The quadratic function f whose zeros are 6 and 5 is represented by the formula f(x) = (x - 6)(x - 5). This formula utilizes the fact that the zeros of a quadratic function, also known as the roots, are the x-values for which the function equals zero.
Explanation:To write a quadratic function f whose zeros are 6 and 5, we first identify the zeros. These zeros are the roots of the equation, meaning the points at which the curve of the function hits the x-axis.
A quadratic function is in the form f(x) = a(x - p)(x - q), where p and q are the zeros. Therefore, if the zeros are 6 and 5, our function becomes f(x) = a(x - 6)(x - 5), with 'a' being any real number. If we take 'a' as 1 (for simplicity), the function becomes f(x) = (x - 6)(x - 5).
So the quadratic function with zeros 6 and 5 is f(x) = (x - 6)(x - 5).
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solve for the unknown variable 2/5(3x-4)=-4
Answer:
x = -2
Step-by-step explanation:
Solve for x:
(2 (3 x - 4))/5 = -4
Multiply both sides of (2 (3 x - 4))/5 = -4 by 5/2:
(5×2 (3 x - 4))/(2×5) = -4×5/2
5/2×2/5 = (5×2)/(2×5):
(5×2)/(2×5) (3 x - 4) = -4×5/2
5/2 (-4) = (5 (-4))/2:
(5×2 (3 x - 4))/(2×5) = (-4×5)/2
(5×2 (3 x - 4))/(2×5) = (2×5)/(2×5)×(3 x - 4) = 3 x - 4:
3 x - 4 = (-4×5)/2
(-4)/2 = (2 (-2))/2 = -2:
3 x - 4 = 5×-2
5 (-2) = -10:
3 x - 4 = -10
Add 4 to both sides:
3 x + (4 - 4) = 4 - 10
4 - 4 = 0:
3 x = 4 - 10
4 - 10 = -6:
3 x = -6
Divide both sides of 3 x = -6 by 3:
(3 x)/3 = (-6)/3
3/3 = 1:
x = (-6)/3
The gcd of -6 and 3 is 3, so (-6)/3 = (3 (-2))/(3×1) = 3/3×-2 = -2:
Answer: x = -2
Step-by-step explanation:
HERE IS HOW YOU COULD SOLVE IT !!
Different ways to solve equations. We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal.
WHICH THE ANSWER WOULD BE x= -2
A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,
in feet after t seconds is given by the function h=-16t^2 + 120t + 10. How long does it take to
reach maximum height? What is the boulder's maximum height? Round to the nearest
hundredth, if necessary.
a. Reaches a maximum height of 235.00 feet in 3.75 seconds.
b. Reaches a maximum height of 10.00 feet in 7.50 seconds.
c. Reaches a maximum height of 7.58 feet in 3.75 seconds.
d. Reaches a maximum height of 15.16 feet in 7.5 seconds.
Answer:
The boulder's maximum height is:
a. Reaches a maximum height of 235.00 feet in 3.75 seconds.
Step-by-step explanation:
The easiest way to solve the unknown is to replace the time in the given equation, with the values given in the answer, look for the highest value and check if the height value decreases as the time increases or decreases.
First the equation provided is taken:
h = -16t ^ 2 + 120t + 10The time values in the options are 3.75 seconds and 7.5 seconds, therefore we proceed to replace this formula with those values:
h (3.75) = - 16 (3.75) ^ 2 + 120 (3.75) + 10 = 235 h (7.5) = - 16 (7.5) ^ 2 + 120 (7.5) + 10 = 10Since a higher height value is obtained with 3.75 seconds (235 feet), this time will be taken as appropriate, however, it is best to check that by using more time and less time, the height decreases from that value, so we will take two very close times: 3.74 seconds and 3.76 seconds:
h (3.74) = - 16 (3.74) ^ 2 + 120 (3.74) + 10 = 234.9984 h (3.76) = - 16 (3.76) ^ 2 + 120 (3.76) + 10 = 220.5884As you can see, if slightly higher or lower time values are taken, the height of the rock still decreases from 235 feet, so we can be sure that the time in which it reaches its maximum height is 3.75 seconds.
Which answer choice shows in order from greatest to least?
A. 11.09, 11.283, 11.301, 12.08, 12.8
B. 12.08, 12.8, 11.301, 11.283, 11.09
C. 12.8, 12.08, 11.301, 11.283, 11.09
D. 11.09, 11.283, 11.301, 12.8, 12.08
Answer:
C. 12.8, 12.08, 11.301, 11.283, 11.09
Students are running a relay race. The race is 1/3 mile total. How far will each students run?
