[tex]\sqrt{2^{2}+6^{2}}=\sqrt{4+36}=\sqrt{40}=\boxed{2\sqrt{10}}[/tex]
Question 2 of 18
For which pair of functions is the vertex of g(x) 4 units to the right of the
vertex of f(x)?
A. f(x) = x² and g(x) = x² + 4
B. f(x) = x² and g(x) = (x − 4)²
C. f(x)=x² and g(x) = (x+4)²
D. f(x) = x² and g(x) = x² - 4
Answer:
B
Step-by-step explanation:
g(x)=(4-4)²
g(x) =0
and f(x)=x²
f(x)=0²
A boat is 400 feet away from one dock and 500 feet away from the another dock. the angle between the paths is 45°. what is the approximate distance between the docks?
Answer:
The approximate distance between the docks is 357 feet
Step-by-step explanation:
Let the distance between docks be d.
This is the opposite side to 45° angle of triangle with other sides 400 ft and 500 ft.
Use the law of cosines to find the value of d:
[tex]d = \sqrt{400^2+500^2-2*400*500*cos45} =357[/tex] (rounded)Point Z is equidistant from the vertices of ΔTUV.
Point Z is equidistant from the vertices of triangle T U V. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C.
Which must be true?
Line segment T A is-congruent-to line segment T B
Line segment A Z is-congruent-to line segment B Z
AngleBTZ Is-congruent-to AngleBUZ
AngleTZA Is-congruent-to AngleTZB
An isosceles triangle is one with two equal-length sides. The correct option is C.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
The diagram as per the given conditions is drawn below.
In ΔUTZ, since the sides UZ and TZ are equal because the point z is equidistance from T and U, therefore, the triangle is an isosceles triangle. Thus, ∠BTZ≅TZB.
Hence, the correct option is C.
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If B=3n-10B=3n−10 and C=n^{2}-6n-6,C=n
2
−6n−6, find an expression that equals 2B-3C2B−3C in standard form.
The expression of 2B - 3C in standard form is -3n^2 + 24n - 2
Functions and valuesGiven the following expressions
B = 3n - 10
C = n^2-6n-6
Required
2B - 3C
Substitute
2B - 3C = 2(3n -10) - 3(n^2-6n-6)
2B - 3C = 6n - 20 -3n^2+18n+18
2B - 3C = -3n^2 + 24n - 2
Hence expression of 2B - 3C in standard form is -3n^2 + 24n - 2
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Y is inversely proportional to the square root of x if y=3 when x=25 find y when x is 9
Answer:
[tex]y=5[/tex]
Step-by-step explanation:
[tex]\textsf{If }y \textsf{ is \underline{inversely proportional} to the square root of }x, \textsf{ then}:[/tex]
[tex]y \propto\dfrac{1}{\sqrt{x}} \implies y=\dfrac{k}{\sqrt{x}}\quad \textsf{(where k is some constant)}[/tex]
[tex]\textsf{When }x=25, y = 3:[/tex]
[tex]\implies 3=\dfrac{k}{\sqrt{25}}[/tex]
[tex]\implies 3=\dfrac{k}{5}[/tex]
[tex]\implies k=15[/tex]
Inputting the found value of k into the equation:
[tex]\implies y=\dfrac{15}{\sqrt{x}}[/tex]
To find the value of y when x is 9, substitute x = 9 into the found equation:
[tex]\implies y=\dfrac{15}{\sqrt{9}}[/tex]
[tex]\implies y=\dfrac{15}{3}[/tex]
[tex]\implies y=5[/tex]
Suzanne walks four miles every third day. What is the fewest number of miles she can walk in February
36 miles is the fewest number of miles she can walk in February
There are 28 days in February.
Every third day is 28/3 = 9.333 = 9 days of walking.
since she walks four miles,
9*4 = 36
Hence, 36 miles is the fewest number of miles she can walk in February
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A coupon gives a total 20% off a total of 5 cans of green beans at the grocery store. If the green beans cost $0.75 per can, how much money is saved with the coupon?
$0.75
$0.15
$3.75
$1.88
CD player: $142.00
Sales tax: 5.5%
The total amount paid by a customer who purchased a CD player at $142.00 and sales tax of 5.5% is $149.81
Sales taxCost of CD player = $142.00Sales tax = 5.5%Amount of sales tax = 5.5% of $142.00
= 5.5/100 × 142
= 0.055 × 142
= $7.81
Total amount paid by customers = Cost of CD player + Amount of sales tax
= $142.00 + $7.81
= $149.81
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how many 4-digit positive intergers have four different digits where the leading digit is not zero, the interger is amultiple of 5 and 5 is the largest digit
The 4-digit positive integers have four different digits where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit is 108.
