Answer:
The value of k is 4 and q is 16.
Step-by-step explanation:
First, you have to expand the brackets by applying :
[tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]
[tex] {x}^{2} + 8x + q = {(x + k)}^{2} [/tex]
[tex] {x}^{2} + 8x + q = {x}^{2} + 2kx + {k}^{2} [/tex]
Next, you have to do it by comparison :
[tex] {x}^{2} + 8x + q = {x}^{2} + 2kx + {k}^{2} [/tex]
[tex]by \: comparison[/tex]
[tex]8x = 2kx[/tex]
[tex]8 = 2k[/tex]
[tex]k = 4[/tex]
[tex]q = {k}^{2} [/tex]
[tex]q = {4}^{2} [/tex]
[tex]q = 16[/tex]
If f(x)=3x-1 and g(x)=x+2, find (f-g)(x)
Answer:
2x - 3
Step-by-step explanation:
[tex]f(x) = 3x - 1 \\ g(x) = x + 2 \\ (f - g)(x) = f(x) - g(x) \\ = 3x - 1 - (x + 2) \\ = 3x - 1 - x - 2 \\ = 3x - x - 1 - 2 \\ (f - g)(x) = 2x - 3[/tex]
Solve and check |2x − 1| = |4x + 9|
Answer:
x = -5 or x = -4/3
Step-by-step explanation:
First possibility.
|2x − 1| = |4x + 9|
2x - 1 = 4x + 9
2x - 4x = 9 + 1
-2x = 10
x = 10/-2
x = -5
Second possibility.
2x - 1 = - (4x+9)
2x - 1 = -4x - 9
2x + 4x = -9 + 1
6x = -8
x = -8/6
x = -4/3
Answer:
[tex] |2x - 1| = |4x + 9| [/tex]
this equation can be separated into 2 possible cases :
[tex]2x - 1 = 4x + 9[/tex]
and
[tex]2x - 1 = - (4x + 9)[/tex]
solve the 1st possible case:
[tex]2x - 1 = 4x + 9[/tex]
[tex]2x - 4x = 9 + 1[/tex]
[tex] - 2x = 10[/tex]
[tex]x = - \frac{10}{2} [/tex]
[tex]x = - 5[/tex]
solve the 2nd possible case:
[tex]2x - 1 = - (4x + 9)[/tex]
[tex]2x - 1 = - 4x - 9[/tex]
[tex]2x + 4x = - 9 + 1[/tex]
[tex]6x = - 8[/tex]
[tex]x = \frac{ - 8}{6} [/tex]
[tex]x = - \frac{4}{3} [/tex]
so the x value for this equation is:
x = -5 or x = -1.333
Find the acute angle between the sides of a rhombus whose diagonals are 8cm and 12cm long
Answer:
67.38°
Step-by-step explanation:
The diagonals of a rhombus intersect at their midpoints and make a right angle. They also divide the angles of the rhombus in two equal angles.
So, to find the acute angle of the rhombus, we can use the tangent relation of half this angle in the small triangle made when drawing the diagonals:
tan(angle/2) = 4 / 6
tan(angle/2) = 0.666
angle/2 = 33.69
angle = 67.38°
So the acute angle of the rhombus is 67.38 degrees.
Please check the image attached for better comprehension.
Translate into an algebraic expression: If I travel d miles in h hrs downstream on a river with a current of c mph, what would my speed in still water have been?
Answer:
The speed is still water is [tex]v = \frac{d}{h} - c[/tex].
Step-by-step explanation:
Dimentionally speaking, speed is distance divided by time. Since, the person is travelling downstream, absolute speed is equal to the sum of current speed and speed of the person regarding current. Both components are constant. That is:
[tex]c + v = \frac{d}{h}[/tex]
Where:
[tex]c[/tex] - Current speed, measured in miles per hour.
[tex]v[/tex] - Speed of the person regarding current, measured in miles per hour.
[tex]d[/tex] - Distance travelled downstream, measured in miles.
[tex]h[/tex] - Time spent on travelling, measured in hours.
Speed in still water occurs when current speed is zero. Then, such variable is obtained after subtracting current speed on both sides of the expression. Hence:
[tex]v = \frac{d}{h} - c[/tex]
The speed is still water is [tex]v = \frac{d}{h} - c[/tex].
What is the equation of the line that is perpendicular to and
has the same y-intercept as the given line?
