solve the following 4x-1/2 = x + 7 and 3x + 2 = 2x+13/3
Answer:
a. 2.5
b. 2.333
c. 2.85
Step-by-step explanation:
A) 1. subtract -x on both sides 2. to get 3x-1/2=7
3. Add 1/2 on both sides 4. to get 3x=7.5
5. divide 3 on both sides 6. To get... x=2.5
B)1. Same process. 2. x+2=13/3
3. x=13/3-2 4. x= 2.33(repeating)
C) 1. same process. 2. 2x-x/3=3+7/4
3. 2x-x/3=4.75 4. Isolate -x/3
5.-x/3=4.75-2x 6. multiply both sides by 3
7. -x=14.25-6x 8. 5x=14.25
9. x= 2.85
* remember to distribute the 3 to each variable.
Answer:
1) 4x-1/2 = x + 7
Answer : x=5/2
2) 3x + 2 = 2x+13/3
Answer: x=7/3
Step-by-step explanation:
1) 4x-1/2 = x + 7
Solution
Let's solve your equation step-by-step.
4x−1/2=x+7
Step 1: Simplify both sides of the equation.
4x+−1/2=x+7
Step 2: Subtract x from both sides.
4x+−1/2−x=x+7−x
3x+−1/2=7
Step 3: Add 1/2 to both sides.
3x+−1/2+1/2=7+1/2
3x=15/2
Step 4: Divide both sides by 3.
3x/3=15/2/3
x=5/2
2) 3x + 2 = 2x+13/3
Solution
Let's solve your equation step-by-step.
3x+2=2x+13/3
Step 1: Subtract 2x from both sides.
3x+2−2x=2x+13/3−2x
x+2=13/3
Step 2: Subtract 2 from both sides.
x+2−2=13/3−2
x=7/3
a car rents for $ per week plus $ per mile. find the rental cost for a two-week trip of 500 miles for a group of three people.
The equation for a two-week trip of 500 miles' rental cost is Total rent cost = 2x + 500y
Information about the problem:
Car rent per week = xCar rent per mile = yweeks = 2Miles = 500 milesTo solve this problem, we have to state the equation using the information of the problem:
Car rent for 2 weeks = 2x
Car rent for 500 miles = 500y
Total rent cost = 2x + 500y
Example:
Car rent per week = $280/ week
Car rent per miles = $0.75/ mile
Total rent cost = (2 weeks * $280/ week) + (500 miles * $0.75/ mile)
Total rent cost = $560 + $375
Total rent cost = $935
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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Evaluate. 7+2^2⋅6+2^3−6
Which of the following shows the equation after the variables have been collected on the left and the constants have been collected on the right? −2x+13=−7x+28
−9x=15
5 x= 15
5x=41
−9x=41
Rearrange Vf^2=Vi^2+2aX for Vi
Making Vi the subject of formula gives the following expression: Vi = √(Vf² - 2aX).
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to make Vi the subject of formula?In this exercise, you're required to describe the steps that should be taken to rearrange and make Vi the subject of formula. Therefore, the appropriate and required steps are listed as follows:
Vf² = Vi² + 2aX
Subtracting 2aX from both sides of the equation, we have:
Vf² - 2aX = Vi² + 2aX - 2aX
Vi² = Vf² - 2aX
Taking the square root of both sides, we have:
Vi² = Vf² - 2aX
Vi = √(Vf² - 2aX)
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Alisa drove from her house to the beach at a speed of 55 miles per hour. If it took her 1.8 hours to get to the beach, about how many miles away from the beach is Alisa's house?
Alisa's house is about 99 miles from the beach
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
With above formula, we can determine the distance of Alisa's house from the beach. Details below
How to determine the distanceThe following data were obtained from the question:
Speed = 55 miles per hourTime = 1.8 hoursDistance =?The distance of Alisa's house from the beach can be obtained as followed:
Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 55 × 1.8
Distance = 99 miles
Thus, Alisa's house is about 99 miles from the beach
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The distance between the beach and Alisa's house is 99 miles.
About how many miles away from the beach is Alisa's house?Here we need to use the general relation:
Distance = Speed*Time.
Here we know that Alisa's speed is 55 miles per hour, and she drives for 1.8 hours, then we can replace:
Speed = 55 mi/h
Time = 1.8 hours
Replacing that in the distance relation we will get:
D = (55 mi/h)*(1.8 h)= 99 mi
The distance between the beach and Alisa's house is 99 miles.
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the distance a falling object travels towards the earth is directly proportional to the square of the time that it falls. if an orange falls 16 feet in 4 seconds, how far will it fall in 8 seconds ?
The orange will fall 64 feet in 8 seconds.
Distance:
Distance is defined as how much ground an object has covered despite its starting or ending point.
Given,
The distance a falling object travels towards the earth is directly proportional to the square of the time that it falls.
