The zero product property, says that if a product of two real numbers is 0, then one of the numbers must be 0.
a. Write this property formally using quantifiers and variables.
b. Write the contrapositive of your answer to part (a).
c. Write an informal version (without quantifier symbols or variables) for your answer to part (b).
The contrapositive of the zero product property is that if neither of the two real numbers is 0, then the product of the two numbers will not be 0. In plain language, this means that if neither of the two numbers are 0, then the product of the two numbers cannot be 0.
In an informal version, this can be stated as "if neither number is 0, then their product cannot be 0". This can be understood as "if neither number is 0, the result of multiplying them together cannot be 0". In other words, the product of two real numbers will not be 0 if neither of them is 0.
solve: 15x = 180.75
please and thanks
Answer:
x = 12.05
Step-by-step explanation:
Given:
15x=180.75
Divide both sides by 15
15x 180.75
------ = --------
15 15
x = 12.05
Hence, x = 12.05
~lenvy~
Answer:
12.05
Step-by-step explanation:
Divide both sides by the same term
15x/15 = 180.75/15
180.75/15
= 12.05
Hence, x = 12.05
Check Answer:
15(12.05) = 180.75
[RevyBreeze]
12. A plane takes off and climbs at a
9° angle. After flying over 7 miles
of ground, what will the plane's
altitude, h, be? Round to the
nearest tenth of a mile.
The plane’s altitude will be approximately 6,336 feet when it has flown over 7 miles of ground and climbed at a 9° angle.
What is meant by miles?
Miles are a unit of distance used in the United States and some other countries, equal to 5,280 feet or 1.609 kilometres. Miles are commonly used to measure distances between cities, countries, and other geographical locations.
What is meant by angle?
A geometric shape known as an angle is created by two rays or line segments that have a similar terminal (referred to as the vertex). Angles can be expressed as radians or degrees and are used to describe how lines and shapes are oriented, situated, and related to one another. Angles can be categorised according to their size and shape as acute, right, obtuse, straight, or reflex.
According to the given information
The problem can be solved using trigonometry 1. The altitude of the plane can be calculated using the tangent function as follows: tan(9°) = h/7 h = 7 tan(9°) ≈ 1.2 miles ≈ 6,336 feet
Therefore, the plane’s altitude will be approximately 6,336 feet when it has flown over 7 miles of ground and climbed at a 9° angle.
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A food company puts exactly 10 sliced carrots in each bag of frozen vegetables. Let b represent the number of bags of frozen vegetables and c represent the total number of sliced carrots. Identify the independent variable.
A= b- the number of frozen bags
B= c- the total number of sliced carrots
C= there's not enough information given to answer
D= a food company puts carrots in a bag
The independent variable is A, the number of frozen bags.
The independent variable is the number of bags of frozen vegetables, represented by b. This is because the company can choose to package any number of bags, which will then determine the total number of sliced carrots, represented by c. The number of sliced carrots is not independent because it depends on the number of bags of frozen vegetables being packaged. Therefore, the answer is A, the number of frozen bags.
In statistical analysis, the independent variable is the variable that is being manipulated or changed in an experiment to observe the effect on the dependent variable.
In this case, the number of bags of frozen vegetables is the variable being manipulated, while the total number of sliced carrots is the dependent variable being affected by the number of bags. This understanding of independent and dependent variables is crucial in designing experiments and interpreting results in various fields, including food science, agriculture, and health research.
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Please help me with this
Answer:
zero product property of multiplication
Step-by-step explanation:
step 2 is valid, because for the main expression in step 1 to be true, only one of the 2 factors need to be 0, as
0 × something is always 0.
therefore, it is sufficient to find the values of x that renders the expression of one factor to 0.
which number is irrational
Answer:
Any real number that cannot be expressed as a ratio of two integers.Step-by-step explanation:
OPTIONS R NOT HERE
HOPE IT HELP
Answer: i didn't get enough detail but you can use this to help
Step-by-step explanation:
Irrational numbers are the real numbers that cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.
Irrational numbers are expressed usually in the form of R\Q, where the backward slash symbol denotes ‘set minus’. it can also be expressed as R – Q, which states the difference between a set of real numbers and a set of rational numbers.
