Answer:
x = -2 and y = 3
Step-by-step explanation:
In linear combination method we try one of the variables from bopth of equations by
first making the variable equal in vlaue
then either subtracting or adding the two equation as required to eliminate the variable.
_____________________________________________
7x-2y=-20 equation 1
and 9x+4y=-6 equation 2
we see that y has
has value -2 and +4
4 = 2*2
thus, if we multiply equation1 with 2 we will give value for variable y as 4y and hence y can be eliminated easily.
7x-2y=-20
multiplying the LHS and RHS with 2
2(7x-2y)=-20 *2
=> 14x - 4y = -40 eqaution 3
now that we have got 4y
lets add equation 2 and equation 3
9x +4y= -6
+14x - 4y = -40
________________________________
=> 23x + 0 = -46
x = -46/23 = -2
Thus, x = -2
substituitinng x = -2 in 7x-2y=-20
7*-2 -2y=-20
=> -14 -2y = -20
=> -2y = -20+14 = -6
=> y = -6/-2 = 3
Thus, y = 3
solution is x = -2 and y = 3
At which value in the domain does f(x)=0? On a coordinate plane, a function goes through the x-axis at (negative 2.5, 0), (negative 0.75, 0), (0, negative 3), and (1, 0).
Answer:
The values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.
Step-by-step explanation:
Since we are given the points (-2.5,0), (-0.75, 0), (0, -3) and (1,0) where the coordinates are in ordered pairs of (x, y) where y = f(x).
To find the values in the domain where f(x) = 0, we look at the ordered pairs given.
We look for the pair in which f(x) = 0.
So f(x) = 0 in (-2.5, 0)
f(x) = 0 in (-0.75, 0)
and f(x) = 0 in (1, 0)
The corresponding values of x in which f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.
So, the values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.
Answer:
C. [tex]x=1[/tex]
Step-by-step explanation:
When x is 1, y is 0.
If point Q is reflected across x = 1, what are the coordinates of its reflection image?
Answer:
(-1, -2) last answer
Step-by-step explanation:
x = 1 is a vertical line
Answer:
(-1, -2)
Step-by-step explanation:
This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.
Will give the brains of me brains and my brains and maby ur brain to u how many brains can i give u if u ask this quetion right?
Answer:
2.4 bags
Step-by-step explanation:
Uh you can keep your brains.
Using the data table, we get:
1, 2, 2, 3, 4 as our data.
Finding the mean:
(1+2+2+3+4)÷5=
12÷5=
2.4 bags
Making Purchasing decision.
Q1) A restaurant meal usually cost Nu 80. A special rate of Nu 60 is offered for lunch on Thursday only. Calculate the percent discount.
Answer:
25%
Step-by-step explanation:
Given that a restaurant meal usually cost Nu 80 but on Thursdays it cost Nu 80.
To determine the discount, we have to find the ratio between the difference between the usual cost and the cost on Thursday to the usual cost of meals. It is given by:
Percent discount = (Usual cost - Cost of meal on Thursday)/ Usual cost × 100%
Percent discount = (80 - 60) / 80 × 100% = 20 / 80 × 100%
Percent discount = 25%
You've decided you want a plant for your room. At the gardening store, there are 444 different kinds of plants (tulip, fern, cactus, and ficus) and 444 different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot). If you randomly pick the plant and the pot, what is the probability that you'll end up with a tulip in a plastic pot?
Answer:
1/197136
Step-by-step explanation:
If there would be one pot and one plant the possibility would be 1 to take it.
It there were 2 plants and 1 pot it would be 1/2*1 = 1/2
If there were 2 plants and 2 pots it would be 1/2*2 = 1/4
With 444 plants and 444 pots it is 1/444*444 = 1/197136
There are 4×4 = 16 different combinations of plant and pot. Of those, 7 are either clay pot or cactus. Thus the probability you won't get a clay pot or a cactuis is 9/16.
The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
A. g(x) = -x2 + 2
B. g(x) = -X2 - 2
C. g(x) = (-x)2 - 2
D. g(x) = (-x)2 + 2
B. [tex]-x^2-2[/tex].
Hope this helps.
