Step-by-step explanation:
(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!
Step-by-step explanation:
Given the system of equation, \left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.{
2x−3y=−19
x+6y=28
, solve by elimination.
\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.{
2x−3y=−19
−2(x+6y=28)
, multiply the top equation by -2.
We get, \left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.{
2x−3y=−19
−2x−12y=−56
+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right. , add the equations together.
We get, -15y=75−15y=75 , we just eliminated the variable, x, we can now solve this equation for y.
-15y=-75 = > y=\frac{-75}{-15}−15y=−75=>y=
−15
−75
, y=\frac{75}{15} = > y=5y=
15
75
=>y=5
We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...
x+6y=28 = > x+6(5)=28 = > x+30=28x+6y=28=>x+6(5)=28=>x+30=28 , subtract the value, 30, from both sides. We get, x=-2x=−2 .
We found the value x, x=-2.
Thus the solution to the given system of equations is (-2,5).
Answer:
Comparing given eqn of line i.e.y=4x + 1 with
y=mx+c,we get,
m=4
We know that parallel lines have same value for m and the line parallel to y=4x+1 passes through the point (-2,-5) i.e (x1,y1)
Now,using point slope formula,we get
y-(-5)=4{x-(-2)}
or,y+5=4(X+2)
or,y+5=4x+8
or,y=4x+8-5
:.y=4x+3 is the req eqn for line parallel to y=4x+1
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Trapezoid LMNO with bases LM and ON , and Median PQ
If PQ = t +6, LM = t +3 and ON = 3t – 7, find ON
The length of base ON of trapezoid LMNO is 17 units
We know that the median theorem of trapezoid, which states that the median of a trapezoid is parallel to each base. Also, the length of the median equals one-half the sum of the lengths of the two bases.
Consider the following diagram of trapezoid LMNO with bases LM and ON , and Median PQ.
Given that the equations for the bases and median of trapezoid LMNO .
PQ = t +6, LM = t +3 and ON = 3t – 7
From above theorem,
PQ = 1/2 (LM + ON)
t + 6 = 1/2 ( t + 3 + 3t - 7)
2(t + 6) = 4t + 3 - 7
2t + 12 = 4t - 4
4t - 2t = 12 + 4
2t = 16
t = 8 units
So, ON = 3t - 7
ON = 3(8) - 7
ON = 24 - 7
ON = 17 units
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Find X to this problem.
Point C is tangent to the circle and will be a right angle which is 90 degrees.
The three inside angles of a triangle need to equal 180.
X = 180-90-64 = 26
X = 26 degrees
An adult seal eats 48.5 pounds of food daily. how many full days would 785.7 pounds of food last?
16 full days will be covered by the 785.7 pounds of food.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
We are able to locate the missing value using the unitary technique.
This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
According to our question-
1 pound of food will last = 1/48.5 day
Pounds equal 785.7*(1/48.5) = 785.7
= 785.7/48.5
= 16.2
Only full days will be counted, therefore
We'll only count up to 16.
So, the 785.
16 days will pass after 7 days.
The 785.7 pounds of food will therefore be plenty for 16 full days.
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the function f(x)=80(0.5)^ represents the distance after a pendulum begins swinging,where x is the number of swings
It looks like there may be a typo in the function you provided. It appears that you meant to write "f(x) = 80(0.5)^x", which would represent the distance after a pendulum begins swinging, where x is the number of swings.
This function indicates that the distance traveled by the pendulum decreases by half with each swing. For example, after the first swing, the distance traveled would be 80(0.5)^1 = 40 units. After the second swing, the distance traveled would be 80(0.5)^2 = 20 units. And so on.
The exponent x in the function represents the number of swings, so the distance traveled by the pendulum can be calculated by plugging in the desired value of x into the function. For example, to calculate the distance traveled after 10 swings, we can plug in x = 10:
f(10) = 80(0.5)^10 = 0.390625 units
This indicates that the pendulum has traveled a distance of approximately 0.39 units after 10 swings.
(6) (Bonus) A rectangular tank with a bottom and sides but no top is to have volume 500 cubic feet. Determine the dimensions (length, width, height) with the smallest possible surface area.
The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.
