The 8 problem-solving strategies are Draw a picture, Guess and check, Make a list, Make a table, Act it out, Work backward, Write a number sentence and Use objects.
8 problem-solving strategies are :
Draw a picture - Will a drawing assist me in comprehending and resolving the issue?Guess and check - Input numbers. Is the response logical? If not, try again using a different set of numbers.Make a listMake a tableAct it out - Grab a buddy and act out the word puzzle.Work backward - Work backward from the most recent piece of information.Write a number sentence - Is there a formula I can use to solve this issue? Do I need to multiply, divide, add, or subtract?Use objects - Are there classroom manipulatives I can use, such counters or base-10 blocks?To learn more about problem-solving here:
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Solve for
x
xx.
Assume the equation has a solution for
x
xx.
19
x
+
r
x
=
−
37
x
+
w
The value of x in the Algebraic expressions is x = w / (56+r).
What is Algebra?
Algebra is a branch of mathematics focused on the study of mathematical symbols and the rules for manipulating those symbols. In algebra, letters and other symbols represent numbers, which can be manipulated and combined to solve equations and other mathematical problems. Algebra is used in a variety of different fields, from engineering to economics, and is essential for anyone studying mathematics. Algebra can be used to solve problems involving linear equations, quadratic equations, polynomials, and more. Algebra also provides an important foundation for more advanced fields of mathematics, such as calculus. By learning the basics of algebra, students can gain an understanding of key mathematical concepts and gain the skills necessary to solve complex problems.
The solution is,
given: 19x + rx = -37x + w
( 19x + 37x) = w - rx
56x + rx = w
x(56+r ) = w
x = w / (56+r)
Therefore the value of x in the algebraic expression is x = w / (56+r).
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A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 50% magical syrup by volume (and the rest is just water), and blue potion, which is 10% magical syrup by volume. (Perhaps you're wondering how the same syrup can produce both red and blue potions. That's why it's magic syrup!)
(a) Find the amount of red potion (in mL) that must be added to 200 mL of blue potion in order to produce potion that is 30% magical syrup by volume.
(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce 150 mL of a potion that is 30% magical syrup by volume.
(c) Does there exist a combination of red potion and blue potion that can produce a potion that is 20% magical syrup by volume?
Answer:
Step-by-step explanation:
its a
Evaluate the expression.
(6 x 4) + (15÷ 5) =
?
Answer:
27
Step-by-step explanation:
first you multiply 6x4 which is 24 the you divive 15 by 5 you'll get 3 then you add 24 + 3 and your answer is 27
How do you know if AB and CD are congruent?
If the length of two segments is equal then the two segments are congruent.
If l(AB) = l(CD) then seg AB ≅ seg CD.
Two line segments to be congruent if and only if they have the same length.
Two shapes are congruent if they are exactly the same shape and exactly the same size. In congruent shapes, all corresponding sides will be the same length and all corresponding angle will be the same measure.
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Explain why (0,3) is not a solution to y
Answer:
Step-by-step explanation:
3< 0 + 2
3 < 2
the inequality is false because 3 is greater than 2, so the ordered pair (0,3) can’t be a solution of the inequality
Answer:
(0, 3) is not a solution to y < x + 2.
Step-by-step explanation:
Plug the given coordinates in to the inequality:
(0, 3) → x = 0, y = 3
y < x + 2
3 < 0 + 2
3 ≮ 2
(0, 3) is not a solution to y < x + 2.
EVALUATE ₈C₇ and ₁₁P₅
₈C₇=
₁₁P₅=
The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440
How to determine the permutation and combination expressions?From the question, we have
⁸C₇ and ¹¹P₅
The combination expression: ⁸C₇
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 8 and r = 7
Substitute the known values in the above equation
Total = ⁸C₇
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
⁸C₇ = 8!/7!1!
Evaluate
⁸C₇ = 8
(b) The permutation expression: ¹¹P₅
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 11 and r = 5
Substitute the known values in the above equation
Total = ¹¹P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)
So, we have
¹¹P₅ = 11!/6!
Evaluate
¹¹P₅ = 55440
Hence, the values are 8 and 55440
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The graph shows the amount of book sales
over several days. Determine if the
relationship is proportional. Find and
interpret the slope. Then find the unit rate
and compare it to the slope.
The two quantities have proportional relationship and it's slope is 333.33
ProportionsProportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
In this case, we have to determine is there's a uniform increase or decrease of the quantity.
