The George's integer must be true for option D)I and IV.
What is integer?
A full number (not a fraction) that can be positive, negative, or zero is called an integer . -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers. Integer, which means full or whole in Latin, is the root of the English term integer. A particular category of numbers called integers includes zero, positive numbers, and negative numbers. All whole numbers, both negative and positive, and 0 are considered integers.
Here the opposite of George integer is -53.
We know that opposite value of x is -x.
Then George integer is 53.
George integer must be true for The given options I. the integer is 53 and IV.The integer has absolute value of 53.
Therefore the correct option is D) I and IV.
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Factor completely x^(3)-2x^(2)-24x
Answer:
x(x - 6)(x + 4)
Step-by-step explanation:
x³ - 2x² - 24x ← factor out x from each term
= x(x² - 2x - 24) ← factor the quadratic
consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 2)
the factors are - 6 and + 4 , then
x² - 2x - 24 = (x - 6)(x + 4)
then
x³ - 2x² - 24x = x(x - 6)(x + 4)
What is the answer to this question
Ann and Ben translate documents from German to English.
A set of documents that would take Ann 10 days would take Ben 12 days.
Ann starts to translate the document.
After 2 days Ann and Ben both work on translating the documents.
How many more days will it take to complete the work?
They would require more 4 8/22 days to complete the work.
Ann can translate the document in 10days
In 1 day he can translate 1/10 of the document
In 2 days he translates = 2 x 1/10
Ben can translate the same document in 12 days
In 1 day he can translate 1/12
Work left after Ann works for 2 days is 1 - 2/10 = 8/10
When working together they can work in 1 day is= 1/10 + 1/12 = 22/120
They do 22/120 work in 1 day
For 1 work, they require 1/(22/120) = 120/22
for 8/10, they would require (120/22)(8/10) = 96/22 = 4 8/22
Therefore, They would require more 4 8/22 days to complete the work.
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Please I need help please
Answer:
Scale Factor
[tex]k=5[/tex]
Side Congruency
AL ≅ TD
TK ≅ AH
DK ≅ LH
Angle Congruency
∠A ≅ ∠T
∠D ≅ ∠L
∠H ≅ ∠K or ∠K ≅ ∠H
Step-by-step explanation:
Scale Factor
First, to determine the scale factor, I will choose two corresponding segments: AL and TD.
By counting on the graph, I can see that they are the following lengths:
[tex]TD=15\\AL=3[/tex]
Therefore the ratio of the large triangle to the small triangle is 15:3. Written as a fraction and simplified, this is:
[tex]\frac{15}{3}=5[/tex]
5 is the scale factor, or k.
Congruency
Each segment on the small triangle corresponds to the same side on the large triangle. Therefore:
AL ≅ TD
TK ≅ AH
DK ≅ LH
The same goes for the angles, except the angles are actually equal as well:
∠A ≅ ∠T
∠D ≅ ∠L
The bottom of your image is cut off, but I assume the question is one of these:
∠H ≅ ∠K
∠K ≅ ∠H
If p + q = 11 and 2p + q = 1 it says that 3p + 2q = 12 but I can't understand how they got to the answer. Please can someone explain? Thank you!
The value of p and q in the equation are -10 and 21 respectively.
How to solve system of equation?The value of p and q will be found in the equation before we can form another equation with p and q.
Therefore,
p + q = 11
2p+ q = 1
using elimination method
p = 1 - 11
p = -10
q = 11 + 10
q = 21
Therefore,
3p + 2q = 12 (let's check if its correct)
3(-10) + 2(21) = -30 + 42 = 12
Therefore, 3p + 2q = 12 is correct.
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To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)^2 + (4/5)^2 =. The distance between (2, -5) and (-7, -5) is The midpoint of the line segment that joins the given points is given by: (, ).
(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = 1 .
(b) The distance between points (2,-5) and (-7,-5) is 9 units .
(c) The midpoint of the line segment that joins the given points is given by: (-5/2,-5) .
