Answer:
-2-2√3, -2+2√3
Step-by-step explanation:
Let x represent one of the numbers. Then the other number is -4-x. We want the product to be -8:
x(-4-x) = -8
-4x -x^2 = -8 . . . . . eliminate parentheses
x^2 +4x = 8 . . . . . . multiply by -1
x^2 +4x +4 = 12 . . . add 4 to complete the square
(x +2)^2 = 12
x +2 = ±√12 = ±2√3
x = -2±2√3
The two numbers are -2-2√3 ≈ -5.4641, and -2+2√3 ≈ 1.4641.
To find two numbers that multiply to -8 and add to -4, we can guess and check until we find a pair that satisfies both conditions. The two numbers in this case are -4 and 2.
Explanation:
The question is asking for two numbers that, when multiplied together, equal -8 and, when added together, equal -4. This falls under the category of quadratic equations. To solve this problem, we would typically use the formula "x = [ -b ± sqrt(b² - 4ac) ] / 2a", but in this case, it's easier to guess and check numbers. The two numbers that satisfy the conditions are -4 and 2. Their multiplication gives us -8 (-4*2) and their addition gives us -4 (-4+2).
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Joanne buys a rectangular rug with an area of 35/4 square meters. The length of the rug is 7/2 meters. What is the with, in meters, of the rug? Answer in fraction pls!!
Answer: 5/2 meters
Step-by-step explanation:
You can find the area of a rectangle using this equation:
A = bh, where b is the base (length) and h is the height.
So, your rectangle is:
[tex]\frac{35}{4} = \frac{7}{2}h[/tex]
You can then divide both sides by 7/2 to find h.
[tex]\frac{\frac{35}{4}}{\frac{7}{2}}[/tex]
To divide, you can flip the fraction in the denominator to multiply:
[tex]\frac{35}{4}*\frac{2}{7}[/tex]
So, your width is 70/28. You can divide both sides by 14 to get 5/2.
3. Use an inequality symbol (<, >, 2, =) to compare -26_54
OOOO
O A.<
O B. =
O c.
O D.>
It would be A or < since 54 is positive and -26 isn't, that makes 54 greater than -26.
Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $20dollar out of his present on board games at the end of each month until his money ran out. Let f(n) be the amount of money that remained from Takuya's present during month n, where n=1 represents the month he received his present.
f is a sequence. What kind of sequence is it?
p.s" tell me if it is a geometric sequence or arithmetic and find the explicit formula
The amount of money that remained from Takuya's presence during month n is expressed as an=120-20n and the sequence is an arithmetic sequence.
What is an arithmetic sequence?The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms. Let us recall what is a sequence. A sequence is a collection of numbers that follow a pattern. The general form of an arithmetic sequence is an=a+(n-1)d.
If Takuya's parents gave him $100 as a birthday gift and she spent $20 each month on board games until his money ran out, this means he keeps spending $20 every month and his money keeps reducing by the same amount each month until his money ran out, the following can be inferred;
initial amount = $100
If he spends $20 each month,
Balance at the end of 1st month = $100-$20 = $80
Balance at the end of 2nd month = $80-$20 = $60
Balance at the end of 3rd month = $60-$20 = $40 and so on
Since the amount keeps reducing by the same value i.e $20, then the sequence formed is an arithmetic sequence.
a is the first term of the sequence = 100
d is the common difference = 80-100 = 60-80 = 40-60 = -20
n is the number of terms
Substituting the given values in the formula we have; an=100+(n-1)(-20)
⇒an=100+(-20n+20)
⇒an=100-20n+20
⇒an=120-20n
Therefore, the amount of money that remained from Takuya's presence during month n is expressed as an=120-20n and the sequence is an arithmetic sequence.
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1) Option (A) arithmetic sequence.
2) The recursive formula is f(n) = f(n-1) - 20 with an initial condition of f(1) = 100.
3) The explicit formula is f(n) = 120 - 20n.
