Think back to the definition of absolute value:
• If x ≥ 0, then |x| = x.
• If x < 0, then |x| = -x.
In other words, the absolute value always returns a positive number. So if x is positive, leave it alone; but if it's negative, then you have to negate it to get a positive number back.
This means that you cannot simply reduce |x - y | to x - y because you need to consider the possibility that x - y may be negative, in which case |x - y | would reduce to -(x - y) = y - x.
In this case,
|4√2 - 6| = -(4√2 - 6) = 6 - 4√2
because 4√2 < 6, which you can determine by comparing both of these numbers as square roots:
4√2 = √16 √2 = √32
6 = √36
and √32 < √36 because 32 < 36.
Similarly,
|2√10 - 6| = 2√10 - 6
because
2√10 = √4 √10 = √40
6 = √36
So ultimately,
|4√2 - 6| + |2√10 - 6| = (6 - 4√2) + (2√10 - 6) = 2√10 - 4√2
is (6,3) a solution to this system of equations y=3x - 3 3x - y =3
Answer:
It is not a solution
Step-by-step explanation:
Plug the point into the equations and check to see if they are true
y=3x - 3
3 = 3(6) -3
3 = 18-3
3 = 15
False
We do not need to check the other equation since this is false
Calculate the compound interest a saleswoman would have to pay if she borrows
$54 000 for 9 years at 12% per annum compound interest.
Given:
Principal = $54,000
Time = 9 years
Rate of compound interest = 12% per annum.
To find:
The compound interest.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is the rate of interest in decimal, n is the number of time interest compounded and t is the number of years.
The interest is compounded annually, so [tex]n=1[/tex].
Substituting [tex]P=54000,\ t=9,\ n=1,\ r=0.12[/tex] in the above formula, we get
[tex]A=54000\left(1+\dfrac{0.12}{1}\right)^{1(9)}[/tex]
[tex]A=54000\left(1.12\right)^{9}[/tex]
[tex]A=149746.252902[/tex]
[tex]A\approx 149746.25[/tex]
The amount after 9 years is $149746.25.
Now, the compound interest is:
[tex]C.I.=A-P[/tex]
Where, C.I. is compound interest, A is amount and P is principal.
[tex]C.I.=149746.25-54000[/tex]
[tex]C.I.=95746.25[/tex]
Therefore, the compound interest is $95746.25.
what fraction of 42 is 6
The fraction of 42 that is 6 is mathematically given as
42*1/7
What fraction of 42 is 6?Generally, the equation for the statement is mathematically given as
42/x=6
Therefore
x=42/5
x=7
In conclusion, The fraction of 42 that is 6 is
42*1/7
Read more about fraction
https://brainly.com/question/10708469
#SPJ2
Determine f(a+h)-f(a)/h for f(x)=x^2+5x
Answer:
2x + 5
ok.. slightly silly question...
you will eventually learn that this formula is the
formula for the "derivative" in calculus....
A[tex]x^{b}[/tex] becomes (a*b) [tex]x^{b-1}[/tex]
2x + 5
Step-by-step explanation:
What type of angel is 107 degrees
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
⏩ 107° angle will be an obtuse angle because its measurement is more than 90° but less than 180°.
⁺˚*･༓☾✧.* ☽༓･*˚⁺‧
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Answer:
An obtuse angle
Step-by-step explanation:
Angles are classified by how large their degree measure is. Here is a list of the basic classifications of an angle,
acute: degree measure between (0) and (90) degrees
right: exactly (90) degrees,
obtuse: degree measure between (90) and (180) degrees
reflex: degree measure between (180) and (360) degrees
HELPPP QUICK W THIS QUESTION
***
A
What is the value of x in the proportion
نانا اتيت |cr
X
2
CO
C
5
53
الIl F
10
3
12
20
Answer:
it's second option
[tex]5 \times \frac{2}{5} [/tex]
Step-by-step explanation:
for this change them to points so it be easier to solve
[tex] \frac{2.25}{x} = \frac{1.5}{3.6} \\ \\ x = \frac{3.6 \times 2.25}{1.5} = 5.4[/tex]
and then 5.4 equals 5(2/5)
Zach bought a car for $20,000. He
paid a $5,000 down payment and
will pay $450 per month for 5
years. What type of liability is this
for Zach?
A. liquid
B. long-term
C. short term
D. budget
Answer:
The correct answer is B. Long-term.
Step-by-step explanation:
Since Zach has bought a car for $ 20,000 paying a down payment of $ 5,000 and monthly payments of $ 450 per month for 5 years, he will be paying a total of $ 32,000 for that car (5,000 + 450 x 12 x 5). Thus, the responsibility that Zach has incurred forces him to maintain his monthly payment obligation for 5 years, thus becoming a long term liability.
Helena has five different flowers. She plans to give one flower to each of her five teachers in any order. She gives the first flower to one of her teachers in the morning.
In how many different ways can she give the four remaining flowers to the rest of the teachers in the afternoon?
