All the real numbers x which satisfy the given inequality x²<4 , in interval form is (-2, 2).
As given in the question,
Given inequality is given by :
x²< 4
Simplify the given inequality x² < 4 to get all the real numbers x we have,
x² < 4
⇒ x² - 4 < 0
⇒ x² - 2² < 0
Apply a² - b² = ( a - b ) ( a + b ) we get,
⇒ ( x - 2 ) ( x + 2 ) < 0
⇒ x ∈ ( -2 , 2 ) as less than symbol represent open interval.
Therefore, all the real numbers x which satisfy the given inequality x²<4 , in interval form is (-2, 2).
The complete question is :
Find all real numbers x such that x^2 < 4. Give your answer in interval notation.
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what is greater 23/20 or 110%
Answer:
23/20
Step-by-step explanation:
110% of 20 is 22/20, so 23/20 is more.
Step-by-step explanation:
23/20 = 1,15
110% = 1,1
1,15 > 1,1
⇒ 23/20 > 110%
Mariana tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.54.54, point, 5 milliliters per second. After 171717 seconds, 148.5148.5148, point, 5 milliliters of slushy remained.
How much slushy was originally in the cup?
milliliters
How long did it take Mariana to drink all the slushy?
seconds
The amount of slushy that was originally in the cup is 225 milliliters and the time it took Mariana to drink all the slushy is 50 seconds.
How to find the original quantity?Total quantity she took
Total quantity = 4.5 × 17
Total quantity = 76.5 milliliters
Original quantity = 148.5 + 76.5
Original quantity = 225 milliliters
b. Time taken to drink all
Time =225 milliliters /2.5
Time = 50 seconds
Therefore original quantity 225 milliliters and the time is 50 seconds.
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I need to know how to solve it please
For the given pair of intersecting lines, we find out that the value of x is 1 and the measure of the angle 1 is 169°.
From the figure we see that there are two lines intersecting each other.
We know,
Sum of all the angles formed = 360
We also know that
If there are a pair of two intersecting lines, then the vertically opposite angles are equal.
=> 20x+11 = 25x-14
=> 5x = 5
=> x = 1
Substituting the value of x in 20x+11 , we have
20*1 + 11 = 21°
Substituting the value of x in 25x-14 , we have
25*1 - 14 = 11°
It is also known to us that the sum of the adjacent angles of a pair of intersecting lines is equal to 180°. This implies that
11° + 1 = 180°
=> 1 = 180° - 11°
=> 1 = 169°
Thus, for the given pair of intersecting lines, we find out that the value of x is 1 and the measure of the angle 1 is 169°.
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2 3/5 x 1 3/7 i need help
Answer:
26x/7
Step-by-step explanation:
If 2 i added to a number and the um i tripled, the reult i 16 more than the number. Find the number
The number for this equation is 5.
What is equation?
In arithmetic, Associate in Nursing equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
let the number be x.
So , according to question =
3(x+2) = x+16
Now solving this equation , we will get the answer
⇒ 3x +6 = x+16
now moving x to left side and taking the constant to right,
⇒ 3x-x = 16 -6
⇒ 2x = 10
⇒ x=5
Hence the number is 5.
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Quadrlateral proofs (Reasons Only)
prove abcd is a rhombus
help pls i hate proofs....
Which fraction is the smallest?
3/5 1/2 2/3 4/7 3/8
Find a formula for the nth term of the arithmetic sequence-2 -8 -14 -20…. (I did that already) but explain in detail using words on how you got the answer -6
The general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]
The given arithmetic sequence is -2, -8, -14, -20
The first term = a = -2,
The common difference = d = -8 -(-2) = -8 +2 = -6
The general term of the arithmetic sequence is given by
[tex]T_{n} = a + (n-1)d[/tex]
Now, putting the values of the first term and common difference in the general term.
[tex]T_{n} = -2 +(n-1) (-6)\\\\T_{n} = -2 -6n +6\\ \\T_{n} = -6n +4[/tex]
Hence, the general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]
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Chloe has 4 sundaes for her friends. She has 8
4
9
ounces of sprinkles to put equally on the sundaes. How many ounces of sprinkles will be on each sundae?
There are 19/9 ounces in each sprinkle of sundae
How to determine the number of ounces of sprinkles on each sundaeFrom the question, we have the following parameters that can be used in our solution:
Number of sundaes = 4
Ounces of sprinkles = [tex]8\frac49[/tex] ounces
From the above parameter, we can calculate the amount of sprinkles using the constant of proportionality formula
This is represented as
Ounces per sprinkle = Ounces of sprinkles/Number of sprinkles
Substitute the known values in the above equation
So, we have the following equation
Ounces per sprinkle = [tex]8\frac49[/tex]/4
Evaluate the quotient
Ounces per sprinkle = 19/9
Hence, the ounces per sprinkle is 19/9 ounces
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help me solve this problem
The value of GK = 18.6, GM = 14.5 AND JZ = 19.9.
