Answer:
A. (1,2)
Step-by-step explanation:
A solution to the system of inequalities lies beyond the boundary line where the inequality is satisfied.
Hence let us assume that (yx)^2 - 4 = 0
We tried all the ordered pairs but the right answer was given by A. (1,2)
putting x = 1 and y = 2 in the expression:
(1*2)^2 - 4 = 0
0 = 0 which is true.
Answer:
A. (1,2)
Step-by-step explanation:
Solve h2-42 = -h using the quadratic formula.
A) h = 0 or h = 7
B) h = -6 or h = 7
C) h = 6 or h= -7
D) h = -6 or h = -7
Answer: Option C
h = 6 or h= -7
Step-by-step explanation:
We have the expression
[tex]h^2-42 = -h[/tex]
To solve add h on both sides of the equality
[tex]h^2+h-42 = -h+h[/tex]
[tex]h^2+h-42 = 0[/tex]
For an equation of the form [tex]ah^2 +bh +c[/tex] the quadratic formula is
[tex]h=\frac{-b \± \sqrt{b^2 -4ac}}{2a}[/tex]
In this case
[tex]a = 1\\b= 1\\c =-42[/tex]
[tex]h=\frac{-1 \± \sqrt{1^2 -4(1)(-42)}}{2(1)}[/tex]
[tex]h_1=6[/tex]
[tex]h_2=-7[/tex]
The answer is the option C
How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?
Answer:
2520
Step-by-step explanation:
7×6×5×4×3 = 2520
Imagine □□□□□
For the 1st □, there are 7 choices
For the 2nd □, there are 6 choices (since 1 out of the 7 numbers is already used)
For the 3rd □, there are 5 choices (since 2 out of the 7 numbers are used)
And so on...
The total number of 5-digit numbers that can be formed with the digits 1 to 7, without repetition, is 2520.
Explanation:Your question pertains to the concept of permutations - the number of ways items can be arranged without repetition. In this case, you are considering how many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 without repeating any digit.
A helpful way to think about this is to think of the 5 places for our 5-digit number (i.e., _ _ _ _ _). For the first position, you have 7 choices (the digits 1 to 7) to choose from. Once you have chosen a digit, you are left with 6 choices for the second position, 5 for the third position, 4 for the fourth, and finally 3 for the fifth. So, the total number of 5-digit numbers you can form is 7 × 6 × 5 × 4 × 3 = 2520.
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ11
Estimate the x-coordinates at which the relative maxima and relative minima occur for the function.
f(x) = 3x3 + 9x2 – 1
ANSWER
Relative minimum occurs at x=0
Relative maximum occurs at x=-2
EXPLANATION
The given function is;
[tex]f(x) = 3 {x}^{3} + 9 {x}^{2} - 1[/tex]
We take the first derivative to get:
[tex]f'(x) = 9 {x}^{2} + 18x[/tex]
At turning point f'(x)=0
[tex] 9 {x}^{2} + 18x = 0[/tex]
[tex] 9x(x + 2) = 0[/tex]
[tex]x = 0 \: or \: x = - 2[/tex]
We take the second derivative to get
[tex]f''(x) = 18x + 18
[/tex]
[tex]f''(0) = 18(0) + 18 = 18 \: > \: 0[/tex]
Relative minimum occurs at x=0
[tex]f''( - 2) = 18( - 2)+ 18 = - 18 \: < \: 0[/tex]
Relative maximum occurs at x=-2
Answer:
Relative minimum occurs at x=0
Relative maximum occurs at x=-2
Step-by-step explanation:
1. On delivery, eggs should be rejected if:
A. There is only one USDA inspection stamp on each carton
B. The shells of the eggs have cracks in them
c. The shells vary in color
D. The eggs are odorless
When eggs are delivered, if one notices that B. The shells of the eggs have cracks in them, the eggs should be rejected.
Eggs that have cracks in them can be potentially dangerous to people because microorganisms like bacteria can enter through those cracks and either spoil the egg or make it harmful for consumption.
It is therefore best that an egg that has a crack, be rejected upon delivery.
