Given,
[tex]\begin{gathered} 3x-2y=-9\ldots\ldots\ldots(1) \\ 5x+10y=-5\ldots\ldots\text{.}(2) \end{gathered}[/tex]Multiply 1st equation by 5.
[tex]\begin{gathered} 5(3x-2y=-9) \\ 15x-10y=-45\ldots\ldots\text{.}(3) \end{gathered}[/tex]Solve equations (2) and (3)
[tex]\begin{gathered} 20x=-50 \\ x=\frac{-5}{2} \end{gathered}[/tex]Put x =-5/2 in equation (1)
[tex]\begin{gathered} 3x-2y=-9 \\ 3\times\frac{-5}{2}-2y=-9 \\ \frac{-15}{2}-2y=-9 \\ -2y=-9+\frac{15}{2} \end{gathered}[/tex]Further solved as,
[tex]\begin{gathered} -2y=\frac{-45+15}{5} \\ -2y=\frac{-30}{5} \\ -2y=-6 \\ y=3 \end{gathered}[/tex]Therefore, the value of x and y is -5/2 and 3.
[tex]7x(x + 4) = [/tex]simplify
Given expression:
[tex]=\text{ 7x(x + 4)}[/tex]Expanding:
[tex]\begin{gathered} =\text{ 7x }\times\text{ x + 7x }\times\text{ 4} \\ =\text{ 7 }\times\text{ x }\times\text{ x + 7 }\times\text{ x }\times\text{ 4} \\ =\text{ 7 }\times x^2\text{ + 7 }\times\text{ 4 }\times\text{ x} \end{gathered}[/tex]Simplifying the expression:
[tex]\begin{gathered} =7\times x^2\text{ + }28\times x \\ =7x^2\text{ + 28x} \end{gathered}[/tex]Answer:
[tex]7x^2\text{ + 28x}[/tex]If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true?
The figure must be an isosceles trapezoid because it has 2 congruent base angles.
The figure must be a rectangle because all rectangles have exactly 2 lines of symmetry.
The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
The figure could be a square because the diagonals of a square bisect the right angles.
The third option is correct. That is, the figure could be a rhombus because the 2 lines of symmetry bisect the angles.
What is rhombus?
A rhombus is a quadrilateral that is an equilateral parallelogram and has all of its opposite pairs of sides parallel. Sometimes the word "rhombus" is substituted with "rhomb," and a rhombus is also referred to as a "diamond."
Given: A quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors.
Since the two lines of symmetry in a quadrilateral are angle bisectors, the figure may be a rhombus if the quadrilateral has exactly two lines of symmetry. Figures with four sides and angles are called quadrilaterals. Rectangle is a type of quadrilateral.
Therefore, If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then the figure could be a rhombus because the 2 lines of symmetry bisect the angles.
To know more about the rhombus, click on the link
https://brainly.com/question/20627264
#SPJ13
Answer:
third option
Step-by-step explanation:
Based on the information given in the following graph of a power function, can you determinethe equation of the power function? Why or why not? If you can, find the equation of the powerfunction. If not, describe the equation of the power function as much as you can.
SOLUTIONS
To determine the equation of the power function? Why or why not? If you can, find the equation of the power
[tex]\begin{gathered} (4,2) \\ x=4,y=2 \end{gathered}[/tex]It is easy to get the graph of the exponential function since x - value = 4 and y - value = 2.
An exponential function is defined by the formula f(x) = x^a, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The general equation of an exponential function is
[tex]y=x^a[/tex][tex]\begin{gathered} y=2,x=4 \\ 2=4^a \\ 4^{\frac{1}{2}}=4^a \\ a=\frac{1}{2} \end{gathered}[/tex][tex]y=x^{\frac{1}{2}}[/tex]Work out the lenght off x
Using the Pythagorean theorem, the length of the side x is √147.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.So, the formula of the Pythagorean theorem:
H² = l² + w², where H is the hypotenuse.Now, substitute the values and calculate as follows:
14² = 7² + x²x² = 14² - 7²x² = 196 - 49x² = 147x = √147Therefore, using the Pythagorean theorem, the length of the side x is √147.
