Binomial: A polynomial that is the sum of two terms, each of which are monomials. The answer here would be A. b² - 14, because it is comprised of two terms. Answer B is a monomial because it only has ONE term, C is a trinomial because it has three terms, and D. is a multinomial, or a polynomial because it has more than three terms. Hope that helps!
Find r if (r, 6) and (5, -4) are two points on a line with a slope of 5/7 (Hint: use the slope formula)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](r,\ 6),\ (5,\ -4)\\\\m=\dfrac{5}{7}[/tex]
Substitute
[tex]\dfrac{-4-6}{5-r}=\dfrac{5}{7}\\\\\dfrac{-10}{5-r}=\dfrac{5}{7}\qquad|\text{cross multiply}\\\\5(5-r)=(-10)(7)\qquad|\text{use distributive property}\\\\25-5r=-70\qquad|-25\\\\-5r=-95\qquad|:(-5)\\\\\boxed{r=19}[/tex]
I need help, can anyone help?
What is the slope of the line that passes through (1, 4) and (1, −3)?
Always remember (y2-y1)/(x2-x1) for finding slope
So (-3)-4 / 1-1=
-7 / 0
So undefined
What needs to happen for the equation CH4 + O2 → CO2 + H2O to be balanced?
A. A coefficient of 2 must be added before both products.
B. A coefficient of 2 must be added before the second reactant and the second product.
C. Nothing, the equation is already balanced.
D. A coefficient of 2 must be added before both products and reactants.
g(t)=t^3-5t^2
h(t)=-t+5 find
(g/h)(t)
Please help
50pts who ever gets it
Answer:
Step-by-step explanation:
(g/h)(t) = g(t) / h(t)
=( t³-5t² ) /(t+5) we cannot simplify this further so
(g/h)(t) = ( t³-5t² ) /(t+5)
=
Answer:
The awnser is C and trust me
Step-by-step explanation:
Find two consecutive internet's whose sum is 75
37 and 38
consecutive integers have a difference of 1 between them
let n and n + 1 be the consecutive integers, then
n + n + 1 = 75 ( subtract 1 from both sides )
2n = 74 ( divide both sides by 2 )
n = [tex]\frac{74}{2}[/tex] = 37
the integers are 37 and 37 + 1 = 38
Write a real-world problem three yards of fabric will be cut into pieces so that each piece is 8 inches long.How many pieces can be cut?
Answer:
Stacy made a blanket using some fabric, she had 3 yards left over and decided to use the leftover pieces to make pot holders. She cut each piece into 8 inches long. Stacy had enough fabric to create 4.5 pieces.
Step-by-step explanation:
we find that 13 full pieces of fabric, each 8 inches long, can be cut from three yards of fabric.
The question asks how many pieces of fabric, each measuring 8 inches in length, can be cut from a total length of three yards of fabric. To begin with, we need to convert yards to inches, because the unit of measurement for the fabric pieces is in inches, not yards. We know that 1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches, hence 3 feet x 12 inches/foot = 36 inches). Therefore, three yards of fabric is 3 x 36 inches, which equals 108 inches.
Now, if each piece is to be 8 inches long, we divide the total number of inches by the length of one piece to find out how many pieces can be made:
108 inches / 8 inches/piece = 13.5 pieces.
However, since we cannot have half a piece of fabric, we can only make 13 full pieces, with a small remaining piece that would be less than 8 inches long.
Which construction is illustrated above?
A. a parallel line to a given line from a point not on the line
B. an angle congruent to a given angle
C. the bisector of an angle
D. a perpendicular to a given line from a point on the line
Construction of an angle congruent to a given angle.
.What are congruent angles?Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.
For two angles to be congruent their measurements must be equal.
Therefore, we can conclude that the construction above is angle congruent to a given angle.
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An angle congruent to a given angle construction is illustrated in the figure. Option B is the right choice.
Congruent angles share an identical measure, establishing equality between their angular dimensions.