And an orange falls 16 feet in 4 seconds.
Here we need to find the how far it will fall in 8 seconds.
Based on the given details,
We know the that distance is,
D = kt²
where
k is the constant of proportionality.
To find the value of k we have to apply the given values on the equation.
=> 16 = k x (4)²
=> 16 = k x 16
=> k = 16/16
=> k = 1.
So, in 8 seconds it will fall at
=> D = 1 x (8)²
=> D = 1 x 64
=> D = 64 feet.
Therefore, the orange will fall at 64 feet in 8 seconds.
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2 Shape 1 and Shape 2 are congruent pentagons.
Shape 1
Shape 2
Shape 2 is congruent to Shape 1 because -
A.
Shape 2 is a translation of Shape 1.
B. Shape 2 is a reflection of Shape 1.
C. Shape 2 is a rotation of Shape 1.
D. Shape 2 and Shape 1 are both pentagons.
Option B) is correct that is shape 2 is congruent to shape 1 because shape 2 is reflection of shape 1.
We know that two figures or objects are congruent if they have the same shape and size or they are the mirror image of each other.
Translation : It simply means moving. Every point should be moved in same distance and in same direction
Rotation : It means turning around a center.
Reflection : In this, the image is of the same size as the pre-image.
So according to the given figure we can see that the shape is not translated or rotated from a center but is reflected as shape 1 is the image of shape 2.
Hence shape 2 is congruent to shape 1 because shape 2 is reflection of shape 1.
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a drug company wanted to test a new weight reduction medication. researchers identified 500 adults from the age of 30 to 40 and randomly assigned them to two groups. the first group received the medication and the second group received a placebo. after 6 weeks the percentage of each group who lost more than five pounds was recorded and compared. what type of experimental design is this?
The drug company uses the Pre experimental design to test a new weight reduction medication.
Experimental Design:
Experimental design refers to how participants are allocated to the different groups in an experiment. Types of design include repeated measures, independent groups, and matched pairs designs.
Basically, there are 3 major types of experimental designs.
They are,
Pre-experimental Research DesignQuasi-experimental Research DesignTrue Experimental Research DesignGiven,
A drug company wanted to test a new weight reduction medication.
The researchers identified 500 adults from the age of 30 to 40 and randomly assigned them to two groups.
The first group received the medication and the second group received a placebo.
After 6 weeks the percentage of each group who lost more than five pounds was recorded and compared.
Here we need to find in which experimental design is used.
Here, they used the Pre-Experimental design concept,
In the Pre-Experimental concept,
They used the static group comparison method,
Basically, the process of static group comparison method is,
In a static-group comparison study, 2 or more groups are placed under observation, where only one of the groups is subjected to some treatment while the other groups are held static. All the groups are post-tested, and the observed differences between the groups are assumed to be a result of the treatment.
Therefore, in this experiment they used the Pre-Experimental design.
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Rewrite 20 − 4x^3 using a common factor.
4x(5 − x^2)
4(5 − 4x^3)
2x(10 − 2x^2)
2(10 − 2x^3)
Answer:
4x(5 − x^2)
Step-by-step explanation:
20 − 4x^3
= 4x(5 − x^2)
The equivalent expression after taking a common factor is,
⇒ 2 (10 - 2x³)
What is Mathematical expression?
The combination of numbers and variables by using sign addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The expression is;
⇒ 20 - 4x³
Now, Take common factor as;
⇒ 20 - 4x³ = 2 × 10 - 2 × 2x³
= 2 (10 - 2x³)
Thus, The equivalent expression after taking a common factor is,
⇒ 2 (10 - 2x³)
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Mark is baking cookies for a bake sale. He needs 2 1/2 cups of flour for each batch of cookies, and he needs to make 4 1/3 batches.
How much flour does Mark need to make his cookies?
Answer: D. 10 5/6
Step-by-step explanation: K12 UNIT TEST
Rectangle ABCD has coordinates of A(-5,5) B(-5,-3), C(6,-3), D(6,5). If the rectangle is dilated using a scale factor of 1.5 how long is side AD
The length of the side AD after undergoing a dilation using a scale factor of 1.5 as required in the task content is; 16.5.
What is the length of the side AD after a dilation using 1.5 scale factor?To evaluate the length of side AD prior to the transformation which involves a dilation.
The distance between two points is given by;
D = √((y2 - y1)² + (x2 x1)²)
It follows that the lengths of the pre-image can be determined as follows;
AD = √((-5-6)² + (5 -5)²)
AD = √(-11)² + 0²
AD = √121
AD = 11
Ultimately, upon undergoing a dilation using a scale factor of 1.5, the length of AD becomes; 11 × 1.5
Hence, AD = 16.5.
