So, we have the two following equation systems:
I. a.) 3x - 4y = 10
I. b.) 6x + y = 38
and
II. a.) -9x + 12y = -30
II. b.) 9x - 3y = 48
We know that these two systems are equivalent, which means that each equation from the second system can be formed as a linear combination of the other two equations from the first system.
From the equation II. a. we have that (with z and w being integer numbers)
z*3x + w*6x = -9x or 3z + 6w = -9
z*(-4y) + w*y = 12y or -4z + w = 12
z*10 + w* 38 = -30 or 10z + 38w = -30
Solving that system for z and w, we discover that z = -3 and w = 0, wich means that equation II. a. is formed by all terms from equation I. a. multiplied by -3.
Doing the same for equation II. b., we have:
z*3x + w*6x = 9x or 3z + 6w = 9
z*(-4y) + w*y = -3y or -4z + w = -3
z*10 + w* 38 = 48 or 10z + 38w = 48
Solving that system for z and w, we discover that z = 1 and w = 1, wich means that equation II. b. is formed by the sum of all terms from the equations I. a. and I. b.
Need to know the answers or how to do them.#1 please
Looking at angle G, it inscribes the arc FH, which is a diameter of the circle.
Since an inscribed angle measures half the inscribed arc (and arc FH measures 180°), angle G measures 90°.
Now, let's calculate angle F:
[tex]\begin{gathered} F+G+H=180\\ \\ F+90+48=180\\ \\ F+138=180\\ \\ F=180-138\\ \\ F=42° \end{gathered}[/tex]Arc GH is inscribed by the angle F, so we have:
[tex]\begin{gathered} F=\frac{1}{2}GH\\ \\ 42=\frac{1}{2}GH\\ \\ GH=2\cdot42\\ \\ GH=84° \end{gathered}[/tex]So the indicated arc measures 84°.
A suit was marked with a 10% discount.
If the discount is $10.00, what was the original price of the suit?
Answer:
The suit originally cost $100.
Step-by-step explanation:
To find the original price of the suit, you can set up a ratio and solve for the missing variable. In this case, we can set up a ratio as such:
10%/100% = $10.00/x, where x is the original price, and $10.00 is 10% of the original. In fraction form, this looks like [tex]\frac{10}{100} =\frac{10}{x}[/tex]. Here, it is clear that for these two to be equal, x must be equal to 100.
The opposite of -10 is?A. -(-(-10))B. -10C. -|10| Which symbol is used to make -5? -8 a true statement?A. >B.B.
The opposite of -10 is 10.
The symbol to make a true statment is -5>-8.
The symbol to make a true statement is -6<|-8|
The only set of integers that are sort from least to greatest is:
C. -8,5,6,|-7|,8
as |-7|=7.
-10 -8 -6 -4 -2 0 2 4 6 8 10 Use the number line to help you answer the question. 8 10 Which statements are true? Check all that apply. -4<-8|-4|<|-8||-5|>1-5>1|-2|=|2|
a) |-4| < |-8| This is true
b) |-5| > 1 This is true
c) -5 > 1 This is false
d) |-2| = |2| This is true
I have to solve to p but I need help with this I don't understandkn + mp = q
kn + mp = q
Solve for p
Subtract kn from both sides of the equation:
kn-kn+mp = q - kn
mp= q-kn
Divide both sides by m
mp/m = (q-kn)/m
p= (q-kn)/m
what's 3/4 put of 12?
Maria had 12 pieces of fruit. Three-fourths were apples.
We want to find how many fruits were apples,
That would be;
[tex]\begin{gathered} \frac{3}{4}\times12=\frac{36}{4} \\ =9 \end{gathered}[/tex]Therefore, 9 of the fruits were apples.
determine the length of side DFTriangle ABC is similar to triangle DEF
Answer:
DF = 13.5
Explanation:
If the triangles are similar, the proportion between their corresponding sides is constant, so, if BC is corresponding to EF and AC is corresponding to DF, we get:
[tex]\frac{EF}{BC}=\frac{DF}{AC}[/tex]So, replacing EF by 6, BC by 4, and AC by 9, we get:
[tex]\frac{6}{4}=\frac{DF}{9}[/tex]Then, we can solve for DF:
[tex]\begin{gathered} \frac{6}{4}\times9=\frac{DF}{9}\times9 \\ \frac{6\times9}{4}=DF \\ \frac{54}{4}=DF \\ 13.5=DF \end{gathered}[/tex]Therefore, the length of side DF is 13.5
Stage if the following are perfect square trinomials. Show work that justifies.