Other options are incorrect because:
One USDA inspection stamp is good enough proof that the eggs are good Shell color has no effect on whether an egg is bad or not Eggs are supposed to be odorlessIn conclusion, if an egg has a crack in it upon delivery, it should be rejected.
Find out more at https://brainly.com/question/17894532.
In 2014, there were approximately 900,000 sworn law enforcement officers serving in the U.S. Approximately 12% of those officers were female. How many officers were females?
Answer:
108,000 females
Step-by-step explanation:
12% of 900,000 is 108,000.
Therefore, there are 108,000 female officers in the U.S.
Answer: 108,000
Step-by-step explanation:
In 2014, 900,000 sworn law enforcement officers who were serving in the United States and 12% of those officers were female. To find the number of females that were law enforcement officers, we multiply the percentage of females by the total number of law enforcement officers. This will be:
= 12% of 900000
= 12/100 × 900000
= 0.12 × 900000
= 108,000
There were 108,000 females as law enforcement officers serving in the United States.
Combine the radicals -2/13 + 19/13
Answer:
17/13
Step-by-step explanation:
Answer:
Step-by-step explanation:
" / " indicates "division" and should not be used in this context.
If you meant: -2 square root 13 plus 19 square root 13, the simplest result would be 17 square root 13.
Note that if you click on the "omega" symbol (below), a menu of symbols will appear, including the square root symbol √.
Then: -2√13 + 19√13 = 17√13.
The polynomial (x - 2) is a factor of the polynomial 4x2 - 6x-4. True or false?
Answer plz ASAP!!!!!!!
Let the base = x
Then the height would be 2x ( twice the length of the base.
Now using the given formula you get:
25 = 1/2 * 2x *x
Multiply 2x by 1/2:
1/2 * 2x = 2x/2
25 = 2x/2 * x
2x/2 = 1x, now you have:
25 = x *x
Multiply x by x:
25 = x^2
Take the square root of both sides:
x = √25
x = 5
Hector paid $68 for a taxi ride. This driver has a sign above his mirror that recommends a 20% tip. Estimate the amount the driver expects to be tipped to the nearest dollar.
Answer:
Answer:
The answer is 14
Step-by-step explanation:
IT IS NOT 82 I JUST TOOK THE TEST AND IT WAS WRONG...THE ANSWER IS 14!
The driver expects to be tipped approximately $14.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Hector paid $68 for a taxi ride. This driver has a sign above his mirror that recommends a 20% tip.
The amount recieved as a tip is given as -
20% of 68
20/100 x 68
13.6
Therefore, the driver expects to be tipped approximately $14.
To solve more questions on algebraic expressions, visit the link below-
brainly.com/question/1041084
#SPJ6
GEOMETRY Please help me!!!!
Answer:
The correct answer is first option
512 cubic mm
Step-by-step explanation:
Points to remember
Volume of hexagonal pyramid = Base area * height
To find the volume of hexagonal pyramid
It is given that, base area = 64 square mm and
height = 8 mm
Volume = Base area * Height
= 64 * 8
= 512 cubic mm
Therefore the correct answer is first option
512 cubic mm
What is the answer to this question
What factor is used to convert feet per minute into miles per hour?
To convert feet per minute into miles per hour, use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Divide the given value by 5280 to get the number of miles, then divide the result by 60 to convert minutes to hours.
Explanation:To convert feet per minute into miles per hour, you need to use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Here's the step-by-step calculation:
First, determine the number of miles in the given feet per minute by dividing the given value by 5280.Next, divide the result by 60 to convert minutes to hours.The final result will be the given value in feet per minute converted to miles per hour.For example, if you have a speed of 300 feet per minute:
300 feet per minute / 5280 feet per mile = 0.056818 miles per minute.0.056818 miles per minute / 60 minutes per hour = 0.000947 miles per hour.Therefore, 300 feet per minute is equal to 0.000947 miles per hour.Learn more about Unit Conversion here:https://brainly.com/question/19420601
#SPJ12
if you shift the linear parent function, f(x)=x, up 13 units, what is the equation of the new function?
