Answer:
(a) 21, 22, 23
(b) 11, 13, 15
Step-by-step explanation:
Natural numbers are the set of numbers 1, 2, 3... Not numbers that we think of as fractions or decimals or negative numbers.
Let x = the first number
Let x+ 1 = the second number
Let x+ 2 = the third number
x + x+ 1 + x + 2 = 66 Combine like terms
3x + 3 = 66 Subtract 3 from both sides
3x = 63 Divide both sides by 3
x = 21
Check:
21 + 22 + 23 = 66
Let x + the first number
Let x + 2 = the second number
Let x + 4 = the thirds number
x + x + 2 + x + 4 = 39 Combine like terms
3x + 6 = 39 Subtract 6 from both sides
3x = 33 Divide both sides by 3
x = 11
Check: 11 =+ 13 + 15 = 39
insert a monomial into each trinomial such that the results is a perfect square. 16y^2+ ...+81
The resulting perfect square using the given trinomial is found as (4y + 9)².
Explain the term perfect square?If a number's square root is indeed an integer—that is, if it is the product of an integer and itself—it is a perfect square and perhaps a square number.We need to ensure that our producing trinomials have the following form since we want to add an one term (monomial) here to given binomial (16y^2+__+81) so that the producing trinomial may be represented as the square of some other binomial:a²-2ab+b² or a²+2ab+b²
since:
a²-2ab+b² = (a-b)²
and
a²+2ab+b² = (a+b)²
A trinomial is written as the square of the a binomial in the equations above.
Knowing that the aforementioned equations are correct, we may use the binomial that has been provided and proceed backwards from there:
= (4y)² +__+ (9)² ....eq 1
a = 4y and b = 9.
Thus, 2ab = 2(4y)(9) = 72y
Put in eq 1;
= (4y)² + 72y + (9)²
The resulting perfect square:
= (4y + 9)²
Thus, resulting perfect square using the given trinomial is found as (4y + 9)².
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Harper calculated the slopes of both AB and XY. "That can't be right," she
said to herself after she calculated the slopes. "I got the same answer for both
lines. I must have made a mistake." She ponders the problem, but cannot figure
out what to do. She explains "I used completely different points when I calculated
the slopes. How can the slopes be the same?" she asks.
What do you think? Give Harper some suggestions and advice. Be clear and
complete
The slopes of the segments can be the same as long as the change in y divided by the change in x of both segments is the same. This means that the two segments are parallel.
How to obtain the slope of a line?The slope of a linear function represents the rate of change of the output variable y relative to the input variable x.
Hence, given two points on a line, the slope is calculated by the division of the change in y divided by the change in x.
As long as the changes are the same, two different segments can have the same slope, which is the case when they are parallel, meaning that they meet only at infinity.
One possible example of two parallel segments is given as follows:
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Name the vertices of the following points when they have been translated 6 units to the right and 10 units up A(1,-1) B (2, -2) C(-2,2)
A. C’(8,8)
B. C’(-8,-8)
C. C’(4,12)
D. C’(-4,12)
The translated points are A'(7, 9), B'(8, 8), and C'(4, 12) when they have been translated 6 units to the right and 10 units up.
What is a coordinate plane ?A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.
The given points are,
A(1, -1), B (2, -2) and C(-2, 2).
When the points are translated 6 units to the right and 10 units up implies that,
There will be increase of 6 units in x coordinate and increase of 10 units in y coordinate
The point coverts as
A'(7, 9), B'(8, 8), and C'(4, 12)
The translated points are A'(7, 9), B'(8, 8), and C'(4, 12).
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the b value is 0.4 per year. what percentage growth rate would the population show in the absence of constraints? (round your answer to the nearest whole number.)
Answer:
Step-by-step explanation:
3. Write an equation that represents the line that passes through the point (7,4) and has a slope of 4/9
Richard and Teo have a combined age of 32. Richard is 8 years older than twice Teo's age. How old are Richard and Teo?
Answer: Richard =24 Teo = 8
Step-by-step explanation:
32-8 = 24
24-8 = 16
16/2= 8
You are preparing to purchase some items online. You have a total of $320 to spend. You see several styles of shoes you like and each pair costs $16. You also like several pairs of jeans and each pair costs $32. You want to purchase more than 6 items. Let x represent the number of pairs of shoes you can buy, and y represent the number of pairs of jeans you can buy. In terms of this scenario, what does the point (9 , 1) mean?