Let's address Takuya's birthday gift scenario step by step.
1. Type of Sequence
The sequence described is an arithmetic sequence because the same amount of money, $20, is spent each month, leading to a consistent decrease in the balance.
2. Recursive Formula
Initially, he had $100. So,
f(1) = 100
Given the monthly spending of $20, the recursive formula is: f(n) = f(n-1) - 20
3. Explicit Formula
To find the explicit formula of the arithmetic sequence, we use the initial value and the common difference:
f(n) = 100 - 20(n-1)
Simplifying gives us:
f(n) = 120 - 20n
Thus, the balance remaining after n months can be calculated using this explicit formula.
Complete question:
Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $ 20 dollars out of his present on board games at the end of each month until his money ran out. Let f(n) be the amount of money that remained from Takuya's present during month n, where n=1 represents the month he received his present.
1) f is a sequence. What kind of sequence is it?
Choose 1 answer:
A ) Arithmetic sequence
B) Geometric sequence
2) Complete the recursive formula for f(n).
f(1) = □
f(n) = □
3) Find the explicit formula.
Find the area of the figure. *
12 yd
12 yd
Answer:
144 yards
Step-by-step explanation:
Multiply 12 yd by 12 yd =
144 yards
Answer: The answer is 144yd squared
Step-by-step explanation:
A sandwich shop offers two types of breads and 5 types of meat. How many sandwiches that are made of one type of bread and one type of meat are possible
Ángel won 84% of the skating competitions he entered last years. if Ángel entered 250 competitions ,how many did he win?
Answer:
210
Step-by-step explanation:
multipy the percent of the won skating competitions by the total amout of competions to get the result of how mant he won. 84% x 250 competitions= 210 competitions won!
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
x^2 + (y – 3)^2 = 36
Step-by-step explanation:
The standard equation of a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2.
If the center lies on the y-axis, then h = 0: (x - 0)^2 + (y - k)^2 = r^2
If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36
So, among the given equations, your
x^2 + (y – 3)^2 = 36 is correct (but only if you use " ^ " for exponentiation).
The equations that represent circles with a diameter of 12 units and a center on the y-axis are x² + (y - 6)² = 36 and x² + (y + 6)² = 36.
Explanation:The equations that represent circles with a diameter of 12 units and a center on the y-axis are:
x² + (y - 6)² = 36x² + (y + 6)² = 36To determine if an equation represents a circle, we need to check if the equation follows the standard form of a circle equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. In this case, since the center lies on the y-axis, the x-coordinate of the center is 0, and we only need to consider the y-coordinate.
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PLEASE ANSWER ASAP!!!
WHAT SHOULD 2.33 BE MULTIPLIED BY TO MAKE IT INTO A WHOLE NUMBRR??
Answer:
2.331 = (2.33 × 100)(1 × 100) = 233100. As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 233100 is also equal to 233100 when expressed as a mixed number.
Step-by-step explanation:
or mutilpy by 100
Answer:
2.33 * 100 because
2.33*100=233
Ase the points (-1,1) and (1, -1) on the graph of y = 2x -3
Step-by-step explanation:
[tex]y = 2x - 3 \\ plug \: x = - 1 \\ y = 2( - 1) - 3 = - 2 - 3 = - 5 \neq1 \\ hence \: ( - 1, \: 1) \: does \: not \: lie \: on \: the \: \\ graph \: of \: y = 2x - 3. \\ \\ y = 2x - 3 \\ plug \: x = 1 \\ y = 2 \times 1- 3 = 2 - 3 = - 1 \\ hence \: ( - 1, \: 1) \: lie \: on \: the \: graph \: of \: \\ y = 2x - 3. \\ \\ [/tex]
Consider the data set:
20, 30, 39, 44, 52
How much does 52 deviate from the mean?