The formula of proportionality is often given as
y = kx
k = constant of proportionalityLet's take two points and check if they share the same constant of proportionality
2000 = k(6)
k = 333.33
1000 = k(3)
k = 333.33
The relationship between sales and day is proportional.
The slope of the graph is given as
m = y₂ - y₁ / x₂ - x₁
m = 2000 - 1000 / 6 - 3
m = 333.33
NB: The slope and constant of proportionality in this case are the same quantity.
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The population of a country has been decreasing for several decades. In 1990, the population was about 152 million people. In 2010, the population was about 147 million people. Determine the percent decrease in the country's population during this time period.
During the time period of 20 years the percent decreases in the country's population is 3.28%.
What is Percentage?Percentage is a number or ratio which is a fraction of hundred.
Given,
Population of the country in 1990 = 152 million
Population of the country in 2010 = 147 million
Percent decrease in the population will be ,
= [ (1990's population - 2010's population)/1990's population ]*100
= [ (152 - 147 )/152]*100
= [5/152]*100
= 3.28%
Hence , the decrease in the population will be 3.28%.
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NO LINKS!! Use tests for symmetry to determine which graphs from the list below are symmetric with respect to the y-axis, the x-axis, and the origin. (Select all that apply.) Part 1
Answer:
[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]
[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]
Step-by-step explanation:
Part (a)A graph is symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph.
Linear functions are not symmetric with respect to the y-axis.
Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.
Cubic functions are not symmetric about the y-axis.
Square root functions are not symmetric about the y-axis.
There are two quadratic functions with x² in the given answer options.
Test to see if they are symmetric with respect to the y-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.
Given function:
[tex]y=-6x^2[/tex]
Replace x with (-x):
[tex]\implies y=-6(-x)^2[/tex]
[tex]\implies y=-6x^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Given function:
[tex]y=4x^2-2[/tex]
Replace y with (-y) and x with (-x):
[tex]\implies y=4(-x)^2-2[/tex]
[tex]\implies y=4x^2-2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Part (b)A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.
Linear functions are not symmetric with respect to the x-axis.
Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.
Cubic functions are not symmetric about the x-axis.
Square root functions are not symmetric about the x-axis.
There is one quadratic functions with y² in the given answer options.
Test to see if it is symmetric with respect to the x-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
Given function:
[tex]x=\dfrac{1}{4}y^2[/tex]
Replace y with (-y):
[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]
[tex]\implies x=\dfrac{1}{4}y^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.
The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) = t + 6, v(0) = 7, 0 ≤ t ≤ 10 (a) Find the velocity at time t. v(t) = Correct: Your answer is correct. m/s (b) Find the distance traveled during the given time interval.
a) The function velocity of the particle is v(t) = 0.5 · t² + 6 · t + 7, b) The distance traveled by the particle is 467 feet.
How to determine the velocity and the distance traveled by a particleIn this problem we have the equation that represents the acceleration of a particle. The function velocity (v) is obtained by integrating the function acceleration (a) and the function position is obtained by integrating the function velocity. Now we present the definitions of each function:
Velocity
v(t) = ∫ a(t) + C
Position
s(t) = ∫ v(t) + C
Where C is the integration constant.
The distance traveled during the time interval is found means of definite integrals:
Δs = [tex]\int\limits^b_a {v(x)} \, dx[/tex]= s(b) - s(a)
a) First, determine the function velocity of the particle:
v(t) = ∫ (t + 6) dt + C
v(t) = 0.5 · t² + 6 · t + C
7 = C
v(t) = 0.5 · t² + 6 · t + 7
b) Second, determine the distance traveled in the given time interval:
Δs = s(10) - s(0)
Δs = 0.167 · 10³ + 3 · 10² + 7 - 0.167 · 0³ - 3 · 0² - 7
Δs = 467
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What does it mean for addition to be closed?
For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.
It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.
Yes, whole numbers are closed under addition
It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.
So the set of whole numbers are closed under addition
Addition of the set of positive integers is closed because the sum of any two integers is also an integer.
Consider subtraction. Positive numbers are not closed under subtraction because picking a larger number to subtract from a smaller one results in a negative number result.
Therefore, For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.
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A car is traveling at a rate of 20 meters per second. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 2 hours? Do not round your answers.
Rate:
Distance traveled in 2 hours:
Answer:
Rate = 72 km per hour
Distance traveled in 2 hours = 144 km
Step-by-step explanation:
The car speed is given as 20 meters per second
There are 3600 seconds in an hour
So in 1 hour the car would travel 20 x 3600 = 72,000 meters. This is equivalent to 72,000 meters per hour
There are 1000 meters in a kilometer
So, in terms of kilometers, the car would travel 72,000/1000 = 72 km i one hour. This is equivalent to a speed of 72 km per hour
In 2 hours the car would travel 72 x 2 = 144 km
(-4x4+6+3/3)x6
What is the solution
Answer:___(-4x⁴+9)x⁶
3
Find the number of distinguishable permutations of the letters in each word below.
