The number of seconds will it take the ball to hit the ground will be 2.078 seconds.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.
As per the given,
h(t)=-16t² + 14t + 40
The time when the ball hit the ground h(t) = 0
-16t² + 14t + 40 = 0
-8t² + 7t + 20 = 0
8t² - 7t - 20 = 0
t = (7 ± 26.25)16
t = 2.078 seconds
Since time can never be negative thus, 2.078 seconds will be correct.
Hence "The number of seconds will it take the ball to hit the ground will be 2.078 seconds".
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compared with randomly paired people, friends are more likely to share the same attitudes and beliefs. this best illustrates the association between ________ and attraction.
Compared with randomly paired people, friends are more likely to share the same attitudes and beliefs. this best illustrates the association between similarity and attraction.
What is social Psychology ?
Social psychology is the scientific study of how individuals's thoughts, feelings, and behaviors are affected by the actual or hypothetical presence of other people.
Social psychology is the study of how individual or group behavior is influenced by the presence and behavior of others.
What is social psychology's primary area of study?
Social psychologists research the ways in which social impact, social perception, and social interaction affect both individual and group behavior.
Some social psychologists concentrate their efforts on studying how people behave.
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HELP MEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: The final balance is $9,013.73.
The total compound interest is $7,513.73.
Step-by-step explanation:
1) if f(x) = x² - 1 and g(x) = x + 1, then when x doesnt equal -1, f(x) / g(x) =
helpp
Answer:
f(x) / g(x) = x - 1 where x ≠ -1.
Step-by-step explanation:
f(x) / g(x) = x² - 1 / x + 1
= (x + 1)(x - 1) / (x + 1)
= x - 1.
can someone pls help me with this one?
Answer:
y = x + 2
Step-by-step explanation:
Use the slope-intercept form:
y=mx+b
M represents the slope of the line
B represents the y-intercept
Rose is mailing a package of magazines and
chips to her kids at camp. The package weighs
a total of 9 pounds and has 14 items inside. The
magazines each weigh 1 pound and the chips
each weigh .5 pounds. How many magazines, x,
and chips, y, is Rose mailing in the package?
x + y = 14
x + 0.5y = 9
if a gardener fences in the total rectangular area shown in the illustration instead of just the square area, he will need twice as much fencing to enclose the garden. how much fencing will he need?
The fencing needed to enclose the garden is equal to the perimeter of the rectangle and it will be 5x + 56.
The perimeter of the rectangle: The sum of all the sides of the rectangle will be known as the perimeter of the rectangle.
Let L be the length and W be the width of the rectangle.
Then the perimeter of the rectangle will be
The perimeter of the rectangle = Sum of all the sides
If the gardener fences in the total rectangular area shown in the illustration instead of just the square area, he will need twice as much fencing to enclose the garden.
From the diagram, the length is 28 + x. And the width is x. Then the perimeters of the rectangle will be
P = 28 + x + 28 + x + x + x + x
P = 56 + 5x
The fencing needed is equal to the perimeter and will be 5x + 56.
Refer to the image to know more details about question 5.
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(PLEASE HELP)
Consider circle O with diameter GB. Line AD is tangent to circle O at point A and line DB is tangent to circle O at point B. The measure of ∠GBA is 38°. Chord GC bisects ∠G. Determine each measure
The angles GBD, GBD and G measures 90 , 90, 52 degree respectively.
GB is the diameter given.
AD is the tangent given.
The tangent makes 90 degree angle with diameter.
hence the angle GBD will be : 90°
Similarly, GBA will also be 90°
The angle GBA is given as 38°
Hence the angle G will be = 90 - 38 =52
All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its centre.
The radius must typically be a positive integer. A degenerate situation is a circle with radius equal to zero (one point). Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.
