Answer: y = -1/2
Step-by-step explanation:
Use the elimination method. When setting the equations up, you can see that the y values already cancel out. This makes it easy to find the x value.
3x+4y=4 3x+4y=4
2x-4y=6 -----> (-) 2x-4y=6
For the x value, you would get 2. 5x=10 therefore x=2.
Now that you have your x value, choose one of the original equations(either works). I chose 3x+4y=4. Now, substitute 2 into the x value then solve your equation for the y-value.
3x+4y=4 ---> 3(2)+4y=4
3(2)+4y=4 then becomes 4y=-2 and when you isolate the variable, you get -1/2.
Find the midpoint and distance for each:
1. A(0, 0) & B(8,4)
The midpoint between two points A(0,0) and B(8,4) is (4,2)
The distance between two points A(0,0) and B(8,4) is 4√5
To find the midpoint of two points,
We need to take an average of both the x and y components of both points
Two points A(x ₁,y₁) and B(x₂ ,y₂) are (0,0) and (8,4) respectively
Let M be the mid-point M(x, y),
x = x₁+x₂/2
= 0+8/2
= 8/2
= 4
Similarly
y = y₁+y₂/2
= 0+4/2
= 4/2
= 2
So, the midpoint of the two points A(0,0) and B(8,4) is (4,2)
To find the distance between two points,
We need to take the square root of the difference square of x and y, which is
d² = Δx² + Δy²
d = √(Δx²+Δy²)
Δx = x₂-x₁
= 8-0
= 8
Δy = y₂-y₁
= 4-0
= 4
Thus,
d = √(8²+4²)
d = √(64 + 16)
d = √80
d = 4√5
So the distance between the two points is 4√5
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What is the simplified form of each expression?
b. 11¹/² . 11¹/²
The simplified form of the expression is 11.
Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.
You may also hear the simplest form called "lowest term."
In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:
Combine Like terms
Factoring
Increasing (the opposite of factoring)
Clean out fractions by multiplying
Recognizing a pattern you have seen earlier, just like the difference between squares
Simplify the following:
sqrt(11) * sqrt(11)
sqrt(11) * sqrt(11) = 11:
Answer: 11
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PLEASE HELP QUICK
Use function notation to write the equation of the line.
Answer:
Step-by-step explanation:
Answer: f(x) = x
Step-by-step explanation:
nfs anyone ig lah.cj2x ??????????????????????????????????
Answer:
huh?
Step-by-step explanation:
For the following geometric sequence find the recursive formula.
(1, -3, 9, ...)
an-3-an-1 where a₁ = 1
Oan= (-3) -1
an=-3-an-1 where a₁ = -1
an=-1-(-3) -1
Answer: the 2nd one
Step-by-step explanation: first term (a1) is -1
recursive formula goes like this
is the nth term
is the term before that
we normally have
we see each term is multipying by -3 to get next one
so that would be
where a1=-1
the 3rd option is correct except that it is the explicit formula
so answer is 2nd one.
Answer:
45
Step-by-step explanation:
run plus duck equals to the implement
10 is at least the product of a number h and 5
Answer:
h =2
Step-by-step explanation:
10=h ×5
10=h5
DBS by 5
10÷5=h5÷5
h=2
In the following diagram, a is parallel to b and m is parallel n.
m<2=x^2+5x
m<4=11x+16
Note: the diagram may not be drawn to scale.
The is a parallel to b and m is parallel n.
The values of x is -2 and 8.That both values not work in geometric problem.Given that
a is parallel to b and m is parallel n.m∠2=x²+5xm∠4=11x+16To find
The value of x.That both values of x are working with this problem.So, according to the question
We have,
a is parallel to b and m is parallel n.and the value of two angles m∠2 and m∠4.
m∠2=x²+5xm∠4=11x+16From diagram we can see a is parallel to b and m is parallel to n.
So, we can say that
m∠4 = m∠3 { they are vertical congruent angles } and
m∠3 = m∠2 { they are congruent angles}
∴ m∠4 = m∠2 -------------(1)
Now, putting the values in equation(1)
So, will be get
m∠4 = m∠2 -------------(1)
11x+16 = x²+5x
x²+5x - 11x-16 = 0
x²- 6x-16 = 0
x²-8x+2x-16 = 0
x(x-8)+2(x-8) = 0
(x-8)(x+2) = 0
If (x+8) = 0
x = 8
And if (x+2) = 0
x = -2
The values of x is -2 and 8.