[tex]5*4*3*1+4*4*3*1=60+28=108[/tex]
Positive integers are the numbers we use to depend: 1,2, 3,4, 1 , 2, three, four, and so forth. Numbers with a fractional component not identical to zero and poor numbers are excluded from a fixed of high-quality integers. The operations of addition, subtraction, multiplication, and division can be finished with tremendous integers.
Positive integers are definitely your counting numbers. wonderful integers are in reality a part of a larger institution of numbers referred to as integers. Integers are all of the whole numbers, each advantageous and poor. by complete numbers, we imply numbers without fractions or decimals.
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We make four cases based on where the multiple of the 5 digits (0 or5) is. The number has to end with either 5 or 0 since it's a multiple of5. In all but the last case, 5 and 0 are used at the end and in another spot that separates the cases.
Case 1: The first digit can't be 0 so it must be 5. There are 4.3 to choose the middle two digits. After that, the last digit has to be 0, so there are a total of 1.4.3.1=12 numbers.
Case 2: The second digit can be 5, leaving 2 choices. The first and third numbers can be chosen in 4.3 ways, like last time. The last digit has to be 0 or 5, but not the one we already used. There are a total of 4.2.3.1=24 numbers.
Case 3: There are the same choices, but the digits 0 and 5 are at the last and second-to-last spots. So there are 4.2.3.1 =24 numbers again.
Case 4: There are 4.3.2 ways to choose the first three numbers. There has to be a 5 in the number because the largest digit is 5. Coincidentally, there are 4.2.3.1 numbers again.
There are a total of 12 + 24.3= (D)84 numbers.
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Area=
Help me please thanks
The area of the shaded region shown in the figure is 80π unit²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Area of the shaded region = area of semicircle IL - area of semicircle JK + area of semicircle IJ + area of semicircle KL
Area of the shaded region = area of semicircle IL + area of semicircle IJ = (0.5 * π * 12²) + (0.5 * π * (12/3)²) = 80π
The area of the shaded region shown in the figure is 80π unit²
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A worker has four different job offers, each with a contract for six years. assuming the job descriptions are identical, which offer will allow the worker to earn the most over six years?
Assuming the salary is included in the job descriptions, then they all pay the same amount for the same length of time, meaning he will earn the same amount at any of the jobs. This looks like a trick question.
A group of summer campers went on a trip.
22 campers rode in cars with their parents
while the rest filled four buses. How many
campers were on each bus if a total of 150
campers went on the trip?
Answer:
Answer is 32
Step-by-step explanation:
150-22=128
128÷4=32
Independent Practice
An image on a slide is similar to its projected image. A slide is 35 mm wide and 21 mm high. Its projected image is 85 cm wide. To the nearest centimeter, how high
is the image?
A. 51 cm
B. 5.1 cm
C.
D.
142 cm
9 cm
Answer:
Projected height = (85 *21) / 35 = 51 cm
Step-by-step explanation:
Since the images are similar, we can set up the proportional equation like this:
Slide width / Slide height = Projected width / Projected height
35 mm / 21 mm = 85 cm / Projected height (in cm)
Projected height = (85 *21) / 35 = 51 cm
Line I has a slope of 13/7. The line through which of the following pair
of points is perpendicular to l?
Answer:
Step-by-step explanation:
You need to find the set of points that will yield a slope that is the negative reciprocal of the slope of Line L because perpendicular lines have negative reciprocal slopes. The negative reciprocal of 13/7 is -7/13. Which set of points will produce this result? The formula for finding the slope is:
m = (y2 - y1)/(x2 - x1)
Consider the second set of coordinates.
(2 - (-5))/(-7 - 6) = (2 + 5)/(-13) = -7/13
The second set of coordinates satisfy the condition.
write 8n^2-13n+5 in factor form
Answer:
[tex](8n - 5)(n-1)[/tex]
Step-by-step explanation:
Hello!
We can factor this by grouping. We have to find two numbers that add up to -13 but multiply to 8 * 5 .
The two numbers that work are -8 and -5. Expand -13n to -8n and -5n.
Factor by Grouping[tex]8n^2 - 13n + 5[/tex][tex]8n^2 - 8n - 5n + 5[/tex][tex]8n(n -1) -5(n - 1)[/tex][tex](8n - 5)(n-1)[/tex]The factored expression is [tex](8n - 5)(n-1)[/tex].
How many passwords are there that start with a letter, contain only numbers and upper and lowercase letters, and are exactly 6 characters long
There are 1,86,78,66,560 possinbe passwords.
The easiest way to count the acceptable passwords is to note that there are 36^6 six-character strings made up of upper-case letters and digits, and 26^6 of them are made up entirely of letters, so there are 36^6 − 26^6 that include at least one digit.
⇒ 36^6 - 26^6
⇒ 2,17,67,82,336 - 30,89,15,776
⇒ 1,86,78,66,560
The answer is 1,86,78,66,560.