Volume=lbh
lbh=500 cubic feet
h=500/lb
Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}
S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}
S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}
for S to be minimum dS/dl=0 and dS/db=0
dS/dl= b-1000/l^2
dS/dl=0
b=1000/l^2...(2)
dS/db= l-1000/b^2
dS/db=0
l=1000/b^2
l=1000/(1000/l^2)^2 {substituting the value of b from 2}
l=(1000 x l^4)/(1000000)
1000000/1000=l^4/l
1000=l^3
l=10 feet
b=1000/l^2
b=1000/100=10 feet
lbh=500
h=500/(10x10(
h=5 feet
S=10x10+2x5x10+2x10x5
S=300 square feet
Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the rectangular tank.
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Estimate the area of the circle. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units
The area of the circle is A. 3 square units
How to determine the area of the circleThe formula for determining the area of a circle is expressed as;
A = πr² or 1/4πd²
Given that;
A is the area of the circleπ takes the value 3.14 or 22/7r is the radius of the circled is the diameter of the circleAlso, the formula for calculating the radius of a circle is given as;
Radius = diameter/2
Substitute the value, we have;
Radius = 2/2
Radius = 1
Substitute the value into the formula
Area, A = 3. 14 × (1)²
Find the square
Area, A = 3. 14 square units
Hence, the value is 3 square units. Option A
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The complete question
Estimate the area of the circle, given the diameter as 2 unit. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units
What is equal function with example?
The given two functions are said to be equal functions if and only if both it's domain and range are equal.
In mathematics we use functions to show the relation between two objects.
They are used in various aspects of real life. The domain of a function is known as all the possible input values which can be given to the function.
The range of the function is the set of all the possible outputs which can be obtained from a function. We also have co-domain of a function which can be defined as the set of outputs for a relation or function , it can be equal to the range.
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If 3% discount is given to electricity bill of Rs.1600 and 13% VAT is added to it, how much should be paid
curled an 8 inch by 10 inch rectangular piece of paper along one of its sides to form an open cylinder with a height of 10 inches. Which measure of the cylinder will be 8 inches? the radius of the base the diameter of the base the area of the base the circumference of the base
Answer:
circumference of the base
Step-by-step explanation:
Given that
The height of the cylinder is 10 inches
And, the 8 inches show the circumference of the base or the circumference of the circle
So,
C = 2r π
or
8 = 2r π
So, the 8 inches represent the same as shown above
Hence, the last option is correct
Answer:
circumference of the base.. D
Step-by-step explanation:
ANSWER D OPTION D
PLEASE FAST MY GRADE IS A 71 AND REPORT CARDS ARE TMR BRAINY PLEASE ANYONE
Answer:
I believe it to be A.
I need help with question 9. It’s all about functuons
Answer:
gay
Step-by-step explanation:
gayayayayayayaydyfyfaygaygagya
Write an equation of the line that passes through the points (-7,-3) and (8, -3)
y=
Answer:
y = - 3
Step-by-step explanation:
Call the line y = a + bx (d)
Since d go through (-7;-3) so -7 = a - 3b (1)
Since d go through (8;-3) so 8 = a - 3b (2)
From (1) and (2), we have equations: [tex]\left \{ {{a - 3b = -7} \atop {a - 3b = 8}} \right.[/tex]
Solve the equations, we have [tex]\left \{ {{a = 0} \atop {b = -3}} \right.[/tex]
PLEASE HURRY IM ON A TIMER!!!!
Please answer question 9!!!
It is A because it is only $40.000 so therefore it is A.
19
Work out the highest common factor (HCF) of 75 and 105
The Greatest Common Factor (GCF) for 75 and 105, notation CGF(75,105), is 15. Explanation: The factors of 75 are 1,3,5,15,25,75; The factors of 105 are 1,3,5,7,15,21,35,105.
THANKS!
FROM CAMBRIDGE UNIVERSITY
:)
The highest common factor (HCF) of 75 and 105 is 15.
The factor of a number is a number that can divide another number perfectly without any remainder.
Factors of 75 are 1, 3, 5, 15, 25, 75 Factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.Common factors of 75 and 105 are 1,3, 4, 15The highest common factor is 15.
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Why is the vertex of vertex form y=a(x-h)^2+k (h,k) rather than (-h,k)? If that was y=2(x-5)^2+6, the vertex would be at (5,6) which is (-h,k).