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If the discriminant, b^2-4ac is ___, a quadratic will have two real roots, two points of intersection with the x-axis.
a) negative
b) positive
c) complex
d) zero
If the discriminant, b² - 4ac is positive
How to complete the statement?From the question, we have the following equation of discriminant
The discriminant (d) is calculated as
d = b² - 4ac
The solutions of a quadratic equation are dependent on the following conditions
If d = 0, the quadratic equation has 1 real solutionIf d < 0, the quadratic equation has imaginary solutionsIf d > 0, the quadratic equation has 2 different real solutionsThis means that "d > 0, the quadratic equation has 2 different real solutions" implies that the discriminant is positive
Hence, the complete statement is (b) positive
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please help me PLEASE
The value of x in the linear inequality 5/8x - 1 ≥ 9 is x ≥ 16
What is Linear InequalityLinear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1. There are several ways to represent various kinds of linear inequalities.
The inequality given is
5/8x - 1 ≥ 9
5/8x ≥ 9 + 1
5/8x ≥ 10
5x ≥ 10 * 8
5x ≥ 80
x ≥ 16
The value of x is greater than or equal to 16
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suppose that the trace of a matrix is , and the determinant is . find the eigenvalues of . smaller eigenvalue = , larger eigenvalue = .
The eigenvalues of A are 5 and 10.
What is eigenvalues ?
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.
The eigenvalues of the 2 x 2 matrix are described by the following characteristic polynomial:
[tex]$$t^2-{tr}(A) \cdot t+{det}(A)=0$$[/tex]
The roots of the characteristic polynomial are deflned by the quadratic formula:
[tex]t=\frac{{tr}(A) \pm \sqrt{[{tr}(A)]^2-4-{det}(A)}}{2} \text { (2) }$$[/tex]
If we know that [tex]${tr}(A)=15$[/tex]and [tex]${det}(A)=50$[/tex], then the elgenvalues of A are:
[tex]$$\begin{aligned}& t=\frac{15 \pm \sqrt{15^2-4 \cdot(50)}}{2} \\& t_1=10 \vee t_2=5\end{aligned}$$[/tex]
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the heights of a maple tree and a cherry tree currently have a ratio of 5:2. if the maple tree grew 20 centimeters, and 20 centimeters was cut off the top of the cherry tree, the ratio of their heights would be 3:1. before this change, how much taller was the maple tree than the cherry tree, in centimeters?
Before the change maple tree was 240 cm longer than cherry tree when the heights of a maple tree and a cherry tree currently have a ratio of 5:2. if the maple tree grew 20 centimeters, and 20 centimeters was cut off the top of the cherry tree, the ratio of their heights would be 3:1.
Define ratio.One quantity can be expressed as a fraction of another using a ratio, which is a number. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given,
Current ratio = 5:2
Let y equal the height of the cherry tree, and x represent the height of a maple tree.
x/y = 5/2
New ratio = 3:1
x+20/y-20 = 3/1
Cross multiplying,
x + 20 = 3(y - 20)
x = 3(y - 20) -20
Equating values in x/y = 5/2
3(y-20) - 20/y = 5/2
5y = 2(3y - 60) -20
5y = 6y - 160
y = 160
Now, for value of x,
Equating values in x = 3(y - 20) -20
x = 3(160 - 20) - 20
x = 480 - 60 - 20
x = 400
For the height,
400 - 160
240
Before the change maple tree was 240 cm longer than cherry tree when the heights of a maple tree and a cherry tree currently have a ratio of 5:2. if the maple tree grew 20 centimeters, and 20 centimeters was cut off the top of the cherry tree, the ratio of their heights would be 3:1.
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The Quotient of a number b and four plus seven is two
The algebraic form of the statement is b/4 + 7 = 2 and the value of b is -20.
What is the numerical value of the b?Given the statement; the quotient of a number b and four plus seven is two.
First, we convert the statement into an algebraic equation.
Quotient of a number b and 4 ⇒ b/4Plus 7 ⇒ + 7 Is two ⇒ = 2Now, combine the terms and equality sign.
b/4 + 7 = 2
Next, solve for the numerical value of b.
b/4 + 7 = 2
Subtract 7 from both sides
b/4 + 7 - 7 = 2 - 7
Simplify the left-hand side
b/4 = 2 - 7
Subtract 7 from 2
b/4 = -5
Next, multiply both sides by 4
b/4 × 4 = -5 × 4
b = -5 × 4
b = -20
Therefore, the numerical value of b is -20.
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If y = x-4, which point corresponds to the location where y = -7? (Hint: Keep in mind that this question gives you the
value of y, not x.)
