We want to convert litres L to Hectolitres hL.
[tex]1L=0.01L[/tex]one litre equals 0.01 hectolitre.
So, to convert 2L to hL, we have;
[tex]\begin{gathered} 1L=0.01L \\ 2L=0.02L \end{gathered}[/tex]which of the following is the correct factorization of the polynomial below?27x^3+1000
The polynomial is given to be:
[tex]27x^3+1000[/tex]We can rewrite this expression by applying the knowledge of exponents:
[tex]\Rightarrow(3x)^3+10^3[/tex]Apply the sum of cubes formula:
[tex]x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)[/tex]Therefore, we have:
[tex]\left(3x\right)^3+10^3=\left(3x+10\right)\left(3^2x^2-10\cdot \:3x+10^2\right)[/tex]Hence, we can simplify the expression to give the answer:
[tex]27x^3+1000=\left(3x+10\right)\left(9x^2-30x+100\right)[/tex]The correct option is OPTION B.
I'm having trouble finding the length of NP and MN, thinking it has something to do with tan, cos, and sin, but not completely sure.
Bisects: to divide into two equal parts.
In this case, DB is bisecting the ∠ABC, then the ∠ABD
As OP is bisecting ∠MON, that means that ∠NOP and ∠POM have the same measure.
Then:
[tex]m\angle MON=m\angle NOP+m\angle POM[/tex]As ∠NOP = ∠POM, we get:
[tex]m\angle MON=m\angle NOP+m\angle NOP=2\cdot m\angle NOP[/tex]Replacing the value we get:
[tex]m\angle MON=2\cdot20=40[/tex]Based on this, we can use the trigonometric functions, as we have an angle and one side. Specifically, the tangent function:
[tex]\tan \alpha=\frac{opposite}{\text{adyacent}}[/tex]First, to calculate NP, we get the following:
[tex]\tan 20=\frac{NP}{6}[/tex]Isolating for NP:
[tex]NP=6\cdot\tan 20[/tex][tex]NP=2.18[/tex]Then, calculating for MN we get the following:
[tex]\tan 40=\frac{MN}{6}[/tex]Isolating for MN:
[tex]MN=6\cdot\tan 40[/tex][tex]MN=5.03[/tex]Answer:
• NP = 2.18
,• MN = 5.03
the function is shaped like a u what is the standard form or basic function.
The function shaped like a U is in the form of a basic quadratic equation and is represented as a parabola.
The graph of a quadratic function is a U-shaped curve called a parabola. An important feature of graphs is that they have extreme points called vertices.
When the parabola opens upwards, the vertex represents the lowest point of the graph, or the minimum value of the quadratic function. When the parabola opens downwards, the vertex represents the highest point or maximum of the graph.
In both cases, the vertex is the inflection point of the graph. Graphs are also symmetrical about a vertical line through the vertices called the axis of symmetry.
The standard form or basic function for a parabola will be in the form of a quadratic function such as -
[tex]f(x)=a(x-h)^{2} +k[/tex]
where, [tex](h,k)[/tex] = vertex
Thus, the function shaped like a U is in the form of a basic quadratic equation and is represented as a parabola.
To learn more about parabola visit https://brainly.com/question/21685473
#SPJ9
what is the answer
1-m=6-6m
Answer:
m = 1
Explanaton:
Given the expression;
1 - m = 6 - 6m
Collect the like terms
-m + 6m = 6 - 1
5m = 5
Divide both sides by 5
5m/5 = 5/5
m = 1
Hence the value of m is 1
Use a system of equations to solve the following problem.The sum of three integers is 244. The sum of the first and second integers exceeds the third by 48. The third integer is 36 less than the first Findthe three integersAnswer How to enter your answer topens in new windon 5 PointsKeypadKeyboard Shartofirst integer =second integer =third integer =
Given:
The sum of three integers is 244. The sum of the first and second integers exceeds the third by 48. The third integer is 36 less than the first.
Aim:
We need to find the values of all three integers.
Explanation:
Let x be the first integer.
Let y be the second integer.
Let z be the third interger.
The sum of three integers is 244.
[tex]x+y+z=244[/tex]The sum of the first and second integers exceeds the third by 48.
[tex]x+y=z+48[/tex]The third integer is 36 less than the first.
[tex]z=x-36[/tex]Substitute z=x-36 in the equation x+y=z-48 .
[tex]x+y=x-36+48[/tex][tex]x+y=x+12[/tex]Subtract x from both sides of the equation.
[tex]x+y-x=x+12-x[/tex][tex]y=12[/tex]Substitute z=x-36 and y=12 in the equation x+y+z=244.
[tex]x+12+x-36=244[/tex]Add 24 to both sides of the equation.
[tex]2x-24+24=244+24[/tex][tex]2x=268[/tex]Divide both sides by 2.
[tex]\frac{2x}{2}=\frac{268}{2}[/tex][tex]x=134[/tex]Substitute x=134 in the equation z=x-36
[tex]z=134-36[/tex][tex]z=98[/tex]We get x=128, y=12 and z =98.
Final answer:
first integer = 128
second integer =`12
third integer = 98.
Help me with math and explain it in a short solution
The perimeter is the sum of all the sides of a geometric figure. Since it is a parallelogram, then its opposite sides are equal, so
[tex]\begin{gathered} QR=TS \\ \text{and} \\ QT=RS \end{gathered}[/tex]In the graph, we can see that the distance between points Q and R is 7 units. To find the distance between points Q and T we can use the formula of the distance between two points in the plane, that is,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points } \end{gathered}[/tex]Then, we have
[tex]\begin{gathered} Q(-3,3) \\ T(-5,-3) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Replace} \\ d=\sqrt[]{(-5-(-3))^2+(-3-3)^2} \\ d=\sqrt[]{(-5+3)^2+(-3-3)^2} \\ d=\sqrt[]{(-2)^2+(-6)^2} \\ d=\sqrt[]{4+36} \\ d=\sqrt[]{40} \end{gathered}[/tex]Finally, we have
[tex]\begin{gathered} \text{ Perimeter }=QR+RS+TS+QT \\ \text{ Perimeter }=7+\sqrt[]{40}+7+\sqrt[]{40} \\ \text{ Perimeter }=26.65 \end{gathered}[/tex]Therefore, the perimeter of parallelogram QRST is 26.65 units and the correct answer is option B.
A single die is rolled 4 times. Find the probability of getting at least one 6.
When a dice is rolled the probability of getting one 6 is,
[tex]P(\text{Getting one 6) = }\frac{1}{6}[/tex]The probability of not getting 6 when a dice is rolled is ,
[tex]P(\text{Not getting 6) = }\frac{5}{6}[/tex]The probability of getting 6 is independent on how many times the dice is rolled.
The probability of not getting 6 is given as,
[tex]P(\text{ getting atleast one 6) = 1 - P(Not getting 6)}[/tex]Therefore the probability of getting atleast one 6 when a dice is rolled 4 times is calculated as,
[tex]\begin{gathered} P(\text{Getting 6) = 1 - (}\frac{5}{6})^4 \\ P(\text{Getting 6) = 1 - }\frac{625}{1296} \\ P(\text{Getting 6) = }0.5177 \\ \end{gathered}[/tex]Thus the probability of getting atleast one 6 when a dice is rolled 4 times is 0.5177 .
Solve the equation for x, and enter your answer below.3x-3 + 5x = 37
The given equation is-
[tex]3x-3+5x=37[/tex]First, we reduce like terms
[tex]8x-3=37[/tex]Now, we sum 3 on each side
[tex]\begin{gathered} 8x-3+3=37+3 \\ 8x=40 \end{gathered}[/tex]At last, we divide the equation by 8
[tex]\begin{gathered} \frac{8x}{8}=\frac{40}{8} \\ x=5 \end{gathered}[/tex]Therefore, the solution is 5.find the odds of an event occurring given the probability of the event 6/7
Odds is the ratio of favourable outcomes to non-favourable outcomes:
Let:
P = probability of an event occurring = 6/7
Q = probability of the event not occurring = 1 - P = 1 - 6/7 = 1/7
Therefore, the odds will be:
[tex]\frac{P}{Q}=\frac{\frac{6}{7}}{\frac{1}{7}}=6[/tex]Consider the following linear equation.2y = -1-ainStep 2 of 2: Graph the line.
