Answer: 9,-9
Step-by-step explanation:
Answer: 9
Step-by-step explanation:
9x9=81
This table shows the ratio of drummers to flute players in the school band.
The missing value from the table is 4.
What is the missing value?Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained in another value.
In order to determine the missing number, we first have to determine the rate of change of the number of drummers.
Rate of change:
4 - 3 = 1
2 -1 = 1
3 - 2 = 1
So, the rate of change is 1. Thus, the missing number : 3 + 1 = 4
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Answer: missing value is 5
Step-by-step explanation:
An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers.
"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."
The general form an arithmetic sequence is:
[tex]a_{n} = a_{1} + (n- 1) d[/tex]
The function is linear. The sequence consists of either numbers that are increasing or decreasing based on the value of d, the common difference.So, the statement provided is True.
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One leg of a right triangle has a length of 5m. The other sides have lengths that are consecutive integers. Find these lengths.
The lengths of the other two sides of the right triangle are 12 and 13
Pythagorean theoremFrom the question, we are to determine the lengths of the other sides of the triangle
From the given information,
The other sides have lengths that are consecutive integers
Thus,
If the length of the other side is x
Then,
The hypotenuse will be x + 1
By the Pythagorean theorem, we can write that
(x+1)² = x² + 5²
(x+1)(x+1) = x² + 25
x² + x + x + 1 = x² + 25
x² - x² + x + x = 25 - 1
2x = 24
x = 24/2
x = 12
∴ The other leg of the right triangle is 12
Hypotenuse = x + 1 = 12 + 1 = 13
Hence, the lengths of the other two sides are 12 and 13
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How do I solve this?
Answer:
first option
Step-by-step explanation:
to find the zeros equate f(x) to zero , that is
2x² + 8x - 3 = 0 ( add 3 to both sides )
2x² + 8x = 3 ← factor out 2 from each term on the left side
2(x² + 4x) = 3
to complete the square
add/subtract ( half the coefficient of the x- term )² to x² + 4x
2(x² + 2(2)x + 4 - 4) = 3
2(x + 2)² - 8 = 3 ( add 8 to both sides )
2(x + 2)² = 11 ( divide both sides by 2 )
(x + 2)² = [tex]\frac{11}{2}[/tex] ( take square root of both sides )
x + 2 = ± [tex]\sqrt{\frac{11}{2} }[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{\frac{11}{2} }[/tex]
that is
x = - 2 - [tex]\sqrt{\frac{11}{2} }[/tex] , x = - 2 + [tex]\sqrt{\frac{11}{2} }[/tex]
Answer:
x = -2 - √11/2 and - 2 + √11/2.
Step-by-step explanation:
2x^2 + 8x - 3 = 0
Divide first 2 terms by 2:
2(x^2 + 4x) - 3 = 0
2(x^2 + 4x) = 3
Complete the square:
2 [ (x + 2)^2 - 2^2) = 3
2(x + 2)^2 - 8 = 3
2(x + 2)^2 = 11
(x + 2)*2 = 11/2
x + 2 = ± 11/2
x = -2 ± √11/2
the formula for the perimeter of a triangle is the same as that for the circumference of a circle true or false
FALSE
To calculate the perimeter of a triangle, add the length of its sides. For example, if the sides of a triangle are a, b, and c, the perimeter of the triangle is P = a + b + c.
Since all three sides of the triangle are the same length, you can multiply the length of each side by 3 to get the perimeter.
To find the circumference of a circle, multiply the diameter of the circle by π (pi). The circumference can also be calculated by multiplying 2 x radius by pi (π = 3.14).
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What is the solution to the system of equations graphed below?
OA. (1, 2)
B. (0, -1)
O C. (0.4)
D. (2.0)
X₁
5
Answer:
A(1,2)
Step-by-step explanation:
tracing the point of intersection of the two lines on the y and the x axis,on the y we have 2 and on the x we 1.
The equations y = 1/2x + 1 and y= √2x+4 are graphed on the coordinate grid.
How many real solutions does the equation y= √2x+4 = 1/2x + 1 have.
A. 0
B. 1
C. 2
D. cannot be determined from the graph
Answer:
2
Step-by-step explanation:
The graphs intersect at 2 points.
The 2 solutions are x = -2 and x = 6.