In the question ,
it is given that ,
the points given is (3/5 , 4/5)
(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)^2 + (4/5)^2 = 1
that is
9/25 + 16/25 = 1
25/25 = 1
1 = 1
hence proved that the point (3/5, 4/5) is on the unit circle .
(b) The distance between (2, -5) and (-7, -5) is calculated using the formula
[tex]=[/tex]√(x₂ - x₁)² [tex]+[/tex] (y₂ - y₁)²
= √(-7 - 2)² + (-5 -(-5))²
= √(-9)² + (-5 + 5)²
= √(-9)² = √81
= 9 units
(c) the mid point joining the points (2, -5) and (-7, -5) is (a,b) that is calculated by
a = (2-7)/2 , b = (-5-5)/2
a = -5/2 , b = -10/2
a = -5/2 and b = -5
the mid point is (-5/2,-5) .
Therefore , (a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = 1 .
(b) The distance between points (2, -5) and (-7, -5) is 9 units .
(c) The midpoint of the line segment that joins the given points is given by (-5/2,-5) .
The given question is incomplete , the complete question is
(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = .
(b) The distance between (2, -5) and (-7, -5) is .
(c) The midpoint of the line segment that joins the given points is given by ( , ) .
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9. [-10, ∞)
Interval notation
The inequality of the interval notation [-10, ∞) is x ≥ -10
The given interval notation is
[-10, ∞)
We have to convert the interval notation to inequality
The inequality is the mathematical statement that shows the relationship between two expression with inequality sign. The inequality signs are less than, less than or equal, greater than, greater than or equal. The inequality consist of different variables, numbers and mathematical operators.
Interval notation is defined as the method of writing subsets of the real number line
The given interval notation is
[-10, ∞)
Convert the interval notation to inequality
x ≥ -10
Hence, the inequality of the interval notation [-10, ∞) is x ≥ -10
The complete question is
Convert the interval notation [-10, ∞) to inequality
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)A math teacher graded 45 problems in of an hour. At that rate, how many problems
can she grade in 1 hour?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
problems
Subnt
The number of problem that can she grade in hour is 60 problems
The number of problems that math teacher graded in 3/4 of an hour = 45 problem
Here we have to use the unitary method
The unitary method is defined as the method of finding the value of the single unit.
The number of problem that can math teacher grade in 1 hour = The number of problems that math teacher graded in 3/4 of an hour ÷ 3/4
Substitute the value in the equation
The number of problem that can math teacher grade in 1 hour = 45 ÷ (3/4)
= 45 × (4/3)
= 60 problem
Hence, the number of problem that can she grade in hour is 60 problems
The complete question is:
A math teacher graded 45 problems in 3/4 of an hour. At that rate, how many problems can she grade in 1 hour?
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Hannah's least favorite weekly chore is mowing the lawn, even though it only
takes her about 30 minutes. Her family's lawn is 1,000 square yards, but her
parents are thinking about moving to the country, where they would have 5
acres of land. If the time it takes Hannah to mow a lawn is proportional to its
area, how many hours would it take her to mow 5 acres?
Answer:
12.1 hours
Step-by-step explanation:
You want to know the mowing time for 5 acres if Hannah can mow 1000 square yards in 1/2 hour.
Unit conversionWe can convert the acreage to square yards to facilitate the calculation:
5 ac × (4840 yd²)/(1 ac) = 24,200 yd²
Mowing rateHannah mows her lawn at the rate of ...
(1000 yd²)/(0.5 h) = 2000 yd²/h
TimeAt this rate, the time it takes for 24200 yd² will be ...
(24,200 yd²)/(2000 yd²/h) = 12.1 h
It would take Hannah 12.1 hours to mow 5 acres.
Alexander buys ice cream and oranges at the store.
• He pays a total of $34.07.
• He pays $5.65 for the ice cream.
• He buys 7 bags of oranges that each cost the same amount.
Which tape diagram could be used to represent the context if x
represents how much each bag of oranges costs?
If x represents the cost of each bag of oranges then the equation will be 7x+5.65 = 34.07 and the value of x is $4.06.