Answer:
i think its g(x)=-x^2-2
Step-by-step explanation:
A cylinder has a volume of 1200 meters cubed. What is the volume of a cone with the same radius and height? A. 400 m3 B. 900 m3 C. 1600 m3 D. 3600 m3
Hey there!
The volume of a cone is always 1/3 of that of a cylinder with the same except dimensions. You multiply the base by the height and then divide by three!
This means that if the cylinder has a volume of 1200 meters cubed, you simply divide by three, giving you 400 meters cubed !
The answer is A. 400 m³.
Have a wonderful day! :D
Answer:900
Step-by-step explanation:A cylinder has more volume considering because of the space but a cone simply has less
Is 210879 divisible by 3?
PLEASE HELPP
Answer:
Yes
Step-by-step explanation:
Well to figure out if 210879 is divisible by 3 we do,
210879 / 3
= 70 293.
Thus,
210879 is divisible by 3.
Hope this helps :)
Answer: Yes
Explanation: To determine whether 210,879 is divisible by 3, first we need to find the sum of the digits.
Image is provided below.
The divisibility rules tell us that if the sum of the digits is divisible by 3,
then the number is also divisible by 3.
So since 27 is divisible by 3, 210,879 must also divisible by 3.
So our answer is yes, 210,879 is divisible by 3.
If $a$ and $b$ are integers, such that $a\not= 0$ and $b\not= 0$ and $a^2$ and $b^2$ have at most two digits, what is the greatest possible difference between the squares of $a$ and $b?$
Answer:
80
Step-by-step explanation:
t is important to note that a square of any non-zero integer is positive, and therefore there is no advantage in using negative integers instead of positive integers to attain the greatest difference of squares. So we will not consider negative integers.
The greatest value of a^2 - b^2 occurs when a^2 is at its largest and b^2 is at its smallest.
The larger a, the larger a^2:
8 ^ 2 = 64
9 ^ 2 = 81
10 ^ 2= 100
Since a^2 can have at most two digits, a=10 is too large, and so a=9 is the largest integral value of a we can use.
Now, b^2 is at its smallest when b is closest to zero on the number line (the further b gets from zero, the larger its square becomes):
2 ^ 2 = 4
1 ^ 2 =1
0 ^ 2 = 0
Remember to go back to the original problem sometimes, to make sure you are taking everything into account. It states b doesn't =0, and therefore the b=1 is the closest b can get to zero as an integer. So, the greatest difference between b^2 and a^2 is when b=1 and a=9, giving the result:
a^2-b^2 =9^2-1^2 =81-1= 80.
So, 80 is your answer.
Nine-banded armadillos always give birth to quadruplets—four identical babies (called pups). Jenny’s armadillo has produced four female pups. Jenny realizes that each of those pups could eventually have four more armadillos.
a. How many armadillos would Jenny have if the four pups grew up to have four more pups each?
b. What if every generation of Jenny’s armadillos was female? How many armadillos would there be if you only count the ones in the 5th generation? Can you write a formula for the number of armadillos in any given generation? Please explain what each variable and each number in your formula means.
c. According to this formula the world should be overrun with armadillos after 20 to 25 generations. Why isn’t this true in real life?
Answer:
a. 16; b. aₙ = 4ⁿ⁻¹; c. predation and carrying capacity will limit the population
Step-by-step explanation:
a. The first female had 4 pups.
If each of them had 4 pups, there would be 4 × 4 = 4² = 16 pups.
b. 1st generation = 1 pup
2nd generation = 4 × 1 pup = 4 pups
3rd generation = 4 × 4 pups = 16 pups
4th generation = 4 × 16 pups = 64 pups
5th generation = 4 × 64 pups = 256 pups
The sequence is 1, 4, 16, 64, 256, …
We can also write it as 4⁰, 4¹, 4², 4³, 4⁴, …
Note that the exponent is one less than the number of the generation.
