Please help with these 2 questions and explain why it's the answer
First, let's edit the given equations.
In 9:[tex]2(32-x^2)=4x4-2\\\\64-2x^2=14[/tex]
Then, to check if [tex]x=5[/tex] is a solution to this equation, let's put the [tex]5[/tex].
[tex]64-2(5)^2=14\\\\64-50=14[/tex]
That's correct!
In 10:[tex]4^2-x\leq x(6-5)\\\\16-x\leq 6x-5x\\\\16-x\leq x\\\\16\leq 2x\\\\x\geq 8[/tex]
Then, we must put [tex]15[/tex].
[tex]15\geq 8[/tex]
That's correct!
Good luck! If you have any question(s), then feel free to ask in comments!
Hi Student!
Let us first look at what the first question is asking for us to do and what is provided to do that. Looking at the first question we see that they are asking if x = 5 is a solution to the expression that they provided. This type of problem is fairly simple and what we basically do is just plug in the value 5 for the variable x in the expression and the simplify both sides to see if they are the same.
Plug in the values
[tex]2(32 - x^2) = 4 * 4 - 2[/tex][tex]2(32 - (5)^2) = 4 * 4 - 2[/tex]Simplify the square and subtract inside of the parenthesis
[tex]2(32 - 25) = 4 * 4 - 2[/tex][tex]2(7) = 4 * 4 - 2[/tex]Simplify both sides
[tex]2 * 7 = (4 * 4) - 2[/tex][tex]14 = (16) - 2[/tex][tex]14 = 14[/tex]Looking at the final expression that we have, we can see that we have 14 is equal to 14 which is true and therefore x = 5 is a solution of the expression provided.
Moving onto the next question, we can see that it asks for us to do something really similar to the previous question but this time to check if x = 15 is a solution of a different expression. Let's follow the same steps that we did last time.
Plug in the values
[tex]4^2 - x \le x(6 - 5)[/tex][tex]4^2 - (15) \le 15(6 - 5)[/tex]Distribute the x
[tex]4^2 - (15) \le (15 * 6) + (15 * -5)[/tex][tex]4^2 - (15) \le 90 - 75[/tex]Simplify both sides
[tex]16 - 15 \le 90 - 75[/tex][tex]1 \le 15[/tex]Looking at the final expression that we have, we can see that it states that 1 is less than or equal to 15 and that is true. Therefore, x = 15 is a solution of the expression that was provided.
At Amy's candy store, small boxes (s) of chocolates contain 12 pieces, and large boxes (L) of chocolates
contain 45 pieces. A customer buys 8 boxes of chocolate containing a combined total of 195 pieces. Which
system of equations models this situation?
Step-by-step explanation:
x = number of small boxes
y = number of large boxes
these equations model the situation :
x + y = 8
12x + 45y = 195
FYI - the solution :
from the first equation we get
x = 8 - y
we use that in the second equation
12(8 - y) + 45y = 195
96 - 12y + 45y = 195
33y = 99
y = 3
x = 8 - y = 8 - 3 = 5
The high temperatures for the week of November 27- December 1 were 66 ℉, 7 1 ℉, 68 ℉, 70 ℉, and 65 ℉. What was the average high temperature (in ℉) for that week? Show your work.
Answer:
68 degrees Fahrenheit
Step-by-step explanation:
to find the average also known as mean, just add the numbers and divide by how many numbers there are.
66+71+68+70+65=340
Now, divide by how many numbers there are. There are 5.
So,
340÷5 = 68
the average is 68.
st: Two- and Three-Dimensional Geometry
A solid machine part is to be manufactured as shown in the figure. The part is made by cutting a small cone off the top of a larger cone. The
small cone has a base radius of 3 inches and a height of 5 inches. The larger cone has a base radius of 9 inches and had a height of 15 inches
prior to being cut. What is the volume of the resulting part illustrated in the figure?
Solve: XIV – VI. Show your answer as a Roman Numeral.
A. XIV
B. XII
C. X
D. VIII
Answer:
XIV - VI = VIII
Step-by-step explanation:
14 - 6 = 8
Hope this helps
Q.3 If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many different ways can a student check off one answer to each question? (b) in how many ways can a student check off one answer to each question and get all the answers wrong?
The number of ways to check off one answer to each question is; 20ways.
The number of ways to check off one answer to each question and get it wrong is; 15ways.
In how many number of ways can a student check off one answer to each question?a) Since each question has four possible answers, it therefore follows that the student can choose any of 4 options in each question and consequently, the number of different ways is; 4 × 5 = 20.
b) Since only one option is correct, it follows that there are 3 wrong choices in each question case and hence, the number of ways to pick one wrong answer is; 3 × 5 = 15.
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Which algebraic expression is a polynomial?
The algebraic expression that is a polynomial is -6x³ + x² - √5
How to know a polynomial?Polynomials are algebraic expressions that consist of variables and coefficients.
In a simpler term a polynomial can have constants, variables and exponents, but never division by a variable.
