ANSWER
5.2387 and 5.2437
EXPLANATION
To round a decimal to the nearest hundredth means we should round to two decimal places.
To round to two decimal places we consider the third decimal place.
When we round 5.2387 to the nearest hundredth, we obtain 5.24 because the third decimal place is greater than or equal to 5 so we round up.
When we round 5.2437 to the nearest hundredth, we get 5.24 because the third decimal place less than 5 so we round off.
In fact there are infinitely many decimals that will round to 5.24 when rounding to the nearest hundredth.
5. A deck should have a perimeter of 90 feet and a minimum area
of 450 square feet. Write and solve an inequality to find the
possible width of the deck.
Answer:
The minimum value of the width is 15 ft and the maximum value of the width is 30 ft
Step-by-step explanation:
Let
x -----> the length of the deck
y ----> the width of the deck
we know that
The perimeter of the deck is equal to
[tex]P=2(x+y)[/tex]
[tex]P=90\ ft[/tex]
so
[tex]90=2(x+y)[/tex]
[tex]45=(x+y)[/tex]
[tex]x=45-y[/tex] -----> equation A
The area is equal to
[tex]xy\geq 450[/tex] -----> inequality B
[tex](45-y)y\geq 450\\ \\-y^{2} +45y-450\geq 0[/tex]
Solve the quadratic equation by graphing
The possible width of the deck are the values of y in the interval
[15,30]
All real numbers greater than or equal to 15 ft and less than or equal to 30 ft
see the attached figure
The minimum value of the width is 15 ft and the maximum value of the width is 30 ft
Classify the following triangle. Check all that apply.
Answer:
Scalene and Acute
Step-by-step explanation:
Since all of the leg measures of the triangle are not equal to each other, this triangle would be scalene.
In addition, all of the angle measures of the triangle is less than 90 making it an acute triangle.
Answer:
Scalene and Acute
Step-by-step explanation:
Since none of the sides have the same length: scalene
Isosceles ( 2 sides same length) False
Equilateral( 3 sides same length) False
Acute: all angles less than 90 degrees: True
Right: one angle equal to 90 degree: False
Obtuse: One angle greater than 90 degrees: False
If f(x) = 1/2x-14,then f^-1(x)=
Answer:
f ^-1 (x) = 2x+28
Step-by-step explanation:
f(x) = 1/2x-14
Replace f(x) with y
y = 1/2 x -14
Exchange x and y
x = 1/2 y -14
Solve for y
Add 14 to each side
x+14 = 1/2 y -14+14
x+14 = 1/2 y
Multiply each side by 2
2(x+14)= 1/2 y*2
2x+28 = y
The inverse function is
f ^-1 (x) = 2x+28
if f(x) =3x-2 and g(x) =2x+1 fins (f+ g) (x)
Answer:
5x - 1
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x) = 3x - 2 + 2x + 1 ← collect like terms
= 5x - 1
[tex](f+g)(x)=3x-2+2x+1=5x-1[/tex]
Point x,y reflected across the y axis is what?
Answer:
opposite
Step-by-step explanation:
Answer:
(- x, y)
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y )
Look at the picture
↓↓↓↓↓↓↓↓↓↓
Answer:
2
Step-by-step explanation:
Answer:
The slope of line p is 3.
The slope of line q is -3.
Step-by-step explanation:
Points on line p = [tex](x_1,y_2),(x_2,y_2):(1,-1), (0.-4)[/tex]
Slope of line p ,m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-4-(-1)}{0-(1)}=3[/tex]
The slope of line p is 3.
Points on line q = [tex](x_1,y_2),(x_2,y_2): (0,2), (1,-1)[/tex]
Slope of line q ,m'= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m'=\frac{-1-2}{1-0}=-3[/tex]
The slope of line q is -3.
The graph of which function will have a maximum and a y-intercept of 4? f(x) = 4x2 + 6x – 1 f(x) = –4x2 + 8x + 5 f(x) = –x2 + 2x + 4 f(x) = x2 + 4x – 4
Answer:
It is f(x) = -x^2 + 2x + 4.
Step-by-step explanation:
As it has a maximum the coefficents of x^2 will be negative.
f(x) = -x^2 + 2x + 4
The y-intercept occurs when x = 0 so
y-intercept = 0 + 0 + 4 = 4.
-
ANSWER
[tex]f(x) = - {x}^{2} + 2x + 4[/tex]
EXPLANATION
The graph of the function that will have a maximum and a y-intercept of 4 is
[tex]f(x) = - {x}^{2} + 2x + 4[/tex]
To check for the y-intercept, we put x=0 into the function.
