[tex]|x-4|[/tex] is non-negative, and vanishes when [tex]x=4[/tex].
For all [tex]x\in[-2,1][/tex], we have [tex]x<4[/tex], so by definition of absolute value,
[tex]g(x) = |x-4| + 8 = -(x-4)+8 = -x+4[/tex]
which is strictly decreasing on [-2, 1] since [tex]g'(x)=-1<0[/tex]. Then the minimum value of [tex]g[/tex] on [-2, 1] occurs at the endpoint [tex]x=1[/tex], so that
[tex]\min\left\{g(x) \mid -2\le x\le1\right\} = g(1) = |1-4| + 8 = \boxed{11}[/tex]
RS has endpoints R(3, 5) and S(–3, –1). Which statement explains whether the midpoint M of lies on the y-axis?
M = = (4, –2) does not lie on the x- or y-axis because neither coordinate is zero.
M = = (3, 3) does not lie on the x- or y-axis because neither coordinate is zero.
M = = (2, 0) lies on the y-axis because the y-coordinate is zero.
M = = (0, 2) lies on the y-axis because the x-coordinate is zero.
Mark this and return
Step-by-step explanation:
M = (0, 2), and it lies on the y-axis, because the x-coordinate is 0.
by the way, the first 2 answer options are correct statements too, they are just not specifying the actual midpoint.
Answer:d
Step-by-step explanation:edge2023
Select the sequence that shows the numbers in order from least to greatest.
A. √72, 321-41
5
c. 32. √72.1-41
C.
5
B. |–-41, 32 √72
32
D. √72,|-41, ³²
5
The sequence that shows the numbers in order from least to greatest is
√72 , 5,32, |-41|
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc.
√72 = 8.485
32
|-41| = 41
5
least to greatest is √72 , 5,32, |-41|
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Select all the expressions which are equivalent to –3(0.15 – 0.2 + 0.25p).
A. –0.45 – 0.6 + 0.25p
B. 0.15 – 0.75p
C. 3(0.15 + 0.2 + 0.25p)
D. –3(–0.05 + 0.25p)
E. –3(0.05 + 0.25p)
I need help ASAP.
Answer:
–3(0.15 – 0.2 + 0.25p) is equivalent to –3(-0.05 + 0.25p) and 0.15 – 0.75p
Draw the graph of your= 2x +1
The graph of the equation y = 2x+1 has been plotted
The equation of the line is
y = 2x+1
The domain is defined as the set of all possible inputs of the function.
The range is defined as the set of all possible outputs of the function
Here the equation is y =2x+1, we have to substitute the different values for the x and find the values of y.
The values of the x will be the domain and the values of the y will be the range
At x= -2
y = 2(-2)+1
= -3
At x= -1
y = 2(-1)+1
= -1
At x= 0
y = 2(0)+1
= 1
At x=1
y = 2(1)+1
= 3
At x=2
y = 2(2)+1
= 5
Plot the graph using the values
Hence, the graph of the equation y = 2x+1 has been plotted
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I need this answer as soon as possible
Note: This is grade 6 maths
10.
A gallon = 4 quarts
4 quarts = 4 x 2 = 8 pints.
8 pints = 8 x 16 = 128 (ounces)
So, a gallon equals 128 ounces.
11.
Generally, 2 cups = 1 pint.
-> 4 cups = 2 pint = 1 quart
So, he should (probably) use the entire quart.
12.
Convert all the mixed numbers to fractions, mk.
14(7/9) + 6(5/9)
= 14+6(7/9+5/9) = 20(12/9) = 64/3.
13. 15(11/16) + 21(9/16) = 36(11/16+9/16) = 36(20/16) = 149/4
14. 7(1/2) + 5(1/2) = 12(1/2+1/2) = 13( = 13/1)
15. 17(3/4) - 4(1/4) = 17-4(3/4-1/4) = 13(1/2) = 27/2
16. 23(5/8) - 12(3/8) = 23-12(5/8-3/8) = 11(2/8) = 45/4
17. 27 - 6/8 = 216/8 - 6/8 = 210/8 = 55/2.
Please recheck and if you spot anything wrong tell me.