Which statement best explains the relationship
between lines FG and HJ?
O They are perpendicular because their slopes are
equal.
• They are perpendicular because their slopes are
negative reciprocals.
They are not perpendicular because their slopes are
equal.
O They are not perpendicular because their slopes are
not negative reciprocals.
Answer:
The answer is A
Step-by-step explanation:
i need help answering these im just confused lol
Answers:
12.
Name: Octagon
Regular: Yes
13.
Name: Triangle
Regular: Yes
14.
Name: Rectangle
Regular: No
15.
Name: Pentagon
Regular: No
you are hiking within the northern hardwood forest region of the upper peninsula of michigan and you pass through two small woodlands. because we have turned you into a biology enthusiast, you count and identify all the trees that you pass. in woodland a, you find 50 sugar maple trees, 50 yellow birch trees, and 50 red oak trees. in woodland b, you find 100 sugar maple trees, 48 yellow birch trees and 2 red oak trees. the most accurate comparison of these woodlands would be that
Answer: 300 i believe.
Graph the solution set for the inequality
y > 2x - 5 by following these steps:
Step 1: Identify the slope and y-intercept.
slope = y-intercept =
-4
Answer:
Salutations!
The slope is (2)
And the y-intercept is (-5)
Hope you're having a good day, and may god bless :)
Slope of the given inequality is 2 and the y-intercept of the given inequality is (0, - 5).
What is an inequality?"An inequality is the relationship between two values that are not equal is defined by inequalities. Inequality means not equal."
The given inequality is:
y > 2x - 5
By plotting this inequality, we get:
Slope of the given inequality is 2.
The y-intercept of the given inequality is (0, - 5)
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A square has a perimeter of 100 cm. What is the length of each side?
Answer:
625 \(cm^{2}\)
Step-by-step explanation:
The side lengths of a square are equal so each side must be 25 cm
a =\(s^{2}\) (area = the side squared)
a = \(25^{2}\)
a = 625
Helping in the name of Jesus.
Find the interior angle sum for each polygon.
The measure of the sum of the interior angle of the regular polygon is 1620 degrees.
What is the sum of the interior angle of the polygon?All interior angles in a regular polygon are equal.
For a regular polygon, the sum of the interior angle is expressed as:
Sum of interior angles = ( n - 2 ) × 180°
Where n is the number of sides of the regular polygon.
From the diagram, the polygon has 11 sides.
Number of sides n = 11
Plug n = 11 into the above formula and solve for the sum of the interior angles:
Sum of interior angles = ( n - 2 ) × 180°
Sum of interior angles = ( 11 - 2 ) × 180°
Sum of interior angles = 9 × 180°
Sum of interior angles = 1620°
Therefore, the sum of the interior angles is 1620°
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√80
÷
5=
Can yall please show yall work (Thank you)
Answer:
to the power of 80 is 8.944 ÷5 is 1.788
A two-digit number read from left to right is 20% greater than the same number read from right to left. Find the number.
Answer:
54
Step-by-step explanation:
We'll call the number "ab".
From left to right, the value of this number will be \(10a+b\).
From right to left, the value of this number will ve \(10b+a\).
From the question,
\(10a+b=1.2(a+10b)\\10a+b=1.2a+12b\\8.8a=11b\)
For a and b to be whole numbers,
\(\left \{ {{a=5} \atop {b=4}} \right.\)
So the number is 54.
The science club has m members. The club bought 24 bumper stickers to split among its members. Write an expression that shows how many bumper stickers each member will get.
Answer: 24/m
Step-by-step explanation:
There are m members in the science club.
24 bumper stickers were purchased to be split amongst these m members.
The number of stickers that each member will get is:
= Number of stickers / Number of members
Number of stickers = 24
Number of members = m
The expression is therefore:
= 24/m
A robotics company sells robot vacuum cleaners. Since the newest model was introduced a
while back, the old model has seen its sales fall by a consistent 30% per month. If 8,400 old
vacuum cleaners were sold this month, how many will be sold 3 months from now?
problem 6. let s = { m ∈ mnxn: m = ab −ba, for some a,b ∈ mnxn } . is the vector space mnxnspanned by the set s?
