Final answer:
To factor the expression y^3 - 9y^2 + y - 9 by grouping, divide it into two groups, factor out common factors, and note that (y - 9) is common to both, yielding the final factored form (y^2 + 1)(y - 9).
Explanation:
To factor by grouping the expression y3 − 9y2 + y − 9, we first split it into two parts where common factors are apparent:
(y3 − 9y2) and (y − 9)
Next, we factor out the common factors from each group:
y2(y − 9) + 1(y − 9)
Now, we notice that (y − 9) is a common factor in both terms. So, we factor (y − 9) out of the entire expression:
(y2 + 1)(y − 9)
This gives us the final factored form of y3 − 9y2 + y − 9, which is (y2 + 1)(y − 9).
Ellen wishes to mix candy worth $1.45 per pound with candy worth $3.74 per pound to form 27 pounds of a mixture worth
$3.06 per pound. How many pounds of the more expensive candy should she use?r.
Final answer:
Ellen should use approximately 18.98 pounds of the more expensive candy worth $3.74 per pound to achieve a 27-pound mixture worth $3.06 per pound when mixed with candy worth $1.45 per pound.
Explanation:
To solve the problem of mixing candies to achieve a specific price per pound, we can use the method of weighted averages. Ellen wants to mix candy worth $1.45 per pound with candy worth $3.74 per pound to create a 27-pound mixture that will be worth $3.06 per pound. Let's denote the amount of the more expensive candy as x pounds and the amount of the less expensive candy as 27 - x pounds.
The total value of the expensive candy is x times $3.74, and the total value of the less expensive candy is (27 - x) times $1.45. The total value of the mixture should equal 27 times $3.06, which gives us the equation:
(x × $3.74) + ((27 - x) × $1.45) = 27 × $3.06
Expanding the equation:
$3.74x + $1.45 × 27 - $1.45x = $82.62
Combining like terms:
$3.74x - $1.45x = $82.62 - $1.45 × 27
$2.29x = $82.62 - $39.15
$2.29x = $43.47
Dividing both sides by $2.29 gives us the amount of the more expensive candy:
x = $43.47 / $2.29
x ≈ 18.98 pounds
Ellen should use approximately 18.98 pounds of the more expensive candy to achieve the desired mixture.
To solve this problem, set up a system of equations using the weight and price information. Then solve the system of equations to find the number of pounds of the more expensive candy. Ellen should use 19 pounds of the more expensive candy, which is worth $3.74 per pound.
Explanation:To solve this problem, we can set up a system of equations. Let x represent the number of pounds of candy worth $1.45 per pound and y represent the number of pounds of candy worth $3.74 per pound. We know that the total weight of the mixture is 27 pounds, so we have the equation x + y = 27. We also know that the average price of the mixture is $3.06 per pound, so we can set up the equation (1.45x + 3.74y)/27 = 3.06.
We can solve this system of equations using substitution or elimination methods. Let's use substitution.
From the first equation, we can solve for x in terms of y: x = 27 - y.Substitute this expression for x in the second equation: (1.45(27 - y) + 3.74y)/27 = 3.06.Simplify and solve for y: 39.15 - 1.45y + 3.74y = 82.62.Combine like terms: 2.29y = 43.47.Divide both sides by 2.29: y = 19.So, Ellen should use 19 pounds of the more expensive candy, which is worth $3.74 per pound.
Given: p: x – 5 =10 q: 4x + 1 = 61 Which is the inverse of p → q? If x – 5 ≠ 10, then 4x + 1 ≠ 61. If 4x + 1 ≠ 61, then x – 5 ≠ 10. If x – 5 = 10, then 4x + 1 = 61. If 4x + 1 = 61, then x – 5 = 10.
Answer:If
x – 5 ≠ 10, then 4x + 1 ≠ 61.
Step-by-step explanation:
I just completed the test
Ken got 7 hamsters and 3 mice today. If he does not want to put more than 3 hamsters or mice in a cage, how many cages does he need?
Mark as Brainliest
Answer:
yup 4 cages
Step-by-step explanation:
jamal runs 1 2/5 miles a day to train a race. If he runs the same distance for 3 days a week, what is the distance he runs in one week?
((5x−16)^3−4)^3=216,000
Final answer:
To solve the equation ((5x−16)^3−4)^3=216,000, one must apply the rules of exponents and algebraic manipulation step by step, isolating x and using mathematical operations to simplify the expression.
Explanation:
Solving an Equation with Powers
The problem ((5x−16)^3−4)^3=216,000 involves understanding the rules of exponents and algebraic manipulation. When you're dealing with expressions raised to a power, it's important to remember that the power affects everything inside the parentheses, including the number. This is evident in expressions like (5³)* which is equivalent to 5⅜⅓ and results in 5 multiplied by itself 12 times, giving 5⁼.
When approaching the given equation, you would first look to isolate the base of the cube on one side, leading to the cube root to undo the cube power. You would continue simplifying step by step until you isolate x, the variable in question. The key here is to perform operations that counteract the powers and other mathematical operations presented.
