Answer:
The missing coefficient of the x-term of the product (-x-5)2 is 10.
Step-by-step explanation:
Solution:Through whole square formula.
(-x-5)2 = (-x)^2 -2(-x)(5)+(5)^2
=x^2+10x+25
Therefore, the missing coefficient of the x-term of the product is 10
Answer:
10
Step-by-step explanation:
The given expression is
[tex](-x-5)^2[/tex]
We need to find the coefficient of x.
According to the property of algebra.
[tex](a-b)^2=a^2-2ab+b^2[/tex]
In the given expression a=-x and b=5.
Substitute a=-x and b=5 in the above formula.
[tex](-x-5)^2=(-x)^2-2(-x)(5)+(5)^2[/tex]
On further simplification we get
[tex](-x-5)^2=x^2+10x+25[/tex]
Coefficient of x is a multiplicative factor of x.
Therefore, the coefficient of x is 10.
I need help
You find 20 books that you checked out from the library as you are cleaning your room. You need to take 4 books back to the library, and you want to set them aside in a pile on your desk. Â
How many ways can 4Â of the 20Â books be arranged in a pile?
Answer:
the answer is 20P4 = 4845
Step-by-step explanation:
Answer:
There are 20 ways to pick the first book, 19 ways for the second
Step-by-step explanation:
If order of the 4 books does not matter then
₂₀C₄ = 20! / (20-4)!4! = 20!/(16!*4!) = 4845 ways
The LAST QUESTION PLEASE HELP
The position d of a block that is attached to a spring is given by the formula d=6cos(pi/2 t) where t is in seconds. What is the maximum distance of the block from its equilibrium position (the position at which d = 0)? Find the period of the motion.
Step-by-step explanation:
Waves have the form:
y = A sin (2π/T x + φ) + B
where A is the amplitude (the distance from the center of the wave to the max or min),
T is the period (time it takes for one cycle),
φ is the phase shift (moves the wave left or right),
and B is the offset (moves the wave up or down).
This can also be written with cosine.
Here, we have d = 6 cos(π/2 t).
The amplitude is A = 6, so the maximum distance from the equilibrium position is 6 units.
The period is:
2π / T = π/2
T = 4
So the period is 4 seconds.
The corners of a square are cut off two centimeters from each corner to form an octagon. If the octagon is 10 centimeters wide, what is it's area?
Answer:
92 cm²Explanation:
The area of the octagon may be calculated as the difference of the area of the original square and the area of the four corners cut off.
1) Area of the square.
The original square's side length is the same wide of the formed octagon: 10 cm.
So, the area of such square is: (10 cm)² = 100 cm².
2) Area of the four corners cut off.
Since, the corners were cut off two centimeters from each corner, the form of each piece is an isosceles right triangle with legs of 2 cm.
The area of each right triangle is half the product of the legs (because one leg is the base and the other leg is the height of the triangle).
Then, area of one right triangle: (1/2) × 2cm × 2cm = 2 cm².
Since, they are four pieces, the total cut off area is: 4 × 2 cm² = 8 cm².
3) Area of the octagon:
Area of the square - area of the cut off triangles = 100 cm² - 8cm² = 92 cm².And that is the answer: 92 cm².
what is 12.25 as a fraction
Answer:
[tex]\large\boxed{12.25=\dfrac{49}{4}}[/tex]
Step-by-step explanation:
[tex]12.\underbrace{25}_{2}=\dfrac{1225}{1\underbrace{00}_2}=\dfrac{1225:25}{100:25}=\dfrac{49}{4}\\\\12.25=12+0.25=12+\dfrac{25}{100}=12+\dfrac{25:25}{100:25}=12+\dfrac{1}{4}\\\\=\dfrac{12\cdot4}{4}+\dfrac{1}{4}=\dfrac{48+1}{4}=\dfrac{49}{4}[/tex]
On a number line the directed line segment from Q to S has endpoints Q at -14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio.
Which expression correctly used the formula, to find the location of point R?
Answer:
Step-by-step explanation:
The distance from Q to S is 2 - (-14), or 16.
We start at point Q. Note how 3 and 5 add up to 8, which allows us to write:
R = Q + (3/8)(16), or R = -14 + 6, or R = -8.
From R to S it is (5/8)(16), or 10 units.
The directed line segment is partitioned into segments of lengths 6 and 10, whose combined length is 16, as expected.
Answer:
14/5 or A
Step-by-step explanation:
I just took this assignment.
PLEASE HELP ME
There are two answers!
x=-3
x = -2
x = -1
x = 0
x = 1
x = 2
x = 3
Answer:
x = 0x = 1Step-by-step explanation:
Find two rows in the table that have the same values in the f(x) and g(x) columns.
