The polynomial function, x² + 7 is prime
What is a polynomial?
A polynomial is an expression in mathematics that consists of indeterminates (also known as variables) and coefficients and includes only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x² + 4x + 7 is an example of a polynomial with a single indeterminate x. In three variables, consider x³ + 2xyz² - yz + 1.
The polynomial function, x² + 7 is prime.
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Complete the equation of the line through
10, 3) and
8, 8).
Use exact numbers.
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{10}}} \implies \cfrac{ 5 }{ -2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{5}{2}}(x-\stackrel{x_1}{10}) \\\\\\ y-3=-\cfrac{5}{2}x+25\implies {\Large \begin{array}{llll} y=-\cfrac{5}{2}x+28 \end{array}}[/tex]
Expand
7(9- f)
How do I do it
Answer:
firstly we need multiply out the bracket.
7×9=63
7×f= 7f.
then you subtract 63-7f= 56
your answer is 56
What are the domain and range of the function below?
The domain of the given function is (-∞,5) and the range is (5,∞).
What are domain and range?All the independent variable, x, for which y is defined, is the domain and range of a function. Every possible value of the dependent variable y comes within a function's range.
From the graph, we can see that x varies from -∞ to -5
So, the domain is the interval of (-∞,-5)
The function of f(x) varies from (5,∞)
So, the range is (5,∞).
Therefore, the domain of the given function is (-∞,-5) and the range is (5,∞).
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Which of these types of income is taxed? A federal tax refunds B interest on savings account C interest from municipal bonds
Answer:
the answer is A
Step-by-step explanation: the reason i said A is because the answer is litteraly in the question if you think about it
Nora bought 8-½ pounds of potatoes for $27.63.
What is the price, in dollars, of 1 lb of potatoes?
Answer:
$3.25
Step-by-step explanation:
This question tests on the concept of conversion.
Given from the question,
8.5 pounds = $27.63
(8.5 ÷ 8.5) pounds = $27.63 ÷ 8.5
1 pound = $3.25 (Rounded off to 2 decimal places)
suppose that a poll finds that % of taxpayers who filed their tax return electronically self-prepared their taxes. if three tax returns submitted electronically are randomly selected, what is the probability that all three were self-prepared?
The probability that the three tax returns submitted were self-prepared is 0.0325.
What do we mean by probability?The probability is the likelihood that something will happen, to put it simply.The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out.The study of events that fit into a probability distribution is known as statistics.Both the overall number of favorable outcomes and the likelihood of any specific event are interdependent.A typical definition of probability is the ratio of favorable outcomes to all other outcomes in the sample space.Probability of an Event P(E) = (Number of favorable outcomes) ÷ (Sample space).So, the formula for the binomial probability distribution of x successes in n tries:
[tex]P(X=x)={ }^n C_x p^x(1-p)^{n-x}[/tex]Where the probability of success is p, and n is the number of trials.
If three electronically filed tax returns are randomly chosen, the likelihood that all three were prepared by the taxpayer is given by:
P(X = 3) = ³ C₃ (0.319)³ (1 - 0.319)³⁻³= (1)(0.319)³(1)= 0.032461759 = 0.0325Therefore, the probability that the three tax returns submitted were self-prepared is 0.0325.
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The correct question is given below:
Suppose that a poll finds that 31.9% of taxpayers who filed their tax returns electronically self-prepared their taxes. If three tax returns submitted electronically are randomly selected, what is the probability that all three were self-prepared?
Anyone know the answer for this
Answer: x=17
Step-by-step explanation:
1.Identify relationship
Since both the angles are on the inside of both parallel lines and on the same side of the transversal you know that you have a same side interior relationship that makes them supplementary
2. set up equation
because they are supplementary you know that they are equal to 180 which gives the equation: 3x+6+123=180
3. solve the equation
3x+6+123=180
3x+129=180 | combine like terms
3x=51 | subtract 123 from both sides
x=17 | divide by 3 on both sides
susanne checks the temp. at 11:00am she notices that if the temp. rises by 8 more degrees it will break the record high temp. for the day witch is 82 degreese
The current temperature based on the information given about Sussane is 74°.
What is temperature?It should be noted that temperature is used to illustrate the hotness and the coldness that's in a a particular body.
Let the current temperature be represented as x.