In some cases, you might encounter a polynomial long division such as dividing S=9x⁵ +4x⁴ - 5x³ +6x² + 2x - 3 by another polynomial. This requires knowledge of the long division algorithm adapted for polynomials. Each term is divided individually to find the quotient.
What is the measure of each base angle on an isosceles triangle it it's vertex angle measures 28 degrees and it's 2 congruent sides measure 12 units
Final answer:
The measure of each base angle in an isosceles triangle with a 28-degree vertex angle is 76 degrees, which is the result of subtracting the vertex angle from 180 and dividing by 2.
Explanation:
To find the measure of each base angle of an isosceles triangle when the vertex angle is given, you can use the fact that the sum of all angles in a triangle is 180 degrees. Since in an isosceles triangle the two base angles are congruent (equal in measure), you can subtract the vertex angle from 180 degrees and then divide the result by 2 to find the measure of each base angle.
For the given triangle with a vertex angle of 28 degrees:
Subtract the vertex angle from 180 degrees: 180 - 28 = 152 degrees.Divide the result by 2 to find each base angle: 152 / 2 = 76 degrees.Thus, the measure of each base angle in the given isosceles triangle is 76 degrees.
In an equilateral hexagon, four of the exterior angles each have a measure of x degrees. The other two exterior angles each have a measure of twice the sum of x and 48. Find the measure of each exterior angle. (Show work!!)
Final answer:
The measure of each of the four exterior angles of the hexagon is 21 degrees, and the measure of the remaining two exterior angles is 138 degrees each. This was determined by setting up an equation based on the sum of exterior angles of a polygon, which is always 360 degrees, and solving for x.
Explanation:
To solve this problem, we start by understanding that the sum of the exterior angles of any polygon is always 360 degrees. For a hexagon, this sum is divided among six exterior angles. According to the problem, four of these angles are each x degrees, and the remaining two are each twice the sum of x and 48.
Let's set up the equation reflecting this information:
4x + 2(2x + 96) = 360.
Simplifying this equation, we get:
4x + 4x + 192 = 360,
which combines to:
8x + 192 = 360.
Now, we'll solve for x:
8x = 360 - 192,
8x = 168,
x = 21.
Therefore, each of the four exterior angles is 21 degrees, and each of the remaining two exterior angles is twice the sum of 21 and 48, which is:
2(21 + 48) = 2(69) = 138 degrees.
(ax + 5)(x-b)+4x=(2x × 2x)+ cx-10
Equating coefficients in identities
Can someone figure out the area ?
A study was done to investigate the relationship between outdoor temperature and the amount of fluids an outdoor athlete drinks per day. The correlating linear model is shown below, where x represents the number of degrees over 80°F, and y represents the amount of fluids drank (in liters). Interpret the y-intercept. y = 3.85 + 0.55x A. An athlete drinks 7 L per day when the temperature is 80°F. B. An athlete drinks 4.4 L per day when the temperature is 80°F. C. An athlete drinks 3.85 L per day when the temperature is 80°F. D. An athlete drinks 0.55 L per day when the temperature is 80°F.
Answer:
C. An athlete drinks 3.85 L per day when the temperature is 80°F
Step-by-step explanation:
Y-intercept of a linear model, equation or a straight line refers the point at which a line crosses the y-axis of a graph. It generally indicates a point on the graph where x equals 0.
For the equation y = 3.85 + 0.55x
At y-intercept, x = 0. Substitute x into the equation, we have:
y = 3.85 + 0.55 (0)
y = 3.85 + 0
y = 3.85
This implies that the value of fluid drank by an athlete at the starting temperature of 80°F (at x=0) is 3.85 L per day
48 students are going to the zoo. one-fourth brought umbrellas. how many people did not bring umbrellas
?
In triangle FGH, mF is 94°, mG is 49°, and mH is 37°. The exterior angles of triangle FGH are J, K, and L, and they are adjacent to F, G, and H, respectively.
What is mK?
A. 86°
B. 49°
C. 143°
D. 131°
Using the property of exterior angles, mK is found by adding the measures of the non-adjacent interior angles mF and mH, resulting in mK being equal to 131°.
Explanation:The student is asking to find the measure of exterior angle mK in triangle FGH. To find mK, which is the exterior angle adjacent to G, we need to use the property of exterior angles in a triangle. This property states that the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.
To find mK we add the measures of angles mF and mH:
mK = mF + mH
mK = 94° + 37°
mK = 131°
Therefore, the measure of the exterior angle K is 131°, which corresponds to answer choice D.
What is the range of: 21, 35, 17, 27, 32, 12 and 30
Find 2/9 of 36
write in simplest form 12:3
The value of a is -3
Please help and show work
Mr.holms used 4/5 of a carton of orange juice.he used equal amounts of leftover juice for two servings what fraction of the whole carton of juice did he use for each serving
What is a net? WIll mark brainliest!!!
In Mr.Martinez's sixth period class, there are 8 boys and 12 girls. what is the probability of randomly selecting a girl?