(a) bigger
(b) Hollywood
(c) possess
The number of distinguishable permutations in the given letters are:
a.) Bigger= 720
b.) Hollywood = 362,880
C.) possess = 5040
What is permutation?Permutation is defined as the arrangement of data set in a definite form which involves multiplication from the given number to 1.
The word 'bigger' contains 6 letters. Therefore the permutation of 6 = 6×5×4×3×2×1 = 720
For the word 'hollywood' contains 9 letters. Therefore the permutation of 9 =9×8×7× 6×5×4×3×2×1= 362,880
For the word 'possess' contains 7 letters. Therefore the permutation of 7 = 7× 6×5×4×3×2×1 = 5040.
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Determine where the real zeros of f(x)=x^4-2x^3+x-2 are located.a. at -1 & 2 c. at 0 & 1 b. at 1 & 2 d. at -1 & 1
The real zeroes of the given polynomial are located at (1, 2).
What are zeroes of the polynomial?The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
Given that, x⁴-2x³+x-2
Checking the real zeroes,
Considering point (1, 2)
y = 2 and x = 1
Putting the values,
x⁴-2x³+x-2 = 1-2+1-2 = 2
And, y = 2
Therefore, LHS = RHS
Hence, The real zeroes of the given polynomial are located at (1, 2).
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Write an expression to represent: 8 less than the product of 2 and x.
Match each equation with a graph above:
log (x) a. red R
10× b. black K
e× c. green G
ln (x) d. blue B
The equations are matched as below and the graph is plotted and attached
log (x) b. black K 10× d. blue Be× c. green Gln (x) a. red RWhat is logarithm graph?A log-log graph, also known as a log-log plot, is a two-dimensional graph of numerical data used in science and engineering that use logarithmic scales on both the horizontal and vertical axes.
The exponential graph is the opposite of logarithmic graph
In the given functions
log (x) is logarithmic function
10× is exponential function
Similarly, the natural exponent graph is the opposite of natural logarithm graph
in the given functions
e× is the natural exponential
ln (x) is the natural logarithm
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Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible. Which is it?
Hence, yes we can solve the triangle with the help of Law of Cosines.
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given that,
Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible.
Yes, with the help of Law of Cosines we can solve the triangle and the formula for it is
[tex]c^2=a^2+b^2-2abcos(C)[/tex]
where, [tex]a,b,c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle.
Hence, yes we can solve the triangle with the help of Law of Cosines.
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65 less than twice Janelle's savings
Answer:
x = 2y - 65
Step-by-step explanation:
please help me answer this question
Answer:
this 1
Step-by-step explanation:
same doubt pease any help
Find the amount Erica owes at the end of 6 years if $5300 is loaned to her at a rate of 8 % compounded monthly. use A=P(1+r÷n)ⁿt
The amount owed is $____.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The compound interest implies that Erica owes $10865 after 5 years
How to determine the amount Erica owes?The given variables can be represented as:
Loan amount P = $5300Rate of interest, R = 8%Time to pay back the loan, t = 6 yearsThe compound interest formula is given as
A = P(1 + r/n)^nt
Also from the question, we have
n = 12
This is so because the loan is compounded 12 times in a year as a result of being compounded monthly
Solving further, we replace the variables with their values in the above equation
A = 5300 * (1 + (8%/12))^(6*12)
Evaluate
A = 10865
Hence, the amount owed is $10865
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what is the percent decrease 350 to 200
Answer:
75%
Step-by-step explanation:
First, you subtract 200 from 350 to get the difference, which is 150.
Then, you do 150 divided by 200 since 200 is the starting number and it is increasing by 150.
150/200 = 0.75
To convert the decimal into a fraction multiply by 100.
0.75*100 = 75
How do you match equivalent expressions?
To match equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
In mathematics, equivalent fractions are those with the same denominator and differing numerators.
According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction following simplification. Let's imagine that two fractions, a/b and c/d, were simplified to provide comparable fractions, e/f. In this case, the two fractions are equal to one another.
For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.
We have to find how do we match equivalent expression.
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sqrt((x^(2)-1)^(2))=x^(2)-1
The algebraic expression √((x²-1)²) simplifies to x²-1
How to simply an algebraic expression?
