Answer:
x = -7
Step-by-step explanation:
Solve for x:
5 - 4 x + 3 (3 x + 5) = -15
3 (3 x + 5) = 9 x + 15:
(9 x + 15) - 4 x + 5 = -15
Grouping like terms, 9 x - 4 x + 5 + 15 = (-4 x + 9 x) + (5 + 15):
((-4 x + 9 x) + (5 + 15)) = -15
9 x - 4 x = 5 x:
5 x + (5 + 15) = -15
5 + 15 = 20:
5 x + 20 = -15
Subtract 20 from both sides:
5 x + (20 - 20) = -20 - 15
20 - 20 = 0:
5 x = -20 - 15
-20 - 15 = -35:
5 x = -35
Divide both sides of 5 x = -35 by 5:
(5 x)/5 = (-35)/5
5/5 = 1:
x = (-35)/5
The gcd of -35 and 5 is 5, so (-35)/5 = (5 (-7))/(5×1) = 5/5×-7 = -7:
Answer: x = -7
Answer:
x = -7
--------------------------
Hope this helps!
Have a great day and God bless! :)
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
What is the slope of the line represented by the equation f(x) = -3x + 7?
What is an equation of the line that passes through the point (4,−3) and is parallel to the line x-2y=2?
Answer:
y = 1/2x - 5
or x - 2y = 10
Step-by-step explanation:
x - 2y = 2
2y = x - 2
y = 1/2x - 1
If two lines are parallel, their slopes are equal
so m = 1/2, y = -3, x = 4
y = mx + b
-3 = 1/2(4) + b
-3 = 2 + b
b = -5
so y = 1/2x - 5
or 2y = x - 10
x - 2y = 10
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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Solve two thirds times v plus 6 equals one third times v minus 2.
v equals negative eight thirds
v equals eight thirds
v = −24
v = 24
The value of v in the equation is as follows:
v = -24How to express an equation?Solve two thirds times v plus 6 equals one third times v minus 2.
Therefore, the equation is as follows:
2 / 3 × v + 6 = 1 / 3 × v - 2
2 / 3v + 6 = 1 / 3 v - 2
add 2 to both sides of the equation
2 / 3v + 6 = 1 / 3 v - 2
2 / 3v + 6 + 2 = 1 / 3 v - 2 + 2
2 / 3v + 8 = 1 / 3 v
subtract 2 / 3 v from both sides
2 / 3v + 8 = 1 / 3 v
2 / 3v - 2 / 3 v + 8 = 1 / 3 v - 2 / 3 v
8 = 1v - 2v / 3
cross multiply
24 = - v
v = - 24
Therefore, v = -24
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Select the correct scientific notation form of this numeral using only 3 significant figures. 8,468 L
8,468 written in scientific notation is 8.47 x 10³.
What is the scientific notation?Scientific notation is used to compress large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example:
• The number : 1 x 10² is equivalent to 100
• The number 1 x 10³ is equivalent to 1000
8,468 becomes 8.47 x 10³
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Evaluate the expression when x = 9:
5∣∣6−x∣∣
Answer:
15
Step-by-step explanation:
Change x to the declared value: [tex]5|6-9|[/tex]
Subtract: [tex]5|6-9| = 5|-3|[/tex]
NOTE: remember that little minus big = negative of big minus little.
i.e.: 6-9 = -(9-6) = -(3) = -3
Evaluate the Absolute Value: [tex]5|-3| = 5(3)[/tex]
NOTE: remember that the absolute value of a number = the number's distance from 0 (always a positive number).
i.e.: |-2| = 2; |5| = 5
Multiply: [tex]5(3) = 15[/tex]
a statistician at a metal manufacturing plant is sampling the thickness of metal plates. if an outlier occurs within a particular sample, the statistician must check the configuration of the machine. the distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine? 19.3mm 19.3 millimeters 20.6mm 20.6 millimeters 22.1mm 22.1 millimeters 23.5mm 23.5 millimeters 24.9mm
As per standard deviation criteria for outliers, 26.3 mm is the maximum thickness for which the statistician would need to examine the machine's configuration.
What is the standard deviation?
The standard deviation, a mathematical statistic that describes how distributed evenly a dataset is in regard to its mean, is determined by taking the square root of such variance.The numbers that do not lie within two standard deviations of the mean are considered outliers by the two-standard deviation criteria for outliers.
If the mean is 23.5 mm and the standard deviation is 1.4 mm
Next, the highest thickness needs to be checked: mean Plus 2 (standard deviation)
= 23.5 + (2 *1.4)
= 26.3 mm
Therefore, 26.3 mm is the maximum thickness for which the statistician would need to examine the machine's configuration.
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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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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:
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
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
Evaluate. 7+2^2⋅6+2^3−6
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
What is the measure of angle B if angle C is 34 degrees and angle A is unknown?