A password occasionally called a passcode, is a secret fact, generally a string of characters usually used to confirm a person's identity.
Historically, passwords we're expected to be memorized, but the large range of password-included offerings that common characters get entry to can make memorization of unique passwords for each service impractical.
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The polynomial 2x3 − 5x2 + 4x − 10 is split into two groups, 2x3 + 4x and −5x2 − 10. The GCFs of each group is then factored out.
Answer:
(x² + 2)(2x - 5)
Step-by-step explanation:
assuming the expression has to be factorised
2x³ - 5x² + 4x - 10 ← rearranging terms as indicated
= 2x³ + 4x - 5x² - 10 ( factor the first/second and third/fourth terms )
= 2x(x² + 2) - 5(x² + 2) ← factor out (x² + 2) from each term
= (x² + 2)(2x - 5) ← in factored form
whats the vertex-? Would it be -1???
Answer:
last option : vertex is 2, -1 . axis of symmetry is x = 2
Answer:
D
(2 -1)
*(^_^)*
...............
I have 4 times as many 10 cent stamps as 3 cent stamps. I have one less 2-cent stamp than
The value of the stamp collection in terms of b is; 45b + 43 cents
How to solve algebra word problems?
We are given;
If there are x 3-cent stamps, then there are 4x number 10-cent stamps
So the number of 2-cent stamps is 1 less than 3 cent stamps and that will be x - 1, 2 cent stamps
Number of 2 cents stamps = b
Thus; x - 1 = b
x = b + 1
The value of the stamp collection is as follows;
x number of 3 cents stamps = 3(b + 1) = 3b + 3 cents
4x number of 10 cents stamps = 10(4(b + 1)) = 10(4b + 4) = 40b + 40
The value of the 2 cents stamp = 2b cents
Total value is;
2b + 40b + 40 + 3b + 3 = (45b + 43) cents
Complete Question is;
I have 4 times as many 10-cent stamps as 3-cent stamps. I have one less 2-cent stamp than 3 cent stamp. If I have b2-cent stamps, what is the value of my stamp collection in terms of b ?
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someone please help me
Answer:
20 sq in
Step-by-step explanation:
formula is (base * height)/2 so plug it in:
5*8=40
40/2=20
20 sq in
ayuda necesito resolver este problema con procedimiento ;)
[tex]x^3-2x^2+x-1[/tex] is one of the prime factors of the polynomial
How to factor the expression?The question implies that we determine one of the prime factors of the polynomial.
The polynomial is given as:
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1[/tex]
Expand the polynomial by adding 0's in the form of +a - a
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^7 - 4x^6 +x^6 + 2x^5 -2x^5- 3x^4 + 4x^4 + 2x^3 -6x^3+2x^3- x^2 -3x^2 +4x^2-2x+2x-1[/tex]
Rearrange the terms
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^5 - 3x^4 + 2x^3 - x^2 + 2x^7 - 4x^6 + 4x^4 -6x^3+4x^2-2x+x^6-2x^5+2x^3-3x^2+2x-1[/tex]
Factorize the expression
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^2(x^6-2x^5+2x^3-3x^2+2x-1) + 2x(x^6-2x^5+2x^3-3x^2+2x-1) + 1(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]
Factor out x^6-2x^5+2x^3-3x^2+2x-1
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x^2+2x + 1)(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]
Express x^2 + 2x + 1 as a perfect square
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]
Expand the polynomial by adding 0's in the form of +a - a
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^4-x^3 +x^3-2x^3-x^2 -2x^2 +x+x - 1)[/tex]
Rearrange the terms
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^3-x^4-2x^3-x^2+x+x^3-2x^2 +x - 1)[/tex]
Factorize the expression
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3(x^3-2x^2+x-1) -x(x^3-2x^2+x-1)+1(x^3-2x^2+x-1))[/tex]
Factor out x^3-2x^2+x-1
[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3 -x+1)(x^3-2x^2+x-1)[/tex]
One of the factors of the above polynomial is [tex]x^3-2x^2+x-1[/tex].
This is the same as the option (c)
Hence, [tex]x^3-2x^2+x-1[/tex] is one of the prime factors of the polynomial
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help asap 20 points
Select the correct answer from each drop-down menu.
Answer: (99/13, 150/13)
Step-by-step explanation:
I'm too lazy to explain so here's a screen shot from desmos.
Help me please I would really be happy
The polynomial is not a perfect square trinomial. This is false..
How to illustrate the information?It should be noted that a perfect squares trinomial is the algebraic expression which has the form of ax² + bx + c.
The equation given is 9x² - 30x + 25. This will be expanded as:
9x² - 30x + 25.