As given by the question
There are given that the equation
[tex]y=-1-\frac{2}{5}x[/tex]Now,
The graph of the line is given below:
Find the 8th term of the sequence using the explicit formula: 2 × (7)(n - 1).1647086164706816478061647860
Given:
The explicit formula is
[tex]2\times7^{(n-1)}[/tex]Required:
To find the 8th term of the sequence.
Explanation:
For n=8,
[tex]\begin{gathered} =2\times7^{(8-1)} \\ \\ =2\times7^7 \\ \\ =2\times7\times7\times7\times7\times7\times7\times7 \\ \\ =1647086 \end{gathered}[/tex]Final Answer:
The first option is correct.
[tex]1647086[/tex]dividing 5 by 10 + 1
Given the system of equations: 8x + 14y = 4 and -6x - 7y = - 10, what would youmultiply the bottom equation by to eliminate y when adding the two equationstogether?
We need to multiply the second equation by 2 to eliminate y when adding the two equations
A company purchased 10,000 pairs of men's slacks for $19.16 per pair and marked them up $22.43. What was the selling price of each pair of slacks? Use the formula S=C+M
Given that each slack is purchased at $19.16, so the cost price is $19.16
Also given that each slack is marked at $22.43, so the marked price is $22.43
It is asked to use the formula,
[tex]S=C+M[/tex]Substitute the values and simplify,
[tex]S=19.16+22.43=41.59[/tex]Thus, the selling price of each pair os slacks is $41.59
In the rectangle below, B D = 4x – 2, AC = 5x-11, and m ZAED = 82º.Find AE and m ZECB.BEAE =m ZECB =DС
Given :
[tex]\begin{gathered} BD\text{ = 4x + 2} \\ AC\text{ = 5x - 11} \\ \angle AED=82^0 \end{gathered}[/tex]Required :
[tex]AE\text{ , }\angle\text{ ECB}[/tex]Recall from the properties of a rectangle that
[tex]\text{The diagonals have the same length}[/tex]Hence :
[tex]\begin{gathered} AC\text{ = BD} \\ 5x\text{ - 11 = 4x -2 } \\ \text{collect like terms} \\ 5x\text{ - 4x = 11 - 2} \\ x\text{ = 9} \end{gathered}[/tex].1.2_Updated_FY21 Question: 1-3 The elevation of the Vander's home is -108 feet. The elevation of the Gail's home is exactly of that depth below sea level. What is the elevation of the Gail's home in feet? -36 -72 -162 -180
Given:
Elevation of Vander's home = -108 feet
Elevation of Gali's home is ⅔ of that depth below sea level.
Thus, the elevation of Gali's home is:
⅔ of -108 feet =
[tex]\frac{2}{3}(-108)\text{ = }\frac{2(-108)}{3}=\frac{-216}{3}=\text{ -72 f}eet[/tex]We know that the elevation of Vander's home is already below sea level since it's a negative value.
Therefore, since the elevation of Gali's home is ⅔ of the depth of Vander's home below sea level, the elevation of Gali's home is:
-72 feet
ANSWER:
-72 feet
When 3.5 is added to 7 times a number the result is 65.1 find the number
Let x be the number we are looking for; therefore, 7 times a number is '7x'.
Then, 3.5 added to 7 times a number is
[tex]3.5+7x[/tex]Thus, the whole equation is
[tex]\begin{gathered} 3.5+7x=65.1 \\ \Rightarrow7x=65.1-3.5=61.6 \\ \Rightarrow x=\frac{61.6}{7}=8.8 \end{gathered}[/tex]Hence, the number is 8.8
Five companies have each sent one representative to a competition to pitch their newest business idea to a group of angel investors. The conference has 5 time slots designated for one representative to present their company's idea.How many different ways can the representatives be ordered to present their ideas?