The set S does not span the vector space M_n×n.
To determine if the vector space of square matrices, denoted as M_n×n, is spanned by the set S, we need to check if every matrix in M_n×n can be expressed as a linear combination of matrices formed by the commutator operation.
The set S consists of matrices of the form m = ab − ba, where a and b are matrices in M_n×n. The commutator operation produces a new matrix by taking the difference between the matrix product ab and ba.
To show that S spans M_n×n, we need to demonstrate that any matrix M in M_n×n can be expressed as a linear combination of matrices from S. In other words, we need to find matrices a and b such that M = ab − ba.
However, it is not possible to express every matrix in M_n×n as a commutator of two matrices. This is because not all matrices have a well-defined commutator representation. Therefore, the set S does not span the vector space M_n×n.
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"Use the graphical method to solve this problem:
Minimize Z = 15 X_1 + 20 X_2
Subject to X_1 + 2 X_2 ≥ 10
2X_1 – 3X_2 ≤ 6
X_1 + X_2 ≥ 6
and X_1 ≥ 0, X_2 ≥ 0"
Answer:
(X_1, X_2) = (2, 4)
Z = 110
Step-by-step explanation:
You want a graphical solution to ...
minimize Z = 15 X_1 +20 X_2
subject to ...
X_1 + 2 X_2 ≥ 102X_1 – 3X_2 ≤ 6X_1 + X_2 ≥ 6X_1 ≥ 0 X_2 ≥ 0GraphA graph of the reverse of the inequalities is attached. This makes the feasible solution region be white (rather than shaded multiple times), so its vertices are easier to see. (The dashed lines are part of the solution space.)
The vertex of the solution space that minimized the objective function is (X_1, X_2) = (2, 4). The minimum value of Z is 110.
Change the function f(x)=2x^2+4x+3 into vertex form.
Answer:
f(x) = 2(x + 1)² + 1
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
given
f(x) = 2x² + 4x + 3 ← factor out 2 from the first two terms
= 2(x² + 2x) + 3
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 2x
f(x) = 2(x² + 2(1)x + 1 - 1) + 3
= 2(x + 1)² - 2(1) + 3
= 2(x + 1)² - 2 + 3
= 2(x + 1)² + 1 ← in vertex form
The trapezoidal end of a feeding trough shown below has base dimensions of 1 foot and 2 feet with a base angle of 60º. Grain is placed in the trough using a hemispherical feed scoop with a diameter of 1 foot. What is the maximum number of full scoops that can be placed into the trough without overflowing the interior of the trough?
The maximum number of full scoops that can be placed into the trough without overflowing the interior of the trough is 9 full scoops.
The volume of the trough and the volume of one feed scoop, and then divide the volume of the trough by the volume of one feed scoop to get the maximum number of scoops that can fit inside.
The volume of the trough.
We can split the trough into two parts:
A rectangular prism and a truncated pyramid.
The rectangular prism has a base of 1 foot by 2 feet and a height of 1 foot, so its volume is:
\(V_{rectangular}\) prism = base area × height
= (1 ft × 2 ft) × 1 ft
= 2 cubic feet
The truncated pyramid has a top base of 1 foot, a bottom base of 2 feet, and a height of 1 foot.
To find its volume, we can use the formula:
\(V_{truncated}\) pyramid = (1/3) × height × (top area + bottom area + square root of (top area × bottom area))
The top area is the area of a circle with a diameter of 1 foot, and the bottom area is the area of a trapezoid with base dimensions of 1 foot and 2 feet and a base angle of 60 degrees.
Using the formulas for the area of a circle and the area of a trapezoid, we get:
top area = (1/2) × pi × (1/2 ft)²
= 0.1963 cubic feet
bottom area = (1/2) × (1 ft + 2 ft) × 1 ft × sin(60 degrees)
= 0.866 cubic feet
Plugging in these values, we get:
\(V_{truncated\) pyramid = \((1/3) \times 1 ft \times (0.1963 + 0.866 + \sqrt{(0.1963 \times 0.866))\)
= 0.543 cubic feet
The total volume of the trough is therefore:
\(V_{trough\)= \(V_{rectangular prism\) + \(V_{truncated pyramid\)
= 2 + 0.543
= 2.543 cubic feet
Next, let's find the volume of one feed scoop.
