Answer:
12(x+y)=42
60(y-x)=42
Step-by-step explanation:
12(x+y)=42 (12 seconds, x+y speed each second, 42 metres)
60(y-x)=42 (1 minute = 60 seconds, x-y speed each second, 42 metres)
f(x) = 7x + 1 - 8
g(x) = -2
Find (f - g)(x).
A. (f-g)(x) = |7x - 5|
B. (f-g)(x) = 7x - 7+2
C. (f-g)(x) = |7x| - 5
D. (f-g)(x) = |7x+1-6
Answer: 7x-5
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)=(7x+1-8)-(-2)=\boxed{7x-5}[/tex]
Answer:
D. (f-g)(x) = |7x+1|-6
Step-by-step explanation:
f(x) = |7x + 1| - 8
g(x) = -2
(f - g)(x) = f(x) - g(x) = |7x + 1| - 8 - (-2)
(f-g)(x) = |7x + 1| - 6
Mrs. Carpenter's class is dividing into groups for group work. There are 28 students in the class and 35
desks.
How many students will be in each group if there are 7 equal groups?
Answer:
Step-by-step explanation:
Solution
There are 28 students
There are 7 equal groups
There must by 28/7 = 4
Answer
Each group will have 4 students in it..
A student takes a multiple-choice test that has 12 questions. Each question has five choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly.
The probability that the student will answer 5 correct questions is; P(5) = 0.053
How to solve binomial probability problems?The formula for binomial probability is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
Where;
p = probability of success.
n = number of trials, or the sample size.
x = the number of successes in the probability we are trying to calculate.
Now, we want to find P(5). We are given;
n = 12
x = 5
p = 1/5 = 0.2
Thus;
P(5) = 12C5 * (0.2)⁵ * (1 - 0.2)⁽¹² ⁻ ⁵⁾
P(5) = 0.053
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WORTH 100 POINTS!!!
The indirect proof is unlike the proofs taught during the beginning chapters of geometry. Before you can begin an indirect proof it is important to determine the steps that you will follow. Please put the steps of the indirect proof in the correct order from beginning to end.
1.
2.
3.
4.
5.
1) Identify the statement you want to prove is true
2) Assume temporarily that the statement is false; assume the opposite is true
3) Obtain statements that logically follow from your assumption.
4) Reason logically until you reach a contradiction of a known fact.
5) Point out that your assumption must be false, and the statement must then be true.
provide two more examples of relationship patterns found in mathematics and describe the pattern in each case
The examples of relationship patterns found in mathematics are arithmetic sequence and geometric sequence.
How to depict the sequence?It should be noted that an arithmetic sequence has a common difference. An example is given as: 2, 4, 6, 8. There's a common difference of 2.
For the geometric progression, there's a common ratio. A example is 2, 4, 8, 16, 32. Here, there's a cookie ratio of 2 when the numbers are divided.
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14,392•7 what is the answer step by step
Answer:
100744
Step-by-step explanation:
14392
7
______
4 (carry the 1)
14392
7
______
44 (carry the 6)
14392
7
______
744 ( carry the 2)
14329
7
______
0744 (carry the 3)
14329
7
______
100744 (final answer)
Which of the following choices will evaluate the expression a2 + b when a = 2 and b = 3?
7 evaluates the expression a2 + b.
option a.7 is the correct choice which evaluates the given expression.
Given values are a = 2 and b =3
the given expression is = a2 + b
To evaluate an expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.
Substitute these value in the given expression.
=2 × 2 ₊ 3
=7
Every time we replace the variables with its values we get the answer as 7. The other options present does not satisfy the equation.
For ex: 25 , we don't get this number when we substitute the given values in the expression. 10 is also not what we get when we solve the expression. Likewise other options are also invalid.
Hence we get the answer as 7.
Your question is incomplete. Please find the missing content here.
Which of the following choices will evaluate the expression a2 + b when a = 2 and b = 3?
a. 7
b. 10
c. 25
d. None of these choices are correct
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What are the factors of the trinomial?
