ER is the voltage across the resistor, and EL is the voltage across the inductor. The voltage across the resistor, ER, can be calculated using Ohm's Law (V=IR). The current can be calculated using the total voltage divided by the overall impedance (Z). Therefore, ER can be calculated using the equation ER = IR, where I = ET/Z, and Z is the square root of R^2 + XL^2. With the provided values, we calculate:

Z = sqrt(R^2 + XL^2) = sqrt(40^2 + 30^2) = 50 Ω

I = ET/Z = 120/50 = 2.4 A

Finally, calculate ER:

ER = IR = 2.4 * 40 = 96 volts.

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Answer:

range ⇒ answer D

Step-by-step explanation:

* Lets explain how to solve the problem

- Outlier an extreme value in a set of data which is much higher or

 lower than the other numbers

- Outliers affect the mean value of the data but have little effect on the

 median or mode of a given set of data

* Lets solve the problem

∵ The data are 10 , 12 , 13 , 14 , 15 , 16 , 42

∵ The median is the middle number of the set of data

∵ The middle number is 14

∴ The median is 14

- If we remove the outlier then:

∴ The median will be the average of the two middle numbers 13 , 14

∴ The median = (13 + 14)/2 = 13.5

∵ The mean is the average, where you add all the numbers and then

  divide the sum by the number of numbers

∵ The sum = 10 + 12 + 13 + 14 + 15 + 16 + 42 = 122

∵ They are 7 numbers

∴ The mean = 122/7 = 17.43

- If we remove the outlier then:

∴ The sum = 122 - 42 = 80

∴ The mean = 80/7 = 11.43

∵ The range is the difference between the greatest and the

  smallest values of the data set

∵ The greatest value is 42 and the smallest value is 10

∴ The range = 42 - 10 = 32

- If we remove the outlier then:

∴ The range = 16 - 10 = 6

* The range is the most affected by the outlier

For #10

x=2     w(x)= 5

x=0     w(x)=-9

x=1     w(x)=-1

x=4    w(x)=7

To get these answers, you must use the p(x) table. When x=2, p(x)=6. So you would substitute p(x) for 6 and solve. That would be what you would do for the rest of teh problems.

For #12, the answer would be 5x^2+15x+5

Just mutiply the areas of the out side and inside and subtract them

The total amount of time would be 1 hour and 40 minutes or 1.66666 hours.

I hope this helps :)

both of those mark the answer or number smaller

Division is basically repeated subtraction.

For example, if you ask "what is 6 divided 2?", you're asking "how many times do I need to subtract 2 from 6 until I get to 0?"

Let's see it in action

6/2

6 - 2 - 2 - 2 = 0

As you can see, you subtract 2 from 6 three times, so 6 divided by 2 is 3.

Hey there!!

Shape given - Cylinder

In order to find the amount of gas the vessel can hold, we will have to find the volume of the cylindrical vessel.

How do we find the volume of a cylindrical vessel?

The formula : πr²h

Where ' r ' is the radius and ' h ' is the height.

The height is given by 9 feet.

The diameter is given by 6 feet. This is the tricky part, we will have to use the radius not the diameter.

The diameter = Radius + Radius

6 = radius + radius

6 = 2 × radius

Dividing 2 on both sides

6 ÷ 2 = radius

Hence, the radius is 3 feet.

We have :

Height = 9 feet

Radius = 3 feet

Volume : π ( 3 )² ( 9 )

... π × 9 × 9

... π × 81

... 3.14 × 81

... 254.34 feet³

Hence, the amount could be held in the cylindrical is 254.34

Hope my answer helps!!

Answer:

81 pi or 254.469004941

Hey there!!

Given :

... 4x = 420

If we divide 4 on both sides, we will get the value of ' x '.

... x = 420 / 4  

... x = 105

Hope my answer helps!!

Hello!

Solve for x.

[tex]4x = 420[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓

First you had to divide by 4 from both sides of the equation.

[tex]\frac{4x}{4}=\frac{420}{4}[/tex]

Simplify it should be the correct answer.

[tex]x=105[/tex]

Answer⇒⇒⇒⇒x=105

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

Solution

g(x) = 2[tex]x^{2}[/tex] - 11x

Plugging in x = -1 in g(x), we get

g(-1) = 2[tex](-1)^{2}[/tex] - 11(-1)

Now we have to simplify it.

g(-1) = 2*1 + 11

g(-1) = 2 + 11

g(-1) = 13

So the answer is D) 13.

Thank you. :)

This exercise is about Place Value. The kind of things that have prices with a leftmost digit in hundreds place are:

The kind of things that have prices with a leftmost digit in thousands place are:

The kind of things that have prices with a leftmost digit in ten thousands place are:

Place Value is the value of a digit as given by its position in the number such as ones, tens, hundreds, etc.

For example, the place value of 6 in 3468 is 6 tens, or 60. See the attached image explaining place value of numbers.

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The answer is -10

As the given equation is

[tex]kx - 4y - k = 0[/tex]

Putting the value of x as -1 and y as 5

[tex]k (-1) - 4 (5) - k = 0[/tex]

[tex]-k -20 - k = 0[/tex]

[tex]-2k -20 = 0[/tex]

[tex]K = -10[/tex]

So the value of k is 10

Slope formula: [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex]

Given the two sets of coordinates (8,0) and (0,-2), plug them into the formula to find the slope. x1 is 8, x2 is 0, y1 is 0, y2 is -2.

[tex]\frac{0-(-2)}{8-0}[/tex]

[tex]\frac{0+2}{8-0}=\frac{2}{8}=\frac{1}{4}[/tex]

The slope is[tex]\frac{1}{4}[/tex].

I hope this helps :)

Answer:

3/20

Step-by-step explanation:

First we need to find a common denominator, and since 4*5=20 then 20 is he common denominator.

convert the fractions to twentieths so

3/5*4/4

12/20

1/4*5/5

5/20

now add 12/20+5/20

17/20

that is how many students are doing sports

so subtract 20-17

you get 3/20 students play basketball since you can't simplify that

Last year a man earned 19,200. This year his salary increased to 20,736. What was the percent of his increase ?

Solution

Here we have to use the formula.

Percentage of increase =[tex]\frac{Increase}{Original number}  *100[/tex]

Increase in earning = 20, 736 - 19,200 = $1536

Original number = 19,200

Now plugin these values into the formula, we get

Percentage of increase = [tex]\frac{1536}{19200} *100 = \frac{153600}{19200} = 8[/tex]%

The answer is 8%

Hope you will understand the steps.

Thank you. :)

m = number of medium pizzas; each medium pizza costs $5

5m = cost of m number of medium pizzas

L = number of large pizzas; each large pizza costs $8

8L = cost of L number of large pizzas

The total cost is the sum of the cost of the medium pizzas and the cost of the large pizzas, so the total cost is 5m + 5L.

You have $45, so the total cost of the pizzas must equal $45.

The equation is

5m + 8L = 45

the answer is 0=0 because there is infinite solutions

13 + 3p + 10 = 23+ 3p

23+ 3p= 23+3p

23-23= -3p+3p

0=0

Answer with explanation:

⇒When a design or geometrical shape is reflected over Axis, which is lying in two Dimensional plane,the two, Pre-image that is geometrical shape before reflection and geometrical shape called Image after reflection , they both are congruent to each other.The Line through  which the two,Image and Pre Image , are congruent in the plane, is called "Line of Reflection".

⇒When Reflection through a line takes place, corresponding Sides of two designs are congruent,means equal, and the Corresponding interior Angles of two designs are also Congruent.

Option C:⇒ Congruency