Answer:
15
Step-by-step explanation:
mean = 20 + 30 + 39 + 44 + 52 /5
mean = 185 ÷ 5
mean = 37
52 - 37 = 15
The mean of the data set is 37. The number 52 deviates from the mean by 15. Key concepts include mean, deviation, and data set.
Explanation:The first step in answering the question 'How much does 52 deviate from the mean?' is to calculate the mean (also called the average) of the data set. We do this by adding together each of the numbers in the data set and then dividing by the number of elements. The calculation looks like this: (20 + 30 + 39 + 44 + 52) / 5 = 37. Then, to determine how much 52 deviates from the mean, subtract the mean from 52. This gives us: 52 - 37 = 15. So, 52 deviates from the mean by 15. Mean, deviation, and data set are key mathematical concepts related to this question and answer.
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What is the product of 2x-1 and 2x+6? Write your answer in standard form.
Show your work.
Is the product of 2x-1 and 2x+6 equal to the product of 1x-2 and 6+2x? Explain your answer.
Answers and Step-by-step explanations:
We need to use FOIL (first, outer, inner, last) to solve this.
The first terms of each of the two expressions (2x - 1) and (2x + 6) are 2x and 2x. Multiply these together: 2x * 2x = 4x².
The outer terms are 2x and 6, respectively, and their product is 2x * 6 = 12x.
The inner terms are -1 and 2x, respectively, and their product is -1 * 2x = -2x.
The last terms are -1 and 6, respectively, and their product is -1 * 6 = -6.
Add these together:
4x² + 12x + (-2x) + (-6) = 4x² + 10x - 6
Let's see if this is equal to (1x - 2) * (6 + 2x) by expanding this one using FOIL as well:
The first terms are 1x and 6, respectively, and their product is 1x * 6 = 6x.
The outer terms are 1x and 2x, respectively, and their product is 1x * 2x = 2x².
The inner terms are -2 and 6, respectively, and their product is -2 * 6 = -12.
The last terms are -2 and 2x, respectively, and their product is -2 * 2x = -4x.
Add all these up:
6x + 2x² + (-12) + (-4x) = 2x² + 2x - 12
Clearly, 2x² + 2x - 12 is NOT the same as 4x² + 10x - 6, so (2x - 1)(2x + 6) is not equal to (x - 2)(6 + 2x).
Hope this helps!
Answer:
4x² + 10x - 6
Not equal
Step-by-step explanation:
(2x - 1)(2x + 6)
4x² - 2x + 12x - 6
4x² + 10x - 6
(1x - 2)(6 + 2x)
6x - 12 + 2x² - 4x
2x² + 2x - 12
Not equal
solve the following equation for x: 6( 4x + 5) = 3(x + 8) + 3. round to the nearest hundredth.
Answer:
-0.14
Step-by-step explanation:
First eliminate the parenthesis:
6( 4x + 5) = 3(x + 8) + 3 =>
24x + 30 = 3x + 24 + 3
Then group x terms on the left and constants on the right
24x - 3x = 24 + 3 - 30
21x = -3
Divide by 21 and simplify:
x = -3/21 = -1/7 ≈ -0.14
Answer:
- 1/7
Step-by-step explanation:
6(4x + 5) = 3(x + 8) + 3
Expand the brackets
6 X 4x + 6 x 5 = 3 X x + 3 X 8 + 3
24x + 30 = 3x + 24 + 3
24x + 30 = 3x + 27
Subtract 30 from both sides to eliminate 30 on the left side
24x + 30 - 30 = 3x + 27 - 30
24x = 3x - 3
Subtract 3x from both sides to eliminate bring all variables to one side
24x - 3x = 3x - 3x - 3
21x = -3
Divide both sides by 21 to isolate x
21x/21 = -3/21
x = -1/7
x = - 1/7
PLEASE HELPPP >>>>> There are twenty classes at Northwestern Middle School and twenty classes at Southeastern Middle School. The number of students in each class at each school is shown in the dot plots below.
Number of Students in Each Class at Northeastern Middle School
A dot plot. A number line going from 20 to 29 labeled Number of Students. There are 3 dots above 20, 5 above 21, 7 above 22, 4 above 23, 1 above 24, and 0 above 25, 26, 27, 28, and 29.
Number of Students in Each Class at Southeastern Middle School
A dot plot. A number line going from 20 to 29 labeled Number of Students. There is 1 dot above 20, 2 above 21, 2 above 22, 4 above 23, 3 above 24, 2 above 25, 2 above 26, 2 above 27, 1 above 28, and 1 above 29.
Michela says that the modes of the two data are the same so the median and mean must also be the same. What is Michela’s error?
A. The modes are not the same.
B. The means and medians are not the same.
C. Only the modes and the medians are the same.
D. Only the modes and the means are the same.
Answer:
the answer above is incorrect im sorry i dont know the answer i wish i could help more god bless have a wonderful day
Step-by-step explanation:
Kevin and Jenny are making plaster. Kevin mixes 3 cups of water with 4 pounds of plaster powder. Complete the ratio table. How much water will Kevin need for 20 pounds of plaster?
the highest point in argentina is 6960 meters above sea level. the lowest point is 105 meters below sea level. What is the difference in meters between the highest and lowest elevation points?
Answer:
Step-by-step explanation:
It will be 6855 because it’s telling you the difference of them so you subtract to see
The difference in meters between the highest and lowest elevation points 7065 meters.
What are integers?Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes:
Positive Numbers: A number is positive if it is greater than zero. Example: 1, 2, 3 . . .
Negative Numbers: A number is negative if it is less than zero. Example: -1, -2, -3 . . .
Zero is defined as neither a negative number nor a positive number. It is a whole number.
Z = {... -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, ...}
Given:
highest point= 6960 meters above sea level.
lowest point = 105 meters below sea level.
Considering integers
highest points= +6960
lowest point= -105
So, difference in meters between the highest and lowest elevation points
= 6960 - (-105)
=6960+ 105
= 7065 meters
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Write this word sentence as an inequality. A number y is greater than 1 and is less than or equal to 8 .
Answer:
1<y≤8
Step-by-step explanation:
step 1
The number is y and it is greater than one.
The sign for greater than in mathematics is '>'
Therefore, we can write
y>1
And it means 1 is less than y
Less than = <
1<y
Step 2
y is less than or equal to 8. In mathematics, the 'less than or equal to' sign is '≤'
Therefore, we can write
y≤8
Step 3
We then combine these two inequalities
1<y≤8
Final answer:
The inequality 1 < y ≤ 8 represents a number y that is greater than 1 and less than or equal to 8.
Explanation:
An inequality representing the statement 'A number y is greater than 1 and is less than or equal to 8' can be expressed as:
1 < y ≤ 8
This inequality signifies that y is greater than 1 (1 < y) and at the same time, less than or equal to 8 (y ≤ 8), fulfilling both conditions simultaneously.
Which is the equation of a line with a slope of -1/3 and a yintercept at (0, 1)?
2x + 5
Find the val
3x+15
Answer:
Step 1: Find the x
2x + 5: Solve
[tex]2x + 5 - 5 = 0 - 5[/tex]
[tex]2x / 2 = -5 / 2[/tex]
[tex]x = -5/2[/tex]
3x + 15: Solve
[tex]3x + 15 - 15 = 0 - 15[/tex]
[tex]3x / 3 = -15 / 3[/tex]
[tex]x = -5[/tex]
Math math help very urgent please Q5 and Q6
Answer: 10
Step-by-step explanation:
Answer: the answer is 10
Right △EFG has its right angle at F, EG=8 , and FG=2 .
What is the value of the trigonometric ratio of an angle of the triangle?
tan E
sin G
sec G
In triangle EFG, the right angle is at F. Using the Pythagorean theorem, we can find the length of the hypotenuse and use it to calculate the trigonometric ratios.
Explanation:In triangle EFG, the right angle is at F. Given that EG = 8 and FG = 2, we can use the Pythagorean theorem to find the length of EF. Using the formula a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse, we can calculate that EF = sqrt((EG^2) + (FG^2)) = sqrt((8^2) + (2^2)) = sqrt(64 + 4) = sqrt(68).
To find tan E, we can use the ratio of the opposite side (FG) to the adjacent side (EG). tan E = FG/EG = 2/8 = 1/4.
To find sin G, we can use the ratio of the opposite side (FG) to the hypotenuse (EF). sin G = FG/EF = 2/sqrt(68).
To find sec G, we can use the ratio of the hypotenuse (EF) to the adjacent side (EG). sec G = EF/EG = sqrt(68)/8.
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What is the value of (Negative three-fourths) Superscript negative 4?
The value of (-3/4[tex])^{-4[/tex] is 256/81.
What is Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.
We have to find the value of (-3/4[tex])^{-4[/tex]
First of all make the power positive by reciprocate the number
= (-3/4[tex])^{-4[/tex]
= (-4/ 3 [tex])^4[/tex]
Now, expanding the number we get
= (-4 x -4 x -4 x -4) / (3 x 3 x 3 x 3)
= 256 / 81
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The deli made a 6 foot hero for the party. They need to cut it into 1 /3 inch slices. How many slices
will they get?
Answer:
6 ft = 72 inches
72*1/3=24
24
They will get 24 slices if they cut the 6 foot hero into 1/3 inch slices.
What is a fraction?A fraction is a numerical figure that represents a portion of a total.
Total length of the hero = 6 foot
1 foot = 12 inches
Total length of hero = 72 inches
Length of the slice cut = 1/3 inch
Total no. of slices = (1/3 * 72) = 24 slices
Hence the total no. of slices they will get is 24.
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What are the solutions to the equation x2 + 4x + 5 = 0?
please help PLEASE
Which equations are equal to this equation? 14(8x + 56) = 20
Answer:
x = - 191/28
Step-by-step explanation:
14 (8x + 56) = 20
112x + 784 = 20
112x = 20 - 784
112x = - 764
x = - 764/112
x = - 191/28
Answer:
Here are a few equivalent equations:
112x + 784 = 20
112x = -764
x = -6.82
Step-by-step explanation:
14(8x + 56) = 20
Multiply
112x + 784 = 20
Subtract 784 from both sides of the equation
112x = -764
x = -6.82
Hope this was useful to you!
Use the diagram below to answer the following questions.
Name all segments parallel to XT.
Name all segments parallel to ZY.
Name all segments parallel to ZS.
Name a plane parallel to plane STU.
Name a plane parallel to plane UVZ.
Name all segments skew to SW.
Name all segments skew to UT.
HELPPPPPP PLEASE
Answer:
Segments parallel to XT: YU, ZV, WS
Segments parallel to ZY: VU, WX
Segments parallel to ZS: None
Plane parallel to plane STU: WXY
Plane parallel to plane UVZ: TSW
All segments skew to SW: WX, ST
All segments skew to UT: UY, TX
Step-by-step explanation:
Let's begin by explaining the following:
Two line segments are parallel only if their slopes are identical, allowing them to never intersect.
Hence, according to this definition we have:
Segments parallel to XT: YU, ZV, WS
Segments parallel to ZY: VU, WX
Segments parallel to ZS: None
Now, if we go to the three-dimensional space, two planes are parallel, when they do not share any line, which allows them to never cross in space.
Hence, according to this definition we have:
Plane parallel to plane STU: WXY
Plane parallel to plane UVZ: TSW
Two lines are skew if and only if they are not in the same plane (also known as not coplanar). So, if two lines are not coplanar, they are not parallel and cannot intersect, either.