Given h(x) = − 4x − 4, solve for x when h(x) = −8.
is the number 19 a prime or composite number
Answer:
prime
Step-by-step explanation:
because 19 can only divide 1 and itself
A line with a slope of 3/4 and containing the point (0,2)
An equation of line with a slope of 3/4 and containing the point (0,2) is y = (3/4)x + 2
In this question, we have been given
slope (m) = 3/4
and a point (0, 2)
We need to find an equation of a line with a slope of 3/4 and containing the point (0,2)
Using the formula for the slope-point form of equation of line,
y - y1 = m(x - x1)
y - 2 = 3/4(x - 0)
y - 2 = (3/4)x
y = (3/4)x + 2
Therefore, an equation of line with a slope of 3/4 and containing the point (0,2) is y = (3/4)x + 2
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In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who has a sister also has a brother?
If In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. The probability that a student who has a sister also has a brother is: 3/10.
Determining the probabilityGiven data:
Total number of student = 30
Brother = 13
Sister = 8
Brother and sister = 3
Now let determine the probability that a student has brother and sister using this formula
P ( S n B ) = Brother and sister / Total number of student
Let plug in the formula
P ( S n B ) = 3/30
Therefore we can conclude that 3/30 is the probability.
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Answer:
3/8
Step-by-step explanation:
1. The reduced fraction or mixed number for 375%
Answer:
the answer is shown below for the reduced fractional mixed number for 385 percentage
Step-by-step explanation:
Steps to Convert 375% to Fraction
Place the Percentage Value at the top over 100. The exact form of the fraction is 154. In the decimal form, the fraction can be written as 3.75. In the Mixed Number form, the fraction can be written as 3 .34.
Expand the brackets and simplify the
expression below.
8(3y + 2) + 4y
Answer:
28y+16
Step-by-step explanation:
8(3y+2)+4y
24y+16+4y
28y+16
The simplification of the given expression is 28y+16.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.
We are given an expression as;
8(3y+2)+4y
we need to solve the expression
First open the bracket;
24y+16+4y
Solve the like terms;
28y+16
Therefore, the simplification of the given expression is 28y+16.
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What type of symmetry does this figure have?
this figure has no symmetry
both rotational symmetry and reflectional symmetry
reflectional symmetry
rotational symmetry
This figure has no symmetry is the correct option.
Given:
Given figure is parallelogram ,
The number of lines of symmetry of a parallelogram depends on the type of parallelogram.A non special parallelogram does not have any lines of symmetry. This includes any quadrilateral with two pairs of parallel and equal sides, except for rectangles, squares and rhombuses.
A rectangle is a parallelogram with four right angles. This property allows it to have two lines of symmetry.
A rhombus is a parallelogram with four equal sides. The number of lines of symmetry of a rhombus depends on whether it is a square or not. If it has four right angles, the rhombus is a square and thus has four lines of symmetry. If not, the rhombus only has two lines of symmetry.
Therefore this figure has no symmetry is the correct option.
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A triangle is dilated with a center of dilation at the origin. Point P' is the corresponding point of the image of the dilation. Point P is at (-2,3) and P' is at
(-8,12). What is the scale factor?
The scalar factors are (4,4)
What is dilation?Dilation is a type of transformation in which a shape or geometric figure's size is altered while maintaining its relative proportions and general shape.
Dilation is applied by the rule:
(x, y) → (kx, ky), where k is the scale factor
We have
(x, y) = (-2, 3) and (kx, ky) = (-8, 12)
Substitute and solve for k
-8 = -2k and 12 = 3k ⇒ k = 4
So the rule is
(x, y) → (4x, 4y)
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Finnegan wants to buy a sweater for $29.50 and jeans for $42.50. If the sales tax rate is 8.25%, what will be the amount of sales tax on Finnegan’s purchase?