Since Susanne checks the temp. at 11:00am and she notices that if the temp. rises by 8 more degrees it will break the record high temp. for the day witch is 82 degrees, the current temperature will be:
x + 8 = 82
x = 82 - 8
x = 74°
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I'm not sure , hellp
In the given parallelogram,
∠W = 85°
∠WXV = 59°
Since, VW is parallel to XY,
So,
∠YVX = ∠WXV ............... (Alternate interior angles)
⇒ ∠YVX = 59°
Now,
∠W = ∠Y .................. (Opposite angles of a parallelogram are equal)
⇒ ∠Y = 85°
As we know that opposite sides of a parallelogram are equal,
Therefore,
VW = YX
⇒ 2x = 6
⇒ x = 6/2 = 3 units
What is a Parallelogram?A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides.In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. The Euclidean parallel postulate, or one of its equivalent formulations, is a necessary precondition for both the congruence of opposite sides and opposite angles, and neither condition can be demonstrated without using it.The parallelepiped is a parallelogram's three-dimensional equivalent.Order 2 rotational symmetry (through 180°) is present in a parallelogram (or order 4 if a square). The shape must be either a rhombus or an oblong if it also possesses precisely two lines of reflectional symmetry (a non-square rectangle). A square object is one with four lines of reflectional symmetry.
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The perimeter of the rectangle below is 144 units. Find the length of side RS.
The numerical value of side RS of the rectangle with a perimeter of 144 units is 30 units.
What is the numerical length of RS in the given rectangle?A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The perimeter of a rectangle is expressed as;
P = 2( l + w )
Given the data in the question;
Perimeter of the rectangle P = 144 unitsLength RQ = 4z + 2Width RS = 3zz = ?First we determine the value of the variable z, plug the given values into the perimeter formula and solve for z.
P = 2( l + w )
144 = 2( (4z + 2 ) + (3z) )
144 = 2( 4z + 2+ 3z )
144 = 2( 7z + 2 )
144 = 14z + 4
14z = 144 - 4
14z = 140
z = 140/14
z = 10
Now, find the numerical value of side RS.
Width RS = 3z
RS = 3( 10 )
RS = 30
Therefore, the length of side RS of the rectangle is 30 units.
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Charles buys 50 packs of pens.
There are 15 pens in each pack.
Each pack costs £4.20.
Charles sells each pen for 60p but he only manages to sell of the pens.
How much profit did he make?
By using the method of subtraction, the profit earned by charles is £4.8
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
There are 15 pens in each pack.
Each pack costs £4.20.
Charles sells each pen for 60p but he only manages to sell of the pens.
60p x 15 = 9
So, the profit earned by charles is 9- 4.20 = 4.8
Therefore, the profit earned by charles is £4.8
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I need help with this.
Answer:
2533 km/hr
Step-by-step explanation:
time = 8 hours 30 minutes
[tex]\sf = 8\dfrac{1}{2} \ hours\\\\ =\dfrac{17}{2} \ hours[/tex]
Distance = 298 km
[tex]\sf \boxed{\bf Average \ speed = Distance * time}[/tex]
[tex]\sf = 298 * \dfrac{17}{2}\\\\ = 149 * 17\\\\= 2533 \ km / hr[/tex]
Multiplying Rational Numbers -2/3 (-1/5)
Answer:
[tex]{ \rm{ - \frac{2}{3}( - \frac{1}{5} ) }} \\ \\ = { \rm{( - 1 \times - 1)( \frac{2}{3} \times \frac{1}{5} )}} \\ \\ = { \rm{( \frac{2 \times 1}{3 \times 5} )}} \\ \\ = { \rm{ \frac{2}{15} }}[/tex]
Answer: [tex]\frac{2}{15}[/tex]
Step-by-step explanation:
1. Simplify the expression
[tex]-2/3(-1/5)[/tex]
2. Multiply the fractions
[tex]\frac{\left(-2\cdot -1\right)}{\left(3\cdot 5\right)}\\[/tex]
3. Simplify the arithmetic
[tex]\frac{2}{\left(3\cdot 5\right)}[/tex]
4. Simplify the arithmetic
[tex]\frac{2}{15}[/tex]
Jason was paid 10 cents for every golf ball he found and brought back to the shop.
Answer: C.
Step-by-step explanation:
X would represent the number of golf balls he brought back and .10 is the amount of money he makes for each of them.
Answer:
0.10x
Step-by-step explanation:
x stands for the amount of golf balls he brings back to the shop and 0.10 stands for the 10 cents he gets paid for each ball.
The art department is planning a trip to a museum. The bus costs $100 plus $7 per student. A professor donated $40 to defray the costs. If the school charges students 10$ each, how many students need to go on the trip not to lose money?
Total 20 students should go to the trip to not to lose money.
