5+2y=13, y-5=2(x-1), y/2 = x+7, x=-4 are linear equations.
What is linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1.
Another name for it is a one-degree equation.
A linear equation with one variable has the conventional form Ax + B = 0.
In this case, the variables x and A are variables, while B is a constant.
A linear equation with two variables has the conventional form Ax + By = C.
Here, the variables x and y, the coefficients A and B, and the constant C are all present.
As explained above about linear equation from given option we can verify that
5+2y = 13 can be written as 2y = 8 or 2y-8=0 which represents linear equation in one variable.
[tex]y = \frac{1}{2x^{2} +7}[/tex] cannot be written in any linear form and its highest degree is 2. So, it is not linear equation.
y-5= 2(x-1) can be written as 2x-y=-3 which is in the form of linear equation in two variables. So, it is linear equation in two variables.
x = -4 can be written as x + 4 = 0 which represents linear equation in one variable.
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A googol is the number 1 followed by 100 zeros. Earths mass is 5.972 x 10 to the 24 power kilograms. How many earths are needed to have a total mass of 1 googol kilograms?
To have a total mass of 1 googol kilograms, 1.674480911 × 10 ⁷⁵ earths are needed
How to determine how many earths are needed to have a total mass of 1 googol kilograms?
Given that:
1 googol = 10¹⁰⁰
Earth's mass is 5.972×10²⁴ kilograms
In order to find how many earths are needed to have a total mass of 1 googol kilograms, you need to divide 1 googol kilograms by Earth's mass (5.972×10²⁴ kilograms). Thus:
Number of earths needed = 10¹⁰⁰ / 5.972×10²⁴
Number of earths needed = 1.674480911 × 10 ⁷⁵ earths
Therefore, 1.674480911 × 10 ⁷⁵ earths are needed to have a total mass of 1 googol kilograms
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There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Answer:
the answer will be the option b
hope this helps you
If a 2b - 10 and b= 3a -5, then what is a?
Answer:
a=4
Step-by-step explanation:
we fill in b to find a
a=2(3a-5)-10
a=6a-10-10
a=6a-20
+20 +20
a+20=6a
-a. -a
20=5a
/5. /5
4=a
hopes this helps
F(x)=2x-7
G(x)=3x²-5x-7
Find:f(g(x))
Express your answer as a polynomial in standard form.
The composition function for the given function f(x) and g(x) is,
f(g(x)) = 6x^2 - 10x - 21.
What is composition of function?
The mathematical operation known as "function composition" takes two functions, f and g, and creates a function, h = g o f, such that h(x) = g. This operation involves applying the function g to the outcome of applying the function f to x.
Given:
f(x) = 2x - 7
g(x) = 3x^2 - 5x - 7
We have to find the composition function f(g(x)).
[tex]f(g(x)) = f(3x^2- 5x - 7)[/tex]
Plug x = 3x^2 - 5x - 7 in f(x).
[tex]f(g(x)) = 2(3x^2 - 5x - 7) - 7\\f(g(x)) = 6x^2 - 10x - 14 - 7\\f(g(x)) = 6x^2 - 10x - 21[/tex]
Hence, the composition function for the given function f(x) and g(x) is, f(g(x)) = 6x^2 - 10x - 21.
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Georgia want to end letter to 12 of her friend. Half of the letter will need 1 page each and the other half will need 2 page each. How many page will be needed altogether?
The total no: of pages needed are 18 pages
What is the unitary method?A fundamental idea behind the unitary method is using the value of one unit to determine the values of additional units. Study up on the unitary method. With an increase in units, the value of additional units rises.
What is unitary set?The general unitary group, also known as the group of unitary similitudes, is simply the product of the unitary group and the group of all positive multiples of the identity matrix. It includes all matrices A such that AA is a nonzero multiple of the identity matrix.
