Final answer:
The theorems about parallelograms are used in mathematics to find unknown sides or angles and to prove properties of figures. When dealing with vectors, the parallelogram rule for vector addition helps find the resultant by constructing a parallelogram with the vectors as sides and the diagonal as the resultant.
Explanation:
To use theorems about parallelograms to solve problems, we often apply these principles to find unknown sides or angles or to prove certain properties about the figures we are dealing with. For example, one theorem states that opposite sides of a parallelogram are congruent, which can be useful when you need to find the length of a missing side.
Regarding vector addition, the parallelogram rule is applied. According to this rule, if we are adding two vectors, say vector A and vector B, we place them tail to tail, draw the vectors such that they form adjacent sides of a parallelogram, and then the resultant vector is represented by the diagonal of the parallelogram that starts from the common tail of the two vectors.
Similarly, if we need to find the resultant of three or more vectors, we use the parallelogram rule iteratively. We first find the resultant of the first two vectors and then add the third vector to this resultant using the same rule. This process is based on the associative and commutative properties of vector addition.
The population of Australia is more than 20,000,000 people. You can write 20,000,000 as 2 × 10,000,000. Write 10,000,000 using exponents.
Answer:
10^7
Step-by-step explanation:
So we would start with 10 and a trick to help you is when your turning a number with 10 at the start with each number you raise it by is how many 0 it will have behind it for example 10,000,000 would be 10^7 cause you have 0 zeros in it.
10,000,000 in exponent form is 10⁷. Therefore, 20,000,000 can be written as 2 × 10⁷. This provides a concise mathematical way of expressing large numbers.
To write 10,000,000 using exponents, we recognize that this number is a power of 10. Specifically, 10,000,000 can be written as 10 to the power of 7. This is because:
10,000,000 = 10⁷
When you multiply 10 by itself 7 times (10 × 10 × 10 × 10 × 10 × 10 × 10), you get 10 million. Therefore, the population of Australia, which is more than 20,000,000 people, can be written as:
20,000,000 = 2 × 10,000,000 = 2 × 10⁷
2. A magazine ad states that 4 out of 7 doctors
recommend Flash toothpaste. If 1400 doctors were
surveyed, how many doctors recommended Flash
toothpaste?
Answer:
800
Step-by-step explanation:
Answer:
x = 800
Step-by-step explanation:
This is a ratio problem.
4 / 7 = x / 1400
Cross multiply to get 7x = 5600.
Now divide both sides by 7 in order to isolate x.
x equals 800
Hope this helps you :)
In an ordered pair, what axis represents the input
In an ordered pair for a Cartesian coordinate system, the input is represented by the x-axis. It is denoted as the first value in an (x, y) pair and represents the horizontal direction in a two-dimensional space.
Explanation:In an ordered pair, the input is typically represented by the x-axis in a Cartesian coordinate system. An ordered pair is denoted as (x, y), where 'x' represents the input or independent variable, and 'y' represents the output or dependent variable. For instance, in a function such as y = mx + b, 'x' would be the input and 'y' would be the output. This input value corresponds to the position along the horizontal x-axis.
While the y-axis represents the vertical direction or output value, the x-component of a vector is a dot product with the unit vector in the x-direction. For two-dimensional vector problems, it's also easier to pick a coordinate system that has one horizontal axis (x) and one vertical axis (y), projecting the vectors onto these axes.
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Final answer:
In an ordered pair (x, y), the x-axis represents the input which is the horizontal direction on the Cartesian coordinate system.
Explanation:
In an ordered pair, such as (x, y), the x-axis represents the input, which is the horizontal direction, and the y-axis represents the output, which is the vertical direction. In the Cartesian coordinate system, the origin, where the x and y axes intersect, is the point of projection.
By convention, the positive x-axis generally extends to the right, and the positive y-axis extends upwards. The x-coordinate corresponds to the position along the x-axis while the y-coordinate corresponds to the position along the y-axis.
Select all the expressions that are equivalent to (–60) ÷ 5.
A(60)÷(−5)
B(−60)÷(−5)
C(−60)×15
D(60)×(−15)
E(−60)÷(−15)
Answer:
I think the only one is A
Two angles are supplementary. The measure of the first angle is 10 degrees more than three times the second angle. Find the measure of each angle
Answer:
137.5° and 42.5°
Step-by-step explanation:
supplementary angles are two angles whose sum is equal to 180°.