Hence, according to this definition we have:
All segments skew to SW: WX, ST
WZ and SV do not match the condition, since they are in the same plane where SW is,
All segments skew to UT: UY, TX
UV and ST do not match the condition, since they are in the same plane where UT is.
The following answers can be given as the solution to the given questions:
a) All segments parallel to XT: YU, ZV, WS
b) All segments parallel to ZY: VU, WX
c) All segments parallel to ZS: YT
d) A plane parallel to plane STU: WXY
e) A plane parallel to plane UVZ: TSW
f) All segments skew to SW: ZY, VU, XY, UT
g) All segments skew to UT: SW, WX, VZ, ZY
To give the appropriate answers to the given questions, the following terms must be understood.
i. Parallel lines: Two or more lines are parallel if and only if they do not meet even when extended to infinity.
ii. Skew lines: Two or more skew lines are lines that are neither parallel nor intersecting.
iii. Plane: This is flat surface which can either be in x-axis, y-axis or z-axis.
Therefore, the answers to each of the questions are:
a) All segments parallel to XT: YU, ZV, WS
b) All segments parallel to ZY: VU, WX
c) All segments parallel to ZS: YT
d) A plane parallel to plane STU: WXY
e) A plane parallel to plane UVZ: TSW
f) All segments skew to SW: ZY, VU, XY, UT
g) All segments skew to UT: SW, WX, VZ, ZY
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What is the equation of the line that is perpendicular to and
has the same y-intercept as the given line?
y= 4x+1
(50)
y= 4x+5
tos -
32
2
3
4
5
6
y = 5x + 1
5x + 5
Answer:
y = (-¼)x + 1
Step-by-step explanation:
y = 4x + 1
Slope of the perpedicular:
m = -¼
Equation:
y = (-¼)x + 1
4y = -x + 4
Leona saved $102.50 to buy a computer that is on sale. How much more money does she need to save before she can buy the computer?
1.Total cost of the computer: Let's represent the original price as $x. After an 80% sale, it's 0.8× x.
2. Amount Leona saved: $102.50.
3. Remaining amount needed: Total cost - Amount saved = 0.8 × x - $102.50.
So, Leona needs $102.50 more to afford the computer after her savings.
let's break it down step by step:
1. Find the total cost of the computer: Let's say the original price of the computer is $x, and it's currently on sale. Since Leona saved $102.50, this means the amount she has saved is a part of the total cost of the computer.
2.Calculate the remaining amount needed: We subtract the amount Leona saved from the total cost of the computer to find out how much more money she needs to save.
So, let's go through these steps:
1. Total cost of the computer: Let's represent the original price of the computer as $x. Since the computer is on sale, let's say it's now priced at 80% of its original price.
So, the total cost of the computer after the sale = 0.8 ×x.
2. Amount Leona saved = $102.50.
3. Remaining amount needed = Total cost of the computer - Amount Leona saved.
Let's perform the calculation
Total cost of the computer = 0.8 × x
Amount Leona saved = $102.50
Remaining amount needed = Total cost of the computer - Amount Leona = 0.8 × x - $102.50
So, Leona needs to save $102.50 more to buy the computer.
Graph the function y =13 6x
Answer:
the graph that's got long lines in the top right and bottom left
What is the value of the expression-7 3/4 + 3 1/2
Answer:
45/4 or 11.25 or 11 1/4
Step-by-step explanation:
Answer:
Step-by-step explanation:-15/4
-15/4
if 8 people share a half pound of pasta how much would each get
Answer: 1/16
Do Keep Change Flip (KCF)
Keep: 1/2
Change: ÷ into ×
Flip: 8/1 into 1/8
Your New Problem Should Be: 1/2×1/8
Multiply
1/2 × 1/8 = 1/16
The amount of pasta each would get is 1/16
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
Do Keep Change Flip (KCF)
Keep: 1/2
Change: ÷ into ×
Flip:
8/1 into 1/8
= 1/2×1/8
Multiply,
1/2 × 1/8 = 1/16
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