Use distributive property a(b + c) = ab + ac.
[tex]2x(y^2+3)-5(3+y^2)=(2x)(y^2)+(2x)(3)+(-5)(3)+(-5)(y^2)\\\\=2xy^2+6x-15-5y^2[/tex]
The ordered pairs (1, 6), (2, 12), (3, 18), (4, 24), and (5, 30) represent a function. What is a rule that represents this function? (1 point)
y = 6x
y = (x + 6)2
y = x6
y = 6x
Is the relationship a function that is increasing or decreasing? Is the relationship a function that is linear or non linear?
Number of College Courses Time spent on homework
1 3
2 6
3 8
4 12
increasing; linear
increasing; non linear
decreasing; linear
decreasing; non linear
Okay # 1
Y = 6x (I don't know why there's two answer choices)
# 2
Uhh it should be increasing linear but the (3,8) kinda threw it off
The rule for the first set of ordered pairs is y = 6x, representing a linear, increasing function.
The relationship between the number of college courses and time spent on homework is increasing and non-linear.
Explanation:The ordered pairs (1, 6), (2, 12), (3, 18), (4, 24), and (5, 30) show that for each value of x, y is always six times as much.
Thus, the rule that represents this function is y = 6x.
When you plot these points on a graph, the line will be straight, showing it's a linear function, and because y increases as x increases, it is an increasing function.
Looking at the other set of ordered pairs for the number of college courses versus the time spent on homework, we can see that as the number of courses increases, the time spent also increases, showing that the relationship is increasing.
However, the increase in time is not consistent (3, 6, 8, 12), which suggests the relationship is non-linear.
15/16 - 7/32 Also find the sum or difference
A.13/32
B.23/32
C 3/4
Answer:
yes, the answer is B.
I took the practice so it is correct.
chris has 5 stack of dvd each stack has10 dvds if chris add 2 more identical stacks of dvds to the shelves how many dvds will chris have
Ed has 28 blocks. Sue has 34 blocks who has more blocks? How many more?
Answer:
Sue // 6 More blocks
Step-by-step explanation:
Sue has more blocks because 34>28.
34-28 is 6 so sue has 6 more.
The diagram shows two parallel lines cut by two transversals. Which statement is NOT true?
A. Angle c is congruent to angle e.
B. The measures of angles a, d, and e sum to 180°.
C. Angles a, b, and c are the interior angles of a triangle.
D. Angle b is congruent to angle e.
Answer:
D
Step-by-step explanation:
A) True. Alternate interior angles are congruent so
[tex]\angle c\cong \angle e[/tex]
B) True. Considering the sum of these three angles is equal to a straight angle. Since ∠a+∠d supplementary to ∠e
[tex]\angle a+\angle e+\angle d=180[/tex]
C) True. Since the line segments form a triangle having a (black) line as triangle base.
D) False. ∠b is congruent to its corresponding angle, and ∠e is not its corresponding angle. The corresponding angle of ∠b is the angle vertex opposed to ∠d (not identified).
How would u do this ,?
Answer:
26.4= 26 2/5 millimeters
Step-by-step explanation:
All you do for this problem is see how many times 1/3 goes into 1. Since 1 means a full load of dishes. Which is three times. So you also do 8 4/5 times three too to get your answer.
What is the prime factorization for 180
Answer:
2*2*3*3*5
Step-by-step explanation:
Factor 180 into prime numbers that multiply together to give 180
180 = 20 *9
= 4*5 * 3*3
= 2*2* 5 * 3*3
Now rewrite them from smallest to largest
2*2*3*3*5
Cheddar cheese cost 4.25 per pound. Which equation best represents y, the cost of x pound of cheddar cheese
Answer:
y = 4.25x
Step-by-step explanation:
Answer:
y = 4.25x
Step-by-step explanation:
Cheddar cheese cost 4.25 per pound . This means the cost of cheddar cheese is 4.25 for every pound in weight. Assuming we put a currency to the value we can say 1 pound of cheddar cheese is equals to 4.25 dollars($4.25). Mathematically, it can be represented as
4.25 is the cost for 1 pound of Cheddar cheese
Let the cost of the equation be y as required from the question.
y = cost of the cheddar cheese
x is the weight value in pounds of the Cheddar cheese.
The equation can be best represented as
y = 4.25x
In the equation above if the amount in pounds is 3 pound . the value will be inputted for x and the cost will be gotten which is y.