Thus, the general formula for the nth term, aₙ, is
aₙ = 4ⁿ⁻¹, where
n = the number of the generation
a = the number of pups in that generation.
c. a₂₅ = 4²⁵⁻¹ = 4²⁴ ≈ 281 000 000 000 000 or 281 trillion
The population would not reach that number because there would not be enough food for all those pups. Pups would die of starvation until their numbers equalled the carrying capacity of the ecosystem and would level off at that point.
There would also be increased predation by coyotes, bobcats, etc. This would also keep the population growth in check,
If Line LK = 16, find the length of Line JK.
Answer:
JK = 16√2
Step-by-step explanation:
This triangle is a special case right triangle, where you have 1 90-degree angle and 2 45-degree angles. The sides that correspond to the 45-degree angles are scalable by 1 and the hypotenuse is scalable by √2. Sometimes these are called 1-1-√2 triangles, describing the measurements of the sides.
Since this has a side of 16, the hypotenuse will be 16√2.
Cheers.
Select the correct answer. Compare the two functions.
-
Which statement is true?
A. As x increases, the rate of change of f(x) exceeds the rate of change of g(x).
B. As x increases, the rate of change of g(x) exceeds the rate of change of f(x).
C. At x = 2, the rate of change of g(x) is equal to the rate of change of f(x).
D. On every interval of x, the rate of change of f(x) exceeds the rate of change of g(x).
In other words, f(x) grows faster after a certain point. This is true when comparing any exponential curve to a linear one.
Choice B is false as it contradicts choice A.
Choice C is false as the tables show the function outputs are equal at x = 2, not the rates of change
Choice D is false because there are infinitely many intervals where f(x) grows slower compared to g(x). That's why I mentioned the "after a certain point" portion.
Answer:
A
Step-by-step explanation:
in the equation 3y + 10= 5y-25, what is the value of y
Answer:
y = 35/2Step-by-step explanation:
3y + 10= 5y-25
Group like terms
Send the constants to the right side of the equation and those with variables to the left side
that's
3y - 5y = - 25 - 10
Simplify
- 2y = - 35
Divide both sides by - 2
y = 35/2Hope this helps you
Answer:
y=35/2 or 17.5
Step-by-step explanation:
1) 3y + 10= 5y-25
-3y -3y
2) 10 = 2y - 25
3) 10 = 2y - 25
+25 +25
35= 2y
4)Divide both sides by 2
y=35/2 or 17.5
Which is the correct algebraic expression after combining like terms? 6 + 8 x minus 7 minus x 7 x minus 1 7 x + 13 9 x minus 1 9 x + 13
Answer:
7x-1
Step-by-step explanation:
i did the test
Answer:
7x-1
Step-by-step explanation:
correct answer on edge
area of parallelogram is 30cm^2 .
If the length of two adjacent
sides are 6 cm and 10cm
respectively. Find its diagonal
Answer:
The lengths of the diagonals are;
15.49 cm and 5.66 cm
Step-by-step explanation:
The given area of the parallelogram = 30 cm²
Also the length of 2 adjacent sides are 6 cm and 10 cm
Given that the formula for the area of a parallelogram = Base × Height, h where the base is either of the sides of the parallelogram we have;
When the base b = 10 m and the other side, a = 6 cm the diagonal, d is given by the relationship, d² = (a + √(b² - h²))² + h²
10 × h₁ = 30
h₁ = 30/10 = 3
d₁² = (b + √(a² - h₁²))² + h₁² = (10 + √(6² - 3²))² + 3² = 239.92 cm²
d₁ = √(239.92 cm²) = 15.49 cm
The other diagonal can be found from the following relationship;
d₂² = (b - √(a² - h₁²))² + h₁²
d₂² = (10 - √(6² - 3²))² + 3² = 32.08 cm²
d₂ = √(32.08 cm²) = 5.66 cm.
The roots of x^2 + 5x + 3 = 0 are p and q, and the roots of x^2 + bx + c = 0are p^2 and q^2. Find b + c.