Answer:
f(x) = x + 13
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation
• If c > 0 then vertical shift up ↑ of c units
• If c < 0 then vertical shift down ↓ of c units
here c = + 13, hence
f(x) = x + 13
a right prism has a square base, a surface area of 512 inches squared, and a height of 12 inches. Find the length of the square base
Answer:
8 inches
Step-by-step explanation:
Surface area of a prism is:
S = 2A + Ph
where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.
The base is a square, so A = s² and P = 4s:
S = 2s² + 4sh
Given that S = 512 and h = 12:
512 = 2s² + 4s(12)
512 = 2s² + 48s
256 = s² + 24s
0 = s² + 24s - 256
0 = (s + 32) (s - 8)
s = -32, s = 8
Since s must be positive, s = 8 inches.
Follow below steps;
To find the length of the square base of the right prism:
First, calculate the lateral surface area: 512 in² = 4s * 12 where s is the side length of the square base.
Then, solve for s: 512 = 48s, s = 512 / 48 = 10.67 in.
Therefore, the length of the square base is 10.67 inches.
What is the simplified form expression 2(x-5)?
Answer:
2x-10
Step-by-step explanation:
original equation: 2(×-5)
distributive property: 2(x) 2(-5) =2x-10
Answer:
2x-10
2(x-5)
2*x=2x
2*5=10
please help Solve (x-5)^2=3
Answer:
x = 5 + √3, 5 - √3
which is 6.73 , 3.27 to the nearest hundredth.
Step-by-step explanation:
(x - 5)^2 = 3
Take the square root of both sides:
x - 5 = +/- √3
x = 5 + √3, 5 - √3
Answer:
x = 5 + √3 or x = 5 - √3
Step-by-step explanation:
Equation: (x - 5)² = 3
Square root: x - 5 = ±√3 <-- the square root of a number can be positive or negative.
Subtract: x = 5 + √3 or x = 5 - √3
To the nearest hundredth of a centimeter, what is the length of a leg of the triangle?
[1] cm
84.6 cm
Answer:
The length of a leg of the triangle = 59.83 cm
Step-by-step explanation:
Points to remember
If a right angled triangle with angles 45°, 45° and 90° then the sides are in ratio 1 : 1 : √2
It is given a right angled triangle with 45°, 45° and 90° and hypotenuse = 84.6 cm
To find the length of a leg
Let 'x' be the length of each leg,
From the figure we can write,
1: 1 : √2 = x : x : 84.6
Therefore x = 84.6/√2
= 59.83 cm
Therefore the length of a leg of the triangle = 59.83 cm
ANSWER
59.82
EXPLANATION
The given right angle is an isosceles right triangle.
Let the length of a leg be x cm.
Then by the Pythagoras Theorem,
[tex] {x}^{2} + {x}^{2} = 84.6 ^{2} [/tex]
[tex]2 {x}^{2} = 7157.16[/tex]
Divide both sides by 2.
[tex]{x}^{2} = \frac{7157.16}{2} [/tex]
[tex]{x}^{2} = 3578.58[/tex]
Take positive square root of both sides to get,
[tex]x = 59.82123369[/tex]
Hence the length of a leg is 59.82 to the nearest hundredth.
what is the sum of -36 4/9 - (10 2/9) - (18 2/9)
let's firstly convert the mixed fractions to improper fractions and then add them up.
[tex]\bf \stackrel{mixed}{36\frac{4}{9}}\implies \cfrac{36\cdot 9+4}{9}\implies \stackrel{improper}{\cfrac{329}{9}} \\\\\\ \stackrel{mixed}{10\frac{2}{9}}\implies \cfrac{10\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{92}{9}}~\hfill \stackrel{mixed}{18\frac{2}{9}}\implies \cfrac{18\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{164}{9}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf -\cfrac{329}{9}-\cfrac{92}{9}-\cfrac{164}{9}\implies \stackrel{\textit{using the LCD of 9}}{\cfrac{-329-92-164}{9}}\implies -\cfrac{585}{9}\implies -65[/tex]
helpp me plz respond
What is the pattern in the values as the exponents increase?
Answer:
Option D is correct.
Step-by-step explanation:
We need to find the pattern in the values as the exponents increase.
First value is 1/3
if we multiply 3 with 1/3 i.e. 1/3*3 we get 1
The next value is 1 in the table.