Know more about the Pythagorean theorem here:
https://brainly.com/question/343682
#SPJ1
Below, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotal46246Male2Female 33TotalIf a student is selected at random, find theprobability the student is a junior given that it'smale. Round to the nearest whole percent.[?]%
Male students. 14
Female students: 16
Total students: 30
Since there are 2 male juniors, the probability of being junior and male is: 6.67%
[tex]\frac{2}{30}\cdot100=6.67[/tex]If we round to the nearest whole porcent: 7%
The line that passes through the points (3,0) and (-5,8) isA.)DecreasingB.)IncreasingC.)HorizontalD.)Vertical
The slope of a line
It is a parameter that can help us to know the behavior of a line, specifically if it's increasing, decreasing
At 1:00 AM the temperature was 87º. A cold front came through and at 7:00 PM the temperature was 45°. What is the rate of change in the temperature in degrees per hour?
the rate of change in the temperature per hour is the quotient of the change of temperature divided by the change in hours. Since we have
1:00 AM =1 hr - 87 degrees
7:00 PM=19 hrs - 45 degrees,
then the rate is
[tex]\frac{45-87\text{ }}{19-1}=\frac{-42}{18}=-\frac{7}{3}=-2.33[/tex]Then, the temperature changed -2.33 degrees per hour.
The organizer of a conference is selecting workshops to include. She will select from 3 workshops about anthropology and 10 workshops about psychology. In how many ways can she select 7 workshops if 2 or fewer must be about anthropology?
give the following from the question:
the organizer will select from 3 workshop about anthropology and 10 workshops about psychology.
we were asked in how many ways she can select 7 workshops if 2 or fewer must be anthropology
so,
If 2 or fewer must be anthropology,
Then tha means it is either she selects 2 from anthropology and 5 from psychology or 1 from anthropology and 6 from psycology.
that is:
= 3C2 x 10C5 or 3C1 x 10C6
= 3!/(3-2)!2! x 10!/(10-5)!5! + 3!/(3-1)!1! x 10!/(10-6)!6!
= 3x2!/2! x 10x9x8x7x6x5!/5!5! + 3x2!/2! x 10x9x8x7x6!/4!6!
= 3 x 252 + 3 x 210
= 756 + 630
= 1,386 ways
The ways she can select 7 workshops if 2 or fewer must be about anthroplogy is 1,386 ways
Select all the correct answers Each of these scatter plots has a line of fit for its data points. Which graphs have a line that is a line of best for the data
There should be as much as many dots above the line and below the line . The line of best fits represent the trend of the data whether positive or negative correlation
The graphs that have a line that is best for the data are
Graph 1
Graph 4
si en un determinado lugar el metro cuadrado de terreno cuesta 250 dolares cuanto vale el lote de 400 metros cuadrados
If a square meter of land costs $250 in a certain place, then 1.6 sq. m. of land can be bought there for $400, calculated using the unitary method.
As per the question statement, the cost of per square meter of land in a certain place is $250,
And we are required to calculate the amount of land that can be bought in the above mentioned place for $400.
To solve this question, we will use the unitary method, that is,
Given, the cost of per square meter of land in a certain place is $250,
Or, in $250, one can buy 1 sq. m. of land in this place,
Or, in $1, one can buy (1/250) sq. m. of land,
And, in $400, one can buy [{(1/250) * 400} = (40/25) = (8/5) = 1.6 sq. m.] of land in that place.
