The solution of | x | +5 ≤ 1 is option C, All values are solutions
We need to find the solution of | x | +5 ≤ 1
Upon removing the modulus function, the term presnet within it can be either negative or positive
considering it as postive
| x | +5 ≤ 1
x + 5 ≤ 1
x ≤ 1 - 5
x ≤ -4
considering it as negative
| x | +5 ≤ 1
-x + 5 ≤ 1
-x ≤ 1 - 5
-x ≤ -4
x ≥ -4
Therefore, the solution of | x | +5 ≤ 1 is All values are solutions
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multiply
(−5 2/5) ⋅ 3 7/10.
a. −19 49/50
b. −15 7/25
c. −9 1/10
d. −1 7/10
Answer: -19 49/50 ==> a
Step-by-step explanation:
(−5 2/5) ⋅ 3 7/10=
(−5 - 2/5) ⋅ (3 + 7/10)=
(−25/5 - 2/5) ⋅ (30/10 + 7/10)= ==> make the terms have like denominators
((-25-2)/5) ⋅ ((30+7)/10)=
-27/5 ⋅ 37/10 =
-27 ⋅ 37 / (5 ⋅ 10) =
-999/50=
(-950-49)/50=
-950/50 - 49/50=
-19 - 49/50=-19 49/50 ==> a
A football team receives the ball on their
own 10 yard line.
a. They make a gain of 15 yards in the first play. What yard line is the ball on?
b. What represents zero in this situation? Explain.x
The summation of 10 yards line and 15 yard is 25 yards and the ball represents zero situation when the ball is in net and goals.
Given,
The team receives the ball on their own yards = 10 yards.
that is,
initial position of the ball = 10 yards.
Using summation, (the summation is to add or subtract any two numbers or more terms by doing operation, to get answer).
They make a gain of 15 yards in the first play.
Their final position in 10 yards plus 15 yards
= 10 + 15
=25 yards.
Therefore, the yard line is 25 yards.
The zero situation of the game is when the ball is in net and the player make a goal.
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A pool takes 3,185 gallons to fill. After 2.5 hours the pool is filled with 1,625 gallons how long will it take to fill the whole thing
[tex]\begin{array}{ccll} hours&gallons\\ \cline{1-2} 2.5 & 1625\\ h& 3185 \end{array} \implies \cfrac{2.5}{h}~~=~~\cfrac{1625}{3185}\implies \cfrac{2.5}{h}=\cfrac{25}{49} \\\\\\ (2.5)(49)=25h\implies \cfrac{(2.5)(49)}{25}=h\implies 4.9=h\qquad \textit{4 hours and 54 minutes}[/tex]
[tex]3\sqrt{6w-288[/tex]
I need help with this graph what is the root or factored form of this? Thank you!
Answer:
(2.5×20)2=100 then square root of 100;
✓100=10
Hence answer is 10
A manager of a fast food chain wants to know how his customers rate their service at the restaurany that day. after randomly picking the 9th customer, he surveys every 5th customer that exits the restaurant. which sampling method? your answer: simple random systematic stratified cluster volunteer
The sampling method used in this scenario is random Systematic random sampling
Systematic random sampling
Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.
If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.
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9. There is so much water in the world, that we normally measure large bodies of water in cubic
miles or cubic kilometers instead of gallons. Cayuga Lake in upstate New York contains an
estimated 9.4 km³. How many cubic miles of water does Cayuga Lake contain?
Answer:
Step-by-step explanation:
12.5km
i made that up sorry
The exponential model describes the population, A, of a country in millions, t years after 2003. Use the model A=384. 7e^0. 018t to determine when the population of the country will be 513 million.
The population of the country will be 513 million in __. (Round to the nearest year as needed. )
The population of the country will be 513 million in 2016 with The exponential model A=384. 7e^0. 018t describes the population, A, of a country in millions, t years after 2003.
What is exponential model?The exponential model represents the degrading failure process using an equation like: where Y = degradation, T = time, and A and B = parameters to be predicted using the regression approach using historical data. Exponentials are frequently utilized when the rate of change of a quantity is proportional to its beginning amount. Y represents exponential decay if the coefficient associated with b and/or d is negative. Y represents exponential growth if the coefficient is positive.
Here,
A = 384. 7e^0. 018t
513=384. 7e^0. 018t
513/384.7= e^0.018t
ln(513/384.7) = 0.018t
ln(513/384.7)/0.018 =t
t=15.9895575229 years
t=16 years
2003+16= 2019
In 2016, the country's population will be 513 million people. The exponential model A=384. 7e^0. 018t explains a country's population, A, in millions, t years after 2003.