Let the second angle be x then it is given that the first angle is 10 degrees more than 3 times second angle that is 3(x)+10°.
we know that the sum of first and second angles is 180° (supplementary angles)
so, (3(x)+10°)+(x) = 180°
4(x) = 170°
x = 170°/4 = 42.5°
so, first angle is 3(42.5°)+10° = 137.5°, second angle is x that is 42.5°
therefore, the angles are 137.5° and 42.5°.
Answer:
THE OTHER ONE IS WRONG!!!
Expert verified FOX DUNG!
Step-by-step explanation:
To find the value of the following expression, what operation should you do first? 20-(7+4) x5
Answer:
Distributive Property.
Answer:
-35
Step-by-step explanation:
20-(7+4)*5
20-(11)(5)
20-55
-35
0=(1x+1)(1x-3) if m(x) =10, find the value of x
Answer:
x=1+sqrt(14) & 1-sqrt(14).
Step-by-step explanation:
(1x+1)(1x-3)=0
(x+1)(x-3)=0
m(x)=(x+1)(x-3)=10
(x+1)(x-3)=10
x^2+x-3x-3=10
x^2-2x-3=10
x^2-2x-3-10=0
x^2-2x-13=0
Apply the quadratic formula with a=1, b=-2 and c=-13.
The answer is x=1+sqrt(14) & 1-sqrt(14).
find the solution in slope-intercept form y+7=-3(x-1) and 3x+y=-4
Answer:
The slope intercept form of both given equations is : y = - 3 x - 4.
Step-by-step explanation:
Here, the given equations are:
y +7 = -3 ( x - 1 )
and 3 x + y = - 4
Now,the SLOPE INTERCEPT FORM of any given equation is given as:
y = m x + C : here, C = Y - intercept, m = Slope
Consider equation (1):
y +7 = -3 ( x - 1 ) ⇒ y + 8 = - 3 x + 3
or, y = -3x + 3 - 7 = -3x - 4
⇒ y = -3x -4
Hence, the slope-intercept form of the given equation is y = -3x -4.
Consider equation (2):
3 x + y = - 4 ⇒ y = -4 - 3 x
⇒ y = -3 x - 4
Hence, the slope-intercept form of the given equation is y = -3x -4.
Final answer:
The solution in slope-intercept form for both given equations is y = -3x - 4, showing that they represent the same line.
Explanation:
To find the solution in slope-intercept form for the given equations y+7=-3(x-1) and 3x+y=-4, we need to solve for y in terms of x for each equation.
For the first equation, solve for y:
y + 7 = -3(x - 1)
y = -3x + 3 - 7
y = -3x - 4 (Slope-intercept form of the first equation)
For the second equation, solve for y:
3x + y = -4
y = -3x - 4 (Slope-intercept form of the second equation)
After solving, we observe that both equations have the same slope-intercept form, which indicates that these are actually the equations of the same line.
Which triangles are congruent in the diagram?
Using prime factorization what is the GCF of 42, 65
Answer:
1
Step-by-step explanation:
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The factors of 65 are: 1, 5, 13, 65
Then the greatest common factor is 1.
To find the GCF using prime factorization for 42 and 65, determine their prime factors and find the common factors. The GCF of 42 and 65 is 1.
Explanation:To find the GCF (Greatest Common Factor) of 42 and 65 using prime factorization, we need to find the prime factors of each number and determine their common factors.
Step 1: Prime factorize 42:
42 = 2 x 3 x 7.
Step 2: Prime factorize 65:
65 = 5 x 13.
Step 3: Find the common factors:
The only common prime factor between 42 and 65 is 1.
Therefore, the GCF of 42 and 65 is 1.
Sarah is sellng bracelets for $5 and necklaces for $10. If the equation below represents her total revenue (R), what is the meaning of '10y'?
R = 5x + 10y
Question 10 options:
Number of bracelets sold
Money earned from bracelets
Number of necklaces sold
Answer:
Number of necklaces sold
Step-by-step explanation:
Every necklace sold becomes added up to make up y, and then you multiply that by $10(the money for necklaces).
what expression shows a way to find 20% of 950?