In the realm of geometry, the fundamental criterion for angles to be considered congruent is that their measurements are precisely equal. This equality in angular magnitude implies that the angles exhibit indistinguishable orientations and positions.
Consequently, when engaging in geometric constructions, if a constructed angle aligns in measurement with a given angle, it is deemed congruent to the specified angle.
This fundamental concept is pivotal in geometric reasoning and problem-solving, providing a basis for establishing equivalences between angles and facilitating precise angular constructions. In summary, congruent angles signify an equality in measurement, forming a cornerstone in geometric analyses and constructions.
Option B is the right choice.
For similar question on congruent
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Which values are possible rational roots of 9x^3+14x^2-x+18=0 according to the rational root theorem? Select each correct answer. ±3 ±1/18 ±1/3 ±1/2
ANSWER
The possible rational roots are [tex]\pm3[/tex] and [tex]\pm\frac{1}{3}[/tex]
EXPLANATION
According to the rational roots theorem, the possible rational roots of
[tex]9x^3+14x^2-x+18=0[/tex]
is given by all the possible factors of [tex]18[/tex] which are
[tex]\pm1,\pm2,\pm3,\pm6,\pm9,\pm18[/tex]
expressed over all the possible factors of the coefficient of the highest degree of the polynomial which is [tex]9[/tex] which are
[tex]\pm1,\pm3,\pm9[/tex]
in their simplest form.
One of this possible ratios are [tex]\pm9[/tex] from the factors of 18, over [tex]\pm3[/tex] from the factors of 9.
This will give us
[tex]\frac{\pm9}{\pm3} =\pm3[/tex].
Another possible rational root is
[tex]\pm \frac{1}{3}[/tex].
Hence the correct options are
A and C.
Secrete: Check if the denominator is a factor of 9 and the numerator is also a factor of 18, then these are the correct answers.
The possible rational roots of the polynomial 9x^3+14x^2-x+18=0, according to the Rational Root Theorem, are ±3 and ±1/3. The other given options, ±1/18 and ±1/2, do not meet the criteria set by the theorem.
The question asks for the possible rational roots of the polynomial 9x^3+14x^2-x+18=0 according to the Rational Root Theorem. The Rational Root Theorem states that if a polynomial has a rational root p/q, where p and q are integers and q is not zero, then p is a factor of the constant term and q is a factor of the leading coefficient.
The constant term here is 18 and its factors are ±1, ±2, ±3, ±6, ±9, and ±18. The leading coefficient is 9 and its factors are ±1, ±3, and ±9. According to the theorem, we divide each factor of the constant term by each factor of the leading coefficient to determine the potential rational roots:
±1/1, ±1/3, ±1/9
±2/1, ±2/3, ±2/9
±3/1, ±3/3, ±3/9
±6/1, ±6/3, ±6/9
±9/1, ±9/3, ±9/9
±18/1, ±18/3, ±18/9
Out of the list, the values that match the options given in the question are ±3 and ±1/3. The other options, ±1/18 and ±1/2, are not rational roots because 1/18 is not a factor of 9 (leading coefficient), and 2 is not a factor of 18 (constant term) when considering the reduced form.
Girl works at a book store she gets $145 per week plus 5% for every book sold she wants to have $600 by the end of the week, how many books does she need to sell?
An oven temperature is set to 329 degrees f. What is this setting closest to in degrees celsius?
It is 165 degrees celcius
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Dreya is saving money to purchase a $900 computer, and she saves $10 the first week. Each week after that, she saves $3 more than the previous week, except in the last week, when she reaches $900. To have a final sum of excatly $900, how much money does dreya need to save in her final week of saving?
Name the complex conjugate. Then find the product. 1. -8i
You seem to be missing some information here.
Complex conjugate example:
2 - 16i >> 2 + 16i
Are you sure this is the entire question?
