An equation is formed of two equal expressions. The sum of all possible values of x is 16.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
3x + 2y = 21
3x = 21 - 2y
x = (21-2y)/3
Since the value of x is needed to be positive, the value of 2y must not exceed 21. Also, the value of (21-2y) must be a multiple of two.
Now, the values of y that will satisfy the given condition in the equation are 0, 3, 6, and 9.
Further, the sum of the possible values of x are,
Sum = 7 + 5 + 3 + 1 = 16
Hence, the sum of all possible values of x is 16.
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The surface area of a sphere is 6477 square inches. Which equation can be used to solve for the radius of the
sphere?
64m 4mr
647=2m³
6477= 2m²
64- 4m²
The expression πr² = 6477 can be used to solve for the radius of the sphere.
What is a sphere?It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
Area of sphere A = 6477 square inches
A = 4πr²
A = 6477
4πr² = 6477
πr² = 6477
Thus, the expression πr² = 6477 can be used to solve for the radius of the sphere.
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Which number line represents the solutions to 1-2x) = 4?
O+
O
O
O
-10 -8 -6 -4 -2 0 2 4 6
-10 -8 -6 -4 -2 0 2 4
+
-10 -8 -6 -4 -2 0 2 4 6 8 10
-10 -8 -6 -4 -2 0
8
6
++
10
8 10
2 4 6 8 10
Answer: Option (3)
Step-by-step explanation:
[tex]|-2x|=4\\\\|2x|=4\\\\|x|=2\\\\x=\pm 2[/tex]
The number line represents the solutions to |-2x| = 4 is Number line C.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have Equation: |-2x| = 4
We know the value inside the mod is always positive.
So, 2x = ±4
x= ±4/2
x= ±2
Thus, the required number line is C.
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If you want to study which science course students liked the most during high school, you should survey... science teacher's, because they know what students like. science majors, because they love science. O the lunch room, because they will consist of all genders and ages and be unbiased about science. graduating seniors, because they have taken a wider variety of science courses. If you want to study which science course students liked the most during high school , you should survey ... science teachers , because they know what students like . science majors , because they love science . O the lunch room , because they will consist of all genders and ages and be unbiased about science . graduating seniors , because they have taken a wider variety of science courses .
Answer:
the last option
Step-by-step explanation:
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Study: Factoring Polynomials Completely
What are the possible roots of the polynomial function below? (Check all
that apply.)
F(x) = 2x² + 5x -5
Answer:
x = 0.76556443 x = -3.26556443
Step-by-step explanation:
You can use the quadratic formula to find the roots.
Place the steps for finding f(x) in the correct order.
H
11
K
f(1) = 41 + 7
0·0-0-0-0
For finding the inverse of a function you have to write it as an ecuation.
[tex]y = 4x + 7[/tex]
Invert the values of x and y.
[tex]x = 4y + 7[/tex]
Our objetive now in this new equation is to clear y. First, subtract 7 in both sides of the equation.
[tex]x - 7 = 4y[/tex]
Then, divide both sides by 4.
[tex] \frac{x - 7}{4} = y[/tex]
Finally, invert the values of x and y again and put the equation like a function.
[tex] {f}^{ - 1} (x) = \frac{x - 7}{4} [/tex]
This is correct because f(x) = x is the axis of symmetry for both functions (green one).
he circle graph shows how the annual budget for a company is divided by department. If the amount budgeted for Media and Engineering combined is 31,250,000, what is the total annual budget? Media 4% Support 19% Editorial 6% Engineering 21% Research 32% Sales 18%
Answer:
let's playthe games questiontag
I hate math so I really need help
Answer:
b. 4.5 cm
a. 42 mm is the answer
Use your calculator to find the approximate value of e. (Round to 4 decimal places)
Using a calculator to find the approximate value of e in
F(e)=e^{2e} we have F(e)=229.6516. This is further explained below.
What is maclurin polynomial?Generally, To approximate a function f (x) f (x) f (x) for values of x near to zero, one may use a power series known as a Maclaurin series.
In conclusion, Using your calculator to find the approximate value of e in
F(e)=e^{2e}
We have
F(e)=e^{2e}
F(e)=229.6516
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Suppose you have opened some Nutty Bars to check the company’s claim of an “average” of 8 peanuts per bar. Here is what you found after opening 10 bars: 5, 8, 8, 8, 11, 7, 8, 6, 6, and 6. Which average should the company use to support their claim?
The company should use the median to support their claims.
Which measure of average should the company use?Measures of average commonly used are mean and median.
Mean is the sum of the numbers divided by the total number
Mean : (5 + 6 + 6 + 6 + 7 + 8 + 8 + 8 + 8 + 11) / 10 = 7.3
Median is the number at the center of the dataset when it is arranged either in ascending or descending order.