The expression that can be used to find 20% of 950 is 20/100 × 950
How to write percentage expressions?20% of 950
= 20/100 × 950
= 0.2 × 950
= 190
Therefore, the 20% of 950 is given by 190
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To find 20% of 950, you use the formula (Percentage / 100) × Whole. By applying the formula, 20% of 950 is calculated to be 190.
To find 20% of 950, you can use the formula for finding a percentage of a number:
Part = (Percentage / 100) × Whole
In this case, the percentage is 20 and the whole is 950. Now apply the formula:
Part = (20 / 100) × 950
Part = 0.2 × 950
Part = 190
Therefore, 20% of 950 is 190.
Write the factored form of the equation of a polynomial that has a root of x=3, a zero of x=-2, and an x-intercept of x=-1. Then write that equation in standard form
Answer:
[tex]f(x)=x^3-7x-6[/tex]
Step-by-step explanation:
If x = 3 is a root of a polynomial f(x), then x - 3 is a factor of this polynomial.
If x = -2 is a zero of a polynomial function f(x), then f(-2) = 0 and x - (-2) = x + 2 is a factor of f(x).
If x = -1 is an x-intercept of the function, then y = 0 and x - (-1) = x + 1 is also a factor of the function f(x).
Therefore, the polynomial expression is
[tex]f(x)=(x-3)(x+2)(x+1)[/tex]
In standard form:
[tex]f(x)=(x-3)(x^2+2x+x+2)=(x-3)(x^2+3x+2)=x^3+3x^2+2x-3x^2-9x-6=x^3-7x-6[/tex]
What is the best approximation of the solution to the system to the nearest integer values?
(7, 1)
(7, 0)
(1, 7)
(0, 6)
Graph of a system of linear equations. Equation 1 is x minus y equals negative 6. Equation 2 is 5x plus 3y equals 24.
Answer:
OPTION C: (1,7)
Step-by-step explanation:
The two equations are:
[tex]$ x - y = -6 \hspace{25mm} ....(1) $[/tex]
[tex]$ 5x + 3y = 24 \hspace{25mm} ...(2) $[/tex]
To solve these two equations, multiply (1) by 5 and subtract (1) and (2).
Therefore, we get the value of y.
[tex]$ y = \frac{54}{8} $[/tex]
This is approximately equal to 7.
Substituting y = 7 in (1), we get x - 7 = -6
⇒ x = -6 + 7
∴ x = 1
So, we say the approximate solution to the equations is: (1,7).
In other words, the two lines meet approximately at (1,7).
Answer:
(1,7)
Step-by-step explanation:
I took the k12 test And got it right.
how do i solve 1/4 +1/3
Answer:
[tex]\large\boxed{\dfrac{1}{4}+\dfrac{1}{3}=\dfrac{7}{12}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{4}+\dfrac{1}{3}\qquad\text{find}\ LCD=(4)(3)=12\\\\=\dfrac{1\cdot3}{4\cdot3}+\dfrac{1\cdot4}{3\cdot4}=\dfrac{3}{12}+\dfrac{4}{12}=\dfrac{3+4}{12}=\dfrac{7}{12}[/tex]
Answer:
7/12
Step-by-step explanation:
Write all numerators above the least common denominator which is 12.Divide the denominator 12 by the first denominator 4 and add it to the first numerator 1, your result should be 3.Divide the denominator 12 by the second denominator 3 and add it to the second numerator 1, your result should be 4.Add the numerator since you have a + sign 3+4/12.Answer: 7/12.Write the polynomial 4x2 - 6x6 + 2x3 + 12 - 5x3 + 4x4 in standard form.
Answer:
[tex]\large\boxed{-6x^6+4x^4-3x^3+4x^2+12}[/tex]
Step-by-step explanation:
[tex]4x^2-6x^6+2x^3+12-5x^3+4x^4\\\\=-6x^6+4x^4+2x^3-5x^3+4x^2+12\qquad\text{combine like terms}\\\\=-6x^6+4x^4+(2x^3-5x^3)+4x^2+12\\\\=-6x^6+4x^4-3x^3+4x^2+12[/tex]
Factor the expression.
6y^2 + 13y + 5
Answer:
Step-by-step explanation:
Answer:
If you factorise it you should get (3y+5)(2y+1)
HELP ASAP! A store clerk is unpacking a box of cameras. The line plot displays the weight of each camera. How much do all the cameras in the box weigh?