From the figure:
MZ is a perpendicular bisector of ∆GHJ.
GM = MJ
GM = 14.5
KZ is a perpendicular bisector of ∆GHJ.
GK = KH
GK = 18.6
Z is the circumcenter of ∆GHJ.
JZ = GZ
JZ = 19.9
Therefore the value of GK = 18.6, GM = 14.5 AND JZ = 19.9.
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Lucy i making the ame bracelet for eight of her Friend he ha 32 bead how many bead can you put on each bracelet?
Using the fraction concept, we can say that The number of beads each friend will get is 4.
What are fractions?
Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.
A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.
In the given question, we have:
Number of bead = 32 bead;
Total number of friends = 8;
So,
we need to find how many beads will one friend get:
So,
The number of beads each friend will get : [tex]\frac{32}{8}[/tex]
The number of beads each friend will get is 4.
Hence,
using the fraction concept, we can say that The number of beads each friend will get is 4.
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what is the equation in standard form of the line that passes through the point (1,24) and has a slope of (-3/5)
y = -3/5x - 123/5 is slope-intercept form .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately visible. This form is frequently known as the y = mx + b form.Point = ( 1,24 )
slope = -3/5
the equation in standard form of the line that passes through the point
y - y₁ = m ( x - x₁)
y - 24 = -3/5 ( x - 1)
5 (y - 24) = -3( x - 1 )
5y - 120 = -3x + 3
5y = -3x + 3 + 120
5y = -3x + 123
y = -3/5x - 123/5
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Which equation represents a line with slope of -1/3 and y intercept of 5/3?
A. X-3y=5
B.3x-y=5
C.x+3y=5
D.3x+y=-5
The equation of line with slope is -1/3 and y intercept 5/3 is : x + 3y = 5.
What is equation of line?A straight line's general equation is y = mx + c, while m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents a equation of a straight line having gradient m and intercept c mostly on y-axis.In the form of a slope intercept, the line's equation looks like this:
y = mx + b
where
slope = m
y-intercept = b
Here given slope = -1/3
y-intercept at 5/3
As a result, the line's equation has a slope of -1 / 3.
Let's use the locations to determine the y-intercept 5/3.
y = mx + b
Here b = 5/3
By substituting ,
y = -1/3x + 5/3
Multiplying both sides by 3,
3y = -x + 5
3y + x = 5
= x + 3y = 5.
Therefore the equation of line is x + 3y = 5.
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Explain how you can use a part:part ratio to determine the part:whole ratio.
Let's say we have blue and red balls
Blue : Red
3 : 5
Now we can add another ratio for the whole.
Blue : Red : Total
Total is Blue + Red = 3 + 5 = 8
So
Blue : Red : Total
3 : 5 : 8
Then the part : whole ratio for Blue is...
Blue : Total
3 : 8
✓ Completed
Part 1 of 3
In Progress
Given the following functions, find the indicated values.
f(x)=8-4x
(a) f(-7) (b) f(0) (c) f(4)
(a) f(-7)=
Answer:
(a) 36, (b) 8, (c) - 8======================
Given functionf(x) = 8 - 4xFind the indicated values(a) f(-7)
f(-7) = 8 - 4(-7) = 8 + 28 = 36(b) f(0)
f(0) = 8 - 4(0) = 8 - 0 = 8(c) f(4)
f(4) = 8 - 4(4) = 8 - 16 = - 8Answer:
a) f(-7) = 36 b) f(0) = 8 c) f(4) = -8Step-by-step explanation:
a) f(-7) = ?
→ f(x) = 8 - 4x
→ f(-7) = 8 - 4(-7)
→ f(-7) = 8 + 28
→ f(-7) = 36
Hence, f(-7) = 36.
b) f(0) = ?
→ f(x) = 8 - 4x
→ f(0) = 8 - 4(0)
→ f(0) = 8 - 0
→ f(0) = 8
Hence, f(0) = 8.
c) f(4) = ?
→ f(x) = 8 - 4x
→ f(4) = 8 - 4(4)
→ f(4) = 8 - 16
→ f(4) = -8
Hence, f(4) = -8.
make x the subject of 4(x-3)/a
The rearranged form of equation 4(x-3)/a=y will be x=ay+3.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the expression is, 4(x-3)/a=y
First, we open the bracket to make x the variable in the equation.