Describe the symmetry of the figure. Identify lines of symmetry, if any. Find the angle and the order of any rotational symmetry.
Answer:
The answer is D (line symmetry and rotational symmetry; 180o; order 2.
Step-by-step explanation:
You can fold the figure in half and it would be the same on both sides. The figure also has rotational symmetry because if you rotate the figure 180 degrees about the center, then it basically maps itself, or in other words, its the same. So the ANSWER IS D
line symmetry and rotational symmetry; 180 degree; order 2. Correct option is D.
The figure described exhibits characteristics of both reflectional and rotational symmetry. Firstly, it possesses reflectional symmetry because you can fold it in half, and both sides of the fold will be identical, essentially mirroring each other. This demonstrates that the figure can be divided into two equal parts that are reflections of each other along the fold line.
Furthermore, the figure displays rotational symmetry, specifically a 180-degree rotational symmetry. When you rotate it by 180 degrees about its center, the figure aligns with itself, showing that it remains unchanged upon this rotation. This means that you can rotate the figure halfway, and it will still appear identical.
So, the correct answer is not just "D," but rather a more comprehensive explanation of the figure's symmetrical properties, encompassing both reflectional and rotational symmetry.
to know more about rotational symmetry;
https://brainly.com/question/13268751
#SPJ3
By what factor does the area change if one diagonal is doubled? Explain.
The area of deltoid is defined by formula:
[tex]A=\dfrac{e\cdot f}{2}[/tex]
Where e and f are diagonals.
If you were to double the size of either one. Let's say f. You would result with:
[tex]A=\dfrac{e\cdot2f}{2}=e\cdot f[/tex]
Which means if either of diagonals double in length the area of deltoid will be twice as big as it was before.
Hope this helps.
r3t40
the kite, which looks more like a rhombus but being called a kite, will look like the one in the picture below.
now, as you see in the picture, the kite is really 4 congruent triangles, each with a base of 2.5 and a height of 5, so their area is
[tex]\bf \stackrel{\textit{area of one triangle}}{\cfrac{1}{2}(2.5)(5)}\implies 6.25\qquad \qquad \stackrel{\textit{area of all four triangles}}{4\left[ \cfrac{1}{2}(2.5)(5) \right]}\implies 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doubling the base or height}}{4\left[ \cfrac{1}{2}(2.5)(5)\underline{(2)} \right]}\implies \stackrel{\textit{the area is twice as much as the original}}{\underline{(2)}~~\left[ 4\left[ \cfrac{1}{2}(2.5)(5) \right] \right]}[/tex]
Did I do the first question right? can anyone please help me with the 2nd question? Would really appreciate the Help
Answer:
8. 1483.33
9. 21 months
Step-by-step explanation:
8. Morgan's income after taxes is 55000/12 = 4583.33 per month. The amount available after expenses is 4583.33 -3100.00 = 1483.33 per month.
Morgan is able to put $1483.33 per month into savings.
__
9. If Morgan is able to save $1483.33 per month, it will take her ...
$30,000/$1483.33 ≈ 20.2
months to save $30,000. After 20 months, she won't have quite enough, so it will take her one more month to save the desired amount.
It will take Morgan about 21 months to save $30,000.
_
If you like, you can write an equation for "m", the number of months it will take Morgan to save 30,000:
1483.33×m = 30,000
m = 30,000/1483.33 ≈ 20.2 . . . . . . divide by the coefficient of m
A bag contains marbles: 10 2 are green, 3 are red, and 5 are blue. Debra chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is red and the second is blue? Write your answer as a fraction in simplest form.
Choose the correct reason for each algebraic statement. A. Subtraction Property of Equality B. Combine like terms C. Distributive Property D. Division Property of Equality 3.__ 4.__ 5.__ 6.__
Answer:
b
Step-by-step explanation:
hope this helps
Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
D. 64 and 81
Step-by-step explanation:
The best benchmarks are the ones that are the closest to the value you want the root of. Perfect squares in that neighborhood are ...
7² = 498² = 64your number = 709² = 8110² = 100The closest are 64 and 81.
Research scientists need a certain type of bacteria to conduct an experiment. There are 2,500 bacteria in a certain culture. The culture grows at a rate of 25% daily. The scientists needs at least 10,000 bacteria to conduct an experiment. What is the least number of days they need to wait for the bacteria culture to reach a quantity of 10,000? (Hint: use a guess-and-check method to determine the lowest number of days that satisfy the requirement.)
