System A has 2 real solutions, System B has 0 real solutions and System C has 1 real solution.
Given a system of equations for A is x²+y²=17 and y=-(1÷2)x, a system of equations for B is y=x²-7x10 and y=-6x+5 and a system of equations for C is y=-2x²+9 and 8x-y=-17.
For system A,
The two systems of equations are
x²+y²=17 ......(1)
y=-1÷2x ......(2)
Substitute the value of equation (2) into equation (1) as
x²+(-x÷2)²=17
x²+(x²÷4)=17
Simplify the above equation by taking L.C.M. as
(4x²+x²)÷4=17
5x²=68
x²=68÷5
x=±3.688
Find the value of y by substituting the value of x in equation (2).
When x=3.688 then y is
y=-(1÷2)×3.688
y=-1.844
And When x=-3.688 then y is
y=-(1÷2)×(-3.688)
y=1.844
Thus, the points where the equations of system A intersect each other is (3.688,-1.844) and (-3.688,1.844)
So, the system of equations of A has 2 real solutions.
For system B,
The two systems of equations are
y=x²-7x+10 ......(3)
y=-6x+5 ......(4)
Substitute the value of equation (4) into equation (3) as
-6x+5=x²-7x+10
x²-7x+10+6x-5=0
x²-x+5=0
Simplify the above quadratic equation using the discriminant rule,
x=(-b±√(b²-4ac))÷(2a)
Here, a=1, b=-1 and c=5
Substitute the values in the discriminant rule as
x=(1±√(1-4\times 5\times 1))÷2
x=(1±√(-19))÷2
x=(1±√(19)i)÷2
Here, the value of x goes into the complex.
So, the system of equations of B has 0 real solutions.
For system C,
The two systems of equations are
y=-2x²+9 ......(5)
8x-y=-17 ......(6)
Substitute the value of equation (6) into equation (5) as
8x-(-2x²+9)=-17
8x+2x²-9+17=0
2x²+8x+8=0
Simplify the above quadratic equation using factorization method as
2x²+4x+4x+8=0
2x(x+2)+4(x+2)=0
(2x+4)(x+2)=0
x=-2,-2
Find the value of y by substituting the value of x in equation (5).
When x=-2 then y is
y=-2(-2)²+9
y=-8+9
y=1
Thus, the point where the equations of system C intersect each other is (-2,1)
So, the system of equations of C has 1 real solutions.
Hence, the system of equations for A is x²+y²=17 and y=-(1÷2)x having 2 real solution, a system of equations for B is y=x²-7x10 and y=-6x+5 having 0 real solution and a system of equations for C is y=-2x²+9 and 8x-y=-17 having 1 real solution.
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Describe the transformations of the graph of y=5 times 2^x-2+3 as compared to the graph of y=2^x
the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.Which transformations are used?
We start with the function:
[tex]f(x) = 2^x[/tex]
And we have the transformed function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Bow, let's start with the original function f(x). If first we apply a vertical dilation of scale factor 5, then we have:
g(x) = 5*f(x).
Then we apply a shift of 2 units to the right, so we have:
g(x) = 5*f(x - 2)
Then we apply a shift of 3 units up, so we have:
g(x) = 5*f(x - 2) + 3
Replacing f(x) by the actual function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Then the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.If you want to learn more about transformations:
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Pleaseeeeee helpppppp
They are both factors of 15x-10 because 5(3x-2)=15x-10
factor x factor=product.
In this case 15x-10 is the product
A student is trying to solve the system of two equations given below:
Equation P: x+y=8
Equation Q: 2x + 5y = 24
Which of the following steps can be used to eliminate the x term?
02(x+y=8)
O-2(x+y=8)
O-1(2x + 5y = 24)
O-2(2x + 5y = 24)
Step-by-step explanation:
as the following pic answer should be × -2
Answer:
O -2(x+y=8)
Step-by-step explanation:
If you put the problems beside each other, they look like this;
2x + 5y = 24
x + y = 8
So you are trying to find a way to simplify the x's
Step 1;
See if there are any numbers that you could multiply to the bottom problem that would help you get rid of the x specifically.