Unitary Method: In Mathematics, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then multiplying this single unit value into the number of concerned units, to obtain our desired resultant.To learn more about Unitary Method, click on the link below.
https://brainly.com/question/23330556
#SPJ9
de a and perform the symmetry lest on each of the following is. eld plerd Find the in 16 r2 + 25y2 = 400 A00 (c) r2 + 4y2 = 4 (e) 4x2 + y2 = 64 (B) 9x² + 4y2 = 36 (b) 25x+6y (d) 4x + y = A () Ay? (h) 7x + y - 112 Graph the vertices, foci, endpoints of the minor axis, and endpoints of the latera recta, then draw AB is a chord of the partial ellipse with equation f(x) = ba? - x'. (a) 576x2 + 625y2 = 360,000, A (15,f(15)), B(20, f(20)) (b) 49x 2 + 625y2 = 30,625, A (15, f(15)), B(20,f(20)) – x. Find the length of AB using
The given ellipse is
[tex]576x^2+625y^2=360,000[/tex]Where A(15, f(15)), B(20, f(20)).
First, we find f(15) and f(20) by evaluating the given expression
[tex]\begin{gathered} f(15)=576(15)^2+625y^2=360,000 \\ 576\cdot225+625y^2=360,000 \\ 129,600+625y^2=360,000 \\ 625y^2=360,000-129,600 \\ 625y^2=230,400 \\ y^2=\frac{230,400}{625} \\ y^2=368.64 \\ y=\sqrt[]{368.64} \\ y=19.2 \end{gathered}[/tex]We use the same process to find f(20).
[tex]\begin{gathered} f(20)=576(20)^2+625y^2=360,000 \\ 576\cdot400+625y^2=360,000 \\ 625y^2=360,000-230,400 \\ x^2=\frac{129,600}{576} \\ x=\sqrt[]{225}=15 \\ \end{gathered}[/tex]So, the points are A(15, 19.2) and B(20, 15). To find the distance between these points, we have to use the distance formula
[tex]\begin{gathered} d_{AB}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d_{AB}=\sqrt[]{(20-15)^2+(15-19.2)^2} \\ d_{AB}=\sqrt[]{5^2+(-4.2)^2}=\sqrt[]{25+17.64}=\sqrt[]{42.64} \\ d_{AB}\approx6.5 \end{gathered}[/tex]Hence, the length of AB is around 6.5 units.Find an equation of an ellipse satisfying the given conditions Vertices: (0 - 6) and (0.6) Length of minor axis: 8
As the given vertices are at a distance of 12 units:
As the major axis is vertical you have the next generall equation:
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]To find the center (h,k) of the ellipse use the coordinates of that vertices as follow:
[tex](\frac{0+0}{2},\frac{6-6}{2})=(0,0)[/tex]Now use the distance between those vertices to find a:
[tex]a=\frac{12}{2}=6[/tex]b is the distance of minor axis divided into 2:
[tex]b=\frac{4}{2}=2[/tex]Then, you get the next equation for the given ellipse:
[tex]\begin{gathered} \frac{(x-0)^2}{2^2}+\frac{(y-0)^2}{6^2}=1 \\ \\ \frac{x^2}{4}+\frac{y^2}{36}=1 \end{gathered}[/tex]Which identity/formula was used to simplify from step 2 to step 3?
Solution:
The reciprocal identities of trigonometry include the identities below
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \sec \theta=\frac{1}{\cos \theta} \\ \cot \theta=\frac{1}{\tan \theta} \\ \tan \theta=\frac{1}{\cot \theta} \\ \cos \theta=\frac{1}{\sec \theta} \\ \sin \theta=\frac{1}{\csc \theta} \end{gathered}[/tex]The quotient identity include the identities below
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \cot \theta=\frac{\cos \theta}{\sin \theta} \end{gathered}[/tex]The sum formula of trigonometric identity include
[tex]\begin{gathered} \sin (\alpha+\beta)=\sin \alpha\cos \beta+\cos \alpha\sin \beta \\ \sin (\alpha-\beta)=\sin \alpha\cos \beta-\cos \alpha\sin \beta \\ \cos (\alpha+\beta)=\cos \alpha\cos \beta-\sin \alpha\sin \beta \\ \cos (\alpha-\beta)=\cos \alpha\cos \beta+\sin \alpha\sin \beta \end{gathered}[/tex]The double-angle formula is given below as
Hence,
The final answer is QUOTIENT IDENTITY
I NEED HELP WITH THIS TWO7) the shirt costs $25. the discount is 18% how many dollars is the discount? 8) 40% of 120 students passed the test. How many students passed?
