Answer: [tex]\frac{\sqrt{7}}{7}[/tex]
========================================================
Explanation:
The reciprocal of x is 1/x where x is nonzero. Multiplying x with 1/x leads to 1. For example, the numbers 9 and 1/9 are multiplicative inverses of each other.
We'll stick 1 over the given square root expression. Then follow these steps to rationalize the denominator.
[tex]\frac{1}{\sqrt{7}}\\\\\\\frac{1*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\\\frac{\sqrt{7}}{(\sqrt{7})^2}\\\\\\\frac{\sqrt{7}}{7}\\\\[/tex]
In short, [tex]\frac{1}{\sqrt{7}}=\frac{\sqrt{7}}{7}[/tex]
The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:
The distance are
a. 42.42
b. 15. 52
How to solve for the distance80 = 65 + <ABC
<ABC = 80 - 65
= 15
Through the use of sine rule we would have
By using sine rule,
Sine 15/a = sine 135/b =
sin 30/30.
Next we have to solve b by cross multiplying
b = (30× sin135) / sin 30
= 21.21/0.5
b = 42.42 km
Also, the value of a will be:
= (42.42 × sin 15) / sin 135
= 10.98/0.7071
= 15.52
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in how many ways can the letters in the word payment be arranged if the letters are taken 6 at a time
Considering the definition of permutation, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.
What is PermutationPermutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.
In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:
take all the elements of a set.the elements of the set are not repeated.order matters.To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
[tex]mPn=\frac{m!}{(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
This caseIn this case, you have:
the letter word "PAYMENT", where the number of letters is 7.the letters are taken 6 at a time.Then, you know that:
m= 7n=6Replacing in the definition of permutation:
[tex]7P6=\frac{7!}{(7-6)!}[/tex]
Solving:
[tex]7P6=\frac{7!}{1!}[/tex]
7P6= 5040
Finally, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.
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Write the number in words 203681
Answer:
203681
203,681
Two hundred and three thousand, six hundred eighty-one
Step-by-step explanation:
The number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.
In the question, we are asked to write the number 203681 in words.
In the given number, we have:
1 at the units place,8 at the tens place,6 at the hundreds place,3 at the thousands place,0 at the ten thousand places, and2 and the hundred thousand place.Keeping the thousands as different section, we have 203 in thousands section, and 681 in the remaining.
203 can be named as two hundred and three.
681 can be named as six hundred and eighty-one.
Since, 203 is in the thousands section, we add thousand in its name.
Thus, the name we get is two hundred and three thousands, six hundred and eighty-one.
Thus, the number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.
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Question 1 1.1 Given the quadratic number pattern: 5; 10; 17; 26;.. 1.1.1 Write down the next TWO terms of the pattern. 1.1.2 D Determine the formula for the nth term of the patter 1.1.3 Which term of the pattern will have a value of 1765? 1.2 Given the quadratic pattern:x; 6; 9; y; 24; Calculate the sum of x and y. Question 2 COFF 8(1:2)
The next two terms of the sequence based on the information given is 37 and 50.
How to illustrate the sequence?It should be noted that from the information given, the numbers illustrated are 5, 10, 17, and 26.
In this case, there is an addition of 2 to the previous difference.
Therefore, 26 - 17 = 9.
The next number will be:
= 26 + 9 + 2 =37
The following number will be:
= 37 + 11 + 2
= 50
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Need help with defining this question.
Answer:
B.) 19
Step-by-step explanation:
According to F(5), the question wants you to plug x = 5 into the equation. Then, you need to simplify to find the output.
F(x) = x² - 2x + 4 <----- Original equation
F(5) = (5)² - 2(5) + 4 <----- Plug 5 into "x"
F(5) = 25 - 10 + 4 <----- Solve 5² and -2 x 5
F(5) = 19 <----- Combine like terms
What is the solution to the equation below? (Round your answer to two
decimal places.)