[tex]f(0) = - {0}^{2} + 2(0)+ 4[/tex]
This implies that,
[tex]f(0) = 4[/tex]
We can see that the coefficient of the quadratic term is -1.
Since the coefficient of the quadratic term is less than zero, the graph will have a maximum point.
What is half of 3.334
What is the lcm of xy(x+1) and x(x+2)
[tex]xy(x+1)=x\cdot y\cdot (x+1)\\x(x+2)=x\cdot (x+2)\\\\\text{lcm}(xy(x+1),x(x+2))=x\cdot y \cdot (x+1)\cdot (x+2)=xy(x+1)(x+2)[/tex]
30% of___=100. Need help
Answer:
0.3x = 100
x = 1000/3 = 333 and 1/3
Including 6% sales tax, an inn charges $135.68 per night. Find the inns nightly cost
Answer:
144 dollars
Step-by-step explanation:
Which statement correctly describes the inverse of the following function?
Answer:
D. It is a function
Step-by-step explanation:
When you flip the points of the function, you have:
(2,1) (4,3) (6,5) (8,7)
Each x value has its own y value, so it is a function
Option D is correct. The inverse of the given function is a function since all the element in its co-domain has a unique element in the domain.
For a mapping to be called a function, it must have but the input values called the domain and the output values known as the co-domain.
All the domains must also have a corresponding co-domain, else it is not a function.
From the given mapping, we can see that all the values in the domain have corresponding values in the co-domain and vice versa(in the case of its inverse).
Hence we can conclude that the inverse of the given function is a function making other options incorrect.
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Determine the values of the letters to complete the conditional relative frequency table by column.
a =
b =
Answer:
[tex]a=0.1\\b=0.85[/tex]
Step-by-step explanation:
In this problem we are calculating the relative frequency conditional by columns.
Therefore the sum of the frequencies of each column must be equal to 1.
Then we use this condition to calculate the values of a and b
So:
[tex]0.9 + a = 1\\a = 1-0.9\\a = 0.1[/tex]
[tex]b +0.15 = 1\\b = 1-0.15\\b = 0.85[/tex]
Finally
[tex]a=0.1\\b=0.85[/tex]
Answer:
Values of a and b are:
a=0.1
and b=0.85
Step-by-step explanation:
As we can clearly see from the table that sum of each column is equal to 1.0
i.e. 0.9+a=1.0
and b+0.15=1.0
Hence, a=1.0-0.9
= 0.1
and b=1.0-0.15
=0.85
Hence, Values of a and b are:
a=0.1
and b=0.85
what number should be added to the expression x^2+3x+___ in order to create a perfect square trinomial?
3/2
3
9/4
9
Answer: THIRD OPTION.
Step-by-step explanation:
We need to remember that we can create a perfect square trinomial by squaring a binomial:
[tex](a\±b)^2=a^2\±2ab+b^2[/tex]
Then we need need to pick the coefficient of the x term of the given expression, divide it by 2 and square it:
[tex](\frac{3}{2})^2=\frac{9}{4}[/tex]
Therefore, the number that should be added to the given expression in order to create a perfect square trinomial is:
[tex]\frac{9}{4}[/tex]
Lauren has 108 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 9 kids on her block. Write qn equation to show how many pieces of candy each kid will receive.
Divide the total pieces by the number of kids:
108 pieces / 9 kids = 12 pieces per kid.
Answer:
x= 108/9
Step-by-step explanation:
What is the range of f(x) = 3^x+ 9?
{yly<9}
{yly>9)
{yly> 3}
{yly< 3}
Answer:
ALL REAL NUMBERS actually
Step-by-step explanation:
Any exponential function like this, is ALWAYS R.
Define the following terms. a. Multiplicand b. Multiplier c. Product
Answer:
Multiplicand ;quantity that is to be multiplied by another (the multiplier).
Multiplier ;person or thing that multiplies.a quantity by which a given number (the multiplicand) is to be multiplied.ECONOMICSthe factor by which the return deriving from an expenditure exceeds the expenditure itself.
Product;an article or substance that is manufactured or refined for sale."marketing products and services"2.MATHEMATICSa quantity obtained by multiplying quantities together, or from an analogous algebraic operation.
Step-by-step explanation:
Please mark brainliest!
What is the intercept of the line given by the equation below?
y=-10x + 14
O A. (14,0)
O B. (-10,0)
C. (0, 14)
D. (0, -10
Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 10x + 14 ← is in slope- intercept form
with y- intercept c = 14 ⇒ (0, 14) → C
what should be added to -7/20 to get -2/5
Answer:
-1\20
Step-by-step explanation:
As percentages: ? + -35% = -40%; -5% = ?
As decimals: ? + -0.35 = -0.4; -0.05 = ?