Answer:
3\8 I think is the answer
Step-by-step explanation:
I know because I know!
Answer:
8 3/8
Step-by-step explanation:
I have study island too
a ruby throated hummingbird is about 4 in long and is it noted for its annual non-stop migration of 500 miles across the Gulf of Mexico and for the rabbit flopping of its wings some hummingbirds flap their wings 55 times per second if the ruby-throated hummingbird is only 4 inches long and migrates 500 miles how many of the hummingbird the body length are equal to the distance of its migration
Answer:
7,920,000
Step-by-step explanation:
The question is asking the number of times that 4 inches fits in 500 miles. We need to divide 500 miles by 4 inches, but first we need to convert 500 miles into inches.
12 inches = 1 foot
5280 ft = 1 mile
500 miles * (5280 ft)/(1 mile) * (12 in.)/(1 ft) = 31,680,000 inches
Now that we know that 500 miles is the same as 31,680,000 inches, we divide that number of inches by 4 inches.
(31,680,000 inches)/(4 inches) = 7,920,000
Answer: 7,920,000
the size of the largest angle in a triangle is 3 times the size of the smallest angle.
the third angle is 10° more than the smallest angle
work out the size, in degrees, of each angle in the triangle.
You must show your working (let X be the smallest angle).
The sizes of the angles are 34° , 44° , 102°
Step-by-step explanation:
The given is:
The size of the largest angle in a triangle is 3 times the size of the smallest angleThe third angle is 10° more than the smallest angleThe size of the third angle is xWe need to find the size of each angle in the triangle
∵ The size of the smallest angle = x°
∵ The size of the largest angle is 3 times the size of the smallest angle
∴ The size of the largest angle = x × 3 = (3x)°
∵ The third angle is 10° more than the smallest angle
∴ The size of the third angle = (x + 10)°
Add the size of the three angles and equate the sum by 180°
∵ The sum of the sizes of the interior angles of a Δ is 180°
∴ x + (3x) + (x + 10) = 180
∴ x + 3x + x + 10 = 180
- Add like terms
∴ 5x + 10 = 180
- Subtract 10 from both sides
∴ 5x = 170
- Divide both sides by 5
∴ x = 34
∵ x is the size of the smallest angle
∴ The size of the smallest angle is 34°
∵ 3x is the size of the largest angle
∴ The size of the largest angle = 3(34) = 102°
∵ x + 10 is the size of the third angle
∴ The size of the third angle = 34 + 10 = 44°
The sizes of the angles are 34° , 44° , 102°
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the sum of 80 and 7
Answer:
87
The drawing will help
Answer:
87
Step-by-step explanation:
What is Half of 7 minutes 24 seconds
Answer:
3 min 42 seconds
Step-by-step explanation:
1 minute=60 seconds so 7 minutes = 420 seconds. Plus the other 24 is 444 seconds. 444/2=222 so its 222 seconds or 3 minutes and 42 seconds
7 min = 7 x 60 sec = 420 sec
420 sec + 24 sec = 444 sec
444sec : 2 = 222 sec
222 sec = 3x60sec + 42sec = 3 min 42 sec
HELP ME PLEASE!!!!!!!!!!!! Correct answer only, just don't write or guess or you will get reported!
A plumber charges a flat fee of $45 to answer a service call in addition to an hourly rate of $30.50. The plumber has estimated he will earn at least $197.50 from his next repair job. Which inequality can be used to determine the number of hours, h, that the plumber will work on his next job?
Group of answer choices
$30.50h + 45 > $197.50, with a solution of h>6
$30.50h + 45 < $197.50, with a solution of h<6
$30.50h + 45 ≤ $197.50, with a solution of h≤6
$30.50h + 45 > $197.50, with a solution of h>6
Answer: The second one is correct I believe
Step-by-step explanation:
2.
Rock can read 10 books in 30 minutes. How long does it take
Rock to read 15 books, if the speed is consistent?
Answer:
The answer is 45 minutes.
Step-by-step explanation:
30 divided by 10 is 3. So it's 3 minutes per book. 3 multiplied by 15 is 45.
What is the answer to 5-15n?
This is an expression so I can not solve it. But I can factor it if that is what you mean. Factor 5 out from both terms.
5-15n = 5(1-3n)
This is the factored form.