In this case, -2 would cancel out that other 2 right? Because if you added them, they cancel each other out; 2 -2 = 0
Step 2:
if you multiply, you have to do it to the entire problem;
-2(x + y = 8) (-2 times x, -2 times y, -2 times 8)
-2x + -2y = -16
Step 3:
Go back to your original problem and work it out;
2x + 5y = 24
-2x + -2y = -16
2x and -2x cancel each other out so now you only have;
5y = 24
-2y = -16
Step 4:
Combine like terms;
5y = 24
-2y = -16
3y = 8
Divide by 3
y = 2.6
lcm of 15,18,21
lcm of 56 84 140
lcm
Step-by-step explanation:
The lcm of first question is 630 and second is 840
Answer:
LCM of 15,18,21: 630
LCM of 56,84,140: 840
Step-by-step explanation:
The right method is to list all the multiples of the number and circle the least common ones. In this way you will get your answer for any LCM question!
What can each term of the equation be multiplied by to eliminate the fractions before solving?
1/2x-5/4+2x=5/6+x
Answer:
12
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!
For science class, Cora observed the growth of a pepper plant over time. Below is her log. How much taller was the pepper plant at the end of 4 weeks?
Growth of Plant
Start 3 inches
Week 1 5 inches
Week 2 7 inches
Week 3 9.5 inches
Week 4 11 inches
A. 6.75 inches
B. 7.5 inches
C. 8 inches
D. 10 inches
Answer:
c
Step-by-step explanation:
week 4 = 11
start = 3
11 - 3 = 8
answer is c
The correct Answer is: C. 8 inches
Step-by-step explanation:
If the plant started out at 3 inches and finished after 4 weeks at 11 inches, we can do 11-3 to find how much growth the pepper plant had.
11 - 3 = 8, therefore our answer is
C. 8 inches
If x+y=4 and x-y=k, what does x equal?
If x+y-z=8 and x-y+z=12 then x=
If x=3b and y=2/6b+4, what is x in terms of y?
The values of x are (4+k)/2 and 10. The value of the variable x in terms of y is x = y -4
System of equationsThese are equations that contains several equations and unknowns.
Given the following system of equation
x+y=4
x-y=k
Add both equation
x + x = 4 + k
2x = 4+k
x = (4+k)/2
For the equation
x+y-z=8
x-y+z=12
Add both equations
2x = 8 + 12
2x = 20
x = 10
The value of x from the equation is 10
Given the equations
x=3b
y = 2/6b+4,
______________
b = x/3
Substitute
y = 2/6(x/3)+4
y = x + 4
x = y - 4
Hence the value of the variable x in terms of y is x = y -4
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Ving tools to form the correct answer on the graph.
Graph the line that represents this equation:
y + 2 =
(x+2)
Drawing Tools
Select
Point
Line
Click on a tool to begin drawing.
10
N
27
The graph of the equation is shown in the attached picture which is a straight line.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a graph of a equation:
y + 2 = (x+2)
or
y = x
The above equation is a linear equation or straight line equation the slope of the equation is 1.
m = 1
The y-intercept of the equation is 0.
We can plot the equation y = x by using the slope and y-intercept.
Thus, the graph of the equation is shown in the attached picture which is a straight line.
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Which exponential equation is equivalent to this logarithmic equation? (2)
Answer:
A. e⁴=xStep-by-step explanation:
Log x=4 ➡️ e⁴=x or x= e⁴
Hope it helps
y = 2x² - 9x + 10
solve the following quadratic function by factoring
What is the rate of change of the amount earned with respect to hours worked for this function?
Answer:
72
Step-by-step explanation:
I got to get some bread for you guys
Answer:
I'll do it the answer is truthfully 72 if you don't think go check my page
Here is a rectangle.
A (-3,0)
D(-2,-3)
B (3,2)
C (4,-1) What is CD unit number?
Step-by-step explanation:
Let the area of rectangle with given points are as follows :
A(-3,3)
B(3,2)
C(4,-1) = C( x1,y1)
D(-2,-3) = D( x2, y2)
Now,
The distance of CD = root under(x2-x)^2 +( y2 - y1)^2
= root under (-2-4)^2 + ( -3+1)^2
= root under (-6)^2 + (-2)^2
= root under 36 + 4
= root under 40
= 2root 10
Therefore; the unit number if CD is 2 root 10.
What is the area of a sector with measure of arc equal to 90° and radius equal to 1 foot?
Answer:
0.7855 square feet
Step-by-step explanation:
90/360×3.142×1 squared
=0.7855
A man of height 1.5 m is standing in front of a tower of height 81.5 m. At what angle should he observe the top of the tower from the distance of 80 m?
The angle at which the man should observe is 45 degrees.
To solve the question :Given :
height of man = 1.5m
height of tower = 81.5 m
distance between tower and man = 80 m
Since, ABCD is a rectangle, AD = BC = 80m
Similarly, AB = CD = 1.5m
EC = ED + CD
81.5 = ED + 1.5
ED = 80m
Now, in order to find the angle EAD, we use trigonometric functions,
tan ∅ = perpendicular / base = ED / AD
tan ∅ = 80 /80 = 1
∅ = [tex]tan^{-1} (1)[/tex]
∅ = 45°.
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The average monthly temperature of a city can be modeled by a
cosine graph. Melissa has been living in Phoenix, Arizona, where the
average annual temperature is 75°F. She would like to move, and live
in a location where the average annual temperature is 62°F. When
examining the graphs of the average monthly temperatures for
various locations, Melissa should focus on the
The average monthly temperature of a city can be modeled by a cosine graph, Melissa should focus on the Midline. This is further explained below.
What is Melissa's focus on the Midline.?Generally, The average temperature would be indicated somewhere along the curve, most likely near the middle.
In conclusion, Melissa should concentrate on the Midline, which can be used to model the average monthly temperature of a city.
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Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal. Is Kyle's claim Incorrect or correct? In two or more complete sentences, Justify your answer.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal. Kyle's claim is Incorrect.
What is a quadrilateral?It is a polygon with four sides. The total interior angle is 360 degrees.
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal.
Kyle's claim is Incorrect. Because the shapes are square and rhombus.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal.
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Where would 1.84 be on a number line?
Answer:
It is located to the right of the 0 on the line,
Step-by-step explanation:
the numbers are increasing going from left to right. 1.84 is located 1.84 from 0.
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Find measure of X and Y
X=
Y=
Part B:
Choose the correct degree measure for JKL
A. 98
B. 65.5
C. 262
D. 24.5
Answer:
x = 7 y = 4 JKL = 262 degrees
Step-by-step explanation:
According to a circle theorem, sum of the opposite angles in a circle which touch its circumference must equal 180, hence:
7x + 131 = 180
x = 7
According to another theorem, a quadrilateral inside a circle must equal 360 so:
99 + 7(7) + 131 + 11(7) + y = 360
Note: remember to substitute 7 for all values of x
y = 4
The angle subtended by an arc at the centre is twice the angle subtended at the circumference
Following this rule, we can conclude that:
2(7x) or 2(2 x 7) = 2(49) which is 98
Lastly, 360 - 98 = 262
The first term of an arithmetic progres- sion is 3 and the last term is 9. Find the number of terms in the progression if the common difference is 3/2
Answer:
5 terms
Step-by-step explanation:
The numbers will be 3, 4 1/2, 6, 7 1/2, and 9.
Prove the triangles a re similar
Step-by-step explanation:
LINE B.I is parallel to LINE O.D
therefore :Ô = Î ( alternate angles )
: Ď = B ( alternate angles )
In ️ B. I. G and ️ D O G
O = I ( alternate angles)D = B ( alternate angles)G = G ( 3rd angle of️ )️ BIG is similar to ️ DOG
Which sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent?A)reflection and dilationB)reflection and rotationC)rotation and reflectionD)translation and rotation help please
The sequence of transformations will be relection and dilation. Then the correct option is A.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself and it maintains some spatial correlation between figures.
The sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent.
Reflection does not change the size and shape of the geometry.
Rotation does not change the size and shape of the geometry.
Translation does not change the size and shape of the geometry.
Dilation does not change the shape but changes the size of the geometry.
Then the correct option is A.
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What is the constant in the expression?
Answer:
12
Step-by-step explanation:
A constant in an expression is the number that is not attached to any variable, and this includes the sign that comes with the number.
0.05m +12
In the expression above, m is the variable thus 0.05 is known as the coefficient of m instead of a constant. Coefficients are numbers that are multiplied to variables.
+12, which can simply be written as 12, is not multiplied to any variable and is thus the constant.
The value of the number 12 will not change no matter the value of m. The fact that the value stays the same makes it a constant.
Additional:
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https://brainly.com/question/16517603Answer: 12 ✅
Step-by-step explanation:
Hii, I'd love to help you! (:
This problem is about finding the constant in the expression. This is fun! Let's start our search...
____________________________________________
Wait, how can we find a constant if we don't even know what it is?
No reason to panic!
ConstantsA constant is a number that is not added (or subtracted) from any variables (and a variable is a letter).
_____________________________________________
Ohh now it's easy as winking!
Because the only number in this particular expression that is not added to any letters at all is 12.
______________________________________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
Find the half line in days of Co-60. ROUND YOUR ANSWER TO THE NEAREST TENTH
The half life in days is 1924.0245 days.
What is half life?Half life is the time taken for the radioactivity of a substance to fall to half its original value.
Given:
N= 8
N[tex]_0[/tex]= initial mass
t= in days
So, N= [tex]N_0e^{-kt}[/tex]
Putting the values we get
half value = 5.2713 years or 1924.0245 days
Hence, the half-life is 1924.0245 days.
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Hii! would anyone mind helping me out?
Find the center of this hyperbola
[tex]\large\boldsymbol{9x^2-y^2-72x+8y+119=0}[/tex]
[tex]\bigstar[/tex]
[tex]\underbrace[/tex]
Answer:
(4, 4)
Step-by-step explanation:
This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1[/tex]
Match the values in this hyperbola to those of the standard form. The variable h represents the x-offset from the origin, k represents the y-offset from origin, a.
a = 1
b = 3
k = 4
h = 4
Thus,
[tex](x-4)^2 - \frac{(y-4)^2}{9} = 1[/tex]
The center of a hyperbola follows the form of (h, k). Substitute in the values of h and k.
= (4, 4)
Which solution set matches the equation on the graph?
Answer: C, {(1, -4), (4, -1)}
Step-by-step explanation: Where the two graphs meet are their solutions, and the points where they meet are {(1, -4),(4,-1)}.
Find the common difference and the SIMPLIFIED general term formula.
3) a 14=1322 and a 38 = 3722
I reallyyyy need help!!! ASAP PLEASE!!!!!
Answer:
[tex]a_{n}[/tex] = 100n - 78
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₄ = 1322 and a₃₈ = 3722 , then
a₁ + 13d = 1322 → (1)
a₁ + 37d = 3722 → (2)
subtract (1) from (2) term by term to eliminate a₁
24d = 2400 ( divide both sides by 24 )
d = 100
substitute d = 100 into either of the 2 equations and solve for a₁
substituting into (1)
a₁ + 13(100) = 1322
a₁ + 1300 = 1322 ( subtract 1300 from both sides )
a₁ = 22
then nth term formula is
[tex]a_{n}[/tex] = 22 + 100(n - 1) = 22 + 100n - 100 = 100n - 78
Carly will be going to college in 3 years. she anticipates that she will need $12,000 to pay for the first year. she currently has $2,900 in a savings account. without including any interest earned, what is a reasonable estimate of the amount carly needs to deposit into the savings account per month over the next 3 years to be able to pay for her first year of college? $150 $250 $350 $450
The estimate of the amount carly needs to deposit into the savings account per month over the next 3 years to be able to pay for her first year of college is $250
SavingsAmount needed = $12,000Amount available = $2,900Number of months in three years = 12 × 3 = 36Amount of savings per week = x12,000 = 2900 + 36x
12,000 - 2900 = 36x
9,100 = 36x
x = 9100 / 36
x = 252.777777777777
Approximately,
$250
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Answer:
The answer is B. $250
Step-by-step explanation:
Help Me Uhm In 5th Grade I'm behind in school work and I have to finish by august when my school starts pls help I'm stuck on this question
B
To find the average you add them all up and divide by how many numbers there are. 2+3+6+13+16=40 There are 5 numbers so 40/5=8
A would be 7 and c would be 9, so the answer is b.
Select the true statement about triangle ABC.
13
5
12
A. sin C = sin A
B. sin C = cos B
C. sin C = tan A
D. sin C = cos A
Answer:
sin C = cos A
Step-by-step explanation:
sinC = opp/hyp
=12/13
cosA = adj/hyp
12/13
? Question The point (x, y) is first rotated 180° clockwise about the origin, translated 6 units to the left, and then reflected across the line y = x. Write a function S to represent the sequence of transformations applied to the point (x, y).
The function S to represent the sequence of transformations applied to the point (x, y) is (-y, -x - 6)
Transformation of coordinatesTransformation is a technique used to change the position of an object on an xy-plane.
Given the coordinate (x, y)
Rotation of the coordinate by 180° clockwise about the origin will given;
(x, y) - > (-x, -y)
If the result is translated 6 units to the left, then;
(-x, -y) -> (-x-6, -y)
If it is then reflected across the line y = x, we will switch the coordinates to have:
(-x-6, -y) -> (-y, -x - 6)
The function S to represent the sequence of transformations applied to the point (x, y) is (-y, -x - 6)
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