5 Inx= 3.5
A. x = 4.17
B. x = 3.98
C. x = 42.40
D. x=201
Answer: 2.01
Step-by-step explanation:
[tex]5\ln x=3.5\\\\x=\frac{3.5}{5}\\\\x=e^{3.5/5}\\\\x \approx 2.01[/tex]
Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9 dimes and 15 quarters. What is the total amount of the deposit?
The total amount of the deposit is $592.92.
What is the total amount of the deposit?The total amount of the deposit can be determined by adding all the money deposited together.
(47 x 1) + (22 x 5) + (9 x 10) + (17 x 20) + (67 x 0.01) + (0.05 x 12) + (9 x 0.1) + (15 x 0.25)
47 + 110 + 90 + 340 + 0.67 + 0.60 + 0.9 + 3.75 = $592.92
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Billy eats 28 apples and he had 40 apples at the start a kid asks for an apple how many apples are there left?
Answer: 11
Step-by-step explanation: 40-28= 12-1=11
Answer:
11 apples are left.
Step-by-step explanation:
Since Billy ate 28 apples from the 40 apples he had at the start, you have to subtract 40-28, which equals 12. Lastly, you subtract 12-1, since a kid asks Billy for an apple.
What is the value of p
Answer:
2
Step-by-step explanation:
You have the correct answer selected: 2.
The reason for this is that when there are exponents inside and outside of the parenthesis like this, they are multiplied.
2 times 2 is 4. That's why (8^2)^2 = 8^4
Answer:
p = 2
Step-by-step explanation:
[tex](8^{2}) ^{p}[/tex] = [tex]8^{4}[/tex]
[tex]8^{2p}[/tex] = [tex]8^{4}[/tex]
[tex]8^{p}[/tex] = [tex]8^{\frac{4}{2}[/tex]
p = 2
The Florida VPK assessment is considered a progress monitoring tool when administered at two assessments periods across the school year.
a. True
b. False
The given statement about the Florida VPK assessment administered at two assessments periods across the school year is; B: False
What is the Progress Monitoring Tool?Progress monitoring or CBM is a term used in the education field to describe the process whereby the progress of students in areas like mathematics, reading, and writing are monitored on a daily and weekly basis.
Now, in Florida in the United States, This progress monitoring is called Florida Voluntary Prekindergarten (VPK) Assessment. There is usually a different version of each assessment measure that will be administered at three different times during the school-year VPK Program.
Thus, the given statement is false.
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Answer:
Step-by-step explanation:
false
For csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
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Josh had to make 2,000 cookies for his bakery. 2 pieces of wheat make 8 cookies. How much wheat does he need?
Find the area of the trapezoid. 15ft 10ft 20ft
Answer: 175 ft squared
Step-by-step explanation: A= a + b / 2h= 20 + 152 · 10 = 175
You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in your salary?
Answer: 6 %
Step-by-step explanation: 6 % of 12.5 = 0.75. 12.5 plus 0.75 = 13.25
A tree is 14 meters tall. What is its height in feet? Use the following conversion: 1 meter is 3.3 feet
what is the volume of the following rectangular prism
Answer:
[tex] \large{ \boxed{ \tt{336 \: units ^{3} }}}[/tex]- Please see the attached picture for full solution!:)
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Enter the letter of the graphed
function.
-
-
a.y = (x + 2)(x − 1)(x − 3)
b.y = (x + 2)(x - 1)(x - 3)²
-
c. y = (x + 2)(x − 3)(x - 1)²
d.y= (x - 1)(x − 3)(x + 2)²
e.y = (x - 1)(x - 3)(x + 2)³
The graphed function is: y = (x + 2)(x − 1)(x − 3).
Option (a) is correct.
From the graph given in the question, it can be seen that the graph has 3 critical points, namely, x= -2, x = 1 and x = 3.
From all the five options given, the first option, that is, y = (x + 2)(x − 1)(x − 3), has the critical points x= -2, x = 1 and x = 3.
The critical points for a function are obtained by substituting the function to be equal to zero.
So, (x + 2)(x − 1)(x − 3) = 0
That is, x= -2, x = 1 and x = 3.
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i need this solved asap please do so
The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.