Answer:
7 days
Step-by-step explanation:
At 25% per day, it will take approximately 3 days to double the population, so approximately 6 days for the population to quadruple. Checking that number, we find it is not quite enough for the experiment, so another day is required.
"Guess and check" as a method of solution works especially well if you have an automated checker to evaluate your guess. A graphing calculator or spreadsheet can work well for this.
_____
We guess 3 days as the doubling time using the "rule of 72" that says the product of percentage and doubling time is about 72. That is, 72/25 ≈ 3. (This is only a very rough approximation of doubling time, best for rates near 8%.)
Points A and B have coordinates (3,1,2) and (1,-5,4) respectively. Point C lies on line AB such that AC:BC=3:2. Find position vector of Point C.
Final answer is (-3,-17,8)
Answer:
The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k
Step-by-step explanation:
* Lets revise how to solve the problem
- If the endpoints of a segment are (x1 , y1 , z1) and (x2 , y2 , z2), and
point (x , y , z) divides the segment externally at ratio m1 :m2, then
[tex]x=\frac{m_{1}x_{2}-m_{2}x_{1}}{m_{1} -m_{2}},y=\frac{m_{1}y_{2}-m_{2}y_{1}}{m_{1}-m_{2}},z=\frac{m_{1}z_{2}-m_{2}z_{1}}{m_{1}-m_{2}}[/tex]
* Lets solve the problem
∵ AB is a segment where A = (3 , 1 , 2) and B = (1 , - 5 , 4)
∵ Point C lies on line AB such that AC : BC=3 : 2
∵ From the ratio AC = 3/2 AB
∴ C divides AB externally
- Lets use the rule above to find the coordinates of C
- Let Point A is (x1 , y1 , z1) , point B is (x2 , y2 , z2) and point C is (x , y , z)
and AC : AB is m1 : m2
∴ x1 = 3 , x2 = 1
∴ y1 = 1 , y2 = -5
∴ z1 = 2 , z2 = 4
∴ m1 = 3 , m2 = 2
- By using the rule above
∴ [tex]x=\frac{3(1)-2(3)}{3-2}=\frac{3-6}{1}=\frac{-3}{1}=-3[/tex]
∴ [tex]y=\frac{3(-5)-2(1)}{3-2}=\frac{x=-15-2}{1}=\frac{-17}{1}=-17[/tex]
∴ [tex]z=\frac{3(4)-2(2)}{3-2}=\frac{12-4}{1}=\frac{8}{1}=8[/tex]
∴ The coordinates fo point c are (-3 , -17 , 8)
* The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k
Given the parallelogram ABCD, solve for X when angle A equals (30+ 5x)° and angle D equals (15+10x)° degrees. Also, sides AB and CD opposite each other.
Answer:
x = 9
Step-by-step explanation:
Adjacent angles A and D are supplementary:
(30 +5x)° +(15 +10x)° = 180°
15x +45 = 180 . . . . . collect terms, divide by °
15x = 135 . . . . . . . . . subtract 45
135/15 = x = 9 . . . . . divide by the coefficient of x
The value of x is 9.
Evaluate x2 + 3x – 7+ 8 when x = 4.
Answer:
29
Step-by-step explanation:
Since they have given you x = 4, simply sub it into the equation,
(4)^2 + 3(4) - 7 + 8
= 29
Answer:
29
Step-by-step explanation:
Substitute 4 for x into the expression x^2+3x−7+8 and then simplify using the order of operations.
4^2+3(4)−7+8
16+12−7+8
29
A bag contains pieces of paper numbered from 5 to 9. A piece of paper is drawn at random. What is the theoretical probability of drawing a number less than 8?
Answer: 3/5 probability of choosing a number LESS THAN 8
Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.
Check the picture below.
so the parabola looks more or less like so, bearing in mind that the directrix is a horizontal line, thusu the parabola is a vertical one, so the squared variable is the "x".
The vertex is always half-way between the focus point and the directrix, as you see there, and the distance from the vertex to the focus is "p" distance, since the parabola is opening downwards, "p" is negative, in this case -2.
[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0\\ p=-2 \end{cases}\implies 4(-2)(y-0)=(x-0)^2\implies -8y=x^2\implies y=-\cfrac{1}{8}x^2[/tex]
To find the standard form of the parabola with a focus at (0, -2) and a directrix at y = 2, the process involves identifying the vertex, determining direction, and substituting into the general equation to get x² = -8y.
To find the standard form of the equation of a parabola with a focus at (0, -2) and a directrix at y = 2, we start by identifying key properties of parabolas. The vertex of the parabola is midway between the focus and the directrix. Here, the distance between the focus and the directrix is 4, so the vertex is 2 units away from each, placing it at (0, 0) as the directrix and focus are symmetrically placed above and below the x-axis.