Ilean works as a welder and web designer. As a welder, she earns $18 per hour. Last week she worked 푥 hours as a welder and her friend paid her $75 to design a web page. Write an expression to represent the total amount Ilean earned last week.
The expression that represent the total amount Ilean earned last week is 27(18) + 75
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the total amount Ilean earned last week for working x hours.
Since she worked for 27 hours and earned $75 to design a web page. Hence:
y = 27(18) + 75
The expression that represent the total amount Ilean earned last week is 27(18) + 75
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A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames: a. None will need adjustment
0.385 is the probability under given conditions.
Lets simplify the above problem,
Given n=20, p=0.05, q=0.95
Probability that in a sample of 20 window frames:
None will need adjustments.
P(x=0)= 0.95^20 = 0.3585
At least one will need adjustment?
P(x>=1) = 1 - P(x=0)
= 1 - 0.3585
= 0.6415
More than two will need adjustment?
P(x>2) = 1 - P(x=0) -P(x=1) -P(x=2)
= 1 - 0.3585 - 20C1(0.05)^1*(0.95)^19 - 20C2(0.05)^2*(0.95)^18
= 0.6415 - 20*0.05*0.3774 - 190*0.0025*0.3972
= 0.2641-0.18868
= 0.0755
Hence 0.385 is the solution of the given problem.
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which expression is equivalent to 8x^2 square root 375x+2^3 square root 3x^7,if x =0?
The expression which is equivalent to 8x²√375x + 2³√3x^7 if x = 0 is; 0.
Which expression is equivalent to the expression given?According to the task content, the expression given is; 8x²√375x + 2³√3x^7.
On this note, it follows that when x=0 is substituted into the expression; the evaluation amounts to zero, 0.
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Drag each description to the correct location to complete the flow chart proof. Given: . D is the midpoint of . . Prove: is an isosceles triangle.
The isosceles triangle is proved below.
How to illustrate the triangle?The complete information wasn't found. The proofing of the triangle will be illustrated. It should be noted that the angles opposite to the equal sides of an isosceles triangle are also equal.
Proof: Consider an isosceles triangle ABC where AC = BC.
We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.
We first draw a bisector of ∠ACB and name it as CD.
Now in ∆ACD and ∆BCD we have,
AC = BC (Given)
∠ACD = ∠BCD (By construction)
CD = CD (Common to both)
Thus, ∆ACD ≅∆BCD (By SAS congruence criterion)
So, ∠CAB = ∠CBA (By CPCT)
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p(x)= x2-x-12 and q(x)=x+3 find p(x) ÷ q(x) The question of O-MATH
Hello,
[tex] \frac{p(x)}{q(x)} = \frac{ {x}^{2} - x - 12}{x + 3} = \frac{(x - 4)(x + 3)}{x + 3} = x - 4[/tex]
Answer:
Step-by-step explanation:
Select the correct answer. what is the value of ? i=1 a. 8 b. 7/8 c. 7 d. 7/2
The correct option is c. 7
The summation of the expression [tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex] is 7.
What is summation (∑)?The sum of terms that follow a pattern is denoted by the symbol '∑' "summation," which also serves as a shorthand notation.
A sum of several terms is typically represented by the symbol "∑" This symbol is typically accompanied with a variable index that includes all terms that must be taken into account when calculating the total.
The given expression is;
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex]
The the property of summation, expand the values.
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{2}\right)^{1-1}+4\left(\frac{1}{2}\right)^{2-1}+4\left(\frac{1}{2}\right)^{3-1}[/tex]
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{2}\right)^{0}+4\left(\frac{1}{2}\right)^{1}+4\left(\frac{1}{2}\right)^{2}[/tex]
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{1}\right)+4\left(\frac{1}{2}\right)+4\left(\frac{1}{4}\right)[/tex]
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4+2+1\\[/tex]
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=7\\[/tex]
Therefore the solution of the given equation is 7.
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The correct question is;
What is the value of [tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex] ?
a.7/8
b.8
c.7/2
d.7
For a sample size of 36 and a population Standard Deviation of 3, the sample variance for distribution of the means is:
The sample variance for distribution of the means is 9
The average of the squared differences from the Mean is called Variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.
The Standard Deviation is a measure of how spread out numbers are.
Its symbol is σ (the Greek letter sigma)
Its formula is the square root of the Variance
Given: Standard Deviation = 3
Sample size = 36
∴ By formula we get
3 = √(Variance)
∴ 9 = Variance
Thus the sample variance for distribution of the means is 9
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Find the number of terms in this series: 3x + 5x + 7x + ... + 23x
Help asap please and thank you!
The graph of a relation is shown.
A coordinate plane with a straight line. The line starts in the lower left quadrant and continues up through the uppercase right quadrant. The line passes through the y-axis slightly below the origin, and then passes through the x-axis slightly to the right of the origin.
Which of these values could be the slope of the line? Select two options.
–2
0
The values which could be the slope of the line are numbers > 0.
Which values could be the slope of the line?According to the task content, it follows that the given line originates from the lower left quadrant and continues through the upper right quadrant.
It therefore follows that the line is ascending from left to right in which case, the slope of the line is positive.
Hence, the possible values of the slope include the set of numbers greater than 0.
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Answer: C and D
Step-by-step explanation: Trust me bro
Select all that are measures of angles that are coterminal with a –50° angle.
The expression θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex] represents the family of all angles coterminal with - 50° angle.
What is the family of angles coterminal to a given one?
Two angles are coterminal if and only if their end have the same direction. Two consecutive coterminal angles have a difference of 360°. Then, we can derive an expression representing the family of all angles coterminal to - 50° angle.
θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex]
The expression θ = - 50° ± i · 360°, [tex]i \in \mathbb{N}_{O}[/tex] represents the family of all angles coterminal with - 50° angle.
RemarkThe statement is incomplete and complete form cannot be reconstructed. Thus, we modify the statement to determine the family of angles coterminal to - 50° angle.
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What is the area of this trapezoid?
Enter your answer in the box.
_cm²
Answer:
A = 336 cm²Step-by-step explanation:
Area Formula
A = (a + b) × h/2
A = (28 + 14) * 16/2
A = 42 * 8
A = 336 cm²
A private tutoring company charges $20 for a 1-hour session. Currently, 300 students are each tutored for an hour each week. Since the company is losing money, the owner has decided to increase the price. For each 50¢ increase, she estimates that 5 fewer students will participate. If the company needs to bring in $6,210 per week to stay in business, what price must be charged for a 1-hour tutoring session to produce this amount of revenue?
The price that must be charged for a 1-hour tutoring session to produce this amount of revenue is 24.5 dollars
How to solve Word ProblemThe first thing to do with word problem is to understand the question. After that, make analysis of the question.
It is given that a A private tutoring company charges $20 for a 1-hour session. Currently, 300 students are each tutored for an hour each week. Since the company is losing money, the owner has decided to increase the price. For each 50¢ increase, That is $20.5 for each students.
If she estimates that 5 fewer students will participate, that is, 295 students, and the company needs to bring in $6,210 per week to stay in business.
Let us assume that 1 hour per day. And there are 7 days in a week.
Divide the money by 7 to know the value per day
6210/7 = 887.14
Now, divide the amount per day by 250 students to know the amount per student per hour
887.14/295 = 3.007
The price that must be charged for a 1-hour tutoring session to produce this amount of revenue should be 20.5 + 4 = 24.5 dollars
Therefore, each student will pay $24.5 per hour
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Find the measure of the indicated angle to the nearest degree 35 and 28
The missing indicated angle of the given right angle triangle is; 39°
How to use trigonometric ratios?We can see in the attached image showing the missing figure that it is a right angle triangle and as such we can find the missing angle via trigonometric ratios. In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles
The trigonometric ratios we can use are as follows;
sin x = opposite/adjacent = opp/hyp
cos x = adjacent/hypotenuse = adj/hyp
tan x = opposite/adjacent = opp/adj
Now, we see that the missing angle lies on the side with a length of 28. Thus, adjacent side = 28 and opposite side of it = 23. Thus;
tan x = opposite/adjacent = 23/28
x = tan⁻¹(23/28)
x = tan⁻¹(0.8214)
x = 39.4° ≈ 39°
Thus, we can conclude that the measure of the indicated angle to the nearest degree 35 and 28 is calculated as 39°.
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PLEASE HELP IM STUCK
Answer:
-2
Step-by-step explanation:
The slope of a line is rise/run
So, just see how much the line rises/how much the line runs
In this case, the line rises 2 units for every -1 unit it runs
So, the slope is -2
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The inequality represented by the graph is; B: y > 3x + 2
How to Interpret Inequality Graphs?