Now, if we multiply 1 with 3 i.e. 1*3 we get 3
The next value is 3 in the table.
Now, if we multiply 3 with 3 i.e 3*3 we get 9
So, the next value is 9 in the table.
So, if we multiply 3 with the previous value we get the next value in the table.
Hence Option D multiply the previous value by 3 is correct.
which of the following equations is of a parabola with a vertex at (1,2)
answer choices
1. y=(x-1)^2 - 2
2 . y=(x-1)^ 2 + 2
3 . y=(x+1)^2 - 2
4 . y=(x+1)^2 + 2
ANSWER
The choice is correct.
[tex]y = {(x -1)}^{2} + 2[/tex]
EXPLANATION
The equation of a parabola in vertex form is given by:
[tex]y = a {(x -h)}^{2} + k[/tex]
where (h,k) is vertex of the parabola and 'a' is the leading coefficient of the parabola.
From the given options, the leading coefficient must be a=1.
We also have the vertex of the parabola at (1,2). This implies that h=1 and k=2.
We substitute these values into the formula to get,
[tex]y = {(x -1)}^{2} + 2[/tex]
The second option is correct.
Write a function for p(x), the profit from selling x necklaces.
The revenue from selling x necklaces is r(x) = 10x. The cost of buying x necklaces is c(x) = 4x + 15. The profit from selling x necklaces is p(x) = r(x) – c(x)
ANSWER
[tex]p(x) = 6x - 15[/tex]
EXPLANATION
The revenue from selling x necklaces is
[tex]r(x) = 10x[/tex]
The cost of buying x necklaces is
[tex]c(x) = 4x + 15[/tex]
The profit from selling x necklaces is
[tex]p(x) = r(x) - c(x)[/tex]
We substitute the functions to get;
[tex]p(x) = 10x- (4x + 15)[/tex]
[tex]p(x) = 10x- 4x - 15[/tex]
[tex]p(x) = 6x - 15[/tex]
Therefore the function for the profit is
[tex]p(x) = 6x - 15[/tex]
What is the output of the following function for x 1? F(x)=-x^3-2x^2+7x-10
Answer:
-6
Step-by-step explanation:
Let x =1
F(x)=-x^3-2x^2+7x-10
F(1) = - (1)^3 -2(1)^2 +7(1) -10
= -1 -2 +7-10
= -3+7-10
=-6
The output of the given function F(x)=-x^3-2x^2+7x-10 when x equals 1 is -6. We substituted x=1 into each term to calculate this.
Explanation:The given function is F(x)=-x^3-2x^2+7x-10. To find the output of the function when x equals 1, you substitute '1' in place of 'x' in the equation. So let's calculate:
For -x^3, substituting x=1, we get: -1^3 = -1For -2x^2, substituting x=1, we get: -2*(1^2) = -2For 7x, substituting x=1, we get: 7*1 = 7Lastly, -10 remains the same as there's no x to substituteNow, add all the results together: -1 - 2 + 7 - 10 = -6. Therefore, when x equals 1, the output of the function F(x) is -6.
Learn more about Function Evaluation here:https://brainly.com/question/12056604
#SPJ3
An unknown number x is at most 10. Which graph best represents all the values of x? Number line graph with closed circle on 10 and shading to the right. Number line graph with open circle on 10 and shading to the right. Number line graph with open circle on 10 and shading to the left. Number line graph with closed circle on 10 and shading to the left.
Answer:
Step-by-step explanation:
The question does say at most 10. That includes 10. So the circle on 10 should indicate it is closed or fully filled in.
The shading should go left. It should indicate less than 10.
What is the solution of log2 (3x - 7) = 3?
