The equation a+b+c+d=15 has infinite many solutions
How to determine the number of solutions?From the question, the equation is given as
a+b+c+d = 15
From the above representation of the equation, we can see that:
The equation is a linear equationAlso, the equation has 4 variablesWhen a linear equation that has more than one variable is given, the number of solutions cannot be quantified i.e. infinite number of solutions
Hence, the equation has infinite number of solutions
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A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1487 and the standard deviation was 314. The test scores of four students selected at randon
1870, 1250, 2170, and 1390. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
If a standardized exam's scores are normally distributed. The z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.
How to find the z-score?mu = population mean = 1487
sigma = population standard deviation = 314
x =1870
z = (x - mu)/σ
z = (1870-1487)/314
z = 1.22 (approximately)
x =1250
z = (x - mu)/σ
z = (1250-1487)/314
z = -0.75
x =2170
z = (x - mu)/σ
z = (2170-1487)/314
z = 2.18 (approximately)
x =1390
z = (x - mu)/σ
z = (1390-1487)/314
z = -0.31 (approximately)
Therefore the z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.
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The given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given that the graph of the function has increased and decreasing orders on the coordinate plane.
The interval in which the given graph of the function is increasing is,
(-∞,-6)
(-4,-1)
(3,6)
(8,∞)
Therefore, the given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).
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What value of k will translate the graph of f(x) = 5x + 6 down by 1 when replaced by f(x) + k?
Step-by-step explanation:
"down by one" means that the y values (the function result values) are all decreased by 1.
so, k = -1
what is the inequality of the length of a rectangle is 1 unit more than its width.the width of the rectangle is 2 units and the length of the wire that is used to make this rectangle is a maximum of 57 units. what represent this situation using an inequality
Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives
Perimeter = 2(L + W) ≤ 57 units How to determine the inequality that shows the length and width of a rectangleThe perimeter of a rectangle, P is given by the formula
P = 2(L + W) ≤ 57 units of wire
width, W = 2 units
length, L = 1 + W
= 1 + 2
= 3
The perimeter of the rectangle is given by
P = 2(L + W)
plugging the values of L and W
P = 2 (3 + 1)
P = 2 (4 )
P = 8 units
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Differentiate the function with respect to x.
When we differentiate the given function with respect to x we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
what is Differentiation?
Differentiate is used for calculating rates of change.
How to Differentiate function?
Some of the formulas are; Power Rule: (d/dx) (xn ) = nxn⁻¹. Derivative of a constant, a: (d/dx) (a) = 0.
Here, we have
y = 2x⁵ + 2x⁴ / 5x² -3
when we differentiate a given function with respect to x, we get
dy/dx = {(5x² -3)(10x⁴ + 8x³)} - {(2x⁵ + 2x⁴)(10x -3)}/(5x -3)²
dy/dx = (30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
Hence, after differentiating the given function with respect to x, we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
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What does “more than” mean in math?
Means if a number is bigger than other number.
Write each number as a product using gcf as a factor sipping distributive property the numbers are 28 49 77 and 3 gcf
Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.
Define GCF.The biggest number that both numbers can be divided by to get the two numbers' largest common factor. The smallest number that is a multiple of both numbers is the least common multiple of the two numbers. The largest number that may divide evenly into two or more other numbers is known as the greatest common factor (GCF). This is also sometimes referred to as the highest common factor (HCF) or the greatest common divisor (GCD).
Given,
Factor sipping distributive property,
For the numbers 28 and 49
GCF:
28 + 49
7(4) + 7(7)
7(4+7)
7(11)
77
Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.
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estimate each sum or difference.
74/10+42/5
The sum of the fraction 74/10 + 42/5 is 15 4/5.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the fraction will be illustrated as:
= 74/10 + 42/5
Change to mixed numbers
= 7 4/10 + 8 2/5
= 7 4/10 + 8 4/10
= 15 8/10
= 15 4/5
The value is 15 4/5.