Cost of bus = 100 dollars
For students the charge is 7 dollars per student.
Amount professor donated to defray the cost is 40 dollars.
School is charging 10 dollars per student for the trip.
Therefore, reduced cost = 100 - 40 = 60 dollars
Profit earned from each student is 10 - 7 = 3 dollars.
Hence, minimum students should go to the trip will be 60 ÷ 3 = 20.
Since, 20 × 3 = 60, the cost is covered and no money is lost.
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What is the next digit in the quotient?
5?
8)4184
-40
18
————
Answer: 2
Step-by-step explanation:
The greatest divisor of 8 that is less than 18 is 16, and 16 divided by 8 is 2.
The next digit of quotient is 16.
Here given that,
4184 is divisible by 8
since we know that,
Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.
4184 is divisible by 8 we get,
⇒ 4148/8
⇒ 516
So, the quotient is 516
Hence,
The next digit is 16.
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i) in a certain county there are two political parties, liberal and conservative. it has been observed that between elections a fixed percentage, 45% of liberals switch to the conservative party and a fixed percentage, 32% of conservatives switch to the liberal party. the other voters remain in the same party. assume that there are altogether 7700 eligible voters in the county.
In linear equation, Number of members in liberal party = 32 * 77 = 2464
What does the term "linear equation" mean?
A mathematical function where the variables only occur in the first degree, where the constants are multiplied, and where the only possible combinations are addition and subtraction.
45% Of liberals switch to the conservative party
total number of eligible votes in the country =7700
Number of members change to liberal to conservative = 45% of 7700
= 45/100 * 7700
= 45 * 77 = 3465
32% of conservative switch to the liberals party = 32 % of 7700
= 32/100 * 7700
Number of members in liberal party = 32 * 77 = 2464
An equilibrium in campain contributions one for the each party among the set of contribution to the party.
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The complete question is -
in a certain county there are two political parties, liberal and conservative. it has been observed that between elections a fixed percentage, 45% of liberals switch to the conservative party and a fixed percentage, 32% of conservatives switch to the liberal party. the other voters remain in the same party. assume that there are altogether 7700 eligible voters in the county. Find the equilibrium Values for the system if any?
A local charity raised $7,280 selling T-shirts. Each T-shirt cost $16
Answer:
most have 455 T-shirts
Step-by-step explanation:
if u do $7,280÷$16= 455
Answer:most have 455 T-shirts
Step-by-step explanation:if u do $7,280÷$16=
If you plot the point - 8.85 on a number line, would you place it to the left or right of -8.8? Explain
If you plot the point, - 8.85 on the number line you would put it left of -8.8
- 8.85 is left of -8.8
This is further explained below.
What is a number line?Generally, A image of a graded straight line is what is known as a number line, and its purpose is to provide a visual representation of the actual numbers. It is generally accepted that a real number may be assigned to each point on a number line, and that each point can be assigned to a real number.
In conclusion, The number line follows natural arithmetic rules, Hence
Since
-3,-2,-1,0,1,2,3 is the sequence of the natural arithmetic rules hence,
- 8.85 is left of -8.8
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Keiko is trying to score in the “ryō” range in her math class which is above a 70. Her test scores so far are an 85, 57, and 78. What is the lowest score that she can get on her next test in order to stay in the ryō range when her scores are averaged?
What's the inequality for this story?
Write the steps to solve it
What is the solution?
When this inequality is graphed will the limit be an open or closed circle?
When this inequality is graphed will the line have an arrow pointing to the right or to the left
The lowest score that Keiko is trying to score to get in the "ryo" range is , the inequality to represent this story is (x+85+57+78)/4 > 70 .
In the question ,
it is given that
Keiko need to score average above 70 to get in the ryo range
let x be the marks that Keiko scores in the next test ,
so, the average = (x+85+57+78)/4
According to the question
Average > 70
Substituting the value of average , the inequality becomes
(x+85+57+78)/4 > 70
x+85+57+78 > 280
x+220 > 280
x > 280-220
x > 60
the lowest score that Keiko should get is greater than 60 .
When the inequality x > 60 , will be graphed then the limit will be an open circle as equal to sign is not included in the inequality .
as when the numbers increases , it move towards right side
So, When the inequality is graphed, the line will have an arrow pointing towards the right .
Therefore , the lowest score that Keiko is trying to score to get in the "ryo" range is , the inequality to represent this story is greater than 60 ,
the inequality to represent this story is (x+85+57+78)/4 > 70 ,
the limit of graph will be open circle and arrow will be pointing towards right .
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The cost of 2 rugby balls and 3 golf balls is £18.39.
The cost of 5 rugby balls and 7 golf balls is £45.10.
Work out the cost of
a) a rugby ball.
b) a golf ball.
The cost of a rugby ball is $6.57
The cost of a golf ball is $1.75
How to calculate the cost of a rugby and golf ball ?Let x represent the cost of a rugby ball and y represent the cost of a golf ball
2x + 3y= 18.39.........equation 1
5x + 7y= 45.10.........equation 2
multiply equation 1 by 5 and equation 2 by 2
10x + 15y= 91.95
-
10x + 14y= 90.2
y= 1.75
Substitute 1.75 for y in equation 2
5x + 7(1.75)= 45.10
5x + 12.25= 45.10
5x= 45.10-12.25
5x= 32.85
x= 32.85/5
x= 6.57
Hence the cost of a rugby ball is $6.57 and the cost of a golf ball is $1.75
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( Please help )
Answer the question in photo.
Fred says that the two equations below have the same solution:
Equation A: -3 (x+9)= 18
Equation B: x +9=-6
Describe the acceptable move that proves the two equations are equivalent.
Yes the acceptable move that proves the two equation are equivalent.
What is equivalent equation?
equivalent equation are algebraic equations that have identical solutions or roots. Adding or substracting the same number or expression to both side of an equation produce an equivalent equation. Systems of equations that have the same solutions are said to be equivalent equations. Finding and resolving equivalent equations is an important skill for everyday life as well as for algebra classes. Consider some illustrations of equivalent equations, how to solve them for one or more variables, and practical applications of this knowledge.
Sol-
By observing both equations
In equation A : -3(x+9)=18
Divide the equation A by -3
=> (x+9)=-6
And this result equals to equation B
Hence both equations are equivalent
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HELP PLS I NEED THIS DONE BY TOMORROW!!
PLS BE 100% CORRECT
The answer to the following verbal expressions of inequality are:
A: x ≤ 69;
B: The option that shows the graph of the inequality d<2 is Option C.
C: The option that shows the graph of the inequality of x ≤ 5 is option B.
D: represents the graph of the inequality given in option C that is x > -8
E: The inequality that describes the situation is ≥ 49 (Option B)
What is inequality?In mathematics, inequality is defined as a declaration of an order connection between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
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Please answer this question :) Need Help!
Answer:
Step 3, she forgot to square half of the middle term before adding it to both
sides.
Step-by-step explanation:
yw
How do you solve this equation x²=36
You can see the following steps to know the solvation
x² = 36
x = √36
x = 6.
3. In the diagram below the grey shapes have the same area. Work out the value of x.
Answer:
x = 7 units
Step-by-step explanation:
Left area = (3x-1)(4)
Right area = 8*12 - (4 ( x -3)) and the areas are =
(3x-1)4 = 8*12 - ( 4(x-3)) expand both sides
12x - 4 = 96 - 4x + 12 solve for x = 7 units
Answer:
Area of big rectangle: 8 x 12 =96
Area of white part : 4(x-3)
96-(4(x-3))
96-(4x-12)
96-4x+12
Area of rectangular grey part: 108-4x
Area of other grey figure:
4(3x-1)
= 12x- 4
Finding x:
12x-4 = 108 -4x
-4-108 = -4x - 12x
112 = 16x
x= 7
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Gabril has a roll of tape that is 4 1/2 yd long.He cuts the tape into pieces that are each 3/2 yd long
The number of tapes cut is 3 pieces.
How to find the number of pieces of tape cut?He has a roll of tape that is 4 1/2 yard long.
He cuts the tape into pieces that are each 3/2 yard long.
Therefore, the number of roll of tape cut can be calculated as follows:
Initial length of the tape in yard = 4 1 / 2 = 9 / 2 yards
Length of the tape cut in yard = 3 /2 yards
Hence,
number of tape cut = 9 / 2 ÷ 3 / 2
number of tape cut = 9 / 2 × 2 / 3
number of tape cut = 9 / 3
number of tape cut = 3 pieces
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3.
7 ft
8.7 ft
10 ft
566567889988766433678
Margo can purchase tile at a store for $0.89 per tile and rent a tile saw for $56. At another store she can
borrow the tile saw for free if she buys tiles there for $1.59 per tile. How many tiles must she buy for the
cost to be the same at both stores?
Marco must buy
tiles for the cost to be the same at both stores.
Answer:
80
Step-by-step explanation:
Use trial and error until you find a common multiple.