1 combination
4 combinations
21 combinations
24 combinations
Answer:
24
Step-by-step explanation:
Based on the number of flowers and teachers left, the other ways Helena can distribute the other flowers is in 24 combinations.
How many combinations can Helana use?This can be found as:
= (4 flowers left x 3 flowers after 4th teacher given x 2 flowers x 1 flower for last teacher)
Solving gives:
= 4 x 3 x 2 x 1
= 24 combinations
Find out more on combinations at https://brainly.com/question/295961.
#SPJ9
Find the value of x. Around the length to the nearest tenth.
Answer:
x = 6 m
Step-by-step explanation:
x = 16sin22°
x = 6.0 m
Answer:
Step-by-step explanation:
Use the drawing tools to form the correct answer on the graph
Graph the line that represents this equation:
y +2 = 1/2 (x + 2)
Step-by-step explanation:
answer is in photo above
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is constant.
The graph of the line y +2 = 1/2 (x + 2), can be drawn as shown below. Therefore, the line will be a straight line passing through (0,-1) on the y-axis, and (2,0) on the x-axis.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ2
Find the mode of the data
Answer:
[tex]mode = l _{1} + ( \frac{d _{1} }{d _{1} + d _{2}} ) \times c \\ \\ = 6.5 + (\frac{50}{50 + 88} ) \times 3 \\ = 7.59[/tex]
is it okay to eat 8 day used by bread that been left in the refrigherater
Bread is usually fine to eat if you don't see any mold.
Once refrigerated, it will retain its freshness for three to four days before becoming stale. If you want to extend its shelf life, packaged bread will stay fresh for at least three months in the freezer. If you do see mold, however, throw the bread out.
Someone found 100! And added up all its digits. Then, this person added up the digits of this sum. The process was continued until the sum was a one-digit number. What was that number?
Will give branliest
Find l.
l= [?] in
A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = - 16t^2 + 48t where t equals the time in seconds and the h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? Help please!!!
Answer:
x = 3/2
The axis of symmetry is located at the vertex,
which is the also the highest point in this problem...
the x component of the vertex can be calculated as -b/2a = -48/-32 = 24/16 = 6/4 = 3/2
x = 3/2
Step-by-step explanation:
La Base de un triangulo mide 28 cm y su altura es correspondiente, 3/7 cm de la base. calculen el area del triangulo
Answer:
168 cm²
Step-by-step explanation:
altura = 3/7 × 28 = 12 cm
area = ½×28×12 = 168 cm²
A Galapagos tortoise can 1/5 mile in an hour. How many hours would it take the tortoise to walk 1/6?
Answer:
5/6 hours
Step-by-step explanation:
Create a proportion where x is the number of hours it will take to walk 1/6 of a mile:
[tex]\frac{1/5}{1}[/tex] = [tex]\frac{1/6}{x}[/tex]
Cross multiply and solve for x:
1/5x = 1/6
x = 5/6
So, it will take the tortoise 5/6 hours to walk 1/6 of a mile
find the slope of the line (-5,7) (-3,4)(-1,1)(1,-2)
Answer:
-3 is the gradient.
BONUS: y-interspet is -1
Step-by-step explanation:
The gradient is what you mean by slope I am guessing?
well, the line that contains those points will more or less look like the one in the picture below, and we can use any two points from that set to get its slope, say hmmmmm let's use (-5,7) and (1,-2)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}}\implies \cfrac{-9}{1+5}\implies \cfrac{-9}{6}\implies -\cfrac{3}{2}[/tex]
Plzzz help me with thiss
Answer:
Step-by-step explanation:
rather than doing all of the sums, you should just learn the formula (for the pattern)
it is n(highest + lowest) where n is number of numbers
2
for example 2+3+4+5+6 = 20
5(6+2) = 20
2
~~~~~~~~~~~~~~~~~~~~
1+2+3+4+5+6+7+8 = 36
8(9) = 72/2= 36
2
Work out m and c for the line:2y+6x=4
Answer:
2y +6x=4
Step-by-step explanation:
2y=4-6x
y =(4-6x)÷2
Krystal got $10 from his father and $x from his mother. how much did he get altogether
Answer:
16
Step-by-step explanation:
they got 16 all together in total
Answer:
$10x
Step-by-step explanation:
We know that Krystal got $10 from his father but we don't know how much Krystal got from his mother because there's just x for the amount. So, we can just write that Krystal got $10x altogether.
Hope this helps
20 PTS!! Which best describes the relationship between the line that passes through the points (1, -6) and (3,-2) and the line that
passes through the points (4, 8) and (6, 12)?
A. parallel
B. neither perpendicular nor parallel
C. same line
D. perpendicular
Answer:
A
Step-by-step explanation:
Lines are parallel...
I’ll give brainliest to whoever gets it right. Find the surface area of this prism.
Round to the nearest tenth.