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Solving Equations with the Variable on Each Side:
-6 - 9 x = - 9 x - 4
Answer:
No solution
Step-by-step explanation:
To isolate the variable, begin by adding 9x to each side
-6 - 9x = -9x - 4
-6 - 9x (+ 9x) = -9x (+ 9x) - 4
-6 ≠ -4
The equation in your answer has no solution. If you are supposed to find the value of x, you might want to double check for typos.
Find the sum of E = [3 4 7] and the additive inverse of G = [-2 0 5].
Answer:
[ 5 4 2 ]
Step-by-step explanation:
find the compound interest 316,000 naira in 3yrs if the interest rate is 5% per annum
Answer:
the compound interest will be 365,809.5 naira.
Find the 72nd
term of the following arithmetic sequence.
17, 20, 23, 26,
Answer:
230
The 72nd term in the following arithmetic sequence is 230.
Step-by-step explanation:
Formula: an = a1 +(n−1)d
a1=17
n=72
d=3
a72=17+(72-1)3
Simplify.
a72=17+(71)3
a72=17+213
a72=230
The 72nd term in the following arithmetic sequence is 230.
Hope this helps!
Please mark as brainliest if correct!
Answer:
Step-by-step explanation:
Your take home pay is $1,944 with 19% tax taken out.
What is your gross pay before taxes are taken out?
Find the zeroes of the quadratic polynomial x
2
+ x−12 and verify the relationship between the zeroes
and the coefficients.
Rewrite the given polynomial in the form ax² + bx + c:
To find the zeros, set the function to zero and solve for x using the quadratic formula.
Quadratic formula:
Therefore,
a = 2√3
b = 5
c = - 4√3
Substituting the values into the quadratic formula:
The sum of the roots of a polynomial is -b/a:
The sum of the found roots is:
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
The product of the found roots is:
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
Samwell bought a packet of pens. His receipt is shown above. Assume that sales tax is rounded to the nearest cent. If the 6% sales tax had been computed on the sale price instead of on the regular price, how much lower would the tax have been?
If the 6% sales tax had been computed on the sale price instead of on the regular price, the tax will be $0.04 lower.
How to calculate the difference?It should be noted that from the information, Samwell bought a packet of pens and his receipt is shown above as $2.04.
Assume that sales tax is rounded to the nearest cent, If the 6% sales tax had been computed on the sale price instead of on the regular price, the difference will be:
Sales price = $1.89
Tax = $1.89 × 0.06 = $0.11
Therefore, the difference will be:
= Former tax amount - New tac amount
= $0.15 - 0.11
= $0.04
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DG contains D, E, F, and G, in thy order. If DF = 12, EG = 15, and EF = 4, what is DG
Answer:
23
Step-by-step explanation:
Given line segment DEFG and lengths DF=12, EG=15, EF=4, you want the length DG.
Segment additionThe segment addition theorem tells you the whole is the sum of the parts.
DF = DE +EF
12 = DE + 4
8 = DE . . . . . . subtract 4
And ...
DG = DE +EG
DG = 8 +15 = 23
The length DG is 23 units.
In the picture below, which line segment is parallel to AD.
a. BC
b. EB
c. EH
d. CD
In the cuboid, the line segment parallel to AD is BC as they both lie on same plane and are directed in same direction.
What are parallel lines?Two lines are said to be parallel if they lie on the same plane and are directed towards the same direction.
Given in the question is a labelled cuboid.
From the definition of parallel lines, they should lie on the same plane. Therefore, we will eliminate EB and EH because they don't lie in the plane of AB. CD lies in the plane of AB, but is directed perpendicular to AB. BC is in the same plane in which AB lies and is also directed in the direction of AB.
Therefore, in the cuboid, the line segment parallel to AD is BC.
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Marcie cooked dinner for herself. The original recipe has a serving size of 4 and requires four and four fifths pounds of chicken. How many pounds of chicken will be needed for a single serving?
Pull 4 4/5ths apart - now it is 4 and 4/5ths. Divide both by four - 4/4 = 1, 4/5 / 4 = 1/5th
Now add your answers together;
1 1/5
In 5-7 complete sentences, write a real world situation that can be modeled by the equation. Make it fun by using your name, if you want!
