AnswEr :
Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .
⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]
⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.
[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]
Therefore ,
When , x = 2 ,
First Integer : x , 2 ,Second Integer : ( x +1 ) , 3 & Third Integer : ( x +2 ) = 4 .When , x = –7 ,
First Integer : x , – 7 ,Second Integer : ( x +1 ) , – 6 & Third Integer : ( x +2 ) = – 5 .Answer:
Hi,
Step-by-step explanation:
If the "is" means is equal to
Let's say a-1, a, a+1 the 3 consecutive integers.
[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]
[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]
The two sets are : (0,1,2) and (4,5,6).
Jasmine played in a basketball tournament. The ratio of the number of baskets she missed during the tournament to the number of baskets she made is 3:8. If Jasmine missed 9 baskets during the tournament, how many baskets did she make? Draw a diagram to demonstrate how you found your answer.
By using the given ratio, we will conclude that she made 24 baskets.
how many baskets did she make?
We know that the ratio of the number of baskets she missed to the number of baskets she made is 3:8.
This means, for each 3 missed baskets, she made 8.
Here we know that she missed 9. If we divide that by 3, we get:
9/3 = 3.
This means that she missed 3 baskets 3 times. And for each one of these 3 times she makes 8 baskets (for the given ratio).
Then we conclude that she makes 8*3 = 24 baskets.
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A company boss is planning on ordering a gift for each of his employees. He takes a sample of 30 employees in the company and asks them what gift they would like. The table shows the information about his results. Gift Number of employees iPad 12 phone 5 watch 9 voucher 4 There are 110 employees in the company. Work out how many watches should be ordered.
Answer:
I think the answer is 33
Step-by-step explanation:
Extremely sorry if it's wrong
The product of two numbers is 5, if their sum is 9/2. What are the numbers? with detail explaniation
Answer: The numbers are 2 and 2.5
Explanation:
Let one number be "x" and another "y", Note: 9/2 = 4.5 [in decimal form]
[tex]\rule{185}{2}[/tex]
Their product :
[tex]\hookrightarrow \sf x \ \cdot \ y = 5[/tex]
[tex]\hookrightarrow \sf x = \dfrac{5}{y} \quad \ \ \leftarrow \quad equation _1[/tex]
Their sum :
[tex]\hookrightarrow \sf x + y = 4.5[/tex]
[tex]\hookrightarrow \sf x = 4.5-y \quad \ \ \leftarrow \ equation_2[/tex]
Solve them simultaneously:
[tex]\rightarrow \sf 4.5 - y = \dfrac{5}{y}[/tex]
cross multiply
[tex]\rightarrow \sf y(4.5 - y) = 5[/tex]
distribute inside parenthesis
[tex]\rightarrow \sf -y^2 +4.5y - 5 = 0[/tex]
multiply by -1
[tex]\rightarrow \sf y^2 -4.5y + 5 = 0[/tex]
factor them out
[tex]\rightarrow \sf ( y - 2.5)(y - 2)= 0[/tex]
set to 0
[tex]\rightarrow \sf y = 2.5, \ 2[/tex]
Another number:
When one number is 2.5, then another: 4.5 - 2.5 = 2
When one number is 2, then another: 4.5 - 2 = 2.5
Hence, the numbers are 2.5 and 2
Check:
Product: 2 × 2.5 = 5Sum: 2 + 2.5 = 4.5 or 9/2The numbers obtained by the given condition that the product of two numbers is 5 if their sum is 9/2 will be x =( 2 or 5/2) and y = ( 2 or 5/2).
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say the first number is x and the second is y then
Product xy = 5
Sum x + y = 9/2
substitute y = 9/2 - x into first
x( 9/2 - x) = 5
2x² - 9x + 10 = 0
2x² -5x -4x + 10 = 0
x( 2x - 5 ) -2( 2x -5 ) = 0
(x -2)(2x -5) = 0
x =2 and x = 5/2
Corresponding to x y will be y = 2 and y = 5/2.
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HELPPPPPPPPP!!!!!!!!!!!
Nala wants to find out if the quadrilateral shown is a rectangle. Nala's plan: • Find the slopes of all four sides. • See if there are two pairs of equal slopes. • See if there are two pairs of slopes that are negative reciprocals. Will her plan work? Why or why not?
Checking if the two pairs of slopes are negative reciprocal will help he determine if the lines are perpendicular to each other. Therefore her plan will work.
Proof for a quadrilateral
A quadrilateral are shapes with 4 sides. A rectangle is a quadrilateral with 2 parallel sides.
According to Nala's plan to find out if the quadrilateral shown is a rectangle, she can do the following;
See if there are two pairs of equal slopesSee if there are two pairs of slopes that are negative reciprocalChecking if the two pairs of slopes are negative reciprocal will help he determine if the lines are perpendicular to each other.
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What are the zeros of the quadratic function f(x)=8^2-16-15
Answer:
put formula a square minus b square
Mario is making 12 dozen cookies. Each dozen requires
3
5
cup of flour. How many total cups of flour does Mario use?
Answer:
7 1/5 cups of flour
Step-by-step explanation:
divide 3/5 which is 0.6 then multiply that by 12, which is 7.2
then convert that into a fraction which is 7 1/5
if i spent 35 dollars every 2 weeks how much money would i have spent in a year
Answer:
$910
Step-by-step explanation:
there are 52 weeks in a year
52/2 = 26
if someone spends 35 every two weeks then
35x26=910
Answer:
840$
Step-by-step explanation:
2*2= 1 month (4weeks)
35*2= 70
70*12 (months of the year) = 840$
Help please with me math!!
Answer:
17.3
Step-by-step explanation:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Find the difference between coordinates:
(x2 - x1) = (-9 - 8) = -17
(y2 - y1) = (-6 - -3) = -3
Square the results and sum them up:
(-17)^2 + (-3)^2 = 289 + 9 = 298
Now Find the square root and that's your result:
Exact solution: √298 = √298
Approximate solution: 17.2627
Evaluate the expression.
Please help me, I will give brainliest! :)
Answer:
5 + 24x
Step-by-step explanation:
Given phrase - Five more than the product of 24 and a number.
In the given phrase, the word "more" means "addition". Therefore,
⇒ 5 + than the product of 24 and a numberThe word "product" defines multiplication between two numbers. In this case, the product of 24 and a number is 24(number).
⇒ 5 + 24(number)The question stated to use the "n" to represent the unknown number. Let the unknown number be known as "n".
⇒ 5 + 24nTherefore, the expression is 5 + 24n.
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Solve for x
10
*
90⁰
26
Answer:
x=24
Step-by-step explanation:
x=√(26)²-(10)²
x=√676-100
x=√576
x=24
Just a little help :,(
Find the volume of the cone. Round your answer to the nearest tenth. Use 3.14 for T.
9 in.
in³.
3 in.
The volume is about
If y = –0.96 when x = 2.4, what is y when x = 2.9?
Answer:
It should be -1.16
Step-by-step explanation:
Hope this helps :)
A solution contains 8% salt. How much pure water should be added to 25 ounces of the solution to dilute it to a 3% solution? Round to the nearest hundredth if needed.
41.67 ounce of pure water should be added to 25 ounces of the 8% salt solution to dilute it to a 3% solution
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of pure water needed to dilute the solution. Hence:
8% * 25 = 3% * (x + 25)
2 = 0.03x + 0.75
x = 41.67 ounce
41.67 ounce of pure water should be added to 25 ounces of the 8% salt solution to dilute it to a 3% solution
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Given that the line y=ax+b passes through the points A(0; 3) and B(-2;7), how do I find the values of a and b?
Which represents the inverse of the
function f(x) = 4x?
• h(x) = X + 4
O h(x) = x - 4
O h(x) = 3/4x
O h(x) = 1/4X
Answer:
Step-by-step explanation:
Design an instructional activity that could help learners recognise that decimal
fractions can be applied across environmental situations (relating to activities
in real life).
Fraction refers to a part of a whole; e.g when cup is not completely filled, it covers only a part of the cup
What is fraction?The term fraction refers to a part of a whole. To design an instructional activity that could help learners recognize that decimal fractions can be applied across environmental situations, we could look at certain things in the house.
For instance, when cup is not completely filled, it contains water that covers only an fraction of the cup. Also, we could boil a part and not a whole cup of rice. These are all examples of fractions.
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PLEASE HELP ME!!
Use triangle XYZ to answer questions 3-5.
1) Use special right triangles to help find the length of segment XY. What is the exact height of triangle XYZ?
Click the keyboard button to enter your answer.
2)What is the exact area of triangle XYZ? Leave your answer in radical terms.
Click the keyboard button to enter your answer. Show your work.
3)What is the area of triangle XYZ to the nearest tenth of a square in?
The exact height of the triangle is 20.8ft
The area of the right tringle in radical form is 72√3 ft²
The area of the triangle in decimal form is 124.7 ft²
How to find the side and area of a right angle triangle?The side XY or height of the triangle can be found as follows:
Using trigonometric ratios,
tan 60° = XY / 12
XY = 12 tan 60°
XY = 12 × 1.73205080757
XY = 20.7846096908
height = 20.8ft
The area of XYZ = 1 / 2 bh
where
b = baseh = heightTherefore,
The area of XYZ = 1 / 2 × 12 × 20.8 = 124.707658145 = 124.7 ft²
The area in radical form = 1 / 2 × 12 × 12 tan 60°
The area in radical form = 1 / 2 × 12 × 12 × √3 = 144√3 / 2 = 72√3 ft²
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Solve the system of equations.
4x - 2y = 8
3x + 4y = 17
A. (2, 0)
B. (7, -1)
C. (3, 2)
D. (4, 4,)
Answer:
The answer is option C
Step-by-step explanation:
The solution is in the image
Answer:
Step-by-step explanation:
8x - 4y = 16
3x + 4y = 17
11x = 33
x = 3
12 - 2y = 8
-2y = -4
y = 2
(3, 2)
answer is C
Find the value of n in the following
equation. Give your answer as a
decimal.
n+3.1:6.4= 96
Anne, Bridget, and Sasha shared a sum of money. Anne took 1/3 of the total amount, and Bridget took 1/4 of the remaining money. After both of them had taken their share, Sasha took 1/2 of what was left. If Anne took $160, how much did Sasha take?
Answer:
180
Step-by-step explanation:
160= 1/3 * total
160*3 = total
480 = total
bridget = 1/4(total)
bridget = 1/4(480)
bridget took 120
Sasha took 1/2 of 360
Sasha took $180.
Find the value of x.
33°
107°
x
Answer:
140
Step-by-step explanation:
Angles in a triangle add up 180 :
180 = 107 + 33 + y
y = 180 - (107+33)
y = 180 - 140
y = 40
Angles on a straight line add up to 180 so :
180 = x + y
180 = x + 40
x= 180 - 40
x = 140
Hope this helped and have a good day
Answer:
x = 140°
Step-by-step explanation:
Concepts
The Exterior Angle Theorem states that the two remote angles in a triangle is equal to the exterior angle.
Application
In this case, the two remotes angles are 107 and 33°, and the exterior angle is x. Now, all we have to do is just add 107 and 33 to get our answer.
Solution
107 + 33140°Select the correct answer from each drop-down menu. The graph represents the piecewise function.
The functions will be defined as y = x² if 0 ≤ x < 3, y = -x + 10 if 3 < x ≤ 6, and y = x + 2 if 6 ≤ x ≤ 10.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The graph is given below.
The function can be defined as
The parabolic equation will be
f(x) = x²
The equation of the absolute function will be
f(x) = |x - 6| + 4
Then we have
[tex]f(x) = \left\{\begin{matrix}y=x^2 & 0\leq x < 3 \\\\y=-x+10 & 3 < x\leq 6 \\\\y=x+2 & 6\leq x \leq 10 \\\end{matrix}\right.[/tex]
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Elvera Hilton earns $12 an hour at her job. The hours she worked during each of the last four weeks are shown below
Answer:
12x7 4 times add it up u got the anwser
Ms. Lui earned an annual income of 775,000, what is the weekly salary?
Answer:
$14,903.85
Step-by-step explanation:
So, Ms. Lui earns $775,000 each year. To find the weekly salary, we have to divide the annual income by the amount of weeks in a year. There are about 52 weeks in one year. Let's find the weekly salary:
[tex]\frac{775000}{52} = 14,903.85[/tex]
Therefore, Ms. Lui earns $14,903.85 a week.
Hope this helps! If you have questions about my work, please leave them in the comments!
Find the solution set for |2x-3|=9
Answer:
x = 6, -3
Step-by-step explanation:
. . . . . . . . . . . . . . . . .
math homework help - please
It costs $3 for children and $7 for adults to attend a school game. If 5000 people attended the game and the total taking was 25000, determine no. of children and adults that atteneded
Answer:
The number of children is 2500 and the number of adults that attended the game is also 2500.
Step-by-step explanation:
Let us consider that, number of children be x and number of adults be y that attend game.
Since, total 5000 people attend the game.
It costs $3 for children and $7 for adults and the total takings at the door was $25000
Substitute value of x from equation 1 into equation 2.
So that,
Thus, the number of children is 2500 and the number of adults that attended the game is also 2500.
Isabel’s competition who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. Graph the function in part e. Is your graph discrete or continuous? Explain.
Answer:
x= 1.99
f(x) = 1.99x + 3
Step-by-step explanation:
Hope this helps! (;
Will give 50 points for answer to this question