, You are preparing to purchase some items online. You have a total of $320 to spend. You see several styles of shoes you like and each pair costs $16. You also like several pairs of jeans and each pair costs $32. You want to purchase more than 6 items. Let x represent the number of pairs of shoes you can buy, and y represent the number of pairs of jeans you can buy. In terms of this scenario, what does the point (9 , 1) mean?
The point (9 , 1) means you cannot buy 10 items total.
The point (9 , 1) means you can buy 9 pairs of jeans and 1 pair of shoes.
The point (9 , 1) means you can buy 9 pairs of shoes and 1 pair of jeans.
The point (9 , 1) means you cannot buy 9 pairs of shoes and 1 pair of jeans.
In terms of this scenario, the point (9 , 1) means B. The point (9 , 1) means you can buy 9 pairs of jeans and 1 pair of shoes.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, you have a total of $320 to spend. You see several styles of shoes you like and each pair costs $16. You also like several pairs of jeans and each pair costs $32. You want to purchase more than 6 items.
Let x represent the number of pairs of shoes you can buy, and y represent the number of pairs of jeans you can buy.
The point (9 , 1) means you can buy 9 pairs of jeans and 1 pair of shoes. This can be illustrated as:
9($32) + 1($16)
= $282 + $16
= $298
The correct option is B.
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The area of a rectangle is 2 square feet. The perimeter of the rectangle is 9 ft. Find the length, ll, and width, ww, of the rectangle. What is l^2 + w^2l 2 +w 2 ?.
The rectangle is 4 feet long and 0.5 feet wide. l²+w² equals 16.25 feet².
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area is a phrase used to describe how much room a 2D form or surface occupies.
Here,
Let l be the length and w be the width.
area=2
lw=2
w=2/l
2(l+w)=9
2l+2w=9
2l+2*2/l=9
2l²+4=9l
2l²-9l+4=0
l=0.5,4
w=4,0.5
l=4 and w=0.5
l²+w²=4²+0.5²
=16.25 feet²
The length of rectangle is 4 feet and width is 0.5 feet. The value of l²+w² is 16.25 feet².
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Please help
-2.5(-3+4.2n+8)
Answer:
-12.5 -10.5n
Step-by-step explanation:
Use distributive property to solve:
1. -2.5 x -3 = 7.5
2. -2.5 x 4.2n = -10.5n
3. -2.5 x 8 = -20
Simplify:
7.5-20= -12.5
-12.5 -10.5n
Determine the equation of the parabola that opens up, has vertex (-4,-8)(−4,−8), and a focal diameter of 1616.
The equation of parabola will be;
⇒ y = 4 ( x + 4)² - 8
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The vertex = (- 4, - 8)
And, The focal diameter = 16
Now,
Since, The vertex (h, k) = (- 4, - 8)
And, The focal diameter (4a) = 16
⇒ 4a = 16
⇒ a = 4
Hence, The equation of parabola with vertex (h, k) will be;
⇒ y = a (x - h)² + k
Substitute all the values, we get;
⇒ y = 4 (x - (-4))² + (-8)
⇒ y = 4 ( x + 4)² - 8
Thus, The equation of parabola will be;
⇒ y = 4 ( x + 4)² - 8
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Maria scored 20 goals in 4 soccer games
last season. Approximately how many
points did Maria average per game?
Answer:
idek
Step-by-step explanation:
Identify the common difference: d=
Identify the zero term(starting amount) a=
The formula to find the common difference of an arithmetic sequence is: d = a(n) - a(n - 1), where a(n) is a term in the sequence, and a(n - 1) is its previous term in the sequence
What is arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. For instance, the number sequence 5, 7, 9, 11, 13, and 15 has a common difference of 2 in arithmetic.
Sequences can in fact begin at any number that we choose. A sequence with the general word an is commonly notated as ann=1 a n n = 1.
or d = (an + 1 - an) (an – an-1). AP reduces if the common difference is negative. For instance, the AP drops in these numbers: -4, -6, -8.
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Use f(x) = -4x + 1, g(x) = x2 - 8x + 21, and h(x) = 19 - 3x|
If h(x) = 39, find x.
By using the functions we have found the value of x and it is found out to be as x = -20/3.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Given data:
f(x) = -4x + 1, g(x) = x2 - 8x + 21, and h(x) = 19 - 3x and h(x) = 39.
By using the h(x) function, we can write
h(x) = 19 - 3x
39 = 19 - 3x
3x = 19 - 39
3x = -20
x = -20/3
Hence, by using the functions we have found the value of x and it is found out to be as x = -20/3.
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A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function h(t) = - 16t^2 + 116t + 96 models the balls height about the ground, h(t), in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? __ feet
b) How many seconds does it take until the ball hits the ground? __ seconds
Answer:
the answer is 306.25 feet and b is 8 sec
Step-by-step explanation:
Explanation
The height of the ball as a function of the time is given by the following formula:
A. Maximum height of the ball
To find the value of the maximum height, we maximum the function h(t) computing its first derivative and equalling the result to zero:
Solving the last equation for t, we get time t when the height is maximum:
So the maximum height is given by the value of h(t) when t = 2.5:
The maximum height is 196ft.
B. Time until the ball hits the ground
The ball will hit the ground when h(t) = 0. So we must find the value of t such that:
Solving this equation is equivalent to finding the roots of a second-order polynomial:
Where:
• a = -16,
,
• b = 80,
,
• c = 96.
The roots of this polynomial are given by the following formula:
s
Answer
A. The maximum height of the ball is 196 ft.
Geometry: Which chord is nearest the center and why? (ASAP!!!)
Chord AC is the nearest to the center because the perpendicular distance of chord AC from center O is the smallest.
What is a chord of a circle?
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.
ΔABC is inscribed in O. If AB = 5, BC = 8, and AC =9.
Now if you look carefully at the given diagram, we can see that the perpendicular distance of chord AC from center O will be smaller than the perpendicular distance of chord AB from center O and the perpendicular distance of chord BC from center O.
Hence, Chord AC is the nearest to the center because the perpendicular distance of chord AC from center O is the smallest.
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I am so confused, can anyone help?
Answer: -9/50
Step-by-step explanation: It's asking you to give the answer of A (5/12) - B (3/5), how you do it is simple, you subtract 5/12 and 3/5 like so: 5/12 3/5 = -0.18 and -0.18 as a fraction is -9/50
So there is your answer :)
three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. what is the maximum possible weig...
In linear equation, 3 t is the maximum possible weight .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Assuming x to be lightest , y median and z the heaviest.
So according to given information average is 7 so total sum for three box = 21
thus x+y+z = 21
Given y=9 (median weight)
thus x+z = 12
For maximum possible value for x is 3 such that z= 9
if x=4 then Z= 8(this changes median to 8)
So maximum possible value for lightest box is 3
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Please help ASAPP!!!
Answer: asa
Step-by-step explanation: I just did this
please help me solve this: solve for x
Answer:
x = 100
Step-by-step explanation:
You have to use the equation 15x + 10 = 6x - 6 + 70. This equation finds out that x = 6. Then, you would multiply 6 by 15. This gets 90. Finally, add 10 to that.
Given: CA bisects angle BAD and AD congruent to AB
Prove: Triangle ABC is congruent to Triangle ADC
The theorem or principle that helps to solve the above is the properties of a parallelogram. On the basis of the same, we can state that the proof that Triangle ABC is congruent to Triangle ADC is the property that indicates that each diagonal of a parallelogram separates it into two congruent triangles. Hence, ΔABC ≅ Δ ADC.
What are the qualities of a parallelogram?There are six crucial parallelogram qualities to understand:
Contrary sides are equivalent (AB = DC).Angels opposite each other are congruent (D = B).Consecutive angles are additive (A + D = 180°).If one angle is correct, all angles are correct.A parallelogram's diagonals cross one other.A parallelogram is divided into two congruent triangles by its diagonals.Learn more about parallelograms:
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What interest will be earned if $9,000 is invest for 4 years at 12% compounded monthly? Round to 2 decimals.
The required compound interest is $5,510.03
What is compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods.