Median = 8
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are 12d +36 and 12(d+3) equivalent
Answer:
Yes
Step-by-step explanation:
They are equivalent as 12d + 36 is the expanded form of 12(d + 3)
Answer:
Yes,
just factorize 12d+36 and since 12 is common
12(d+3)
Problem 10-09 (Algorithmic) Cress Electronic Products manufactures components used in the automotive industry. Cress purchases parts for use in its manufacturing operation from a variety of different suppliers. One particular supplier provides a part where the assumptions of the EOQ model are realistic. The annual demand is 5,300 units, the ordering cost is $70 per order, and the annual holding cost rate is 25%.
The economic order quantity is 385 and reorder point is 254.
Economic order quantity (EOQ)a. Economic order quantity (EOQ)
EOQ=√2×D×C÷H
Where:
D =Annual Demand
S = Cost of Ordering
H=Holding cost
Hence:
EOQ=√2×5300×70÷.25×20
EOQ=√742,000÷5
EOQ=√148,400
EOQ=385
b. Reorder point
Reorder point=5300/250×12 days
Reorder point=254
c. Reorder point
Reorder point=5300/250×35 days
Reorder point=742
d. Reorder point
Reorder point=742-385
Reorder point=357
Therefore the economic order quantity is 385 and Reorder point is 254.
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The complete question is:
a. If the cost of the part is $20 per unit, what is the economic order quantity?
b. Assume 250 days of operation per year. If the lead time for an order is 12 days, what
is the reorder point?
c. If the lead time for the part is seven weeks (35 days), what is the reorder point?
d. What is the reorder point for part (c) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position?
Given segment AC and point B that lies on AC,
find CB if AC = 17, AB = 32 + 3x, and CB=57+6x
CB=
I give brainliest
The total length of the segment AC is the sum of AB and CB, which gives, CB = 9
How can the length of CB be found?The given parameters are;
AC = 17AB = 32 + 3•xCB = 57 + 6•xRequired: CB
Solution:
AC = AB + CB by segment addition property
Therefore;
AC = 17 = 32 + 3•x + 57 + 6•x = 89 + 9•x
17 = 89 + 9•x
[tex]x = \frac{17 - 89}{9} = - 8[/tex]
CB = 57 + 6•x = 57 + 6 × (-8) = 9
Therefore;
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You buy tomatoes in 25 pound cases. One portion of salad requires .75 ounces of tomatoes. How many portions can be made with one
case?
The amount of the portions can be made with one case will be 399.25 ounces.
What is conversion?Conversion means to convert the same thing into different units.
You buy tomatoes in 25 pounds (11.34 kg) cases.
We know that 1 pound (0.45 kg) is equal to 16 ounces (0.45 kg).
Then the number of the ounces in 25 pounds (11.34 kg) will be
⇒ 25 x 16
Multiply the numbers, then the expression will be
⇒ 400 ounces (11.33 kg)
In 25 pounds of tomatoes, there will be 400 ounces.
One portion of salad requires 0.75 ounces (0.02 kg) of tomatoes.
Then the amount of the portions can be made with one case will be
⇒ 400 – 0.75
⇒ 399.25 ounces
Thus, the amount of the portions can be made with one case will be 399.25 ounces.
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Five times a number is greater than 25.
5x>25
x>5
Hope it helps!
For every 6 students who purchase a bag of M&M’s, there are 5 students who purchase a pack of gum. Use M for the number of students purchasing bags of M&M’s and G for the number students purchasing packs of gum, write an equation for this statement.
Answer:
M/6 = G/5
Step-by-step explanation:
We are given a relation between the numbers of students in two different groups. That relation can be used to write an equation.
Groups who bought M&Ms
If we consider M&M buyers to be 6 in a group, then the number of those groups is ...
M/6
Groups who bought gumSimilarly, the number of groups who bought gum will be ...
G/5
where there are 5 gum-buyers in each group.
EquationThe problem statement tells us that for each group of one kind, there is a matching group of the other kind. That is, the numbers of groups are equal:
M/6 = G/5
How can we write an algebraic expression to describe a two digit number whose unit's digit is 5
ess than the ten's digit?