Kate has 12 1/2 pounds of chocolate. She gives each of her 5 friends x pounds each and has 3 1/3 pounds left over. How much did she give each of her friends?
The figure consists of two quarter circles and a
square. What is the perimeter of this figure?
Use 3.14 for π .
82.24 in.
114.24 in.
132.48 in.
164.48 in.
(A square with sides measuring 16 in and has two quarter circles attached with with the same measurements.)
Answer:
The perimeter of the figure is [tex]114.24\ in[/tex]
Step-by-step explanation:
we know that
The perimeter of the figure is equivalent to the perimeter of a square plus the perimeter of a semicircle
step 1
Find the perimeter of square
The perimeter of square is equal to
[tex]P=4b[/tex]
where
b is the length side of the square
we have
[tex]b=16\ in[/tex]
substitute
[tex]P=4(16)=64\ in[/tex]
step 2
Find the circumference of a semicircle
The circumference of a semicircle is equal to
[tex]C=\pi r[/tex]
we have
[tex]r=16\ in[/tex]
[tex]\pi=3.14[/tex]
substitute
[tex]C=3.14(16)=50.24\ in[/tex]
step 3
Find the perimeter of the figure
[tex]64\ in+50.24\ in=114.24\ in[/tex]
Which equation can be used to find the unknown length, a, in this triangle?
The unknown length, a, in this triangle can be found using the formula in the first option, a² + 15² = 17².
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Given is a right angled triangle.
We know the Pythagoras Theorem which states that,
Hypotenuse² = Base² + Altitude²
Hypotenuse is the side opposite to the right angle.
Here length of hypotenuse = 17 m
Length of base = 15 m
Length of altitude = a
Using the theorem,
17² = 15² + a²
Or,
a² + 15² = 17²
Hence the correct formula is a² + 15² = 17².
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experts only please.......................
the nth term to a sequence n+7 first 3 terms
The first three terms of sequence whose nth term is n+7 are 8, 9 and 10.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given that the nth term of a sequence is n+7.
We need to find the first three terms of the sequence.
Tₙ=n+7
To find the first 3 terms, replace value of n with 1,2 and 3.
When n=1
T₁=1+7=8
When n=2,
T₂=2+7=9
When n=3
T₃=3+7=10
Hence, the first three terms of sequence whose nth term is n+7 are 8, 9 and 10.
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A tennis star was hired at a convention. She was paid $3000 plus 2% of all admission fees collected at the door. The total amount she received for the day was $3440. Find the total amount collected at the door.
What is the median value of the data set shown on the line plot? Enter your answer in the box. A line plot with twenty-two data values. Labels are at zero, three, six, nine, and twelve. Tick marks are every one unit. Values appear as x marks above the line. Plot data values are one x mark above one, one x mark above two, two x marks above three, two x marks above four, three x marks above five, four x marks above six, three x marks above seven, three x marks above eight, two x marks above nine, and one x mark above eleven.
The median is 6.
This median is easy to find-- you place all your numbers in numerical order and choose the number(s) in the middle-- for this question the median is 6.
I believe your line plot looks like this [Screenshot was taken on K12]:
Please forgive me if this is wrong, and please tell me the correct answer if this incorrect.
what is the place value of 7 in 3.567
Can you help me pleas now?
To arrange the six numbers into three pairs so that the sum of each pair is equal, you could create the pairings of 4 and -2, -1 and 5, and 6 and 8. Each of these pairs has a sum of 2, 4, and 14 respectively.
Explanation:The six number cards provided are 4, -2, -1, 5, 6 and 8. The task is to arrange these into three pairs, such that the sum of each pair is equal. Based on these conditions, our possible pairs are:
4 and -2-1 and 56 and 8These pairs are obtained by adding the numbers together. For example, the pair 4 and -2 results in a sum of 2 (4 + -2 = 2). Similarly, -1 and 5 also results in a sum of 4 (-1 + 5 = 4), and 6 and 8 results in a sum of 14 (6 + 8 = 14). Two pairs have the same sum of 4 while one pair has the sum of 14.
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Therefore, the complete question is
Here are six number cards
-4, -2, -1, 5, 6, 8
Arrange the cards into three pairs with the same total.
• Please write each pair on separate lines and use the word 'and' between the numbers (eg. 7 and -3)
Multiply and simplify. 6xy^3z⋅3x^2yx^2
a) 18(xyz)^10
b) 9x^5y^4z
c) 18x^5y^4z
d) 18x^4y^3z
Multiplying and simplifying 6xy³z · 3x²yx² gives;
C: 18x⁵y⁴z
Solving ExponentsWe want to multiply and simplify;
6xy³z · 3x²yx²
Let us first group the like terms to get;
(6 * 3) * (x · x² · x²) * (y³ · y) * z
According to laws of exponents;
a³ × a² = a⁽³ ⁺ ²⁾ = a⁵
Thus;
(6 * 3) * (x · x² · x²) * (y³ · y) * z = 18x⁵y⁴z
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In one hour 3/4 pint of a chemical can be filtered how long in HOURS will it take to filter 2 1/2 pints of chemical