According to the given data we have the following:
3√45 -4 √225 + √200 - √50
Then to simplify we would have to make the following:
[3 × √3 × √3 × √5] - [√5 × √5 × √5] + [√2 × √2 × √2 × √5 × √5] - [√2 × √5 × √5]
=[3 × 3 × √5] - [5 × √5] + [2 × 5 × √2] - [5 × √2]
=3√5 - 5√5 + 10√2 - 5√2
=√5(3 - 5) + √2(10 - 5)
=(-2√5) + 5√2
Therefore, the answer would be 16√5 + 75√2
x 31 36 41 46y 10 8 6 4I need to find the slope with these points
x 31 36 41 46
y 10 8 6 4
I need to find the slope with these points
we know that
To find out the slope, we need two points
take the points (31,10) and (36,8)
so
m=(8-10)/(36-31)
m=-2/5
m=-2/5
m=-0.40
therefore
the answer is -0.40Part 2)
we have
x -7 -4 -1 2
y -7 14 35 56
take the points (7,-7) and (-4,14)
m=(14+7)/(-4-7)
m=21/-11
m=-21/11
the answer is -21/11he graph of a function is shown.
5
4
3
2
-
y
--5-3-2-1₁ 1 2 3 4 5 x
-2-
-3+
7 9
Which function is represented by the graph?
O f(x) =
O
f(x) = {3
O f(x):
x-3, x<0
3,
x20
11
x + 3, x < 0
x 20
-x+ 3, x ≤ 0
3,
x>0
○ f(x) = { 3*
O
-x-3, x ≤0
x > 0
The function f(x) = {x + 3, x < 0, 3 x ≥ 0} represents the graph.
What is graph?
In mathematics, the set of ordered pairings where f(x)=y exists is the graph of a function f. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
As show in the graph we can see that the function has a graph of x + 3 on left side of the y - axis for x < 0.
And the function has the constant graph y = 3 for x ≥ 0.
Therefore, the given graph is the graph of the function,
f(x) = {x + 3, x < 0, 3 x ≥ 0}.
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PLEASE HELP IT'S DUE NOW.. :(
Slope intercept form of equation of line f and line g is
Equation of line f
y = 1.75x + 3.5
Equation of line g
y = -4x - 8
First option is correct
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
For line f
The line passes through (2, 7) and (4, 10.5)
Slope =
[tex]\frac{10.5 - 7}{4 - 2}\\\frac{3.5}{2}\\\frac{7}{4}[/tex]
Equation of line =
[tex]y - 7 = \frac{7}{4}(x - 2)[/tex]
y = 1.75x - 3.5+7
y = 1.75x + 3.5
For line g
The line passes through (-3, 4) and (-2, 0)
Slope =
[tex]\frac{0-4}{-2-(-3))}\\-4[/tex]
Equation of line =
y - 4 = -4(x - (-3))
y - 4 = -4x-12\\
y =-4x-12+4\\
y = -4x-8
The first option is correct
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PLEASE HELP AND HURRY!!!!!! Simplify: 7/8+3/4
Answer: 1.625
Step-by-step explanation:
13/8 = 1 5/8 = 1.625
z ÷ 12 = 9
PLS NEED HELP FAST
STEP BY STEP
Answer:
z = 108
z/12 = 9
12 x z/12 = 12 x 9
12 x z/12 = 12 x 9
z = 12 x 9
= 108
Answer:
z = 108
Step-by-step explanation:
z / 12 = 9
Multiply 12 and 9
z = 12 * 9
12 * 9 = 108
z = 108
Hope I helped <3
which of the following present for their transformation is equivalent to reflection across the x axis .Arotation 90 degrees about the origin of reflection across the x-axis B rotation 90 degrees about the origin reflection across the y-axisC rotation across degrees about the origin and reflection across the x axis D rotation 180 degrees about the origin reflection across the y axis
for transformation equivalent to reflection across the x axis
rotate 180 degree about the origin and reflection about the x axis.
option C is correct.
1 months amren 5 movies and 3 video games for a total of $36. the next month he went 7 movies and 9 video games for a total of $78. find the rental cost for each movie in each video game.rental cost for each movie:rental cost for each video games:
Each movie cost $3.75 while each video game cost $5.75
Here, we want to get rental costs
We start by using variables to represent the costs of the movie and the video game
Let the cost of a movie be m and the cost of a video game be g
Thus, we have it that;
[tex]5m\text{ + 3g = 36}[/tex]and;
[tex]7m\text{ + 9g = 78}[/tex]So, we have two equations to solve simlutaneously
That would yield;
[tex]\begin{gathered} \text{From i;} \\ 5m\text{ + 3g = 36} \\ 3g\text{ = 36-5m} \\ we\text{ can have equation }ii\text{ as;} \\ 7m\text{ + 3(3g) = 78} \\ 7m\text{ + 3(36-5m) = 78} \\ 7m\text{ + 108-15m = 78} \\ 108-78\text{ = 15m-7m} \\ 8m\text{ = 30} \\ m\text{ = }\frac{30}{8} \\ m\text{ = \$3.75} \end{gathered}[/tex]Now, to get the value of g, we make a substitution into any of the equations;
[tex]\begin{gathered} 3g\text{ = 36-5m} \\ 3g\text{ = 36-5(3.75)} \\ 3g\text{ = 36-18.75} \\ 3g\text{ = 17.25} \\ g\text{ = }\frac{17.25}{3} \\ g\text{ = 5.75} \end{gathered}[/tex]Romano pays 312.50 for a television set. The markup price of the television set is 25%. What equation could you use to find the amount of money that the ...
The equation used to find the amount of money the store bought the television sets is 1.25a = 312.50
How to find the equation that depict the amount of money paid for the television sets?Romano pays 312.50 dollars for a television set. The mark up price of the television set is 25%.
The equation that can be used to find the amount of money the store paid for the television sets can be calculated as follows;
Therefore,
25% of a + a = 312.50
where
a = cost of the television0.25a + a = 312.50
Therefore, the equation is 1.25a = 312.50
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A forty-foot piece of wire was cut into two pieces. The length of one-
piece is 9 times the length of the other. What is the length of the
longer piece? System of equations
The length of the longer piece is 39.4 ft.
Given, a forty-foot piece of wire was cut into two pieces.
The length of one-piece is 9 times the length of the other.
Let the length of one piece be x,
and the length of the other piece be 9x
Now, according to the question
x + 9x = 44
10x = 44
x = 4.4
then, the length of the longer piece be 9×4.4 = 39.4
Hence, the length of the longer piece is 39.4 ft.
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A dozen muffins is 12 muffins. A recipe calls for 3/4 cup of almonds to make half a dozen muffins. Use a complex fraction to find how many cups of almonds are needed to make a dozen muffins.
1) Firstly, let's set a proportion to find out how mny cups of almonds are needed.
muffins cups of almonds
6 3/4
12 x
2)
Cross multiplying it:
6x = 12 * 3/4
6x = 9
x= 9/6
3
Find the scale factor.
Answer:
scale factor k = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
the scale factor of Δ QRS to Δ LMN is the ratio of corresponding sides , image to original.
scale factor = [tex]\frac{QS}{LN}[/tex] = [tex]\frac{4}{3}[/tex]
frequency The table and corresponding polygon show information about the waiting times of some patients at a dentist. Frequency What fraction of patients waited for more than 7 minutes? 10- 0- 5 6 7 8 Waiting time (x minutes) 9 10 x Waiting time (x minutes) 5< x≤6 6< x≤7 7< x≤8 8< x≤9 9< x≤ 10
The 31 minutes for the lowest quartile of the waiting times of patients at this surgery.
Given that,
The histogram displays statistics about the average patient wait time in dental offices, expressed in minutes. 3.24 frequency The table and related polygon display data regarding some patients' wait periods at a dentist.
We have to find frequency How many patients waited for longer than seven minute.
The frequency of a given data value is the number of times it happens. We use f to represent a data value's frequency. For instance, if five students received As in science, the grade A was said to have a frequency of five.
