Elijah made 14 quarts of punch for a party. How many gallons of punch did he make?
Answer:
3.5 gallons of punch
Step-by-step explanation:
There are 4 quarts in 1 gallon.
Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.
Elijah made 3.5 gallons of punch.
f(x) =2x^2+4x-6. g(x)=4x^3-6x^2+3 find (f+g)(x)
Answer:
=4x³-4x²+4x-3
Step-by-step explanation:
(f+g)(x)=4x³+2x²-6x²+4x-6+3
=4x³-4x²+4x-3
11. Find the coordinates of the point located six units behind the yz- plane, seven units to the right of the xz - plane, and eight units above the xy-plane. O x = -6, y = 7, z =-6 O x = -6, y = 7, z = 8 Ox=7, y = 7, z = 8 O x = 6, y= 7, z = 8
Answer: I think
Step-by-step explanation:Let the coordinate of the point be (x,y,z). Since the point is located 3 units behind the YZ− plane, 4 units to the right of XZ− plane and 5 units above the XY−plane ,x=−3,y=4 and z=5 Hence, coordinates of the required points are (−3,4,5)
What is the recursive formula for this geometric sequence?
6, -24, 96, -384, ...
Answer: a1=6
An = An-1 - 4
Step-by-step explanation:
N represent what number in the sequence you choose. So in the equation n-1 would be the umber in the equation subtracting 1 then subtracting the difference. The factor you are multiplying by in this sequence is -4. You find the difference by taking any number in the sequence and dividing it by the previous number in the sequence.
I NEED A.S.A.P PLEASE I WILL GIVE BRAINLIEST
Simplify: 5.9 (9 - 5) + 4^3 + 3.86 A. 63.06 B. 72.83 C. 91.46 D. 98.32
Answer:
C. 91.46
Step-by-step explanation:
Use BODMAS!
Answer:
C. 91.46
Step-by-step explanation:
Using Pemdas to solve:
5.9 (9 - 5) + 4^3 + 3.86
First you have to solve in the parenthesis
5.9 (9 - 5) + 4^3 + 3.86
= 4
New equation:
5.9 x 4 + 4^3 + 3.86
Now solve the exponent:
5.9 x 4 + 4^3 + 3.86
= 64
New equation:
5.9 x 4 + 64 + 3.86
Now we have to do multiplication:
5.9 x 4 + 64 + 3.86
= 23.6
New equation:
23.6 + 64 + 3.86
Now all you have to do is add all that together and you have your answer:
23.6 + 64 + 3.86
= 91.46
Hope this helps.
The slope of a line is 3. The y intercept of the same line is -12
Complete the slope intercept form equation
Answer:
y = 3x - 12
Step-by-step explanation:
Forming the slope-intercept equation :
y = mx + b
m = slopeb = y-interceptSubstitute m = 3 and b = -12 in the equation :
y = 3x - 12Answer:
y = 3x - 12
Step-by-step explanation:
The slope intercept form of a line is y = mx + b, where m is the slope and b is the y intercept. Here, m = 3 and b = -12. Therefore, the slope intercept form for this line is y = 3x - 12.
If sin Q = 4/5, cos P + cos Q
The value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We know that:
P + Q are complementary, which means that
P+Q = 90°
Then R is a right angle, i.e. it measures 90°.
sin(90-x) = cos (x)
cos(90-x) = sin (x)
Then sinQ = 4/5
cos(90-Q) = cosP = 4/5
Now sin²(P) + cos²(P) = 1
sin²(P) = 1 - cos²(P)
sin²(P) = 1 -[4/5]² =9/25
sin(P) = 3/5
cos(Q) = sin(P) = 3/5
cos(P) + cos(Q) = 4/5 + 3/5 = 7/5
Thus, the value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.
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An elevator began in the 9th floor. It went down 7 floors. Then, it went up 4 floors. On which floor did it stop?
Answer: Hope this helps you!
6th floor
Step-by-step explanation:
If it starts on the 9th floor and goes down 7 floors that is:
9 (9 floors) + -7 (down 7 floors)
which is also equal to 9-7
9-7 = 2
Next, we need to go up by 4 floors starting with 2, 2+4
2+4 = 6
Brainliest?
If LogN= 3.8609, find the value of N, to the nearest integer
[tex]~~~~~~~\log_{10} N = 3.8609\\\\\\\implies N = 10^{3.8609} ~~~~~~~~~;[\log_b c =d \implies b^d = c]\\\\\\\implies N \approx 7259[/tex]
Can you do it on paper and photos? the answer!
help me
The value of x in all case is
1. The value of x is 2
2. The value of x is 1
3.The value of x is 57
4.The value of x is 93
What is complementary and supplementary angle?If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
1. As the given angle is 90 degree i.e., complementary angle.
So,
54+10x+16=90
20=10x
x=2
2. 65x-12=43x+10 (Vertically opposite angle)
22x= 22
x=1
3. 72= x+15 (Vertically opposite angle)
x= 57
4.x+244+23=360 (Complete angle)
x=93
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Question 7 of 25
All else being equal, a study with which margin of error would give you the
most confidence in the results?