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Find the value of x in the equation
4^x+16^x= 272
Answer:
x = 2
Step-by-step explanation:
What is the range of f(x)=−3x−1?
Answer:
(−∞,1/3)∪(1/3,∞),{yly≠1/3}
Step-by-step explanation:
DD.1 alculate mean, median, mode, and range What is the mean? If the answer is a decimal, round it to the nearest tenth. 45 46 43 41 43
Answer:
The answer to your question is,
MEAN = 43.6
MEDIAN = 43
MODE = 43
RANGE = 5
Step-by-step explanation:
BC I know math :)
Fin the measurement of the angle
A=
B=
C=
D=
E=
F=
G=
45°
Answer:
Step-by-step explanation:
A=60
B=75
C=45
D=60
E=75
F=45
G=90
Write the equation of the line in fully simplified slope-intercept form.
Answer: y = -x - 8
Step-by-step explanation:
Slope-intercept form is given in y = mx + b where m is the slope and b is the y-intercept.
We can see our b, the y-intercept, is -8 since the line intercepts the y-axis at (0, -8).
For our slope, we can see that the line moves down one and right one for a slope of 1/1=1. Since it's moving downwards, the slope is -1.
Now, we will write the full equation:
y = -x - 8
Write an equation for line L in point-slope form and slope-intercept form?
L is perpendicular to y=5x
Write an equation for the line L in point - slope form
The linear equation in the slope-intercept is:
y = (-1/5)*x - 26/5
And it can be written as:
y = (-1/5)*(x + 1) - 5
How to find the equation for line L?
We can write the equation for line L as:
y = a*x +b
Where a is the slope and b is the y-intercept.
Two lines are perpendicular if the product between the slopes is equal to -1.
So if we want our line to be perpendicular to y= 5x, then we must have:
a*5 = -1
a = -1/5
So our line is something like:
y = (-1/5)*x + b
And the line passes through (-1, -5), replacing these values:
-5 = (-1/5)*-1 + b
-5 = 1/5 + b
-5 - 1/5 = b
-26/5 = b
The linear equation is:
y = (-1/5)*x - 26/5
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The function g(x)=3x^3+x is an odd function.Which transformation of g(x) would result in odd functions?Check all that apply
The transformations of g(x) that would result in odd functions are (a)-g(x) , (b)g(2x) and (d)g(–x) ,
In the question ,
it is given that,
the function is g(x) = 3x³ + x
We know that the function f(x) is called an odd function if f(-x) = -f(x) .
Option(a)
the transformation is given as -g(x)
-g(x) = -(3x³ + x) = -3x³ - x
g(-x) = 3(-x)³ + (-x) = -3x³ - x
so , this is odd function .
Option (b)
the transformation is given as g(2x)
g(-2x) = 3(-2x)³ + (-2x) = -24x³ - 2x
-g(2x) = -{3(2x)³ + (2x)} = -( 24x³ + 2x ) = -24x³ - 2x
so , this is odd function .
Option (c)
the transformation is given as g(x)-3
(g(-x) - 3) = 3(-x)³ + (-x) - 3 = -3x³-x-3
-(g(x) - 3) = -{(3x³ + x) -3} = -3x³ - x +3
So, so , this is not an odd function
Option (d)
the transformation is given as g(-x)
g(-(-x)) = g(x) = 3x³+x
-g(-x) = -(3(-x)³ + (-x)) = -(-3x³ - x) = 3x³+x
so , this is odd function .