Please help need this answer
A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
(2, 0), (-3, 3), (9, 1), (-3, 5) NOT
(9, 1), (-3, 4), (2, 1), (9, 2) NOT
(2, 4), (-3, 2), (9, 1), (-7, 2) YES
(2, 4), (-3, 6), (2, 3), (-7, 2) NOT
PLEAE HELP IM SO CONFUSED!An experiment involves selecting a numbered chip, some black and some white, from a bag of chips. The probability of selecting a black chip with an even number is 12 . The probability of selecting a black chip is 35 . What is the probability of selecting a chip with an even number given that the chip is black?
Answer: The probability of selecting a chip with an even number given that the chip is black = 5/6
Step-by-step explanation:
Let B represents the event of getting black chip,
While E represents the event of getting even chip.
So, according to the question,
It is given, The probability of selecting a black chip with an even number is,
[tex]P(B\cap E)=\frac{1}{2}[/tex]
And, The probability of selecting a black chip is,
[tex]P(B)=\frac{3}{5}[/tex]
Thus, the probability of selecting a chip with an even number given that the chip is black,
[tex]P(\frac{E}{B} )= \frac{P(B\cap E)}{P(B)} = \frac{1/2}{3/5}[/tex] ( By the conditional property )
⇒ [tex]P(\frac{E}{B} )= \frac{5}{6}[/tex]
Kelli is running a mile in gym class. She runs at a pace of 6 minutes per mile. What's the dependent variable in the situation?
A. The length of the race
B. The amount of time passed
C. The distance Kelli has run
D. The speed at which Kelli runs
I need the work please!
If x-1/3 = k and k = 3, what is the value of x ?
A) 2
B) 4
C) 9
D) 10
Answer:
None of the above
Step-by-step explanation:
x-1/3 = k
We know that k=3, so we can substitute that into the equation
x-1/3 = 3
Add 1/3 to each side
x-1/3 + 1/3 = 3+1/3
x = 3 1/3 or as an improper fraction 10/3
Kayson mixes 300 milliliters ( mL ) (mL) of spinach, 200mL of berries, and 42mL of dressing to make a salad. There are s s milligrams ( mg ) (mg) of vitamin C per milliliter of spinach, b mg bmg per milliliter of berries, and d mg dmg per milliliter of dressing. Which expressions can we use to describe how many milligrams of vitamin C are in the salad?
Answer:
X= (300 s + 200 b + 42 d )mg
Step-by-step explanation:
Amount of spinach=300 ml
Amount of berries =200 ml
amount of dressing = 42 ml
Vitamin C in one ml of spinach = s mg
Vitamin C in 300 ml of spinach = 300 s mg
Vitamin C in one ml of berries=b mg
Vitamin C in 200 ml of berries = 200 b mg
Vitamin C in one ml of dressing = d mg
Vitamin C in 42 ml of dressing = 42 d mg
Let total vitamin C be = x
Then
X= (300 s + 200 b + 42 d )mg
is the required expression
The sum of the three angles formed inside a triangle are equal to ____ degrees?
D-I are the measurements of the lengths of the sides of triangles. Identify the types of
triangles
d. 45 cm 61 cm 60 cm e. 30 cm, 31cm, 30 cm f. 4 cm, 5ft, 4 cm
g. 89mm, 89mm, 89mm h. 9 in, 5in, 3 in i. 22cm, 22cm, 22in
J-O are the measurements of the angles of triangles. Identify the type of triangle.
j. 900, 350, 550 k. 600, 600, 600 l. 700, 550, 550
m. 350, 400, 1000 n. 460, 460, 440 o. 1200, 300, 300,
Answer:
The sum of the interior angles of a triangle is 180 degrees.
d. Scalene
e. Isosceles
f. Isosceles
g. Equilateral
h. Scalene
i. Equilateral
j. Right
l. Acute
m. Obtuse - doesn't add to 180 not a triangle
n. Acute - doesn't add to 180 not a triangle
o. Obtuse
Step-by-step explanation:
The interior angles of a triangle add to 180 degrees. There are two ways we classify triangle by side lengths and angle measures.
Side lengths: Compare the side lengths and see if any are equal to determine the type.
Scalene: 3 different lengthsIsosceles: 2 equal lengths and 1 differentEquilateral : 3 equal sidesAngle Measures: Compare the angles measures to 90 degrees.
Right: If one angle is equal to 90Acute: All angles are less than 90 degreesObtuse: One angle is greater than 90 degreesYou have two exponential functions. One function has the formula g(x) = 3 x . The other function has the formula h(x) = 2-x. Which option below shows the graph of k(x) = g(x) - h(x)?