9514 1404 393
Answer:
(5, 6) is (h, k)
Step-by-step explanation:
Vertex form is an instance of the transformation of parent function f(x) = x². It is vertically scaled by a factor of 'a', and translated so the vertex is point (h, k). That is, the transformed vertex is h units right and k units up from that of the parent function (0, 0).
Parent:
f(x) = x^2
Transformed:
f(x) = a(x -h)^2 +k
__
When you compare the form to your specific instance, you need to pay attention to what it is that you're comparing. As the attachment shows, ...
a = 2-h = -5 ⇒ h = 5k = 6Hence the vertex is (h, k) = (5, 6). The second attachment shows this on a graph.
The pic says it all, thanks.
Answer:
Step-by-step explanation:
.
.
.
.
Answer:
The area left is equal to about 2686 [tex]ft^{2}[/tex] (if we will round to the nearest whole number).
Step-by-step explanation:
The area of the backyard that will be left will equal to the area of his backyard minus the area of the circular pool. So we can write it as...
The area left = (area of the backyard) - (area of the pool)
The area left = [tex]60 * 50 - \pi (20 / 2)^{2}[/tex]
The area left = [tex]3000 - 100\pi[/tex]
The area left ≅ 2686 [tex]ft^{2}[/tex]
If the ratio of the model car was 2:35 then what would be the actual length of the car??
PLEASE HELP AND SHOW WORK
The actual length of the car based on the model will be 350 inches.
How to calculate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Since the ratio of the model car was 2:35. If the model is 20 inches long, the actual length of the car will be:
= 20 ÷ 2/35
= 20 × 35/2
= 350 inches.
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Complete question
The ratio of the model car was 2:35. If the model is 20 inches long. then what would be the actual length of the car??
Solve for x and express the zeros in a + bi form x^2=6x-10
Solution of the equation is x = 3 ± i that is a complex number where 3 is the real part and i is the imaginary part.
What is quadratic equation?The equation of two-degree polynomial having one variable is called quadratic equation.
The solution of a quadratic equation is either real or complex. We use quadratic equation formula for solution whenever we cannot expand, and factoring a given two-degree polynomial equation.
How to solve the given equation?given equation, x² = 6x -10
x²-6x +10 =0
This equation cannot be expanded so we need to write the formula for quadratic equation to solve it.
we know that standard form of a quadratic equation is given by
ax² + bx +c = 0
where a is the coefficient of x², b is the coefficient of x and c is the constant.
the solution of the equation is given by x = -b ± √ (b² - 4ac) / 2a
Now, the solution for the above equation is x = 6 ± √ (6² - 4×1×10) / 2×1
x = 6 ± √ (36 -40) / 2
x = 6 ± √-4 / 2
as √-4 = √-1 ×2
x = 6 ± 2 √-1 /2
divide both numerator and denominator by 2
x = 3± i as √-1 = i
this is the solution in (a + bi) form a = 3 and b = 1
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If the radius of a circle is 1 kilometer what is the area of the circle?
Answer:
The area of the circle is [tex]1\pi[/tex] or approximately 3.14 [tex]km^2[/tex]
Step-by-step explanation:
The formula to find the area of a circle is [tex]\pi r^2[/tex], where [tex]r[/tex] represents the radius of the circle. In this case, the area would be [tex]1^2*\pi[/tex] = [tex]\pi[/tex] ≈ 3.14 [tex]km^2[/tex].
Which of these students is least likely to qualify for the national spelling bee in June?
Answer:
tony
Step-by-step explanation:
his fraction is the greatest meaning that it's also the lowest
Write an equation to represent function A
Answer:
y = 312x + 2
Step-by-step explanation:
According to y = mx + b, m stands for slope and b stands for y-intercept. Let us find the y-intercept. To find the y-intercept, the x should be zero in (x, y).
(x, y)
(0, 2) ---> y-intercept (b)
Now that we have found the y-intercept, we will now find the slope by using its formula.
Slope formula:-
m = y2 - y1 / x2 - x1
Pick two random (x, y). I will pick the first and last pairs.
(0, 2) and (4, 1250)
Now plug these two pairs in the formula.
m = y2 - y1 / x2 - x1
m = 1250 - 2 / 4 - 0
m = 1248 / 4
m = 312
This means that the slope (m) is 312. Now put that in y = mx + b form.
y = mx + b
y = 312x + 2
Both of the forms are the same. Hope this helps, thank you :) !!