The amount of sales tax on Finnegan's purchase is $5.94
How to calculate the amount of sales tax on the purchase ?The first step is to calculate the total amount of purchase
Sweater- $29.50
Jeans- $42.50
Total amount
29.50 + 42.50
= 72
The sales tax rate is 8.25%
The amount of sales tax on the purchase can be calculated as follows
8.25/100 × 72
= 0.0825 × 72
= 5.94
Hence the sales tax on the total purchase is $5.94
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help pls i don’t understand and don’t know which option topick
Answer: C
Explanation:
The range of a function is the set of all values of y that satisfy the function. On the graph, it is between the lowest value of y at the bottom and the highest value of y at the top. Looking at the graph, it extends to negative infinity at the bottom and the maximum value at the top y = 4
Thus, in interval notation,
Range = (- ∞, 4]
A ball is thrown upward from the top of a building that is 160 feet tall. The height, H, of the ball T seconds after being thrown is given by the equation H = -16t^2 + 48t + 160.
After how many seconds will the ball hit the ground?
a. 2
b. 3
c. 5
d. 10
Answer:
10
Step-by-step explanation:
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Tyler simplified the expression x Superscript negative 3 Baseline y Superscript negative 9. His procedure is shown below.
x Superscript negative 3 Baseline y Superscript negative 9 = StartFraction 1 Over x cubed EndFraction times StartFraction 1 Over y Superscript negative 9 EndFraction = StartFraction 1 Over x cubed y Superscript negative 9 EndFraction
What is Tyler’s error?
Both powers should be in the numerator with positive exponents.
Both powers should be in the denominator with positive exponents.
The power x cubed should be in the numerator and the power y Superscript 9 in the denominator.
The power y Superscript 9 should be in the numerator and the power x cubed in the denominator.
The Tyler’s error is Both powers should be in the denominator with positive exponents.
what is exponents?The exponent of a number shows how many times the number is multiplied by itself.
For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general, [tex]x^n[/tex]means that x is multiplied by itself for n times.
given:
[tex]x^{-3} y^{-9}[/tex] = 1/x³ × [tex]1/ y^{-9}[/tex]
As, we know using the law of exponents
[tex]a^{-m} = 1/a^m[/tex]
So, [tex]x^ {-3} = 1/[/tex]x³
and, [tex]y^{-9}[/tex] = [tex]1 / y^9[/tex]
Then, we can write
[tex]x^{-3} y^{-9}[/tex] = 1/x³ × [tex]1/ y^{9}[/tex]
Hence, Both powers should be in the denominator with positive exponents.
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-35 represents the starting location of a race car that is 35 yards behind the starting line. 35 represents the ending location of a race car that is 35 yards in front of the starting line
As shown in the number line, The total distance of the racing road is 70 yards.
it is given that the starting location is -35 yards behind the starting line and the ending location of the race court is 35 yards in front of the starting line.
we have to draw a Number line that has -35 and +35 so the origin of that number line is the starting point of the race court.
In the above figure if we are moving forward towards the origin we find that we are moving 35 yards in the number line, after reaching the origin of the number line move forward again 35 yards then we are at the ending location of the racing court.
So,
35 yards + 35 yards = 70 yards
The total racing area of the cars is = 70 yards.
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Holly wants to buy a new house in Cardiff.
She knows that Land Transaction Tax will be added to the price of the house.
Land Transaction Tax rates are shown below:
• pay nothing on the first £180000 of the price of the house,
• pay 3·5% on the part of the price of the house that is above £180000 and up to and including £250000,
• pay 5% on the part of the price of the house that is above £250000 and up to and including £400000.
The most Holly can afford to spend, including Land Transaction Tax, is £327000.
Let x be the highest price of house that Holly can afford.
Write an equation in x and solve it to calculate the highest price of house that Holly can afford.
Answer:
321000
Step-by-step explanation:
The highest price of house that Holly can afford is £343350.
What is tax?In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.
Given that, Holly can afford to spend, including Land Transaction Tax, is £327000.
Here, the tax rate is 5% because that is above £250000 and below £400000.
Let x be the highest price of house that Holly can afford.
x= 327000+5% of 327000
x= 327000+5/100 ×327000
x= 327000+0.05×327000
x= £343350
Therefore, the highest price of house that Holly can afford is £343350.
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Manuela also invests $640.
At the end of 4 years, Manuela has $721.
Find the yearly compound interest rate.