A hemisphere with a diameter of 1 foot has a volume of:
\(V_{hemisphere\) = (1/2) × (4/3) × pi × (1/2 ft)³
= 0.2618 cubic feet
The volume of the trough by the volume of one feed scoop to get the maximum number of scoops that can fit inside:
max number of scoops = \(V_{trough\) / \(V_{hemisphere\)
= 2.543 / 0.2618
≈ 9.71
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A class is divided randomly into two teams for a game of Jeopardy. Tamara, the captain of the winning team, is informed that as a prize she can either get 20 pieces of candy for her team, with the losing team getting 10 pieces, or she can get 15 pieces while the losing team gets none. Based on research using the minimal group paradigm, what prize is Tamara most likely to select
Tamara is most likely to select the prize where her team receives 20 pieces of candy and the losing team gets 10 pieces. This is because of the research findings using the minimal group paradigm, which suggest that individuals tend to prioritize maximizing the relative advantage of their in-group over maximizing their own absolute gains.
In the context of the Jeopardy game, Tamara's primary identification is with her own team, the winning team. The minimal group paradigm research indicates that individuals tend to exhibit a strong in-group bias and favor their own group's welfare even when it comes at the cost of absolute gains for themselves or their group members.
By selecting the option where her team receives 20 pieces of candy while the losing team receives 10 pieces, Tamara can maximize the relative advantage of her team over the losing team. This choice aligns with the tendency to prioritize the in-group's advantage and reinforces the social identity and cohesion within the winning team.
Therefore, based on the findings from research using the minimal group paradigm, Tamara is most likely to choose the option that provides the maximum relative advantage to her team, even if it means receiving fewer absolute gains for herself and her team.
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PLEASE HELP ME I'LL MAKE YOU BRAINLIEST!!!! In 1972, federal vehicle emission standards 3.4 grams hydrocarbons released per mile driven. By 2007, the standards allowed only 0.8 grams hydrocarbons per mile driven. What was the rate of change from 1972 to 2007? Please show work thank you
======================================================
Work Shown:
x = year
y = amount of hydrocarbon emissions in grams, per mile driven
m = rate of change = slope
m = (y2 - y1)/(x2 - x1)
m = (0.8 - 3.4)/(2007 - 1972)
m = -2.6/35
m = -0.0742857 approximately
The approximate rate of change is about -0.0742857 grams per year. The negative rate of change indicates the per mile hydrocarbon amount has gone down by about 0.0742857 grams each year.
What is the area of triangle ABC if a = 7, c = 11, and B = 55°?
Round the answer to the nearest hundredth.
The area of the triangle is 31.54 square units
How to determine the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
We have the following values
a = 7 units
c = 11 units
B = 55 degrees
The area of the triangle is calculated using the following area formula
Area = 1/2absin(C)
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 7 * 11 * sin(55 degrees)
Evaluate
Area = 31.54
Hence, the area is 31.54 square units
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There are six boys to every five girls in an introductory geology course. If there are 374 students enrolled in the course, how many are boys
there are approximately 34 boys in the introductory geology course.
To determine the number of boys in the introductory geology course, we need to calculate the ratio of boys to girls and use the total number of students enrolled.
The given ratio states that there are six boys for every five girls. This can be expressed as 6 boys : 5 girls.
Let's assume the number of boys in the course is represented by B and the number of girls is represented by G.
According to the given information, we can set up the following equation:
6 boys / 5 girls = B / G.
Since the total number of students enrolled in the course is 374, we can write another equation:
B + G = 374.
To solve these equations simultaneously, we can use the concept of proportion.
From the first equation, we can rewrite it as:
6G = 5B.
Now we can substitute this expression into the second equation:
B + G = 374
5B + 6B = 374
11B = 374
B = 374 / 11
B ≈ 34.