If the shirt costs 25 and the discount is 18%, then the amount discounted is shown as follows;
[tex]\begin{gathered} \text{Cost}=25 \\ \text{Discount}=0.18 \\ \text{Discounted amount=25}\times0.18 \\ \text{Discounted amount=4.5} \end{gathered}[/tex]The discount is $4.5.
If 40% of students passed out of 120, then the number that passed is shown below;
[tex]\begin{gathered} Total\text{ number=120} \\ \text{Percentage that passed=0.40} \\ \text{Number that passed=120}\times0.40 \\ \text{Number that passed=48} \end{gathered}[/tex]The number of students that passed is 48
Answer: 7. $20.50 & 8. 48 students
Step-by-step explanation:
1. An equation is shown below. 60 10 100 = Determine the value of the missing numerator. Your answer
m = 6
Explanations:The given equation is:
[tex]\frac{m}{10}=\text{ }\frac{60}{100}[/tex]Cross multiply:
100m = 60 x 10
100m = 600
Divide both sides by 100
[tex]\begin{gathered} \frac{100m}{100}=\text{ }\frac{600}{100} \\ m\text{ = 6} \end{gathered}[/tex]The missing numerator is 6
What is the slope of a line that is perpendicular to the line y = - 1x +5?
○-2
-1/2
1/2
○ 2
The slope of the line that is perpendicular to the line y = - 1x +5 is -1.
What is the slope?The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
Given:
The equation of the line, y = -x + 5
The slope of the line can be calculated by the intercept form,
so m = -1, Here, m is the slope.
The slope of the perpendicular line will be the opposite
So, M = -1
Therefore, the slope of the line that is perpendicular to the line y = - 1x +5 is -1.
To know more about Slope:
https://brainly.com/question/16180119
#SPJ1
A bike wheel as a radius of 13 inches. a. About how far does the bike wheel tra in 1 rotation? 5 rotations? 30 rotations? b. Write an equation relating the distance the bike travels in inches, b, to the number of wheel rotations, x. c. About how many rotations does the bike wheel make when the bike travels 1 mile?
The radius of the bike wheel is given as 13 inches. One rotation would be equal to the entire circumference of the bike wheel. Hence;
[tex]undefined[/tex]E-0-16Name a pair of similar triangles.Explain why each pair of triangles is similar.Use the given information to find each missing measure.
The horizontal arrows denote that segments RS and VT are parallel. This means that angleR and angleV are congruent. Similarly, angleS and angleT are congruent. They are denoted in blue and red color, respectively:
Therefore,
[tex]\Delta\text{TUV}\approx\Delta SUR[/tex]by the AA-theorem (angle-angle theorem). That is because:
[tex]\begin{gathered} \angle R=\angle V \\ \angle S=\angle T \\ \angle U=\angle U \end{gathered}[/tex]Now, lets find the missing measure x. Since the above triangles are similar, we have
[tex]\frac{x}{3}=\frac{x+1}{3+9}[/tex]which gives
[tex]\frac{x}{3}=\frac{x+1}{12}[/tex]By multiplying both side by 3, we get
[tex]x=\frac{x+1}{4}[/tex]and by multiplying both side by 4, we have
[tex]4x=x+1[/tex]then, x is given as
[tex]\begin{gathered} 4x-x=1 \\ 3x=1 \end{gathered}[/tex]therefore, we obtain
[tex]x=\frac{1}{3}[/tex]then, the missing side x measures 1/3.
