Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.
What is function ?Mathematics includes the study of numbers, various variations, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship variable between the number of inputs and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a domain. The letter f is frequently used to denote functions (x).
Here,
Given :
=> f(−4) = −2
=> ƒ'(−4) = 6
=> f(-5) = −4
=> f'(-5) = 1
To find :
=> g(x) = ƒ(2x + 3)
=> g(4) = f(2(-4) + 3)
=> g(4) = f(-5)
=> f(-5) = -4
=> f'(-5) = 1
Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.
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Which of the following numbers is probably an irrational number? 0 1.6490221... 3/4 -5
The number that probably is an irrational number is 1.6490221...
How to determine the irrational numberAn irrational number is a number that cannot be expressed as a finite decimal or a fraction.
The number 0 is not irrational.
The number 1.6490221... is an example of a decimal that goes on forever, which is the characteristic of an irrational number.
The number 3/4 can be expressed as a fraction and is therefore not irrational.
The number -5 is not irrational.
Therefore, the answer is 1.6490221..., which is probably an irrational number.
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In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 23% of your total grade, each major test is worth 21.5%, and the final exam is worth 34%. Compute the weighted average for the following scores: 94 on the lab, 89 on the first major test, 63 on the second major test, and 73 on the final exam. Enter your answer as a whole number.
Answer: 79
Step-by-step explanation: The weighted average for the scores can be calculated as follows:
Lab score: 94 x 0.23 = 21.62
First major test: 89 x 0.215 = 19.135
Second major test: 63 x 0.215 = 13.495
Final exam: 73 x 0.34 = 24.82
Total weighted average: 21.62 + 19.135 + 13.495 + 24.82 = 78.976
Rounding to the nearest whole number, the weighted average is 79.
Write 23.224 as a rational number
Answer:
Step-by-step explanation:
0.10267857142000002
Determine the interval(s) for which the function shown below is decreasing.
The intervals where the function is decreasing are:
(-3, -1) and (4, ∞)
In which intervals is the function decreasing?The function is decreasing when, reading from left to right, the graph goes dondwards.
Now let's find the intervals where that happens.
First that happens between x = -3 and x = 1
And then the function starts decreasing again at x = 4 and keeps decreasing.
Then the intervals where the function decreases are:
(-3, -1) and (4, ∞)
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A survey was carried out to find the favorite beverage of a particular telemarketing company having 2,000 employees. To carry out this survey, two groups of 100 employees each were randomly selected and asked to vote for their favorite beverage. The results obtained are given in the table shown below.
Beverage Group A Group B
Coffee 42 44
Green Tea 9 11
Soft Drinks 28 22
Energy Drinks 21 23
Which of the following statements about the data above is true?
According to the information in the table, the correct options are: The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A. (option B).
How to identify the correct sentence?To identify the correct option that matches the information in the survey table, we must read each of the options and compare it with the information in the table to establish one as true.
Based on the above, we can infer that the correct option is option B because the number of employees who voted for coffee in group B is greater than the number of employees who voted for coffee in group A.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Options:
A. The estimated number of employees who would have voted for green tea is higher when based on the results of Group A rather than Group B.
B. The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.
C. The estimates for both groups show an equal number of employees would have voted for coffee.
D. The estimated number of employees who would have voted for coffee is higher when based on the results of Group A rather than Group B.
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At a football game, 43% were supporting the visiting team. If total number of people attending the game was 2800, how many people were supporters of the home team?
Please help! The question is in the image.
Answer:
Step-by-step explanation:
Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup. How many grams of 25% sugar syrup did Samantha use?
Answer:
40 grams
Step-by-step explanation:
Answer: 120-x
Step-by-step explanation:
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The correct answer from options are,
a) x⁴ – 6x² – 27 = 0,
d) 6(2x + 4)² = (2x + 4) + 2 and,
e) 6x⁴ = -x² + 5.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must contain at least one term of the second degree.
Given equations to find the equations that are quadratic in form,
Standard form refers to the quadratic function f(x) = a(x - h)² + k, where a is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.
so equations that are in form of quadratic are,
x⁴ – 6x² – 27 = 0,
6(2x + 4)² = (2x + 4) + 2,
6x⁴ = -x² + 5
and rest all other equations are not in form of quadratic.