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Three students ran for class president. lisa got 36 votes for class president. she got six times more votes than lauren. chandler got seven times more than lauren. how many votes did lauren get?
Lauren got 5 votes in class president election.
Number of votes Lisa got = 36
Let the number of votes of Lauren be x. So, forming the equation between the number of votes of Lisa and Lauren.
36 = x + 6x
Calculating the value of x from mentioned equation
36 = 7x
Rewriting the equation with 7 as denominator
x = 36/7
Performing division on Right Hand Side of the equation
x = 5.14
Rounding off the digits as number of votes will be whole number
x = 5
Based on the mentioned information, Lauren got 5 votes.
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Write an equation in slope-intercept form
to represent the relationship between x
and y shown in the table.
X
Y
-10 -5 0 5
55
20
-15
-50
10
-85
Answer:
665-09
Step-by-step explanation:
Is y−4=3(x+1) an equation of a line through (-2, 1)? Explain.
Answer:
Yes
Step-by-step explanation:
(1)-4=3((-2)+1)
-3=3(-1)
-3=-3
The answer is yes because if you substitute x and y for -2 and 1 you can simplify the equation. Then you get the answer -3=-3 which means that the equation is equal.
f(-10) = 4, ƒ(8) = -5
Answer: f(x)=-.5x-1
Step-by-step explanation:
I believe this is the answer you are looking for. Because if you plug in -10 for x and it gives you 4. Do the same with 8 and you get -5
Hope this helps :)
Kelly has 97 apples, Jason has 72. How may proportional relationships are there?
There are 6984 inverse proportional relationships and the direct proportional relationships are 97/72.
Given that:
Kelly has 97 apples, and Jason has 72.
The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.
Y/X = k
Substitute the given X and Y values and solve for k.
Suppose, Y = 97, X = 72
then k = 97/72
Distinguish a proportional relationship from other relations, including an inverse relationship (XY = k or Y = k/X).
An inverse proportional relationship is one in which two quantities vary inversely with respect to each other. We say that the variable Y changes inversely with X if
Y = k/X
Substitute the given X and Y values and solve for k.
Suppose, Y = 97, X = 72
then k = 97 x 72
=> k = 6984
Hence, there are 6984 inverse proportional relationships and direct proportional relationships are 97/72 between Kelly which has 97 apples, and Jason which has 72.
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Please Help ASAP!!!!!
Answer:
the forth (7,2).........
1/x-2 identify the asymptotes
The vertical asymptote is x=2 and horizontal asymptote is y = 0
What are asymptotes?An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.
There are three types is asymptotes:
Horizontal asymptote , Vertical asymptote and oblique asymptote.
in the expression 1/x-2, the horizontal asymptote is y=0 since the power of x in the numerator is less than that of denominator.
And the vertical asymptote is found by equation the denominator to zero
therefore x-2= 0
x= 2
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a journalist for an automotive magazine wants to determine how the weight of a passenger vehicle, in kilograms, is related to its length, in centimeters; the maximum number of passengers; and its safety rating on a 5-point scale. what is the correct format for a multiple regression equation?
the correct format for a multiple regression equation is
ŷ= [tex]b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}[/tex]
multiple regression: The relationship between a single dependent or criterion variable and multiple independent or predictor variables is typically explained by multiple regression. The constant term and multiple independent variables with their corresponding coefficients are used to model a dependent variable. The term "multiple regression" refers to the fact that it requires two or more predictor variables.
because, the weight of a passenger vehicle, in kilograms, is related to its length, in centimeters; and the maximum number of passengers.
thus, ŷ=[tex]b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}[/tex] is the multiple regression equation.
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What is the value of blank and 40.01 is close to 1
The number that is the numerator of a fraction with denominator of 40.01 and is equals to a coefficient of one is:
40.01.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:
Fraction = x/y.
The terms are named as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.Hence the quotient of the division is the numerator divided by the denominator.
In this problem, interpreting the blank variable as x, the fraction that represents the situation is:
x/40.01 = 1.
Applying cross multiplication, the numeric value of the variable x is obtained as follows:
x = 40.01 x 1
x = 40.01.
Missing InformationThe complete problem asks for which number divided by 40.01 is close to 1.