An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
Given: sqrt((x^(2)-1)^(2))=x^(2)-1
√((x²-1)²)
The square root will cancel out the square:
Thus, √((x²-1)²) = x²-1
Therefore, √((x²-1)²) simplifies to x²-1
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What are 6 techniques used by propaganda?
Answer:
Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.
Step-by-step explanation:
What is propaganda ?Information—especially that which is slanted or deceptive—used to advance or publicize a specific political cause or point of view.
Glitzy Generalizations
Use expressions or words that sound appealing and are widely accepted.
Card Arranging
Using only those ideas and facts that support your argument.
Plain people
Tell voters that you are a normal person with same needs and beliefs as theirs.
Testimonial
Persuades people to do something by leveraging their popularity as a celebrity or athlete.
Bandwagon
Encourages a tendency to follow the crowd
Using names
Put a bad name on your opponent.
Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.
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3. Represent and Connect Write 2,857 using only hundreds and ones.
By using a linear combination, we can write our number using only hundreds and ones as:
2,857 = 28*100 + 57*1
How to write the number using only hundreds and ones?To write the number using only hundreds and ones we need to write our number as a linear combination of ones and hundreds, so we can write:
2,857 = a*100 + b*1
There are multiple solutions for this, we can use b to cover the ones and the tens, so:
57 = b*1
57 = b
And we can use a to cover the hundreds and thousands, so:
2,800 = a*100
2,800/100 = a
28 = a
Then we can write our number using only hundreds and ones as:
2,857 = 28*100 + 57*1
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Rewrite sin(x-7pi/4) in terms of sin(x) and cos(x)
The expression written in terms of sinx and cosx is
sinx· cos7π/4 - cosx ·sin7π/4
What is an algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given expression is sin(x - 7π/4).
Use the formula for sin(A-B) to rewrite the expression:
sin(x - 7π/4)
= sinx· cos7π/4 - cosx ·sin7π/4
Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4
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please I need help on question 6
The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;
x = 9
DE = 13
EF = 28
DF = 28
What is an isosceles triangle?An isosceles triangle is a triangle that has two angles in the triangle that are congruent and two congruent sides.
The specified parameters are;
∠D is congruent to ∠E in triangle ΔDEF
The length of the segments of ΔDEF are;
DE = x + 4
EF = 4·x - 8
DF = 7·x - 35
The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)
Therefore;
EF = DF (Definition of an isosceles triangle)
4·x - 8 = 7·x - 35
7·x - 4·x = 3·x = 35 - 8 = 27
3·x = 27
x = 27 ÷ 3 = 9
x = 9
DE = x + 4
Therefore;
DE = 9 + 4 = 13
EF = 4·x - 8
Therefore;
EF = 4 × 9 - 8 = 28
DF = 7·x - 35
Therefore;
DF = 7 × 9 - 35 = 28
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Cole and Maggie play table tennis. Maggie has won 4 more games than Cole. Is it possible for Cole to have won 13 games if the sum of the games Cole and Maggie have won together is 30?
*
1 point
Yes; Cole could have won 13 games because 2x + 4 = 30.
Yes; Cole could have won 13 games because 13 + 4 is less than 30.
No; Cole could not have won 13 games because 2x + 13 ≠ 30.
No; Cole could not have won 13 games because 2x + 4 ≠ 30
The answer to this Question is A we can use basic knowledge from linear equations to find the answer
What is Linear Equation?
Linear Equation is a equation in which degree of variables is 1 only
Yes the given case is possible only under some conditions that we can define as follows and as given in Linear Equations from Options
together cole and maggie have won 30 games and we are also given that out of those 30 maggie has won 4 games
we should closely see at Linear Equations given in Options.
therefore cole has won 26 games which is more than 13
Hence the answer to the Question is Yes
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A model rocket is shot straight up from the roof of a school. The height, h, in meters, after t seconds can be approximated by h(t)=-5t2+22t+15. Answer the following questions algebraically, showing all of your work
How long does it take for the rocket to pass a window that is 10m above the ground? (hint: make h=10, group like terms, then solve the quadratic equation)
Answer: [tex]\frac{11+\sqrt{146}}{5}[/tex] seconds
Step-by-step explanation:
[tex]10=-5t^2 +22t+15\\\\5t^2 -22t-5=0\\\\t=\frac{22 \pm \sqrt{(-22)^2 -4(5)(-5)}}{2(5)}\\\\t=\frac{11+\sqrt{146}}{5} \text{ } (t > 0)[/tex]