Given:
The given expression is
[tex]x^2-20x+50[/tex]Find:
we have to check whether the given expression is a perfect square trinomials or not.
Explanation:
An expression obtained from the square of a binomial equation is a perfect square trinomial. An expression is said to a perfect square trinomial if it takes the form ax^2 + bx + c and satisfies the condition b^2 = 4ac.
compare x^2-20x+50 with ax^2 + bx + c, we have
a=1, b = -20, c =50
Now
[tex]\begin{gathered} b^2=(-20)^2=400 \\ 4ac=4(1)(50)=200 \\ \therefore b^2\ne4ac \end{gathered}[/tex]Therefore, b^2 is not equal to 4ac,
Hence the given expression is not a perfect square trinomials.
Gave a nuclear physicist needs 50 liters of a 60 percent acid solution. He currently has a 20% solution and a 70% solution. How many liters of each does he need to make the needed 50 liters of 60% acid solution?
Let the number of liters of 20% solution be "x"
Let the number of liters of 70% solution be "y"
According to the problem, we need 50 liters of the solution. Thus, we can write >>>>
[tex]x+y=50[/tex]Also, given, we need 50 L of 60% solution. Thus, we can write >>>>>
[tex]0.2x+0.7y=0.6\times50[/tex]Let's substitute first equation into the second and solve for "x" >>>>>
[tex]\begin{gathered} x+y=50 \\ 0.2x+0.7y=0.6\times50 \\ --------------- \\ y=50-x \\ \text{Substituting,} \\ 0.2x+0.7(50-x)=30 \\ 0.2x+35-0.7x=30 \\ 0.5x=5 \\ x=\frac{5}{0.5} \\ x=10 \end{gathered}[/tex]So, the "y" value is >>>
[tex]\begin{gathered} x+y=50 \\ 10+y=50 \\ y=50-10 \\ y=40 \end{gathered}[/tex]So, he needs,
Answer10 liters of 20% solution
40 liters of 70% solution
write the equation of the slope intercept form with the given point and slope or two points. (-7,13) slope = -2
Slope-intercept form of a line:
y = mx+ b
where m is the slope and b is the y-intercept.
Replacing into the equation with m = -2 and point (-7, 13) we get:
13 = -2(-7)+ b
13 = 14+ b
13 - 14 = b
-1 = b
Then, the equation is:
y = -2x - 1
Which equation describes a line of symmetry for square ABCD? x = 0 y = x x = -2 y = -2
The equation of the line is DB from y = mx + b
From the graph y = 0 when x =0
this means y = x
The graph cuts through the origin, Meaning the y -intercept = 0
answer is: y = x
write an equation for the line that has a slope of 1/2 and passes through the point (2,4)!!
Answer:
x-2y=-6.
Explanation:
Given a line with a slope of 1/2 that passes through the point (2,4):
[tex]\begin{gathered} m=\frac{1}{2} \\ (x_1,y_1)=(2,4) \end{gathered}[/tex]Substitute these into the point-slope form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]This gives:
[tex]\begin{gathered} y-4=\frac{1}{2}(x-2) \\ y-4=\frac{1}{2}x-\frac{1}{2}(2) \\ y-4=\frac{1}{2}x-1 \end{gathered}[/tex]We can simplify further:
[tex]\begin{gathered} y=\frac{1}{2}x-1+4 \\ y=\frac{1}{2}x+3 \\ \implies y=\frac{x+6}{2} \\ 2y=x+6 \\ x-2y=-6 \end{gathered}[/tex]The equation of the line is x-2y=-6.
A car manufacturer collects data on the number of gallons of gasoline left in the gas tank after driving for different numbers of miles. The manufacturer creates a scatter plot of the data and determines that the correlation coefficient is −0.92.Select each true statement based on this correlation coefficient.g
Solution
- A correlation coefficient of -0.92 implies that:
1. As one variable is increasing, the other variable is decreasing.
2. Since the correlation is close to -1, there is a strong correlation between the variables.
3. Since the correlation is -0.92, there is a negative correlation between the variables.
4. Since correlation coefficient measures the linear relationship between variables, a correlation of -0.92 implies that there is very good reason to believe that a linear correlation/relationship exists between both variables.
Final Answer
The answers are:
1, 2, and 4
Solve the system. 2x + y + 3z = 20 x + 2y - z = -11 3x 2z = -3 Enter your answer as an ordered triple
The procedure 20 x + 2y - z = -11 3x 2z = -3 denotes an ordered triple with x = 1, z = 3, and y = 2.