Let's use the counting principle:
[tex]\begin{gathered} Let: \\ n=number_{\text{ }}slots=5 \\ T=Total_{\text{ }}number_{\text{ }}of_{\text{ }}ways \end{gathered}[/tex]so:
[tex]T=n\cdot(n-1)\cdot(n-2)...1=n![/tex]So:
[tex]\begin{gathered} T=5! \\ T=120 \end{gathered}[/tex]Answer:
120
The number of different ways can the representatives be ordered to present their ideas is 120 ways.
Given that, 5 companies have each sent one representative to a competition to pitch their newest business idea to a group of angel investors.
What are Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Using nPr =n!(n-r)! we get
Here, n=5 and r=5
So, P(n, r) = P(5, 5) = 5!(5-5)!
= 5!/1
= 5×4×3×2×1
= 120 ways
Therefore, the number of different ways can the representatives be ordered to present their ideas is 120 ways.
To learn more about the permutation visit:
https://brainly.com/question/3867157.
#SPJ2
Find the LCD of the list of fractions. 11/20, 1/18, 13/90
LCD state for Least Common Denominator
The given fraction are :
[tex]\frac{11}{20},\text{ }\frac{1}{18},\text{ }\frac{13}{90}[/tex]For the least common denominator, first find the LCM of all the denominator of the given values:
Denominator are : ( 20, 18, 90)
LCM of (20,18, 90) = 180
So, the fraction will value can be written as :
[tex]\begin{gathered} \frac{11}{20}\text{ to make denominator equal to 180,} \\ \text{ Multiply up \& down by 9} \\ \frac{11\times9}{20\times9}=\frac{99}{180} \\ \text{ } \\ \frac{1}{18}\text{ to make denominator equal to 180} \\ \text{ Multiply up and down by 10} \\ \frac{1\times10}{18\times10}=\frac{10}{180} \\ \\ \frac{13}{90},\text{ to make denominator equal to 180} \\ \text{Multiply up and down by 2} \\ \frac{13\times2}{90\times2}=\frac{26}{180} \end{gathered}[/tex]Thus, the fraction will convert as :
[tex]\begin{gathered} \frac{11}{20}=\frac{99}{180} \\ \frac{1}{18}=\frac{10}{180} \\ \frac{13}{90}=\frac{26}{180} \end{gathered}[/tex]The least common denominator is 180
Answer : LCD of 11/20, 1/18, 13/90 is 180
Find the equation of the linear function represented by the table below in slope-intercept form.X1234y691215******
Given:
Given a table.
Required:
To find the equation of the linear function.
Explanation:
From the table
[tex]\begin{gathered} (x1,y1)=(1,6) \\ (x2,y2)=(2,9) \end{gathered}[/tex]The general form of equation is
[tex]y=mx+b[/tex]Here the slope is
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x2} \\ \\ =\frac{9-6}{2-1} \\ \\ =\frac{3}{1} \\ \\ =3 \end{gathered}[/tex]So
[tex]y=3x+b[/tex]Now we have to find the value of b, by using the point (1,6)
[tex]\begin{gathered} 6=3(1)+b \\ \\ 6-3=b \\ \\ b=3 \end{gathered}[/tex]Now
[tex]y=3x+3[/tex]Final Answer:
The linear equation is
[tex]y=3x+3[/tex]Image courtesy of NASAWhich of New Zealand's physical features is circled by number 2 on the map above?A. the Northern PeninsulaB. the Southern AlpsC. the Canterbury PlainsD. the Eastern HillsPlease select the best answer from the choices providedABOeCD
C) Canterbury Plains
|x-2|-3 >or equal to 2
By solving the linear inequation it is obtained that [tex]x \leq -3[/tex] or [tex]x \geq 7[/tex].
What is linear inequation?
Expressions with linear inequalities compare any two values using inequality symbols like ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be either numerical, algebraic, or both. Examples of numerical inequalities include 1011 and 20>17, while algebraic inequalities include x>y, y19-x, and x z > 11 (also called literal inequalities). Here is a lesson on linear inequalities for class 11. Inequality in mathematics, linear inequalities, graphing of linear inequalities, as well as detailed examples are all covered in this article.
