Order the following expressions from least to greatest.
Answer:
[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]
Step-by-step explanation:
The bars either side of an expression or a value are the absolute value symbol. "Absolute value" means how far a number is from zero. Therefore, the absolute value of a number is its positive numerical value.
The values of a, b and c are negative. All expressions except "a" are absolute values, and are therefore positive numerical values. Therefore, "a" is the least expression.
The simplest way to calculate each expression's numerical value is by assigning approximate numbers to each value, then carrying out each calculation.
From inspection of the graph:
a ≈ -3.8b ≈ -1.3c ≈ -0.7[tex]\begin{aligned} \implies |a - b| & \approx |-3.8 - (-1.3)|\\ & = |-2.5| \\ &= 2.5\end{aligned}[/tex]
[tex]\begin{aligned} \implies |b - c| &\approx |-1.3 - (-0.7)| \\ &= |-0.6| \\ &= 0.6\end{aligned}[/tex]
[tex]\implies a \approx -3.8[/tex]
[tex]\begin{aligned} \implies |a - c| &\approx |-3.8 - (-0.7)| \\ &= |-3.1| \\ &= 3.1\end{aligned}[/tex]
Therefore: -3.8 < 0.6 < 2.5 < 3.1
Hence, the expressions from least to greatest are:
[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]
at what rate percent compound interest wil Rs2000 amount to Rs2420 in 2 years.
The Compound Interest of Principle 2000 will become 2420 within 2 years when the rate of interest is 21%
Compound interest = P(1 + R ÷ 100) to the power of n,
where P = Principle
R = Rate of Interest
n = no. of years
According to the given question,
Principle(P) =Rs2000
Rate of interest (R) =?
no. of years(n) = 2 years
given CI (Compound Interest) = Rs2420
CI = 2000(1 + R ÷ 100)² = 2420
= 20(100 +R) = 2420
= 100 + R = 2420 ÷ 20
= 100 + R = 121
= R = 121 - 100
= R = 21%
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a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 6ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?
Answer:
Below in bold.
Step-by-step explanation:
The relation between the height of the ladder and distance from the ground is given by Pythagoras Theorem:
h^2 = 13^2 - L^2
h = (169 - L^2)^1/2
Finding the derivative:
dh/dL = 1/2(169 - L^2)^-1/2 * -2L
= -L / (169 -L^2)^1/2
dL/dt = 6
So, dh/dt = dh/dL * dL/dt
= -6 * L/ (169 - L^2)^1/2
= -6 * 12 / (169 - 12^2)^1/2
= -72/5 ft /second
= -14.4 ft/second.
It's negative because the distance from the ground is decreasing.
need help with this, thanks
The error is that vertical angles are congruent, and don't necessarily add to 180°. Vertical angles only add to 180° if they are right angles.
[tex]13x+45+19x+3=180 \\ \\ 32x+48=180 \\ \\ 32x=132 \\ \\ x=33/8[/tex]
Answer:
x = 7
Step-by-step explanation:
Vertical Angle Theorem
When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent.
Angles on a Straight Line Theorem
The sum of angles formed on a straight line is equal to 180°.
The error made is confusing the Vertical Angle Theorem with the Angles on a Straight Line Theorem. To find x, we should either:
Equal a pair of vertical angles and solve for x, orEqual the sum a pair of angles that form a straight line to 180° and solve for x.Applying the Vertical Angle Theorem:
[tex]\boxed{\begin{aligned} (13x+45)^{\circ} &=(19x+3)^{\circ} \\13x+45&=19x+3\\13x+42&=19x\\42&=6x\\x&=7\end{aligned}}[/tex]
Applying the Angles on a Straight Line Theorem:
[tex]\boxed{\begin{aligned}(6x+2)^{\circ}+(19x+3)^{\circ}&=180^{\circ}\\6x+2+19x+3&=180\\25x+5&=180\\25x&=175\\x&=7\end{aligned}}[/tex]
Therefore, the value of x is [tex]\boxed{x=7}[/tex] .
What is the domain of the following ordered pairs?
(2, 3), (-12, 7), (4, 7)
Answer:
Yes, the relation {(3,2), (4,1), (5,9), (6,12), (7,12)}is a function.