According to the question:-
The no: of pages needed for 6 letters = 6
The no: of pages needed for the other 6 letters= 6*2
=12
Total no: of pages are 18
Hence, the total no: of pages are 18
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Which expression is equivalent to the expression quantity negative 10 over 9 times t plus 1 over 8 end quantity minus expression quantity negative 6 over 18 times t plus 3 over 4 end quantity?
negative 14 over 18 times t minus 5 over 8
negative 14 over 18 times t plus 2 over 8
4 over 9 times t plus 2 over 4
16 over 18 times t plus negative 4 over 8
The expression that is equivalent to the given algebraic expression is; negative 14 over 18 times t minus 5 over 8
How to solve algebraic expressions?We are given the algebraic expression as;
-(10/9)t + (1/8) - [(-6/18)t + (3/4)]
Factorize out 1/72 to get;
(1/72)(-80t + 9 + 24t - 54)
= (1/72)(-45 - 56t)
= (-14/18)t - 5/8
We have used some basic mathematical operations in the expression, it gives us negative 14 over 18 times t minus 5 over 8
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I need to find out what’s given and what’s the reasoning for this statement
1. two-column proof
Given: AB ≅ XY, AC ≅ XZ, BC ≅ YZ
Prove: ∆ABC ≅ ∆XYZ
The other information that must prove by the triangle is that ∠A ≅ ∠X.
How do you understand "ABC" and "DEF"?
The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. applying labels Triangle ABC is congruent to triangle DEF if, in triangles ABC and DEF, angle A = angle D, angle B = angle E, and angle AB = DE.
By SAS or Side-Angle-Side Postulate, the corresponding two sides and it's included angles should be congruent.
Therefore, based on the illustration, the included angle for ∆ABC is ∠A while the included angle for ∆XYZ is ∠X.
Therefore, the other information that must prove by the triangle is that ∠A ≅ ∠X.
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Column A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
-
-
<2 and <3
<2 and <10
<5 and <10
A
<7 and <3
<15 and <10
<14 and <10
<9 and <10
<1 and <6
<15 and <4
<3 and <10
Column B
a. no relationship
b. same side interior
c. linear pair
d. alternate exterior angles
e. alternate interior angles
f. corresponding
g. vertical angles
Answer:
Step-by-step explanation:
what
find the probability that the engineer has to test at least 5 computers in order to find 2 defective ones. g
The probability that the engineer has to test at least 5 computers in order to find 2 defective ones is 0.985.
Given :
A quality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur independently of each other.
So the probability of getting 0 defective computers out of 4 is :
= ( 1 - 0.05 )^4
= 0.95^4
= 0.814.
The probability of getting exactly 1 defective computer out of 4 is :
= 0.05 * ( 1 - 0.05 )^3 * 4! / ( 1! ( 4 - 1 )!)
= 0.05 * 0.95^3 * 24/ ( 1!3! )
= 0.05 * 0.857375 * 24/6
= 0.171.
So the probability of getting only 0 or 1 defective computers out of the 1st 4 is :
= 0.814 + 0.171
= 0.985
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You want to prove a theorem in a two-column proof. You start with your given statement and list deductions in the left-hand column. What are the three main types of reasoning you will use for reasons in the right-hand column?
In an indirect proof, you prove an "if-then" statement is true by assuming the statement is false (stating the inverse or converse), and then disproving the false statement. You want to prove the statement shown below in an indirect proof. What statement should you prove is false? (1 point)
Statement to Prove True: If a figure has exactly three sides, then it is a triangle.
Statement to Prove False
Postulates, corollaries, and common notions are the three main types of reasoning we will use for reasons in the right- hand of column.
What is a two column proof in math?A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.
Postulates, corollaries, and common notions are the three main types of reasoning we will use for reasons in the right- hand of column.
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A plane is flying at a speed of 425 miles per hour. How far will the plane travel in 0.75 hour.
Answer:
318.75 miles
Step-by-step explanation:
Consider the graph shown below.
Write the coordinates of the point CC after a dilation with a scale factor of 55 , centered at the origin.
((
,,
))
Part B
What are the coordinates of the point DD after a dilation with a scale factor of 55, centered at the origin?
(b)
A
D′(0,2)D'\left(0,2\right)D
′
(0,2)
B
D′(0,5)D'\left(0,5\right)D
′
(0,5)
C
D′(0,10)D'\left(0,10\right)D
′
(0,10)
D
D′(10,0)D'\left(10,0\right)D
′
(10,0)
Coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)
Given that,
The point C
C(2, 1)
We have to find what are the coordinates of the point D after a dilation with a scale factor of 5, centered at the origin.
We know that,
The point C
The size of the coordinates of the picture of point P will be 5 times larger than the original coordinates of point C in a dilatation with a scale factor of 5.