Now, lets find y. In this case, we have
[tex]\frac{y}{3}=\frac{2}{9+3}[/tex]then, it yields
[tex]\frac{y}{3}=\frac{2}{12}[/tex]by multipluying both sides by 3, we have
[tex]\begin{gathered} y=3\cdot\frac{2}{12} \\ y=\frac{2}{4} \\ y=\frac{1}{2} \end{gathered}[/tex]Therefore, the missing side y measures 1/2.
Recall: Averaging Two NumbersMaddie earned an 88% on her first test and an 80% onyour second test. What is her average test score? (Note:Click on the little calculator icon above to pull up acalculator.)
We know that
• She earned an 88% on her first test.
,• She earned an 80% on her second test.
To know her average score, we just have to sum these percentages and divide them by 2, since they are just 2.
[tex]\bar{x}=\frac{88+80}{2}=\frac{168}{2}=84[/tex]Therefore, the average test score is 84%.Bobs car rental is offering a special of 40$ a day for a seden as long as you purchase the car damage protection insurance for 20$
In this case, we have a proportional relationship, since the cost varies directly with the days, this means that as x increases, y increases, and as x decreases, y decreases. A proportional relationship has the form:
y=kx
Where k is the constant of proportionality.
The ratio between them (x and y) is always the same, in this case, the ratio or constant of proportionality is 40, since each day the rent cost increases $40, then:
Constant of proportionality = 40 , replacing 40 for k into the above equation, we get:
equation: y = 40x
We can use this equation to find some pair of values (x,y) to fill the table, like this:
For x equals 2:
y= 40*2 = 80
For x equals 3:
y= 40*3 = 120
For x equals 4:
y=40*4 = 160
For x equals 5:
y=40*5=200
Then, we can fill the table as follows:
We can also use these data to graph the relationship, by taking the point (5,200) and joining it to the origin, we get:
Using only the values given in the table for thefunction, f(x), what is the interval of x-values over whichthe function is increasing?Х-6-5-4-3-2.-101f(x)343-10-11-6-1-2-15O (-6,-3)O (-3,-1)O (-3,0)O (-6, -5)
Given the table:
Х f(x)
-6 34
-5 3
-4 -10
-3 -11
-2. -6
-1 -1
0 -2
1 -15
Let's find the increasing intervals.
A function is increasing over the interval when the values of f(x) increases as the values of x increases.
At the interval:
From x = -3 to x = -1, the values of f(x) increases from -11 to -1.
Therefore, the interval of x-values over which the function is increasing is:
(-3, -1)
ANSWER:
(-3, -1)
The coordinates below represents points that were translated.Match the coordinates with the correct algebraic representations
R(1, 8) >> R'(10, -10) ........(x+9, y-18)
V(-2, -10) >> V'(5, -3).......(x+7, x+7)
U(3, -9) >> U'(10, -16).......(x+7, y-7)
T(-4, 7) >> T'(-11, 14)..........(x -7, y+7)
Explanations:When a pont A(x, y) is translated by a in the x-axis, and b in the y-axis, the new point becomes A'(x+a, y+b)
For the expression R(1, 8) >> R'(10, -10)
The coordinates of R' ae formed using the expression (x+9, y-18)
For the expression V(-2, -10) >> V'(5, -3)
The coordinates of V' are formed by using the expression (x+7, x+7)
For the expression U(3, -9) >> U'(10, -16)
The coordinates U' are formed by using the expression (x+7, y-7)
For the expression T(-4, 7) >> T'(-11, 14)
The coordinates T' are formed by using the expression (x -7, y+7)
Grpah the image of square ABCD after a translation 10 units up.
We have to take the points A, B, C, and D from the original square and move all of them 10 units up as shown in the following diagram:
After translating the points we get the image points A', B', C' and D'.
Finally, connecting the image points we get the image of the square:
solve the equation T = 2x + 3y - z for y.
In order to solve this equation for y, we just need to isolate the variable y in the equation.
