[tex]4(a + 3) = - 32 \\ 4a + 12 = - 32 \\ 4a = - 32 - 12 \\ 4a = - 44 \\ a = - 11[/tex]
Hope it helps
Please give brainliest
Step-by-step explanation:
4(a+3)=-32
4(a+3)/4=-32/4
(a+3)=-8
a+3-3=-8-3
a=-11
Make "t" subject by algebra:-
s=ut+at2
Andrea has 3 tiles. One is a regular octagon, one is a regular pentagon and one is a regular hexagon. Andrea thinks the 3 tiles will fit together perfectly, as shown in the diagram. Show calculations to prove that she is wrong.
From calculations, we can say that the given tiles will not fit together perfectly.
How to find the sum of interior angles of a Polygon?If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.
Expression for the measure of the interior angle of a polygon,
Interior angle of a polygon = [(n - 2) * 180]/n
Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°
Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°
Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°
To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°
Sum of all interior angles = 108° + 120° + 135° = 363°
Therefore, given tiles will not fit together perfectly.
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MATH!!! find the surface area of the prism
A chocolate chip recipe that produces 30 cookies calls for 2 1/4 cups of flour. If the math club decides to make fifteen dozen cookies for a bake sale, how many cups of flour will they need?
Answer:
2 1/4
Step-by-step explanation:
Please help!! Consider the equation x/5 -2=11, where x represents the
number of basketball players that have signed up for a
new league. What is a possible scenario that would be
modeled by this equation? Consider how many teams in
the league and the number of players on each team this
equation could describe
Answer:
x=65
Each NBA team can have a maximum of 15 players, 13 of which can be active each game.
65/5=13 so it's safe to say tgat 5 team can be crated
Step-by-step explanation:
x/5-2=11-->transposing x/5=11+2---->x=13×5--->x=65
verification 65/5-2=11--->13-2=11
What is the answer to the question?
Answer:
See attached file for answers and explanation.
Step-by-step explanation:
See attached image.
A survey found that 50% of teenagers prefer to watch a movie at a theater over other viewing options. You want to know the estimated probability that three out of four randomly chosen teenagers do not prefer watching a movie at a theater. How could you design a simulation for this situation?
To design a simulation for this situation, one can generate a set of four numbers by using the number generator with numbers 0 to 5 representing those who prefer watching a movie at a theatre and 6 to 9 representing those who do not.
How to depict the information?From the information given about the probability, the goal here is to design a simulation for this situation.
In this case, to design a simulation for this situation, one can generate a set of four numbers by using the number generator.
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On Friday, a local hamburger shop sold a combined total 312 of hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Friday?
What's an algorithm ?
Answer:An algorithm is a set of instructions for solving a problem or accomplishing a task.
Step-by-step explanation:
Any series of well defined steps that shows a procedure for solving a given type of problem is called an algorithm.
Step-by-step explanation:
Hope it helps you !!
(12 ÷ 3) + 3+ (16-7) × 4
Answer: 43
Step-by-step explanation:
Step 1: Simplify inside the parenthesis
(12 ÷ 3) + 3+ (16-7) × 4
4 + 3 + 9 × 4
Step 2: Multiply 9 by 4
4 + 3 + 36
Step 3: Combine Like Terms
43
The polygon shown is a regular pentagon.
K
108⁰
L
N
M
What is the sum of the measures of all the interior angles of this
pentagon?
OA) 504°
OC) 960°
O B) 540°
OD) 1080°
The sum of the measures of all the interior angles of the pentagon is 540°. Option B
How to determine the sumNote that
Sum of Interior Angles in a Pentagon = 540°
A pentagon is formed from three triangles, so the sum of angles in a pentagon = 3 × 180° = 540°
If one of the interior angles = 108°, then the other two angles = 2 * 108° = 216°
The sum of the interior angles = 108° + 216° = 540°
Therefore, the sum of the measures of all the interior angles of the pentagon is 540°
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Quadratic Equation Question
Answer: 0.68 or 13.92
Step-by-step explanation:
If the height is 47 meters, then the height, h, is equal to 47.
[tex]47=73t-5t^2\\\\5t^2 - 73t+47=0[/tex]
Using the quadratic formula,
[tex]t=\frac{-(-73) \pm \sqrt{(-73)^{2}-4(5)(47)}}{2(5)}\\\\\\t=\frac{73 \pm \sqrt{4389}}{10}\\\\\\ t=\frac{73+\sqrt{4389}}{10}, \frac{73-\sqrt{4389}}{10}\\\\\boxed{t \approx 0.68, 13.92}[/tex]
What is the measure of AC?