Answer:
k(x) = 4x - 2
Please refer attachment for the graph.
Step-by-step explanation:
Given :
g(x) = 3x
h(x) = 2- x
k(x) = g(x)-h(x)
k(x) =3x -(2-x) = 3x -2 +x =4x -2
∴k(x) = 4x - 2
Choose the inequality that could be used to solve the following problem.
Three times a number is no less than negative six.
3x ≤ -6
3x < -6
3x ≥ -6
3x > -6
Answer:
Correct choice is C
Step-by-step explanation:
Let x be unknown number.
Three times a number x is [tex]3\cdot x=3x.[/tex]
Three times a number is no less than negative six means that the number [tex]3x[/tex] can be equal to -6, can be greater than -6, but cannot be less than -6.
Thus, the inequality that could be used to solve the problem is
[tex]3x\ge -6.[/tex]
Answer:
3x ≥ -6
Step-by-step explanation:
point A lies in plane B how many planes can be drawn perpendicular to plane B through point A
1) one
2)two
3) zero
4) infinite
Answer:
4
Step-by-step explanation:
Only one plane can be drawn perpendicular to plane B through point A in three-dimensional space. The correct answer is option 1) that is One.
The question at hand involves geometric concepts, specifically the relationship between planes and lines in three-dimensional space. If point A lies in plane B, then there can be one and only one plane drawn perpendicular to plane B through point A; this is because in three-dimensional space, a point defines a line and only one perpendicular plane can contain that line.
This principle is similar to how any three points not on a single straight line determine a plane and how two lines intersect at a single point or not at all. The perpendicular plane would form a 90-degree angle along every line in plane B that passes through point A.
The correct answer is option 1) that is One
The ratio of soccer players to baseball players on two school teams is 4 to 7. Come up with possible numbers of players on the soccer team and the baseball team.
The correct possible numbers of players on the soccer team and the baseball team that maintain the ratio of 4 to 7 are 4 soccer players to 7 baseball players.
To find possible numbers of players on the soccer team and the baseball team, we can use the given ratio 4:7. This means that for every 4 soccer players, there are 7 baseball players. To maintain this ratio, we can multiply both numbers by a common factor to find a set of possible numbers of players.
Let's denote the common factor by 'k'. Then, the number of soccer players would be 4k and the number of baseball players would be 7k. Here are a few examples with different values of k:
1. If k = 1, then we have:
Soccer players: 4 × 1 = 4
Baseball players: 7 × 1 = 7
2. If k = 2, then we have:
Soccer players: 4 × 2 = 8
Baseball players: 7 × 2 = 14
3. If k = 3, then we have:
Soccer players: 4 × 3 = 12
Baseball players: 7 × 3 = 21
4. If k = 4, then we have:
Soccer players: 4 × 4 = 16
Baseball players: 7 × 4 = 28
And so on. The numbers of players on the soccer and baseball teams can be any multiple of 4 and 7, respectively, while still maintaining the ratio of 4:7.
what is the midpoint of mn?
First off, the length of MN is 2√10, not 8. This is because using Pythagorean Theorem, you get that MN=√4+36=2√10, which is (3).
The midpoint of MN can be found by finding the average of the coordinates of M and N. Therefore, our first part to solving this question is to find the coordinates of M and N. M is (2,5) and N is (4,-1). Finding the average of the x-coordinates gives us 3. Finding the average of the y-coordinates gives us 2, Therefore, the midpoint of MN is (3,2), or answer choice (3).
which is greater 23/44 or 33/64
Answer:
23/44 < 33/64
Step-by-step explanation:
if you don't want to get common denominators multiply the denominator of the second fraction by the numerator of the first (1,427) and the denominator of the first one to the numerator of the second (1,452) the bigger number is greater. 1,427 < 1,452
By converting both fractions into decimals (23/44 becomes 0.5227; 33/64 becomes 0.5156), it is clear that 23/44 is greater than 33/64.
Explanation:To compare which fraction, 23/44 or 33/64, is greater, you need to find a common denominator and then compare the numerators. The calculation can be simplified by converting these fractions into decimals. To do so, divide the numerator by the denominator. Therefore, 23/44 becomes 0.5227 and 33/64 becomes 0.5156. Therefore, 23/44 is greater than 33/64.