The following is the scale factor 5 rule of dilation:
(x, y) → (5x, 5y)
C(2, 1) → (5x, 5y) = (5(2), 5(1)) = C'(10, 5)
Therefore, coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)
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for the 2015 general social survey, a comparison of females and males on the number of hours a day that the subject watched tv gave the following results.
After a comparison of females and males on the number of hours of a day that the subject watched the TV.
The hypotheses of a significance test to analyze whether the population means differ for females and males would be as follows:
(a) H0: μ1 = μ2 (the population means are equal for females and males)
Ha: μ1 ≠ μ2 (the population means are not equal for females and males)
(b) In order to conduct the significance test, we would need to calculate the t-statistic and the P-value. However, the question does not provide the necessary information to do so (e.g. sample means, standard deviations, sample sizes). Without this information, we cannot conduct the significance test and interpret the P-value(c) Without conducting the significance test, we cannot conclude anything about whether there is a gender difference in TV watching.
(d) Similarly, without conducting the significance test and calculating the confidence interval, we cannot determine whether the confidence interval would contain 0 or not.
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A small business produces soap and lotion gift baskets. Labor, utilities, and other fixed expenses
cost $6,000 a month. Each basket costs $8 to produce and sells for $20. How many baskets does
the company need to sell each month to break even?
•
Define n to be the number of gift baskets the company sells in a month
Cost Equation: C(n)= 6000 + 8n
Revenue Equation: R(n) = 20n
Cost
$
12000
11000-
10000+
9000
8000
7000-
6000
5000
4000+
3000
2000
1000-
C(n)
R(n)
100 200 300
400 500 600 700 800
TE
The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.
What is break even point?
In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total revenue are equal, or "even." Although opportunity costs have been paid and capital has received the risk-adjusted, expected return, there is no net loss or gain, and one has "broken even."
In this case we could probably solve the problem from the graph itself, but we can also solve it algebraically by setting the equations equal:
[tex]\begin{gathered}R(n)=C(n) \\20 n=6000+8 n\end{gathered}[/tex]
Subtract 8n from both sides:
[tex]12 n=6000[/tex]
Divide:[tex]n=\frac{6000}{12}=500[/tex]
Evaluate either function at this input: [tex]R(500)=C(500)=10,000[/tex]
The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.
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PLEASE ASAP PLEASE I NEED IT IN A STATEMENTS AND REASONS
In a Kite ABCD the diagonals AC and BD can be proved perpendicular by linear pair perpendicular theorem.
What is linear pair perpendicular theorem?
This theorem states that if two straight lines intersect at a point, and the linear pair of angles they form have an equal measure, then the two lines are perpendicular to each other.
According to the given question:
ABCD is a Kite //Given
AB=BC //Given
BE=BE //Common side, reflexive property of equality
∠ABE ≅ ∠CBE // in a kite the axis of symmetry bisects the angles at
those corners
△ABE≅△CBE //Side-Angle-Side postulate
∠AEB ≅ ∠CEB //Corresponding angles in congruent triangles (CPCTC)
AC⊥BD //Linear Pair Perpendicular Theorem
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using the trap razors below find the measure of angle HMA.
In the given trapezoid, the angle ∠ HMA is 120°.
What is trapezoid?A closed polygon or geometry with four sides, four corners, and four angles is called a trapezium. Each pair of a trapezium's opposing sides is parallel to the other.
In the given trapezoid AMHT,
The angle H = 60°.
To find the angle ∠ HMA,
Since, the sum of angle MHT and angle HMA is equal to 180°.
∠ HMA + ∠ MHT = 180°
∠ HMA + 60 = 180
∠ HMA = 120
The required angle ∠ HMA is 120°.
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Jada has time on the weekends to earn some money. A local bookstore is looking for someone to help sort books and will pay $12.20 an hour. To get to and from the bookstore on a work day, however, Jada would have to spend $7.15 on bus fare.Write an equation that represents Jada’s take-home earnings in dollars, , if she works at the bookstore for hours in one day. One day, Jada takes home $90.45 after working hours and after paying the bus fare. Write an equation to represent this situation. Is 4 a solution to the last equation you wrote? What about 7? If so, be prepared to explain how you know one or both of them are solutions. If not, be prepared to explain why they are not solutions. Then, find the solution. In this situation, what does the solution to the equation tell us?