O y=x+1
Oy=x+5
O y = 5x + 1
O y = 5x + 5
Answer:
y=5x+1 (this may be correct but I can't guarantee because you haven't provided graph)
Step-by-step explanation:
step 1
Find the slope of the given line
we have
(0,1) and (5,0)
m=(0-1)/(5-0)
m=-1/5
step 2
Find the slope of the perpendicular line to the given line
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
m1*m2=-1
m1=-1/5
substitute
(-1/5)*m2=-1
m2=5
step 3
Find the equation of the line with slope m=5 and y-intercept (0,1)
The equation of the line into slope intercept form is equal to
y=mx+b
we have
m=5
b=1
substitute
y=5x+1
please mark me brainliest!
please help fast please
Answer:
here
Step-by-step explanation:
a= 4. 8, 12
b= 4, 7, 10
d= 3, 6, 11
e= 3, 12, 27
PLEASE HELP, SOLVE THIS PROBLEM AND GIVE ME THE ANSWER!!!
Answer:
The answer is option B
f(x) = 4x + 8
g(x) = 9x + 7
(fg)(x) = (4x + 8)(9x + 7)
= 36x² + 28x + 72x + 56
= 36x² + 100x + 56
Hope this helps
Answer:
B
Step-by-step explanation:
4x5-6+22=x what is x?
Answer:
36
Step-by-step explanation:
[tex]4\times 5-6+22=x \\\\20-6+22=x \\\\14+22=x \\\\x=36[/tex]
Hope this helps!
A donut shop is experimenting with two new types of cream-filled treats, one with raspberry filling, and the other with peach. A batch of raspberry donuts cooks in 11 minutes while a batch of peach donuts cooks in only 8 minutes. Let x represent the number of raspberry-filled donuts and let y represent the number of peach-filled donuts. Write an inequality to represent how many batches of the new type of donuts can be produced in a 10 hour day. a. c. b. d.
Step-by-step explanation:
X= raspberry
X = 600 ÷ 11 = 54 batches
[ 60 minutes = 1 hour]
[600 minutes = 10 hours]
Y = peach
Y = 600 ÷ 8 = 75 batches
Answer:
its b
Step-by-step explanation:
it just is
A right pyramid with a square base has a base edge length of 12 meters and slant height of 6 meters. The apothem is meters. The hypotenuse of ΔABC is the . The height is meters. The volume of the pyramid is cubic meters.
Answer:
Apothem: 6m
hypotenuse : slant height : 6√2 m
height :6m
volume: 288m2
Step-by-step explanation:
Hi, the correct values are: (image attached down below)
Base length= 12m
Slant height is actually = 6√2
So, to calculate the apothem (AC)we apply the Pythagorean theorem:
AB^2 = AC^2 + BC^2
√AB^2 -BC^2 = AC
AC = √(6√2)^2 - 6^2
AC =6 meters
Hypotenuse of ABC = AB =6√2 meters
Height = AC = 6 meters
Volume:
Volume of a pyramid = 1/3 x base area x height
area of a square = side length ^2 = 12^2
V= 1/3 x 12^2 x 6 =288 m2
Answer:
A right pyramid with a square base has a base edge length of 12 meters and slant height of 6StartRoot 2 EndRoot meters.
The apothem is
✔ 6
meters.
The hypotenuse of ΔABC is the
✔ slant height
.
The height is
✔ 6
meters.
The volume of the pyramid is
✔ 288
cubic meters.
Step-by-step explanation:
(8x - 4)(7y + 2) multiplying binomials
Step-by-step explanation:
8x(7y+2)-4(7y+2)
=56xy+16x-28y-8
Answer:
56xy+16x-28y-8
Step-by-step explanation:
you have to use the FOIL method to solve this is problem which is
F-First
O-Outer
I-Inner
F-Last
HERE'S A FUN ONE... KINDA! (:
The manager of a local cable company has hired an advertising agency to find out which is the most popular cartoon channel on cable. Which population should the agency sample to get the most reliable information?
A. cable subscribers between the ages of 21 and 40
B. cable subscribers who are parents of children between the ages of 3 and 10
C. children between the ages of 3 and 10
D. children who attend a local elementary school
I'LL ALSO GIVE BRAINLIEST TO WHOEVER ANSWERS CORRECTLY!
Answer:
Your answer is C
Step-by-step explanation:
What is the volume of the prism below?
A. 288 units3
B. 144 units3
C. 180 units3
D. 56 units3
The volume of the given figure is 288 cubic units.
Given a prism with the base dimension of 8×12 units and the height of 3 units.
From the general formula of the volume of the prism,
The volume of a prism is the product of the area of the base and the height of the prism. Prism volume (V) = B × h,
where, B is the area of the base and h is the height of the prism. = l × w × h,
where l, w, and h are the length, width, and height of the rectangular prism.