The yearly compound interest rate of $640 at the end of 4 years would be; 3.07
How to calculate compound interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit of time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]
The final amount becomes as;
[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]
Given that Manuela invests $640. At the end of 4 years, Manuela has $721. then the yearly compound interest rate will be;
[tex]A = P\left(1 +\dfrac{R}{100}\right)^T\\\\\\721 = 640\left(1 +\dfrac{R}{100}\right)^4\\\\721 / 640 =\left(1 +\dfrac{R}{100}\right)^4\\\\\\1.12 = \left(1 +\dfrac{R}{100}\right)^4\\\\\\\sqrt[4]{1.12} = \left(1 +\dfrac{R}{100}\right)\\\\\\R = 3.07[/tex]
Hence, the yearly compound interest rate of $640 at the end of 4 years would be; 3.07
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Matthew wants his run today to take no more than 90 minutes. He already has run 30 minutes at a pace of 10 minutes per mile.
Part A)
Write an inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace. Show or explain the reasoning you used to determine your answer.
The inequality for the given situation is m ≤ 6.
Given that, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.
What is the inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Let the number of miles be m.
m ≤ 90/10 - 30/10
m ≤ 9 - 3
m ≤ 6
Therefore, the inequality for the given situation is m ≤ 6.
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A truck travels some distance at a speed of 35 km h in 120 min and the remaining distance at a speed of 48 km h in 90 min. Determine the: (a) total distance covered. (b) average speed over the entire journey
Answer:
a) 142 km,b) 40.57 km/hStep-by-step explanation:
Use of formula:
speed = distance / timedistance = speed × timea) Find each part of distance and add together. Convert minutes to hours.
35 × (120/60) = 35 × 2 = 70 km,48 × (90/60) = 48 × 1.5 = 72 kmdistance = 70 + 72 = 142 kmb) Average speed is:
speed = 142 /(2 + 1.5) = 142/3.5 = 40.57 km/h (rounded)Answer:
(a) 142 km
(b) 40.57 km/h (2 d.p.)
Step-by-step explanation:
Part (a)[tex]\boxed{\sf Distance=Speed \times Time}[/tex]
Given:
Speed = 35 km/hTime = 120 min = 2 hSubstitute the given values into the distance formula to find the distance travelled:
[tex]\implies \sf Distance = 35 \times 2 = 70\;km[/tex]
Given:
Speed = 48 km/hTime = 90 min = 1.5 hSubstitute the given values into the distance formula to find the distance travelled:
[tex]\implies \sf Distance = 48 \times 1.5 = 72\;km[/tex]
Therefore, the total distance travelled is:
[tex]\implies \sf 70 + 72 = 142 \; km[/tex]
Part (b)[tex]\boxed{\sf Average\;speed=\dfrac{Total\;distance}{Total\;time}}[/tex]
Given:
Total distance = 142 kmTotal time = 2 + 1.5 = 3.5 hSubstitute the given values into the average speed formula to find the average speed over the entire journey:
[tex]\implies \sf Average\:speed=\dfrac{142}{3.5}=40.57\;km/h\;(2\;d.p.)[/tex]
Gigi is going to buy 100 stickers.
Here is some information about the cost of stickers in two shops.
Stickers4u
World Stationery
Pack of 25 stickers for £2.25
Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack 1 free
Gigi wants to buy the stickers for the best possible price.
Which shop should Gigi buy the 100 stickers from?
You must show how you get your answer.
Answer:
Buying from World Stationery shop would profit Gigi.
How to find the most profitable shop?Given,
Gigi is going to buy 100 stickers.
Stickers4u - Pack of 25 stickers for £2.25
World Stationery - Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack 1 free
Solution:
Cost of 1 sticker in Stickers4u = £2.25/25 stickers = £0.09
Cost of 1 sticker in World Stationery = £1.75/ 10 stickers = £0.175
Since it is mentioned, 'Buy 1 pack get 1 pack 1 free' in this shop, the total no of stickers one would get for the price would be doubled.
Hence,
Cost of 1 sticker in World Stationery would be = £1.75/ 20 stickers = £0.0875
On comparing the price per sticker of both the shops, we can say that
buying from World Stationery shop would profit Gigi.