Enter your answer in the box.
°
Image shows a circle with angle A B C inscribed in a circle. Angle B measures 4 x minus 5.5 degrees. Arc A C measures 3 x plus 9 degrees.
Answer:
In the circle, the measure of the arc AC is 21°.
Step-by-step explanation:
Concept: We can use the Inscribed Angle theorem to get the measure of AC.
Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.
Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.
So,
3x - 1.5 = 0.5(3x + 9)
6x - 3 = 3x + 9
3x = 12
x = 4
Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,
intercepted arc AC is 21°.
Hence the intercepted arc AC is 21°.
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I need help lol xoxoxo
Type the expression that results from the following series of
steps:
Start with n, divide by m, then subtract p.
Answer:
(n/m) - p
Step-by-step explanation:
Image attached
Find the derivative of y = x^3/2.
Find the derivative of y = 1/x^3.
Find the derivative of y = 1/√x.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )= \dfrac{3}{2} \sqrt{x} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)= \cfrac{- 3}{ {x}^{4} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)= \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
properties to be used here :
[tex]\qquad \tt \rightarrow \:\cfrac{d}{dx}( {x}^{ n } ) = n \sdot{x}^{n - 1} [/tex]
[tex]\large \textsf{Question : 1} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )[/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3}{2} - 1 } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3 - 2}{2} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{1}{2} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} \sqrt{x} [/tex]
[tex]\large \textsf{Question : 2} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - 3} } )[/tex]
[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 3 - 1} } [/tex]
[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 4} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{- 3}{ {x}^{4} } [/tex]
[tex]\large \textsf{Question : 3} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{{x}^{ \frac{1}{2} } } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - \frac{1}{2} } } )[/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ - \frac{1}{2} - 1} } [/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 1 - 2}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 3}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2{x}^{ \frac{ 3}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
pleasee help with function graphing
Answer: A. The function has two distinct real zeros.
Answer:
C. The function has four distinct real zeros.
Step-by-step explanation:
The function intersects y=0 at x=1/2, 4, and 6 twice. It has two solutions at 6 twice as it is a behavior of polynomial or rational functions
Brian wants to fence in his triangular plot of farm land that measures 1.1 by 1.5 by 2.2 miles. Determine the angles at which the fences of the three sides will meet. 1.1 mi A 1.5 mi 2.2 mi B Rounding each angle to m/A 125 X = COMPLETE m/Ba DONE degrees
The angles at which the fences will meet is 27 , 38 ,114 degree.
What is a Triangle ?A triangle is a polygon with three sides , three angles and three vertices.
It is given that the triangle has sides
1.1 miles * 1.5 miles * 2.2 miles
The law of cosines can be used to calculate the angle
a² = b² + c² -2bc cosA
1.1² = 1.5² + 2.2² -2 *1.5 *2.2 cosA
A = 27.01 degree
Similarly
b² = c² +a² -2ac cosB
1.5² = 2.2² +1.1² -2 * 2.2*1.1 cos B
B = 38.27 degree
By angle sum property
Angle C = 180-38.27-27.01
C = 114.72 degree
Therefore , the angles at which the fences will meet is 27 , 38 ,114 degree.
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its math please help me
Answer:
460
Step-by-step explanation:
if you look at the values you'll notice the next month is just half their value
7360 / 2 = 3680
3680 / 2 = 1840
1840 / 2 = 920
so
920 / 2 = 460 which should be month 5
A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing
equipment at a gym is 10 feet high and extends 6 feet horizontally. Which statement best compares the slopes of the
two pieces of equipment?
Answer:
First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct
Step-by-step explanation:
This question deals with Slope of a line.
Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet
Thus, slope = 6/4 = 3/2 ≈ 1.5
For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet
Thus, slope= 10/6 = 5/3 ≈ 1.66
Thus,
Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3
Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct
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Please help me i would really appreciate it, worth 11 points
The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.
How to Evaluate a Function?We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:
h(t) = 0 (height of the ground is 0)t = seconds the waste takes to height the groundInitial height = 400 feetPlug in the values into the equation of the function
0 = -16t² + 400
Solve for t
0 - 400 = -16t²
-400 = -16t²
-400/-16 = t²
400/16 = t²
√(400/16) = t
20/4 = t
5 = t
t = 5
The number of seconds it takes is: 5 seconds.