Answer:533.33 meters
Step-by-step explanation:
The mile would be four laps around a track which is 400 meters so 400x4 divided by 3 (I ran track that’s the only reason I figured this out)
Which sequence of transformations will verify that
a) ABC and A'B'C' are congruent?
b) ABC is moved onto A'B'C' after translating -16 units horizontally and 6
units vertically, and then reflecting across the y-axis.
c) ABC is moved onto A'B'C' after translating 16 units horizontally and -6
units vertically, and then reflecting across the y-axis.
d) ABC is moved onto A'B'C' after translating -16 units horizontally and 6
units vertically, and then reflecting across the x-axis.
ABC is moved onto A'B'C' after translating 16 units horizontally and -6
units vertically, and then reflecting across the x-axis.
Answer:
C) △ABC is moved onto △A'B'C' after translating −16 units horizontally and 6 units vertically, and then reflecting across the x-axis.
Explanation: I did USA Test Prep.
Which choices are in the solution set of the equation below? Check all that
apply.
25x = 40
The solution set for the equation 25x = 40 is {1.6}, obtained by dividing both sides by 25 and verifying the solution by substitution.
Explanation:To find the solution set of the equation 25x = 40, we need to isolate the variable x by performing algebraic operations. The goal is to get x by itself on one side of the equation. This involves dividing both sides of the equation by the coefficient of x, which in this case is 25. Following this step, we arrive at the equation x = 40 / 25.
By simplifying 40 / 25, we find that x = 1.6. Therefore, the solution set for the equation 25x = 40 is {1.6}. It’s important to check the solution by substituting it back into the original equation to ensure that it satisfies the equation:
25(1.6) = 40
40 = 40
This indeed confirms that x = 1.6 is the correct solution. In mathematics, solving linear equations such as this one is a fundamental skill that involves understanding algebraic manipulation and the properties of equality.
The solution set for the equation 25x = 40 is x = 8/5. In other words, the only value for x that satisfies the equation is 8/5.
The solution set for the equation 25x = 40, we can isolate the variable x by dividing both sides of the equation by 25:
x = 40/25
Simplifying the right side gives:
x = 8/5
So, the solution set for this equation is {8/5}. In other words, the only value for x that satisfies the equation is 8/5. To understand this, you can substitute this value back into the original equation:
25 * (8/5) = 40
Simplifying the left side:
200/5 = 40
Indeed, the equation holds true.
In summary, the only choice in the solution set for the equation 25x = 40 is x = 8/5. This means that when you substitute 8/5 for x in the equation, both sides will be equal.
hich is the graph of the linear function that is represented by the equation y= 1/2x-2 ?
Answer:
this is the best way i could explain
Step-by-step explanation:
remember that the equation of a line is y = mx +b, where m is the slope and b is the y-intercept.
Start with your first point on the y-axis at -2. Your slope is 1/2 (rise/run), so go up 1 and over 2 for your next point. Keep going with this and you'll find your points.
Another way to find your y-values is to plug in the x's you have. y = 1/2(2) - 2 = 1 - 2 = -1, so your first point is (2,-1). This should show up on your graph, as well.
What do you get when you plug in the 0? Your answer should be your first point on your graph, since along the y-axis, x = 0.
The graph of the equation given is attached to the solution.
Given that, an equation y = 1/2 x - 2, we need to graph it,
So, for the same, we will first find the coordinates points,
Therefore,
y = 1/2 x - 2
Put y = 0,
1/2 x - 2 = 0
x = 4
The point = (4, 0)
Put x = 0,
y = -2
The point = (-2, 0)
Put the coordinates in the graph and join the points, we will have a straight line, this straight is the graph of the linear equation given,
That mean the equation is a linear equation.
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ILS
What type of triangle is shown below?
630
4.50
O
A. Acute
O
B. Obtuse
O
c. right
For a project, Gabrielle made a model of an Egyptian pyramid. The square base has a side length measuring 10 inches.
The pyramid is 12 inches tall.
What is the surface area of the model?
240
260
340
360
Find the area of the rectangle.
square feet:
Answer:
4x9=36
Step-by-step explanation:
36
Answer:
36 sq ft.