(x + 1) and (x – 4)
(x + 4) and (x – 1)
(x + 5) and (x – 4)
(x + 4) and (x – 5)
The factors of the trinomial to the given quadratic expression are (x+1) and (x-4)
Factoring quadratic equationGiven the quadratic equation below
f(x) = x^2 - 3x - 4
Factorize
f(x) = x^2 - 4x + x - 4 = 0
f(x) = x(x - 4) + 1(x - 4) = 0
(x+1)(x-4) = 0
Hence the factors of the trinomial to the given quadratic expression are (x+1) and (x-4)
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draw a basic market graph. Title it the market for the product in your news article. Label axes, curves, eqilibruim price and equilibrium quantity
The basic market graph is attached below.
What do you mean by market equilibrium?A market is said to have reached equilibrium price when the supply of goods matches demand.
The equilibrium price is the only price where the plans of consumers and the plans of producers agree, where the amount consumers want to buy of the product, quantity demanded, is equal to the amount producers want to sell, quantity supplied. This common quantity is called the equilibrium quantity.
Quantity of gasoline:
Explanation of graph: The demand curve, D, and the supply curve, S, intersect at the equilibrium point E, with an equilibrium price of 1.4 dollars and an equilibrium quantity of 600.
The equilibrium is the only price where quantity demanded is equal to quantity supplied. At a price above equilibrium, like 1.8 dollars, quantity supplied exceeds the quantity demanded, so there is excess supply.
At a price below equilibrium, such as 1.2 dollars, quantity demanded exceeds quantity supplied, so there is excess demand.
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A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x2−10x+25 yd2.
The length of the flagpole is x - 5 yards
How to determine the length of the flagpole?The complete question is in the image
The area of the flagpole is given as:
Area = x^2 - 10x + 25
Expand the expression
Area = x^2 - 5x -5x + 25
Factorize the expression
Area = (x - 5)(x - 5)
Express as squares
Area =(x - 5)^2
The area of a square is
Area = Length^2
So, we have:
Length = x - 5
Hence, the length of the flagpole is x - 5 yards
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(01.05 LC)
Which of the following is an equivalent form of the compound inequality −44 > −2x − 8 ≥ −48?
−2x − 8 > −44 and −2x − 8 ≥ −48
−2x > −44 and −8 ≥ −48
−2x − 8 < −44 and −2x − 8 ≤ −48
−2x − 8 < −44 and −2x − 8 ≥ −48
The equivalent form of the compound inequality are −2x − 8 < -44 and −2x − 8 ≥ −4
Compound inequalityInequality are expression not separated by an equal sign. Given the compound inequality
−44 > −2x − 8 ≥ −48?
Add 8 to all the sides
−44 + 8> −2x − 8+8 ≥ −48 + 8
−36 > −2x ≥ −40
This can be also be written as
−44 > −2x − 8 and −2x − 8 ≥ −48
Changing the sides will change the sign to have
−2x − 8 < -44 and −2x − 8 ≥ −48
Hence the equivalent form of the compound inequality are −2x − 8 < -44 and −2x − 8 ≥ −4
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Find a in degrees.
3
V58
7
?
Answer:
23.20°
Step-by-step explanation:
All three sides of this right triangle are given, so the acute angle of interest can be found using any of the inverse trig functions.
Trig relationThe tangent of the angle is the ratio of opposite and adjacent sides:
Tan = Opposite/Adjacent
Here, that means ...
tan(α) = 3/7
To find the value of α, we need to use the inverse tangent function, also called the arctangent function.
