Step-by-step explanation:
[tex]23 - 7x = 3x + 8 \\ - 7x - 3x = 8 - 23 \\ - 10x = - 15 \\ - 10x = - 15 \\ - 10 \: \: \: \: \: \: \: \: \: \: \: \: - 10 \\ x = \frac{15}{10 \\ } \\ x = 1.5[/tex]
The value of the Equation 23 - 7x = 3x + 8 is x = 3.1
What is an Equation?A mathematical statement that shows that two mathematical expressions are equal.
Given an equation, 23 - 7x = 3x + 8
7x + 3x = 23 + 8
10x = 31
x = 3.1
Hence, The value of the Equation 23 - 7x = 3x + 8 is x = 3.1
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What is the slope of the line that passes through the points (2,8) and (-3,14)?
The slope of the line that passes through the coordinates is -6/5.
What is defined as the slope of the line?The slope of a line is a measurement of its steepness and direction. Whatever two distinct points on a line can be used to calculate the slope of that line. The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line. The net y coordinate change is Δy, whereas the net x coordinate change is Δx.The slope of the line is given by;
m = (y₂ - y₁)/(x₂ - x₁)
Where, the coordinates are given.
(x₁ ,y₁) = (2, 8)
(x₂, y₂) = (-3, 14)
Put the value in the slope;
m = (14 - 8)/(-3 - 2)
m = 6/-5
m = -6/5
Therefore, the slope of line passing from the points is -6/5
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A web designer charges customers an initial consultation fee plus an hourly rate. The table shows the linear relationship between x, the number of hours and y, the total cost of hiring the designer. a. Find the rate of change b. What does the rate of change represent in the context of the situation?
The rate of change means that the designer hourly charge is $55 per hour
Linear equation
A linear equation is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the total cost of hiring the designer after x hours.
From the table, using the point (0, 125) and (15, 950):
m = y₂-y₁/x₂-x₁= 950- 125/15-0 = 55The rate of change means that the designer hourly charge is $55 per hour
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A red plastic strip binds the three identical cylinders. The cross-sectional area enclosed by the strip is 115 cm². What is the radius of each cylinder? What is the length of the plastic strip?
The radius of each cylinder is approximately 3.49 cm and the length of the plastic strip is approximately 65.84 cm.
Cylinder is a basic 3 dimensional solid with a curved surface. A cylinder can be identified as a prism with circular base.
The cross-section of a cylinder gives a circle whose area can be represented by πr² where r is the radius of the base of the cylinder.
Here the plastic wire encloses the area of cross-section of three cylinders.
Therefore area of cross-section of one cylinder=115÷3=(115/3) cm ²
Since area of cross-section of a cylinder=πr²
Therefore πr²=(115/3)
or, r=3.4931...
or, r≈3.49 cm
Hence the radius of each cylinder is approximately 3.49 cm
Now the plastic strip covers 3 cylinders .
Circumference of each cross-section of cylinder is given by =2πr
Total length of 3 cylinders = 2πr×3 = 6πr cm
Therefore total length= 64.843...cm ≈ 65.84 cm
Therefore the length of the plastic strip is approximately 65.84 cm
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x+1, 2x-1 and 3x + 1 are the first three terms of a G.P. If x=0, find the common ratio.
Step-by-step explanation:
if that is a geometric sequence to find the common ratio
[tex] \frac{t2}{t1} [/tex]
you divide the exceeded term with the previous term
simply you can say
[tex] \frac{tn}{t(n - 1)} [/tex]
therefore now we have
[tex] \frac{2x - 1}{x + 1} or \\ \frac{3x + 1}{2x - 1} [/tex]
therefore you will substitute x=0 in any of the given equations they should give youbthe same answer
[tex] \frac{2(0) -1 }{0 + 1} = - 1[/tex]
or
[tex] \frac{3(0) + 1}{2(0) - 1} = - 1[/tex]
the common ratio is -101.07 Operations with Scientific Notation
CCSS.Math.Content.8.EE.A.4
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Two random numbers 180000000 and 0.00000534 can be written as 1.8 x 10⁸ and 5.34 x 10⁻⁶.
What is a scientific notation?Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It may be called scientific form.
When a number is written using only the digits of the number, that is considered standard notation. Since words are not used in conventional number notation, this is the way that numbers are typically written.
Let the bigger number by 180000000 and the smaller number be 0.00000534. The two numbers in scientific notations can be written as below:-
180000000 = 1.8 x 10⁸
0.00000534 = 5.34 x 10⁻⁶.