What is meant by mathematical equations?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. The true power of equations lies in their ability to precisely describe various aspects of the world. (This is why, when one can be found, a solution to an equation can be useful.)Therefore,
let x + 2y + 3z = 14...…(1)
3x + y + 2z = 11.....(2)
2x + 3y + z = 11.....(3)
multiplying (2) by 2 and subtracting (1) from it we get,
=5x + z = 8...…..(4)
again multiplying (2) by 3 and subtracting (3) from it we get,
= 7x + 5z = 22.....(5)
Now multiply (4) by 5 and subtract (5) from it we get 18x = 18
therefore x = 1
substituting the x in (4) we get the value of z as
= 5(1) + z = 8
∴ z = 8 - 5 = 3
and substitute x and z in (1) we get
1 + 2y + 3(3) = 14
2y = 14 - 1 - 9 = 4
∴ y=2
The complete question is:
The solutions of the equations x+2y+3z=14, 3x+y+2z = 11, 2x + 3y + z = 11
A [tex]$\quad \mathrm{x}=\mathrm{O}, \mathrm{y}=2, \mathrm{z}=4$[/tex]
B [tex]$\quad \mathrm{x}=1, \mathrm{y}=\mathrm{O}, \mathrm{z}=4$[/tex]
C [tex]$\mathrm{x}=\mathrm{O}, \mathrm{y}=1, \mathrm{z}=8$[/tex]
D [tex]$x=1, y=2, z=3$[/tex]
To learn more about mathematical equations, refer to:
https://brainly.com/question/22688504
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Which point is located at (0, -7)? O 4 8
The point with the coordinates x=0 and y=-7 is point E
How Much Paint Would Cover This Pyramid Without The Square Base ?
To answer this question, we will assume that the pyramid's slant height is 10ft.
We have a square pyramid in which we have:
• The pyramid's base is a square with a side that measures 6ft.
,• The height of the pyramid is equal to 8ft.
,• The slant height is 10ft
Then we need to find the surface area of the pyramid without the square base, and we can see that:
1. We can see that the surface area of the pyramid without the square base is represented by four (4) triangles with equal base (6ft) and equal height (10ft). Then since the area of a triangle is given by:
[tex]A___{triangle}=\frac{bh}{2}[/tex]2. Therefore, we need to find the area of one of the triangles, and then multiply this result by 4 to find the asked area as follows:
[tex]A_{triangle}=\frac{6ft*10ft}{2}=\frac{60ft^2}{2}=30ft^2[/tex]3. Then the total area of the pyramid without the square base is:
[tex]\begin{gathered} A_{4triangles}=4(30ft^2)=120ft^2 \\ \\ A_{4triangles}=120ft^2 \end{gathered}[/tex]Therefore, in summary, the paint would cover 120ft² (square feet) without the square base.
Parallel lines never meet and will never cross each other.
True
Parallel lens are never meet and cross each other
Hey there! I know this is prob really simple and I am beginning to understand it, but my problem isSec 60°Now I know all the SOH CAO TOH stuff, and things like that, I just don't understand how to find the value because it changes all the time with the right triangle and the number of their sides. Really just need the formula on how to solve stuff.
Formula to solve a triangle
Lets begin with
Tan 45
is a right traingle, with angles 45,45 and 90°
Then, to find Tan 45
Tan 45= [√(1^2) + (1^2) ]/2 = √2/2
Tan 45= √2/2
NOW find Sec 60°
Sec 60° = 1/Sin 60°
Sin 60°is found by a triangle, with angles 30,60,90
Sin 60°= √3/2 , thats because
What does x equal for any y-intercept?
Y intercept means the point where the line touches the y axis
Because any point in y axis have coordinate x= 0
y axis passes through the origin then always does x equal ZERO at y- intercept.
So then the answer is : for any y- intercept x ALWAYS equals ZERO
For any x- intercept y equals ZERO
Determine the domain and range of the quadratic function. (Enter your answer using interval notation.)f(x) = 2x2 − 4x + 2domain range
we have the equation
[tex]f\mleft(x\mright)=2x^2−4x+2[/tex]The domain of any quadratic equation is all real numbers
so
The domain is the interval (-infinite, infinite)To find out the range, we need the vertex
Convert the given equation into vertex form
[tex]\begin{gathered} f\mleft(x\mright)=2x^2−4x+2 \\ f(x)=2(x^2-2x)+2 \end{gathered}[/tex]Complete the square
[tex]\begin{gathered} f(x)=2(x^2-2x+1-1)+2 \\ f(x)=2(x^2-2x+1)+2-2 \\ f(x)=2(x^2-2x+1) \\ f(x)=2(x-1)^2 \end{gathered}[/tex]The vertex is the point (1,0)
The vertical parabola opens upward (the leading coefficient is positive)
The vertex is a minimum
therefore
The range is the interval [0, infinite)All real numbers greater than or equal to zero
3(x-y) when x=4 and y=1
Find θ for 0 < θ< 2 pisin θ =0.3148
The given trigonometric expression is:
sin θ =0.3148
To find the value of θ, we need to find the arc sin of 0.3148
[tex]\begin{gathered} θ=\sin^{-1}0.3148 \\ θ=18.35^0,161.65^0\text{ } \end{gathered}[/tex]- FENCE The heights of two vertical posts are 2 meters and0.45 meter. When the shorter post casts a shadow that is 0.85meter long, what is the length of the longer post's 'shadow tothe nearest hundredth?