The general equation for a parabola opening upwards or downwards is (x - h)² = 4p(y - k), where (h, k) is the vertex of the parabola, and p is the distance from the vertex to the focus (positive if the parabola opens upwards, negative if downwards). Given the focus (0, -2) and the vertex (0, 0), p = -2, indicating the parabola opens downwards. Applying these values to the general equation yields: x² = -8y, which is the standard form of the equation for the described parabola.
Given 250 mL of HCl HCI at 65% concentration how many milliliters of pure HCl are in the mixture? Help please
Multiply the total amount by the percentage.
250 mL x 0.65 = 162.5
The answer is 162.5 mL
Adelia drove from her house to Townsville one evening. Her distance was 180 miles. She left home at 6:27 and was at townsville at 6:42 what was her speed
Answer: 720 mph or 12 miles a minute
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
(I actually have the problem in front of me, and I think you switched the minute and hour hands on the clock)
Adel
left at 5:30 and arrived at 8:30. That’s 3 hours, which is 180 minutes. 180/180 = 1 mile per minute
60 minutes in an hour
60*1 = 60 mph
NEED HELP. PLEASE EXPLAIN.
Answer:
see explanation
Step-by-step explanation:
Using the exact values
sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]
Since the triangle is right use the sine/cosine ratios, that is
sin45° = [tex]\frac{TU}{TV}[/tex] = [tex]\frac{TU}{9\sqrt{2} }[/tex]
Multiply both sides by 9[tex]\sqrt{2}[/tex]
9[tex]\sqrt{2}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex] = TU, hence
TU = 9
-------------------------------------------------------------------------------
cos45° = [tex]\frac{UV}{TV}[/tex] = [tex]\frac{UV}{9\sqrt{2} }[/tex]
Multiply both sides by 9 [tex]\sqrt{2}[/tex]
9[tex]\sqrt{2}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex] = UV, hence
UV = 9
Since TU = UV = 9 , then triangle is isosceles
and ∠T = ∠V = 45°
Since we have computer algebra systems that can solve polynomial division problems for us, why is it necessary to learn how to do these things by hand?
Answer:
Probably because learning to do polynomials by hand boosts understanding of the topic and improves general algebraic solving ability,both of which are required in further topics like advanced calculus and algebra
Learning polynomial division by hand is crucial for understanding concepts, enhancing problem-solving skills, and fostering critical thinking in mathematics.
Explanation:The importance of learning polynomial division by hand despite the availability of computer algebra systems lies in developing a deep understanding of the underlying concepts, fostering problem-solving skills, and enabling visualization of geometric interpretations.
By manually carrying out mathematical operations, students can better grasp the logic behind the processes, which aids in building a strong foundation for more complex mathematical tasks.
Furthermore, mastering hand calculations equips students with the ability to perform quick mental math, apply critical thinking skills, and comprehend the practical applications of the mathematical concepts.
. Solve the following system of equations: 1. y - 3x + 15 = 10
2. 6 - 4x = y
The first equation can be further simplified so first do that by subtracting 15 to both sides
y - 3x + (15 - 15) = 10 - 15
y - 3x = -5
We know from the second equation that y is 6 - 4x so in the equation y - 3x = -5 plug in 6 - 4x for y
(6 - 4x) - 3x = -5
6 - 4x - 3x = -5
Combine like terms
6 - 7x = -5
(6 - 6) - 7x = -5 - 6
-7x = -11
Isolate x
-7x/-7 = -11/-7
x = 11/7
To solve for y plug in 11/7 in for x in the equation 6 - 4x = y
6 - 4(11/7) =y
6 - 44/7 = y
y = -2/7
so...
(11/7 , -2/7)
Hope this helped!
~Just a girl in love with Shawn Mendes
1.) Solving for X problem 1#
y-3x+15=10
-3x+15-15=10-15-y
-3x=-y-5
-3x/-3=-y-5/3
x=(-y-5)/3
2.) Solving for Y problem 1#
y-3x+15=10
y-3x+3x+15-15=10-15+3x
y=3x-5
1.) Solving for X problem 2#
6-4x=y
-4x+6-6=y-6
-4x/4=y-6/4
x=(y-6)/4
2.) Solving for Y problem 2#
6-4x=y
y=-4x+6
Hamad made a cuboid of size 2cm X 3cm X 4cm. How many such cuboids will be required to make a cube?