We are told that the line goes through the coordinates;
(-3, -7) and (0, 2)
Now, formula to find the slope is;
m = (y2 - y1)/(x2 - x1)
m = (2 - (-7))/(0 - (-3))
m = 9/3
m = 3
Since it's a dashed straight line and everything to the left is shaded, then it means that the inequality represented by the graph is;
y > 3x + 2
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Answer:
B
Step-by-step explanation:
edge 23
On friday , march 16, mr posts beginning checking balance is 80 and his account is created for a deposit is for 50 the same day, several transactions are posted totaling 90 mr posts bank charges a 25 overdraft fee. his bank credits deposits before it post checks. what will mr. posts account balance be at the end of the day?
Account balance at the end of day is 195.
word problemA word problem is a type of mathematics exercise where the majority of the problem's context is supplied in spoken language as opposed to mathematical notation.
now according to question
initial balance in account on march 16 =80
deposit in account on the same day = 50
overdraft fee charged by bank=25
several transactions amount deposited in bank=90
total amount deposited /available in bank account.
=80+50+90
=220
total amount deducted from account
=25
account balance at the end of day
=220-25
=195
hence answer is 195
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Find the unknown angles
Answer:
Se below
Step-by-step explanation:
The two angles form a straight line which is 180° angle
4z + z = 180
5z = 180
z = 36 ° 4z = 144°
Find the five-number summary for the data.
{236, 202, 218, 208, 225, 229, 211, 237, 223, 206, 217, 216, 232, 225, 208}
Minimum: 202
Quartile (Q1): 208
Median: 218
Quartile Q3: 229
Maximum: 237
What is the Five-Number Summary?The max and min value, the lower and upper quartiles, and the median of a data comprise the five-number summary.
Given the data: 236, 202, 218, 208, 225, 229, 211, 237, 223, 206, 217, 216, 232, 225, 208, we would have the following:
Minimum: 202 (least value)
Quartile (Q1): 208 (center of the first half of the data)
Median: 218 (center of the data when ordered)
Quartile Q3: 229 (center of the second half of the data)
Maximum: 237 (highest value).
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The factorization of x² + 3x -4 is modeled with algebra
tiles.
+X
+
+
+
+
+X
+X
+X
+X
+X
+X
Ť
T
What are the factors of x² + 3x - 4?
O(x + 4) and (x-4)
O(x + 3) and (x-4)
(x + 4) and (x-1)
O(x+3) and (x-1)
Option C
Find the inverse of 6x^2-7
Answer:
[tex] y = \pm \sqrt{\dfrac{x - 7}{6}} [/tex]
Step-by-step explanation:
f(x) = 6x² - 7
y = 6x² - 7
x = 6y² - 7
6y² = x - 7
[tex] y^2 = \dfrac{x - 7}{6} [/tex]
[tex] y = \pm \sqrt{\dfrac{x - 7}{6}} [/tex]
Each score in a set of data is multiplied by 3, and then 4 is subtracted from the result. If the original mean is 10 and the original standard deviation is 5, what are the new mean and new standard deviation
The new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.
According to the question,
Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.
First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.
Mean: 10*3 = 30
Standard deviation: 5*3 = 15
Secondly "change of origin" when every score in a data set by a constant, its mean get added or subtracted by the same constant and standard deviation remains constant.
Applying change of origin in the above mean and standard deviation
Mean: 30 - 4 = 26
Standard deviation: Remains same = 15
Hence, the new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.
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3. Today, Dahlia folded 29 paper cranes. Now there are 41 paper cranes in class. How many cranes were there in class yesterday? Each paper crane has a length of 10 centimetres. How many centimetres were there total for all the paper cranes?
Answer:
There were 12 cranes in class yesterday. For all the cranes, there were a total of 290 centimeters.
Step-by-step explanation:
41-29=12.
29*10=290
Mary had 81 fliers to post around town. last week, she posted 1/3 of them. this week, she posted 2/3 of the remaining fliers. how many fliers has she still not posted?
Answer:
18 posters
Step-by-step explanation:
Posters posted last week: 81/3 = 27 posters
Remaining posters: 81-27 = 54 posters
Posters posted this week: 54/3 = 18*2 = 36 posters
Posters remaining: 54-36 = 18 posters