Equation that represents Jada’s take-home earnings in dollars E = 12.20(h)-7.15
The equation that represents the situation is h=6.82 hours.
What is equation?An equation, a formula that is express the equality of two expressions. The equation is representing direct proportion is , by the commenting them with in the equal sign .
As per the given question
Pay hour = $12.20 per hour
Bus fare = $7.15
1.Equation:
Assume that
She has work for "h" hours
Total earning = E
So, E = 12.20(h) - 7.15
If, Total earning = E = $90.45
So, E = 12.20(h) - 7.15
90.45 = 12.20(h) - 7.15
h = 6.82 hours
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PLS HELP ME ASAP!! 30 points! Which triangle congruence theorem could be used to prove the following two triangles congruent? ASA, SAS, AAS, or not enough info
The best triangle congruent theorem for the image is Angle-Angle-Side (AAS)
How to prove congruency of Triangles?Two triangles are congruent if they have exactly the same three sides and exactly the same three angles.
From triangle ABC,
<BAC is given
<ABC=90⁰
<BCA is not given
Also, in triangle ACD,
<ACD is given
<CDA =90⁰
<DAC is not given
Therefore <BAC=<ACD (given)
<CDA=<ABC=90
<DAC=<BCA (not given)
Therefore, ΔABC=ΔACD (AAS)
In conclusion, The two triangles are congruent with SSA theorem.
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First try was incorrect
What is the value of x? Your answer may be exact or rounded to the
nearest tenth.
(4x-8)"
131*
61"
Answer: 19.5
Step-by-step explanation:
obtuse + acute = 180
131 + t = 180
t = 49 degrees for the top angle
49 + 61 + 4x-8 = 180 degrees in a triangle
110 + 4x - 8 = 180
102 + 4x = 180
4x = 78
x = 19.5
Answer:
x = 19.5
Step-by-step explanation:
The interior angles of a triangle will ALWAYS have a sum of 180°
best answer gets brainliest! please explain
Answer: t = 11
Step-by-step explanation:
f(11)= 5(11) -7
f(11) = 55 - 7
f(11) = 48
Answer:
f(11) = 48
Step-by-step explanation:
f(t) = 5t-7
we have to find out what t is
5t - 7 =48
+7 +7
5t = 55
/5 /5
t = 11
7) What is the better deal? A 12 pack of gatorade for $25.20 or a 15 pack of gatorade for $33?
Answer: 12 pack.
Step-by-step explanation: 25.20 divided by 12 shows us that each gatorade costs 2.1 dollars. Now add the 3 gatorade worth to 25.2. You get 31.5 which is less than 33, showing that 12 pack is more worth as you pay less for 15 aswell.
laura has saved her babysitting money for the past two weeks. currently has 5 time her weekly pay. this week she spent a less then 2 times her weekly pay and now has 156. how much does laura earn each week
Answer:
To find out how much Laura earns each week, you can set up an equation using the information given. Let's call Laura's weekly pay "W".
You know that Laura has saved 5 times her weekly pay, so you can write this as 5W.
You also know that she spent less than 2 times her weekly pay this week, so you can write this as 2W - X, where X is the amount that she spent less than 2 times her weekly pay.
Finally, you know that she has 156 left after spending some money, so you can write this as 156.
You can now set up the equation:
5W + (2W - X) = 156
Combining like terms, you get:
7W - X = 156
Adding X to both sides, you get:
7W = 156 + X
Dividing both sides by 7, you get:
W = (156 + X) / 7
Thus, Laura's weekly pay is equal to (156 + X) / 7. You know that she spent less than 2 times her weekly pay this week, so X must be less than 2W. However, you don't know the exact value of X, so you can't find the exact value of Laura's weekly pay.
:
If laura has saved her babysitting money for the past two weeks then Laura earns 52 dollars per week.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let Laura earns x dollars per week.
According to the problem, after two weeks of saving, she has 5 times her weekly pay, which means she has saved 5x dollars.
This week, she spent less than 2 times her weekly pay, which means she spent less than 2x dollars.
Now, she has 156 dollars left, so we can set up the equation:
5x - 2x = 156
Simplifying this equation, we get:
3x= 156
Divide both sides by 3
x = 52
Hence, Laura earns 52 dollars per week.