Step-by-step explanation:
To solve for the area of a rectangle, all you need to do is multiply the length by the width which gives you:
4×9= 36 sq ft.
which event has exactly 12 possible outcomes
Final answer:
An event with exactly 12 possible outcomes may refer to rolling a single 12-sided die, rolling two six-sided dice with one specific number on one die and any number on the other, or flipping a coin and rolling a six-sided die.
Explanation:
The event that has exactly 12 possible outcomes could be the rolling of a 12-sided die once, which would result in one of the twelve numbers coming up. Another example is rolling two six-sided dice and considering the situation where one specific number must come up on one die, while any of the six numbers could come up on the other die, thus also resulting in 12 possible outcomes (6 possible outcomes for the second die, times 1 fixed outcome for the first die), assuming the outcome of interest is only about the second die. Yet another example could be flipping a coin and rolling a six-sided die, where the coin has two possible outcomes (heads or tails) and the die has six possible outcomes, giving us a total of 12 outcomes (2 x 6 = 12).
Classify this triangle by the angles and lengths of sides shown.
A.) acute, equilateral
B.) acute, scalene
C.) acute, isosceles
D.) obtuse, scalene
The measures of the angles in a triangle are 1.5x, 2.4x, and 3.3x. Write an equation to determine the measure of each angle in the triangle. Use the equation to determine the exact measure of each angle in the triangle.
Answer:
[tex]37.5^{\circ}\,,\,60^{\circ}\,,\,82.5^{\circ}[/tex]
Step-by-step explanation:
Given: measures of the angles in a triangle are [tex]1.5x,2.4x,3.3x[/tex]
To find: equation to determine the measure of each angle in the triangle and exact measure of each angle in the triangle
Solution:
According to angle sum property, sum of angles of a triangle is [tex]180^{\circ}[/tex]
So, equation to determine the measure of each angle in the triangle is [tex]1.5x+2.4x+3.3x=180^{\circ}[/tex]
[tex]1.5x+2.4x+3.3x=180^{\circ}\\7.2x=180^{\circ}\\x=\frac{180^{\circ}}{7.2}=25^{\circ}[/tex]
So,
[tex]1.5x=1.5(25^{\circ})=37.5^{\circ}\\2.4x=2.4(25^{\circ})=60^{\circ}\\3.3x=3.3(25^{\circ})=82.5^{\circ}[/tex]
Determine is the following set is a function or not: (-3,5) (1,3) (4,5 (3,5) (-3,5)
Answer:
It is
Step-by-step explanation:
The reason being is both times you imputed -3 you got an output of 5.
A doctor has found that the number of hours students sleep each night is inversely related to the amount of time they spend playing video games. He collected the data below.
If the trend the doctor has observed holds true, how many hours of sleep would you expect of a student who plays video games for 6 hours?
A. 6.5 hours
B. 7.5 hours
C. 7.25 hours
D. 6.25 hours
Answer: 6.25
Step-by-step explanation:
Hey, so whats 4d > 16 in a graph?
Answer:
see below
Step-by-step explanation:
4d>16
Divide each side by 4
4d/4 >16/4
d >4
Which fraction shows the number of hours Amy's dog slept sleeps for every 2 hours in the day? Complete the Fraction
Answer: 1/2
Step-by-step explanation:12 is divided by 2
fraction that shows the number of hours Amy's dog sleeps is 1/2.
What is fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator and the bottom part is numerator.
Given is Amy's dog who sleeps for every 2 hours in the day.
Since Amy's dog sleep for 2 hours a day, then in a complete day he would sleep for 12 hours out of 24 hours. So, we can write the fraction as-
12/24 = 1/2
Therefore, fraction that shows the number of hours Amy's dog sleeps is 1/2.
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Johnny prepares a solution by mixing sodium acetate and water. To calculate the molarity of the solution, Johnny should calculate the moles of which substance, and why? *
sodium acetate, because it is the solvent
sodium acetate, because it is the solute
water, because it is the solvent
water, because it is the solute
Answer is B, sodium acetate, because it is the solute .
Which expression is equivalent to StartFraction 4 a + 4 Over 2 a EndFraction times StartFraction a squared Over a + 1 EndFraction? StartFraction 2 (a + 1) squared Over a cubed EndFraction 6a 2a StartFraction 6 a squared Over a + 1 EndFraction
Answer:
C. 2a
Step-by-step explanation:
i did this because I love you- angelo (junior 11th grade) CCHS 2021
The expression that is equivalent to (4a + 4)/2a × a²/(a + 1) is: 2a.
What are Equivalent Expressions?Equivalent expressions are expressions that have the same value when simplified.