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What is the nth term rule of the linear sequence below?
27, 25, 23, 21, 19, ...
Answer:
Step-by-step explanation:
Comment
This is an arithmetic series. It has the following givens.
a = 27 The first term
d = - 2 The difference between one term and the one behind it.
n = quite small
Tn = a + (n - 1)*d
tn = 27 - 2n + 2
tn = 29 - 2n
Instructions: Write the equation for the following
function. Do not use any spaces in your answer.
X
0
1
2
-1
y
0
-2
-4
-12
Y=
The function of the given data would be F(x) = y = 4x.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
X(input) Y ( output)
0 0
1 4
2 8
3 12
We can see that
When the input is zero the output is also zero.
And when the input is some real number the output gives the multiple of 4.
Thus, The function could be
f(x) = 4x
The given function is represented by x as the independent variable.
Therefore, The function of the given data would be F(x) = y = 4x.
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the cost of 10 water bottles is $55. find the unit cost of the water bottle
Answer:
$5.50
Step-by-step explanation:
For one water bottle you divide the 55 dollars by 10
55/10= 5.5
Answer:
$5.50
Step-by-step explanation:
We must divide to solve so lets do that now :)
55/10 = 5.50
Each bottle will cost 5 dollars and 50 cents :)
Have an amazing day!!
Please rate and mark brainliest!!
6. Given that the term independent of x in the binomial expansion of (x²+p/x)^6 is 240,
(a) find the value of the positive constant p
By the binomial theorem,
[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]
where
[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]
is the so-called binomial coefficient.
The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have
[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]
but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]
Write the rationalized expression of:
Answer:
A
Step-by-step explanation:
First, simplify the numerator:
[tex]\frac{3 }{\sqrt{3} + \sqrt{x} } \\[/tex]
Next, multiply the numerator and denominator by the opposite of the denominator to rationalize the expression.
[tex]\frac{3}{\sqrt{3}+\sqrt{x} }*\frac{\sqrt{3}-\sqrt{x} }{\sqrt{3}-\sqrt{x}}[/tex]
Finally, evaluate the denominator by multiplying them together.
[tex]\frac{3(\sqrt{3}-\sqrt{x})} {(\sqrt{3}+\sqrt{x})(\sqrt{3}-\sqrt{x})}[/tex]
Simplify:
[tex]\frac{3(\sqrt{3}-\sqrt{x})} {3-x}[/tex]
And done! :)
PLEASE HELP ASAP!!!!!
Which equation is the polar equivalent to the equation y=−3√x?
A. 0= pi/6
B. 0=pi/3
C. 0=2pi/3
D. 0=5pi/6
The value of θ = pi /3 , Option B is the correct answer.
What is an Equation ?A statement in mathematics used to correlate two algebraic expressions by using an equal sign is called an Equation.
x = rcosθ
y = rsinθ
The equation given is
[tex]y = -\sqrt{3} \;x[/tex]
rsinθ = - [tex]\sqrt{3}[/tex] [tex]\rm {r \; cos\; \theta}[/tex]
sin θ / cos θ = - [tex]\sqrt{3}[/tex]
tan θ = -[tex]\sqrt{3}[/tex]
θ = pi /3
Therefore Option B is the correct answer.
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What is equivalent to 3(5-2i)?
Answer:
Step-by-step explanation:
One equivalent can be obtain by distributing multiplication with 3 over subtraction 5-2i
3(5-2i) =
3·5 -3·2·i =
15 -6i or -6i +15
On day 1, Perry shipped packages and tracked their weight to the nearest kilogram. The packages weighed 1, 8, 1, 12, 1, 11, 7, and 6 kilograms.
On day 2, Perry shipped 12 kilograms more weight than he did on day 1 while shipping the same number of packages.
What is the increase in the mean kilograms per package for the second day compared to the first?
Enter your answer in the box.
Answer:
1.5kg
Step-by-step explanation:
The mean for the packages on day 1 will be:
= (1 + 8 + 1 + 12 + 1 + 11 + 7 + 6)/8
= 47/8
= 5.875
The mean for day 2 will be:
= (47 + 12)/8
= 59/8
= 7.375
The increase in mean:
= 7.375 - 5.875
= 1.5
Use the law of cosines to find each missing side. Round to the nearest tenth
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
As per the law of cosine, the measure of angle x can be written as,
[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]
Hence, the value of x is 117.8°. thus, the correct option is A.
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