Find a and b so that the polynomial, p(x)=x^2+ax-b passes through the points (6,-9) and (1, 16)
The given equation is:
p(x) = x^2 + ax - b
We write this in terms of y:
y = x^2 + ax – b
To solve for the values of the constants a and b, we are given the following conditions:
When x = 6, y = -9
When x = 1, y = 16
From these conditions, we can formulate two equation by substituting the values of y:
-9 = 6^2 + a(6) – b
6a = b – 45 ---> 1
16 = 1^2 + a(1) – b
a = b + 15 ---> 2
Combining equations 1 and 2:
6 (b + 15) = b – 45
6b + 90 = b – 45
5b = -135
b = -27
calculating for a using equation 1:
a = b + 15
a = -27 + 15
a = -12
Answers:
a = -12
b = -27
y=4x -1 and 12x=3y+7
The field hockey coach is purchasing new uniforms for the team. Company A charges a one-time printing fee of $100 and $12 per uniform. Company B charges a one-time fee of $61 and $15 per uniform. How many uniforms must the coach buy to get a better deal from Company A?
Hot dogs come in packs of 10 and buns come in packs of 8. Whats the least amount of packs you can buy to have the same amount of hot dogs and buns.
How would I solve this?
A man paid $71.40 for a radio. The radio was marked 15% off the original selling price. What was the original selling price?
f(x) = Square root of x plus eight.; g(x) = 8x - 12 Find f(g(x))
Final answer:
To find f(g(x)), substitute g(x) into f(x) and simplify the expression to get the final answer. The final answer to the question would be as f(g(x)) = 8x⁴ - 32x³ + 32x² + 3
Explanation:
To find the value of f(g(x)) the following steps to be followed where the value of f(x) be substituted in g(x).
f(x) = 2x² + 3; g(x) = −2x² + 4x
Find f(g(x)) by substituting g(x) into f(x): f(g(x)) = 2(-2x² + 4x)² + 3
Simplify the expression: f(g(x)) = 2(4x⁴ - 16x³ + 16x²) + 3
Final answer after expansion: f(g(x)) = 8x⁴ - 32x³ + 32x² + 3
Choose the missing exponent to create a polynomial: 3x^4+4x^2-9x^-?+2
A)2
B)3
C)-9
D)7
E)4
For a Polynominal 3x^4+4x^2-9x^-?+2 the missing part is mathematically given as
3x^4+4x^2-9x^-(-9)+2
-9, Option C is correct
What is a Polynomial?
Polynomials are summations of elements of the format of kxn, having k as any digit and n is +ve integer
Generally, the expression for the Polynominal is mathematically given as
3x^4+4x^2-9x^-?+2
In conclusion, the Polynominal must have all positive exponents, hence the value must be negative to give a positive exponent
Hence, -9 is correct
Read more about Polynomial
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In a large bag of marbles, 30% of them are red. a child chooses 4 marbles from this bag. if the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles? 0.0756 0.1764 0.2646 0.0810
An angle measures 7pi/9 radians. What is the degree measure of the angle?
If the discriminant of an equation is negative, which of the following is true of the equation
A it has two complex solutions
B it has one real solution
C it had two real solutions
Answer:
A. It has two complex roots.
Step-by-step explanation:
We are given that
Discriminant of an equation =negative
We have to find which is true about the equation .
Let quadratic equation
[tex]ax^2+bx+c=0[/tex]
Discriminant=[tex]D=b^2-4ac[/tex]
If D < 0 , then the equation has complex roots.
Therefore, if the discriminant of an equation is negative then the equation has two complex roots.
Answer:A. It has two complex roots.
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what is this answer
Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.
n | an
1 | 9
2 | 3
3 | −3
Can square root of 32 be simplified
A triangle has side lengths of 20 cm, 99 cm, and 108 cm. Classify it as acute, obtuse, or right.
A. acute
B. obtuse
C. right
If conner spent $36 to buy a new collar for each of his dogs.if each collar cost $6,how many dogs dose conner have?
In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.
Find a quadratic model for the data in the table. Type your answer below. Show your work.
Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 17 ft by 17 ft by 2 in. for a patio if the concrete costs $40.00 per cubic yard? (1 cubic yard = 27 cubic feet)
Answer:
It will cost approximately $71.360.
Step-by-step explanation:
Given,
The dimension of the concrete is 17 ft by 17 ft by 2 in.
1 ft = 12 inches ⇒ 2 inches = 1/12 × 2 = 1/6 ft.
Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.
Now, the volume of the concrete = 17 × 17 × 1/6
[tex]=\frac{289}{6}\text{ cubic ft}[/tex]
We know that,
1 cubic yard = 27 cubic feet
[tex]\implies 1 \text{ cubic feet}=\frac{1}{27}\text{ cubic yards}[/tex]
[tex]\implies \frac{289}{6}\text{ cubic ft}=\frac{289}{6}\times \frac{1}{27} = \frac{289}{162}\text{ cubic yards}[/tex]
Since, the concrete costs $40.00 per cubic yard.
Hence, the total cost of concrete = [tex]\frac{289}{162}\times 40=\frac{11560}{162}=\$71.3580247\approx \$71.360[/tex]
The total cost of concrete is,
C = $71.4
We have to give that,
Dimensions of the concrete are,
17 ft by 17 ft by 2 in.
