We have to solve the expression:
[tex]\frac{9}{14}+\frac{2}{6}[/tex]We have to find a common denominator for the fractions and then solve it.
We can start by simplifying the fractions that can be simplified, like 2/6.
[tex]\frac{9}{14}+\frac{2}{6}=\frac{9}{14}+\frac{1}{3}[/tex]Then, the common denominator between 14 and 3 is 14*3=42, so we end with:
[tex]\frac{9\cdot3}{14\cdot3}+\frac{1\cdot14}{3\cdot14}=\frac{27}{42}+\frac{14}{42}=\frac{27+14}{42}=\frac{41}{42}[/tex]Answer: 41/42
Graph the following inequalitiesy ≥ -x/4 + 5
Solution
The graph of the inequality is shown below
1) To win the small county lottery, one must correctly select 3 numbers from 30 numbers. The order in which the selection is made does not matter. How many different selections are possible?
This problem involves combination with taken n Items taken r at a time
The formula for this combination is :
[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]Where n is the total number of items
and r is the objects taken at a time
The factorial, n! denotes n x (n-1) x (n-2) x (n-3) x ... x (1)
For example :
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
Now from the given problem :
we have n = 30 numbers
r = selection of 3
Then the formula will be :
[tex]30C_3=\frac{30!}{(30-3)!\times3!}[/tex]Simplifying :
27 up to 1 will be cancelled from numerator and the denominator..
Evaluating the expression will be :
24360/6 = 4060
The answer is 4060
15. Graph the rational function ya*-*Both branches of the rational function pass through which quadrant?Quadrant 2Quadrant 3Quadrant 1Quadrant 4
SOLUTION:
CONCLUSION:
Both branches of the rational function pass through Quadrant 1.
A window had a length of 2ft & width of 3ft. What is the area of the window?
The formula used to calculate the area of the window will be
[tex]\begin{gathered} \text{Area}=l\times w \\ \text{where,} \\ l=2ft \\ w=3ft \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=l\times w \\ \text{Area}=2ft\times3ft \\ \text{Area}=6ft^2 \end{gathered}[/tex]Hence,
The final answer = 6ft²
How many people were using program 2 but not program 3?
Let Program 1, Program 2, and Program 3 be represented by P1, P2, and P3.
Given:
n(P1 n P2) = 6
n(P2 n P3) =8
n(P1 n P3) = 5
n(P1 n P2 n P3) = 2
n(P1 U P2' U P3') =18
n(P2) = 22
n(P3 U P1 U P2') = 16
n(P1 U P2 U P3)' = 17
Representing the information on a Venn diagram:
The number of people that were using Program 2 but not Program 3:
[tex]\begin{gathered} n(P_2UP_3^{\prime})=n(P_2)-n(P_2nP_3)\text{ } \\ =\text{ 22 - 8} \\ =\text{ 16} \end{gathered}[/tex]Number of people surveyed
The number of people surveyed is the sum of the individual subsets:
[tex]\begin{gathered} =\text{ 18 + 10 + 13 + 4 + 6 + 3 + }2\text{ + 17} \\ =\text{ 73} \end{gathered}[/tex]A circle has a circumference of 25 feet, what is the diameter? Your answer
Given :
The circumference of the circle = 25 feet
π = 3.14
The circumference of the circle =
[tex]2\pi\cdot r=\pi\cdot d[/tex]Where r is the radius and d is the diameter
so,
[tex]\begin{gathered} \pi\cdot d=25 \\ \\ d=\frac{25}{\pi}=\frac{25}{3.14}\approx7.96 \end{gathered}[/tex]if we rounded to the nearest feet, the diameter = 8 feet
Solve the following equation for x. (x - 5) -6 2 OX= -2 O x=2 x=-17 X=-7
You have teh following equation:
(x - 5)/2 = - 6
In order to find the solution to the previous equation, proceed as follow:
(x - 5)/2 = -6 multiply by 2 both sides
x - 5 = -6(2)
x - 5 = -12 add 5 both sides
x = -12 + 5 simlify
x = -7
Hence, the solution to the gicen equation is x = -7
PLEASE HELP 15 POINTS!! I'M GIVING BRAINLIEST
The value of sinα in the right angle triangle is [tex]\frac{16\sqrt{281} }{78961}[/tex]
What is a right-angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle. The right triangle plays an important role in trigonometry.
