Answer:
[tex]D. \\x>\frac{3}{2}[/tex]
Step-by-step explanation:
12(1/2x - 1/3) > 8 - 2x
6x - 4 > 8 - 2x
6x + 2x - 4 > 8 - 2x + 2x
8x - 4 > 8
8x - 4 + 4 > 8 + 4
8x > 12
8x ÷ 8 > 12 ÷ 8
x > 1.5
(2x-3)(x-4)(3x-1)
How do u get the 35x2 and 47x?
Answer:
70 x 47x = 3290
.
. . . . . . . . . . ........
Answer: 6x^3-35x^2+47x-12
Step-by-step explanation:
(2x-3)(x-4)(3x-1)
=(2x^2-11x+12)(3x-1)
=6x^3-35x^2+47x-12
When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 21% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 58 of the dragon eggs to incubate. Consider all the possible samples of 58 dragon eggs.
What is the usual number of yellow eggs in samples of 58 eggs? (Give answers as SENSIBLE whole numbers.)
minimum usual number of yellow eggs =
maximum usual number of yellow eggs
Answer:
usual number of yellow eggs = 12
Usual maximum = 21
Usual minimum = 3
Step-by-step explanation:
To solve this, we will use the expected value of a binomial probability.
The formula is;
E(X) = np
Where;
n is sample size
p is probability of success.
We are given;
n = 58
p = 21%
Thus;
usual number of yellow eggs in samples = np = 58 × 21% = 12.18 ≈ 12
From USL(Upper specification limit) and LSL(Lower specification limit) formula, we can find the maximum usual number and minimum usual number of eggs respectively.
Thus;
USL = n(p + 3√(p(1 - p)/n)
USL = 58(0.21 + 3√(0.21(1 - 0.21)/58)
USL = 21.48 ≈ 21
LSL = n(p - 3√(p(1 - p)/n)
LSL = 58(0.21 - 3√(0.21(1 - 0.21)/58)
LSL = 2.87 ≈ 3
Which is the correct form of the partial fraction decomposition for the expression StartFraction 4 x cubed + 3 x squared Over (x + 1) squared (x squared + 7) squared EndFraction?
Given:
The expression is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
To find:
The correct form of the partial fraction decomposition for the given expression.
Solution:
We have,
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
By partial fraction decomposition, it can be written as:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{A}{x+1}+\dfrac{B}{(x+1)^2}+\dfrac{Cx+D}{x^2+7}[/tex] ...(i)
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B}{(x+1)^2(x^2+7)}[/tex]
[tex]4x^3+3x^2=(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B[/tex]
[tex]4x^3+3x^2=x^3A+x^3C+x^2A+x^2B+2x^2C+x^2D+7xA+xC+2xD+7A+7B+D[/tex]
[tex]4x^3+3x^2=x^3(A+C)+x^2(A+B+2C+D)+x(7A+C+2D)+7A+7B+D[/tex]
On comparing both sides, we get
[tex]A+C=4[/tex]
[tex]A+B+2C+D=3[/tex]
[tex]7A+C+2D=0[/tex]
[tex]7A+7B+D=0[/tex]
On solving these equations, we get
[tex]A=\dfrac{23}{32},B=-\dfrac{1}{8},C=\dfrac{105}{32},D=-\dfrac{133}{32}[/tex]
Substituting these values in (i), we get
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Therefore, the required partial fraction decomposition is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Answer:
A on Edg
Step-by-step explanation:
got it right
Which numbers are integers? Check all that apply.
04
-15
-10
2.5
0-4
0.13
ILL GIVE BRAINLIEST
Please help me find this box guys I’m struggling
Answer:
(0,-9)
Step-by-step explanation:
To find the y-intercept, substitute x=0
y=(0)^2+4(0)-9
=-9
Here's a tip to help you find the y-intercept faster, it is usually the constant of the graph equation
Answer:
see explanation
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
The equation of the axis of symmetry which is also the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 4x - 9 ← is in standard form
with a = 1, b = 4 , then
x = - [tex]\frac{4}{2}[/tex] = - 2
x = - 2 is the equation of the axis of symmetry
Substitute x = - 2 into the equation for corresponding y- coordinate of vertex
y = (- 2)² + 4(- 2) - 9 = 4 - 8 - 9 = - 13
vertex = (- 2, - 13 )
To find the y- intercept let x = 0 and solve for y
y = 0² + 4(0) - 9 = 0 + 0 - 9 = - 9
y- intercept = (0, - 9)
From the standard form of the parabola
• If a > 0 then vertex is a minimum
• If a < 0 then vertex is a maximum
Here a = 1 , that is > 0
vertex (- 2, - 13 ) is a minimum
Is the relationship shown by the data linear? If so, model the data with an equation. x y –7 5 –5 9 –3 13 –1 17
Given:
The table of values is:
x : -7 -5 -3 -1
y : 5 9 13 17
To find:
Whether the given data is linear and then find the equation.
Solution:
The given data is linear if the slope and rate of change is constant.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using the slope formula. we get
[tex]\dfrac{9-5}{-5-(-7)}=2[/tex]
[tex]\dfrac{13-9}{-3-(-5)}=2[/tex]
[tex]\dfrac{17-13}{-1-(-3)}=2[/tex]
Since the rate of change is constant, i.e., 2, therefore the given data is linear.
The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-5=2(x-(-7))[/tex]
[tex]y-5=2(x+7)[/tex]
[tex]y-5=2x+14[/tex]
Adding 5 on both sides, we get
[tex]y-5+5=2x+14+5[/tex]
[tex]y=2x+19[/tex]
Therefore, the equation for the given data is [tex]y=2x+19[/tex].
Enter the equation of the line in slope-intercept form.
Slope is 4, and (5,2) is on the line.
The equation of the line is y =
Answer:
y = 4x -18
Step-by-step explanation:
y-2 = 4(x-5)
y = 4x -20+2
y = 4x -18
Answer:
y = 4x-18
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = 4x+b
Substitute the point in the equation and solve for b
2 = 4(5)+b
2 = 20+b
2-20 = b
-18 =b
y = 4x-18
You have 80$ panted cost 29$ And shirts cost 12$. Mom told you to buy one pair of pants and use the rest of the money to buy shirts. Use this information to write and solve and inequality how many shirts can you buy
Answer: 4 Shirts
Step-by-step explanation:
Given
Person has [tex]\$80[/tex]
Pant costs [tex]\$29[/tex] and shirt costs [tex]\$12[/tex]
Suppose [tex]x\ \text{and}\ y[/tex] as number of pant and shirts
Spent money must be equal or less than the total money. The inequality becomes
[tex]\Rightarrow 80\geq29x+12y[/tex]
For 1 pair of pants that is, 1 pants
[tex]\Rightarrow 80\geq 29+12y\\\Rightarrow 51\geq 12y\\\Rightarrow 4.25\geq y[/tex]
That is maximum number of shirts that can be bought are 4.
SOMEONE HELP ME PLEASE
Answer:
9/10 or 90 %
Step-by-step explanation:
There are 54+27+5+4 total people = 90
The people with diploma is 54+27 = 81
P (diploma) = number with diploma / total
= 81/90
=9/10
90%
Ryan rented a truck for one day. There was a base fee of $16.99, and there was an additional charge of 74 cents for each mile driven. Ryan had to pay $133.17 when he returned the truck. For how many miles did he drive the truck?
Answer:
157 miles
Step-by-step explanation:
total cost = flat fee + cost per mile * miles
133.17 = 16.99 + .74 * m
Subtract 16.99 from each side
116.18 = .74m
Divide each side by .74
116.18 / .74 = .74m/.74
157 = m
In Owen's class, there are 15 girls and 12 boys. Write the ratio of boys to girls.
Answer:
4 : 5
Step-by-step explanation:
boys : girls
12 15
Divide each by 3
12/3 : 15/3
4 : 5
Answer: 4:5
Step-by-step explanation:
To simplify the ratio 12:15, divide both numbers by the GCF of the 2 numbers (3). This gives you the simplified ratio, 4:5.
The speed of a toy car is 20 m/s. The time taken for a trip is 200seconds. Find the
distance covered in meter
Distance = time/ speed
Distance = 200 seconds / 20 m/s
Distance = 10 meters
Answer:
Distance:
[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 20 \times 200}} \\ { \tt{ = 4000 \: metres}}[/tex]
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x-4
h(x) = 3/4x
h(x) = 1/4x
Answer:
Let the inverse of f(x) be h(x):
[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]
Please help me with question a), b) and c). I have been trying for so long. (Show working), thank you.
Answer:
b)48 km/hr (12 km in .25 hrs)
c) avg speed: 60/3 = 20 km/hr
Step-by-step explanation:
a)
.5 18
.75 18
1 30
1.5 30
2 40
2.25 40
3 60
A is 2 times older than B. Identify the appropriate expression.
Answer:
C. 2x
Step-by-step explanation:
Let
B's age = x years
A's age = 2 times older than B
= 2 * x
= 2x years
A's age = 2x years
For instance, if B's age is 17 years
Then,
A's age = 2x
= 2(17)
= 34 years old
HELPPP ME OUTTTTTT!!!!!!!
Answer:
3/5
Step-by-step explanation:
cos A = adjacent side / hypotenuse in a right triangle
cos A = 24/40
Cos A = 6/10
cos A = 3/5
guys, please help i can't move on
Answer:
15
Step-by-step explanation:
32-19 = 13 that have both
70-57= 13 that have both again from that sample
total number of people that have both : 13 + 13 = 26
11 kids don't have either one, so :
26-11 = 15
PERE
Given: ZABC is a right angle and ZDEF is a right angle.
Prove: All right angles are congruent by showing that ZABC = ZDEF.
What are the missing reasons in the steps of the proof?
ZABC, ZDEF are
right angles
M2ABC = 90°
m2DEF = 90°
m2ABC = m_DEF
ZABC = ZDEF
Given
A
B
A:
B:
C:
Intro
Answers:
A) Definition of right anglesB) SubstitutionC) Definition of congruence=========================================
Explanation:
A) The term "right angle" is another way of saying "90 degree angle". This is a definition. Think of a definition in a dictionary. B) The substitution property allows us to replace one thing for another, as long as the two things are equal. The transitive property works as a similar idea.C) If two angles have the same measure, then they are congruent. This is the definition of congruence (or one form of it).In this exercise we have to use the knowledge of angles, in this way we can say that:
A) Right angles
B) Substitution
C) Congruence
So punctuating some necessary definitions we have that:
A) This alternative is a right angle, that is, an angle that has 90 degrees.
B) The substitution property allows us to replace one thing for another, as long as the two things are equal.
C) IIn this alternative, we are dealing with congruent angles, that is, angles that have the same measure, normally less than 90 degrees.
See more about angles at brainly.com/question/15767203
Given: `bar(DE)` and `bar(DF)` are midsegments of `Delta` ABC as shown. Prove: A midsegment of `Delta`ABC is half the length of the side of `Delta`ABC to which it is parallel. Match each statement to its corresponding reason. Scroll down to see all the choices. Drag the items on the left to the correct location on the right.
Answer:
here
Step-by-step explanation:
Which expression is equivalent to 2(a+2b)-a-2b
o 3a+2b
o 3a-2b
o a-2b
Answer:
a -2b
Step-by-step explanation:
2(a+2b)-a-2b
Distribute
2a+4b -a-2b
Combine like terms
a -2b
Draw a plane, showing the three (non-linear) points that define it.
Draw a plane, showing the three (non-linear) points that define it.[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
See this attachment
CANNNN SOMEONEEEEE HELPPPP MEEE OUTTTTT !!!!!
Answer:
sin X = 21/ 29
Step-by-step explanation:
Since this is a right triangle
sin X = opp side/ hypotenuse
sin X = 21/ 29
Answer:
[tex]\boxed{\sf sinX =\frac{21}{29}}[/tex]
Step-by-step explanation:
We need to find out the value of sinX using the given triangle . Here we can see that the sides of the triangle are 21 , 29 and 20.
We know that the ratio of sine is perpendicular to hypontenuse .
[tex]\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}[/tex]
Here we can see that the side opposite to angle X is 21 , therefore the perpendicular of the triangle is 21. And the side opposite to 90° angle is 29 . So it's the hypontenuse . On using the ratio of sine ,
[tex]\sf\longrightarrow sinX =\dfrac{ p}{h}=\dfrac{ZY}{ZX}[/tex]
Substitute the respective values ,
[tex]\sf\longrightarrow \boxed{\blue{\sf sin\ X =\dfrac{21}{29}}}[/tex]
Hence the required answer is 21/29 .
On an electricity bill of $40.80, Mrs.
Miller pays only $38.76 because she pays
before a certain date. What percent
discount is Mrs. Miller allowed?
Answer:
100%_$40.80
? × _$38.76
Step-by-step explanation:
100%×$38.76÷$40.80=95%
Answer:
40.80
Step-by-step explanation:
Find the surface area and the volume of the prism.
10
26
18
If ABCD is dilated by a factor of 2, the
coordinate of A' would be:
Answer: -5, -1
Step-by-step explanation:
The cars of a circular Ferris wheel at an amusement park are equally spaced about the wheel's circumference. They are numbered consecutively beginning with 1. The cars numbered 14 and 30 lie on opposite ends of a diameter. How many cars are on the Ferris wheel?
Answer:
32 cars
Step-by-step explanation:
we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32
Math step-by-step:
30-14=16
16×2=32
plzzz helppp i need to pass this classs
Answer:
C
Step-by-step explanation:
x + 40 + 100 + x=360. (sum of angles at a point)
2x+140=360
2x=360-140
2x=220
x=220/2
x=110⁰
please help with this problem!
Answer:
Second option
Step-by-step explanation:
Let's assume that x is 1 and y is 3
a) [tex]\frac{1}{2}[/tex] < [tex]\frac{3}{2}[/tex] = true
b) -1 < -3 = false
c) 1+2 < 3+2 = true
d) 2 x 1 < 2 x 3 = true
Mr. James asked his students that which of the following equations can be formed using the expression x = 5:
a)2 x + 3 = 13
b)3x + 2 = 13
c)x –5 =
1d)4x –9 = 21
Answer:
[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]
I NEEDDDD D HELPPPPP!!!
Answer:
70 degrees
Step-by-step explanation:
there are multiple ways, as all the trigonometric functions are related.
let's try it this way :
consider the missing side to be the radius of a circle.
then 41 would be the cos value of the angle (multiplied by that radius, of course).
so, let's calculate the missing side per Pythagoras
c² = a² + b² = 113² + 41² = 12769 + 1681 = 14450
c = 120.21
and now
41 = cos(?) × 120.21
cos(?) = 41/120.21 = 0.341...
? = 70.0576... ≈ 70 degrees
Answer:
70°
Step-by-step explanation:
tangent θ = (opposite side / adjacent side)
tangent θ = (113 / 41)
θ = arctan (113 / 41)
θ = 70.0576°
*Note: "arctan" is the same as "inverse tangent"
**Note: "soh-cah-toa" (and "cho-sha-cao" for sec, csc, & cot) is an easy mnemonic device to remember the trig functions (sin, cos, & tan) and their relations to the sides of a given angle.