How to determine the domain of a rational function
In this problem we have a rational function, the domain of rational functions is the set of all real numbers except the values such that the denominator becomes zero. First, we need to simplify the division of two rational functions:
[tex]h(x) = \frac{\frac{3\cdot x^{2} + 17\cdot x + 20}{3\cdot x^{2} + 10\cdot x - 8} }{\frac{3 \cdot x^{2} + 8\cdot x + 5}{x^{2}-3\cdot x - 4} }[/tex]
[tex]h(x) = \frac{(3\cdot x^{2}+17\cdot x + 20)\cdot (x^{2}-3\cdot x - 4)}{(3\cdot x^{2}+10\cdot x - 8)\cdot (3\cdot x^{2}+8\cdot x + 5)}[/tex]
[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x^{2}+\frac{17}{3}\cdot x + \frac{20}{3} \right)\cdot (x^{2}-3\cdot x - 4)}{\left(x^{2}+\frac{10}{3}\cdot x -\frac{8}{3}\right)\cdot \left(x^{2}+\frac{8}{3}\cdot x +\frac{5}{3} \right)}[/tex]
[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x + \frac{5}{3} \right)\cdot (x+4)\cdot (x - 4)\cdot (x+ 1)}{\left(x-\frac{2}{3} \right)\cdot (x + 4)\cdot (x + 1)\cdot \left(x + \frac{5}{3} \right)}[/tex]
[tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex]
The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.
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Geometry Question!! PLEASE HELp
The difference between the distance travelled by any point on the record and it's label is; 27.57cm.
What is the difference between the distance travelled in each case?According to the task content, it follows from observation that the quantity required is the difference between the circumference in each case and can be evaluated as follows;
Difference = π(17.78 - 9)
Difference = (22/7) × 8.78
Difference = 27.57cm.
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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! pls <3
Answer:
[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]
Step-by-step explanation:
Let's write the equation of the line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.
Identify 2 coordinates on the line to calculate the slope.
The 2 points are (1, 2) and (4, 4).
Slope
[tex]=\frac{y_1-y_2}{x_1-x_2}[/tex]
= [tex]\frac{4-2}{4-1}[/tex]
= [tex]\frac{2}{3}[/tex]
Substitute the value of the slope into m:
[tex]y=\frac{2}{3}x+c[/tex]
Substitute any point into the equation to find c:
When x= 1, y= 2,
[tex]2= \frac{2}{3}(1)+c[/tex]
Solve for c:
[tex]c= 2-\frac{2}{3}[/tex]
c= [tex]\frac{4}{3}[/tex]
Thus, the equation that represents the line is [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex].
Additional:
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https://brainly.com/question/26351470Name the figure below in two different ways!
Need help fast!
Answer:
IM and YM
Step-by-step explanation:
not sure about the symbol part, but it's a ray !!
Answer: IM and YM
Step-by-step explanation:
It can be broken down into to different rays
Find the remainder when f(x) = 8x^3+4x^2-13x+3 is divided by 2x+5
Answer:
-129
Step-by-step explanation:
good luck
Petsmart's marketing team finds in their most recent report that they sell 45 guinea pigs a
year. Their sales team wanted to increase their sales and grabbed a sample of 8 types of
rodents to put on a flash sale. They sold an average of 34 rodents with a standard
deviation of 21 rodents.
Answer:
p(x)=x3-3x2+4x+50 and g(x)=x-3
Which choice is a term in this expression -3x - 7(x+4)
-3x is a term in the expression -3x - 7(x+4)
How to determine the term?The expression is given as:
-3x - 7(x+4)
Considering the following expression
Ax + B(x - b)
The terms in the expressions are Ax and B(x - b)
This means that -3x is a term in the expression -3x - 7(x+4)
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josh is looking to get a new car because he decided he was spending too much on gas. over the past year he found that he drove 7,700 miles. at current gas prices [ youll need to actually consider your current cost for gasoline ]. he was getting about 27 miles per gallon. if he bought a vehicle that realizes 33 miles per gallon. what might be a reasonable estimate of monthly gas costs?