In the picture we can see the answer.
Therefore, The 31 minutes for the lowest quartile of the waiting times of patients at this surgery.
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2d a researcher wanted to know if there was a significant difference in cyber security breaches between cities on two different continents. what test should he conduct to determine if there is a significant difference in cyber security breaches between the continents? write up the results and determine what do the results mean? here is the data set: asia europe 40 25 52 35 63 20 70 18 25 19 19 14 11 9
There is no significant difference between the cyber security breaches of the two destinations and the values are t-value is 0.16221, the p-value is .874721.
We use two sample t-test to check for the significance.
We take the sample of Asia as treatment 1 and that of Europe as treatment 2
Treatment 1
[tex]N_{1}[/tex]: 5
[tex]df_{1}[/tex] = N - 1 = 5 - 1 = 4
[tex]M_{1}[/tex]: 24.6
[tex]SS_{1}[/tex]: 77.2
[tex]S^{2} _{1}[/tex] = [tex]SS_{1}[/tex]/(N - 1) = 77.2/(5-1) = 19.3
Treatment 2
[tex]N_{2}[/tex]: 6
[tex]df_{2}[/tex] = N - 1 = 6 - 1 = 5
[tex]M_{2}[/tex]: 23.5
[tex]SS_{2}[/tex]: 1051.5
[tex]S^{2} _{2}[/tex] = [tex]SS_{2}[/tex]/(N - 1) = 1051.5/(6-1) = 210.3
T-value Calculation
[tex]S^{2} p_{}[/tex] = (( df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((4/9) * 19.3) + ((5/9) * 210.3) = 125.41
s2M1 = s2p/N1 = 125.41/5 = 25.08
s2M2 = s2p/N2 = 125.41/6 = 20.9
t = (M1 - M2)/√(s2M1 + s2M2) = 1.1/√45.98 = 0.16
The t-value is 0.16221. The p-value is .874721. The result is not significant at p < .05
Hence the answer is there is no significant difference between the cyber security breaches of the two destinations and the values are t-value is 0.16221, the p-value is .874721.
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lin is mixing orange paint for a play. the color takes 3 parts red to 2 parts yellow. if lin has 18 cups of yellow paint how many cups of red does he need?
the number of cups of red Lin needs is 27 cups
Explanation:number of parts of red = 3
number of parts of yellow = 2
the ratio of red to yellow = 3:2
when lin's number of cups of yellow = 18
let the number of cups of red = x
3 red = 2 yellow
x red = 18 yellow
cross multiply:
3(18) = 2(x)
54 = 2x
divide both sides by 2:
54/2 = 2x/2
x = 27
Hence, the number of cups of red Lin needs is 27 cups
(Lesson 9.8: Other Steady-State Methods.) Consider the following observations: 54 70 75 62 If we choose a batch size of 3, calculate all of the overlapping batch means for me. a. 65.25 b. 62.0, 68.5 c. 66.3, 69.0 d. 65.25 +3 e. None of the above
All of the overlapping batch means for me is (66.3, 69.0).
Given observations:
54 70 75 62
From the given data, if we choose a batch size of 3, then calculating all of the overlapping batch means for me in total
that is :
= 1/3 * (54 + 70 + 75)
= 66.3
and
= 1/3 * (70 + 75 + 62)
= 69.0
So often, the option c is correct from the given
that is 66.3, 69.0
Hence the answer is all of the overlapping batch means for me is (66.3, 69.0).
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The volume of a cube is 614.125 cubic inches. What is the length of each side of the cube?
The length of the side of cube is 8.5 inches.
What is volume of a cube?
A cube is a solid object that is three dimensional and has six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, and the only regular hexahedron, is the cube. It consists of 8 vertices, 12 edges, and 6 faces.
The volume of a cube is a^3 cubic inches where a is the length of side of cube.
Give volume of a cube is 614.125 cubic inches.
Let the length of a side of cube is x inches.
Then volume of cube = x^3 cubic inches.
Now,
x^3 = 614.125
Finding cube root and we get
=> x^3 = 8.5 * 8.5 * 8.5
=> x = 8.5 inches
Therefore, the length of the side of cube is 8.5 inches.