O A. 13 percentage points
OB. +12 percentage points
OC. 19 percentage points
OD. 16 percentage points
SUBMIT
Answer:
+12 percentage points
Step-by-step explanation:
All options have positive percentage in themselves
So lesser marginal error should be more applicable as lower the marginal errors lower the probability of doing mistakes so higher marks .
Option B
Question in the Picture
Step-by-step explanation:
the picture is not representing the real angle sizes. so, don't let yourself get confused by that.
the right neighbor angle of 90° at E is also 90°.
it has to be, because it is the supplementary angle to the left 90° (that means together they are 180°).
remember, all angles around a single point on one side of a line have to sum up to 180° (because the line can be seen as the diameter of a circle, with the point being the center of the circle, and so one side of the line is representing a half-circle and therefore 180°).
for the same reason angle 1 (the lower neighbor of the 90° angle at A) is also 90°.
for the same reason the lower neighbor angle of the 60° angle at E is 180 - 60 = 120°.
for the same reason the angle ABC is 180 - 40 = 140°.
for the angle BCD we need to remember :
the sum of interior angles of a polygon with n sides is
(n − 2) × 180°.
in our case ABCDE has 5 sides, so the sum of all interior angles is
(5 - 2) × 180 = 3×180 = 540°
we know 4 of the interior angles already, so
angle BCD = 540 - 90 - 90 - 120 - 140 = 100°
x is now the supplementary angle to the angle BCD.
so,
x = 180 - 100 = 80°
help solve these algebraic fractions please, with explanation would be great
Step-by-step explanation:
i answered it , and tried to give explanation too...
hope its helpful ,
If the coordinate of A is (0, -2) and the coordinate of B is (10, -6), the then midpoint of \overline{AB} AB is: Part A The X portion of the midpoint is __________________. Part B The Y portion of the midpoint is _________________.
Step-by-step explanation:
it is very simple :
the midpoint coordinates are created as the midpoint of the x coordinates, and the midpoint of the y coordinates.
the x coordinate of the midpoint is
(0 + 10)/2 = 10/2 = 5
the y coordinate of the midpoint is
(-2 + -6)/2 = -8/2 = -4
Year(x) 1971
Percent(y) 42.4
1978
37.4
1980
37.1
1984
34.1
1989
32.1
1993
28.8
1997
25.7
2000
25.5
Answer:
25.5
Step-by-step explanation:
I did the same assignment
Which pair of angles shares ray A and F as a common side?
The pair of angles that share a ray as a common side in the given diagram is: ∠FAB and ∠FAD.
What are Adjacent Angles?Adjacent angles are angles that lie adjacent or next to each other sharing a common vertex and have the same ray as a common side.
In the diagram attached below, ∠FAB and ∠FAD share a common vertex, A, and a ray FA as a common side.
Therefore, the pair of angles is: ∠FAB and ∠FAD.
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Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
B and C
Step-by-step explanation:
vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.
the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.
Compare the equations represented in the table, equation, and graph over
the interval
[-5, 3]. Which function is increasing the fastest?
Answer:
Tabled Function
Step-by-step explanation:
To determine which function is increasing the fastest over the interval [-5, 3], we need to calculate and compare each function's average rate of change over the given interval.
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given interval: -5 ≤ x ≤ 3
Therefore, a = -5 and b = 3
Tabled function[tex]f(3)=7[/tex]
[tex]f(-5)=-17[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-(-17)}{3+5}=3[/tex]
Equation: y = x² - 2[tex]f(3)=(3)^2-2=7[/tex]
[tex]f(-5)=(-5)^2-2=23[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-23}{3-(-5)}=-2[/tex]
Graphed functionFrom inspection of the graph:
[tex]f(3)\approx8[/tex]
[tex]f(-5) \approx 0[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)} \approx \dfrac{8-0}{3-(-5)}=1[/tex]
Therefore, the Tabled Function has the greatest average rate of change in the interval [-5, 3] and so it is increasing the fastest.
A bakery sold a total of 300 cupcakes in a day, and 57 of them were mocha flavored. What percentage of cupcakes sold that day were mocha flavored?
Write and simplify the expression equivalent to 2(7x + 3) + 9x.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression 2(7x+3)+9x.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
We need to multiply 2 times 7x and 3, and then add 9x.So, let's compute...
\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\//\\//\\\/
After performing multiplication we obtain
[tex]\star~\mathrm{14x+6+9x}[/tex]
Now add 9x:
[tex]\star~\mathrm{23x+6}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
Simplify the expression.
(x6y-6)
————
(x8y-8)
Mo buys a house for £120 000
He sells the house for £150 000
Work out the percentage profit that Mo makes.
Answer:
25%Step-by-step explanation:
The profit = 150 000 - 120 000 = 30 000
………………………………………………………
The profit percentage is :
[tex]=\frac{30000}{120000} \times 100=0.25 \times 100 = 25 \%[/tex]
true or false? The sum of the difference is not always zero for any distribution consisting of n observations
Answer:
i believe the answer is false !