In our case,
l = 12
w =8
h =3
Volume of the prism = 12 *8 * 3
Volume of the prism = 288
Therefore, the volume of the prism will be 288 cubic units.
Learn more about Volume here:
https://brainly.com/question/1578538
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what is the answer of this attachment:
Answer:
(B) 2
Step-by-step explanation:
=> [tex]\frac{\sqrt{32}+ \sqrt{48} }{\sqrt{8}+\sqrt{12} }[/tex]
=> [tex]\frac{4\sqrt{2}+4\sqrt{3} }{2\sqrt{2}+2\sqrt{3} }[/tex]
=> [tex]\frac{4(\sqrt{2}+\sqrt{3}) }{2(\sqrt{2}+\sqrt{3)} }[/tex]
Cancelling [tex]\sqrt{2}+\sqrt{3}[/tex]
=> [tex]\frac{4}{2}[/tex]
=> 2
if you can answer this you are a star , plzz i need help
Answer:
[tex]\left[\begin{array}{ccc}9\\10\\\end{array}\right][/tex]
Step-by-step explanation:
Multiply the components of A by 3 then add corresponding components of
3a + b
3[tex]\left[\begin{array}{ccc}2\\4\\\end{array}\right][/tex] + [tex]\left[\begin{array}{ccc}3\\-2\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}6\\12\\\end{array}\right][/tex] + [tex]\left[\begin{array}{ccc}3\\-2\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}6+3\\12-2\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}9\\10\\\end{array}\right][/tex]
PLease help asap I will give 5 stars please help
[tex]answer \\ < a = 114 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Work of the size of one exterior angle
Answer:
<x = 36°
Step-by-step explanation:
In a regular decagon, Every interior angles is equal to 144.
So,
<x + 144 = 180 [Angles on a straight line]
<x = 180-144
<x = 36°
Given that ABCD is a rhombus, find the value of x.
Answer:
C
Step-by-step explanation:
The diagonals of a rhombus are perpendicular bisectors of each other.
Thus the angle at the intersection of the diagonals is 90°
The sum of the 3 angles in a triangle = 180°
Sum the angles in the lower triangle and equate to 180, that is
90 + x + x + 40 = 180
2x + 130 = 180 ( subtract 130 from both sides )
2x = 50 ( divide both sides by 2 )
x = 25 → C
The value of x is 25.
What are some of the properties of a rhombus?
All four sides are equal.Diagonals bisect each other at 90°.Given
ABCD is a rhombus,
∠CAD = x°,
∠BDA = (x + 40)°.
Find the equation in x
Let the point where the diagonals intersect be E.
Then, using the property of the rhombus ∠AED = 90°.
We know, in a triangle that the sum of all the three interior angles equals 180°. So, we get,
∠AED + ∠BDA + ∠CAD = 180°
⇒ ∠BDA + ∠CAD = 180° - ∠AED
= 180° - 90° = 90° (∠AED = 90°)
Put the given values of these angles,
(x + 40)° + x° = 90°.
This is the equation to be solved to obtain x.
Solve for x
(x + 40)° + x° = 90°
⇒ (2x)° = 90° - 40° = 50°
⇒ x° = (50 / 2)°
⇒ x = 25.
The required value of x is 25.
Learn more about the properties of a rhombus here
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help me pls if you now the question
Answer:
a) 7540
b) 43.39
Step-by-step explanation:
a)
[tex]\frac{245*20^2}{13} =\\\\\frac{245*400}{13}=\\\\\frac{98000}{13}=\\\\7540[/tex]
(to the nearest 10.)
b)
[tex]\sqrt{58-29}+38=\\\sqrt{29}+38=\\5.39+38=\\43.39\\or\\43.38[/tex]
(to the nearest hundredth)
43.38 is rounding down, 43.39 is rounding up. (43.385)
Mr. Bloop can high jump 5.75 feet. How far short is that of Charles Austin's record of 7 ft 10 in?
Answer:
5.75 feet is the same as 5 ft 9 inches (because 12 in = 1 ft and 0.75 * 12 = 9 so its 9 in). 7 ft 10 in - 5 ft 9 in = 2 ft 1 in.
At work Bret must check and record the internal temperature of the freezer on an hourly basis when working properly the temperature should remain constant over time.What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly
Answer:
The slope of the line will be ZERO.
From the question given above, we are told that when the freezer is working perfectly that the temperature will remain constant over time. This means that if the graph of temperature and time is drawn, the slope of the graph will be constant from one point of the graph to the other, which means that the values will cancel each other out and will be zero.