Answer:
576 cuboids
Step-by-step explanation:
Let
x -----> the length side of the cube
n -----> number of cuboids that are needed
we know that
The volume of the cuboid is equal to
[tex]V=(2)(3)(4)=24\ cm^{3}[/tex]
The volume of the cube is equal to
[tex]V=x^{3}[/tex]
Find the number of cuboids that are needed
[tex](n)24=x^{3}}[/tex]
n*24 must be a perfect cube
so
The minimum value that satisfied n to make n*24 a perfect cube is n=576
[tex]576*24=13,824=24^{3}[/tex]
Answer:
576 Cuboids
Step-by-step explanation:
Help !!!!! GEOMETRY PEOPLE HELP ME LOVES
The new triangle produced is an exact remake of the first one. The angles or size does not change between the two. Thus, this transformation is an Isometry.
Please help me with this problem.
Answer:
3
Step-by-step explanation:
You know that ...
1000 = 10³
when you take the logarithm to base 10, you get
log₁₀(1000) = 3
In the spinner below, the large wedges are twice the size of the smaller ones. What is true about the probability of landing on 4 and the probability of landing on 1?
Answer:
B The probability's are equal
Step-by-step explanation:
FOR APEX Hope i helped
Option: B is the correct answer.
The probabilities are equal.
( Since, probability of landing on 1 and on 4 are equal i.e. 1/8 )
Step-by-step explanation:The spinner is divided into two sizes such that the larger wedges are twice the size of the smaller ones.
The numbers that come on the smaller wedge are: 1,3,4 and 6
and those who come on the large wedge are: 2 and 5
If we divide the wedge which ere twice into equal sections then the total number of sections are:
8
We know that the probability of an event is defined as the ratio of number of favorable outcomes to the total number of outcomes.
The probability that the spinner lands on 1: 1/8( Since 1 is comprised of just one section out of total 8 sections)
Similarly,
The probability that the spinner lands on 2: 2/8( Since 2 is comprised of two sections out of total 8 sections)
The probability that the spinner lands on 3: 1/8( Since 3 is comprised of just one section out of total 8 sections)
Similarly,
The probability that the spinner lands on 4: 1/8The probability that the spinner lands on 5: 2/8The probability that the spinner lands on 6: 1/8HELP PLEASE! ONLY 5 MORE MINUTES! Look at the following shape below: Please find the PERIMETER of the following shape using the correct formulas. Use 3.14 for pi.
Answer:
The perimeter is [tex]P=73.12\ cm[/tex]
Step-by-step explanation:
we know that
The perimeter of the figure is equal to the circumference of a semicircle
plus the perimeter of a square minus the diameter of the circle
so
[tex]P=\pi r+4(b)-D[/tex]
we have
[tex]r=8\ cm[/tex]
[tex]b=16\ cm[/tex]
[tex]D=16\ cm[/tex]
The diameter of the circle is equal to the length side of the square
substitute
[tex]P=(3.14)(8)+4(16)-16[/tex]
[tex]P=25.12+64-16[/tex]
[tex]P=73.12\ cm[/tex]
PLEASE HELP ME!!!
Find p(–5) and p(3) for the function p(x) = 2x5 – 9x4 – 2x2 + 12x – 2. Question 8 options: –11,915; –251 –4,487; –551 –11,985; –225 –11,987; –227
Answer:
p(-5)=-11,987
p(3)=-227
Step-by-step explanation:
To find the value of the function p(-5) just substitute x=-5 into the function expression instead of x:
[tex]p(-5)=2\cdot (-5)^5-9\cdot (-5)^4-2\cdot (-5)^2+12\cdot (-5)-2=\\ \\=-6,250-5,625-50-60-2=-11,987[/tex]
To find the value of the function p(3) just substitute x=3 into the function expression instead of x:
[tex]p(3)=2\cdot 3^5-9\cdot 3^4-2\cdot 3^2+12\cdot 3-2=\\ \\=486-729-18+36-2=-227[/tex]
Answer with Step-by-step explanation:
We are given a function:
[tex]p(x) = 2x^5-9x^4-2x^2+12x-2[/tex]
We have to find the value of p(-5) and p(3)
[tex]p(-5) = 2\times (-5)^5-9\times (-5)^4-2\times (-5)^2+12\times (-5)-2\\\\=-6250-5625-50-60-2\\\\=-11987[/tex]
[tex]p(3) = 2\times 3^5-9\times 3^4-2\times 3^2+12\times 3-2\\\\=486-729-18+36-2\\\\=-227[/tex]
Hence, p(-5)= -11987
and p(3)= -227
The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to –z standard deviations from the mean?
Answer:
The right answer is B: The probability is equal to p%.
Step-by-step explanation: