Answer:
(–∞, 8)
Step-by-step explanation:
the sum of two squares of two consecutive natural numbers is 41.Find the numbers
The 2 unknown numbers are 4 and 5 .
Explanation :Let the numbers be x and x + 1.
From the given information,
[tex]\dashrightarrow\sf \ \ \ x^2 + (x + 1)^2 = 41 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 = 41 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 - 41=0 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ {x}^{2} + x - 20 = 0 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ (x + 5)(x - 4)=0 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ { \underline{ \boxed{ \bf{ \red{x = - 5,4}}}}} \ \bigstar \\ \\ [/tex]
But, as we know -5 is not a natural number,
Hence, x = 4 .
So the 2 unknown numbers are :
x = 4 [1st number]x + 1 = 4 + 1 = 5 [2nd number]━━━━━━━━━━━━━━━★ Solution :
Let the number be x and x + 1.
[tex]\rule{130}1[/tex]
[tex]\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccording} \: to \: \mathscr {Q} \bf{uestion} ....}}}[/tex]
[tex]:\implies\sf x^2 + (x + 1)^2 = 41 \\\\\\:\implies\sf 2x^2 + 2x + 1 - 41 = 0\\\\\\:\implies\sf 2x^2 + 2x + 40 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + 5x - 4x - 20 = 0\\\\\\:\implies\sf x(x + 5) - 4(x + 5) = 0\\\\\\:\implies\sf (x + 5)(x - 4) = 0\\\\\\:\implies\underline{\boxed{\sf x = -5, 4}}[/tex]
⠀
We know that -5 is not a natural number. Hence, x = 4.
[tex]\therefore\:\underline{\textsf{The two consecutive natural number is \textbf{4 and 5}}}.[/tex]
If six is decreased by four times a number n, the result is 12. Find the solution
Answer:
n=-1.5
Step-by-step explanation:
6-4n=12
Subtract 6 from 12
-4n=12-6
Simplify
-4n=6
Divide each side by -4
-4n/-4=6/-4
Simplify
n=-1.5
If Cody makes $10 an hour at his after school job, how many hours will it take him to earn $150?
Answer:
It will take him 15 hours, Good luck!!
Step-by-step explanation:
the lunch lady has 6 pounds of lasagna. if she makes 1/2-pounds servings using this lasagna, how many servings can she make?
Answer:
[tex]\boxed{12}[/tex]
Step-by-step explanation:
[tex]6/\frac{1}{2} =6*2=12[/tex]
4.Why might there be a break in the vertical axis on a line graph?
A. Numbers in that range have been left out.
B. Those numbers aren't important.
C. There was no data available for those numbers.
D. The creator of the graph made a mistake.
Answer:
there was no data available for those numbers
Step-by-step explanation:
if you want to graph at intervals of (for example) 15, but your numbers are ranging from 115 - 200, you don't want to a huge blank space from 0 - 115 on the y-axis.
if you create a break at the bottom (and only the bottom) you can start at 100 and have intervals of 15 from there. this eliminates dead space on a graph.
Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For Each Hour Over 40 Hours Of Work Per week.For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?
a. $550
b. $605
c. $625
d. $750
e. $825
Answer:
$605
Step-by-step explanation:
The correct question is
Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?
a. $550
b. $605
c. $625
d. $750
e. $825
For the first $40 that Taho works, he earns $11 x 40 = $440
For the extra $10 (since he worked 50 hrs that week)
1½ of $11 per hr = 1.5 x $11 = $16.5
for the 10 days extra = $16.5 x 10 = $165
total pay = $440 + $165 = $605
Part B
plot point C(2,7). If M is the midpoint of CD what are the coordinates of D
Answer:
The midpoint of CD is [tex](\frac{2+a}{2},\ \frac{7+b}{2})[/tex].
Step-by-step explanation:
Consider a line CD.
The point C is (2, 7).
Assume that the point D is, (a, b).
The formula to compute the midpoint is:
[tex](x,y)=(\frac{x_{1}+x_{2}}{2},\ \frac{y_{1}+y_{2}}{2})[/tex]
Compute the midpoint of CD as follows:
[tex](x,y)=(\frac{x_{1}+x_{2}}{2},\ \frac{y_{1}+y_{2}}{2})[/tex]
[tex]=(\frac{2+a}{2},\ \frac{7+b}{2})[/tex]
Thus, the midpoint of CD is [tex](\frac{2+a}{2},\ \frac{7+b}{2})[/tex].
x+2/x–2 –x–2/x+2 = 5/6
Answer:
(x-10)(5x+2)
Step-by-step explanation:
this is the answer of the question.you can clearly see in the pic of the solution
write and equation that represents a vertical stretch by a factor of 3 and a reflection in the x-axis of the graph of g(x)=|x|
Answer:
g(x) = -3|x|.
Step-by-step explanation:
Multiplying by 3 stretches the graph vertically by a factor 3 and the negative reflects in the x-axis.
The equation that represents a vertical stretch by a factor of 3 and reflection in x-axis of the graph of function g ( x ) = | x | is given by
f ( x ) = -3 | x |
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs),
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the function be g ( x ) = | x |
Now , let the transformed function be f ( x )
The value of the function f ( x ) is calculated by
Step 1 :
Vertical stretch by a factor of 3
The Vertical stretch by a factor is done by
k: y = k × f(x)
So , multiplying the parent function by 3 , we get
f ( x ) = 3 | x |
Step 2 :
Reflection in the x-axis ,
The value of f ( x ) is multiplied by -1
So ,
f ( x ) = -3 | x |
Therefore , the transformed function f ( x ) = -3 | x |
Hence , The equation that represents a vertical stretch by a factor of 3 and reflection in x-axis of the graph of function g ( x ) = | x | is given by
f ( x ) = -3 | x |
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Owen plots the numbers 4, –6, –8, and –3 on a horizontal number line. Which list shows the numbers in the order in which they would appear from left to right on the number line? –8, –6, –3, 4
Answer:-8, -6,-3, 4 is the correct answer
Step-by-step explanation:
Answer:
Answer A
Step-by-step explanation:
What is the area of a square with the vertices (3, 3), (6, 6), (9,3), and (6,0)?
Answer:
A = 18 square unitsStep-by-step explanation:
taking A(3, 3), B(6, 6), C(9,3) and D(6,0)
we have: [tex]y_A=y_C\quad and\quad x_B=x_D[/tex] so the AC and BD are diagonals, that means:
AB = BC = CD = DA = s
[tex]s=\sqrt{(6-3)^2+(6-3)^2}=\sqrt{3^2+3^2}=\sqrt{18}\\\\\\A=s^2=(\sqrt{18})^2=18[/tex]
Susan charges $8 per hour walking her neighbor’s dog. She charges $12 per hour babysitting. Part A: Define the variables. Part B: Write an expression to represent the amount Susan earns dog walking and babysitting
Answer:
the total she earns with "d" hours of dog walking and "b" hours of babysitting is given by: 8 d + 12 b
Step-by-step explanation:
If we use "d" to represent the number of hours that Susan walks the dog, and we define "b" as the number of hours she babysits, then the expression that represents the amount she earns by walking the dog is: $8 times d = 8 d
Similarly, the amount she earns by babysitting is $12 times b = 12 b
Then the total she earns with "d" hours of dog walking and "b" hours of babysitting is: 8 d + 12 b
8) За (x-y) - (х-у)
Answer:
[tex]3a \times x - y - x - y \\ 3a \times x - x - y - y \\ 3a \times - 2y - \\ - 6ay[/tex]
Answer:
8,3
Step-by-step explanation:
Foreshadowing is a storytelling device that...
A)Gives hints to reader about a future event.
B)Provides details about a past event.
C)Tells readers that something bad always happens.
D)Creates confusion for the reader.
Answer:A)Gives hints to reader about a future event.
Step-by-step explanation:
Answer:
A) Gives hints to reader about a future event.
Step-by-step explanation:
Foreshadowing is one of the storytelling device that gives hints to readers about the future events.
Hope this helps ;) ❤❤❤
The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent. Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent. Explain how a calculation for change in percentage (increase or decrease) is different from a calculation that involves multiplying by percentages. Why is the wording of percentage problems so important? Give examples to illustrate your point.
Answer:
Step-by-step explanation:
Given the expressions :
The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent.
Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent.
Let the original price = x
Expression 1 : The list price of the item is 80 percent of the original price
List price = 80% of x
List price = 0.8x
Expression 2: The price of the item has been reduced by 80 percent
Price = x - 80% of x
Price = x - 0.8x
Price = 0.2x
Multiply by percentages is different from an Incremental or decrement in percentage. The first expression above signifies a direct multiplication by the stated percentage while the second signifies a decrease in price based on a certain percentage of the original price.
Wording of percentages are so important for clarity in other to understand if the statement signifies a direct application of the percentage prescribed or a change in quantity, amount or size relative to the base unit.
Have you ever been on or seen a ride like this at a fair or amusement park? Imagine being strapped into your seat at the bottom of this 350-foot tower, with your feet dangling just above the ground. You make the trip up the tower at a steady rate of 20 feet per second, stop at the top of the tower to hang for a few seconds, then suddenly drop in a free fall for 288 feet! The trip up the tower is a linear relationship. The height of the riders, h, is equal to the constant rate multiplied by the time, t, since they began the trip up. The free fall down the tower is a quadratic relationship. The distance from the top to the bottom of the free fall, d, is modeled by this equation, where t is the time since the free fall began and is the initial distance above the bottom of the free fall.
Answer:
no
Step-by-step explanation:
The only question here seems to be ...
Have you ever been on or seen a ride like this at a fair or amusement park?
__
I have not seen such a ride.
I have not seen such a ride.
What is an Amusement Park?A large outdoor area with fairground rides, shows, refreshments, games of chance or skill, and other entertainments.
Determining:The only question here seems to be ...
Have you ever been on or seen a ride like this at a fair or amusement park?
I have not seen such a ride.
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there are 15 black marbles and 10 white marbles in a bag. If you pick a marble from the bag without looking, what are your chances of picking a white marble?
Answer: 40%
Step-by-step explanation:
Answer: 2/5 or 40%
Step-by-step explanation: 15 + 10 = 25 and 10/25 simplifies to 2/5.
The discount on a new refrigerator was $250. This was a discount of 18 %
Step 2 of 3: What was the sale price? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
Answer:
x = 1388.89
Step-by-step explanation:
x - the sale price of new refrigerator
18%x = 0.18x - the discount
0.18x = 250
x = 250÷0.18 = 1388.8888...
x = 1388.89
14b + 6 = 6 14b = Subtract 6 from both sides b = Divide both sides by 14
Answer:
Step-by-step explanation:
((b+2)(b+12)/(b+2)(b+3))*(b+3)
= (b+12)
A price decreases from $986 to $828.24. What is the percent change?
Answer:
-16% change
Step-by-step explanation:
The formula for a percent decrease is [tex]\frac{original-new}{original}\cdot100[/tex]. The original value was 986, and the new value is 828.24, so we can substitute inside the equation.
[tex]\frac{986-828.24}{986} \cdot100\\\\\frac{157.76}{986} \cdot100\\\\0.16\cdot100\\\\16[/tex]
So the percent change is -16%.
Hope this helped!
A gaming console cost $299.99. Each game that comes with the console is an additional cost of $20.00. Mr. Yao decide to by x number of games Write a variable expression for the number of games Mr. Yao bought
This question is not correctly written
Complete Question
A gaming console cost $299.99. Each game that comes with the console is an additional cost of $20.00. Mr. Yao decide to by x number of games Write a variable expression for cost of the number of games Mr. Yao bought
Answer:
Variable expression for the cost of the number of games that Mr Yao bought =
$20x
Where x = number of games that he bought.
Step-by-step explanation:
A variable expression can be defined as a mathematical expression where there is at least one (or more) unknown variable(s)that we have to look or solve for.
The unknown variable is always represented by letters of the alphabet, a, b, x, y e.t.c.
A variable expression can also be called an algebraic expression.
From the above question, we are told that:
Cost of a gaming console = $299.99
If you buy a game with the console = Additional $20.00
My Yao bought = x number of games
Variable expression for the cost of the x number of games that Mr Yao bought
$20 × x
= $20x
Where x = number of games that Mr Yao bought.
A company placed $500,000 in three different investment plans.
The company placed some money into short-term notes paying 5.5% per year. They placed three times as much into government bonds paying 5% per year. They placed the rest in utility bonds paying 4.5% per year.
The income for one year was $25,000. How much more money did the company place in government bonds than in utility bonds?
A. $100,000
B. $200,000
C. $300,000
D. $400,000
Answer:
B. $200,000
Step-by-step explanation:
Let x be the amount placed at 5.5%
3x is the amount placed at 5%
This leaves the rest for the 4.5 % 500000- x - 3x = 500000-4x
Assuming simple interest
I = PRT where I is interest, P is principle, rate is rate and t is time
Interest for the 5.5% for 1 year is
I = x * .055 * 1 = .055x
Interest for the 5.% for 1 year is
I = 3x * .05 * 1 = .15x
Interest for the 4.5% for 1 year is
I = 500000-4x * .045 * 1 = 22500 - 0.18 x
Add the interest together to get the income for 1 year
.055x+ .15x+22500 - 0.18 x=25,000
Combine like terms
0.025x+22500=25000
Subtract 22500
.025x =2500
Divide by .025
x =100000
short term notes is 100000
3*x = 300000 = government bonds
The rest is utility bonds 500000- 100000-300000 = 100000
We want how much more in government bond than utility bond
300000 -100000 = 200000
Answer:
200000
Step-by-step explanation:
the short term =x
government bonds =3x
utility bonds: 500000-4x
0.055x+3(0.05(x)+0.045(500000-4x)=25000
0.055x+0.15x+22500-0.18x=25000-22500
0.055x+0.15x+22500-0.18x-22500=2500
0.025x=2500
x=2500/0.25
x=100000
government bonds=3x=3(100000)=300000
utility bond=(500000-400000)=100000
government bonds than in utility bonds:
300000-100000=200000
what is this −n+(−4)−(−4n)+6
Answer:
3n + 2
Step-by-step explanation:
[tex]−n+(−4)−(−4n)+6[/tex]
Open the parentheses
[tex] - n - 4 + 4n + 6 \\ [/tex]
Add similar elements
[tex] - n + 4n - 4 + 6 \\ 3n + 2 \\ [/tex]
Answer:
[tex] - n + 6[/tex]
Step-by-step explanation:
[tex] - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6[/tex]
Which table shows a proportional relationship between x and y? A. x y 2 4 3 6 4 9 B. x y 3 4 9 16 15 20 C. x y 4 12 5 15 6 18 D. x y 1 4 2 8 3 15
Answer:
C.
Step-by-step explanation:
The relationship is proportion if y/x is constant.
So it is C because 12/4 = 15/5 = 18/6 = 3.
Please help me to prove this..
Step-by-step explanation:
1 / (sin 10°) − √3 / (cos 10°)
Multiply top and bottom of the first fraction by ½ cos 10°.
½ cos 10° / (½ cos 10° sin 10°) − √3 / (cos 10°)
Multiply top and bottom of the second fraction by ½ sin 10°.
½ cos 10° / (½ cos 10° sin 10°) − ½√3 sin 10° / (½ sin 10° cos 10°)
Combine fractions.