Four photographers are taking pictures at a school dance. Photographer A takes 25 of the pictures, Photographer B takes 4%, Photographer C takes 0.29, and Photographer D takes 27100.
Which choice lists the photographers in order from least to greatest by the amount of pictures they take?
Answer:
1) Photographer B (4%)
2) Photographer D (27%)
3) Photographer C (29%)
4) Photographer A (40%)
Step-by-step explanation:
The correct question is
Four photographers are taking pictures at a school dance. Photographer A takes 2/5 of the pictures, Photographer B takes 4% , Photographer C takes 0.29 , and Photographer D takes 27/100 . Which choice lists the photographers in order from least to greatest by the amount of pictures they take?
we know that
1) Photographer A takes 2/5 of the pictures
That means
the amount of pictures take by photographer A in percent form is equal to multiply the fraction by 100
[tex]2/5(100)=40\%[/tex] ---> percentage form
2) Photographer B takes 4%
3) Photographer C takes 0.29
That means
the amount of pictures take by photographer C in percent form is equal to multiply the decimal number by 100
[tex]0.29(100)=29\%[/tex] ---> percentage form
4) Photographer D takes 27/100
That means
the amount of pictures take by photographer D in percent form is equal to multiply the fraction by 100
[tex](27/100)(100)=27\%[/tex] ---> percentage form
Lists the photographers in order from least to greatest by the amount of pictures they take
1) Photographer B (4%)
2) Photographer D (27%)
3) Photographer C (29%)
4) Photographer A (40%)
The probability that a family visits City Museum is 0.46, and the probability that a family rides on the Three Rivers Ferry is 0.47. The probability that a family does both is 0.12. Find the probability that the family visits the museum or rides the ferry.
Considering the definition of probability, the probability that the family visits the museum or rides the ferry is 81%.
Definition of Probabitity
Probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
Union of events
The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.
Events and probability in this case
Let A be the event that a family visits the City Museum, and B be the event that a family rides the Three Rivers Ferry. The given probabilities are:
P(A)= 0.46
P(B)= 0.47
P(A and B)= P(A∩B)= 0.12
In this case, considering the definition of union of eventes, the probability that a course has a final exam or a research project is calculated as:
P(A∪B)= P(A) + P(B) -P(A∩B)
P(A∪B)= 0.46 + 0.47 -0.32
P(F∪R)= 0.81= 81%
Finally, the probability that the family visits the museum or rides the ferry is 81%.
What are the factor paira of 48
Answer:
1 x 48 = 48
2 x 24 = 48
3 x 16 = 48
4 x 12 = 48
6 x 8 = 48
8 x 6 = 48
12 x 4 = 48
16 x 3 = 48
24 x 2 = 48
48 x 1 = 48
Step-by-step explanation:
Answer:
The factor pair for 48 is 1,2,3,4,6,8,12,16,24 and 48
Your welcome!
Ace in pudge pink cucumbers to earn money to attend Bible college pudge picked 3 pounds for every 4 pounds ace picked if ace picked 716 pounds how many pounds did pudge pick
Pudge picked 537 pounds of cucumber.
Step-by-step explanation:
Ratio of picking cucumbers,
Pudge to Ace = 3:4
Cucumbers picked by Ace = 716 pounds
Let,
x be the cucumbers picked by pudge.
New ratio of pudge to ace = x:716
Using proportion;
Ratio of pudge to ace :: New ratio of pudge to ace
[tex]3:4::x:716[/tex]
Product of mean = Product of extreme
[tex]4*x=3*716\\4x=2148[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{2148}{4}\\x=537[/tex]
Pudge picked 537 pounds of cucumber.
Keywords: Ratio, proportion
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9 lb 4 oz − 2 lb 12 oz
Answer: 6 LB 12 OZ
16 OZ in a LB
9 LB - 2 LB = 7 LB
4 OZ - 12 OZ difference of 8 OZ
4 - 4 = 0 then 16 OZ in a LB
4 remaining - 16 = 12 dropping the 7 LB to 6 LB
Step-by-step explanation:
First, turn into just ounces (1lb. = 16oz.)
9 lb 4 oz = 148 oz
2 lb 12 oz = 44 oz
Second, subtract.
148 - 44 = 104 oz
Third, turn into pounds and ounces.
104 oz = 6 lb 8 oz
______
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