PLEASE HELP, SOLVE THIS PROBLEM AND GIVE ME THE ANSWER!!!
Hey there! :)
Answer:
C.
Step-by-step explanation:
(f · g)(x), substitute in g(x) for 'x':
[tex](f og)(x)=\frac{4}{\frac{1}{8x}+ 7 }[/tex]
Make denominator contain a common denominator:
[tex](fog)(x) = \frac{4}{\frac{1+56x}{8x} }[/tex]
Dividing fractions, so multiply by reciprocal:
[tex](fog)(x) = 4 * \frac{8x}{1+56x}[/tex]
Multiply and simplify:
[tex](fog)(x) = \frac{32x}{1+56x}[/tex]
Therefore, the correct answer is C.
Jimmie invested $27,500 at 6.27% compounded continuously. What will Jimmie's account balance be in 50 years?
Answer:
Input:
6.27
Result:
6.27
HELP ASAP PLEASE!!! Solve: 3x – 2y when x = 2 and y = 10. A. 5 B. -14 C. -12 D. NONE OF THESE E. 16
Answer:
3x - 2y
= 3(2) - 2(10)
= 6 - 20
= -14
the answer is C
Answer:
[tex]x=2[/tex]
[tex]y=10[/tex]
So the multiply 3 × 2
[tex]3 * 2=6[/tex]
Then multiply 2 × 10
[tex]2 * 10=20[/tex]
Then subtract 6 - 20.
This shows that the answer will be negative.
[tex]6-20= -14[/tex]
So the answer is [tex]-14[/tex]
Hope this helps
(＾▽＾)
Someone plsss plss help me ima cryy!!!
Answer:
1) Business costs less. It costs $8 less.
2) they cost the same at 14 HCF both equaling $24. Residential would cost more if it goes over 14 HCF per month.
Give your answers to 1 d.p. where necessary
Answer:
Step-by-step explanation:
Since the drawing is in millimeters (mm), and the scale is 1 cm to 1 m, then, considering that 10 mm equal 1 cm, we can easily convert the given values to cm by simply dividing the numbers by ten, and then use those numbers as real meters based on the
I'm taking a class in FLVS I finished segment 1 and I need to add another course for segment 2 and I don't know how to do that? Please help
Answer:
You could simply go to your course selection book (if there is one) and see if it's there. If not, then ask your guidance counselor for help or if you can automatically advance.
Step-by-step explanation:
Solve the simultaneous equations 2x + 4y = 1 3x - 5y = 7
Answer:
(1.5, - 0.5 )
Step-by-step explanation:
Given the 2 equations
2x + 4y = 1 → (1)
3x - 5y = 7 → (2)
Multiplying (1) by 3 and (2) by - 2 and adding will eliminate the x- term
6x + 12y = 3 → (3)
- 6x + 10y = - 14 → (4)
Add (3) and (4) term by term to eliminate x
22y = - 11 ( divide both sides by 22 )
y = - 0.5
Substitute y = - 0.5 into either of the 2 equations and solve for x
Substituting into (1)
2x + 4(- 0.5) = 1
2x - 2 = 1 ( add 2 to both sides )
2x = 3 ( divide both sides by 2 )
x = 1.5
Solution is (1.5, - 0.5 )
Enter the solutions from least to greatest. (x +1)(3x +4)=0 urgent i need help
Answer:
x = - [tex]\frac{4}{3}[/tex], x = - 1
Step-by-step explanation:
Given
(x + 1)(3x + 4) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
3x + 4 = 0 ⇒ 3x = - 4 ⇒ x = - [tex]\frac{4}{3}[/tex]
Solutions from least to greatest are
x = - [tex]\frac{4}{3}[/tex] , x = - 1
Help would really be appreciated :) A box of a truck has dimensions 1m by 2m by 4m. Explain how this truck was able to carry 9m cubed of sand?
(I'm in the volume unit & will give brainliest)
Answer:
The truck will be able to carry 9m because the volume is 8m.
Step-by-step explanation: The questions give the demensions, so you have to multipy it. 1x2x4 is 8. So it would be able to carry 9m of sand.
Answer:
The shape of the box of the truck is a rectangular prism.
volume = length * width * height
volume = 4 m * 2 m * 1 m = 8 m^3
The volume of the box of the truck is 8 m^3.
One way it can carry more than that volume is if it does not have a roof. Then 8 m^3 can be loaded up to the height of the box, and an extra 1 m^3 can by on top of that, above the sides of the box.
Another way is, if it does have a roof, to fill the inside of the box with 8 m^3 and place an extra 1 m^3 on top of the roof of the box.