Therefore, two random numbers 180000000 and 0.00000534 can be written as 1.8 x 10⁸ and 5.34 x 10⁻⁶.
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Does the table represent a function? Why or why not?
X23345
45677
у
A. Yes, because every x-value corresponds to exactly one y-value.
OB. No, because one x-value corresponds to two different y-values.
C. Yes, because there are two x-values that are the same.
OD. No, because there are two y-values that are the same.
Based on table shown above, we have that: B. No, because one x-value corresponds to two different y-values.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Based on table shown above, we can reasonably infer and logically deduce that this table does not represent a function because one x-value corresponds to two different y-values.
In conclusion, this table is not a function because no function can have the same x-values (3) for different y-values (5 and 6).
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In 2019, the distribution of golfer Lexi Thompson’s driving distance had a mean of 276 yards. Assuming that her distribution of driving distance is approximately normal with an 80th percentile of 290 yards, calculate its standard deviation.
Standard Deviation = ___ yards. (Round to 2 decimal places.)
If mean is 276 yards, percentile is 80, sample mean is 290 yards then the standard deviation is equal to 16.63.
Given that mean is 276 yards, percentile is 80, sample mean is 290 yards.
We are required to find the value of standard deviation.
A Z-score is basically a numerical measurement that describes a value's relationship to the mean of a group of values.
Z=(X-μ)/σ--------1
Z score for 80th percentile is 0.842.
X is given as 290 and μ as 276.
We have to just put the values of mean and Z score in formula 1 to find the standard deviation.
0.842=(290-276)/σ
σ=14/0.842
σ=16.63
Hence if mean is 276 yards, percentile is 80, sample mean is 290 yards then the standard deviation is equal to 16.63.
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A hole the size of a photograph is cut from a red piece of paper to use in a picture frame. 5 4 3 2 photograph -5-4-3-2-1₁- 2/9 -2. -3- red paper -5 1 2 3 5 X What is the area of the piece of red paper after the hole for the photograph has been cut? O 17 square units 25 square units 39 square units 47 square units
Answer:57
Step-by-step explanation:
Which sum or difference is equivalent to the following expression?
2x+3/4
A. x/2 + 3/4
B. x/2 - 3/4
C. 3x/4 + 3/4
D. 8x +24
The expression that is equivalent to (2x + 3)/4 is: A. x/2 + 3/4.
How to Find Expressions that are Equivalent?Express the given expressions in their simplest form to determine the expression that is equivalent to (2x + 3)/4.
A. x/2 + 3/4
Find the common denominator. The common denominator is 4. Therefore:
= 2(x) + 1(3)/4
= (2x + 3)/4
x/2 + 3/4 ≠ (2x + 3)/4
Thus, the expression, x/2 + 3/4 is equivalent to (2x + 3)/4.
B. x/2 - 3/4 = (2x - 3)/4
Therefore, x/2 - 3/4 ≠ (2x + 3)/4
C. 3x/4 + 3/4 = (3x + 3)/4
Therefore, 3x/4 + 3/4 ≠ (2x + 3)/4
D. 8x + 24 ≠ (2x + 3)/4
Therefore, 8x + 24 ≠ (2x + 3)/4
In summary, we can conclude that, the expressions, x/2 - 3/4, 3x/4 + 3/4, and 8x +24x/2 + 3/4 is not equivalent to (2x + 3)/4. Thus, the expression that is equivalent to (2x + 3)/4 is: A. x/2 + 3/4.
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The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
a. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer weights
For the given word problem on the recommended weight of a soccer ball, we have:
An absolute value equation to find the minimum and maximum acceptable soccer weights is |x - 430| ≤ ±20. The minimum and maximum acceptable soccer weights are equal to 410 grams and 450 grams respectively.What is an absolute value equation?An absolute value equation can be defined as a type of equation that consist of an algebraic equation, which is placed within absolute value symbols.
In order to write and solve this absolute value equation, we would assign a variable (x) to the actual weight and then evaluate the resulting algebraic equation as follows:
Let x represent the actual weight.
Next, we would write an absolute value equation as follows:
|x - 430| ≤ ±20
-20 ≤ x - 430 ≤ 20
By applying the addition property of inequalities, we have:
x ≤ 430 - 20
Minimum acceptable soccer weights, x = 430 - 20 = 410 grams.
x ≤ 430 + 20
Maximum acceptable soccer weights, x = 430 + 20 = 450 grams.