Let's x be ten's digit
Answer:
required expression = 11x-5
Step-by-step explanation:
We have information about the following things :
Its a two digit numberUnits digit is 5 less than the tens digittens digit is xSince units digit is 5 less than the tens digit, then the unit digit will become
x-5
Now we have these two things:
Tens digit is xUnits digit is x-5Now let us look at some two digit numbers like 29 , 43 and 78
in 29, tens digit is 2 and units digit is 9
29 is formed by multiplying the tens digit by 10 and multiplying the units digit by 1 like this : 29 = (2×10) + (9×1)
Similarly;
43 = (4×10) + (3×1)
78 = (7×10)+(8×1)
Now to get out two digit number from the question, we similarly need to multiply the tens digit with 10 and units digit with 1 and add them like this:
tens digit : x
Units digit : x-5
Hence the number is (x × 10) + [(x-5)×1] = 10x + x-5 = 11x-5
hence the required algebraic expression is 11x-5
The mean of a set of numbers is 500. a. If 10 is added to each of the numbers in the set, then what will be the mean of the new set? The mean of a set of numbers is 500 . a . If 10 is added to each of the numbers in the set , then what will be the mean of the new set ?
Answer:
510
Step-by-step explanation:
Assume 2 numbers 500,500.. with a mean of 500
so if we add 10 to each of the two numbers, mean will be:
[tex]\frac{510+510}{2}=510[/tex]
Of course you can vary the set and the numbers and still get the same mean
What is another way to summarize this proof?
A. Angles forming a linear pair are congruent.
B. Vertical angles are supplementary.
C. Vertical angles are congruent.
D. Angles forming a linear pair are supplementary.
Another way to summarize this proof is to say vertical angles are congruent.
Vertical anglesLines are shortest distance between two point and angles are forned from the intersection of two lines.
From the given figure, they are trying to prove that the angles ANR and VNE are equal. Since these angles are formed at the point of intersection, hence another way to summarize this proof is to say vertical angles are congruent.
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A teacher takes her AP calculus class of 8 students to lunch. They sit around a circular dining table.
a. How many seating arrangements are possible?
b. How many seating arrangements are there if the teacher has to sit on the chair closest to the soda fountain?
c. Among the students are one set of triplets. How many seating arrangements are there without all three of them sitting together?
Step-by-step explanation:
it is 8+1 people (8 students and 1 teacher).
a.
how many seating arrangements are possible ?
start with any of the 9 seats. there are 9 possibilities who will sit in that chair.
the next seat has then only 8 possibilities left. the next one 7. the next b one 6. and so on.
so, all possibilities are
9×8×7×6×...×1 = 9! = 362,880
b.
if the teacher is fixed to a specific seat, then this position is constant in all seating arrangements.
that means for the variable part we have only 8 people remaining.
and that gives us now only
8! = 40,320
possibilities
c.
how many combinations are there for the triplets, when they sit together, to arrange their internal sitting sequence ?
3! = 6
and we need to block these 6 combinations for each of the freely selectable seats as starting seat for such a block of 3.
to visualize this, let's give each seat an identifier.
we have the seats s1, s2, s3, ... s8, s9.
for all the combinations of these 9 seats, we need to eliminate the 6 combinations, where the triplets sit on s1, s2, s3.
and then the 6 combinations, where they sit at s2, s3, s4.
and then at s3, s4, s5. then at s4, s5, s6. ... s8, s9, s1. and s9, s1, s2.
it is not clear if b. still applies here (and the teacher has a fixed seat), or if we are back to the general a. scenario.
if we have again all 9 people picking their seats freely, and we only block the triplets from sitting together, then we need to block these 6 combinations for each of the 9 seats (as visualized above) giving us
9! / (9×3!) = 362,880 / 54 = 6,720 remaining possibilities.
if we have again the teacher blocking one fixed seat, then we need to block the 6 triplets combinations theoretically for each of the 8 remaining seats as above.
but : the teacher is now a separator disabling some of these blocks of 3.
e.g. let's say the teacher's seat is s9. then the teacher automatically separates the triplets in otherwise "illegal" blocks of 3.
s7, s8, s1 is now a valid seat combination for the triplets (because there is the fixed s9 in between).
the same for s8, s1, s2.
so, we need to eliminate the 6 combinations not for all 8 starting seats, but only for 6.
and that gives us
8! / (6×3!) = 40,320 / 36 = 1,120 remaining possibilities.
Jamie had seven posters, but only 3 could fit on his closet door. How many different ways can he arrange the three posters out of the seven on his door?
A. 52.5
B. 210
C. 1260
D. 5040
Answer:
210 ways
Step-by-step explanation:
7 P 3 = 210 ways
or 7 C 3 = 35 choices of 3 posters which can bearrranged in 6 different ways 6 * 35 = 210 ways
Given h(f)=-2(f+5)^2+4 find h(-8)
Answer:
h(-8)= -14
Step-by-step explanation:
[tex]h(-8)=-2(-8+5)^2+4 \\h(-8)=-18+4=-14[/tex]
[tex]\huge\boxed{-14}[/tex]
We have the following equation:
[tex]h(f)=-2(f+5)^2+4[/tex]
Substitute in [tex]-8[/tex] for [tex]f[/tex] and simplify.