Answer:
The measure of B is 56 degrees.
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
Select the correct answer from each drop-down menu.
Consider the equation below.
The equation was solved using the following steps.
Step 1:
Step 2:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Complete the statements below with the process used to achieve steps 1-4.
Step 3:
Step 4:
-2(5z + 8) = 14 + 6x
-2 to 5x and 8.
6x.
16.
-16.
-10 16 = 14 + 6x
-162 16 = 14
-16z
30
-
H
11
11
11
- 15
For solve the equation there are following prpperties are used
Step -1 Distributive properties,
Step - 2 Subtraction,
Step - 3 Addition, and
Step - 4 Division.
The distributive property of multiplication , simplify expressions wherein multiply a number by a sum or difference. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products.
Given equation -
-2(5x + 8) = 14 + 6x
The equation was solved using the following steps.
Step 1: -10x - 16 = 14 + 6x
Step 2: -10x - 6x - 16 = 14 = -16x -16 = 14
Step 3: -16x = 30
Step 4: x = -30 / 16
Step 5: x = -15/8.
Complete the statements with the process used to achieve steps 1-4.
Step 1 - here we are using distributive properties
-10x -16 = 14 + 6x
distribute -2 in the parenthesis to 5x and 8
Step 2 - by subtraction method
-16x - 16 = 14
subtraction of -6x
Step 3 - Aply addition
-16x = 30
Addition of 16
Step 4 - Division
x = -30/16
division of -16
x = -15 / 8
Hence , Step- 1, 2, 3, and 4 are distributive properties, subtraction, addition, and division respectively.
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Ordering 5-Digit Numbers Fill in the space below with the numbers in ascending (smallest to largest) order. 84 945 91 504 75 136, 2 94 054 85 105 93 405 73 156
We need to know about arranging numbers in an ascending order to solve the problem. The numbers arranged in ascending order is 73156, 75136, 84945, 85105, 91504, 93405, 94054.
There are two ways to arrange numbers- ascending order and descending order. Ascending order is the method of arranging numbers from lowest to highest and descending order is the method of arranging numbers from highest to lowest. To arrange 5-digit numbers in an ascending order we will need to know how to find the lowest number first. For 5-digit number we will be checking the first two digits of the number first that will tell us the numbers in tens of thousands, after we find the smallest tens of thousand in the list we follow the same process to find the consecutive numbers. If two numbers have same first two digits then we chcek the hundreds and so on. For the given question the numbers arranged in ascending order will be
73156, 75136, 84945, 85105, 91504, 93405, 94054
Therefore we found the ascending order arrangement of the 5-digit numbers which is 73156, 75136, 84945, 85105, 91504, 93405, 94054.
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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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6 is added to the product of 7 and a number.
Answer:
7x+6
Product means multiplication
and we'll use X for "number"
and add 6
so 7x+6
The required equation model as of the given condition is 6 + 7×x.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
Here,
Let the number be x,
6 is added to the product of 7 and a number.
= 6 + 7 × x
Thus, the required equation model as of the given condition is 6 + 7 × x.
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Need it fast
The number 48 is the least common multiple of which set of numbers?
9 and 16
10 and 16
16 and 24
9 and 24
Answer: the answer to your question is 16 and 24
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)
How is the graph of g(x) = -(2x)³ related to
the graph of f(x) = x³ ?
The graph of g(x) is a vertical compression of
the graph of f(x) by a factor of 2 and a reflection
across the x-axis.
The graph of g(x) is a horizontal compression of
1
the graph of f(x) by a factor of 2 and a reflection
across the x-axis.
The graph of g(x) is a horizontal stretch of the
graph of f(x) by a factor of 2 and a reflection
across the y-axis.
pls help no wrong answers will report
Find the weighted average of these values.
Value Weight
7.00 75.0%
8.00 15.0%
9.00 10.0%
By using the concept of weighted averages, the weighted average of the given values is equal to 7.35.
How to determine weighted averages?
Weighted average is a kind of average in which each element has an specific weight in contrast with uniform average, where each element has the same weight. In this problem we have three values associated to three distinct weights, whose weighted average is:
x = 0.75 · 7 + 0.15 · 8 + 0.10 · 9
x = 7.35
By using the concept of weighted averages, the weighted average of the given values is equal to 7.35.
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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
8:12
24:36
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
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
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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identify the sampling technique used for the following study. a school administrator chooses ten people at random from each class.
It is the stratified random sampling technique that was used by the school administrator.
Sampling methods are defined as how we choose members for study purposes from the population.When a person is not randomly selected which maybe it be biased somehow, the data may not be representative of the population. Stratified random sample, In this sampling, the population chosen is split first into groups ., the overall sample consists of some members from every group, and those members are chosen randomly from every group, this sampling guarantees that members from each group will be represented in the sample.
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