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Triangle ABC with coordinates A (4,2), B (-1, 3), and C (2, -3) was reflected across the line
y=x. What is the image of B?
A. (3,-1)
B. (1, -3)
C. (-1, -3)
D. (-3,-1)
Answer:
A. (3,-1)
Step-by-step explanation:
A reflection of y = x would be:
[tex](x,y)\rightarrow(y,x)[/tex]
Therefore:
[tex](-1, 3) \rightarrow (3, -1)[/tex]
The correct option should be A.
Hope this helps.
Can someone Please help me
Answer:
B. none of other works. Only hue rate of change of Function F is higher than Function G
How do I do y=mx+b calculations in these type of questions
pls help
and show me the mx+B calculations
1. y<-3/4x+2
2. y≤5
3. x+y>6
The calculations for the slope-intercept forms of the equations are (1) m=-[tex]\frac{3}{4}[/tex],B=2 (2)m=1, B=5 (3) m=-1, B=6
How to use the Slope -intercept form?
Slope of a line is a number that describes both the direction and the steepness of the line.
The intercept of a line is defined as the point at which it intersects the y-axis in a graph.
The equation of a line is expressed as follows;
Y=MX+B
Where M=slope and B=intercept
From the equations:
(1) y<[tex]\frac{-3x}{4}[/tex]+2
Applying the equation of slope-intercept form,
m=[tex]\frac{-3}{4} , B=2[/tex]
(2) Y[tex]\leq 5[/tex]
Applying the equation: Y=MX+B
m=1, B=5
(3) x+y>6
Applying the formula: Y=MX+B
Re-arrange the equation
y>-x+6(1)
⇒ m=-1, B=6
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i dont get this help
Answer:
x = 11
Explanation:
It looks like the total distance between points I and K is -3 + x. Since I to J and J to K is also the total distance, I to K is also equal to 6 + 2x - 20. You can represent this in an equation and solve for x.
-3 + x = 6 + 2x - 20
-3 + x = 2x - 14
- 3 = x - 14
11 = x
Kyle ran the width of a field, a ditance of 35 meter. Then he ran the length of the field, a ditance of 84 meter. Finally, he ran diagonally acro it to get back to hi tarting point. How far did Kyle run?
By using Pythagoras theorem, Kyle run for the distance of 210 m.
What is the Pythagorean theorem ?
According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.
Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.
The given length of the field is 84 m.
And, the width is 35 m.
Now, the diagonal of the field can be calculated using Pythagoras theorem as below,
Diagonal = √((84)² +(35)²)
= 91
Then, the total length is found by summing the length, width and the diagonal as below,
= 84 + 35 + 91
= 210
Hence, Kyle run for the distance of 210 m.
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Solve each system by elimination: 8x-3y=-11 2x-5y=27
Answer:
(-4,-7)
Step-by-step explanation:
8x - 3y = -11
2x - 5y = 27
8x - 3y = -11
4(2x - 5y) = 27 (4)
8x - 3y = -11
8x - 20y =108
8x - 8x = 0
-3y - (-20y) = 17y
- 11 - 108 = -119
17y = -119
17/17 y = -119/17
y = - 7
2x - 5(-7) = 27
2x + 35 = 27
2x = 27 - 35
2x = - 8
2/2 x = -8/2
x = -4
Adriano mixed 19/24 pound of butter with 3/16 pound of honey he ay that he ued 16/8 pound of butter than honey i hi tatement reaonable
The statements that Adriano mixed 19/24 pound of butter with 3/16 pound of honey he ay that he ued 16/8 pound of butter than honey is not reasonable.
what is mixture?A mixture is a substance made of two or more additional chemical compounds or substances that do not chemically combine. It is actually the physical blending of two or more substances so that they can still be distinguished from one another when combined as solutions, suspensions, or colloids. Physical means can be used to separate them. The different components in any mixture are not created through any sort of chemical transformation. As a result, each component's unique properties are unaltered.
A mixture's constituent parts also do not combine chemically to form new material, in contrast to a compound. Instead, they just combine while retaining their individual traits. because there are variable quantities of the components
Ratio 19/24 is nearby ¾
Ratio 3/16 is nearby ¼
And ratio 16/8 is nearby 2
So, that his statements is not reasonable.
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