α = arctan(3/7) ≈ 23.19859°
α≈ 23.20°
the function f(x)= x1/3 is transformed to get function h. h(x)= (2x)1/3+5 which statements are true about function h
The transformation of a function may involve any change. The function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f(\dfrac{x}{k})The function f(x)=x^(1/3) is transformed to form the function of h(x)=(2x)^(1/3)+5. Therefore, the transformation made to the function is,
Vertically stretched by a factor of 2^(1/3) ⇒ 2^(1/3) × x^(1/3) = (2x)^(1/3)
Up by 5 units ⇒ (2x)^(1/3) + 5
Hence, the function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
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solve the equation using complete square method x²-x-2=0
The values of x in x²-x-2=0 are x = 2 or -1
How to solve the equation?The equation is given as:
x²-x-2=0
Add 2 to both sides
x² - x = 2
Take the coefficient of x
k = -1
Divide by 2
k/2 = -1/2
Square both sides
(k/2)² = 1/4
Add 1/4 to both sides of x² - x = 2
x² - x + 1/4= 2 + 1/4
Evaluate
x² - x + 1/4= 9/4
Express as perfect square
(x - 1/2)² = 9/4
Take the square roots
x - 1/2 = ±3/2
This gives
x = 1/2 ±3/2
Evaluate
x = 2 or -1
Hence, the values of x in x²-x-2=0 are x = 2 or -1
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A coal car on a train weighs 30 tons plus 1 ton per cubic yard of coal x that it carries. The total weight of a coal car is: f(x)=x+30. How will the graph of this function change if the coal car weight is changed to 26 tons?
Answer: Then the graph of the function f(x) will change shifting vertically down (because the negative sign in 4) by 4 tons.
It cost Allison $5.80 to send 58 text messages. How much would it cost to send 40 text messages?
Answer:
4$
Step-by-step explanation:
The ratio between the $5.80 spent for 58 text messages is $0.10. This means that each text message sent is $0.10. So you just multiply $0.10 and 40 text messages to find that it costs $4 to send 40 messages.
Simplify.
(2 + 8i) + (3 + 8i)
Answer:
Step-by-step explanation:
5+16i
Answer:
5 + 16i
Step-by-step explanation:
(2 + 8i) + (3 + 8i)
• Collect the like terms:
2 + 3 + 8i + 8i
⇒ 5 + 16i
The square of the product of 6 and a number.
The statement, square of the product of 6 and a number can be written as 6x²
Mathematical expressionProduct = multiplication (×)let
x = unknown number
product of 6 and a number= 6 × x
= 6x
square of the product of 6 and a number= 6x²
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In a plane, if line ℓ is perpendicular to line m and _____, then ℓ ⊥ n.
Answer:
n
Step-by-step explanation:
Children develop spatial awareness as they hear position words when you give directions or narrate as children demonstrate the action in their play. Which of the following demonstrate narration as Bailey plays on the slide?
A.Teacher : Good job Bailey , You are a great climber.
B. Teacher : Bailey you are climbing up the ladder to the top of the slide and now you are going down the slide.
C. Teacher: Bailey, be sure to wait your turn and be careful up there
In the equation 4x-2=3x+1, what is the value of x with which the expressions 4x-2=3x+1 represent the same number? with everything and multiplications please give crown
[tex]\sf{\qquad\qquad\huge\underline{{\sf Answer}}}[/tex]
An equation is called any equality that contains one or more unknown quantities, which are called unknowns, and that are only generally verified for certain values of the unknowns.
Thus, for example: 4x - 2 = 3x + 1~4x−2=3x+1 is an equation because it is an equality in which there is one unknown, xx .
⇝Equation resolution:
[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1
[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1[/tex]
We transpose the term 3x to the first member.
3x to the first member.We will have:
[tex] \qquad \sf \dashrightarrow4x - 2 - 3x = 14x−2−3x=1[/tex]
Next we transpose the term -2 to the second member.
We will have:
[tex] \qquad \sf \dashrightarrow4x - 3x = 1 + 24x−3x=1+2[/tex]
[tex] \qquad \sf \dashrightarrow \: x = 3x = 3[/tex]
Let's check that x = 3x=3 satisfies the given equation:
[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1[/tex]
[tex] \qquad \sf \dashrightarrow4(3) - 2 = 3(3) + 14(3)−2=3(3)+1[/tex]
[tex] \qquad \sf \dashrightarrow12 - 2 =9+ 112−2=9+1[/tex]
[tex] \qquad \sf \dashrightarrow10 = 10 \: \: \: \: \:10=10[/tex]
That is, 10 = 10, as we wanted to verify.
I hope I've helped : )
Answer:
The value of x is 3
When x = 3 then both the LHS and RHS of the equation equal to the same number; 10.