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If you divide an inequality with a less than sign by -3, what inequality sign would it
change to?
help pleaseeeeeeeeeeeee
Answer:
Inverse property
Step-by-step explanation:
3/4 is the reciprocal of 4/3 which means they would cancel each other out. So you would only be left with x=x
Which situation shows the expressions ordered from LEAST to GREATEST?
OA.
B.
-6-(-8)
2.5-8
-1.9-4.3
-6-(-8)
-1.9-4.3
-1.9-4.3
2.5 8
2.5 8
2.5-8
-6-(-8)
-6-(-8)
-1.9-4.3
Answer: I hope this helps.
Step-by-step explanation:
Read each question. Then write the letter of the correct. answer on your page. The population of a town is modeled by the equation P=16,581 e⁰.⁰²t where P represents the population t years after 2000 . According to the model, what will the population of the town be in 2020 ?
(A) 16,916
(B) 17,258
(C) 20,252
(D) 24,736
The correct option is (D) 24,736.
The population growth of the town be in 2020 is 24,736.
What is termed as exponential population growth?Charles Darwin was heavily influenced by English clergyman Thomas Malthus in developing his theory of natural selection.
In 1798, Malthus published a book in which he stated that population numbers with unlimited natural resources expand quickly, but then population growth slows as resources deplete. This accelerating sequence of population growth is known as exponential growth.The stated condition is; P = 16,581 e(⁰.⁰²t)
Where, t = total number of years after 2000.
P = population t years after 2000
The total number of years between 2020 and 2000
t = 2020 - 2000
t = 20 years.
Substituting the value of the number of years 't' in the given exponential expression,
=> P = 16,581 e(⁰.⁰²×20)
=> P = 16,581 e∧(0.4)
=> P = 16,581×1.49
=> P = 24,735.94
=> P = 24,736
Therefore, the population growth of the town be in 2020 is found to be 24,736.
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Evaluate (3n)! for n=2.
Ayudaaa por favor
Tenemos un barril del que vaciamos la mitad y luego 3⁄4 de lo que
queda. ¿Qué fracción del barril ha quedado con agua? Si el barril tiene
una capacidad de 80 litros, ¿qué cantidad de líquido queda?
Answer:
1/8th
10 litres
Step-by-step explanation:
d=rt (Distance formula distance=rate•time)
t
if d=150 when r=60, find t
Answer:
25
Step-by-step explanation:
if the formula for distance is distance = rate times time then you have to divide the rate 60 by the distance 150 to get 25 .
Find the area of a rectangle with a base of 2 and a height of 6.
Answer:
12
Step-by-step explanation:
2 x 6 = 12
to find area you multiply length x width or in this case base x height
6.5 * 5 3/4 that is my question
6.5 can be translated to 6 1/2 times 5 3/4 or 5 3/4 can be translated to 5.75 times 6.5 which equals 37.375
An equation of a line through (3, 10) which is parallel to the line y = 5x + 4 has slope:
And y-intercept at:
Parallel lines have the same slope, so the slope is 5.
The equation in point-slope form is y-10=5(x-3). Substituting x=0, we get y - 10 = -15, and thus the y intercept is (0, -5).
i dont know how if tried quite a few times and cant get it
Answer:
2/3 and 3/2
Step-by-step explanation:
→ Divide the smaller triangle by the larger one for the first one
8 ÷ 12 = 8/12 = 2/3
→ Divide the larger triangle by the smaller one for the second one
12 ÷ 8 = 12/8 = 3/2
find the missing terms
_,-9,_,3,9
Answer:
-15,-9,-3,3,9
Step-by-step explanation:
A right triangle has a hypotenuse
with length 17 and a leg with
length 10. How long is the
triangle's other leg?
Answer:
[tex]3\sqrt{21}[/tex]
Step-by-step explanation:
By the Pythagorean theorem,
[tex]\sqrt{17^2-10^2}=\sqrt{189}=3\sqrt{21}[/tex]
Mei has a weekly taxable income of $265.85. her state tax rate is 6.4% and her local county tax rate is 4.7%. How much state and local tax should be withheld from her weekly pay?
The state and local tax that will be paid by Mei will be $17 and $12.50 respectively.
How to calculate the tax?From the information, Mei has a weekly taxable income of $265.85. her state tax rate is 6.4% and her local county tax rate is 4.7%.
The state tax that will be paid will be:
= Rate × Income
= 6.4% × $265.85
= 0.064 × $265.85.