sin α = opposite/hypotenuse
opposite = 16, hypotenuse [tex]\sqrt{281}[/tex]
sin α = [tex]\frac{16}{\sqrt{281} }[/tex]
By rationalizing, the denominator which means multiply the fraction by [tex]\frac{\sqrt{281} }{\sqrt{281} }[/tex]
[tex]\frac{16}{\sqrt{281} }[/tex] x [tex]\frac{\sqrt{281} }{\sqrt{281} }[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
sin [tex]\alpha[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
In conclusion, the value of sin[tex]\alpha[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
Learn more about trigonometric ratios: https://brainly.com/question/1165363
#SPJ1
Brightness up inequality which can be used to determine o, The number of outfit Joseph can’t purchase well staying within his budget.
let o be the number of outfits, then
o*53.96 shoud be less than or equal to 620 - all what he bought, so:
Total money: $620
Spent money: $620 - $440.12 - $19.26 - 25.72 = $134.9
The inequality will be:
53.96o ≤ 134.9
o ≤ 2.5
If cos(0) = 24/25, and 0 is in Quadrant I, then what is cos(0/2)? Simplify your answer completely, rationalize the denominator, and enter it in fractional form.
The given information is:
[tex]\begin{gathered} \cos (\theta)=\frac{24}{25} \\ \theta\text{ is in quadrant I} \end{gathered}[/tex]cos (theta/2) is given by:
[tex]\cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]In Quadrant I, cos (theta) is positive, then the answer is positive. By replacing the known values:
[tex]\begin{gathered} \cos (\frac{\theta}{2})=\sqrt[]{\frac{1+\frac{24}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{25+24}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{49}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{49}{25\times2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{49}{50}} \\ \cos (\frac{\theta}{2})=\frac{\sqrt[]{49}}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7}{\sqrt[]{50}}\cdot\frac{\sqrt[]{50}}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{50}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{25\times2}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\cdot\sqrt[]{25}\cdot\sqrt[]{2}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\cdot5\cdot\sqrt[]{2}}{50} \\ \text{Simplify 5/50} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{2}}{10} \end{gathered}[/tex]What are all the ordered pairs that are solutions to the inequality 2x-3y>=12
To answer this question, we need to solve this inequality for y as follows:
[tex]2x-3y\ge12[/tex]Then, we have:
[tex]-3y\ge12-2x\Rightarrow\frac{-3y}{-3}\leq\frac{12}{-3}-\frac{2x}{-3}\Rightarrow y\leq-4+\frac{2x}{3}[/tex]As we can see the direction of the inequality changed because we multiplied it by a negative number.
Then, if we can see the inequality, we find that the values that make this inequality true
are infinite values (the values of y are in function of the values of x).
Then, since we have the values given in the options, we need to check which of these values make the inequality true or we can graph a line for this inequality.
We have that the line is given by:
y = 2x/3 - 4
The x-intercept for this line is:
[tex]undefined[/tex]2 radical 6 minus -2 radical 24 adding and subtracting radicals
Substraction:
1. Find prime factors of 24
[tex]\sqrt[]{24}=\sqrt[]{2^2\cdot6}[/tex]2. As 2 squared has a exact square root extract it from the radical:
[tex]\sqrt[]{24}=2\sqrt[]{6}[/tex]Then, you have the next expression:
[tex]\begin{gathered} 2\sqrt[]{6}-2\sqrt[]{24}=2\sqrt[]{6}-2(2\sqrt[]{6}) \\ \\ =2\sqrt[]{6}-4\sqrt[]{6} \end{gathered}[/tex]Substract similar terms (taking square root of 6 as a common factor):
[tex]\begin{gathered} =(2-4)\cdot\sqrt[]{6} \\ \\ =-2\sqrt[]{6} \end{gathered}[/tex]SOLVE PLEASE -2x^2+18x+____
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
- 2x² + 18x + _________
Step 02:
(a + b) = a² + 2ab + b²
a² = -2x²
[tex]a\text{ = }\sqrt[]{-2\cdot x^{2}}\text{ = x }\sqrt[]{-2}[/tex][tex]a\text{ = }\sqrt[]{2}i[/tex]2ab = 18x
[tex]2(x\sqrt[\text{ }]{-2)}\cdot\text{ b = 18 x}[/tex][tex]b\text{ = }\frac{18x}{2x\sqrt[]{-2}}=\frac{9}{\sqrt[]{-2}}=\frac{9}{\sqrt[]{2\text{ }}i}[/tex]Two ways to express the solution:
[tex]\begin{gathered} -2x^{2\text{ }}+\text{ 18x + 9/}\sqrt[]{-2} \\ -2x^2+18x\text{ + 9 / }\sqrt[]{2}i \end{gathered}[/tex]A girl cycled a total of 15 kilometers by making 5 trips to work. How many trips will she have to make to cover a total of 24 kilometers? Solve using unit rates.