[tex]\begin{aligned}h(-8)&=-2(-8+5)^2+4&\textsf{Substitute.}\\&=-2(-3)^2+4&\textsf{Add.}\\&=-2\cdot9+4&\textsf{Simplify the power.}\\&=-18+4&\textsf{Multiply.}\\&=\boxed{-14}&\textsf{Add.}\end{aligned}[/tex]
Find cos(A). Show your work and reduce the ratio if necessary
Using relations in a right triangle, it is found that:
cos(A) = 3/5 = 0.6.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this triangle:
The adjacent side to A has length 30.The hypotenuse has length 50.Hence:
cos(A) = 30/50 = 3/5 = 0.6.
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There's 18 deer and 52 lions if 10 lions eat 17 deer how many deer are left
Answer:
1 deer
Step-by-step explanation:
18 deer minus 17 eaten leaves 1 deer
When sending a letter, Bobby pays a fixed amount for letters weighing up to an ounce. He then pays a smaller, fixed amount for each additional ounce (or part of an ounce). The cost of sending the letter in cents is modeled by the function y = 30 + 20(x - 1), where x is the weight of the letter in ounces. What does the number 20 describe?
A function assigns the values. The number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
In the given function y = 30 + 20(x - 1), the number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.
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Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B and height H. Consider these ideas or others: combine two copies of a trapezoid to make a parallelogram. Subdivide the trapezoid into two triangles one with base b and one with base a.
The two ways that can be used to find the area of a trapezoid include:
A = (a + b) × h/2A = a × hHow to illustrate the information?It should be noted that a trapezoid simply means a four sided shape that has parallel sides.
To find the area of the shape goes thus:
Find the length of each base.
Find the height of the trapezoid.
Substitute the values into the formula: A = (a + b) × h/2
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The product of 12, x and y. Translate the following phrase into an algebraic expression. Do Not simplify.
The product of 12, x, and y written in an algebraic expression is 12xy.
What are algebraic expressions?Algebraic expressions are mathematical expressions containing variables, coefficients, and their arithmetic operators such as addition, subtraction, multiplication, and division.
An algebraic expression can be used to interpret and solve mathematical word problems.
From the information given:
The algebraic expression can be translated as 12x × y = 12 xy.
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The algebraic expression that can be translated as product of 12, x and y is 12 xy.
What are algebraic expressions?Expressions are used to interpret mathematical problems
From the question given we are to translate the product of 12, x and y.
The product of 12 and x is 12x
The product of 12x and y is 12xy, hence the algebraic expression that can be translated as product of 12, x and y is 12 xy.
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Volume (to the nearest tenth)
Answer:
913
Step-by-step explanation:
cylinder:
radius=5.6 height=7
first lets find the volume of the cylinder the formula for the volume of a cylinder is pi times radius squared times height. so after plugging in the height and radius you get 689.64242
cone:
radius=5.6 height=6.8
now the volume of the cone, the formula for the volume of a cone is pi times radius squared times height/3. so after plugging in the height and radius of the cone you get 223.31278
so 689.64242 + 223.31278= 912.9552 and that rounded to the nearest tenth is 913
PLS ANSWER PLS!
Two functions are represented below.
FUNCTION A FUNCTION B
y=35x (looked at linked image)
What is the difference in the rate of change between Function A and Function B? Be sure to include the rate of change of each function in your answer
The difference in the rate of change of both functions is: 15.
What is the Rate of Change of a Function?Rate of change of a linear function = change in y / change in x.
Function A is given as: y = 35x. The rate of change for function A is 35.
From the graph of function B, using two points, (1, 50) and (2, 100):
Rate of change = (100 - 50)/(2 - 1)
Rate of change = 50.
Therefore, the difference in the rate of change of both functions = 50 - 35 = 15.
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12) Becky bought a digital camera on the installment plan. The purchase price was $859.95. She paid $150 down
and made 12 monthly payments of $65.25. Find the finance charge she paid.
O a.) $71.45
Ob.) $75.35
Oc.) $74.50
Od.) $73.05
Which expression is equivalent to (3x² + 4x-7)(x-2)?
A. (3x² + 4x-7)(x) + (3x² + 4x-7)(-2)
B. 2x(3x² + 4x-7)
OC. x(3x² + 4x-7) - 2
D. x(3x2 + 4x-7)+2(3x² + 4x-7)
Answer: A. (3x² + 4x-7)(x) + (3x² + 4x-7)(-2)
Step-by-step explanation:
The expressions are equivalent by the distributive property.