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if p=3x+4 and v=x+5, find pv-2p+v
Use substitution to simplify the expression.
pv - 2p + v
(3x + 4)(x + 5) - 2(3x + 4) + x + 5
3x² + 15x + 4x + 20 - 6x - 8 + x + 5
3x² + 15x + 4x + x - 6x + 20 + 5 - 8
3x² + 14x + 17
Find the number of different ways that an instructor can choose 4 students from a class of 23 students for a field trip.
We have to find how many ways we can group 23 students in groups of 4.
This can be calculated as a combination of 23 in 4, as order does not matter and there is no repetition.
We can calculate it as:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ C(23,4)=\frac{23!}{4!(23-4)!} \\ C(23,4)=\frac{23!}{4!19!} \\ C(23,4)=\frac{23\cdot22\cdot21\cdot20}{4\cdot3\cdot2\cdot1} \\ C(23,4)=\frac{212520}{24} \\ C(23,4)=8855 \end{gathered}[/tex]Answer: there are 8855 ways.
PLEASE HELP If each side has a scale factor of 1 in. to 5 ft., the actualperimeter is and the actual area isO 60 ft, 80 ftO 300 ft, 80 ft?80 ft, 60 ft280 ft, 300 ft
The perimeter is determine as the add of the sides of the figure. In this case:
[tex]P=(5+2+2+2+1+1+1+2)(5ft)[/tex][tex]P=16(1in5tf)=80ft[/tex]For the area we will divide the figure as follow:
The total area will be:
[tex]A=A_a+A_b[/tex]We find the are of a rectangle by:
[tex]A=h\cdot b[/tex]Where h is height and b is base
Then:
[tex]A_a=5\cdot2=10[/tex][tex]A_b=2\cdot1=2[/tex]Then the total area is:
[tex]A=10+2=12^{\doubleprime}[/tex]In feets:
[tex]12(5ft)=60ft^2[/tex]Complete the table below to find solutions to the linear equation y = 5x + 35
y = 5x + 35
When x = 0, we substitute x = 0 into the equation above and then solve for y
y = 5(0) + 35
y = 0+ 35
y = 35
when x =3, substitute into the equation and then solve for y
y = 5(3) + 35
y = 15 + 35
y = 50
when x=-7, substitute x=-7 into the equation above and then solve for y
y = 5(-7) + 35
y = -35+ 35
y=0
x y (x,y)
0 35 (0, 35)
3 50 (3, 50)
-7 0 (-7, 0)
Using the function F(x)= 3x-1 solve for the following values F(-2)=
For the function F(x)=3x-1, the value for F(-2) will be (-7).
How to tackle this type of question of function?
Put value of variable in the given function.
Here,
x=-2
then, F(-2) = 3(-2) - 1
F(-2) = -6 - 1
F(-2) = -7
Hence, F(-2) = (-7)
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What is the equation of the line that passes
through the point (-8, -8) and has a slope
of o?
Answer: y+8=m(x+8)
Step-by-step explanation: because you follow the form y-y1=m(x-x1)
Determine whether a relation is a function.
2 gallons = 9 litres
16
to convert 17 gallons into liters
Answer:
Step-by-step explanation:
17/2=8.5
8.5 x 9=76.5
which exponential function has an x- intercept?(picture of functions below )
Question: which exponential function has an x-intercept?
Explanation:
Let the function:
[tex]f(x)=100^{x\text{ -5 }}\text{ - 1}[/tex]An x-intercept or zero of the function is when y= f(x)=0. In this case, notice that this occurs when x=5, since:
[tex]f(5)=100^{5\text{ -5 }}\text{ - 1= 100}^0\text{ - 1 = 1-1 =0}[/tex]thus, this function must cross the x-axis at the point x= 5. On the other hand, this function has a horizontal asymptote at y=-1, so the range of this function would be all y > -1. This fact further evidences that this function crosses the x-axis.