Step-by-step explanation:
To which quadrants is tan^-1 x restricted?
A. Quadrants I and IV
B. Quadrants III and IV
C. Quadrants II and III
The quadrants is tan⁻¹x restricted is A. Quadrants I and IV
To answer the question, we need to know what tan⁻¹x is.
What is tan⁻¹x?tan⁻¹x is the inverse trigonometric function of tanx, which is the value of the angle for tanx.
Quadrant in which tan⁻¹x is restrictedTo find the quadrants in which tan⁻¹x is restricted, we know that tanx lies in the range
-∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°.
Since the inverse function of tanx is x.tan⁻¹x lies between -90° and 90°. That is -90° ≤ tan⁻¹x ≤ 90°.Since 90° lies in first quadrant and -90° lies in the fourth quadranttan⁻¹x lies between quadrant I and IV
So, the quadrants is tan⁻¹x restricted is A. Quadrants I and IV
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Solve the system of equations using substitution.
y=x+2,5x-4y=-3
Answer:
x=5 and y=7
Step-by-step explanation:
Just substitute in y=x+2 into the equation 5x-4y=-3 to get 5x-4(x+2)=-3 which simplifies to x=5. Substitute x into y=x+2 to find y=7
n music, a quaver is one-eighth of a semibreve (whole note). What fraction of a semibreve is a hemidemisemiquaver? (Hint: hemi-, demi-, and semi- are prefixes each of which represents a multiplication by one-half).
Answer:
[tex]\dfrac{1}{64}[/tex]
Step-by-step explanation:
Hemi-, demi- and semi- are prefixes which mean half.
When applied to musical notation, each time a prefix is added it means the note's value is halved.
Therefore, if a quaver is one-eighth of a semibreve, then a semiquaver is half of a quaver, which means it's one-sixteenth of a semibreve.
[tex]\large \begin{aligned}\sf quaver & = \sf\dfrac{1}{8}\:of\:a\:semibreve\\\\\implies \sf hemisemidemiquaver & = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times quaver\\\\& = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{8}\\\\& = \sf \dfrac{1}{64}\:of\:a\:semibreve\end{aligned}[/tex]
Therefore, a hemisemidemiquaver is one-sixty-fourth of a semibreve.
Helppp
The functions f and g are defined as follows:
#a
[tex]\\ \rm\Rrightarrow f(-4)[/tex]
[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]
[tex]\\ \rm\Rrightarrow -12+2[/tex]
[tex]\\ \rm\Rrightarrow -10[/tex]
#b
#1
[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]
Interchange x,y[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]
Find y
[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]
Inverse is
[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]
#2
[tex]\\ \rm\Rrightarrow gof(x)[/tex]
[tex]\\ \rm\Rrightarrow g(f(x))[/tex]
[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]
If we factor out
[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]
[tex]\\ \rm\Rrightarrow 2x+1[/tex]
#c
[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]
[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow 3(3x+2)=2x-1[/tex]
[tex]\\ \rm\Rrightarrow 9x+6=2x-1[/tex]
[tex]\\ \rm\Rrightarrow 7x=-7[/tex]
[tex]\\ \rm\Rrightarrow x=-1[/tex]
Answer:
Given functions:
[tex]f(x)=3x+2[/tex]
[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]
Part (a)
[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]
Part (b)(i)
[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]
Part (b)(ii)
[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]
n triangle ABC (see sketch), AD is the angle bisector of the angle A and BH is the height from side AC. The obtuse angle between BH and AD is four times the side of DAB. How big is the angle CAB?
A. 30 B.45 C.60 D.75 E.90
Answer: C
Step-by-step explanation:
We know that [tex]\angle AHB=90^{\circ}[/tex], and thus by the exterior angle theorem,
[tex]90^{\circ}+\alpha=4\alpha\\\\90=3\alpha\\\\\alpha=30^{\circ}[/tex]
Thus, [tex]\angle CAB=2\theta=\boxed{60^{\circ}}[/tex]
PLEASE HELP ASAP <3
Evaluate: 23+x/8 for x = 8
O 24
O 3.875
O 20
O 18
Answer:
Your first step would be to rewrite the equation, were x =8 so it would look like this
Step-by-step explanation:
23 + 8/8 = ?
than solve. 8/ 8 = 1 and 23+1 = 24
PLEASE HELP!!!!!!!!!
Answer:
CE = 4.6 ft
Step-by-step explanation:
(a)
given 2 secants drawn from an external point to the circle , then
the product of the external part of one secant and the entire secant is equal to the product of the other secant's external part and that entire secant, that is
BE × BC = AB × DB
(b)
substituting given values into the equation
BE × 10 = 3 × 18
10 BE = 54 ( divide both sides by 10 )
BE = 5.4 ft
then
CE = CB - BE = 10 - 5.4 = 4.6 ft