Thus:
(4a + 4)/2a × a²/(a + 1)
Multiply
[(4a + 4)(a²)] / [(2a)(a + 1)]
(4a³ + 4a²) / (2a² + 2a)
2a(2a² + 2a) / 2a(a + 1)
(2a² + 2a) / (a + 1)
2a(a + 1) / (a + 1)
= 2a
Therefore, the expression that is equivalent to (4a + 4)/2a × a²/(a + 1) is: 2a.
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Is the following situation represented by a positive integer, a negative integer, or zero?
Before taking off, the plane was on the ground.
Zero
Positive
Negative
Answer:
zero
Step-by-step explanation:
because it hasn't taken off. It is its starting position
What is the average rate of change for ƒ(x) = 2^x + 10 over the interval 2 ≤ x ≤ 4?
A.) 4
B.) 6
C.) 8
D.) 12
What is the vertex of the parabola whose equation is y = (x + 1)2 + 3?
(-1,-3)
(-1,3)
(1,3)
Answer:
Step-by-step explanation:
(-1,3)
At the store Jason finds the total volume of soda in a pack is 50.24 cubic inches . If each cylinder -shaped can has a height of 4 inches and a diameter of 2 inches , how many soda cans are in a pack ? (Use 3.14 for pi)
A) 4
B) 5
C) 13
D) 2
Explain:
Answer: A) 4
Step-by-step explanation:
Hi, to answer this, first, we have to calculate the volume of each can:
Volume of a cylinder: π x radius^2 x height
Since:
Diameter: 2 radius
2 = 2r
2/2 =r
r=1
Back with the volume formula:
V = 3.14 ( 1)² 4 =12.54 cubic inches
Now, we have to divide the total volume of soda by the volume of each can:
50.24/12.54= 4 soda cans
Feel free to ask for more if needed or if you did not understand something.
A worker makes a ramp by placing one end of an 8-foot-long board on the bed of a pickup truck and the other end on the ground. The bed of the truck is 3 feet above
the ground. Which expression could be used to determine the angle between the board and the ground?
The expression sin^-1(3/8) can be used to determine the angle between the board and the ground in this scenario. This utilizes the sine function in trigonometry, which involves the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right-angle triangle.
Explanation:The subject of this question is Mathematics, specifically trigonometry. In such a problem, we can utilize the concept of trigonometric functions, in this case is the sine function. The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse. In this scenario, the board acts as the hypotenuse, the height of the truck is the side opposite the angle, and the angle we're trying to determine is between the ground (which we can consider as the adjacent side) and the board.
So, to determine the angle, we would use the expression: sin^-1(opposite/hypotenuse) = sin^-1(3/8).
The sine inverse or 'sin^-1' is used to find the angle when we know the sine value. Also, note that the answer will be in radians and can be converted into degrees by multiplying by 180/pi if necessary.
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What property must you do to eliminate the parentheses in an equation.
A. Distributive Property
B. Associative Property
C. Multiplication Property
D. Commutative Property
I need the answer
Answer:
distributive
Step-by-step explanation:
Answer:
A. Distributive Property
Step-by-step explanation:
two owls leave the same tree at 9:00 p.m. One owl flies west at 7 miles per hour and the other flies east at 13 miles per hour. In how many hours will they be 60 miles apart?
Answer:
3 hours.
Step-by-step explanation:
Trust me...
Which equation represents a linear function? Equation 1: y^3 = 2x +1 Equation 2: y= 3x +1 Equation 3: y= 5x^2 - 1 Equation 4: y=4x^4 -1
A student graphed the line y = 3x + 2 plotting and connecting points A, B, and C. How can the student use points A, B, and C to find the graph of y =3x - 5?
Answer:
The student has to translate the points A, B and C 7 units down to create points A', B' and C', and then connect these points
Step-by-step explanation:
The slope of the lines is the same (3). The difference between the lines is their y-intercept (from the first line is 2 and for the second one is -5). This means that the lines are parallel and separated by 2 - (-5) = 7 units
Approximate the value of 11−−√ to the nearest tenths place. Plot the approximation on the number line.
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Approximate the value of [tex]\sqrt{11}[/tex] to the nearest tenths place. Plot the approximation on the number line.
(Please have a look at the attached photo)
My answer:
The value nearest tenths place of [tex]\sqrt{11}[/tex] is: 3.3
Hope it will find you well.
Please help with steps
Answer:
what is the question
Step-by-step explanation: