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
What is the value of x in the equation -3/4 = x/24
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 18}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{ - 3}{4} = \frac{x}{24} [/tex]
➼ [tex] \: x = \frac{ - 3 \times 24}{4} [/tex]
➼ [tex] \: x = \frac{ - 72}{4} [/tex]
➼ [tex] \: x = - 18[/tex]
Therefore the value of [tex]x[/tex] is -18.
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex] \frac{ - 3}{4} = \frac{ - 18}{24} [/tex]
➼ [tex] \: \frac{ - 3}{4} = \frac{ - 3}{4} [/tex]
➼ L. H. S. = R. H. S.
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35♨}}}}⋆[/tex]
these marbles are placed in a bag and two of them are randomly drawn. what is the probability of drawing two blue marbles if the first marble is placed back in the bag before the second draw
In other words, the number 4 goes in the green box.
============================================================
Explanation:
2 yellow + 3 pink + 5 blue = 10 total marbles
We have 5 blue out of 10 total, so 5/10 = 1/2 represents the probability of picking a blue marble.
Picking two marbles in a row is represented by the probability (1/2)*(1/2) = 1/4
The fraction 1/2 stays the same for both selections because we put the first marble back.
A=9 b=12 c=15 sin b cos b tan b
Answer:
according to right , we use Phythgorous
tanb= 9/12
cosb=12/15
and sinb=9/15
When 4 is added to three times of a number, the answer is the same as subtracting 2 from the number. What is the number ?
Answer:
- 3
Step-by-step explanation:
let n be the number , then
3n + 4 = n - 2 ( subtract n from both sides )
2n + 4 = - 2 ( subtract 4 from both sides )
2n = - 6 ( divide both sides by 2 )
n = - 3
The number is - 3
The number is - 3.
To find the number.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. All the whole numbers are also integers, because integers include all the positive and negative numbers.
Given that:
let n be the number , then
3n + 4 = n - 2 ( subtract n from both sides )
2n + 4 = - 2 ( subtract 4 from both sides )
2n = - 6 ( divide both sides by 2 )
n = - 3
So, the number is - 3.
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Which of the following are solutions to the quadratic equation? Check all that
apply.
x2 + 8x + 16 = 7
Answer:
[tex]x=-4+\sqrt{7}[/tex]
[tex]x= -4-\sqrt{7}[/tex]
Step-by-step explanation:
Quadratic
F
is directly proportional to
a
.
If
F
=
25
when
a
=
5
find,
F
when
a
=
8
Since F and a are directly proportional, we can relate F to our unknown F, and a to our other known a.
25 / 5 = F / 8
Cross-multiply to solve.
5F = 200
F = 40
Hope this helps!
Question 9 of 10 Based only on the given information, it is guaranteed that AB I CD. A D . Given: AABC ZDAC = ZDBC O A. True O B. False
Answer:
False
Step-by-step explanation:
False
There is not enough information to guarantee the lines are perpendicular.
No, we can not say that AB and CD are perpendicular from the information given.
What are perpendicular line?Two geometric objects are perpendicular if their intersection forms right angles at the point of intersection called a foot.
The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.
Given that a triangle ABC, divided into two triangles by a line DC, also
angle DAC and DBC are congruent,
From the given information we can not conclude any relation between both triangles,
Hence, we can not say that AB ⊥ CD
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A parabola can be represented by the equation x2 = –20y.
What are the coordinates of the focus of the parabola?
(–5,0)
(5,0)
(0,5)
(0,–5)
Answer:
[tex] {x}^{2} = - 20y \\ y = - \frac{1}{20} {x}^{2} \\ { \tt{y = 4a {x}^{2} }} \\ a = - \frac{1}{5} \\ \\ { \tt{focus = (0, \: - 5)}}[/tex]
The requried coordinates of the focus of the parabola x² = -20y are (0, -2.5), which corresponds to the option (0, -5).
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation y = 4ax².
The standard form of the equation of a parabola is (y - k) = (1 / 4p)(x - h)², where (h, k) is the vertex and p is the distance from the vertex to the focus. We can convert the given equation x² = -20y into this standard form by completing the square:
x² = -20y
x² / (-20) = y
x² / (-20) + 0 = y + 0
(x - 0)² = -20(y - 0)
Comparing this equation to the standard form, we can see that the vertex is at (h, k) = (0, 0), and that 4p = -20, so p = -5/2.