So, we have that:
[tex]\begin{gathered} T=2x+3y-z_{} \\ 3y=T-2x+z \\ y=\frac{T-2x+z}{3} \end{gathered}[/tex]So we have that y = (T - 2x + z) / 3
Locker codes at Lincoln High School consist of 4 digits. No digit can be used more than once. How many locker codes are available at Lincoln High School? A 210 B 3,024 C 5,040 D 10,000
To obtain the number of locker codes available, the following steps are necessary:
Step 1: Create a diagram to represent the slot for each of the digits, as below;
Step 2: State the number ways that each digit can be used to fill any of the spots, as below:
Given that there are the numbers 0,1,2,3,4,5,6,7,8,9 - a total of 10 numbers,
- The first slot can be filled with any of the digits above, and thus can be filled in 10 ways
- The second slot can be filled with any of the remaining 9 numbers after one of them has already been used to fill the first slot. Thus, there are 9 ways the second slot can be filled.
- The same line of reasoning tells us that the third slot will be filled in 8 ways
- Lastly, the fourth slot will be filled in 7 ways
The diagram below gives a better illustration:
Step 3: Multiply the numbers of ways to find the total number of locker codes that are available, as follows:
[tex]10\times9\times8\times7\text{ = 5040}[/tex]Therefore, there are a total of 5040 available locker codes at Lincoln High School
Correct answer = Option C
how do you find the length of a side of a triangle when given the length of only one other side?
WE can find the sides if the triangle by apply the Sine rule :
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]where, a,b & c are the sides of triangle
For eg :
Consider an triangle with one side AB = 5
and angles A = 60, angle B = 45 and angle C= 75
So, substitute the value in the expression of Sine
[tex]\begin{gathered} \frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C} \\ \frac{BC}{\sin 60}=\frac{AC}{\sin 45}=\frac{5}{\sin 75} \\ \text{ Substitute the values :} \\ \frac{BC}{\sin60}=\frac{AC}{\sin45}=\frac{5}{\sin75} \\ \frac{BC}{0.866}=\frac{AC}{0.707}=\frac{5}{0.965} \\ \text{ Simplify : }\frac{AC}{0.707}=\frac{5}{0.965} \\ \frac{AC}{0.707}=\frac{5}{0.965} \\ AC=\frac{5}{0.965}\times0.707 \\ AC=3.66 \\ \text{Now, Simplify: }\frac{BC}{0.866}=\frac{5}{0.965} \\ BC=\frac{5}{0.965}\times0.866 \\ BC=4.4 \end{gathered}[/tex]The sides : AB = 5, AC = 3.66 & BC = 4.4
What is the accumulated value if the money is compounded semiannually?
Given:
[tex]\begin{gathered} P=20,000 \\ t=6years \\ r=5.5\% \end{gathered}[/tex]Required:
To find the accumulated value.
Explanation:
Consider
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here
[tex]\begin{gathered} =20000(1+\frac{0.055}{2})^{2\times6} \\ \\ =20000(1+0.0275)^{12} \\ \\ =27,695.68 \end{gathered}[/tex]Final Answer:
The accumulated value is $27,695.7
how do you solve y=x-2 and graph it
The equation
y = x - 2
is the equation of a line in the slope-intercept form with a slope of 1 and a y-intercept at (0, -2).
You can graph it by locating two points on the line. One point is (0, -2). The other one can be found with the slope. The slope of 1 means that the next point is 1 unit to the left and 1 unit up, respect the previous point. In this case, the next point is (1, -1). After you locate these two points, draw the line that connects them, as follows
PLSSSSSS HELPPPP ASAPP i only need everything in measuring segments , congruent segments and segment addition
the answer are:
1. A(X +Y),,B (X+Y) OR d(A,B)
2. If two segments having the same length are congruent segments.This is written as for example: AB is congruent with CD.
AB=CD
3. AC=B, because B is inside points A and C it means that it was the additional point to add and arrive at C.
[tex]1144 \times \frac{25}{3699} + 114 \sqrt[1441]{36} - y + x \div 15663 = 2 - \sqrt[44410]{3651} + {2554}^{2} [/tex]first equation. then text
how does equation look in session history???