Create a scatter plot using the data
in the table above.
Answer:
Step-by-step explanation:
A scatter plot is a chart type that is normally used to observe and visually display the relationship between variables. It is also known as a scattergram, scatter graph, or scatter chart
If a = 12 and B = 43 degrees, find c.
Answer:
74
Step-by-step explanation:
You subtract 43 from 12 you get 31 then you add 43 and 31 you get 74 bye
Answer:
c=35 degrees
Step-by-step explanation:
Its a right angle triangle which is equal to 90 degrees
so 43 +12=55 degrees.
90-55=35 degrees
c=35 degrees
Tim shows his work To answer a subtraction problem. Tell how to find an equation to represent the problem Tim starts with and its answer. 863+7=870 870+30=900 900+55=955
As you can see, we turned the fraction 10100 into its decimal representation, 0.1, in a single simple computation.
what is fraction?Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.
With 100 as the denominator, decimal fractions in the hundredth place are written. We shall discover how each square is split into 100 equal sections in this section. A tenth is a portion that is just partially shaded. The fraction is expressed as 1/100 in decimal form.
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4. If 3x − 1 = 11, the 2x = ?
a. 20/3
b. 2
c. 4
d. 8
e. 72
Answer:
Your answer is C
Step-by-step explanation:
3(4)-1 = 11
Answer:
d. 8
Step-by-step explanation:
3x − 1 = 11
add 1 to both sides
3x = 12
Divide both sides by 3
x = 4
-----------------
2x = 2*4 = 8
Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters, how many of each coin does he have?
quarters
nickels
The number of coins of nickels and quarters will be 27 and 13, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters.
Let 'x' be the number of nickels and 'y' be the number of quarters. Then the equations are given as,
x = y + 14 ....1
0.05x + 0.25y = 4.60 ....2
From equations 1 and 2, then we have
0.05(y + 14) + 0.25y = 1
0.05y + 0.70 + 0.25y = 4.60
0.30y = 3.9
y = 13
Then the value of 'x' is given as,
x = 13 + 14
x = 27
The number of coins of nickels and quarters will be 27 and 13, respectively.
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there is 10 oranges and 12 apples in a bag each time one fruit gets taken out of the bag what is the probability of picking an orange then picking an apple write your answer as a percent
Answer:
25.9%
Step-by-step explanation:
10/22 x 12/21 = 25.9%
Members of the science club voted for their favorite planet. The picture graph shows the total votes. How many more members voted for Mars than for Earth?
The members voted 2 more for mars than earth.
What are the number of planets in the solar system?The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune.
Given here, Mars has 8 votes while earth has 6 votes
Thus difference in votes is =8-6
= 2
Hence, Mars got two more members than earth
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Yesterday, Camille's Snack Shack went through 1/4 of a bottle of ketchup. If they used 2/3 as much mustard as ketchup, how many bottles of mustard did they go through?
The number of bottles of mustard they went through is given by the equation A = 1/6 of the bottle
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of bottles of mustard be represented as A
Now , the equation will be
The amount of ketchup used by Camille's Snack Shack = ( 1/4 ) of the bottle
Now , the amount of bottle of mustard used = ( 2/3 ) of the bottle of ketchup
Substituting the values in the equation , we get
The number of bottles of mustard used A = ( 2/3 ) of ( 1/4 ) of the bottle
On simplifying the equation , we get
The number of bottles of mustard used A = ( 2/3 ) x ( 1/4 )
The number of bottles of mustard used A = ( 1/6 ) of the bottle
Therefore , the value of A is 1/6
Hence , the number of bottles is 1/6
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PLZ DONT IGNORE THIS
Joan flipped a coin 100 times during a mathematics experiment. The coin landed on tails 36 times. Based on Joan's results, which of these statements is true?
(A)The coin landed on tails more than expected.
(B)The coin landed on heads less than expected.
(C)The coin landed on heads more than tails.
(D)The coin landed on heads less than tails.
Answer:
c
Step-by-step explanation:
the theoretical guess would be a 50/50 split for heads and tail, but tails was landed on less than 50 times, so heads landed more. the answer would be c. hope this helps