We need to find how many trips she will have to make to cover a total of 24 kilometers.
We know that she covered 15 kilometers by making 5 trips. Thus, the number of kilometers made on each trip is:
[tex]\frac{15\text{ kilometers}}{5\text{ trips}}=\frac{15\div5\text{ kilometers}}{5\div5\text{ trip}}=\frac{3\text{ kilometers}}{1\text{ trip}}[/tex]Then, she made 3 kilometers on 1 trip (unit rate).
Now, to cover 24 kilometers, she needs to make 8 trips, because:
[tex]\begin{gathered} 3\text{ kilometers }\times8=24\text{ kilometers} \\ \\ 1\text{ trip }\times8=8\text{ trips} \end{gathered}[/tex]Thus:
[tex]\frac{3\text{ kilometers}}{1\text{ trip}}=\frac{3\text{ kilometers}}{1\text{ trip}}\times\frac{8}{8}=\frac{3\times8\text{ kilometers}}{1\times8\text{ trips}}=\frac{24\text{ kilometers}}{8\text{ trips}}[/tex]Answer: She will have to make 8 trips.
This is so hard I don’t understand this pls help
From the given question
There are given that the matrix.
Now,
To find the inverse of any matrix, first find their determinant.
Then,
According to the properties of the matrix:
If the determinant of any matrix is zero, then their inverse has undefined.
So,
From the determinant of the given matrix:
[tex]\begin{gathered} \begin{bmatrix}{4} & {8} & {} \\ {7} & {14} & \\ {} & {} & {}\end{bmatrix}=(14\times4)-(8\times7) \\ =56-56 \\ =0 \end{gathered}[/tex]The determinant of the given matrix is zero
So, their inverse has not been defined.
Hence, the correct option is A.
Lines m and n are parallel. Which are corresponding angles?Angles 1 and 3Angles 1 and 5Angles 1 and 4Angles 1 and 2
EXPLANATION
By the corresponding angles theorem, we can affirm that the following angles are corresponding ones:
angles 1 and 5 are corresponding because they occupy the same relative position.
solve the system by substitution type your stepsx=2y-53x-y=5
Answer:
The solution to the system of equations is
x = 3
y = 4
Explanation:
Given the pair of equations:
[tex]\begin{gathered} x=2y-5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ 3x-y=5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]To solve these simultaneously, use the expression for x in equation (1) in equation (2)
[tex]\begin{gathered} 3(2y-5)-y=5 \\ 6y-15-y=5 \\ 6y-y-15=5 \\ 5y-15=5 \\ \\ \text{Add 15 to both sides} \\ 5y-15+15=5+15 \\ 5y=20 \\ \\ \text{Divide both sides by 5} \\ \frac{5y}{5}=\frac{20}{5} \\ \\ y=4 \end{gathered}[/tex]Using y = 4 in equation (1)
[tex]\begin{gathered} x=2(4)-5 \\ =8-5 \\ =3 \end{gathered}[/tex]Therefore, x = 3, and y = 4
(a) Find an angle between 0 and 2pi that is coterminal with 10pi/3.(b) Find an angle between 0° and 360° that is coterminal with -300°.Give exact values for your answers.(a) __ radians(b) __ °
To find a coterminal angle between 0 and 2pi, you can subtract 2pi from the given angle, like this
[tex]\frac{10\pi}{3}-2\pi\text{ }[/tex]To do the subtraction, you can convert 2pi into a fraction, like this
[tex]\frac{2\pi\cdot3}{3}=\frac{6\pi}{3}[/tex]So, you have
[tex]\frac{10\pi}{3}-2\pi=\frac{10\pi}{3}-\frac{6\pi}{3}=\frac{4\pi}{3}[/tex]Therefore, 4pi/3 is the angle between 0 and 2pi that y is coterminal with 10pi/3.