Therefore, the odd transformations are -g(x) , g(2x) and g(–x) ,
The given question is incomplete , the complete question is
The function g(x)=3x³+x is an odd function. Which transformation of g(x) would result in odd functions? Check all that apply
(a) -g(x)
(b) g(2x)
(c) g(x) − 3
(d) g(–x)
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Find(f-g)(x)if f(x)=/4x and g(x)=/16x
The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x
How to evaluate the composite function?The definitions of the functions are given as
f(x) = √4x and g(x) = √16x
Evaluate the square roots in the above equations
This gives
f(x) = 2√x and g(x) = 4√x
To find the composition (f - g)(x), we make use of
(f - g)(x) = f(x) - g(x)
Substitute the known values in the above equation So, we have the following equation
(f - g)(x) = 2√x - 4√x
Evaluate the like terms
This gives
(f - g)(x) = -2√x
Hence, the value of the composition is (c) (f - g)(x) = -2√x
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Simplify the experession
6²-3³)÷7
Answer:
9/7 or 1.285714
Step-by-step explanation:
Answer:9/7
Step-by-step explanation:
Question 9 of 10
Solve (x-3)² = 5.
A. x=-3+√√5
B. x=3+√5
C. x = 8 and x = -2
OD. x=5± √√3
Answer:
B (x = 3 + √5)
Explanation:
x² + 9 = 5
Take square root of both sides
x + 3 = ± √5
Add 3 to both sides
x = 3 + √5 or x = 3 - √5
Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
Sandy earn 306.9 dollars in commission and 1739.1 dollars in hourly wages.
How to find Sandy hour wages and commission?Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales.
She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.
The amount she will earn in her hourly wages and commission is as follows:
amount earn in commission = 15% of 2046
amount earn in commission = 15 / 100 × 2046
amount earn in commission = 30690 / 100
amount earn in commission = 306.9 dollars
Therefore,
amount earn in hourly wages = 2046 - 306.9
amount earn in hourly wages = 1739.1 dollars.
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The equation a = 12850 + 530h gives a hiker's altitude a (in feet), h hours after beginning his hike.
A. At what rate, in feet per hour, is the hiker gaining altitude?
The rate of gaining altitude for the hiker is 530 feet per hour.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
The given equation for hiker's altitude is as below,
a = 12850 + 530h
Here a is the altitude in feet and h is time in hours.
In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,
a = 12850 + 530h
Differentiate the above equation w.r.t h as,
da/dh = 0 + 530
= 530
Hence, the rate of gaining altitude is 530 feet per hour.
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The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 4
3 1, 2, 6
4 1, 3, 7
5 1, 1
6 5
Key: 3|2 means 3.2
What is the mean, and what does it tell you in terms of the problem?
The mean is 38.5. It tell us that the average distance a heavy ball was thrown is 38.5 feet.
What is the mean?A stem-and-leaf plot is table that displays a data set in ascending order. used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. In this stem-and-leaf plot, the stem is the tens digit and the leaf is the units digit. For example, in the number 32, 3 is the stem 2 is the leaf.
The mean is a measure of the center of a dataset that is used to determine the average of a set of numbers
Mean = sum of numbers / total numbers in the data set
(20 + 21 + 24 + 31 + 32 + 36 + 41 + 43 + 47 + 51 + 51 + 65) / 12
462 / 12 = 38.5
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Find the value of x .. assume that segments that appear to be tangent are tangent .
We got x = 16.54 by using Pythagorean theorem .
What is the Pythagorean theorem in plain English?
According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90° .
18² = 7.1² + x²
324 = 50.41 + x²
x² = 324 - 50.41
= 273.59
x = √ 273.59
x = 16.54
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a certain washing machine uses 29 gallons of water for each load of laundry washed. How many gallons of water would the washing machine use for 156 loads of laundry?
Answer:156
Step-by-step explanation:
18. How does the
product change when one of the factors in
a multiplication problem is doubled? Give
two examples to support your conclusion.
The product doubles when one of the factors in a multiplication problem is doubled
What is a product?A product in mathematics is the result of multiplication, or an expression that identifies the objects to be multiplied, known as factors. For instance, 30 is the sum of 6 and 5.
In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product.
For example, 2 × 3 = 6. When 2 is doubled, it becomes 4 and the product will be:
= 4 × 3 = 12
Therefore, the product doubles too.