According to the question,
We have the following information:
Alexander buys ice cream and oranges at the store.
• He pays a total of $34.07.
• He pays $5.65 for the ice cream.
• He buys 7 bags of oranges that each cost the same amount.
Let's take the cost of each bag of oranges to be $x.
We have the following equation:
7x+5.65 = 34.07
Subtracting 5.65 from both sides:
7x = 34.07-5.65
7x = 28.42
x = 28.42/7
x = 4.06
Hence, if x represents the cost of each bag of oranges then the equation will be 7x+5.65 = 34.07 and the value of x is $4.06.
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suppose you plot the location of the animals on a number line which animale would represent by the point farthest from 0 on the number line ? explaine
The animal that is farthest from 0 on the number line is the Fanfin anglerfish.
What number is farthest from 0 on the number line?
A number line is a marked straight line that is used to visually represent real numbers.
The values given in the table are negative number. A negative number is a number that has a value less than zero. A negative number is represented with a minus sign. The table has decimals, mixed numbers and fractions.
The larger a number is, the farther the distance of the number from 0 on the number line. In the given table, the largest number is -2 1/4. Thus, -2 1/4 is the farthest from the number line.
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Write an equation the line perpendicular to y-3=-10(x-2) with an x-intercept of (-20, 0) in slope-intercept form.
please show work as detailed as possible
Answer:
y=1/10x+2
Step-by-step explanation:
y-3=-10(x-2) This equation is in point-slope form so the slope is -10
The perpendicular slope is the negative reciprocal so 1/10.
Slope intercept form is y=mx+b
Plug in the points of the x-intercept and slope into y=mx+b
0=-20(1/10)+b
0=-2+b
b=2
y=1/10x+2
Find the missing values for the exponential function represented by the table below.
The missing values for the exponential function are y = 16.875 and y = 25.3125
How to find the missing values for the exponential function?The general form of the exponential function is y = abˣ
From the table, when x = 0, y = 11.25. Substitute the values into the function:
y = abˣ
11.25 = ab⁰ (Note: b⁰ = 1)
11.25 = a(1)
11.25 = a
a = 11.25
Also, from the table, when x = -1, y = 7.5. Substitute the values into the function:
7.5 = 11.25b⁻¹
7.5 = 11.25/b (Note: b⁻¹ = 1/b)
7.5b = 11.25
b = 11.25/7.5 = 1.5
We can now write the exponential function for this case:
y = abˣ
y = 11.25(1.5)ˣ
We can find the missing values now:
when x = 1:
y = 11.25(1.5)ˣ
y = 11.25(1.5)¹
y = 16.875
when x = 2:
y = 11.25(1.5)ˣ
y = 11.25(1.5)²
y = 25.3125
Therefore, the missing values are 16.875 and 25.3125. Option c is the correct answer
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Is 8/20 equal to 4/5
Answer: no
Step-by-step explanation:
8 and 20 can both be divided by 4
8 divided by 4 = 2
and 20 divided by 4 = 5
based on this, we can tell that 8/20 is not equivalent to 4/ but rather 2/5
I hope that helps
Answer:
No
Step-by-step explanation:
Because if you divide the numerator by something you have to do the same for the denominator. This means the if you do 8÷2 to get 4 then you do 20÷2 you get. 8/20=4/10/2/5
A boat is heading towards a lighthouse, where Deion is watching from a vertical distance of 140 feet above the water. Deion measures an angle of depression to the boat at point AA to be 15^{\circ}
∘
. At some later time, Deion takes another measurement and finds the angle of depression to the boat (now at point BB) to be 51^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Using trigonometric ratio, the horizontal distance from A to B is 314 feet
Trigonometric RatioTrigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.
To calculate the distance from point A to point B, we can use trigonometric ratio here.
Note: We are going to add the two angles and then use the vertical distance as the adjacent side of the triangle.