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Marsha is buying salt and sand for defrosting her driveway. The salt cost $4 per bag, and the sand cost $10 per bag. She wants to buy at least 5 bags of sand and can spend no more than $100. Write a system of linear inequalities to model the situation
Answer:
The system of linear inequalities is equal to
[tex]4x+10y\leq 100[/tex]
[tex]y\geq 5[/tex]
Step-by-step explanation:
Let
x-----> the number of bags of salt
y-----> the number of bags of sand
we know that
[tex]4x+10y\leq 100[/tex] -----> inequality A
[tex]y\geq 5[/tex] ------> inequality B
Using a graphing tool
see the attached figure
The solution of the system of inequalities is the triangular shaded area
what is 3a ^2 + a ^2 added to a +6 ?
Answer:
it is a polynomial
3a^2+a^2= 4a^2
4a^2+6
Step-by-step explanation:
3a^2 +a^2 = 4a^2+6
=4a^2+6
The student's question simplifies to 4a^2 + a + 6 after combining like terms.
Explanation:This problem draws upon the concepts of linear equations and variables in mathematics. When you encounter 3a^2 + a^2 added to a + 6, you want first to combine like terms. In this case, 3a^2 and a^2 are like terms, meaning they can be added together. So, this results in 4a^2 + a + 6.
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solve for x
1 = − 4 + x
Answer: x = 5
Step-by-step explanation:
1 = -4 + x
We have to isolate x, and remember, what we do to one side we do to the other.
1 + 4 = -4 + 4 + x
5 = x
Check:
-4 + 5 = 1
1=1
-7/10 divided by 2/5 in it's simplest form
To divide fractions, multiply the first fraction (-7/10) by the reciprocal of the second one (5/2). This gives -35/20 which simplifies to -7/4 or -1 3/4.
Explanation:When dividing fractions, the conventional method is to multiply the first fraction, which is the dividend, by the reciprocal of the second fraction, which is the divisor. In this case, let's take the content loaded -7/10 divided by 2/5.
The reciprocal of 2/5 is 5/2. So, to divide -7/10 by 2/5, we instead multiply -7/10 by the reciprocal of 2/5.
-7/10 * 5/2 = -35/20.
Finally, we simplify this to its simplest form, by reducing to the lowest terms. We find that, -35/20= -7/4 or -1 3/4 if expressed as a mixed number.
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what is the slope of line t? and what y-intercept of line t?
Answer:
slope = [tex]\frac{1}{3}[/tex], y- intercept = - 1
Step-by-step explanation:
to calculate the slope m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (3, 0) ← 2 points on the line
m = [tex]\frac{0+1}{3-0}[/tex] = [tex]\frac{1}{3}[/tex] → B
the y-intercept c is where the line crosses the y- axis
that is c = - 1 ← y- intercept
an 8 in. by 10 in. photo is reduced so that the width (the shorter dimension) is 3 in. what is the length of the reduced photo
Answer:
Step-by-step explanation:
The length can be found by setting up a proportion. If the width is reduced by some ratio, then the length will share the same ratio.
3 / 8 = x / 10 Multiply both sides by 10.
3 * 10 / 8 = x Multiply first
30/8 = x Divide next. You don't need to do it in this order.
3 6/8 Simplify
3 3/4 Give another choice
3.75
The length = 3.75 inches
If none of these are correct, please leave a note with your choices.
Answer:
The length = 3.75 inches
Step-by-step explanation:
5th term in expansion of (x-2)^7
Answer:
560x^3
Step-by-step explanation:
The formula is
(r + 1)th term of (a + x)^n = nCr a^(n-r)x^r
So 5th term = (4 + 1)th term
= 7C4 x^(7-4) (-2)^4
= 35x^3*16
= 560x^3
How many milliliters can fit into 5 liters.
Answer:
5000.
Step-by-step explanation:
1000 milliliter is one liter. So if you have 5 liters 5 x 1000 can fit inside.
-6a>66 and please graph the inequalitie
[tex] - 6a > 66[/tex]
Answer:
a < -11 (picture included)
Step-by-step explanation:
To solve an inequality, you work it like a regular equation, with a few exceptions, such as flipping the inequality sign when you multiple or divide a number by a negative. Let's solve.
-6a > 66
Divide both sides by -6 and flip the inequality sign because we divided by a negative number.
a < -11
On a number line, it should look like the picture. It has an open hole because the inequality sign does not have a line under it.
-6a > 66 change the signs
6a < -66 divide both sides by 6
a < -11