= $17
The local tax that will be paid will be:
= Rate × Income
= 4.7% × $265.85
= 0.047 × $265.85.
= $12.50
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Find the x-intercept and y-intercept
from the following linear equation:
8x - 9y = 144
Answer:
X intercept (18,0)
Y intercept(0,16)
Step-by-step explanation:
hope this was helpful!
A theme park collected $900 in entry fees for 150 visitors on Friday. The amount collected varies directly with the number of visitors on a particular day.
Write an equation that gives the amount collected in fees,f for a given number of visitors,v
The equation which gives relation between entry fee collected and number of visitors in theme park: f = 6v.
What is defined as the direct proportional?A direct proportion is an arithmetical comparison of two numbers whose ratio is equal to a fixed value."When the relation between different quantities is so that if we increase one, the second will also increase, so if we decrease one, the other will also decrease, therefore the two quantities are considered to be in a direct proportion," according to the definition.The given condition is;
The total collect cost for entry in theme park = $900.
The total number of visitors = 150.
Let 'f' be the collected fee.
Let 'v' be the number of visitors.
Then, the amount collected varies directly with the number of visitors on a particular day.
f ∝ v
Removing proportional will bring the constant k;
f = kv .......eq1
v = 150 and f = 900
Put the values;
900 = 150 k
k = 6 ; put in eq 1.
f = 6v
Thus, the relation between fee and number of visitors is given by equation; f = 6v.
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The function y = log(x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
The function [y = log(x)] is translated 1 unit to the right and 2 units down, yielding [g(x) = log(x - 1) - 2] as the translated function. and this may be established by using the transformation's rules.
Given:
One unit to the right and two units down translate the function y=log(x).
The translated function's graph can be drawn using the procedures listed below:
First, write the function that is supplied.
y = log(x) (x)
Step 2: Multiply the given function in the right direction—that is, in the positive x-axis direction—by factor 1 in accordance with the data provided. The aforementioned function is now:
f(x) = lox (x - 1)
Step 3: Next, move the graph of the function f(x) in a downward direction, or in the opposite direction of the y-axis.
g(x) = log(x - 1) - 2
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como se escribe la cantidad en letra de 855672019
La cantidad 855672019 descrita en palabras es Ochocientos cincuenta y cinco millones seiscientos setenta y dos mil diecinueve.
¿Cómo representar una cantidad mediante una frase?
En este ejercicio debemos representar en palabras la cantidad asociada al conjunto de dígitos descritos en el enunciado. Para leer y describir un número se lee de izquierda a derecha, en donde un dígito a la derecha tiene más magnitud que un dígito a la izquierda, de modo que se comienza con el dígito de mayor magnitud hasta alcanzar el de menor magnitud.
8 - Ochocientos millones
5 - Cincuenta millones
5 - Cinco millones
6 - Seiscientos mil
7 - Setenta mil
2 - Dos mil
01 - Diez
9 - Nueve
En consecuencia, la cantidad 855672019 es Ochocientos cincuenta y cinco millones seiscientos setenta y dos mil diecinueve.
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Find the domain and the range of each function.
y=log₂(x-3)
The domain of the function is (3,∞) , {x|x>3}
and the range of the function is (−∞,∞), {y|y ∈ R}
given the function is y = log₂(x ₋ 3)
Set the argument in log₂(x ₋ 3) greater than 0 to find where the expression is defined.
x ₋ 3 > 0
Add 3 to both sides of the inequality.
x > 3
The domain is all values of x that make the expression defined.
Interval Notation:
(3,∞)
Set-Builder Notation:
{x|x>3}
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
(−∞,∞)
Set-Builder Notation:
{y|y∈R}
Determine the domain and range.
Domain: (3,∞) , {x|x>3}
Range : (−∞,∞), {y|y ∈ R}
Hence we get the required domain and range of the given function.
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Write
24/25
as a percentage.
Answer: 96%
How to Solve
Formula:
y ÷ x *100
Substitute
=> 24 ÷ 25 * 100
Lets Multiply 24 * 100 (or you can divde 24 and 25 then multiply with 100. do as you're convenience, answer will remain)
Answer 2400
Now As our formula says divide 2400 by 25
Answer 96
Hence 96%
So, 24/25
as a percentage is 96%
All done!
Answer:
96%
Step-by-step explanation:
First, divide 100 but 25 (the denominator) and you get 4. This means that to get a number over 100, which is a percentage you need to multiply the initial fraction by 4. You get 96/100, and you can remove the 100 to get 96%