4x - 12/a = y
4x - 12 = ay
4x = ay + 12
x = ay + 12/4
x = ay + 3
Thus, the rearranged form of equation 4(x-3)/a=y will be x=ay+3.
The question is incomplete,
The complete question is"Rearrange to make x the subject of 4(x-3)/a=y:
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50 POINTS TO WHOEVER SOLVES THIS QUESTION!!!! PLEASE HELP
The total segment AE is 46.
What is SAS(Side -Angle-Side) triangle?
"SAS" is when we know two sides and the angle between them.
To solve an SAS triangle we use "The Law of Cosines" to calculate the unknown side.
The Law of Cosines = a² = b² + c² − 2bc cosA
where
'b' and 'c' are two given sides
'A' is the angle between side 'b' and 'c' and
a' is the unknown side which we have to find.
In ΔABC , b=21, c=20, a= AC
By the Cosine law
a² = 21²+20² - 2*21*20 cos90°
a² =441 + 400 - 0 (∵cos 90° =0)
a² = 841
a=√841
a=29= AC.
Now, in ΔCDE, b=8, c=15 and a = CE
By the Cosine law
a² = 8² + 15²- 2*8*15cos90°
a² = 64 + 225 - 0 (∵cos 90° =0)
a²= 289
a = 17 = CE.
AE = AC + CE
AE = 29+17= 46.
Therefore, the total segment AE is 46.
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How many millimeters are in 1 centimeter
Answer:
10mm = 1cm
Step-by-step explanation:
Milli means 1000th of
Centi means 100th of
1000 / 100 = 10
So,
10mm = 1cm
Can anyone explain to me how to do this if so u get 90 points or wtv
The transformations to function f(x) that results in function g(x) are described as follows:
5. Reflection over the x-axis, vertical stretch by a factor of 2.
6. Shift right of 6 units, shift up of 4 units.
7. The rule for g(x) after the transformation is given as follows:
[tex]g(x) = \sqrt[3]{-x + 7}[/tex]
What are the transformations to each function?For item 5, the functions are given as follows:
Parent function: [tex]f(x) = \sqrt{x}[/tex]Transformed function: [tex]g(x) = -2\sqrt{x}[/tex]The transformation is a multiplication by -2, which means that the function was:
Vertically stretched by a factor of 2, due to the multiplication by a number with absolute value of 2.Reflected over the x-axis, due to the multiplication by a negative number.For item 6, the functions are given as follows:
Parent function: [tex]f(x) = \sqrt[3]{x}[/tex]Transformed function: [tex]g(x) = \sqrt[3]{x - 6} + 4[/tex]Then the transformations are explained as follows:
Shift right of six units, due to the transformation x -> x - 6.Shift up of four units, due to the addition by 4.For item 7, the parent function is:
[tex]f(x) = \sqrt[3]{x}[/tex]
Then the transformations and their effects are given as follows:
Reflection over the y-axis: x -> -x.Translation 7 units right: -x -> -x + 7.Hence the function is:
[tex]g(x) = \sqrt[3]{-x + 7}[/tex]
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Flooring costs £10 per m². How much will it cost to buy enough flooring for this room?
Check the picture below.
[tex]18m^2~~ + ~~10m^2\implies 28m^2\hspace{5em}(\stackrel{m^2}{28})(\stackrel{\pounds}{10})\implies \text{\LARGE \pounds280}[/tex]
Can you write an equation to show how much the total cost, y, to travel in x miles?
Don’t forget: in slope-intercept form, y=mx+b, m is the slope and b is the y-intercept.
Answer:
y = 3x + 2
Step-by-step explanation:
The slope is the rate of change. The y intercept is the y value when x is 0.
A line intersects the points
(4, -2) and (3, 3).
m = -5
Write an equation in point-slope form
using the point (4, -2).
y - [?] =(x-[
Answer:
y-(-2)= -5(x-4)
= -5x-y+18
Step-by-step explanation:
y-(-2)= -5(x-4)
y+2= -5x +20
y= -5x+18
-5x-y+18= 0
Write the correct function in the table below
Answer:
y = 2x + 3
Step-by-step explanation:
The slope
As the y changes by 2, the x changes by 1. 2/1 is 2
The y intercpet is 3. This what y is when x is 0.
Joe went to the hobby shop and bought 2 model sports cars at $8.95 each and some paints. If he spent a total of 23.65, what was the cost of the paints? Can you give the equation pleaseee
If Joe spent a total of $23.65 , then the cost of the paints is $5.75 .