9x² - 15x - 15x + 25
3x(3x - 5) - 5(3x - 5)
= (3x - 5)(3x - 5)
In this case, 9x² - 30x + 25 is a perfect square binomial of 3x - 5 and not a trinomial.
Therefore, the correct option is false.
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Suppose there are 1,000 total sales representatives in the midwest and northeast regions, with 500 sales re
region. describe the best way for the sales director to include 200 sales representatives, with an equal num
region and an equal number in each group, while yielding valid conclusions in the study.
Making 20 groups of 10 is the sampling strategy that can be used to select 200 sales representatives.
What is sampling?
Sampling is the phrase used to describe a statistical procedure in which a predetermined number of observations are chosen from a larger population. More precisely, sampling can be described as the process of choosing a portion of a statistical population in order to estimate the characteristics of the entire population. Samples that are representative of the population under study are sought for by statisticians.
Making 20 groups of 10 is the most effective way of sampling that can be employed here for the sales director to incorporate 200 sales representatives in this situation, with an equal amount of representatives from each region.
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A courier travels due North at an average speed of 40km/h for 6 minutes to collect a parcel, before travelling 10km due East to deliver it. He then travels due South at an average speed of 30km/h for 12 minutes to collect another parcel. Find the shortest distance between the courier and his starting point.
Answer:
Step-by-step explanation:
Answer:10.2km
He took the route eastwards then southwards
Which of the following represents a function?
(5, 1), (5, 2), (5, 3), (5, 4)
(-5, 6), (-5, 6), (-5, -6), (-5, -6)
(8, 3), (8, 3), (-8, -3), (-8, -3)
(3, 9), (-7, 1), (6, 12), (3, -9)
Answer:
(8,3),(8,3),(-8,-3),(-8,-3)
Step-by-step explanation:
A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).
This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.
The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x=8, then y=3, and if x=-8, then x=-3.
In the other sets of ordered pairs, however, one x-value has more than one possible y-value. Let's use the first set as an example:
(5,1),(5,2),(5,3),(5,4)
Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.
from two points one on each leg of an isosceles triangle perpendicular are drawn to the base prove that the triangles formed are similar
The description below proves that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.
How to prove an Isosceles Triangle?Let ABC be an isosceles triangle such that AB = AC.
Let AD be the bisector of ∠A.
We want to prove that BD=DC
In △ABD & △ACD
AB = AC(Thus, △ABC is an isosceles triangle)
∠BAD =∠CAD(Because AD is the bisector of ∠A)
AD = AD(Common sides)
By SAS Congruency, we have;
△ABD ≅ △ACD
By corresponding parts of congruent triangles, we can say that; BD=DC
Thus, this proves that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.
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The formula for the perimeter of a rectangle is P=2(l+w). Part A. Rewrite the formula for the perimeter of a rectangle in terms of the width, w. In your final answer, include all of your work. Part B. In two or more complete sentences, describe the process you followed while isolating the variable w in the equation P=2(l+w).
The expression that represents the width is w = (P-2l)/2
Subject of formulaGiven the formula for calculating the perimeter of a triangle expressed as:
P = 2(l + w)
where
l is the length
w is the width
Make w the subject of the formula
Given
P = 2(l + w)
Expand
P = 2l + 2w
Subtract 2l from both sides
P - 2l = 2w
Divide both sides by2
2w/2 = (P-2l)/2
w = (P-2l)/2
Hence the expression that represents the width is w = (P-2l)/2
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The formula s = startroot startfraction s a over 6 endfraction endroot gives the length of the side, s, of a cube with a surface area, sa. how much longer is the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters? startroot 30 endroot minus 4 startroot 5 endroot meters m startroot 30 endroot minus 2 startroot 5 endroot meters m startroot 10 endroot meters m 2 startroot 15 endroot meters m
Step-by-step explanation:
so, let me get this straight :
s = sqrt(sa/6)
this is because the surface area of a cube consists of 6 squares (as everybody knows that dice have 6 equal sides).
and the area of a single square is side².
for a cube with sa = 180 m² we have
s = sqrt(180/6) = sqrt(30)
for a cube with sa = 120 m² we have
s = sqrt(120/6) = sqrt(20) = sqrt(4×5) = 2×sqrt(5)
so, the side length of the larger cube is
sqrt(30) - 2×sqrt(5) meters
longer than the side length of the smaller cube.
in other words, the difference between both side lengths.
Answer:
answer above is correct, its B
Step-by-step explanation:
Explain weather this equation is a linear equation
4. y = 1 - x
Answer:
Yes, it is a linear equation.
Step-by-step explanation:
Linear equation:An equation of the form ax + by +c = 0, where x and y are two variables and a, b,c are the non-zero real numbers is called a linear equation and the degree of the equation is 1.
y = 1 - x
x + y - 1 = 0
Where a = 1 ; b=1 and c = -1
So, y = 1 -x is a linear equation.