Therefore, the polynomial among the options is as follows:
-6x³ + x² - √5
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A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for pi , and round your answer to the nearest tenth.
The area and the perimeter of the figure will be 38.13 in² and 23.42 inches respectively.
How to calculate the area?The area will be:
= Area of semi circle + Area of rectangle
= (1/2 × 3.14 × 3²) + (6 × 4)
= 14.13 + 24
= 38.13 inches²
The perimeter will be:
= (3.14 × 3) + (4 + 6 + 4 + 9.42)
= 23.42 inches
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19% of what number is $6.46?
Answer:
here's the answer
Step-by-step explanation:
19/100*x=6.46
x=$34
Find the remainder when x4 - 5x3 + x2 - 10x - 5 is divided by x + 3.
Use the remainder theorem: we can decompose the given polynomial in terms of quotient and remainder polynomials [tex]q(x)[/tex] and [tex]r(x)[/tex], respectively, such that
[tex]x^4 - 5x^3 + x^2 - 10x - 5 = (x + 3) q(x) + r(x)[/tex]
Then letting x = -3 makes the quotient term vanish, and we're left with a remainder of
[tex]r(-3) = (-3)^4 - 5\times(-3)^4 + (-3)^2 - 10\times(-3) - 5 = \boxed{250}[/tex]
y is directly proportional to x 2 . If y = 12 when x = 2 find x when y = 300
An icicle drips at a rate that can be represented by the function f(x) = −x2 + 8x − 7, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.
Find when f(x) = 0. By factorizing, we have
-x² + 8x - 7 = - (x - 7) (x - 1) = 0
so either x - 7 = 0 or x - 1 = 0, or simply x = 1 or x = 7.
Split the domain into three intervals, and check the sign of f(x) over each interval at some test point in the interval. The sign will tell you when the icicle is dripping (positive) or not (negative).
• [0, 1) : at x = 0, we have f(0) = -7 < 0
• (1, 7) : at x = 2, we have f(2) = 5 > 0
• (7, 10] : at x = 8, we have f(8) = -7 < 0
This tells us that the icicle is not dripping when 0 ≤ x < 1, begins to drip when x = 1, drips for the duration of 1 < x < 7, stops dripping when x = 7, and keeps on not dripping when 7 < x ≤ 10.
5
The photograph shows identical red books and identical black books.
All pages have the same thickness.
Which pile has the greater
mean number of pages per book?
Pile W
Pile Y
Explain how you know.
Pile Y has the greater mean number of pages per book because it is 5 books less than pile W.
How to calculate greater mean number of pages?From the complete information, we can deduce that the number of each pile of book is given as follows:
For pile W;
Red books = 10 × 5 = 50 red books.
Blue books = 5 × 5 = 25 blue books.
Therefore, total books in pile W = 50 + 25 = 75 books.
Mathematically, the mean for each pile can be calculated by using the following formula:
Mean = [F(x)]/n
Mean = 75/10
Mean = 7.5.
For pile Y;
Red books = 10 × 5 = 50 red books.
Mean = [F(x)]/n
Mean = 50/5
Mean = 10.
In conclusion, pile Y has the greater mean number of pages per book because it is 5 books less than pile W.
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Factor by grouping
5y^3(y-2)-15y(y-2)
5y³(y-2)-15y(y-2)
= (y-2)×(5y³-15y)
help me omg omg omg omg omg
Answer:
= -1.2 + 3.28d
Step-by-step explanation:
0.4 * -3 + 0.4 * 8.2d
= -1.2 + 3.28d
There is a rack of 11 billiards balls, numbered from 1 to 11. If one ball is selected at random, determine the odds in favor of it being at an even-number ball.
Answer:
5/11 odds / 45.45% chance of being even-numbered
Step-by-step explanation:
There are 5 even-numbered balls (2, 4, 6, 8, 10) and 6 odd-numbered balls (1, 3, 5, 7, 9, 11). So, 5 / 11 balls are even-numbered
if a ball is selected, it has a chance of 5/11 for being even-numbered
5/11 also = 45.45 % [rounded] chance of being even-numbered
Question 1 Justify whether P(x) 5x+0.3x4 √3x + 4x² x3 is a polynomial or not.
Answer:
square root = not polynomial
George and Maria decided to create a garden in their backyard. George works on the garden every third day and Maria works on the garden every fourth day.
If they worked on the garden today, the number of days until they work on the same day again would be.
what is a variable in mathematics?
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Step-by-step explanation:
In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
Type the correct answer in the box. Rewrite the quadratic function in the form that best reveals the zeros of the function. f(x)=2(2x2+4x)+3
Try this suggested option:
Step-by-step explanation:
f(x)=2(2x²+4x)+3; ⇔
f(x)=4(x²+2x)+3; ⇔
f(x)=4(x²+2x+1)+3-4; ⇔
f(x)=4(x+1)²-1; ⇔
f(x)=(2x+1)(2x+3).
Then the roots are:
[tex]\left[\begin{array}{ccc}x=-1.5\\x=-0.5\end{array}.[/tex]
Which value of w makes this equation true?