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Multiply (4x^2 +8)^2
Answer:
5/2 or 2.5
Step-by-step explanation
Five over two or two and 5 tenths
Solve -7+2(-4x-3)=11. Justify each step
Answer:
x=-3
Step-by-step explanation:
Let's solve your equation step-by-step.
−7+2(−4x−3)=11
Step 1: Simplify both sides of the equation.
−7+2(−4x−3)=11
−7+(2)(−4x)+(2)(−3)=11(Distribute)
−7+−8x+−6=11
(−8x)+(−7+−6)=11(Combine Like Terms)
−8x+−13=11
−8x−13=11
Step 2: Add 13 to both sides.
−8x−13+13=11+13
−8x=24
Step 3: Divide both sides by -8.
−8x
−8
=
24
−8
x=−3
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
8:12
24:36
The following figure shows the entire graph of a relationship. A coordinate plane. The x- and y-axes each scale by one. There is a vertical line graphed at x equals negative five. A coordinate plane. The x- and y-axes each scale by one. There is a vertical line graphed at x equals negative five. Does the graph represent a function? Choose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No
Answer:
(Choice A) A Yes
Step-by-step explanation:
Please help ASAP
What is the prime factorization of 90?
2 × 3 × 5
2 × 3 × 5
2 × 2 × 3 × 5
2 × 2 × 3 × 5
2 × 3 × 3 × 5
2 × 3 × 3 × 5
2 × 5 × 9
Answer:
the prime factorizime of 90 is this 2 × 3 × 3 × 5 or 2 × 3² ×5
Please look at ALL of the screenshots and answer correctly! 20 points that's half of all of mine<: there will be another half with it!!!! the link to it is https://brainly.com/question/28634975?answeringSource=feedPublic%2FhomePage%2F21
Answer:
1. 13^5
2. prime
3. 8
4. 13
5. 6
guys help please. Enter the value for x that makes the equation 5x-2+3+-7 HELP
Step-by-step explanation:
5x-2+3-7
0=5x-9+3
0=5x-6
6=5x
x=6/5
State the minimum monthly income and hourly wage per worker needed to cover monthly expenses for the family you used in part a. Then, explain how to calculate the hourly wage based on the monthly income and state the hourly wage. Assume that each full-time worker works four 40-hour work weeks per month, and each part-time worker works two 40-hour weeks per month.
(Please Answer with good details)
Answer:
Full-time worker minimum monthly income = US$ 7,846.40
Part-time worker minimum monthly income = US$ 7,846.40
Full-time worker hourly wage = US$ 49.04
Part-time worker hourly wage = US$ 98.08
Step-by-step explanation:
1. Let's review the information given to answer the question correctly:
Monthly costs of a 2-adult and 3-children family in the Modesto metro area = US$ 7,846
Full-time worker = 4 weeks of 40-hour per month
Part-time worker = 2 weeks of 40-hour per month
2. Let's calculate the minimum monthly income and hourly wage per worker
Full-time worker hourly wage = Monthly costs/160
Part-time worker hourly wage = Monthly costs/80
Full-time worker hourly wage = 7,846/160
Part-time worker hourly wage = 7,846/80
Full-time worker hourly wage = US$ 49.04
Part-time worker hourly wage = US$ 98.08
Full-time worker minimum monthly income = Hourly wage * 160
Part-time worker minimum monthly income = Hourly wage * 80
Full-time worker minimum monthly income = US$ 7,846.40
Part-time worker minimum monthly income = US$ 7,846.40
a fort has enough food for 80 soliders for 60 days how long will the food lasts if 20 more solidets join after 15 days
Answer:36
Step-by-step explanation: 36 days
A fort is provided with food for 80 soldiers to last for 60 days. After 15 days, the food is sufficient for 80 soldiers for (60 – 15) days = 45 days. After 15 days, 20 additional soldiers join the fort. = 36 days.
Answer:
Step-by-step explanation:
A fort has food for 80 soldiers to last for 60 days.
Next 15 days the food is for 80 soldiers (60 – 15) days = 45 days.
Next 15 days, 20 MORE soldiers join the fort. = 36
ASNWER: 36 DAYS
Hanna's restaurant sells burrito bowls. The amount charged for a burrito bowl(b) is based on the cost for a plain taco plus an additional charge for each topping (t) as shown in the equation
B(t) = 0.25t +6
(A) If bill ordered a burrito bowl with 4 toppings how much would it cost.
(B) if Paul spent 7.50 how many toppings did he order
Answer:
The answer is 1
Step-by-step explanation:
The reason the answer is 1 its because 1 its a good number and everybody loves 1
Given the functions f and g, explain why you cannot find f * g.
f = { (-1,7), (1,3), (3,4), (6,8), (7,0) }
g = { (0,1), (2, -6), (4,7), (5,1), (8, -1) }
Answer:
g={(0,1), (2,-6),(4,7),(5,1), (8,1) } its korrect now
leslie drew a scale drawing of a city park. in real life, the soccer field is 99 meters long. it is 187 millimeters long in the drawing. what scale did leslie use?
leslie uses the scaling factor as 1 m actual size of soccer field is 1.89 mm in drawing.