Since the focus is a distance of p below the vertex, the focus is at (h, k - p) = (0, -5/2), which is the same as (0, -2.5).
Therefore, the coordinates of the focus of the parabola x² = -20y are (0, -2.5), which corresponds to the option (0, -5).
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When you find the surface area of a cube, you ________ the length of the cube and
multiply by 6
Answer:
The word for the blank would be "square".
Step-by-step explanation:
Since the area of a face of a cube would be square its side length, the total surface area of a cube would be that times 6.
Hope this helped!
Answer:
square
Step-by-step explanation:
the area of a cube is found by squaring the length
13
What is the Pythagorean Theorem?
A) a + b + c
B
a2+b2=c2
a2-b2=c2
D) abc = d
Answer:
a2 +b2=c2
Step-by-step explanation:
......
hope it helps
Answer: its a^2+b^2=c^2
Step-by-step explanation:
please solve this fast.
Help please if you don’t mind Thankyouu!
Answer:
(3V) / b = h
Step-by-step explanation:
V = (1/3)bh multiply both sides by 3
3V = bh divide both sides by b
(3V) / b = h
Select a figure from the options which will replace the(?) as established by the problem figure
Answer:
a) is the correct answer.
In the triangles, GK PN and HG 2MP.
Which statement correctly compares the angles?
H
M
Angle G is congruent to angle P.
O Angle G is smaller than angle P.
O Angle G is larger than angle P.
O Angle G is congruent to angle N.
32 cm
40 cm
G
K
P
N
Answer:
G is smaller than P. Visually comparing G to P you are doing a rough comparison to a 90° (or right) angle. Angle G is a little bit tilted to the right making it just under 90°
The statement which correctly compares the angles is Angle G is smaller than angle P.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given are two triangles.
Given that,
GK is congruent to PN.
HG is congruent to MP.
Also, given that,
HK = 32 cm and MN = 40 cm
Angle G is opposite to the side HK.
Angle P is opposite to the side MN.
Angles opposite to the greater side will be greater.
So angle P is greater than angle G
Or, angle G is smaller than angle P.
Hence, Angle G is smaller than angle P.
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What is the multiplicative rate of change of the
function?
Answer:
0.25×5=0.125
0.125×0.5=0.0625
0.0625×0.5=0.03125
the multiplicative rate of chage of the function is 0.5
The local humane society is trying to determine how many racoons there are in a city. They catch and tag 18 raccoons. Later on, they catch 67 raccoons, and 2 of them are tagged. What is the best estimate of the raccoon population? Answer to the closest whole number.
Answer:
83 racoons
Step-by-step explanation:
18+67- 2
you would subtract the two they found with tags
Please help me!! Thank you.
Answer:
8640
Step-by-step explanation:
According to question,
P= 6000
T=3 year 8 months = 11/3 years
R= 12% per annum
Simple interest is given by :
[tex]SI=\frac{PRT}{100} \\SI=\frac{6000*12}{100} *\frac{11}{3} \\SI=24*11\\SI=2640 Rs[/tex]
Now,
Amount = P+SI
Amount=6000+2640
Amount=8640 Rs
8640 Rs amount which will clear her debt
What is the recursive formula for this geometric sequence?
-3, -21, -147, -1029, ...
A fruit seller buys lemons at 2 for a dollar and sells them at 5 for three dollars. What is his gain percent?
a)10%
b)15%
c)20%
d)25%
Evaluate x2+9/x2 for each of the given values.
What is the value of the expression when x = 3?
2
3
10
undefined
What is the value of the expression when x = 1?
2
3
10
undefined
What is the value of the expression when x = 0?
2
3
10
undefined
Answer:
ok so we just substate the number in so
6+9/6
6+1 1/3 = 7 1/3
so for part a the answer is 7.33
for part b
2+9/2
3+4 1/2 =7 1/2
so the answer is 7.5
A:7.33
B:7.5
Hope This Helps!!!
Answer:
A, 2
B, 10
C, undefined
Step-by-step explanation:
Just did the assignment E2021
Consider the following simple regression model: y = 0 + 1 x 1 + u. In order to obtain consistent estimators of 0 and 1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov( z, x) 0 and Cov ( z, u) = 0. The variable z is called a(n) _____ variable. 答案选项组 dummy instrumental lagged dependent random
Answer:
Instrumental variable
Step-by-step explanation:
cov(z,u) shows that the instrumental variable is exogenous. An instrumental variable can also be regarded as a third variable, It is included in the model if you have an issue of endogeneity in your regression model. An endogeneity problem arises if there are other variables are being influenced by other independent variable in the same regression model. we use z to account for these behaviours in the model. this variable controls for measurement errors as well as confounding errors.
please help! i think the answer is 12 but any verification would be greatly appreciated!
Answer:
13.9 or 14
Step-by-step explanation:
a^2 + b^2 = c^2
5^2 + 13^2 = c^2
25 + 169 = 197
square root 197 to get c
c = 13.9 (14 rounded up)
Helpful thing to note is that the hyptoenuse will always be longer than your "long side" of the triangle
KoKo Chocolatiers sells their truffes in rectangular boxes. They are going to start ordering circular boxes, too. The rectangular box is made from metal that is 0.3 cm thick. The circular box will be constructed from laminated cardboard that is 0.2 cm thick. The height of the circular box will be the same as the rectangular box. If the volumes of the two boxes are equal, then what is the radius (r) of the circular box?
Answer:
r = 9.61 cm
Step-by-step explanation:
Volume of a rectangular box = length × width × height
= 21.5 cm × 13.5 cm × 6 cm
= 1,741.5 cm³
Volume of a rectangular box = 1,741.5 cm³
Since,
Volume of a rectangular box = Volume of a circular box
Then,
1,741.5 cm³ = Volume of a circular box
Volume of a circular box = πr²h
1,741.5 cm³ = 3.14 * r² * 6 cm
1,741.5 = 18.84r²
r² = 1,741.5/18.84
r² = 92.436305732484
r = √92.436305732484
r = 9.6143801533163
Approximately,
r = 9.61 cm
What is the value of x in the equation of 7x-8=13
PLEASE HELP MEEE
Answer:
x = 3
Step-by-step explanation:
7x-8=13
Add 8 to each side
7x-8+8=13+8
7x = 21
Divide each side by 7
7x/7 = 21/7
x = 3
(First correct answer will get brainliest) Determine the length of AB. Write your anseer in simplest form
Answer:
[tex] \frac{6}{6 + AB} = \frac{8}{8 + 10} \\ \\ 6 + AB = \frac{6 \times (8 + 10)}{8} \\ 6 + AB = 13.5 \\ AB = 7.5 [/tex]
The product of (3+2i) and a complex number is (17+7i)
The complex number is______
Answer:
The complex number is;
37 + 55i
Step-by-step explanation:
Here, we want to find the product of the two
We proceed as follows;
(3 + 2i)(17+ 7i)
= 3(17 + 7i) + 2i(17 + 7i)
= 51 + 21i + 34i + 14(i)^2
Recall; i = √(-1)
Thus, we have it that;
51 + 55i -14
= 51-14 + 55i
= 37 + 55i
Please help I’ll give brainliest
Answer:
1000 cubic metre
Step-by-step explanation:
hopes it help
Answer:
solution,
length=10 cm
volume=?
now,
volume of cube=l×l×l
=10×10×10
therefore,the answer is 1000 cubic centimeter
Plz solve this question correctly.
Show the steps needed to solve it.
Answer: 378y^3
Step-by-step explanation:
the formula for volume is V = L * w * h , where V=volume, L=length, W=width, and H=height
if we plug the numbers from the picture in, the formula would look like this:
V = 9y * 7y * 6y
to solve you just multiply them together
V = 378 y^3
How much almond milk does James use per teaspoon of cashew butter
The container of orange juice held 53 cups of juice. If a serving of orange juice is ã of a cup of orange juice, to the
nearest whole serving, how many servings were in the container?
05 servings
O 6 servings
15 servings
19 servings
Mark this and return
Save and Exit
Next
Submit
Answer:
5 servings = 265 cups of orange juices
5 servings = 318 cups of orange juices
5 servings = 795 cups of orange juices
5 servings = 1,007 cups of orange juices
Step-by-step explanation:
Given:
1 serving contain = 53 cups of orange juices
Find:
Serving in;
5 servings
6 servings
15 servings
19 servings
Computation:
5 servings = 53 x 5
5 servings = 265 cups of orange juices
5 servings = 53 x 6
5 servings = 318 cups of orange juices
5 servings = 53 x 15
5 servings = 795 cups of orange juices
5 servings = 53 x 19
5 servings = 1,007 cups of orange juices