Josh's monthly fuel expenses are $1,050.
PricesGiven that Josh is looking to get a new car because he decided he was spending too much on gas, and over the past year he found that he drove 7,700 miles, and at current gas prices of $4.5 he was getting about 27 miles per gallon, To determine, if he bought a vehicle that realizes 33 miles per gallon, what might be a reasonable estimate of monthly gas costs, the following calculation must be made:
27 = 10033 = X3300 / 27 = X122.22 = X122.22 = 100100 = X10000 / 122.22 = X81.81 = X(7700 / 33) x 4.5 = X233.33 x 4.5 = X1050 = XTherefore, Josh's monthly fuel expenses are $1,050.
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Answer:Josh's monthly fuel expenses are $1,050.
Step-by-step explanation:
What is the sum of the
HCF and
LCM of the
number
2³ x 3² x 5x7 and
2² x 5² x 11
Step-by-step explanation:
. Find the factors of 330.
(a)2 x 4 x 5 x 11
(b)2 x 3 x 7 x 13
(c)2 x 3 x 5 x 13
(d)2 x 3 x 5 x 11
Show Answer
2. Find the factors of 1122.
(a)3 x 9 x 17 x 2
(b)3 x 11 x 17 x 2
(c)9 x 9 x 17 x 2
(d)3 x 11 x 17 x 3
Show Answer
3. 252 can be expressed as a product of primes as
(a)2 x 2 x 3 x 3 x 7
(b)2 x 2 x 2 x 3 x 7
(c)3 x 3 x 3 x 3 x 7
(d)2 x 3 x 3 x 3 x 7
Show Answer
4. Which of the following has most number of divisors?
(a)99
(b)101
(c)176
(d)182
Show Answer
5. A number n is said to be perfect if the sum of all its divisors (excluding n itself) is equal to n. An example of perfect number is
(a)6
(b)9
(c)15
(d)21
Show Answer
6. 1095/1168 when expressed in simplest form is
(a)13 / 16
(b)15 / 16
(c)17 / 26
(d)25 / 26
Show Answer
7. Reduce 128352 / 238368 to its lowest terms
(a)3/4
(b)5/13
(c)7/13
(d)9/13
Show Answer
8. The simplest reduction to the lowest terms of 116,690,151 / 427,863,887 is
(a)3/11
(b)7/11
(c)11/3
(d)None of these
Show Answer
9. The highest common factor of 0 and 6 is
(a)0
(b)3
(c)6
(d)Undefined
Show Answer
10. The H.C.F. of 2² x 3³ x 5⁵, 2³ x 3² x 5² x 7 and 2⁴ x 3⁴ x 5 x 7² x 11 is
(a)2² x 3² x 5
(b)2² x 3² x 5 x 7 x 11
(c)2⁴ x 3⁴ x 5⁵
(d)2⁴ x 3⁴ x 5⁵ x 7 x 11
Show Answer
11. The H.C.F. of 2⁴ x 3² x 5³ x 7, 2³ x 3³ x 5² x 7² and 3 x 5 x 7 x 11 is
(a)105
(b)1155
(c)2310
(d)27720
Show Answer
12. H.C.F. of 4 x 27 x 3125, 8 x 9 x 25 x 7 & 16 x 81 x 5 x 11 x 49 is
(a)180
(b)360
(c)540
(d)1260
Show Answer
13. Find the highest common factor of 36 and 84.
(a)4
(b)6
(c)12
(d)18
Show Answer
14. Even numbers are formed by taking at least two at a time from the numbers 0, 4, 8, 9. Their H.C.F. is
(a)2
(b)4
(c)10
(d)None of these
Show Answer
5.5(x+6 1/2)-(x+9 1/3) - (19-x)
The simplest form of the expression given in the task content is; 5.5x +7.42.
What is the simplest form of the expression?The expression given in the task content is;
5.5(x+6 1/2)-(x+9 1/3) - (19-x)
Hence, the expression can be written in its simplest form as follows;
5.5x + 35.75 -x -9.33 -19 +x
= 5.5x +7.42.