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g(x)=5x+50 answer please
The answer to the linear equation g(x) = 5x+50 is plotted on the graph.
What is a linear equation?A linear equation is one in which the variable's maximum power is always one.A one-degree equation is another term for it.A linear equation in one variable takes the conventional form Ax + B = 0. x is a variable, A is a coefficient, and B is constant in this equation.Given equation:
g(x)=5x+50
The equation can also be written as y = 5x+50.
Now, we can replace the value of x for different numbers in the given equation to get the value of y to create the coordinates.
When we put x = 0 in the equation, we get y = 0 + 50 = 50.
Similarly, if we substitute the value of x as 1 in the equation, we get y = 5(1) + 50 = 55.
If we substitute the value of x as 2, y = 5(2) + 50 = 60
If we substitute the value of x as -1 and -2, we get the value of y as,
y = 5(-1) + 50 = 45 and y = 5(-2) + 50 = 40.
These pairs of values satisfy the linear equation and are plotted on the graph given below.
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find X. would love the help thank you
Answer:
120
Step-by-step explanation:
x + the angle = 180 because it makes a line
we know from the picture that the triangle is equilateral so the angle has to be 60
so 180 = x + 60 and solve for x
3(3v - 4) = 51 solve for v simplify your answer as much as possible
Answer: v = 7
Step-by-step explanation:
1. Distribute
3 (3v - 4) = 51
9v - 12 = 51
2. Add 12 to both sides
9v - 12 = 51
+ 12 + 12
3. Cancel out 12 + 12
51 + 12 = 63
9v = 63
4. Divide 9 on both sides
9v/9 = 63/9
5. Cancel out 9v/9
v = 7
Solve the quadratic equation.
x² + 9x - 36 = 0
O A. x = 3 or 12
OB. x = 3 or -12
O C. x = 6 or -6
OD. no real solution
Answer:
B x = 3 or -12
Step-by-step explanation:
(btw this / is a fraction sign and this ^ is the power of sign)
Let's solve your equation step-by-step.
x^2+9x−36=0
For this equation: a=1, b=9, c=-36
1x^2+9x+−36=0
Step 1: Use quadratic formula with a=1, b=9, c=-36.
x= −b±√b^2−4ac/2a
x= −(9)±√(9)2−4(1)(−36)/2(1)
x= −9±√225/2
= x= 3 or x= -12
Evaluate the expression.
4−32⋅(−0.25)−12÷1/3
Answer:
Step-by-step explanation:
4
(50 points) Show that x+2 is a factor of p(x)=[tex]x^4+2x^3+4x^2+x-14[/tex]. Then write p(x) as the product of x+2 and another factor. Please show work.
Answer:
Let p(x)=x
3
−4x
2
−2x+20
By factor theorem, (x+2) is a factor of p(x) if p(−2)=0.
∴ It is sufficient to show that (x+2) is a factor of p(x)
Now, p(x)=x
3
−4x
2
−2x+20
∴p(−2)=(−2)
3
−4(−2)
2
−2(−2)+20=−8−16+4+20=0
∴(x+2) is a factor of p(x)=x
3
−4x
2
−2x+20
$m\angle U=2x\degree$ , and $m\angle V=2\left(m\angle U\right)$ . Find the value of $x$ that makes $\angle U$ and $\angle V$ complementary angles
The value of x that makes ∠U and ∠V a complement of each other is; x = 9
How to find Complementary Angles?
There are different equal angle theorems in math's such as complementary angles, supplementary angles, linear pairs e.t.c
Now, complementary angles are defined as angles that sum up to 90 degrees.
We are given that;
m∠U = 2x°
m∠V = 4m∠U = 4(2x)°
We want to find the value of x that makes ∠U and ∠V a complement of each other.
This means that by the definition of complementary angles, they will sum up to 90 degrees. Thus;
2x + 4(2x) = 90
2x + 8x = 90
10x = 90
x = 90/10
x = 9
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Complete question is;
m∠U = 2x°, and m∠V = 4m∠U. Which value of x makes ∠U and ∠V complement of each other? A. 25 B. 9 C. 36 D. 18