What is scaling ?
It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.
It is given that, leslie drew a scale drawing of soccer field. in real life, the soccer field is 99 meters long. it is 187 millimeters long in the drawing.
Now, corelating the scale given which means for 99m of actual side of the soccer field scale is 187 mm. Now, the scaling factor is calculated by dividing 99 m with 187 mm.
99 m actual size of soccer field = 187 mm in drawing
1 m actual size of soccer field = (187/ 99) mm in drawing = 1.89 mm in drawing
Therefore, leslie uses the scaling factor as 1 m actual size of soccer field is 1.89 mm in drawing.
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The scale she used for the length of the park in real to her drawing is 529:1.
What is ratio ?Ratio is comparison of two or more similar units written in simplest form.
According to the given question leslie drew a drawing of a city park. in real life, the soccer field is 99 meters long. it is 187 millimetres long in the drawing.
We have to find the scale she used in her drawing.
We know 1 meter is 1000 millimetre.
∴ 99 meters is 99000 millimetres.
We know a:b can be written as a/b.
So the scale ratio of the length in real life to her drawing is
99000/187.
529/1 approx.
Which is 529:1.
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Over line TU has a midpoint at M(5,5) . Point T is at (1,8). Find the coordinates of point U.
Using the midpoint formula, the coordinates of point U are: (9, 2).
How to Apply the Midpoint Formula?The midpoint formula is: M[(x2 + x1)/2, (y2 + y1)/2]
Given the following:
Midpoint of TU is at: M(5,5)
Point T is at (1, 8), therefore, let:
M(5,5) = (x, y)
T(1, 8) = (x1, y1)
U(?, ?) = (x2, y2)
Plug in the values
M(5, 5) = [(x2 + 1)/2, (y2 + 8)/2]
5 = (x2 + 1)/2
10 = x2 + 1
10 - 1 = x2
9 = x2
x2 = 9
5 = (y2 + 8)/2
10 = y2 + 8
10 - 8 = y2
2 = y2
y2 = 2
The coordinates of point U are: (9, 2).
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question 3 consider a certain type of nucleus that has a decay rate constant of 0.0250 min-1. calculate the time required for the sample to decay to one-fourth of its initial value.
Answer:
since the decay rate constant of0.0 250 min.
hence the time required for the sample to decay to one forth of it's initial value is
Step-by-step explanation:
Answer:
Step-by-step explanation:
What is the value of the expression that is described as “half the difference of 14 and 8”?
Answer:
I would say 6
Step-by-step explanation:
Difference is subtraction.
when w=3 , x=2 , y= -4 , z= -2
wx/2 +y
Answer:
=-1
Step-by-step explanation:
3x2/2 + -4
6/2 + -4
3 + (-4)
=-1
Answer:
-1
Step-by-step explanation:
Brackets
Indicies
Division
Multiplication
Addition
Subtraction
3 × 2/2 + -4
no brackets. no indicies.
Division
2/2 = 1
3 × 1 + -4
Multiplication
3 × 1 = 3
Addition
3 + -4 = -1
Suppose you can buy 24 eggs for $3.79. How much is 1 egg? How much are one dozen eggs?
Answer:
0.16 for one egg. 1.90 for a dozen.
Step-by-step explanation:
For 24 eggs it is 3.79 dollars, so to find the price of one egg we just divide 3.79 by 24, which is 0.16.
There are 12 eggs in a dozen, and it's 3.79 for 24 eggs, so I can divide it by 2 to get to a dozen, so 3.79/2 = 1.90
Answer:
.16 per egg
1.90 for a dozen
Step-by-step explanation:
Take the total cost and divide by the number of eggs to find the cost for one egg
3.79/24 =.157916667
Since this is money we round to the nearest cent
.16
The cost per one egg is .16 or 16 cents
Multiply this by 12 to get the cost of 12 eggs
3.79/24 * 12 =1.895
This will round to 1.90
(Do not use the rounded answer to find the cost of a dozen eggs, because it will be higher. We need to use the exact answer when calculating)
Ben’s annual salary is £22000. He spends 15% of this on rent. How much is his rent per month
Answer:
£275
Step-by-step explanation:
To find how much Ben's rent is per month, we first have to find how much Ben spends on rent annually (every year). We can do this by multiplying his annual salary by the percentage spent on rent.
22000 · 0.15 = 3300
Now that we know Ben spends 3300 on rent a year, we can divide that amount by 12 (the number of months in a year) to find out how much his rent is per month.
3300 / 12 = 275