Hence options A, D, and E are correct.
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PLEASE HELP ASAP DONT IGNORE:(((
Answer:
Step-by-step explanation:
Notebooks Total Cost
0 0.00
1 3.00
2 6.00
3 9.00
If a fair die is rolled 5 times what is the probability of rolling 3 sixes to the nearest thousandth
The probability of rolling 3 sixes to the nearest thousandth is 0.556.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Using binomial distribution.
[tex]^nC_r P^cQ^{n - r}[/tex]
Now,
Probability of getting a six = 1/6
P = 1/6
Probability of not getting a six = 5/6
Q = 5/6
Now,
n = 5 and r = 3
So,
[tex]^nC_r P^rQ^{n - r}[/tex]
= [tex]^5C_3(1/2)^3(5/6)^2[/tex]
= (5 x 4)/2 x (1/2) x (1/2) x (1/2) x (5/6) x (5/6)
= 10 x 1/8 x 25/36
= 5/9
= 0.556
Thus,
The probability of rolling 3 sixes is 0.556.
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A teacher is placing a border around the classroom bulletin board which measures 28 7/8 inches long by 22 one fourths inches wide what is the length of the border
On solving the provided question we cans ay that area of bulletin board would be 22*10 = 220 cm sq.
What is area?The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.
This question depends on how thick you would want the border to be.
One simple way to find this is finding the perimeter of the bulletin board. You can do this by using the formula: 2(L) + 2(W)
(L) Represents Length
(W) Represents Width
In this situation, it would be 2(4) + 2(6)
that would turn into 8 + 12
which turns into 20 feet.
area of bulletin board would be 22*10 = 220 cm sq.
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A person who is exercising should not exceed his or her maximum heart
rate, which is determined on the basis of that person's gender, age, and
resting heart rate. The table relates resting heart rate and maximum heart
rate for a 20-year-old man.
a) Use a graphing calculator to model the data with a linear function.
b) Estimate the maximum heart rate if the resting heart rate is 40, 60, 72,
and 80.
c) What is the correlation coefficient? How confident are you about using
the regression line to estimate function values?
Answer:5 star would be greatly aprreciated
For b) Estimating the maximum heart rate, a common formula used to calculate maximum heart rate is:
Max HR = 220 - Age
Since the person is 20 years old, the maximum heart rate can be estimated as:
Max HR = 220 - 20 = 200 beats per minute.
To estimate the maximum heart rate given a resting heart rate, we can use the formula:
Max HR = Resting HR + (Max HR - Resting HR) * Percentage of Max HR
Assuming a typical range of 70-85% of maximum heart rate during exercise, the estimated maximum heart rate for a resting heart rate of 40, 60, 72, and 80 beats per minute would be:
Resting HR = 40: Max HR = 140 + (200 - 140) * 0.85 = 170 beats per minute
Resting HR = 60: Max HR = 140 + (200 - 140) * 0.80 = 176 beats per minute
Resting HR = 72: Max HR = 140 + (200 - 140) * 0.75 = 182 beats per minute
Resting HR = 80: Max HR = 140 + (200 - 140) * 0.70 = 188 beats per minute
For c) the correlation coefficient, the coefficient measures the strength and direction of the linear relationship between two variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.
Step-by-step explanation:
For b) Estimating the maximum heart rate, a common formula used to calculate maximum heart rate is:
Max HR = 220 - Age
Since the person is 20 years old, the maximum heart rate can be estimated as:
Max HR = 220 - 20 = 200 beats per minute.
To estimate the maximum heart rate given a resting heart rate, we can use the formula:
Max HR = Resting HR + (Max HR - Resting HR) * Percentage of Max HR
Assuming a typical range of 70-85% of maximum heart rate during exercise, the estimated maximum heart rate for a resting heart rate of 40, 60, 72, and 80 beats per minute would be:
Resting HR = 40: Max HR = 140 + (200 - 140) * 0.85 = 170 beats per minute
Resting HR = 60: Max HR = 140 + (200 - 140) * 0.80 = 176 beats per minute
Resting HR = 72: Max HR = 140 + (200 - 140) * 0.75 = 182 beats per minute
Resting HR = 80: Max HR = 140 + (200 - 140) * 0.70 = 188 beats per minute
For c) the correlation coefficient, the coefficient measures the strength and direction of the linear relationship between two variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.