Answer:
[tex]\large \boxed{\sf \ \ \ b=-19, \ \ c=9, \ \ \ b+c=-10 }[/tex]
Step-by-step explanation:
Hello,
we can write
[tex]x^2+5x+3=(x-p)(x-q)=x^2-(p+q)x+pq[/tex]
it means that p+q = -5 and pq=3
And then we are looking for b and c so that
[tex]x^2+bx+c=(x-p^2)(x-q^2)=x^2-(p^2+q^2)x+p^2q^2[/tex]
So
[tex]b=-(p^2+q^2)=-[(p+q)^2-2pq]=-[(-5)^2-2*3]=-(25-6)=-19\\\\c=p^2q^2=3^2=9[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
b + c = -10
Step-by-step explanation:
Notice that according to he quadratic formula, the solutions to a quadratic equation of the form:
[tex]x^2+bx+c=0[/tex]
are:
[tex]x=\frac{-b+/-\sqrt{b^2-4\,c} }{2}[/tex]
and such solutions verify the following conditions:
a) the product of the solutions is:
[tex](\frac{-b+\sqrt{b^2-4c} }{2} )\,(\frac{-b-\sqrt{b^2-4c} }{2} )=\frac{b^2-(b^2-4c)}{4} =\frac{4\,c}{4} =c[/tex]
b) the addition of the solutions is:
[tex](\frac{-b+\sqrt{b^2-4c} }{2} )+(\frac{-b-\sqrt{b^2-4c} }{2} )=\frac{-b-b}{2} =\frac{-2\,b}{2} =-b[/tex]
Therefore, applying these to the first equation, we get that the solutions p and q must verify:
[tex]p\,*\,q=3\,\,\,\,and\,\,\,\,p\,+\,q=-\,5[/tex]
On the other hand, we know that the solutions of the equation
[tex]x^2+bx+c=0[/tex]
are [tex]p^2\,\,\, and \,\,\,q^2[/tex]
Then considering what we found in step a), the product of these two solutions should equal the constant term"c":
[tex]p^2\,*\,q^2= c\\(p\,*\,q)\,(p\,*\,q)=c\\3\,*\,3 = c\\9=c[/tex]
so we know the value of "c" in the second quadratic expression: c = 9
Now, according to what we found in step b), the addition of the two solutions for the second quadratic expression should equal the opposite of the coefficient in the linear term. That is:
[tex]p^2+q^2=-b[/tex]
So, we need to find what the addition of these two squares is in order to find "b". We consider then what the expression [tex](p+q)^2[/tex] renders, since we know that [tex](p+q)=-5[/tex]:
[tex](p+q)^2=p^2+2\,p\,q+q^2\\(-5)^2=p^2+q^2+2\,(p\,*\,q)\\25=p^2+q^2+2\,(3)\\p^2+q^2=25-6\\p^2+q^2=19[/tex]
This means that
[tex]-b=19\\\\b=-19[/tex]
Now, knowing b and c, we can find what b+c is:
[tex]b+c=-19+9=-10[/tex]
if R is inversely proportional to S and r=15 when S =12 what is the value of S when R =60
Answer:
s = 3Step-by-step explanation:
The variation above is written as
[tex]R = \frac{k}{S} [/tex]
Where k is the constant of variation
when R = 15
S = 12
k = R × S
k = 15 × 12
k = 180
So the formula for the variation is
[tex]R = \frac{180}{S} [/tex]
When R = 60
We have
[tex]60 = \frac{180}{S} [/tex]
Cross multiply
That's
60S = 180
Divide both sides by 60
S = 3
Hope this helps you
please help me solve
Answer:
20
Step-by-step explanation:
She will be 10 in 5 years witch means she is 5
Double five you get 10
10 + 10 = 20
Answer:
the answer is B.) 20 years old
Step-by-step explanation:
if in 5 years melissa is 10, then right now she is 5 years old. since laura is twice as old as melissa, then laura is currently 10 years old. and if Kim is 10 years older then laura, then Kim is 20 years old
Tl;Dr:
10-5=5
5x2=10
10+10=20
A carpenter makes wooden chairs. He has enough wood to make 30 chairs. He makes $60 profit on a dining chair and $90 profit on a rocking chair. It takes him 1 hour to make a dining chair and 2 hours to make a rocking chair. He only has 40 hours available to work on the chairs. The carpenter wants to maximize his profit given the constraints. He draws the graph below to represent this situation. Drag and drop the correct numbers to complete the statements below. Given the restraints, the carpenter can maximize profits by making Response area dining chairs and Response area rocking chairs. His total profit for all the chairs will be $Response area.