Remarks: The complete task requires that the expression be written in its simplest form.
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ped
Complete question :
Juan is rewriting the expression 12 d minus 26 c as a product. Which statements about the expression are accurate and relevant to his rewriting the expression? Select two options. The GCF of the numbers in each term in the expression is 2. The GCF of the numbers in each term in th
So the correct statement is:
" The GCF of the numbers in each term in the expression is 2"
How to rewrite the expression as a product?Here we have the expression:
12d - 26c
To rewrite ti as a product, we need to find the greatest common factor between 12 and 26.
The decomposition of these two numbers is:
12 = 2*2*3
26 = 2*13
The greatest common factor between the two numbers is 2, then we can rewrite:
12d - 26c = 2*(6d - 13c)
So the correct statement is:
" The GCF of the numbers in each term in the expression is 2"
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The height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t^2 + 88t where "t" is the time it is in the air. For how many seconds the ball is in the air before it hits the ground?
By definition of the zeros of ta quadratic function, for 5.5 seconds the ball is in the air before it hits the ground.
Zeros of a functionThe points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.
That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.
In summary, the roots or zeros of the quadratic function are those values of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.
Time the ball is in the air before it hits the groundIn this case, the height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t² + 88t, where "t" is the time it is in the air.
When the ball hits he ground, he height h has a value of zero. This is h=0. Replacing in the previous expression for the height you get:
0= -16t² + 88t
It can be solved by extracting the term "t" as a common factor:
0= t×(-16t + 88)
The Zero Product Principle says that if the product of two numbers is 0, then at least one of the factors is 0. Then:
t= 0
or
0= -16t + 88
Solving: -88= -16t
(-88)÷ (-16)=t
5.5= t
Finally, this means that for 5.5 seconds the ball is in the air before it hits the ground.
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A=(-3,-2) B=x,3 C=(4,5) if AB = BC what is the value of X
Answer:
x=1
Step-by-step explanation:
[tex] \sqrt{( - 3 - x) ^{2} + {( - 2 - 3)}^{2} } = \\ \sqrt{ {(4 - x)}^{2} + {(5 - 3)}^{2} } \\ \\ 9 + 6x + {x}^{2} + 25 = \\ 16 - 8x + {x}^{2} + 4 = = = > \\ 34 + 6x = 20 - 8x = > \\ 14 = 14x = = = > x = 1[/tex]
Done
The value of x that makes up the coordinate of B is -1
How to find the value of xTo find the value of x, we need to determine the coordinates of point B.
Since A to (B) = B to (C), the distance from point A to point B is equal to the distance from point B to point C. The distance between two points in a coordinate plane can be calculated using the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's calculate the distances:
Distance A to (B):
x₁ = -3 (x-coordinate of point A)
y₁ = -2 (y-coordinate of point A)
x₂ = x (x-coordinate of point B)
y₂ = 3 (y-coordinate of point B)
Distance A to (B) = √((x - (-3))² + (3 - (-2))²)
Distance A to (B) =√((x + 3)² + 5²)
Distance A to (B) = √(x² + 6x + 9 + 25)
Distance A to (B) = √(x² + 6x + 34)
Distance B to (C):
x₁ = x (x-coordinate of point B)
y₁ = 3 (y-coordinate of point B)
x₂ = 4 (x-coordinate of point C)
y₂ = 5 (y-coordinate of point C)
Distance B to (C) = √((4 - x)² + (5 - 3)²)
Distance B to (C) = √((4 - x)² + 2²)
Distance B to (C) = √((4 - x)² + 4)
Distance B to (C) = √(x² - 8x + 20)
Since A to (B) = B to (C):
√(x² + 6x + 34) = √(x² - 8x + 20)
Now, we can square both sides to get rid of the square root:
x² + 6x + 34 = x² - 8x + 20
Next, move all the x terms to one side of the equation:
x² - x² + 6x + 8x = 20 - 34
Combine like terms:
14x = -14
Finally, solve for x:
x = -14 / 14
x = -1
So the value of x is -1. Point B is located at (-1, 3).
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