And, the concrete costs $40.00 per cubic yard.
Since we know that,
1 feet = 12 inches
Hence,
2 inches = 2/12 = 1/6 feet
Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.
So, the Volume of the concrete,
V = 17 x 17 x 1/6
V = 48.2 cubic feet
Here, 1 cubic yard = 27 cubic feet
And, the concrete costs $40.00 per cubic yard.
Hence, the total cost of concrete is,
C = 48.2 × 40 / 27
C = $71.4
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The equation of a line is y = mx + 2. What is the value of m (the slope) if the line passes through point A(−5, −18)?
M=-4
M=4
M=1/4
M=7/8
Two sandboxes with the same area are shown. The equation w(3w+1)=5^2 represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter.
A.) 2.72 meters
B.) 3.06 meters
C.) 9.16 meters
D.) 10.18 meters
sandbox 1 area = 5*5 = 25 square m
sandbox 2
25=w*(3w+1)=
3w^2+w-25=0
w=2.7248 (round to 2.72 m)
2.72*3=8.16+1 = 9.16
Longest side = 9.16 meters
Answer:
C.) 9.16 meters
Step-by-step explanation:
We are given that the two sandboxes have same area and the equation is given by 25 = w*(3w+1).
Now, we simplify this equation in order to find the value of unknown variable 'w'.
i.e. 25 = 3[tex]w^{2}[/tex]+w
i.e. 3[tex]w^{2}[/tex]+w-25=0
The two factors of this quadratic equation are w=2.72 and w= -3.05.
But, as 'w' represents the length of the box, so it cannot be negative.
Therefore, w = 2.72
So, the longest side of the box is (3w+1) = 3*2.72+1 = 9.16 meter
Hence, the length of longest side to the nearest hundredth is 9.16 meter.
If (44)x = 432, what is the value of x?
4
7
8
28
44 x 4 = 176
44 x 7 =308
44 x 8 = 352
44 x 28 =1232
none of those will =432
are you sure you have the right numbers?
(44)x=432
x=432/44 = 9.8181
Does anyone know the answer to this question?
f(x) = x-3
g(x) = 2f(x)
g(2) = 2(2-3) = 2 * -1 = -2
If the sum of 7 and 9 is more than 12 add 3; if less, subtract 2. the correct answer is
The sum of 7 and 9 is:
7 + 9 = 16
The sum which is 16 is greater than 12. Therefore we add 3 to the sum:
16 + 3 = 19
Therefore the correct answer to this problem is 19.
A triangle has side lengths 9, 10, and 12. is it acute, obtuse, or right? explain.
Final answer:
By applying the Pythagorean theorem and comparing the square of the longest side to the sum of the squares of the other two sides, it is determined that a triangle with sides of 9, 10, and 12 is an acute triangle since 144 is less than 181.
Explanation:
To determine whether a triangle with side lengths of 9, 10, and 12 is acute, obtuse, or right, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides. If this condition is met, the triangle is right-angled. If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse. Conversely, if the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute.
For this triangle, the side lengths squared are:
9² = 8110² = 10012² = 144Adding the squares of the two shorter sides: 81 + 100 = 181.
Since 144 < 181, the square of the longest side (12²) is less than the sum of the squares of the other two sides, indicating that this triangle is acute.
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −3
0 0
1 3
g(x)
g(x) = 7x + 2
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
A roller coaster climbs 84 feet on the first hill then drop 60 feet down. on the second hill the roller coaster climb another 32 feet then drops 44 feet. what is te height at the end of the second hill ?
Answer:
12 feet.
Step-by-step explanation:
A roller coaster climbs the height on first hill = 84 feet.
Then drops down = 60 feet.
Height gained by the roller coaster = 84 - 60
= 24 feet
On other hill roller coaster climbs = 32 feet
Height gained by the roller coaster = 24 + 32 = 56 feet.
It drops again to the height = 44 feet
So the final height at the second hill = 56 - 44
= 12 feet
Therefore, height of roller coaster on the second hill is 12 feet.
which best describes the diameter of a circle?
A. The distance from the center to any point of the circle
B. The length of a chord that contains the center of the circle
C. The distance around the circle
D. The length of a chord that does not contain the center of the circle
Which best describes the diameter of a circle?
Statements
A. The distance from the center to any point of the circle
This statement describes the radius of the circle
B. The length of a chord that contains the center of the circle
This statement describes the diameter of the circle
C. The distance around the circle
This statement describes the circumference of the circle
D. The length of a chord that does not contain the center of the circle
This statement describes a line segment linking any two points on a circle that does not contain the center of the circle
therefore
the answer is the option
B. The length of a chord that contains the center of the circle
The correct answer is:
B) The length of a chord that contains the center of the circle
Explanation:
A chord is a segment that goes across a circle, with both endpoints on the circle.
A diameter goes through the center of a circle and has both endpoints on the circle; this makes it a chord that goes through the center.
Convert: 52 cups = ________ qt.
1 cup = 0.25 quarts
52 *0.25 = 13 quarts
13 is the answer HOPE THAT HELPS
- ( 1 + 7x ) - 6 ( -7 - x ) = 36
Please solve and show work