Answer:
The carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100
Step-by-step explanation:
Let x be the no. of dining chairs and y be the no. of rocking chair
Time taken by carpenter to make 1 dining chair = 1 hour
Time taken by carpenter to make x dining chairs = x hours
Time taken by carpenter to make 1 rocking chair = 2 hour
Time taken by carpenter to make y rocking chairs = 2y hours
He only has 40 hours available to work on the chairs.
[tex]\Rightarrow x+2y \leq 40[/tex]
He has enough wood to make 30 chairs.
[tex]\Rightarrow x+y\leq30[/tex]
He makes $60 profit on a dining chair and $90 profit on a rocking chair.
So, profit =60x+90y
Plot the equations on graph
Refer the attached figure
Coordinates of feasible region
(0,20),(20,10) and (30,0)
Profit =60x+90y
At(0,20)
Profit = 1800
At(20,10)
Profit = 1200+900=2100
At(30,0)
Profit=900
So,the carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100
The triangles are congruent by the SSS congruence theorem. Triangles F G H and V W X are shown. Triangle F G H is rotated about point G and then is shifted to the right to form triangle V W X. Which rigid transformation(s) can map TriangleFGH onto TriangleVWX? reflection, then rotation reflection, then translation rotation, then translation rotation, then dilation
Answer:
C. rotation, then translation
Step-by-step explanation:
edge 2021
I think it's C "rotation, then translation"
not 100% sure so check other answers too
Write 0.00000414 in scientific notation.
Answer:
[tex]4.14*10^{-6}[/tex]
Step-by-step explanation:
Well scientific notation is (something*10^(other thing))
so we count have many zeroes there are, and there are 6, so we move the decimal point 6 times and get
[tex]4.14*10^{-6}[/tex]
Answer: It would take 6 "jumps" the left of 4.14 x 10^-6 to move the decimal back to where it actually is when not in scientific notation. 0.00000414
Step-by-step explanation:
hope this helps you :)
3 3/8 divided by 9 equals
Answer:
3/8
Step-by-step explanation:
Hey there!
Well we need to turn 3 3/8 into an improper fraction.
3*8 = 24
24 + 3 = 27
27 ÷ 9 = 3
3/8
Hope this helps :)
The answer of the given equation is 0.375
Given that,
3 3 by 8 divided by 9.Based on the above information, the calculation is as follows:
[tex]= 3 \frac{3}{8} \div 9\\\\ = \frac{27}{8} \div 9\\\\ = 3.375 \div 9\\\\ = 0.375[/tex]
Learn more: https://brainly.com/question/12522729?referrer=searchResults
Circle Y is shown. Chords R T and S U intersect at point Z. Arc S R is 100 degrees and arc T U is 72 degrees. In circle Y, what is m∠SZT?
Answer:
m∠SZT = 86°
Step-by-step explanation:
First we draw the diagram from the given information. Find attached the diagram.
when two chords intersect inside a circle, the measure of the angle formed is 1/2(the sum of the measure of the arcs intercepted each other).
From the above,
m∠SZT = 1/2 (Arc SR + arc TU)
Arc SR =100 degrees
Arc TU =72 degrees
m∠SZT = 1/2 (100° + 72°)
m∠SZT = 1/2 (172°)
m∠SZT = 86°
These are circles that include lines and angles. The measure of angle m∠SZT from the given diagram is 86°
Coordinate geometryThese are circles that include lines and angles. Using the theorem, the measure of the vertex is half that of its intercepted arc.