To model the data with a linear function, find the slope using two points from the table, and use the slope-intercept form of the equation to find the y-intercept. To estimate the maximum heart rate for different resting heart rates, substitute the values into the equation. The correlation coefficient cannot be determined based on the given table of data.
Explanation:To model the data with a linear function, we can use the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m). The slope is given by the formula: m = (y2 - y1) / (x2 - x1). We can choose any two points from the table to calculate the slope. Let's choose (60, 200) and (70, 180) as our two points.
Using the formula, we have m = (180 - 200) / (70 - 60) = -20 / 10 = -2.
Now, we can use the slope-intercept form of the equation to find the y-intercept (b). Let's substitute one of the points into the equation: 200 = -2(60) + b. Solving for b, we get b = 320.
Therefore, the equation of the linear function that models the data is y = -2x + 320.
To estimate the maximum heart rate for different resting heart rates, we can substitute the given values into the equation:
If the resting heart rate is 40: y = -2(40) + 320 = 240.
If the resting heart rate is 60: y = -2(60) + 320 = 200.
If the resting heart rate is 72: y = -2(72) + 320 = 176.
If the resting heart rate is 80: y = -2(80) + 320 = 160.
The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, it represents the correlation between resting heart rate and maximum heart rate. The closer the correlation coefficient is to 1 or -1, the stronger the correlation. However, since we are given a table of data and not actual data points, we cannot calculate the correlation coefficient. We can only estimate it visually based on the scatter plot of the data points.
Therefore, the correlation coefficient cannot be determined and our confidence in using the regression line to estimate function values is limited.
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Write a system of linear inequalities represented by the graph.
The inequalities representing the graph are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
First, we have to determine the two lines.
Line₁.
(0, 2) and (1, - 1).
m = (- 1 - 2)/(1 - 0).
m = - 3.
- 1 = - 3(1) + b.
b = 2.
y = - 3x + 2.
Line₂.
(0, - 2) and (3, 0).
m = (0 + 2)/(3 - 0).
m = 2/3.
0 = (2/3)(3) + b.
b = - 1.
y = (2/3)x - 1.
So, The two inequalities are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.
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The scale on a 1:50 000 ordnance survey map indicates that 2cm on the map = 1km on the ground. How many centimetres would 1km be represented by on a 1:25 000 scale map
1km would be represented by 4cm on a 1 : 25000 scale map.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The scale on a 1 : 50000 ordnance survey map indicates that 2cm on the map = 1km on the ground.
We know 1 km = 1×100000 = 100000 cm.
So, If 2 cm represents 100000 cm it has a scale factor of 100000/2 = 50000.
Now, Again 1 km = 100000 cm,
So, 1km will be represented by 100000/25000 = 4 cm.
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Question 9 find the height of the building
were going to need a lil more than that to answer :(
A mallard duck has 13 ducklings. Five of the ducklings are male. What
is the ratio of male to female ducklings?
Answer: 13 ducklings 5 male 7 female so the answer is 5:7
Step-by-step explanation:
The area of the circular base of a cone is 25π cm², and the slant height of the cone is four times the radius of the cone.
What is the approximate lateral area of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest whole number in the box.
The approximate lateral area of the cone is equal to 314 cm².
How to calculate the lateral area of the cone?Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:
Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)
Where
l represents the slant height of the cone.r represents the radius of the cone.h represents the height of the cone.How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area of a circular base = πr²
25π = πr²
Radius, r = √25
Radius, r = 5 cm.
Substituting the given parameters into the lateral area of a cone formula, we have the following;
Lateral surface area of a cone, LSA = πrl = πr4(r)
Lateral surface area of a cone, LSA = 3.14 × 5 × 20
Lateral surface area of a cone, LSA = 314 cm².