Here,
The given linear inequation is
[tex]|x - 2| - 3 \geq 2[/tex]
Now,
[tex]|x -2| - 3 \geq 2\\|x - 2| \geq 2+3\\|x-2| \geq 5\\[/tex]
For [tex]x \geq 2\\[/tex]
[tex]x - 2 \geq 5\\x \geq 2 + 5\\x\geq 7[/tex]
For [tex]x < 2[/tex]
[tex]2 - x \geq 5\\x \leq 2 - 5\\x \leq -3[/tex]
So the solution set is [tex]x \leq -3[/tex] or [tex]x \geq 7[/tex]
To learn more about linear inequation, refer to the link:
https://brainly.com/question/24372553
#SPJ1
A python (p) is 3.9 feet longer than a boa constrictor (6).Select an expression from each box to create an equation that compares the lengths of the snakes
Since the python is 3.9 feet longer than the boa.
Therefore,
p=b+3.9
This implies that,
b=p - 3.9
In the first box you pick b
In the second box pick p-3.9
(Right angle) Trigonometry Help me find the X value please!
To solve for x, we will simply use the trigonometric ratio
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]From the figure given;
θ=24.3 opposite=2.06 and hypotenuse =x
substitute the values and evaluate
[tex]\sin 24.3=\frac{2.06}{x}[/tex]cross-multiply
x sin24.3 = 2.06
Divide both-side by sin24.3
[tex]x=\frac{2.06}{\sin 24.3}[/tex][tex]x\approx5.0[/tex]17. Show your work-Factor the expression: 35x+63 * Your answer
35x + 63
7 can go into the two
7 (5x + 9)
The diagram shows how 6-foot boards and 8-foot boards are joined to form rectangular frames in a wall. Which is closest to the length of the diagonal brace for the wall? 6 ft 8 ft A. 10 ft B. 12 ft C. 13 ft D. 11 ft
A right triangle is formed, where 6 ft and 8 ft are the legs, and the hypotenuse is unknown. Using the Pythagorean theorem:
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = √100
c = 10 ft
Question 8: What is the measure of Angle C?*c525°47°43°1330
SOLUTION
Angle C is 133 degrees
From the image , angle c is the same as angle a, reason been that they are vertically opposite angles and they are always equal.. let us call angle c and a = x
Angle b = 47 degrees, because they are both vertically opposite angles, and they are always equal.
Angle c + angle a + angle b + 47 = 360 ( sum of angles at a point)
x + x + 47 + 47 = 360
2x + 94 =360
2x = 360-94
2x =266
x= 266/2
x=133 degrees
So angle C is 133 degrees
Option D
a line has a slope of 3 and a y-i yet dot of 5. what is it’s equation in slope-intercept form? write you answer using integers, proper fractions, and improper fractions in simplest form.
y = 3x + 5
Explanation:slope = 3
y - intercept = 5
To get the equation in slope intercept form, we'll use:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex][tex]\begin{gathered} \text{The equation becomes:} \\ y\text{ = 3x + 5} \\ \end{gathered}[/tex]Which is NOT true?a) 9+4=17-4b)8+7=14+3c)11=19-8d)5+8=20-7
To determine which expression is true, we have to do the operations and check that on both sides of the equation is the same number.
Then, in this case we have:
[tex]\begin{gathered} a)9+4=13 \\ 17-4=13 \\ b)8+7=15 \\ 14+3=17 \\ c)19-8=11 \\ d)5+8=13 \\ 20-7=13 \end{gathered}[/tex]notice that the only option that don't match is b, therefore, the option b is not true
if you are paid $4.50 per hour, how many hours will you have to work to earn $1000.00
Answer:
222.22 hours
Explanation:
To know how many hours you will have to work, we need to use the given rate of $4.50 per hour as follows:
[tex]\text{ \$1000}\times\frac{1\text{ hour}}{\text{ \$4.50}}=\frac{1000\times1}{4.5}=\frac{1000}{4.5}=222.22\text{ hours}[/tex]Because 1 hour is equivalent to $4.50.
Therefore, you will have to work 222.22 hours to earn $1000