Data;
Angle = 66°Adjacent = 140ftOpposite = ABUsing tangent of the angle;
Tanθ = opposite / adjacent
tan 66 = AB / 140
AB = 140 tan66
AB = 314ft
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whats this? comment the answer-3.9 = x - 0.9
A vehicle purchased for $27500 depreciates at a constant rate of 8% Determine the approximate value of the vehicle 10 years after purchase Round to the nearest whole number.
The approximate value of the vehicle 10 years after purchase is $11,945.68.
What is the approximate value of the vehicle?Depreciation is when the value of an asset falls with the passage of time as a result of wear and tear of the asset. Deprecation would reduce the price of the vehicle each year.
The equation that can be used to determine the value of the vehicle after 10 years is:
FV = P (1 - r)^t
Where:
FV= value of the vehicle in 10 years P = value of the vehicle when it was purchased r = rate of decline t = number of yearsFV = 27,500 (1 - 0.08)^10
FV = 27,500 x (0.92^10)
FV = $11,945.68
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if 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?
There are 19 triangels can be formed whose vertices are among the 9 points.
A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides. In other words, a triangle is defined as a three-sided two-dimensional figure whose interior angles are equal to 180°.
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.
From the question, we know that we have 9 point from 2 line parallel. There are 19 triangels (the same shape is not counted twice) can be formed whose vertices are among the 9 points that shown in the following picture.
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1) Sarah received three fifths of her sister's book collection. If Sarah received 18
books, how many books did her sister have before giving any to Sarah?
The number of books that her sister has before giving any to Sarah is 30 books
Sarah received three fifths of her sister's book collection
Number of books that Sarah received = 18 books
The fraction of the books that Sarah received = 3/5
Consider the total number of books as x
Then we have to find the total number of books
So the equation will be
x × (3/5) = 18
Divide the terms in the equation
x × 0.6 = 18
Move 0.6 to the right hand side of the equation
x = 18 / 0.6
Divide the terms
x = 30 books
Hence, number of books that her sister has before giving any to Sarah is 30 books
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Si los lados de un cuadrado miden 3 cm cuántos centímetros cuadrados medirá su área.
The area of the square that has 3 cm of side is 9 cm^2
The formula and procedure to solve this geometry exercise is:
A = s²
Where:
A = area of the squares = sideProblem information:
A = ?s = 3 cmUsing the formula of the square area we get:
A = s²
A = (3 cm)²
A = 9 cm²
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft2, m2
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A chunk meat weighs 8kg.After reducing it a bit a bit,it weighs 6 1/2kg. Find the percentage decrease
Answer: 18.75%
Step-by-step explanation:
To find the percentage decrease, the formula is shown below.
Plug in the values and calculate:
[tex]\frac{8-6.5}{8} *100=18.75%[/tex]
So, the chunk of meat lost 18.75% of its initial weight.
Show all work to multiply (3+√16) (6-√64)
After the multiplication of (3+√16) (6-√64), the resultant answer is -14.
What is multiplication?Multiplying in math is the same as adding equal groups.
The number of items in the group grows as we multiply.
Parts of a multiplication issue include the product, the two factors, and the product.
The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.
So, the multiplication of:
(3+√16) (6-√64)
Now, multiply as follows:
(3+√16) (6-√64)
We know that: 3+√16 = 7
7(6-√64)
We know that: 6-√64 = -2
7(-2)
-14
Therefore, after the multiplication of (3+√16) (6-√64), the resultant answer is -14.
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the radius of a circle is 15inches. what is the circumference of the circle? writte your answer using pie.
Answer:
circumference of the circle is= 2πr
if radius is 15 then we should put that into the formula
30π
if pie is given as 3.14 then it would be
94.2
good luck
Answer:
30 pi inches
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi * r
C = 2 * pi * 15
C = 30 pi inches
7. f(x)=x2 and g(x)=x-1 Evaluate f(g(3)) =
please solve 2y+x=6 and 2y-3x=-2
Linear Equations
2y+x=6 ... (i)
2y-3x=-2 (ii)
x=2
y=2
To solve this problem, we will use a substitution method.
We would first transform equation (i) to get the formula for x-value.