For this case we have a complex number of the form:
[tex]a + (b) (i)\\[/tex]
Where:
a: It's the real part [tex](b) (i)[/tex]: It is the imaginary partThus, given 1-8i, its complex conjugate is given by:
[tex]1 + 8i\\[/tex]
On the other hand, the product of both is given by:
[tex](1 + 8i) (1-8i) =\\\\(1 ^ 2-8i + 8i-64 (i ^ 2)) =\\\\1-64 (-1) =\\\\1 + 64 = 65\\[/tex]
Answer:
Conjugate complex: [tex]1 + 8i\\[/tex]
Product: 65
PLEASE HELP! The high school band wants to sell two types of cookies, chocolate chip and peanut butter, as a fundraiser. A dozen chocolate chip cookies requires 2 cups of flour and 1 egg. A dozen peanut butter cookies uses 3 cups of flour and 4 eggs. The club has 90 cups of flour and 80 eggs on hand. The profit on the chocolate chip cookies is $1 per dozen and on the peanut butter is $1.50 per dozen. If they want to offer both types of cookies, how many of each cookie should the club make to maximize profits?
a.
infeasible solutions
c.
24 dozen chocolate chip
14 dozen peanut butter
b.
30 dozen chocolate chip
25 dozen peanut butter
d.
20 dozen chocolate chip
18 dozen peanut butter
Answer:
24 dozen chocolate chip
14 dozen peanut butter
Step-by-step explanation:
x = number of dozen chocolate chip cookies
y = number of dozen peanut butter cookies
Total number of cups of flour is:
2x + 3y ≤ 90
Total number of eggs is:
x + 4y ≤ 80
Total profit is:
P = x + 1.5y
Since this is multiple choice, one method would be to calculate the profit for each option, then choose the one that's largest.
But let's try solving this algebraically. x and y are positive integers, and we want them to be as large as possible.
Let's start by assuming the solution is on the line 2x + 3y = 90.
x + 4y ≤ 80
2x + 8y ≤ 160
90 − 3y + 8y ≤ 160
5y ≤ 70
y ≤ 14
If y = 14, x = 24, and P = 45.
Now let's assume the solution is on the line x + 4y = 80.
2x + 3y ≤ 90
2 (80 − 4y) + 3y ≤ 90
160 − 8y + 3y ≤ 90
70 ≤ 5y
14 ≤ y
Therefore, to maximize the profit, they should bake 24 dozen chocolate chip cookies and 14 dozen peanut butter cookies.
Which graph represents the solution set of the system of inequalities?
{ x+y<1
2y ≥ x-4
Answer:
The graph in option (c) is the correct answer.
Step-by-step explanation:
The line corresponding to the inequality [tex]x+y<1[/tex] represents the dashed line and the line corresponding to the inequality [tex]2y\geq x-4[/tex] represents the solid line.
In order to figure out the correct shaded region, we test one point from each of the four possible regions and figure out the point at which both the inequalities bold true. The region containing that point would be the correct shaded region.
Let us test the point (0,0).
First inequality [tex]0+0<1[/tex], that is, [tex]0<1[/tex] holds true.
The second inequality [tex]2(0)\geq 0-4[/tex] that is, [tex]0\geq -4[/tex] as well holds true.
Since both the inequalities hold true at point (0,0), therefore, region containing origin is the correct answer. Thus, the correct answer is forth option. Since the options are not labeled, I have attached the correct graph with my solution in order to make sure you get the correct answer.
What are the outliers in this data set 78, 87, 81, 16, 64, 100, 88, 10, 87, 110, 108, 149
Answer: 10 & 16
Step-by-step explanation:
Last year a business had profits of $8,000.This year its profits are 5 times as great.This are this year's profits?
Given the formula for the perimeter of a rectangle where l represents the length and w represents the width.
2(l + w)
What does the 2 represent in this formula?
A) The 2 represents the perimeter.
B) The 2 represents the two width pairs.
C) The 2 represents the two length pairs.