4
5
Answer:
x = 5
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{2}[/tex](3x - 7) = 3, then
3x - 7 = 2³ = 8 ( add 7 to both sides )
3x = 15 ( divide both sides by 3 )
x = 5
The required solution of logarithmic expression log2 (3x - 7) = 3 is x = 5. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To solve for x in the equation log2 (3x - 7) = 3, we first use the definition of a logarithm to change the logarithmic form to the exponential form.
log2 (3x - 7) = 3
2³ = 3x - 7
Next, we solve for x by adding 7 to both sides of the equation:
8 + 7= 3x - 7 + 7
15 = 3x
Finally, we divide both sides of the equation by 3:
x = 5
So, the solution of log2 (3x - 7) = 3 is x = 5.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ6
When is a lower annual interest fee better than a low annual fee
Answer: a lower annual interest fee is better than a low annual fee if you expect to pay your balance in full during most months
Final answer:
A lower annual interest fee is generally better than a low annual fee when it leads to significant savings over time, especially with large amounts or long-term financial products. Interest rates dictate the overall cost of borrowing more than annual fees, particularly for longer terms or larger sums. However, for small, short-term borrowing, a low annual fee might be more beneficial.
Explanation:
When comparing a lower annual interest rate versus a low annual fee, it is essential to consider the specific financial situation and the amount of money involved. As a general rule, a lower interest rate is beneficial when it leads to significant savings on the overall interest paid throughout the loan or credit product term. This is often the case for larger amounts or longer terms where the interest accumulates considerably over time.
For example, financial investors who choose a Certificate of Deposit (CD) earn a higher interest rate compared to savings accounts, as they agree to leave the money deposited for a fixed period, forgoing liquidity. However, if interest rates rise after a loan is made, the existing loan with the lower interest rates becomes less attractive. On the other hand, if the economy experiences a fall in interest rates, the value of the loan with the previously fixed lower rate increases.
Therefore, while a low annual fee can seem attractive, it's the annual interest that ultimately has a more significant impact on the cost of borrowing, especially over longer periods or with larger sums of money. Conversely, for small short-term loans or when the outstanding balance is frequently paid off, a low annual fee might be more advantageous than a lower interest rate, as the interest charges could be minimal.
-1/64 has what value
Answer:
If you're looking for the absolute value, its 1/64
Step-by-step explanation:
The absolute value is the distance a number is from 0.
1/64 is 1/64th away from 0/64
So, the answer would be 1/64
I hope this helped you! :)
What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?
For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.
So, we have the following expressions:
[tex]42a ^ 5b ^ 3\\35a ^ 3b ^ 4\\42ab ^ 4[/tex]
We look for the positive integers that divide to 35 and 42 without leaving residue:
42: 1,2,3,6,7,14,21
35: 1,5,7
Thus, the GCF of 42 and 35 is 7
Then, the GCF of the three expressions is:
[tex]7ab ^ 3[/tex]
Answer:
[tex]7ab ^ 3[/tex]
Answer:
A) 7ab^3
Step-by-step explanation:
EDG2021
what is the y-interceptof the line shown?
Answer:
y- intercept = 4
Step-by-step explanation:
The y- intercept is the value of the y- coordinate where the line crosses the y- axis.
Here the y- intercept = 4 or (0, 4) ← coordinates of point
Answer:
( 0 , 4 )
Step-by-step explanation:
The y - intercept of the line is where the line hit's or crosses the y - axis and in the case since the line goes through 4 on the y - axis
Solve the following system of equations using the substitution method.
-X + 9y = -5
x - 5y = 1
Answer: x=8.5 y=1.5
Step-by-step explanation:
Use the second problem and get X by itself. X= 5y+1. Now plug that equation into the 1st equation.
-(5y+1) +9y =-5.
-5y-1+9y=-5.
-5y+9y= 1+5
4y= 6
Y=1.5
Now that you know what is the value of Y you can plug that into any equation.
5(1.5) +1
7.5+1
X=8.5
For this case we have the following system of equations:
[tex]-x + 9y = -5\\x-5y = 1[/tex]
We clear "x" from the second equation and replace it in the first:
[tex]x = 1 + 5y[/tex]
Substituting in the first equation:
[tex]- (1 + 5y) + 9y = -5\\-1-5y + 9y = -5[/tex]
We have similar terms:
[tex]-1 + 4y = -5[/tex]
Adding 1 to both sides of the equation:
[tex]4y = -5 + 1\\4y = -4\\y = \frac {-4} {4}\\y = -1[/tex]
We look for the value of "x":
[tex]x = 1 + 5 (-1)\\x = 1-5\\x = -4[/tex]
Answer:
[tex](x, y): (- 4, -1)[/tex]