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Write an equation of the line, in point-slope form, that passes through the two given points.
points: (-2,10), (10 -14)
The required equation of the line will be y = 2x + 6 which passes through the points (-2,10), (10 -14).
What is the slope of the line?The slope of a line is defined as the gradient of the line.
Given that line passes through the points (-2,10), (10 -14)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -2, y₁ = 10
x₂ = 10, y₂ = -14
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 10 = (-14 - 10)/(10-(-2))[x -(-2)]
⇒ y - 10 = (-24)/(12 )[x +2]
⇒ y - 10 = -2(x +2)
⇒ y = -2x - 4 + 10
⇒ y = -2x + 6
Therefore, the equation of the line would be y = 2x + 6 which passes through the points (-2,10), (10 -14).
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What value of b will complete the square in the expression below and make the
expression a perfect square trinomial?
x²+bx+144
Enter the perfect square trinomial as a squared binomial.
At b= 24 will complete the square in the expression x^2 + bx + 144.
What is perfect square trinomial?
A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b^2 = 4ac has the form ax^2 + bx + c, it is said to be a perfect square. The formula for the perfect square trinomial is (ax)^2 + 2abx + b^2 = (ax + b)^2.
Consider the given expression
x^2 + bx + 144
For this type of expression [tex]b = 2\sqrt{c}[/tex] will complete the square.
Here, c = 144
√144 = 12
So, b√c = 2(12) = 24
The expression becomes,
x^2 + 24x + 144 = (x + 12)^2
This is the perfect square.
Hence, b = 24 will complete the square in the expression x^2 + bx + 144.
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you cannot remember your 5-digit bike-lock combination. what is the probability that you guess the combination correctly? (enter your probability as a fraction.)
The probability that you guess the combination correctly 0.00001.
We know that the probability of an event is (possible outcome/total outcome)
I will assume that repeats are allowed as in most combination locks so the number of possible codes
= 10⁵ = 100000
We also know that there is only one correct combination so the probability that you guess the combination correctly
= 1/10⁵ = 1/100000 = 0.00001
Orchestrating individuals, digits, numbers, letters in order, letters, and tones are instances of changes. Choice of menu, food, garments, subjects, and group are instances of combination.
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Determine the slope of the graph of x2 = ln(xy) at the point (1, e).
The slope of the given graph x^2 = ln (xy) at the point (1, e) is e
We have been given a graph x^2 = ln (xy) and a point (1, e)
Differentiate the given graph on both sides
d/dx x^2 = d/dx (ln (xy))
⇒ 2x = 1/xy × d/dx (xy)
⇒ 2x × xy = x.dy/dx + y.dx/dx
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y - y = x.dy/dx
⇒ (2x^2y - y)/x = dy/dx … (1)
The slope at the point (1, e)
m = dy/dx at x = 1, y = e
Substitute the values in Equation (1)
⇒ m = (2(1)^2 (e) - e)/1
⇒ m = (2e - e)/1
⇒ m = e/1
⇒ m = e
Hence, the slope of the given graph is e.
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If f(x) = 10 - 200 and g(x) = 25x2 + 90, the value of f (4) - g (2) is:
As function f(x) is not completely right i assume it to be like f(x)= 10x-200.
Acc. to which the answer is -350.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.
Main Body:
f(x)= 10x-200
f(4)= 10*4-200
= 40-200
=-160
g(x)= 25[tex]x^{2}[/tex]+90
g(2)= 25*(2)² +90
= 25*4+90
=190
So, f(4)-g(2) = -160-190
= -350
Therefore the answer is -350.
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can anyone please help with this! it’s so confusing! 100 points to whoever can help me with all of them! and please show how u did it not just answers!! tysm
Answer:
Step-by-step explanation:
(a is in the file)
B. An add 3 inches to height would affect the surface area more than 3 inches to weight because if the same number was multiplied to 0.13 and 0.08… 0.13 would have the greater outcome.
c. a number more than 10 but less than 11 is 10.5
The height is 50 so plug those two numbers into the equation
10.5=0.08W+(0.13)50-1.03
10.5=0.08W+ 6.5-1.03
10.5=0.08W+5.47
Subtract 5.47 from both sides
5.3=0.08
Divide by 0.08 on both sides
= 62.87lbs in one possibility for the value of W
D. a number between 12 and 13 is 12.5
12.5= 0.08w+ 0.13H-1.03
Subtract 1.03 on both sides
11.47= 0.08w+ 0.13H
Divide 11.47 in 2 so that weight and height can be added up to equal 11.47 in the end
5.73=0.08 5.73=0.13
71.68=W 44.07=H
Which inequality represents the phrase "nine less than two
times a number is no more than 45?"