**-⅖ = -8\20 [Least Common Denominator]
Guy decides to get in shape by running. The first day, he runs 1 mile in 12 minutes. Two months later he has decreased his mile time by 25%. What is his mile time now? 6 minutes 7.5 minutes 8 minutes 9 minutes
Answer:
[tex]25 \div 100 \times 12 = 3[/tex]
[tex]12 - 3 = 9[/tex]
[tex] = 9minutes[/tex]
Answer:
9 minutes
Step-by-step explanation:
solve the system...................
Answer:
first option
(8, -1)
Step-by-step explanation:
We have the following system of linear equations
[tex]\left \{{{x+6y=2} \atop {5x+4y=36}} \right.[/tex]
To solve the system multiply the first equation by -5 and then add it to the second equation.
[tex]-5*(x+6y)=2*(-5)[/tex]
[tex]-5x -30y=-10\\5x+4y=36[/tex]
-----------------
[tex]-26y = 26[/tex]
[tex]y = -1[/tex]
substitute [tex]y = -1[/tex] in any of the two equations and then solve for x
[tex]5x+4(-1)=36\\5x-4=36\\5x = 36+4\\5x = 40\\[/tex]
[tex]x =8[/tex]
The answer is the first option
(8, -1)
What are the discontinuity and zero of the function f(x) = x^2 + 8x + 7 / x + 1
Answer:
- Discontinuity at (-1,6)
- The zero is at (-7,0)
Step-by-step explanation:
Given the function [tex]f(x)=\frac{x^2 + 8x + 7}{x+1}[/tex], you need to factor the numerator. Find two number whose sum be 8 and whose product be 7. These are 1 and 7, then:
[tex]f(x)=\frac{(x+1)(x+7)}{(x+1)}[/tex]
Then, the denominator is zero when [tex]x=-1[/tex]
Therefore, [tex]x=-1[/tex] does not belong to the Domain of the function. Then, (-1,6) is a discontinuity point.
Simplifying, you get:
[tex]f(x)=x+7[/tex]
You can observe that a linear function is obtained.
This function is equal to zero when [tex]x=-7[/tex], therefore the zero of the function is at (-7,0).
ANSWER
Discontinuity:
[tex]x = - 1[/tex]
Zero:
[tex]x = - 7[/tex]
EXPLANATION
The given rational function is
[tex]f(x) = \frac{ {x}^{2} + 8x + 7 }{x + 1} [/tex]
We factor function to obtain:
[tex]f(x) = \frac{(x + 1)(x + 7)}{x + 1} [/tex]
This function is not continuous when
[tex](x + 1) = 0[/tex]
The function is not continuous at
[tex]x = - 1[/tex]
When we simplify the function, we get;
[tex]f(x) = x + 7[/tex]
The zero(s) occur at
[tex]x + 7 = 0[/tex]
[tex]x = - 7[/tex]
Solve for x: 5 − (x + 5) > −2(x + 4)
Answer:
x > -8
Step-by-step explanation:
5 - (x+5) > -2(x+4)
5 - x - 5 > -2x -8
- x > -2x -8
-x +2x > -8
x > -8
The answer is X > -8
Here is it graphed:
Perform the indicated operation. x/2+y/3-z/4
[tex]\bf \cfrac{x}{2}+\cfrac{y}{3}-\cfrac{z}{4}\implies \stackrel{\textit{using the LCD of 12}}{\cfrac{(6)x~~+~~(4)y~~-~~(3)z}{12}}\implies \cfrac{6x+4y-3z}{12}[/tex]
Question: Perform the indicated operation. [tex]\frac{x}{2}+\frac{y}{3}-\frac{z}{4} = ?[/tex]
Answer: [tex]\frac{6x+4y-3z}{12}[/tex]
Hope I helped!!! :)
(I had this same question)
Evaluate 4x - 2 when x = 5.
Answer: D is correct, 18
Step-by-step explanation:
You plug in 5 for x...
4(5)-2=you answer
20-2=your answer
18= your answer
Which group of ordered pairs are on the line given by the equation 5x−2y=65x-2y=6?
The ordered pairs (294.5, 61), (364, 70), and (605.5, 88.5) are on the line given by the equation 5x - 2y = 6.
Explanation:The equation given is 5x - 2y = 6. To determine which group of ordered pairs lies on this line, we can substitute the x and y values of each ordered pair into the equation and check if the equation holds true:
For the ordered pair (294.5, 61), substituting x = 294.5 and y = 61 gives: 5(294.5) - 2(61) = 6, which is true.For the ordered pair (364, 70), substituting x = 364 and y = 70 gives: 5(364) - 2(70) = 6, which is true.For the ordered pair (605.5, 88.5), substituting x = 605.5 and y = 88.5 gives: 5(605.5) - 2(88.5) = 6, which is true.Therefore, all three ordered pairs (294.5, 61), (364, 70), and (605.5, 88.5) lie on the line given by the equation 5x - 2y = 6.