For point (b), you can add 360° at the angle given, like this
[tex]360+(-300)=360-300=60[/tex]Therefore, an angle between 0° and 360° that is coterminal with -300° is 60°.
is it option one or two I don't need to work
From the options, the function has the next form
[tex]y=a\cdot b^x[/tex]where a and b are two constants.
The function pass through the point (0, 2), then:
[tex]\begin{gathered} 2=a\cdot b^0 \\ 2=a\cdot1 \\ 2=a \end{gathered}[/tex]The function pass through the point (1, 10), then:
[tex]\begin{gathered} 10=2\cdot b^1 \\ \frac{10}{2}=b \\ 5=b \end{gathered}[/tex]Therefore, the function is:
[tex]y=2\cdot5^x^{}[/tex]Given the following data, find the diameter that represents the 69th percentile.AnswerHow to enter your answer (opens in new window)Diameters of Golf Balls1.531.36 1.69 1.68 1.701.601.601.361.34 1.531.32 1.401.39 1.391.44
Given that there is a Table given of diameters
How does g(t) = 1/2t change over the interval t = 0 to t = 1?
we have the equation
[tex]g(t)=\frac{1}{3^t}[/tex]Find out the rate of change over the interval [0,1]
Remember that
the formula to calculate the rate of change is equal to
[tex]\frac{g(b)-g(a)}{b-a}[/tex]In this problem
a=0
b=1
g(a)=g(0)=1
g(b)=g(1)=1/3
therefore
the function decreases by a factor of 3Which describes the effect of the transformations on the graph of f(x) = x? when changed to f(x) = - = (x - 2) = 3?A)B)reflected over x-axis, stretched vertically, shifted left 2 units, and shifteddown 3 unitsreflected over x-axis, compressed vertically, shifted right 2 units, and shiftedup 3 unitsreflected over y-axis, stretched vertically, shifted left 2 units, and shifteddown 3 unitsreflected over y-axis, compressed vertically, shifted right 2 units, and shiftedup 3 units09D)
Let me start by telling you that there is a typo in the actual question (given the answers they provide for selection)
I am going to tell you the transformations that have been applied to change the function:
[tex]f(x)=x^2[/tex]into the function:
[tex]f(x)=\frac{1}{8}(x-2)^2+3[/tex]Then, these transformations consist on:
a reflection around the x axis (due to the negative sign in front),
a horizontal shift in TWO units to the right (given by the subtraction of 2 inside the parenthesis,
then a vertical compression in 1/8 (due to the factor 1/8 outside the parenthesis
and then a vertical shift of 3 units UP due to the +3 added at the end
Then, please select answer B in the list provided
What is the difference between area and perimeter of a two-dimension figure? What is the difference in the area formulas for a parallelogram and triangle
The perimeter is a measure of the distance around the shape. This means that to find the perimeter we usually are going to add the lenghts of the sides of the figure (the circle is an exception to that rule since this is a curve figure).
The are is a measure of the space inside the figure. This means that to find the area we usually are going to multiply the lenghts of the sides of the figure to get the area.
Now the area of a triangle is given as:
[tex]A=\frac{1}{2}bh[/tex]whereas the area of a paralelogram is given by:
[tex]A=bh[/tex]From this we notice that the area of the triangle is half the area of a parallelogram.
What is the approximate diameter of the largest Circle she can make
We have that the circumference of a circle can be represented with the following equation:
[tex]C=\pi d[/tex]where d represents the diameter of the circle.