(½ cos 10° − ½√3 sin 10°) / (½ sin 10° cos 10°)
Change ½ to sin 30°, and change ½√3 to cos 30°.
(sin 30° cos 10° − cos 30° sin 10°) / (½ sin 10° cos 10°)
Use angle sum formula.
sin(30° − 10°) / (½ sin 10° cos 10°)
sin 20° / (½ sin 10° cos 10°)
Multiply top and bottom by 4.
4 sin 20° / (2 sin 10° cos 10°)
Use double angle formula.
4 sin 20° / sin 20°
4
We are given the equation 1 / sin(10°) - √3 / cos(10°) = 4, and want to prove that 1 / sin(10°) - √3 / cos(10°) equals 4.
Let's start by combining the expressions '1 / sin(10°)' and '√3 / cos(10°)' in the expression '1 / sin(10°) - √3 / cos(10°).'
1 / sin(10°) - √3 / cos(10°)
= cos(10°) - √3sin(10°) / sin(10°) [tex]*[/tex] cos(10°)
Now let's multiply the numerator and denominator by a common value. In this case it's most suitable to multiply both by 2. We will receive the expression 2(cos(10°) - √3sin(10°)) / 2(sin(10°) [tex]*[/tex] cos(10°)). We can further simplify this expression knowing that 2(sin(10°) [tex]*[/tex] cos(10°)) = 2sin(20°).
2(cos(10°) - √3sin(10°)) / 2sin(20°)
We can now bring the two on the bottom to the numerator, becoming 1 / 2. Remember that the ' 1 / 2 ' will be distributed now. After the distribution we receive the expression 4( 1 / 2(cos(10°) - √3 / 2sin(10°)) / 2sin(20°). We can now use the trivial functions 1 / 2 = sin(30°), and √3 / 2 = cos(30°).
4(sin(30°)(cos(10°) - cos(30°)(sin(10°) ) / sin(20°))
= 4((sin(30 - 10°)) / sin(20°) = 4
Does anyone know how to solve this? It’s really starting to stress me out.
PS: You just can solve the lim(x->2) instead of lim(u->0) if u want
Answer:
π − 12
Step-by-step explanation:
lim(x→2) (sin(πx) + 8 − x³) / (x − 2)
If we substitute x = u + 2:
lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)
lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u
Distribute the cube:
lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u
lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u
lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u
Using angle sum formula:
lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u
lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u
Divide:
lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]
lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)
lim(u→0) (sin(πu) / u) − 12
Multiply and divide by π.
lim(u→0) (π sin(πu) / (πu)) − 12
π lim(u→0) (sin(πu) / (πu)) − 12
Use special identity, lim(x→0) ((sin x) / x ) = 1.
π (1) − 12
π − 12
x2 + 2x -1 = 0 in English words
Answer:
a number squared plus twice a number minus one equals zero
Step-by-step explanation:
GUYS I NEED HELP I have no idea what to do and I can’t ask the teacher for help because it’s night already-
Answer:
x=6
Step-by-step explanation:
127-83=9x-10
44=9x-10
+10.0 +10.0
54=9x
divide by 9 on both sides
x = 6
Expand and combine like terms.
(8 – n^7)(8 +n^7)
Answer:
Step-by-step explanation:
(a - b)(a + b) = a² - b²
(8 - n⁷)(8 + n⁷) = 8² - (n⁷)² = 64 - n¹⁴ {(aˣ)ⁿ = aˣ*ⁿ }
Or
Use FOIL method
(8 - n⁷)(8 + n⁷) = 8*8 + 8*n⁷ + (-n⁷)*8 + (-n⁷)*n⁷
= 64 + 8n⁷ - 8n⁷ - n⁷⁺⁷
= 64 - n¹⁴
Name the line and plane shown in the diagram. PLZ ANSWER ASAP, DUE IN 1 HOUR
Answer:
Line PQ. Not enough Info for the Plano tho.
Step-by-step explanation:
Look at the 2 points, and thats the name of the line.