2y+x=6
x=6-2y... (iii)
Next, we will substitute the equation (iii) into (ii) to find the value of y.
2y-3x=-2
2y-3(6-2y)=-2
2y-18+6y=-2
8y-18=-2
8y=16
y=2... (iv)
Then we would substitute the equation (iii) with the value y on the equation (iv)
x=6-2y
x=6-2(2)
x=6-4
×=2
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Answer:
(2, 2 )
Step-by-step explanation:
2y + x = 6 → (1)
2y - 3x = - 2 → (2)
subtract (2) from (1) term by term to eliminate y
(2y - 2y) + x - (- 3x) = 6 - (- 2) , that is
x + 3x = 6 + 2
4x = 8 ( divide both sides by 4 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (1)
2y + 2 = 6 ( subtract 2 from both sides )
2y = 4 ( divide both sides by 2 )
y = 2
solution is (2, 2 )
2 lines 3y-2x=21 and 4y+5x=5, intersect at the point Q. Find the coordinates of Q
Answer: (-3,5)
Step-by-Step Solution:
1. Set 1 equation equal to y
3y-2x=21
3y=2x+21
y=2/3x+7
2. Set the other equation equal to y
4y+5x=5
4y=-5x+5
y=-5/4x+5/4
3. Set the equations equal to each other, and solve for x
2/3x+7=-5/4x+5/4
2/3x+23/4=-5/4x
(Multiply by 12 on both sides to get rid of fractions)
8x+69=-15x
8x=-15x-69
23x=-69
x=-3
4. Solve for y
(Choose any of the equations)
y=2/3x+7
y=2/3(-3)+7
y=-2+7
y=5
ANSWER: (-3,5)
8.26 cats, part i. the following regression output is for predicting the heart weight (in g) of cats from their body weight (in kg). the coefficients are estimated using a dataset of 144 domestic cats
The correlation coefficient is the square root of the coefficient of determination.
A. The linear model is y' = -0.357+4.034x
Where y' is the predicted heart weight and X is the body weight
B. The intercept of -0.357 is actually showing the non existence of the heart weight when the body weight is absent, ie. When X=0
C. The slope indicates that with each unit increase in the body weight x, the heart weight y increases 4.034 times.
D. R^2 = 64.66% indicates that 64.66% variation in the dependent variable that is explained by our model.
E. Given that the coefficient of determination = 0.6466
Thus the correlation coefficient is the square root of the coefficient of determination
Thus, R = √0.6466 = 0.8041
( Since the slope is positive the correlation ought to be positive)
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The question was incomplete. Check below the complete question.
The following regression output is for predicting the heart weight (in g) of cats from their body weight (in kg). The coefficients are estimated using dataset of 144 domestic cats_ Estimate Std. Error t value Pr(> /tl_ 20 (Intercept _ -0.357 0.692 -0.515 0.607 body wt 4.034 0.250 16.119 0.000 ? 15 1.452 R2 64.66% Radj 64.41% 1 Write out the linear model. [ 10 Interpret the intercept_ Interpret the slope. Interpret R?_ 2.0 Calculate the correlation coefficient 2.5 3.0 3.5 Body weight (kg) 4.0.
Please help me, I don't understand a thing
Answer:
Step-by-step explanation:
Let M(x,y) be the median of ΔABC through A to BC.M will be the midpoint of BC.x1=5,y1=3x2=3,y2=−1By midpoint formula, x=(x1+x2)/2∴x=(5+3)/2=8/2=4By midpoint formula, y=(y1+y2)/2∴y=(3+(−2))/2=2/2=1Hence the co-ordinates of M are (4,1).By diatnce formula, d(AM)=[(x2−x1)2+(y2−y1)2]x1=7,y1=−3x2=4,y2=1
PLEASE HELP- I cant figure out this problem
John uses 4 cups of flour for every 4/7 cups of chocolate chips. How much flour will he use for one cup of chocolate chips?
Answer:
7
Step-by-step explanation:
4 divided by 4/7 = 7