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The diagram below represents the measurements of Jennie’s yard. The yard’s width is x feet shorter than its length. If the area of the yard is 540 square feet, how many feet shorter than the length is the width?
Answer: The width is 12 feet shorter than the length.
Step-by-step explanation:
The area of a rectangle can be calculated with this formula:
[tex]A=lw[/tex]
Where "l" is the lenght and "w" is the width of the rectangle.
We know that lenght of Jennie's yard is 30 feet, the width is [tex](30-x)ft[/tex] and the area is 540 square feet. Then:
[tex]l=30\\w=(30-x)\\A=540[/tex]
Substitute these values into the formula and then solve for "x":
[tex]A=lw\\\\540=30(30-x)\\\\540=900-30x\\\\30x=900-540\\\\x=\frac{360}{30}\\\\x=12[/tex]
Therefore, the width is 12 feet shorter than the length.
Answer:
C
Step-by-step explanation:
got it on edge
If you are just building your payment history, how many points from a perfect score will you possibly miss?
A new borrower cannot achieve a perfect credit score, but the number of points missed is not specific and varies individually. Fair credit decisions are based on facts, not personal attributes. Late payment fees and interest on carried balances also affect your credit score.
Explanation:When you are building your payment history, it's essential to understand the impact of your actions on your credit score. A perfect credit score is typically seen as 850. As a new borrower, lacking a lengthy credit history, you may not have a perfect score, but the exact number of points you may miss cannot be precisely determined without considering individual credit activities. However, every lender has different criteria for evaluating credit scores, and it is fair practice that race, gender, religion, and other such attributes are not considered in credit scoring.
If you carry a credit card balance from month to month, you will incur interest charges, which can quickly accumulate and affect your credit utilization ratio, thereby potentially lowering your credit score. Promptly paying off credit card balances and keeping a low utilization rate are key strategies to maintain and improve your credit score.
Remember that late payments can result in additional charges, as in the case where a credit card company charges a $10 late fee and $5 daily until the payment is settled. Such penalties not only burden you financially but can also impact your credit score if late payments are reported to credit bureaus.
Final answer:
When starting to build your payment history, it's not possible to achieve a perfect credit score instantly due to the short credit history length and other factors. Payment history is the most significant component, affecting 35% of the FICO score. Keeping accounts in good standing and credit utilization under 30% are key steps to improving your score.
Explanation:
When you're building your payment history, establishing a perfect score immediately is not typically possible. A perfect FICO score is 850, and payment history is the most influential factor, accounting for 35% of your score. As a new credit user, your credit history length is shorter, which negatively affects your score. Unfortunately, it's not possible to quantify exactly how many points you'll miss from a perfect score as it varies depending on the individual credit report and the scoring model used.
It's important to keep your accounts in good standing to build a strong credit history over time. Also, being mindful of your Amounts Owed, which makes up 30% of the FICO score, can help improve your standing. Striving to utilize no more than 30% of your available credit is recommended. Over time, with good financial habits such as these, your credit score will naturally improve, moving closer to the ideal score of 700 or higher.
Other factors influencing your score include the length of your credit history (15%), new credit, and the mix of credit types you have. It's crucial to avoid opening too many new accounts at once, as this can lower your average account age and result in hard inquiries, both of which can reduce your score somewhat.
what is the order of magnitude for the number of states in the United states
The order of magnitude is (1)
Step-by-step explanation:
50 = 5.0 x10^1
Final answer:
Order of magnitude provides an estimation of the scale of a value expressed in powers of 10. For the number of states in the United States, the order of magnitude is approximately 10¹.
Explanation:
Order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 represents a different order of magnitude. For example, 10¹, 10², 10³ are all different orders of magnitude. We can estimate that the number of states in the United States is of the order of magnitude 10¹. This means there are approximately 10 to the power of 1 states in the United States.
Find the value of "m" that gives infinitely many solutions ! PLEASE HELP!!
18 + 2 (X-7) = 4+ Mx
THIS IS A 8TH GRADE SUMMER PACKET! PLEASE HELP! I'LL MARK ANYONE WHO HELPS BRAINLIEST, if you can explain
Answer: 2x
Step-by-step explanation: 18+2(x-7)=4+M. First distribute 2 to (x-7), then you will be left with 18+2x-14=4+M. You can further simplify the left side of the equation by subtracting 14 from 18, now you are left with 2x+4=4+M. Subtract 4 from both sides to solve for M, 2x=M.