Answer:
(- 3, - 7 )
Step-by-step explanation:
given
y = x - 4 ← substitute y = - 7 into the equation and solve for x
- 7 = x - 4 ( add 4 to both sides )
- 3 = x
then point is (x, y ) = (- 3, - 7 )
Answer:
(-3, -7)
Step-by-step explanation:
y=-7
y=x-4
-7 = x - 4 ==> since y=-7 and y=x-4, -7 = x-4
-7 + 4 = x - 4 + 4 ==> solve for x by adding 4 on both sides
-3 = x
x = -3
x=-3, y=-7 ==> (-3, -7)
(Factoring Algebraic Expressions MC)
Factor −3x2 + 12x.
The factor is -3x(x - 4) and value of x is 4.
Define Algebraic Expression
An expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)
Define Factorization
Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
Given expression,
-3x² + 12x
Take -3x common
⇒ -3x(x - 4)
Now, if you want to find the value of x then write it in standard form like this
-3x(x - 4) = 0
Now, find x
x - 4 = 0
x = 4
Hence, the factor is -3x(x - 4) and value of x is 4.
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What is 1/3 of 18? :)
what is another name for a chord that passes through the center of the circle? A) Diameter B) Circumference C) center D) radius
Answer:
A
Step-by-step explanation:
diameter
The another name for the chord that passes through the center of the circle is the diameter.
The correct option is (A).
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
As per the given data:
We have to find out the alternate name for a chord that passes through the center of a circle out of the given options.
Diameter:
It's a chord that passes through the center and touches the ends of the circumference of the circle.
Hence, this is correct.
Circumference:
It's the length of the boundary of a circle, hence this cannot be a chord.
This is incorrect.
Center:
It's a point and a chord is a line, hence this cannot be true.
Radius:
A radius is not a chord, as it does not touch the endpoints on the circumference of the circle.
The another name for the chord that passes through the center of the circle is the diameter.
Hence, The another name for the chord that passes through the center of the circle is the diameter.
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Use I = PRT to solve.
(time is in years).
P = $400 find I
R = 9%
T = 0.25 years
(Remember 9% = .09 in decimal form)
Answer:
Step-by-step explanation:
Given,
[tex]P = $400 find I\\R = 9%\\\\T = 0.25 years[/tex]
[tex]T=0.25[/tex](Remember 9% = .09 in decimal form)
So We convert it into a decimal form
[tex]\frac{9}{100} =0.09[/tex]
Now we find the Interest,
[tex]I=PRT\\[/tex][tex]I = 400X0.09X0.25\\I=36X0.25\\I=9$[/tex]
9$ is the answer
Solve pls Brainliest
Answer:
The ordered pair that satisfies the system of equations is (7, -1)
Step-by-step explanation:
⭐What is a system of equations?
a system of equations is 2 or more equations that intersect at a point (x,y)When we solve for an ordered pair that satisfies the system of equations, we are finding at what point do the equations intersect.
⭐How can we solve a system of equations?
eliminationsubstitutiongraphingFor this problem, I find elimination to be the easiest. I will demonstrate how to use elimination to solve this system of equations.
⭐What is the elimination method?
the elimination method consists of literally eliminating a variable from both equations to solve for another variableWe have the system: [tex]{ x+7y = 0\\\\2x - 8y = 22[/tex]. Let's eliminate the variable "x".
To do so, multiply the first equation by -2, then add both equations.
[tex]-2(x+7y = 0)\\-2x -14y = 0[/tex]
Now add this new equation with the second equation. This eliminates the x variable.
[tex]-2x - 14y = 0 \\+2x -8y = 22\\\\-22y = 22\\y = -1[/tex]
∴ y = -1
Next, we need to solve for the x variable. To do so, substitute the y variable into one of the equations we added and solve for x.
I will substitute y into the equation [tex]2x - 8y = 22[/tex], but you can also substitute it into [tex]-2x-14y = 0[/tex]
[tex]2x - 8y = 22[/tex]
[tex]2x-8(-1) = 22[/tex]
[tex]2x + 8 = 22[/tex]
[tex]2x = 14[/tex]
[tex]x = 7[/tex]
∴ The ordered pair that satisfies the system of equations is (7, -1)
⭐if this response helped you, please mark it the "brainliest"!⭐
How can I solve this ? What is the angle whose tangent is 456/321?