The heights of two vertical posts are 2 meters and
0.45 meter. When the shorter post casts a shadow that is 0.85
meter long, what is the length of the longer post's 'shadow to
the nearest hundredth?
Applying proportion
0.85/0.45=x/2
solve for x
x=(0.85/0.45)*2
x=3.78 m
answer is 3.78 meters
two angles in a triangle measure (2.3×+25)° and (5.8×+11)°. what is the value of x if the angles are congruent to one another?
If the angles are congruent to one another, we can conclude:
[tex]\begin{gathered} (2.3x+25)=(5.8x+11) \\ \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} 25-11=5.8x-2.3x \\ 14=3.5x \\ x=\frac{14}{3.5} \\ x=4 \end{gathered}[/tex])) How many terms are in this expression? 7c+ 3d Submit
The number of terms is the expression is equal to 2.
7c
3d
In algebra, terms are the values on which the mathematical operations take place in an expression.
A term can be a constant or a variable or both in an expression.
In the expression, 7ca + 3d, 7c and 3d are terms.
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Write the nth rule for each geometric sequence.4) -3, 1, -1/3, 1/9...
In a geometric sequence each term is found by multiplying the previous term by a constant.
To find the nth term in a geometric sequence we use:
[tex]a_n=ar^{n-1}[/tex]where a is the first term and r is the common ratio.
To find the common ratio we can divide the second term by the first:
[tex]\frac{1}{-3}=-\frac{1}{3}[/tex]and the third one by the second:
[tex]\frac{-\frac{1}{3}}{1}=-\frac{1}{3}[/tex]we notice that this in fact is the common ratio. Now we plug it in the formula above, therefore the geometric sequence is:
[tex]a_n=-3(-\frac{1}{3})^{n-1}[/tex]What percent of 33 is 21?
33 represents 100%. To find what percent represents 21, we can use the next proportion:
[tex]\frac{33}{21}=\frac{100\text{ \%}}{x\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 33\cdot x=21\cdot100 \\ x=\frac{2100}{33} \\ x=63.6\text{ \%} \end{gathered}[/tex]Exercise 3. A farmer raises chickens and pigs. His animals together have a total of 95 heads and 310 legs,How many chickens and how many pigs does the farmer have?
can someone help me find the valunof x?i bealive that is 8 but i need a little help?
value of x = 8
Explanation:Two lines are parallel. The triangles are similar, so we can use similar triangles theorem:
The ratio of corresponding sides are equal.
[tex]\frac{x}{4+x}=\frac{10}{10\text{ + 5}}[/tex][tex]\begin{gathered} \frac{x}{4+x}=\frac{10}{15} \\ \text{cross multiply:} \\ 15(x)\text{ = 10(4 + x)} \end{gathered}[/tex][tex]\begin{gathered} 15x\text{ = 10(4) + 10(x)} \\ 15x\text{ = 40 + 10x} \\ \text{subtract 10x from both sides:} \\ 15x\text{ - }10x\text{ = 40 + 10x - 10x} \end{gathered}[/tex][tex]\begin{gathered} 5x\text{ = 40} \\ \text{divide both sides by 5:} \\ \frac{5x}{5}=\frac{40}{5} \\ x\text{ = 8} \end{gathered}[/tex]Find the mean for the scores: 3,860; 5,300; 8,560; 4,400, 5,360..The mean for the scores is
We have to find the mean of this list of scores.
We can calculate the mean as:
[tex]\begin{gathered} M=\dfrac{1}{n}\sum ^n_{i=1}\, x_i \\ M=\dfrac{1}{5}(3860+5300+8560+4400+5360) \\ M=\dfrac{27480}{5} \\ M=5496 \end{gathered}[/tex]Answer: The mean of this set of values is 5,496.