6.72 cm
5.78 cm
12.7 cm
[ ? ]cm
Answer:
493.29[tex]cm^2[/tex]
Step-by-step explanation:
Multiply all values (6.72, 5.78, and 12.7) together, then round to the nearest tenth.
Solve for CD using the following image
Here,
BC = 12
CD+BD=12
2x-9+x-9 =12
3x-18 12
3x =12+18
x =30/3
x =10
Now,
CD = 2x-9
= 2×10-9
= 20-9
= 11
Therefore,CD = 11
Hope this solution may help you!!☺
The value of the segment CD is 11 units for the given line segment.
A line segment is a fundamental geometric object that represents a portion of a straight line with defined endpoints. It is a finite portion of a line that connects two distinct points. The endpoints of a line segment are specific points that mark its boundaries.
From the given image the value of x will be calculated as,
CD + DE = 12
(2x - 9 ) + ( x - 9 ) = 12
3x - 18 = 12
3x = 30
x = 10
The measure of the segment CD is,
CD = 2x - 9
CD = 2(10) - 9
CD = 20 - 19
CD = 11
Therefore, the value of the segment is 11.
To know more about line segments follow
https://brainly.com/question/17374569
#SPJ2
In a right angle triangle , the two shorter sides are 6cm and 8cm in length . What is the length of the longest side
Answer:
10 cm
Step-by-step explanation:
In a right triangle, there are three sides, A, B, and C.
A and B are the short sides, while C is the long side.
So we know that A = 6 cm, and B = 8 cm.
We can then use the Pythagorean theorem which states that
[tex]C=\sqrt{(A^2)+(B^2)[/tex]
Once we plug in the numbers we get
[tex]C=\sqrt{6^2+8^2}[/tex]
[tex]C=\sqrt{36+64}[/tex]
[tex]C=\sqrt{100}[/tex]
C=10 cm
someone please help me ASAP
Answer:
(x + (2), y - (4))
Step-by-step explanation:
An easy way to figure out how a shape has undergone a ridge transformation (meaning a transformation only in location and not size) is to compare corresponding points on the figure.
In this figure, use point (C) to describe the transformation. Point (C) is located at (-2, 4). However, its corresponding point (C') is located at (0,0). To go from (-2, 4) to (0,0) one has to add (2) units to the (x-coordinate) and subtract (4) units from the (y-coordinate). Therefore, the transformation can be described as the following,
(x + (2), y - (4))
2. Find the perimeter of a triangle with vertices A(–3, 5), B(–3, 2), and C(1, 2).
Answer:
12 units
Step-by-step explanation:
the perimeter = 3 + 4 + 5 = 12 units
The perimeter of a triangle is 12 cm.
To find the perimeter of the triangle.
What is triangle?
A triangle has three sides, three vertices, and three angles. The sum of the three interior angles of a triangle is always 180°.
Use the distance formula to find the length between point A and B, B and C, C and A. Then add all three lengths together to get the perimeter.
Distance = √ ( (x2 - x1)2 + (y2 - y1)2 )
Points A and B:
d = √(-3 +3)2 + (2 - 5)2
d = √ 0 + 9
d = √9
d = 3
Points B and C:
d = √ (1+ 3)2 + (2 -2)2
d = √ 16 + 0
d = √ 16
d = 4
Points C and A:
d = √ (-3 - 1)2 + (2 -5)2
d = √ 16 + 9
d = √ 25
d = 5
Perimeter= 3 + 5 + 4 = 12
So, the perimeter of a triangle is 12 cm.
Learn more about triangle here:
https://brainly.com/question/24106844
#SPJ2
I need help pls answer:
Express in simplest form:
4(X^2-1)-(X^2-8x-5)
Answer:
3x² + 8x + 1
Step-by-step explanation:
Given
4(x² - 1) - (x² - 8x - 5) ← distribute both parenthesis
= 4x² - 4 - x² + 8x + 5 ← collect like terms
= 3x² + 8x + 1
solve it : -
[tex] \sqrt{8 \times 5 \times 10} [/tex]
______
Answer:
20
Step-by-step explanation:
8 * 5 = 40
40 * 10 = 400
√400 = 20
Answer:
20
Step-by-step explanation:
sqrt(8*5*10)
sqrt(400)
sqrt(20*20)
20
PLEASE HELP!!!!!!!!!!!!!
Answer:
[tex]\text{C. }\pm \frac{1}{2}[/tex]
Step-by-step explanation:
Start by moving the 2 to the right (so we can multiply both sides by the denominator):
[tex]\frac{1}{2x^2-1}=-2[/tex]
Multiply both sides by [tex]2x^2-1[/tex]:
[tex]1=-2(2x^2-1),\\1=-4x^2+2[/tex]
Move everything to one side:
[tex]4x^2-2+1=0,\\4x^2-1=0,\\4x^2=1,\\x^2=\frac{1}{4},\\x=\boxed{\pm\frac{1}{2}}[/tex]
Answer:
the answer for this is C.