D) The 2 represents the two sets of length and width pairs.
For this one, I would go with D.
D makes the most sense, giving that there is two sets of each and, that it is just a shorter way to say "add all the sides."
B and C would only give us half or part of the perimeter and then A does not make much sense.
D would be the answer through process of elimination.
If it is 11:30, what time would it be in 40 minutes?
in 40 minutes it will be 12:10
Find the slope of the line.
The slope:
[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]
Look at the picture.
6 units down → -6
2 units right → 2
[tex]m=\dfrac{-6}{2}=-3[/tex]
Answer: Slope = m = -3answer: [tex] \frac{3}{-1} x[/tex]
explanation:
slope-intercept formula ==> [tex]y = mx + b[/tex]
[tex]m[/tex] is slope , and [tex]b[/tex] is y-intercept
to find the slope you need to start at the y intercept and go 3 units up and 1 unit left. and if you repeat it again, until you reach the top of the graph and that would make partial of the line.
so, the slope is [tex]\frac{rise}{run}[/tex], so if you plug it in it would look like this
[tex]y = \frac{3}{-1} x + b[/tex]
A D D I T I O N A L I N F O
then you find the y-intercept which would be where the line intersects at the y axis, which is -10. plug the number into the equation
[tex]y = \frac{3}{-1} x - 10[/tex]
and that would make our final answer.
hope this helps! correct me if there is anything wrong ❤ from peachimin
Defined Terms:
Opposite rays form a:
point
ray
line
plane
Rays are always named with two points rays
Ankur estimated the quotient of 15 1/3 divided by -4 2/3 to be 3. Which best describes his error?
Ankur multiplied the compatible numbers 15 and –3.
Ankur found that the quotient of a positive number and a negative number is negative.
Ankur found that the quotient of a positive number and a negative number is positive.
Ankur added the compatible numbers 15 and –3.
When dividing a positive number by a negative number, the result is negative.
A better estimation would be -3.
Solution:
As the two numbers [tex]15 \frac{1}{3} {\text{and} -4\frac{2}{3}[/tex] are mixed fractions.
[tex]15 \frac{1}{3}= \frac{46}{3} \\\\ -4\frac{2}{3}= \frac{-14}{3}[/tex]
Now, [tex]\frac{ \frac{46}{3}}{\frac{-14}{3}}[/tex] = - 3
Ankur's answer= 3
The mistake he has committed , while dividing two fractions , he must have forgot that one of the fraction which is in the denominator bears negative sign before it.
So, [tex]\frac {+}{-}= -[/tex].
Ankur forgot to put negative sign before 3.
So, The correct option which describes ankur's error is : Ankur found that the quotient of a positive number and a negative number is positive.
Option 3 is right choice.
What is the solution of the equation when solved over the complex numbers? X2+24=0
The solution to the equation x² + 24 = 0 over the complex numbers is x = ±2√(6)i. After isolating x² on one side, we take the square root of both sides and introduce the imaginary unit i because the number under the square root is negative.
Explanation:To solve the equation x² + 24 = 0 over the complex numbers, we need to find values of x that satisfy the equation. This is a quadratic equation with 'a' as 1 (the coefficient of x²), 'b' as 0 (since there is no x term), and 'c' as 24.
We will first isolate x² by subtracting 24 from both sides of the equation:
x² = -24
Next, to find x, we take the square root of both sides. Remember that when we take the square root of a negative number, we get an imaginary number. The square root of -24 can be expressed as:
x = ±√(-24)
This simplifies to:
x = ±√(24) × ±i
Since √(24) is √(4 × 6), which simplifies to 2√(6), the final solution in terms of complex numbers is:
x = ±2√(6)i
I'll Mark The First To Answer And Work Shown Brainliest!!!!!!!! PLEASE HELP ASAP
In 2005, there were 12,000 students at Beacon High. In 2010, there were 12,250. What is the rate of change in the number of students?