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over the course of an 18 year research project, the height of an oceanside cliff actually dropped due to soil erosion. At the end of this period, its height was measured as -3 inches compared to what it had been at the beginning of the research project. What was the average amount that the cliff's height changed each year?
The average amount of cliff's height that decreased each year is 1/6 inches.
What is unit rate?The rate at which one value changes with respect to per unit change in the other value is called the unit rate. Mathematically -
{ r } = y/x .... Eq { 1 }
Given is that over the course of an 18 year research project, the height of an oceanside cliff actually dropped due to soil erosion. At the end of this period, its height was measured as -3 inches compared to what it had been at the beginning of the research project.
We can write the the average amount of cliff's height that changed each year as -
{r} = |h|/|t|
{r} = 3/18
{r} = 1/6
Therefore, the average amount of cliff's height that decreased each year is 1/6 inches.
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Look at the figure. Find the value of CG.
VIEW THE IMAGE ATTACHED BELOW.
Answer:
CG = 8
Step-by-step explanation:
Given CG = 4x-16 is congruent to AG = 2x -4, you want the value of CG.
SetupThe congruent segments are equal length:
CG = AG
4x -16 = 2x -4
Solution2x = 12 . . . . . . . . . . add 16 -2x
Substitute into the expression for AG:
2x -4 = 12 -4 = 8
AG is congruent to CG, so ...
CG = 8
__
Additional comment
You know triangles GBC and GBA are congruent by the HA theorem, since GB bisects angle ABG. Corresponding parts of congruent triangles are congruent, so CG ≅ AG.
Question in image, PLEASE HELP
The value of ST = 10 for the given rectangle.
What is a rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
In the given triangle PQRS, the diagonals bisect each other, that is they divide each other in equal halves.
Thus. PT = TR
Since, PT = 10 we have TR = 10,
The diagonals of the rectangle are equal, hence we also have:
TR = ST
Since, the value of TR = 10, then the value of ST = 10.
Hence, the value of ST = 10 for the given rectangle.
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Sam is moving bags of soil from a loading dock into a storeroom. The topsoil
weighs 40 pounds per bag, and the mulch weighs 20 pounds per bag. The
cart Sam uses to move the bags can only carry up to 480 pounds.
Which graph represents the number of topsoil bags and mulch bags that Sam
can move in a single trip? Graphed
The inequality that can be used to represent the number of topsoil and mulch Sam can carry is, 40x + 20y ≤ 480
And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that:
Weight of top soil = 40 pounds
Weight of mulch = 20 pounds
Total weight Sam can carry = 480 pounds
Now, Let number of bags of top but soil = x
And, The number of weight of mulch = y
Hence, The inequality is,
⇒ 40x + 20y ≤ 480
Therefore, the inequality that can be used to represent the number of topsoil and mulch Sam can carry is 40x + 20y ≤ 480
And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.
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Find the ordered pair that is a member of both -6x + 3y = 84 and
-6x - 3y = 24 or indicate if it does not exist or there are infinite
possibilities.
Answer:
(- 9, 10 )
Step-by-step explanation:
Solve the equations simultaneously to find solution to both
- 6x + 3y = 84 → (1)
- 6x - 3y = 24 → (2)
add (1) and (2) term by term to eliminate y
- 12x + 0 = 108
- 12x = 108 ( divide both sides by - 12 )
x = - 9
substitute x = - 9 into either of the 2 equations and solve for y
substituting into (1)
- 6(- 9) + 3y = 84
54 + 3y = 84 ( subtract 54 from both sides )
3y = 30 ( divide both sides by 3 )
y = 10
solution is (- 9, 10 )
A savings account with simple annual interest rate of 3.92% and an initial deposit of $5,460.75 yields a final account balance of $6,370.51 after 51 months. - Part A: Using the rate and term as the simple interest account, calculate the final account balance if the initial deposit is invested for the same number of months, with interest compounded semiannually. Show all work.- Part B: Compare that simple interest final account balance with the compound interest final account balance.
The final account balance with compound interest is $6,440.30.