The expression of the inequality is [tex]9 < 2x\le45[/tex]. It can be obtained using the operations of inequality.
What is inequality?
In matmathematics if two numbers are not equal even then there is a relationship. This relationship can be defined by inequality relationship.
According to the pharase, 9 is less than two times a number. Hence, consider the number is x and its two times means 2x. Now, 9 should be less than this number. Hence, 9<2x. Now, again the number 2x is not more than 45. Means, it can be equal to 45. Hence, it will give the expression [tex]2x\le45[/tex].
Now, combine the two expressions as follows:
9<2x
[tex]2x\le45[/tex]
[tex]9 < 2x\le45[/tex]
Hence, the expression of the inequality is [tex]9 < 2x\le45[/tex].
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HELP MEEE PLEASEEEE
Answer:
5.8 cm
Step-by-step explanation:
the Pythagorean theorem states that a^2=b^2+c^2, where a is the hypotenuse, and b and c are the legs. Plugging in your values, we get:
4^2 + 4.2^2 = a^2
Simplify: 16 + 17.64=a^2
Simplify again: 33.64 = a^2
Square root both sides: 5.8 = a
solve for x and y
picture provided
The value of x will be 15 and the value of y will be 4.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Here in the image, we have a triangle having sub-triangles. The value of x is calculated by considering two right-hand triangles.
x / ( x + 5 ) = 18 / ( 18 + 6 )
x / ( x + 5 ) = 18 / 24
24x = 18x + 90
6x = 90
x = 15
The value of y will be calculated by considering the two left-hand triangles.
12 / ( 12 + y) = 15 / 20
240 = 180 + 15y
15y = 60
y = 60 / 15
y = 4
Therefore, the value of x will be 15 and the value of y will be 4.
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In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles.
Based on the given information, answer the questions below. Round each answer to the nearest tenth.
Part A: How tall is the pole? Show your work.
Part B: How far from the base of the pole does Wire 2 attach to the ground? Show your work.
Part C: How long is Wire 1? Show your work.
The answers are a) 29.55 ft, b) 23.08 feet and c) 45.05 feet
What are trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.
Given is a figure, of two wires 1 and 2 attached to a pole and ground
Using trigonometric ratios, we have,
a) tan41° = Height of pole/34
Height of pole = tan41°x34
Height of pole = 29.55 ft
b) tan38° = (distance of wire 2 from the base of pole)/29.55
Distance of wire 2 from the base of pole = tan38°x29.55 = 23.08 feet
c) cos41° = 34/length of wire 1
Length of wire 1 = 34/cos41°
Length of wire 1 = 45.05 feet
Hence, The answers are a) 29.55 ft, b) 23.08 feet and c) 45.05 feet
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What is the radius of the circle made by anas brother in the blue car? use 3. 14 and round your answer to the nearest tenth
The radius of Ana's brother's circle in the blue car is 35 feet.
Define the term radius of the circle?A radius is a line segment that connects the center towards the perimeter of a circle or sphere. The radius length remains constant as from center either to point on the circle or sphere's perimeter.For the given question-
The total distance covered by the Ana's brother in the blue car = 220 feet.
Total distance = circumference of the circle.
circumference of the circle = 2 π r
r = radius of the circle.
π = 3.14
Thus,
220 = 2 x 3.14 x r
r = 220 / (3.14 x 2)
r = 35.03
r = 35 feet.
As a result, the radius of Ana's brother's circle in the blue car is 35 feet.
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The complete question-
The missing data from the question is given in diagram attached.
Use the distributive property to remove the parentheses.
3c³(7c8 +8c+7)
Simplify your answer as much as possible.
Answer: 21 c^16 + 24c^9+ 21 c^8
Step-by-step explanation: To multiply exponents with the same base, add them.
Answer:
3c^3(7c^8+8c+7)
=(3c^3)(7c^8+8c+7)
=(3c^3)(7c^8)+(3c^3)(8c)+(3c^3)(7)
=21c^11 + 24c^4 + 21c^3
Step-by-step explanation:
Remember.... ^ is for power
If your weekly salary is $1,015.00, how much do you have left each week after you pay for the following? Rent - $443.50 Cable TV -$23.99 Electricity - $45.62 Groceries - $124.87 ?
(need explanation.)