Given, Principal = $9,000
Time = 4 years
Interest = 12% = 0.12
For compounded monthly, n = 12
The compound amount for monthly compounded is given by
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
or, A = [tex]9000(1 + \frac{0.12}{12} )^{12*4}[/tex]
or, A = 9000[tex](1+0.01)^{48}[/tex]
A = $14510.03
Compound interest = $14510.03 - $9,000 = $5,510.03
Hence, the required compound interest is $5,510.03
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Translate this phrase into an algebraic expression.
60 decreased by twice Jenny's score
Use the variable to represent Jenny's score. please help.
The expression for 60 decreased by twice Jenny's score 60 - 2x.
What is an algebraic expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Let Jenny's score be x.
Twice Jenny's score will be 2x.
Therefore, the expression will be:
= 60 - 2x
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can somebody please help
Answer:
(4,12) Quadrant l
(-5,2) Quadrant ll
(-9,-4) Quadrant lV
(3,-3) Quadrant lll
Step-by-step explanation:
hope this helps!
Drag the cards to create a two-digit number that matches these rules.
Note: Not all cards will be used.
●
0
2 is one of the digits
10 is the nearest ten when rounding
1
Irse challenge
2 3
Answer:
12
Step-by-step explanation:
You want a 2-digit number that rounds to 10 and has 2 as one of its digits.
Rounds to 10The integers that round to 10 are in the rangle 5–14. The only one of these that has a digit of 2 is 12.
The 2-digit number is 12.
Find the measure of ∠c given the information below.
A = 155
E= 69
The image is below giving brainliest for whoever answers correctly + explaining !
Answer:
c=65
Step-by-step explanation:
a=115
180-115=b
b=65
b=c
c=65
a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?
If the expected value of d is not equal to d, then the property that d hat exhibit is option (E) d hat is biased
Here a certain statistic d cap is being used to estimate a population parameter d
The central limit theorem states that "the distribution of sample means approximates a normal distribution as the sample size gets larger."
According to the central limit theorem,
The expected value is μ = p
Then the standard error will be
s = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
Here it is given that the expected value of d cap is not equal to d. So it is different from the expected value μ = p.
Therefore, the d hat is biased
I have answered the question in general, as the given question is incomplete
The complete question is :
A certain statistic d hat is being used to estimate a population parameter D. The expected value of d hat is not equal to D. What property does d hat exhibit?
A. The sampling distribution of d hat is normal.
B. The sampling distribution of d hat is binomial.
C. The sampling distribution of d hat is uniform.
D. d hat is unbiased.
E. d hat is biased.
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Denise earns $225 a week with a part time job at the local florist. She decides to put 30% of the amount into a saving account. How much money does Denise put in the savings account each week?
Denise puts $67.50 in the savings account every week.
What is a percentage?
Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.
To find out how much money Denise puts in the savings account each week, you need to multiply her weekly earnings by the percentage she puts into the savings account.
First, convert the percentage to a decimal by dividing by 100: 30% = 0.30
Then, multiply Denise's weekly earnings by this decimal to find the amount she puts into the savings account each week:
=$225 * 0.30
=67.50.
Hence, Denise puts $67.50 in the savings account each week.
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Peter and John are running around the town around the town in opposite directions. Peter can go around the town in 2.5 hours, and John can do the same in 15 hours. Assuming they start at the same time and same place, how many times will they pass each other going in opposite directions in a 24-hour period?
Answer:
90
I am not too sure but this question is VERY BRAIN-INTENSIVE
Sorry, if i am wrong
The graph below shows the number of hours Dario
worked and the amount he earned.
Earnings (in dollars)
100
90
80
70
60
50
40
30
DARIO'S EARNINGS
(2, 24)
(5, 60)
(8, 96)
0 1 2 3 4 5 6 7 8 9 10
Time (in hours)
What was Dario's hourly wage?
A $10
B $12
$24
D $54
Answer: answer is b 12$.
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The corresponding sides of two similar triangles a
The corresponding angles of two similar triangles are
The solutions are that Two comparable triangles have proportional corresponding sides. And Two comparable triangles matching angles
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
For a regular polygon of any number of sides, therefore the sum of its exterior angle is 360°.
Given statements that the corresponding sides might be altered, they must still be proportionate.
The triangles will be congruent also, if they are.
But the angles must always line up otherwise the triangle's overall shape will change and it won't look the same.
Two comparable triangles must have proportional corresponding sides.
Two comparable triangles must matching angles match up.
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