In this case, we have a circle of circumference C = 30 ft made with the lights, then, using the equation and solving for d, assuming that pi equals 3.14, we get:
[tex]\begin{gathered} 30=(3.14)d \\ \Rightarrow d=\frac{30}{3.14}=9.55\approx10ft \end{gathered}[/tex]therefore, the approximate diameter of the largest circle is 10 ft
a square pyramid has a base height edge length of 3m and a slant height of 6m. find the lateral area and surface area of the pyramid
hello
given that the pyramid has the shape of a triangle, we can easily find the height of the pyramid using pythagoran's theorem
from triangle b, let's use the formula and solve for y
[tex]\begin{gathered} x^2=h^2+z^2 \\ 6^2=h^2+1.5^2 \\ 36=h^2+2.25 \\ \text{collect like terms} \\ h^2=36-2.25 \\ h^2=33.75 \\ \text{solve for h} \\ h=\sqrt[]{33.75} \\ h=5.809\approx5.81m \end{gathered}[/tex]having known the value of the heigh of the pyramid, we can now proceed to solve for the lateral area and surface area
for the lateral area, the formula is given as
[tex]\begin{gathered} A_l=l\sqrt[]{l^2+4h} \\ l=\text{edge length} \\ h=\text{height of pyramid} \end{gathered}[/tex][tex]\begin{gathered} A_l=l\sqrt[]{l^2+4h} \\ l=3m \\ h=5.81m \\ A_l=3\sqrt[]{3^2+4\times5.81_{}} \\ A_l=17.03m^2 \end{gathered}[/tex]the lateral area of the figure is 17.03 squared meter.
let's solve for the surface area
the formula for the surface area of a square pyramid is given as
[tex]\begin{gathered} A=l^2+2l\sqrt[]{\frac{l^2}{4}+4h^2} \\ l=3m \\ h=5.81 \\ A=3^2+2\times3\sqrt[]{\frac{3^2}{4}+4\times5.81^2} \\ A=9+6\sqrt[]{\frac{9}{4}+135.0244} \\ A=79.298\approx79.3m \end{gathered}[/tex]a bag contains 30 marbles. 8 are pink, 11 are blue, 4 are yellow and 7 are purple. Calculate the probability of randomly selecting a marble that is not blue .
In order to find the probability of a marble not being blue, we need to find how many marbles are not blue.
To do so, we just need to sum the number of pink, yellow and purple marbles:
[tex]8+4+7=19[/tex]Now, to find the probability, we just need to divide the number of non-blue marbles by the total number of marbles.
[tex]\frac{19}{30}=0.6333=63.33\text{\%}[/tex]You need 3 sticks of butter for every 24 cookies you bake. How many cookies can I make with 5 sticks?
ANSWER
[tex]40\text{ cookies}[/tex]EXPLANATION
We want to find the number of cookies that can be made with 5 sticks.
To solve this, we have to apply proportions. Let the number of cookies that can be made be x.
We have that:
[tex]\begin{gathered} 3s=24c \\ 5s=x \end{gathered}[/tex]Now, cross-multiply:
[tex]\begin{gathered} 3\cdot x=24\cdot5 \\ \Rightarrow x=\frac{24\cdot5}{3} \\ x=40\text{ cookies} \end{gathered}[/tex]That is the number of cookies that can be made.
Last weekend, 5% of the tickets sold at Seaworldwere discount tickets. If Seaworld sold 60 tickets inall, howmany discount tickets did it sell? Use thepercent proportion.
Let:
N = Total tickets
d = discount tickets
r = percent of discount tickets sold
so:
[tex]\begin{gathered} d=N\cdot r \\ where\colon \\ N=60 \\ r=0.05 \\ so\colon \\ d=60\cdot0.05 \\ d=3 \end{gathered}[/tex]3 discount tickets were sold
Which of the following describes the transformation of the graph y = x 2 in graphing y = -x 2 - 5?reflect over the x-axis and shift down 5reflect over the y-axis and shift down 5reflect over the x-axis and shift left 5
The parent function of the graph is,
[tex]y=x^2[/tex]The transformed image of the graph is,
[tex]y_1=-x^2-5[/tex]Let us sketch out the graph of both the parent function and the transformed function.
From the image above, the parent function, y=x² was first reflected over the y-axis. Therefore, the transformation resulted into y= -x² .
After that, it was now shifted down by 5 units, which now resulted into
[tex]y=-x^2-5[/tex]Hence, the correct answer is B(Second option), which is the parent function was reflected over the y-axis and shifted downward by 5 units.
NEED ANSWER ASAP Solve this system of equations:3x - 2y = - 8y= 3/2x - 2I NEED ALL THE STEPS
Let's solve it by replacing in the first equation.
3x-2y=-8
y=3/2x-2
So,
3x-2(3/2x -2)=-8
3x-3x+4=-8