Answer:
x² - 10x + 25
Step-by-step explanation:
The formula for squaring any binomial (an expression with two terms) is:
(a ± b)² = a² ± 2ab + b²
Let a = x and b = 5.
∴ Substituting:
(x - 5)² = x² - 2(x)(5) + (-5)²
= x² - 10x + 25
If students sit 4 per row on a rollercoaster, 6 students are left without a seat.
If they sit 6 per row, there are 3 rows left empty. How many students are
there?
An expression is defined as a set of numbers, variables, and mathematical operations. The total number of students is 54.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Let the number of columns in the rollercoaster be represented by x.
If students sit 4 per row on a rollercoaster, 6 students are left without a seat. Therefore, the number of students can be written as,
Total number of students = 4x + 6
If they sit 6 per row, there are 3 rows left empty. Therefore, the total number of students can be written as,
Total number of students = 6(x-3)
The total number of students can be written as,
4x + 6 = 6(x - 3)
4x + 6 = 6x - 18
2x = 24
x = 12
Now, the total number of students in the class are,
4x + 6 = 4(12) + 6 = 54
Hence, the total number of students are 54.
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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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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:
Sandhu lights a candle at 6 pm. It is 30 cm high. At 7pm, the candle is 27 cm high. At 8pm, it is 24cm high. a) How many cm does the candle burn down every hour? b) How high is the candle at 11 pm?
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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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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MisterBrainly (also known as Enstine) lets out 100 feet of string on a kite from a hand height of 3 feet. The angle between horizontal hand height and the kite is 25º. Find the height of the kite above the ground, to the nearest foot.
Answer: I love the picture example
Step-by-step explanation:
We will first find the heigh of the kite from his hand to a point in the air.
Then, we will add 3 feet to the result.
So, how to find the vertical line of the right triangle?
Well, we have the vertical line = x
We also got the hypothenuse, equal to 100 feet
And also theta, equal to 25 degrees.
We can calculate sine because the sine of 25 degrees = opposite side (the height line) over (divided by) the hypothenuse
sin(25) = x/100 feet
multiply 100 feet on both sides, to cancel to 100 feet on the right side.
100sin(25) = x
100(0.442) = x
x = 42.2 feet
Height = 42.2 + 3 feet (the yoda's hand =) = 45.2 feet (total)
Rounded to the nearest tenth.
I also did the verification, so it is the correct answer.
Easy as that =]]
Height of the kite from 3ft above the ground
[tex]\\ \rm\Rrightarrow sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow sin25=\dfrac{P}{100}[/tex]
[tex]\\ \rm\Rrightarrow P=100sin25[/tex]
[tex]\\ \rm\Rrightarrow P=42.26\approx 42ft[/tex]
Height from the ground
42+345ft(Rounded)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]
The chart below shows the distribution of the number of books in a library.Sahira chooses a random sample from the library and records the type of books in the chart below.
Answer:
you have jbjhgbjhih7g6ginyfygino
Jean had $25.86 in her pocket. If shoes cost $7.50 a pair plus 10% of tax. How many pairs can she buy?
Answer:
3 pairs
Step-by-step explanation:
10% of 7.50 is 0.75. So one pair will cost $8.25. Now, 25.86/8.25 and you get 3 pairs
Answer:
[tex]\fbox {3 pairs}[/tex]
Step-by-step explanation:
Cost of 3 pairs with tax :
⇒ 7.50 × 3
⇒ 22.50
* Adding tax *
⇒ 22.50 + 22.5 (0.1)
⇒ 22.50 + 2.25
⇒ 24.75
∴ Since 24.75 is less than 25.86, Jean can buy 3 pairs of shoes.
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!!
find the maxium value of 16x+ 96y
follow p
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
It is given that x² - y² = 30 and x - y = 5. Find the value of (x + y)².
Answer:
36
Step-by-step explanation:
when solving for two variables, we need to find one variable in terms of the other.
so, we can turn:
x - y = 5
into
x - y = 5
+ y + y
x = y + 5
Then, we can substitute "x" in the given equation with "y + 5"
x² - y² = 30
(y+5)² - y² = 30
(y + 5)(y + 5)
F: y² O: +5y I: +5y L: 25 {foil}
y² + 10y + 25 - y² = 30 {cancel y² - y²}
10y + 25 = 30
-25 -25
10y = 5
÷10 ÷10
y = 0.5
x = y + 5
x = 0.5 + 5
x = 5.5
check:
(5.5)² - (0.5)²
30.25 - 0.25 = 30
30 = 30
(TRUE)
now, we must find the value of:
(5.5 + 0.5)²
= (6)²
= 36
So, the value of (x + y)² is found to be 36
hope this helps!!
Answer:
(x + y)² = 36
Step-by-step explanation:
x² - y² ← is a difference of squares and factors as
(x - y)(x + y) , then
5(x + y) = x² - y² = 30 ( divide both sides by 5 )
(x + y) = 6 , then
(x + y)² = 6² = 36
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 !!I need help lol xoxoxo
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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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
(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
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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PLEASE HELP - image attachment below, thanks! :)
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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Make "t" subject by algebra:-
s=ut+at2
help me with this question please, thank you !
Answer:
2
Step-by-step explanation:
[(27divided by (-3)-9] divided by [15-21}
=[-9-9] divided by 3
= 6divided by 3 = 2
if answer is correct so mark me as brain lest :-)
Give your answer in the form y = mx + c , where m and care integers or fractions in their simplest forms.
PLLLEAASSEE HELP ME!!
AND IF YOU DON"T MIND EXPLANING TO ME HOW TO SLOVE THESIS TYPE OF PROBLEMS CAUSE IM SO CONFUSED
Answer:
75 Seconds
Step-by-step explanation:
First divide 90,000 by 16 then square root that answer for 75 and when you plug it in you'll end up with -90,000 + 90,000
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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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
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