In the question ,
it is given that ,
From the hobby shop , Joe bought 2 model sportscars for $8.95 each
the cost for 2 sports car = 8.95*2 = 17.9
the total amount spent by Joe at the shop = $23.65
let the cost of the paint be "$x" .
the above situation can be represented by the equation .
total cost = cost for 2 model cars + cost of paint
substituting the values from above ,
we get ,
23.65 = 17.9 + x
x = 23.65 - 17.9
x = 5.75
Therefore , If Joe spent a total of $23.65 , then the cost of the paints is $5.75 .
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What is the square root of 144?
Answer:
12
Step-by-step explanation:
12*12=144
Answer: 12 is the correct answer
Step-by-step explanation:
144 = a × a = 122
Then a = √144 = √(12 × 12)
12 × 12 = 144 or -12 × -12 = 144
The square root of 144 is +12 or -12
This shows that 144 is a perfect square.
(REPOST) 13. Find the measure of
(5x +27)°
(2x + 10)°
(4x + 2)°
The measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
Given data ,
The angles of the triangle ABC are
∠A = ( 2x + 10 )°
∠B = ( 4x + 2 )°
Let angle ∠C be y
The sum of ∠A + ∠B + ∠C = 180°
So ,
( 2x + 10 )° + ( 4x + 2 )° + y = 180° be equation (1)
Now , we can see that AD is a straight line and C is a point on the line AD
The total angle of C on the line AD is 180°
So , ( 5x + 27 )° + y = 180°
y = 180° - ( 5x + 27 )° be equation (2)
Substituting the value of equation (2) in equation (1) , we get
( 2x + 10 )° + ( 4x + 2 )° + 180° - ( 5x + 27 )° = 180°
On Simplifying , we get
( 2x + 10 )° + ( 4x + 2 )° - ( 5x + 27 )° = 0
( 2x + 4x - 5x ) + ( 10 + 2 - 27 ) = 0
x - 15 = 0
Adding 15 on both sides , we get
x = 15°
Substituting the value of x in the ∠A , ∠B and ∠C equation , we get
∠A = ( 2x + 10 )°
= 40°
∠B = ( 4x + 2 )°
= 62°
∠C = 180° - ( ∠A + ∠B )
= 180° - 102°
= 78°
Therefore , the angles of the triangle ABC are 40° , 62° and 78°
The measure of ( 5x + 27 )° is
= ( 5 x 15 + 27 )°
= 102°
Hence , the measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively
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consider a wire 2 ft long cut into two pieces. one piece forms a circle with radius r and the other forms a square with side length x. (a) determine a formula for the radius r in terms of x .
The formula for the radius r in terms of x . and for the maximum areas is x=2/[tex]\pi[/tex]+4
Given that,
y forms a circle of radius r
y=2[tex]\pi[/tex]r
r=y/2[tex]\pi[/tex]
(2-y)- forms Square Side x
(2-y) = 4x
x=(2-y)/4
Now Sum of Area's=Area of Square +Area of Circle
Sum = [tex]\pi[/tex]r² + x²
Substitute the r and x values in above equation,
A(y)= y²/4[tex]\pi[/tex]+(y-2)²/ 16
To maximize Area A(y)
A'(y)= 0
2y/4[tex]\pi[/tex] + 2(y-2)/16 =0
y/2[tex]\pi[/tex] + (y-2)/8 =0
y = 2[tex]\pi[/tex]/[tex]\pi[/tex]+4
Y max will be max, x to be maximum.
for maximum sum of areas,
x=2/[tex]\pi[/tex]+4
Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/[tex]\pi[/tex]+4
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A rain gutter is made from sheets of
aluminum that are 14 inches wide by
turning up the edges to form right
angles. Determine the depth of the
gutter that will maximize its cross-
sectional area and allow the greatest
amount of water to flow. What is the
maximum cross-sectional area?
Explanation:
Let x = depth of the gutter
then
14-2x = width of the gutter
:
Cross section area:
A = depth * width
A = x(14-2x)
A = 14x - 2x^2
:
Axis of symmetry will give x value for max area: x = -b/(2a)
x = -14/2 * -2
x = -14/-4
x = +3.5 inches is the depth for max area
:
:
Max area: 3.5 * 9 = 31.5 sq/in
someone please help me
Answer:
a= im not sure sorry
h= horizontal shift
k= vertical shift
Step-by-step explanation:
a = the vertical stretch or compression factor
h = is the x-translation, that is it moves the graph right or left
k = The 'k' is the "vertical shift".
If positive, moves graph up k units.
If negative, moves graph down k units.
Simplify.
-2.3-9.0875
Answer: -11.3875
Step-by-step explanation: