this is the answer: -5 < -12/40 < 19/38
Pls answer only 16 and 19
Question 16:
[tex]\alpha[/tex] and [tex]\beta[/tex] are the roots of the equation.
That means [tex](x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0\\[/tex]
[tex](x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0[/tex]
[tex]2x^{2} -6x+5 = 0\\x^{2} -3x+\frac{5}{2} =0[/tex]
[tex](x-\alpha )(x-\beta ) =x^{2} - (\alpha +\beta )x +\alpha \beta[/tex]
So,
[tex]x^{2} - (\alpha +\beta )x +\alpha \beta = x^{2} -3x+\frac{5}{2}[/tex]
Compare coefficient
[tex]\alpha +\beta = 3\\\alpha \beta = \frac{5}{2}[/tex]
Consider [tex]\frac{\beta }{\alpha } + \frac{\alpha }{\beta }[/tex]
[tex]\frac{\beta }{\alpha } + \frac{\alpha }{\beta } =\frac{ \alpha ^{2} +\beta ^{2}}{\alpha \beta }[/tex]
[tex]= \frac{(\alpha +\beta )^{2} -2\alpha \beta }{\alpha \beta } \\= \frac{3^{2} -2*\frac{5}{2} }{\frac{5}{2} } \\= 4*\frac{2}{5} \\=\frac{8}{5}[/tex]
Ans: 8/5
Question 19:
[tex]f(x+2) = 2x^{2} +5x-3\\[/tex]
Substitute x with -1
So,
[tex]f(1) = 2(-1)^{2} +5(-1)-3\\=2-5-3\\=-6[/tex]
Ans: -6
Janie walked 10 miles. Then she walked 15
that distance. How far did she wall all together? Select all that apply.
E. , 10 × 45
B. , 10 ×15
D. 10(1 + 15)
C. 10 +15×10
A. 10 + 15
F. 10×65
Triangle P is rotated 180° about (0, 0) to give triangle Q. Triangle Q is translated by 5 2 to give triangle R. (a) Describe fully the single transformation that maps triangle P onto triangle R.
Answer:
(x, y) ⇒ (-x +5, -y +2)
Step-by-step explanation:
Rotation 180° is described by ...
(x, y) ⇒ (-x, -y)
Translation right 5 and up 2 is described by ...
(x, y) ⇒ (x +5, y +2)
The two transformations together that map P to R are described by ...
(x, y) ⇒ (-x +5, -y +2)
Luke has a piece of rope that is 3.6 meters long. He cuts the rope into two pieces. One is 1.93 meters long. How long is the other piece of rope?
PLEASE HELP ASAP OF YOU DO FOD BLESS YOU BECAUSE IT WILL RAISE MY GRADE
Answer:
8
Step-by-step explanation:
The basic form of the equation is y=mx+b. The b stands for the y-intercept. In this equation, 8 is b due to its position in the equation, and -8/7 is m. Since we know that 8 is b and that b is the y-intercept, we know that 8 is the y-intercept.
Hope this helps!
A person bought a water tank of circular base having the radius 1.05 meter and height 3.5 m for the use of own house from the shop. If the upper part of the tank is semi spherical , how many liters of water will be contained in the tank. Find it!
Help!! :)
11000 litre of water is needed to fill the tank.
Answer:
solution given:
radius [r]=1.05m
Total height[H]=3.5m
height of cylinder[h]=2.45m
Now
The volume of the cylindrical part of tank=[tex]\pi r^2h=3.14*1.05^2 *2.45=8.4815m^3[/tex]
again
the volume of semi-spherical part of tank=[tex]\frac{2}{3} \pi r^{3} =\frac{2}{3}*3.14*1.05^3=2.4233m^3[/tex]
now
total volume=volume of the cylindrical part of tank + volume of semi-spherical part of tank
=8.4815+2.4233=10.9048 [tex]m^{3}[/tex]
we have
[tex]1m^3=1000litre[/tex]
[tex]10.9048m^3=1000*10.9048=10904.8\:litre[/tex]
Step-by-step explanation:
Choose the graph that matches the following system of equations:
x + y = 4
2x + 3y = 18
Picture of coordinate plane with line y equals negative x plus 4 and line y = equals negative 2 thirds x plus 6. They intersect at negative 6, 10.
Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x plus 6. They intersect at 6, 2.
Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x minus 6. They intersect at negative 1.2, negative 5.2.
Picture of coordinate plane with line y equals x plus 4 and line y equals negative 2x plus 6. They intersect at 0.67, 4.67.
Answer:
Line x-intersect: -6
y-intersect: 10
Step-by-step explanation:
X + y = 4
x = 4-y
2(4-y) + 3y = 18 (substitution)
8-2y+3y = 18
y = 18-8
y = 10
x + 10 = 4
x = -6
60 points!!! Please answer immediately and the entire page please I will also give you five stars
Answer:
Step-by-step explanation:
9. Correct, D
-3Y + 9X <= 12
3Y - 9X => -12
3Y => -12 + 9X
Y => -4 + 3X
10. D
11. D
12. Correct, B
13. Correct, E
14. A
15. B
A jar is filled with pennies, nickels, and dimes. The probability of picking a penny is
1
4
, and the probability of picking a dime is
1
3
. What is the probability of picking a nickel?
Answer:
1
3 maybe
Step-by-step explanation:
The diameter of a circle is 3 miles what is the area
Answer:
[tex]2.25\pi[/tex] or [tex]7.07 mi^{2}[/tex]
Step-by-step explanation:
The formula for the area of a circle is:
[tex]\pi r^{2}=A[/tex]
Radius is half of the diameter of a circle so you will get this:
[tex]\pi (\frac{3}{2}) ^{2}\\\\\pi (1.5)^2\\\\2.25\pi \\\\7.07[/tex]
What is the value of z?
A line passes through the points (-2, 9) and (1, 3).
Provide work for calculating the slope and y-intercept. Then, write the equation for the line in slope-intercept form.
Answer:
slope = -2
y-intercept = 5
Step-by-step explanation:
1) Find slope:
[tex]\frac{3-9}{1-(-2)}[/tex] = [tex]\frac{-6}{3}[/tex] = -2
-2 = slope
2) Find y intercept trough point slope and slope-intercept forms
y - y1 = m (x - x1)
y - 9 = -2 (x + 2)
y - 9 = -2x -4
+ 9 + 9
y = -2x + 5
y = mx + b with b being the y-intercept
5 = y-intercept
A number consists of two digits whose sum is 9. If 9 is added to the number its digits are inter changed. Find the number.
Solution:
Let the two digits of a number be X and Y
Let the digit at 10's place = X
Let the digit at 1's place = Y
The two digit number = 10X+Y
Given that
The sum of the digits = 9
⇛ X+Y = 9
⇛X = 9-Y →→→→eqn(i)
If 9 is added to the number the digits interchanged
⇛10X+Y +9 = 10Y+X
⇛10X+Y+9-10Y-X = 0
⇛9X-9Y +9 = 0
⇛9(X-Y+1) = 0
⇛X-Y+1 = 0
⇛9-Y-Y+1 = 0
⇛10-2Y = 0
⇛2Y = 10
⇛Y = 10/2
⇛Y = 5
Now
X = 9-5 = 4
Therefore the number = 45 Ans.
also read other questions: Increases the number of free hydrogen ions or protons (H+) in the inter-membrane space of the mitochondria (between the outer and inner membranes).
https://brainly.com/question/4179342?referrer
Answer:
see that attachment
I hope it's help you
If no denominator equals zero, which expression is equivalent to ? A. B. C. D.
The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] and it can be determined by using LCM and fraction.
Given that,Expression;[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]
If no denominator equals zero,
We have to determine,Which expression is equivalent to the given expression?
According to the question,Expression;
[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]
If no denominator equals zero,
To determine the equivalent relation of the given equation following all the steps given below.
Step1; First take the LCM,[tex]\rm= \dfrac{15}{x-6}+\dfrac{7}{x+6}\\\\=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}[/tex]
Step2; Multiply the terms and simplify the equation,[tex]\rm=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}\\\\= \dfrac{15x+90 + 7x-42}{x(x+6) -6 (x+6)}\\\\= \dfrac{22x+48}{x^2+6x -6 x-36}\\\\= \dfrac{22x+48}{x^2-36}\\\\[/tex]
Hence, The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] .
For more details about Expression refer to the link given below.
https://brainly.com/question/14610993
pls help!!!!!!! its applications in pre calc
The total weight W of such a plane is equal to
W = w + gf
where
w = weight of plane without fuel
g = number of gallons of fuel
f = weight of 1 gallon of fuel.
When carrying g = 10 gallons, the total weight is W = 1955, so
1955 = w + 10f
When carrying g = 42 gallons, the weight is W = 2131, so
2131 = w + 42f
We want to find W when g = 52, and to do this we first need to find the weight of the plane w and the weight of 1 gallon of fuel f.
Solve the system of equations,
w + 10f = 1955
w + 42f = 2131
We can combine the equations like so to eliminate w and solve for f :
(w + 42f) - (w + 10f) = 2131 - 1955
32f = 176
f = 11/2 = 5.5
Then solving for w, we get
w + 10 (5.5) = 1955
w + 55 = 1955
w = 1900
So, when the plane carries g = 52 gallons of fuel, the total weight is
W = 1900 + 52 (5.5) = 2186
About how many years would it take you to earn $1000 simple
interest on an investment of $800 at 9% annual interest?
A)
8
B)
10
C)
12
D)
14
Ratios and Proportional Relationships
(ZRP 3) Solve Problems
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14 year it would take to earn $1000 simple interest on an investment of $800 at 9% annual interest.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let the number of years be represented as T
Now , the equation will be
The simple interest I = $ 1000
The rate of interest R = 9 %
The principal amount P = $ 800
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
1000 = ( 800 x 9 x T ) / 100
On simplifying the equation , we get
72T = 1000
Divide by 72 on both sides of the equation , we get
T = 13.89 years
Therefore , the number of years is approximated to 14 years
To learn more on Percentage click:
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Which equation represents the line that passes through the points (0, 3) and (2,6)
A y = -3/2x + 3
B y = 2/3x + 3
C y = 3/2x + 3
D y = 3/2x
Answer:
C) y=3/2x+3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-3)/(2-0)
m=3/2
y-y1=m(x-x1)
y-3=3/2(x-0)
y=3/2(x)+3
y=3/2x+3
Answer:
C) y=3/2x+3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-3)/(2-0)
m=3/2
y-y1=m(x-x1)
y-3=3/2(x-0)
y=3/2(x)+3
y=3/2x+3
if i have decent grades, but miss a lot of school
will they fail me???
Answer:
I think it's no
Step-by-step explanation:
because you will study hard
A motorcycle can run 108km in 2h20mn Find the average speed
Answer:
do it got a picture
on the edge2020
Step-by-step explanation:
Quadrilateral MNOP was dilated with the origin as the center of dilation to create quadrilateral M'N'O'P'. The quadrilateral was dilated using a scale factor of 1.5. The coordinates of the vertices of quadrilateral MNOP are given. What are the coordinates of N'?
A) (4,5)
B) (1.5, 2)
C) (4.5, 5.25)
D) (2, 2.3)
With the center of dilation at the origin, the image is given by the product
of the corresponding point on the preimage and the scale factor.
The coordinates of N' is; [tex]\underline{C) \ (4.5, \ 5.25)}[/tex]Reasons:
The center of dilation of quadrilateral MNOP = The origin
The image following the dilation of MNOP = M'N'O'P'
The scale factor of dilation = 1.5
Required:
The coordinates of N'
Solution:
The coordinates of N in MNOP = N(3, 3.5)
The coordinate of a point (x', y') on the image following the dilation with center at the origin, of the preimage (x, y) by a scale factor is given as follows;
(x', y') = Scale factor × (x, y)Which gives;
The coordinates of N' = 1.5 × N(3, 3.5) = N'(1.5 × 3, 1.5 × 3.5) = N'(4.5, 5.25)
The coordinates of N' = C) (4.5, 5.25)Learn more about dilation transformation here:
https://brainly.com/question/12561082
Answer:
C) (4.5, 5.25)
Step-by-step explanation:
Find the 62nd term of the arithmetic sequence
15, 13, 11, ...
Answer:
[tex]a_{62}=-107[/tex]
Step-by-step explanation:
This is an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
where d is the common difference and n is the index of any given term.
The common difference of the given sequence is -2:
[tex]13-15=-2\\11-13=-2[/tex]
Using the first term and the common difference, you can write the equation for this sequence:
[tex]a_n=15+(n-1)(-2)[/tex]
And using that equation, you can find the 62nd term:
[tex]a_{62}=15+(62-1)(-2)\\a_{62}=15+(61)(-2)\\a_{62}=15-122\\a_{62}=-107[/tex]
Find an ordered pair (x, y) that is a solution to the equation 3x-y=4
Answer:
(0,-4)
Step-by-step explanation:
3(0) - (-4) = 4
0 + 4 = 4
Which value for x proves that abc=def by sss
Answer:
7
Step-by-step explanation:
DE corresponds to AB.
37=5x+2
-2 -2
35=5x
7=x
3. A rock is lying on a rock ledge that is 3 m high. The rock as 120 J of potential energy.
What is the mass of the rock?
Answer:
For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters. Notice that gravitational potential energy has the same units as kinetic energy, kg m2 / s2.
Step-by-step explanation:
Is the graph increasing, decreasing, or constant?
A. Constant
B. Decreasing
C. Increasing
th graph is increasing I'm pretty sure
solve the system of equations please help
can somebody please help me with these, I don’t know if they’re right and I don’t understand how to do it
Answer:
ur right!!
Step-by-step explanation:
1.
In a proportional relationship between the variables x and y, which of the following
expressions would be constant?
(1) x + y
(3) xy
(2) y-x
(4)Y/x
Yes
Answer:
y/x
Step-by-step explanation:
If x is proportional to y, then:
y = kx, where k is a constant
This can be rearranged to give:
k = y/x
As mentioned, k is a constant, therefore, the answer is y/x
rectangle A and B are identical. each has a perimeter of 40cm. they are put together to make a new rectangle. the perimeter of the new rectangle is 68cm. work out the length and width of rectangle A.
Answer:
6 cm by 14 cm
Step-by-step explanation:
The perimeter of the joined figure will be the sum of the perimeters of rectangles A and B, less the lengths of the sides that are joined. The two joined sides have a total length of ...
(40 cm) +(40 cm) -(68 cm) = 12 cm
Then the length of the joined sides is 6 cm. The length of the other side of the rectangle is the difference between half the perimeter and this, or ...
(40 cm)/2 -6 cm = 14 cm
The length and width of rectangles A and B are 14 cm and 6 cm. When put together, they are joined on the 6 cm side.
Logan spent $42 to buy 4 basketballs. What was the price per basketball
Answer:
$10.5
Step-by-step explanation:
$42 for 4 basketballs
price of 1 basketball = 42/4
42/4 = 10.5
-Chetan K
Answer:
10.5 dollars
Step-by-step explanation:
42÷4=10.5