Answer: we can conclude that the correct answer is:
[tex]f(x)=100^{x\text{ -5 }}\text{ - 1}[/tex]Determine the solution to the inequality. |4x − 4| ≥ 8 x ≤ −1 or x ≥ 3 x ≤ −2 or x ≥ 3 x ≤ −3 or x ≥ 4 x ≤ −4 or x ≥ 4
The solution to the inequality will be -
x ≥ 3 or x ≤ -1
What is an Inequality? What is a expression? What is a mathematical equation?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the given inequality as -
|4x − 4| ≥ 8
We have the inequality as -
|4x − 4| ≥ 8
4x - 4 ≥ 8 or 4x - 4 ≤ - 8
4x ≥ 12 or 4x ≤ - 4
x ≥ 3 or x ≤ -1
Therefore, the solution to the inequality will be -
x ≥ 3 or x ≤ -1
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From the graph , determine the value of x when F(x) = 4
for this we locate the point where y = 4, and find its ordered pair on the x-axis, and from the graph, x = - 3
answer: x = - 3
What are the coordinates of point A? ES 2 (8,6) (-6, 8) (-5.7) Save and Exit
To write the coordinates of a point in a x - y plane you:
1. Find the distance in x-axis:
The given point A is 7 units distance in x-axis
2. Find the distance in y- axis
The given point A is -5 units distance in y-axis
You write the coordinates in form (x,y)
As x=7 and y=-5
Point A is (7, -5)Answer: -5,7
Step-by-step explanation:
If x>0, then x^(3/4)/x^(-¼)
HELPP PLEASEEE
Answer:
x
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
given
[tex]\frac{x^{\frac{3}{4} } }{x^{-\frac{1}{4} } }[/tex]
= [tex]x^{\frac{3}{4}-(-\frac{1}{4}) }[/tex]
= [tex]x^{(\frac{3}{4}+\frac{1}{4}) }[/tex]
= [tex]x^{1}[/tex]
= x
Answer:
[tex]\large\text{$\dfrac{x^{\left(\frac{3}{4}\right)}}{x^{\left(-\frac{1}{4}\right)}}=x$}[/tex]
Step-by-step explanation:
Given expression:
[tex]\large\text{$\dfrac{x^{\left(\frac{3}{4}\right)}}{x^{\left(-\frac{1}{4}\right)}}$}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \large\text{$x^{\left(\frac{3}{4}-\left(-\frac{1}{4}\right)\right)}$}[/tex]
Simplify:
[tex]\implies \large\text{$x^{\left(\frac{3}{4}+\frac{1}{4}\right)}$}[/tex]
[tex]\implies \large\text{$x^{\left(\frac{4}{4}\right)}$}[/tex]
[tex]\implies \large\text{$x^{1}$}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies \large\text{$x$}[/tex]
On the prior screen, you sketched `ΔMJN` on the graph with vertices `M(16,-8)`, `J(16,2)`, and `N(4,0)`. What is the area of `ΔMJN`?
The triangle has an area of 60 square units.
How to determine the area of the triangle based on the location of its vertices
Herein we find the case of a triangle whose vertices are set on a Cartesian plane and whose area can be determined by means of the Heron's formula:
A = √[s · (s - MJ) · (s - JN) · (s - MN)]
s = (MJ + JN + MN) / 2
Where MJ, JN and MN are the side lengths of the triangle and s is the semiperimeter of the triangle.
First, determine the side lengths:
MJ = √[(16 - 16)² + [2 - (- 8)]²]
MJ = 10
JN = √[(4 - 16)² + (0 - 2)²]
JN = √[(- 12)² + (- 2)²]
JN = 2√37
MN = √[(4 - 16)² + [0 - (- 8)]²]
MN = √[(- 12)² + 8²]
MN = 4√13
Second, determine the semiperimeter:
s = (1 / 2) · (10 + 2√37 + 4√13)
s ≈ 18.294
Third, calculate the area of the circle:
A = √[18.294 · (18.294 - 10) · (18.294 - 2√37) · (18.294 - 4√13)]
A ≈ 60.002
The area of the triangle is approximately equal to 60 square units.
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