16x=14x+8
A possible real world scenario is that the product of your age and 16 is 8 more than the product of your age and 14
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to model the expression by a real world situation?The equation is given as
16x = 14x + 8
In the above equation, the variable of the equation is x while the number 8 is a constant
A possible real world scenario is that:
The product of your age and 16 is 8 more than the product of your age and 14
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Question
Write in scientific notation.
215 × 107
Responses
2.15 × 1092.15 × 109
2.15 × 1052.15 × 105
2.15 × 1072.15 × 107
2.15 × 1014
It should be noted that calculating 215 * 107 in scientific notation will be 2.15 × 10⁴
How to illustrate the information?It should be noted that from the information, we want to calculate 215 * 107 in scientific notation.
It should be noted that 215 = 2.15 × 10²
It should be noted that 107 = 1.07 × 10²
Therefore, calculating 215 * 107 in scientific notation will be:
= 215 × 107.
= 2.15 × 10² × 1.07 × 10²
= 2.15 × 10⁴
Therefore it should be noted that calculating 215 * 107 in scientific notation will be 2.15 × 10⁴
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Question in florida, 55% of adults live in a house, 25 of adults live in an apartment, 4.6% of adults live in a condo and the rest live on a boat. what percent of people live on a boat? write the equivalent decimal and fraction to represent the percent you solved for.
The percentage of people living on boat in Florida is 15.4%. The equivalent of this percentage to decimal is 0.154 and to fraction is 77/500.
55% live in a house, 25% live in an apartment, 4.6% in condo while the rest live on a boat. If all the percentages are summed up, they must be equal to 100%.
Let a% equals to the percentage of adult living on boat
55+25+4.6+a = 100
84.6 + a = 100
Collect like terms
a = 100 - 84.6
a = 15.4%
Therefore, the percentage of adult living on boat is 15.4%
To convert the percentage to decimal equivalence, one must divide it by 100%
15.4%/100%
= 15.4/100
= 0.154
To convert the percentage to fraction equivalence, one have to divide it by 100%
15.4%/100%
= 15.4/100
One has to make both the numerator and denominator of the fraction whole numbers, to do that one has to shift the decimal place behind the last digit, for a number without decimal point a 0 is added to the back of the number.
= 154/1000
Reducing the fraction to its lowest term, this is done by diving the numerator and denominator by a common factor
= 77/500
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In your own words, explain why solving 4 = 2x uses the division property of equality. Provide an example with your explanation
In the given particular sum we have to give reason why asolving 4 = 2x uses the division property of equality.
The reason for that why it is using division property of equality we wneed to know what is division property of equality : It states that when both side of the equation is divided by a real number other than 0 then the quotients remain same . It can be written as following : if a,b,c are real numbers where a = b , c ≠ 0 then ac = bc
for example suppose we have two breads of same size . We cut each of them into halfs and give it to our friends , if we measure the remaining portions we will see that we are left with same portions of bread . Here at initial both the breads were same and we divide it by 2 and find that they are still same.
Solving 4 = 2x using the division property because in order to get the last portion that answer we have divide the both sides by 2 to get x by itself .
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| 7x+35 |=7 has two solutions
What is the distance in the solutions?
[tex]|7x+35|=7 \\7x_{1} + 35 = 7 \\ 7x_{1} = - 28 \\ x_{1} = - 4[/tex]
[tex]|7x+35|=7 \\7x_{2} + 35 = - 7 \\ 7x_{2} = - 42\\ x_{2} = - 6[/tex]
[tex]distance = | x_{1}-x_{2}| = | - 4-( - 6)| \\ distance = | 2| = 2[/tex]
A rectangular garden has an area of 3m - 7m - 6.
Use the dimensions from Part A to determine an expression that gives the perimeter of the garden.
Reminder: P = 2L + 2W.
The perimeter of the whole figure includes the sum of the side lengths and the value is -2 - 4m units
What are areas?The area of a shape is the amount of space on the shape.