The final account balance when compounded semiannually is higher.
How to calculate the final account balance?
The formula for compound interest is:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment, including interest
P = the principal investment amount
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
Part A:
r = 3.92% = 0.0392, P = $5,460.75, n = 2 (semiannually means twice a year), t = 51 months = 4.25 years
A = P (1 + r/n)^(nt)
A = 5,460.75 (1 + 0.0392/2)^(2*4.25)
A = 5,460.75 (1 .0196)^(8.5)
A = $6,440.30
Thus, the final account balance is $6,440.30
Part B:
difference = 6,440.30 - $5,460.75 = $975.55
When the initial deposit is invested with interest compounded semiannually, the final account balance is higher.
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The area of the circular base of a cone is 16π cm², and the slant height of the cone is 4 times the radius of the cone.
What is the approximate lateral area of the cone?
The approximate lateral area of the cone is equal to 200.96 cm².
How to calculate the lateral area of the cone?Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:
Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)
Where
l represents the slant height of the cone.r represents the radius of the cone.h represents the height of the cone.How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area of a circular base = πr²
16π = πr²
Radius, r = √16
Radius, r = 4 cm.
Substituting the given parameters into the lateral area of a cone formula, we have the following;
Lateral surface area of a cone, LSA = πrl = πr4(r)
Lateral surface area of a cone, LSA = 3.14 × 4 × 16
Lateral surface area of a cone, LSA = 200.96 cm².
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Answer:
201 beause you are rounding to the nearest whole number
Step-by-step explanation:
Please helppp I've been stuck on this for sooo long
The relation between a and c can be written as:
a = c + 24
Which is the relationship between a and c?First we know two equations:
a = b + 12
b = c + 12
So we have relations between a and b, and between b and c, and we want a relation between a and c.
If we replace the b of the first equation with the second equation, then we will get:
a = (c + 12) + 12
a = c + 24
That is the relation between a and c.
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At a coffee shop, the first 100 customers'
orders were as follows.
Small
Medium
Large
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered
a large given that he or she ordered a hot drink?
Rounded to the nearest percent, [ ? ]%
Enter
Answer:bro chilll
Step-by-step explanation:
I'll give you brainliest and extra points if it's right! :)
Answer:
see explanation
Step-by-step explanation:
given the ratio of 2 similar figures is [tex]\frac{a}{b}[/tex]
then the ratio of perimeters is also [tex]\frac{a}{b}[/tex]
and the ratio of areas is ( [tex]\frac{a}{b}[/tex] )² = [tex]\frac{a^2}{b^2}[/tex]
the ratio of side lengths, yellow to green is
[tex]\frac{36}{60}[/tex] = [tex]\frac{3}{5}[/tex] ( cancelling 36 and 60 by 12 )
the ratio of perimeters is equal to ratio of sides, that is [tex]\frac{3}{5}[/tex]
the ratio of areas = [tex]\frac{3^2}{5^2}[/tex] = [tex]\frac{9}{25}[/tex]
let x be the area of the green figure, then by proportion
[tex]\frac{45}{x}[/tex] = [tex]\frac{9}{25}[/tex] ( cross- multiply )
9x = 1125 ( divide both sides by 9 )
x = 125
that is the area of the green figure is 125 units²
What is a number that when you multiply it by 7 and add 2 to the product, you get 30?
Answer:
4
7 * 4 = 28
28 + 2 = 30
Step-by-step explanation:
Hope it helps! =D
Solution is in the attachment!!
You have a credit card and on January 1 the balance is $700. On January 8th you purchase a new sofa for $1100. On the 14th you make a payment of $550. On the 22nd you make a purchase of lamps and other household items for $475. What is the average daily balance for January?
Answer:pls brainliest :D
Step-by-step explanation:
To find the average daily balance for January, we need to find the total balance for the month and divide by the number of days in the month.
Starting balance: $700
Sofa purchase: $1100
Payment on January 14th: $550
Lamps and household items purchase: $475
Total balance: $700 + $1100 + $475 - $550 = $1825
There are 31 days in January, so the average daily balance is: $1825 / 31 = $58.87.