Step-by-step explanation:
[tex]4x - 2 = 3x + 1 \\ 4x - 3x = 1 + 2 \\ x = 3 \\ [/tex]
When we substitute the value for x in the expression, we see that the expression represents the same number. i.e
[tex]4x - 2 = 3x + 1 \\ 4(3) - 2 = 3(3) + 1 \\ 12 - 2 = 9 + 1 \\10 = 10 \\ [/tex]
Which equation shows that the pythagorean identity is true for 0=3n/2 ?
Answer:
d
Step-by-step expladnation:
Find the magnitude of −3i
.
Answer:What is the magnitude of 3i?
3i invested c.
Step-by-step explanation: $182m in Magnitude Software in 2019 to accelerate its global growth ambitions through new product development and investments in sales & marketing, and to build a more integrated enterprise software business.
which table represents a linear function? x=1,2,3,4 y=3,7,11,15 x=1,2,3,4 y=3,8,15,21 x=1,2,3,4, y=3,9,3,9 x=1,2,3,4 y=3,9,27,81?
Answer:
x=1,2,3,4 y=3,7,11,15
firstly find d such that d=7-3=4
afunction f(x)= 3+4(x-1)
and x= 1,2,3,4 y=3,9,27,81
y=x²
Find the natural antilogarithm of the given logarithm. 0.0058887
The natural antilogarithm of the given logarithm can be evaluated as; 1.014.
What is the natural antilogarithm of the number?The natural logarithm of the number given in the task content can be evaluated by multiplying by 2.303 as follows;
Natural logarithm value is; 2.303 × 0.0058887
= 0.01356.
On this note, it follows that the natural antilogarithm of the result can be evaluated as;
= 1.014.
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Solve the inequality.
8(x/4-6)>4
[10 points]
Simplify both sides of the inequality.
2x - 48 ≥ 4Add 48 to both sides.
2x - 48 + 48 ≥ 4 + 482x ≥ 52Divide both sides by 2.
[tex]\bf{\dfrac{2x }{2}\geq \dfrac{52}{2} }[/tex][tex]\bf{x\geq 26 \ \ \to \ \ \ Answer}[/tex]Therefore, the correct option is "D".
{ Pisces04 }Solve the inequality. 8(x/4-6)>4
O A. × ≥ 11
O B. × ≥ 5
O C. × ≥ - 22
∅ D. × ≥ 26
Given 8(×/4-6)>4
then simplify both sides of the inequality
[ 2 × - 48 ≥ 4 ]
Add 48 to both sides
[ 2 × ≥ 52 ]
Devide both sides by 2
[ 2×/2 ≥ 52/2 ] = [ × ≥ 26 ]
CarryOnLearning <(￣︶￣)>
Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?
Answer the questions to show how to write and simplify expressions that represent the problem.
Answer:
$4.5
Step-by-step explanation:
We apply sales tax to the total cost, which in this case is $40 + $50 = $90.
Thus, we have 5% * $90 = $4.5
It even works individually if you apply the tax to both orders separately and add them together:
(50 * 5%) + (40 * 5%) = 4.5
2.5 + 2 = 4.5
an angle is equal to five times of its complementary angles, find the angle
Answer:
75°Step-by-step explanation:
the sum is 90°add 5 + 1 to find the units5 + 1 = 6 units
divide 90 ° by 6 to find the value of one unit90 : 6 = 15 (one unit)
multiply the result by five to find the angle15 * 5 = 75°
Geometry worded problem
What is the total cost of material for bunny costumes?
Answer: $201.81
Step-by-step explanation:
The total amount of faux fur required is [tex]6(3.1)=18.6[/tex] square yards.
Multiplying this by $10.85 per square yard, we get the total cost is [tex](18.6)(10.85)=\$201.81[/tex]
NOTE: Angles not necessarily drawn to scale.
Answer:
x = 45°
Step-by-step explanation:
Vertical Angle Theorem
When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent (equal).
From inspection of the given diagram, the straight line with points C and D and the straight line with points F and G intersect at point E.
Therefore, angles ∠FEC and ∠DEG are vertically opposite, and so they are equal.
From inspection of the diagram:
∠FEC = x°∠DEG = 20° + 25° = 45°Therefore:
⇒ ∠FEC =∠DEG
⇒ x = 45°