Step-by-step explanation:
Answer:
It's a triangle just like you, except you're acute one.
Step-by-step explanation:
Write the equation that is the translation of y = |x| left 9 units and up 11 units.
The translation of y = |x| left 9 units and up 11 units is y = |x+9|+11 .
The process of translating an existing graph or equation into a new graph is known as graph translation.
The alteration of algebraic equations is a typical form of algebraic challenge.A translation modifies the graph of a parent function. Dilations, reflections, and translations are the three distinct types of translation. The y-values of a function can be changed vertically, or the x-values can be changed horizontally (affects the x-values).We know that for translation we have to change the x-coordinate and the y-coordinate by the amount that is stated in the translation.
Therefore from the graph we can see that the graph of y =|x| is represented by the blue line and the graph of translation y = |x+9|+11 is represented by the red line.
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Simplify:
5/8(-8j+24)
Answer: -5j+15
step by step equation
Mrs. Ellis has 4 children. She is going to feed them leftover pizza for dinner. If she has 2/3 of pizza left, how much pizza will each child get?
45 percent of what number is 99
actually the number is "x", which oddly enough is the 100%, so we know that 45% of "x" is 99, what is "x" anyway?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 99& 45 \end{array} \implies \cfrac{x}{99}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{x}{99}=\cfrac{20}{9}\implies 9x=1980\implies x=\cfrac{1980}{9}\implies x=220[/tex]
Anna is following this recipe to make biscuits.
Anna uses 120 g of chocolate.
How many grams of margarine will she need?
Recipe: Makes 24 biscuits
80 g sugar
120 ml syrup
200 g oats
120 g margarine
40 g chocolate
Anna uses 120 g of chocolate and 360 grams of margarine to needed to bake biscuits.
We have data as follows; To make 24 biscuits Anna uses following proportion of Ingredients;
80 g sugar
120 ml syrup
200 g oats
120 g margarine
40 g chocolate
Now We can analysis that anna uses 40 g chocolate to make 24 biscuits
So for 120 g of chocolate Anna can bake [tex] \frac{24(120)}{40} [/tex]
= 24 (3)
= 72 biscuits
∴ Anna can bake 72 biscuits if she uses 120 g of chocolate.
We want to find how many grams of margarine will she need to make 72 biscuits and this can be done as follows;
Ingredients for 24 biscuits require 120 g margarine
∴ For 72 biscuits anna require [tex] \frac{72(120)}{24} [/tex] g of margarine
= 3 (120)
= 360 g of margarine.
Hence 360 grams of margarine anna needed.
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Combine like terms to simplify the expression. 2x - 10 - 5x - 1 + x
Combine X. which is 2x, -5x, x.
we combine -2x and -5x and gives me -3x.
2x -10 -5x -1 +x
now i combine the last x, which is -3x and x and gives us -2x.
-3x -10 -1 +x
now we just combine the rest of the numbers. -10 and -1 and gives me -11.
-2x -10 -1
we have now combine all the numbers and there's nothing else to combine. we're done combining. :))
ANSWER:
-2x-11
Expand
−
10
(
b
−
9
)
Answer:
Step-by-step explanation:
Expand · Evaluate Fractions · Linear Equations · Quadratic Equations ... 7 + 4 s = 10 ( 6 - 9 s ). 7+4s=10(6−9s) ... 7 + 4 s = 10 ( 6 - 9 s ).
Answer:
-10b × 90
Step-by-step explanation:
-10 * b =-10b
10 *9=90
Your welcome :)
6. The price x of a new car minus à 25% down payment.
The expression that shows the price x of a new car minus à 25% down payment is x - 0.25 = 0.75x
How to illustrate the information?Based on the information given, it should be noted that the information is to simply illustrate find the expression that shows the price x of a new car minus a 25% down payment.
This will be illustrated as:
= x - (25% × x)
= x - 0.25x
= 0.75x
Therefore, the expression is 0.75x.
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I need help on Question 3. Ignore the other ones please. Thank you so much!! 15 points if you get it right!
The value of x and y for given equation are (2,15) and (12,24).