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-10b+3 ≤-37
Compound inequalities
10. Reduce the fraction 36/48 to its lowest terms.
O A. 114
O B. %
O C. 112/48
O D.34
Answer:
if D is 3/4 then it is the answer
Step-by-step explanation:
Because both 36 and 48 can be divided by 12 and 36/12 = 3 and 48/12=4 so the answer is 3/4
Anna makes a round pizza. She wants to put a cheese layer on the pizza. If the
pizza is 11 in in diameter, how many square cm of cheese layer does she need
to put on the pizza?
The number of square cm of cheese layers that Anna needs to put on the pizza is 30.25π square cm.
What is the area of a circle?
In geometry, the area of a circle is the space occupied by the circle.
To find the area of a circle having radius "r", we can use the formula.
Area of a circle = π×r².
In the given question, the diameter of the pizza is 11 cm.
so the radius will be = 11/2 = 5.5 cm.
Area of the pizza = π×r²
= π×(5.5)²
= 30.25π square cm.
Hence, the number of square cm of cheese layers that need to be put on the pizza is 30.25π square cm.
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a. Use the points (5, 1273) and (10, 2546) to write an equation for the line.
Type an equation in y=mx form
(Type an equation: Use integers or fractions for any numbers in the equation.)
Using the points (5, 1273) and (10, 2546), equation for the line is 5y = 1273x.
Define equation.There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Given,
Coordinates (5, 1273) and (10,2546)
For slope, m
m = y₂ - y₁/ x₂ - x₁
m = 2546 - 1273/10 -5
m = 1273/5
Equation in y = mx form,
y = 1273/5 x
Cross multiplying,
5y = 1273x
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If y varies directly as x, find the constant of variation k and the direct variation equation for the situation.
y=2 when x= 10
Variation refers to differences in characteristics between individuals of the same species or between different genera or species. The formula is y = 0.25x.
What is meant by variation equation?A variation is a relationship between one set of values for one variable and another set of values for another variable. Variation in direct. If m is a nonzero constant and b = 0, then the function y = mx (often written y = kx) is a direct variation of the equation y = mx + b. If y varies directly as x and y = 6 when x = 2, the constant of variation is k = 3. As a result, the equation for this direct variation is y = 3x.The direct variation equation is a two-variable linear equation given by y = kx, where k is the constant proportionality. In a coordinate plane, the direct variation graph is a straight line.Therefore,
y=0.25 x
the initial statement is y ∝ x
to convert to an equation multiply by k the constant of
⇒ y=k x
to find k use the given condition
y=0.5 when x=2
[tex]$y=k x \Rightarrow k=\frac{y}{x}=\frac{0.5}{2}=0.25$$[/tex]
the equation is y = 0.25x
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The variation equation is [tex]y=\frac{1}{5} x[/tex]
What do you mean by direct variation?If two quantities change by the same amount, they are said to follow a direct variation. As a result, when one quantity changes, the other follows suit, increasing when the first changes and decreasing when the first changes. To put it another way, two quantities are said to be directly proportional to one another if the ratio of the first to the second is a constant term. The coefficient or constant of proportionality is the name given to this constant quantity.The mathematical relationship between the two quantities in the direct variation formula makes it so that one of the variables is a constant multiple of the other. The sign "∝" is used to indicate that two quantities are directly proportional to one another or directly varying from one another. Assuming that x and y are two quantities that are directly varying, they are stated as follows: y∝ xThe direct variation formula is expressed as follows when the proportionality sign is omitted.Calculation
Given, y =2 and x=10
we know the direct relation in y∝ x
so, y = kx, where k is the proportionality constant
2= k*10
k = [tex]\frac{2}{10} =\frac{1}{5}[/tex]
Therefore, the direct variation equation for this situation is [tex]y=\frac{1}{5} x[/tex]
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