Based on the theorem;
m∠SZT = 1/2 (arcSR + arcTU)
Given
Arc SR =100 degrees
Arc TU =72 degrees
Substitute
m∠SZT = 1/2 (100° + 72°)
m∠SZT = 1/2 (172°)
m∠SZT = 86°
The measure of angle m∠SZT from the given diagram is 86°
Learn more on coordinate geometry here: https://brainly.com/question/18269861
#SPJ2
Please answer it now in two minutes
Answer:
3.9
Step-by-step explanation:
Pythagorean theorem:
a^2 + b^2 = c^2
a^2 + 1^2 = 4^2
a^2 + 1 = 16
a^2 = 15
a = sqrt(15)
a = 3.9
Answer a = 3.9 yards
Answer:
[tex]\boxed{3.9}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
Apply Pythagorean theorem.
[tex]a^2 + b^2 = c^2[/tex]
[tex]a^2 + 1^2 = 4^2[/tex]
[tex]a^2 + 1 = 16[/tex]
[tex]a^2 = 15[/tex]
[tex]a=\sqrt{15}[/tex]
[tex]a \approx 3.872983[/tex]
What is 4/5 ( 4 over 5) times 3?
What is the solution of the inequality shown a-1>11
Answer:
a > 12
Solutions can be anything over 12
Step-by-step explanation:
Well this one is pretty simple we just add 1 to both sides so the inequality turns into,
a > 12
Answer:
[tex]a>12[/tex]
Step-by-step explanation:
[tex]a-1>11[/tex]
Add [tex]1[/tex] on both sides.
The [tex]a[/tex] variable must be isolated on one side.
[tex]a-1+1>11+1[/tex]
[tex]a>12[/tex]
Plot the image of point D under a dilation about point P with a scale factor of 1/3
Answer:
check the graph below
Step-by-step explanation:
Dilation involves changing the size and position of a point
The image of the dilation is (4,-3)
From the figure, the coordinates of point D and point P are:
[tex]D = (13,2)[/tex]
[tex]P = (1,11)[/tex]
The scale factor of dilation is given as:
[tex]k = \frac{1}{3}[/tex]
The rule of dilation about point P is then calculated as:
[tex](x,y) \to k(x_D - x_P, y_D - y_P)[/tex]
So, we have:
[tex](x,y) \to \frac 13 \times (13 - 1, 2- 11)[/tex]
Simplify
[tex](x,y) \to \frac 13 \times (12, -9)[/tex]
Expand
[tex](x,y) \to (\frac 13 \times 12, -\frac 13 \times9)[/tex]
[tex](x,y) \to (4, -3 )[/tex]
This means that, the image of the dilation is (4,-3)
See attachment for the image of the dilation
Read more about dilation at:
https://brainly.com/question/8532602
Which system of inequalities has this graph as it’s solution
Answer:
Option (B)
Step-by-step explanation:
In the graph attached,
Two lines graphed have the equations as,
y = 2x - 3 [A line having y-intercept as (-3)]
[tex]y=\frac{1}{3}x+4[/tex] [Line having y-intercept as (4)]
Since both the lines have been represented by the dotted lines therefore, these lines will represent the inequalities [having the signs less than (<) or greater than (>)].
Now shaded region will decide the signs of the inequalities.
Since, shaded region of y = 2x - 3 is on the left side, inequality showing this region will be,
y > 2x - 3
Since, shaded region of [tex]y=\frac{1}{3}x+4[/tex] is above the line, inequality showing this region will be,
[tex]y>\frac{1}{3}x+4[/tex]
Therefore, Option (B) will be the answer.
Answer:
B
Step-by-step explanation:
Just is cuh
Can someone help me?
Answer:
sq. root(330)
Step-by-step explanation:
[tex] \sqrt{-55 \sqrt[3]{-216} } = \sqrt{-55(-6)} = \sqrt{330} [/tex]
[Cube root of -216 = -6]
write an equation of a line with the given slope and y intercept m =1/4,b=-3/4
Answer: y=1/4x-3/4
Step-by-step explanation:
We have our equation of a line formula y=mx+b
Then we substitute the given and get y=1/4x-3/4