Using hit and trial method, we can calculate that the values of given equation are (2,15) and (12,24)
What is hit and trial method?
The hit and trial approach is used to balance chemical equations by selecting the least whole number coefficient. tally the instances of each ingredient on either side of a reaction. The element with the lowest frequency of recurrence is considered to be balanced.
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I need help on 5,6, and 7 !
In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.
Given that,
In the picture there are 2 problems.
We have to find the difference and similarities of question in the picture.
The similarities are they 2 are word problems.
Another similarity is they two have to find 2 question.
1. How much money for 10 days and How many days to collect the money $1.05?
2.How much gallon of water need for 50 minutes and How much time take to fill the pool?
Another similarity is they two have to justified the answer in a mathematical model.
Now,
The difference is,
First question has given sisters and money problem where as the second has given pool and gallon water problem.
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List all the factors of 12.
Answer: The factors of 12 are 1, 2, 3, 4, 6, and 12
Hope this helps!
Answer:
The factors of 12 are 1, 2, 3, 4, 6 and 12.
help me i am helpless.
Answer: -5x >[-3x,4x,1.5x] 10>[11] 6xy>[-7.85xy, -98xy, 155xy]
Step-by-step explanation:
3*19*14+18/2 whats the awnser
Answer:
807
Step-by-step explanation:
because u multipy 3x19x14+18/2 and u get 807
Answer:
807
Step-by-step explanation:
3*19*12=798
18/2 = 9
798 + 9 = 807
suppose that the weight, x, in pounds, of a 40-year-old man is a normal random variable with mean 147 and standard deviation 16. calculate p(120≤x≤153). round your answer to four decimal places.
0.6004 is standard deviation of equation .
Why is there a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.An individual collection of data is compared to the average of several other sets of data using the standard deviation. You can compute two different forms of standard deviation: When data are gathered from every person in a population or collection, it is the population standard deviation.=0.6004$P(120≤X≤153)=0.6004
The mean is μ=147, and the standard deviation is σ=16.
0.6462−0.0458=0.6004.
Thus, P(120≤X≤153)=0.6004.
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Which equation is the inverse of y = 16x2 + 1?
y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot
y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction
y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth
The inverse of the given function, y = 16x² + 1 is: B. y = ±√(x - 1)/16
What is an inverse function?In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).
Generally speaking, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x.
In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:
y = 16x² + 1
x = 16y² + 1
Subtracting 1 from both sides, we have:
16y² + 1 - 1 = x - 1
16y² = x - 1
Dividing both sides by 16, we have:
y² = (x - 1)/16
Taking the square root of both sides, we have:
y = ±√(x - 1)/16
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given the expression 3x^4 - 5x + 2 state what each of the following represents
-5
2
3x^4
4
Given the algebraic expression 3x⁴ - 5x + 2, each of following represents:
-5 = coefficient.2 = constant3x⁴ = monomial4 = exponent.What is an algebraic expression?An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.
What is a coefficient?In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.
In conclusion, an exponent is an operation that raises a numerical value or quantity to the power of another and it is generally written as bⁿ.
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Math
Language arts
Geometry B.10 Midpoint formula: find the midpoint 2YG
Submit
Recommendations
Skill p
B(-2, -13) and C(-3, 6) are the endpoints of a line segment. What is the midpoint M of that
line segment?
Write the coordinates as decimals or integers.
M =
Please help
m=x1+x2/2 or m=y1+y2/2
hope you understand
Ramu's sister's age is 28 years old. She is 3 years older than five times Ramu's Age? What is Ramu's age?
Answer:
Ramu's sister's Age= 28
ramus age=×
28=5×+3
5×=28-3
=25
×=25/5
×=5
so the age of Ramu is 5 years old.
Answer:
25 because 5×5= 25 and 25+3=28 so ramu's age is 25
Please help!!! What are the domain and range of the function?
Answer: Option D
Step-by-step explanation:
Step-by-step explanation:
As we know domain of a function is represented by x values on the graph and y values represents the range of the function.
From the given table domain will be the set of all real numbers.
Range of the same function will be y > 4
Option D is the answer. there you go o(*￣︶￣*)o it was hard to but now its easy
find the equation of the line parallel to y=3x+4 and that passes through the point (-5,4)
Answer:
y = 3x + 19
Step-by-step explanation:
Equation of line in slope y-intercept form: y = mx +bHere m is the slope and b is the y-intercept.
y = 3x + 4
m = 3
Parallel lines have same slope.
m = 3
y = 3x + b
Substitute (-5,4) in the above equation.
4 = 3*(-5) + b
4 = -15 + b
4 + 15 = b
b = 19
Equation of the line: y = 3x + 19
Answer: y = 3x +19
Step-by-step explanation:
-Parallel lines have the same gradient
y = 3x + c
rearrange to give c= y - 3x
substitute x = -5 and y = 4
c = 3 - (3x-5)
c= 19
so the equation is y = 3x + 19
Calculate the measure of ∠1 using the Exterior Angle Theorem.
Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB. We have angles ∠B=35°,∠U=62°,∠P=21°. The angles are ∠1=56° and ∠2=62°.
Given that,
In picture there is a triangle with the intersection line in between the triangles.
Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB.
We have angles
∠B=35°,∠U=62°,∠P=21°
We have to find the angle of angle 1 and 2.
We know,
In triangle sum of the 3 angles is 180°.
Now, we take ΔPMB
We find the other angle of M.
21°+35°+M=180°
M=180°-21°-35°
M=180°-56°
M=124°
So, now we can find the angle 1.
the straight line has a angles of 180°.
124°+∠1=180°
∠1=180°-124°
∠1=56°
Now, we find angle 2.
Take ΔPUM
62°+∠1+∠2=180°
62°+56°+∠2=180°
∠2=180°-62°-56°
∠2=180°-118°
∠2=62°
Therefore, the angles are ∠1=56° and ∠2=62°.
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WILL GIVE BRAINLIEST
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
The maximum that the company can expect for returned items is C. $5972.65
How to calculate the value?From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The maximum the company can expect for returned items will be:
= (15% + 4%) × Profit
= 19% × $31,435
= 0.19 × $31,435
= $5972.65
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Write and solve an equation to solve the problem.
Lisa is 4 centimeters taller than her friend lan. lan is 8 centimeters taller than Jim. Every month, their heights increase by 2 centimeters. In 4 months, the sum of lan's and Jim's heights will be 170 centimeters more than Lisa's height. How tall is lan now? Let h be lan's height today in centimeters.
(h+8)( )+8=( )+8+170
Ian is ___ centimeters tall now.
Ian is 144 centimeters tall now by solving the equation.
What is an equation?A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.
Let Lisa, Ian, and Jim's real heights are L, I, and J, respectively.
Lisa's friend Ian is 4 centimeters taller than her, therefore L=4+I
In the sentence "Ian is 8 cm taller than Jim.": I=8+J,
Hence, J=I-8
Thus, Lisa, Ian, and Jim are 4+I, I, and I-8 correspondingly in height.
Since their heights increase by 2 cm every 4 months, this results in an 8-centimeter height increase.
Thus, after four months, Lisa, Ian, and Jim reach the following heights:
4+I+I+8, I+8, and I-8+8 that equal to I+12, I+8, and I respectively
"The total of Ian's and Jim's heights will be 140 centimeters more than Lisa's height in four months" means:
(I + 8) + I = 140 + (I + 12)
⇒2I + 8 = 152+I
⇒I = 144
⇒I=152-8
=144
Therefore, Ian is 144 centimeters tall now.
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1. the sum of three and seven divided
by two
2.the sum of four and nine times three
3.ten divided by the product of four
and five
4.the sum of one and two divided
by twenty
Answer:
1. (3 + 7) ÷ 2 = 5
2. (4 + 9) x 3 = 39
3. 10 ÷ (4 x 5) = 1/2
4.(1 + 2) ÷ 20 = 3/20
-¾ ÷ (-0.06)
Can someone help me with this question please
Answer:
12.5
Step-by-step explanation:
-3\4÷[-0.06]
convert -0.06to fraction
-3\50
then divide
-3\4÷-3\50
sign changes
-3\4 ÷ 50\3
=50\4
=12.5