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a circular treehouse has a floor that is 490.625ft.to add a thin strip of waterproofing around the floor how many feet are needed
Answer:
The answer is 1548.99ft.
Step-by-step explanation:
To determine the length of the strip needed for waterproofing, you need to calculate the circumference of the circular floor. The formula for the circumference of a circle is 2π times the radius. If the floor of the treehouse has a radius of 490.625/2= 245.3125ft, then the circumference of the floor is:
2π x 245.3125ft = 1548.99ft
So, the length of the strip needed for waterproofing around the floor is approximately 1548.99ft.
I would greatly appreciate Brainliest
Have a nice day.
60 divided by 3 = g - 8 divided by 2 what does g equal?
Answer:
g = 48
Step-by-step explanation:
60/3 = g-8/2
20 = g-8/2
40 = g-8
g = 48
Answer:
g = 28
Step-by-step explanation:
60 ÷ 3 = g - 8 , that is
20 = g - 8 ( add 8 to both sides )
28 = g
NEED THIS NOW. 100pts + brainliest.
Question 1 Part B (3 points): Andrew spends 120 minutes in the gym everyday doing strength training and running on the treadmill. He runs on the treadmill for 60 minutes longer than he does strength training. How much time does Andrew spend doing strength training?
A. 30 minutes.
B. 60 minutes.
C. 90 minutes.
D. 120 minutes.
Answer:
A. 30 minutes
Step-by-step explanation:
30 minutes - strength training
90 minutes - treadmill
Express 1.32 bar on 32 + 0.35 bar on 35
1.32 (bar on 32) + 0.35 (bar on 35) is equal to 166/99 in the simplest form.
To express 1.32 (bar on 32) + 0.35 (bar on 35) in fractional form, we can use the following steps:
Step 1: Let x = 1.32 (bar on 32)
So, x = 1.323232... (since the bar notation indicates that the digits after the bar repeat infinitely).
This means that 100x = 132.323232...
Step 2: Subtract x from 100x to eliminate the repeating decimal:
100x - x = 132.323232... - 1.323232...
99x = 131
x = 131/99
Step 3: Let y = 0.35 (bar on 35)
So, y = 0.353535...(since the bar notation indicates that the digits after the bar repeat infinitely).
This means that 10y = 3.5
Step 4: Subtract y from 100y to eliminate the repeating decimal:
100y = 35.353535...
100y - y = 35.3535... - 0.3535..
99y = 35
y = 35/99
Step 5: Add x and y to get the sum in the fractional form:
1.32 + 0.35 = (131/99) + (35/99)
Step 6: Simplify the sum by finding a common denominator and adding the numerators:
1.32 + 0.35 = (131/99) + (35/99)
1.32 + 0.35 = 166/99
Therefore, 1.32 (bar on 32) + 0.35 (bar on 35) is equal to 166/99 in the simplest form.
The question was Incomplete, Find the full content below :
Express 1.32 (bar on 32) + 0.35 (bar on 35) as a fraction in the simplest form
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Andre and Diego were each trying to solve 2+6=3−8. Describe the first step they each make to the equation.The result of Diego’s first step was 6=−8.
Step-by-step explanation:
2+6=3-8
2+6=8
3-8=-5
8=-5
Choose the letter of the word or phrase that best completes each statement.
a. ratio
b. proportion
c. means
d. extremes
e. similar
f. scale factor
g. AA Similarity Post.
h. SSS Similarity Theorem
i. SAS Similarity Theorem
j. midsegment
k. dilation
I. enlargement
m . reduction
A(n) ___?___ of a triangle has endpoints that are the midpoints of two sides of the triangle.
The correct answer is j. midsegment. The midsegment can be used to explore properties of similar triangles and their ratios or proportions.
A midsegment of a triangle has endpoints that are the midpoints of two sides of the triangle. It is a line segment that connects the midpoints of two sides of a triangle. The midsegment is parallel to the third side of the triangle, and its length is half the length of the third side. The midsegment divides the triangle into two smaller triangles, each of which is similar to the original triangle. Therefore, the midsegment can be used to explore properties of similar triangles and their ratios or proportions.
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