a. 250/yr
b. 50/yr
c. 42/yr
d. 200/yr
Answer:
Step-by-step explanation:
(2005, 12,000) (2005, 12,000)
x1 y1 x2 y2
m= (12,250-1200) / (2010-2005) = 250/5 = 50/1 = or 50
item 10 question 1 identify the percent of change as an increase or a decrease. 5/4 to 3/8
[tex]\frac{(new) - (original)}{original} = \frac{\frac{3}{8}- \frac{5}{4} }{\frac{5}{4} }[/tex]
[tex]\frac{3}{8} - \frac{5}{4} (\frac{2}{2}) = \frac{3}{8} - \frac{10}{8} = \frac{-7}{8}[/tex]
[tex]\frac{-7}{8}[/tex] ÷ [tex]\frac{5}{4}[/tex]
= [tex]\frac{-7}{8}[/tex] * [tex]\frac{4}{5}[/tex]
= [tex]\frac{-7(4)}{8(5)}[/tex]
= [tex]\frac{-7}{2(5)}[/tex]
= [tex]\frac{-7}{10}[/tex]
= -0.70
multiply by 100 to get the percent: - 70% (the negative represents decrease)
Answer: 70% decrease
(04.05)Marcus spent 10 hours doing his homework last week. This week he spent 11 hours doing homework. He says that he spent 110% more time doing homework this week. Is he correct? Show your work to justify your decision.
Answer:
No
Step-by-step explanation:
11-10 = 1
He spent 1 hour more this week
Which is:
1/10 × 100 = 10% more
Marcus spent 10% more time doing homework this week. His calculation is wrong.
Time used last week by marcus = 10 hours
Time used this week by marcus = 11 hours
Difference in hours = 11 - 10 = 1 hour
This means that Marcus used 1 more hour this week than last week
% increase = 1/10 * 100
% increase = 10%
This shows that he spent 10% more time doing homework this week.
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Geoff has a bag that contains 4 red marbles and 6 blue marbles. He chooses two marbles at random and does not replace them. What is the probability that the first marble is blue and the second marble is red? A. B. C. D.
Answer: [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
First pick (blue) and Second pick (red)
[tex]\frac{6}{10}[/tex] x [tex]\frac{4}{9}[/tex]
= [tex]\frac{6(4)}{10(9)}[/tex]
= [tex]\frac{2(2)}{5(3)}[/tex]
= [tex]\frac{4}{15}[/tex]
Answer:
The answer is 4/15 hopefully this helps!
WILL GIVE 5 STARS!!
Marshall uses the polynomial identity (x−y)^2=x^2−2xy+y^2 to show that 8² = 64.
What values can Marshall use for x and y?
Answer: C
Step-by-step explanation:
(x - y)²
we want (8)², so need: x - y = 8
There are many options that satisfy x - y = 8 but of the options provided to you, 10 - 2 is the only one that works.
A) 2 - 6 = -4
B) 64 - 0 = 64
C) 10 - 2 = 8
D) 8 - 64 = -56
What is the equation of the line with a slope of 3/4 that goes through the point (4,1) in slope-intercept form ?
The slope-point form of a line:
[tex]y-y_0=m(x-x_0)[/tex]
We have
[tex]m=\dfrac{3}{4}\\\\(4,\ 1)\to x_0=4,\ y_0=1[/tex]
Substitute:
[tex]y-1=\dfrac{3}{4}(x-4)[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
Solve for y:
[tex]y-1=\dfrac{3}{4}(x-4)\qquad|\text{use distributive property}\\\\y-1=\dfrac{3}{4}x-3\qquad|\text{add 1 to both sides}\\\\y=\dfrac{3}{4}x-2[/tex]
Answer: D.
To make fruit salad sara uses 28 ounces of pineapple 21 ounces of apples 19 ounces of bannas and 16onces of mango how many 6-ounce serving of fruit salaf can sarah make?