For most regular shapes, the area is the product of their width and the length
How to determine the expression for the perimeter of the figure?The area of this rectangle is given as
Area = 3m - 7m - 6
Evaluate the like terms
So, we have
Area = -4m - 6
The common factor of 4 and 6 is 2
So, we have the following equation
Area = 2(-2m - 3)
The area of the rectangle is
Area = Length * Width
So, we have
Length, L = 2
Width, W = -2m - 3
The perimeter of the rectangle is calculated as
P = 2 x (L + W)
So, we have
P = 2 x (2 - 2m - 3)
Evaluate the like terms in the above expression
So, we have
P = 2 x (-1 - 2m)
Open the bracket in the above expression
So, we have
P = -2 - 4m
Hence, the perimeter of the whole figure is -2 - 4m units
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Ilana says that a fraction with a prime number in the numerator is always in simplest form. Is Ilana correct? Explain.
Answer:
She is correct.
In order to turn a fraction into its simplist form, you need to not be able to divide the numerator or the denominator by ANY integer. A prime number is not divisible by anything, so it is its simplist form.
Determine whether each logarithm is a common logarithm.
C. (log₁₀100)
Yes , the given logarithm is a common logarithmic.
A base 10 logarithm is a common logarithm.It is also known as decimal logarithm and is named after its base. It is also known as the Briggs logarithm, and the "standard logarithm", after Henry Briggs, the English mathematician who pioneered its use.Calculators usually say "logarithm", but mathematicians usually mean the natural logarithm (the logarithm with base e ≈ 2.71828), not the common logarithm when writing "logarithm". To reduce this ambiguity [tex]log_{10}x[/tex] should be written lg(x) and [tex]log_ex[/tex] must be ln(x).We have given an logarithm function which is [tex]log_{10}100[/tex] ..... (1)
As , we can see that this log has a base of 10 so , it is a common logarithm.
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Find BC if B(8, -7) and C(-4,-2).
Solving the Question
We're given:
B(8, -7)C(-4,-2)Find BCWe can use the distance equation to help us solve this question:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the endpoints of the line segmentPlug in the given points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d=\sqrt{(8-(-4))^2+(-7-(-2))^2}\\d=\sqrt{(8+4)^2+(-7+2)^2}\\d=\sqrt{(12)^2+(-5)^2}\\d=\sqrt{144+25}\\d=\sqrt{169}\\d=13[/tex]
AnswerThe length of line segment BC is 13 units.
Using the distance formula, the length of BC is: 13 units.
How to Apply the Distance Formula?Given that:
B(8, -7) = (x1, y1)
C(-4,-2) = (x2, y2)
The distance formula that would be used to find BC is, d =[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Thus, applying the distance formula, we have:
BC = √[(−4 − 8)² + (−2 − (−7))²]
BC = √[(−12)² + (5)²]
BC = √(144 + 25)
BC = √169
BC = 13 units
Therefore, using the distance formula, the length of BC is: 13 units.
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solve for y
7y+16=3y
Answer:7y7=3y-16
Step-by-step explanation:
Solve for
Subtract from both sides
Answer: -4
Step-by-step explanation: Tell me if it's correct. :)
The product of 15 and √2 can be expressed as
15√2. Which of these is a true statement
about the expression 15√2?
Answer:
The alternative form would be ≈ 21.213203
Step-by-step explanation:
8y - 9y = -8 hhhhhhhh
Answer:
-y
Step-by-step explanation:
i did the test
Answer:
Y=8
Step-by-step explanation:
Move all terms that don't contain y to the right side and solve.
When making lasagna, Mr. Singleton uses 1 pound of sausage for every 3/4 of a pound of mozzarella cheese. For a dinner party, Mr. Singleton wants to make an extra lasagna with 1 pound of mozzarella cheese. How much sausage will he need?
Using ratio we can calculate that Mr. Singleton used approximately 1.33 pounds of sausage .
A ratio demonstrates how frequently one number is found within another. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.
A ratio can therefore be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value represented by this fraction. Ratios of counts that are expressed in terms of (non-zero) natural numbers are rational numbers and occasionally natural numbers as well. The ratio of two numbers is a dimensionless number when they are measured using the same unit, which happens frequently. A rate is the product of two quantities that are divided by their respective units of measurement.He uses 1 pound sausage for every 3/4 pound of cheese.
Ratio of sausage to cheese = 1 : 0.75 = 4 : 3 .
Now he uses 1 pound of cheese therefore let he uses x pounds of sausage.
Now using ratio:
x : 1 = 4 : 3
or , x / 1 = 4 / 3
or, x = 1.333..
or, x ≈ 1.33 pounds
Hence he uses 1.33 about pounds of sausage
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