[tex]\frac{5w + 4 }{3} = \frac{3w}{2}
Answer: -8
Step-by-step explanation:
[tex]\frac{5w+4}{3}=\frac{3w}{2}[/tex]
Cross-multiplying,
[tex]2(5w+4)=9w\\10w+8=9w\\w+8=0\\w=\boxed{-8}[/tex]
The monthly rents for five apartments advertised in a newspaper were $650, $650, $800, $1900, and $820. Use the mean, median, and mode of the rents to answer the question. Which value best describes the monthly rents?
Answer:
The Median Best Describes The Monthly Rents
the mean is add up all the numbers and then divide by the amount of numbers so it is 4820 then divide by 5 = 964 so the mean of all of then is 964
the median you have to put it in slamets to biggest so 650 650 800 820 1900 and then you have to put the one(s) in the middle witch is 800 so the median is 800
the mode is the most common numbers that show up and there is 2 650 and one of everything else so the mode is 650
Hope This Helped
check whether the system of equations is consistent or inconsistent 7/2x-2/3y+9=0; 2x-3y-8=0
Answer:
hi,
Step-by-step explanation:
A consistent system of equations has at least one solution, and an inconsistent system has no solution.
Here the system has one solution.
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days, what is the amountof her deposit to the
nearest dollar (zero decimal place). Use a 360-day year
The amount of Rita deposit is $2556.
What is Simple Interest ?The interest calculated on the principal amount or the initial investment.
It is given in the question
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days.
P = ?
S.I. = $63.90
Interest = 6%
T = 150days
S.I. = (P *R*T)/100
63.90 = P * 6 * 150*100 /360
63.90 * 360*100 /( 150 *6) = P
P = $2556
Therefore the amount of Rita deposit is $2556.
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the diagram below shows the use of diverging lens for correction of
Answer:
E
Step-by-step explanation:
The diagram below shows the correct use of diverging lens for correction of myopia.
27 Which describes how the data for word 2 should be plotted on a coordinate grid? From the origin, go 2 units to the right and 9 units up. From the origin, go 2 units to the right and 12 units up. From the origin, go 9 units to the right and 12 units up. From the origin, go 12 units to the right and 9 units up.
The statement which describes how the data should be plotted on a coordinate grid is: C. from the origin, go 9 units to the right and 12 units up.
What is a coordinate grid?A coordinate grid can be defined as a two-dimensional plane which comprises a horizontal line (x-axis) and a vertical line (y-axis) that are perpendicular to one another.
For this coordinate grid, the number of letters in the data for word 2 should be plotted on the x-axis and the percentage of students who spelled the word correctly on the y-axis.
Based on the table, the number of letters for word 2 is equal to 9 while the percentage of students who spelt it correctly is 12.
In conclusion, to plot the data on a coordinate grid, from the origin, go 9 units to the right and 12 units up.
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Complete Question:
The table of values below shows data for a five-word spelling test. Number of Letters vs. Percentage who Spelled Correctly Word Number of letters in the word Percentage of students who spelled the word correctly. Which describes how the data for word 2 should be plotted on a coordinate grid?
I need help this is due tomorrow
The stem-leaf plot shows student’s scores on the last math test.
Answer:
1) 8
2) the median of the scores is 81
3) So, 8 students scored in the 70s, and the median score is 81
Step-by-step explanation:
1) the number of numbers listed is how many numbers there are
EX: 4| 1, 2, 5, 6 (where 4|1 equals 41) there are four numbers listed: 41, 42, 45, 462) the median is the middle number! when you list all of the numbers, the one in the middle is the median!
EX: 2, 4, 5, 8, 10the median would be 5! why? because it's in the middle!let me know if any of this is confusing and i'll try to explain it further :)
What is the Reciprocal of 5 1/2
Answer:
2/11
Step-by-step explanation:
A reciprocal is a number or fraction flipped. So, 5 1/2=11/2. 11/2 flipped is 2/11.
Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-half x minus three-halves?
f Superscript negative 1 Baseline (x) = one-half x minus three-halves
A function assigns the value of each element of one set to the other specific element of another set. The inverse of the function g(x)=-2x -3.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Two function are inverse of each other if,
f(g(x))=x
g(f(x)) = x
Since the function is inverse, therefore, we can write,
g(f(x)) = a(-1x/2 - 3/2) + b
x = -ax/2 - 3x/2 + b
-a/2 = 1
a = -2
-3a/2 + b = 0
b= -3
Thus, the inverse of the function g(x)=-2x -3.
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Answer:
the inverse of the function g(x)=-2x +3 .
Step-by-step explanation:
Fill in the blank (check all that apply).
2y and ____ are like terms.
Answer:
y,3y,4y,5y,6y,7y,8y,9y,10y ----------
Step-by-step explanation:
because if the variable is similar with y it is like term of 2y
Answer:
y,3y,4y,5y,6y,7y,8y,9y,10y ----------
Step-by-step explanation:
because if the variable is similar with y it is like term of 2y