The angle whose tangent is 456/321 is 54.85°
The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.
The Tangent Formula is given as:
Tan A = Opposite Side/Adjacent side
In terms of sine and cosine, tangent may be represented as:
Tan A = Sin A / Cos A
We know that the sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side whereas the cosine of the angle is the ratio of the length of the adjacent side to the ratio of the hypotenuse side.
That is, Sin A = Opposite Side/ Hypotenuse Side
Cos A = Adjacent Side/ Hypotenuse Side
Therefore, tan A = Opposite Side/ Adjacent Side
[tex]tan^{-1} (1.42056)[/tex] =54.85°
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What is the vertex form of the equation? y = – x 2 + 12 x – 4 show steps of how you solved please
The vertex form of the equation is in the form of y = a(x-h)^2 + k.
Step 1: Use the formula below to solve for a.
a = -1/4 * (4 - 12) = -1
Step 2: Use the formula below to solve for h.
h = -b/(2a) = 12/(2(-1)) = -6
Step 3: Use the formula below to solve for k.
k = f(h) = -(-6)^2 + 12(-6) - 4 = 36
Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.
In mathematics, what is the vertex?A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedra, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.
What is the vertex location?Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.
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Jaheem invests $10,000 in two different money markets. The first earned 12.5% in one year, the second earned 8.25%. If he earned $925 in interest, how much did he invest in each account?
Answer:
Let X be the amount Jaheem invested in the first money market, and Y be the amount he invested in the second money market. We can set up the following system of equations to represent the given information:
X + Y = 10000 (1)
0.125X + 0.0825Y = 925 (2)
We can solve this system of equations using any method of your choice, such as elimination or substitution.
Using elimination, we can multiply equation (1) by 0.125 and equation (2) by 10,000 to eliminate Y:
1.25X + 1250Y = 1250000
125X + 82500Y = 9250000
Subtracting the first equation from the second gives us:
124X + 82350Y = 8037500
Y = (8037500 - 124X)/82350
Substituting this expression for Y into equation (1) and solving for X gives us:
X + (8037500 - 124X)/82350 = 10000
X = $7,500
Therefore, Jaheem invested $7,500 in the first money market and $2,500 in the second money market.
Step-by-step explanation:
SELF EXPLANATORY
Which of the following is the standard form of the equation y = -3x + 4?
A. 3x - y = 4
C. 3x + y = 4
B. 3x + y = -4
D. 3x - y = -4
Answer:
3x + y = 4
Step-by-step explanation:
The standard form of an equation can be written as: ax + by = c
The equation is currently written in slope-intercept form.
In order to turn it into standard form, we must have both x and y on one side of the equation. So...
y = -3x + 4 Add 3x to both sides
3x + y = 4
Therefore the standard form of the equation y = -3x + 4 is 3x + y = 4
what is the point-slope form of -4,7?
An equation for this line in the point-slope form will be y-7 = -2(x + 4).
What is the Point-slope form?
The equation of the straight line has its slope and given point. If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation. Point-slope is a specific form of linear equations in two variables:
y - y₁ = m(x - x₁)
Which is the required equation of a line in a point-slope form.
We need to find the equation of the line that passes through (-4, 7) and whose slope is -2.
Well, we will simply plug m = -2, x₁= -4, and y₁ = 7 into point-slope form.
y-y₁ = m(x-x₁)
Now substitute;
y-7 = -2(x - (-4))
y-7 = -2(x + 4)
Therefore, an equation for this line in the point-slope form will be y-7 = -2(x + 4).
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Find the area enclosed by the circle (x-2)^2 + y^2 = 4 and the line x = 3.
Step-by-step explanation:
(3-2)^2+y^2=4
(9-4)+y^2=2^2
the power of y and 2 should be cut now
5+y=2
5-2=y
3=y
y=3
:. the area of enclosed by a circle is 3 cm
The table below shows the amount of money needed to buy certain amounts of fabric. If the price is the same for each yard, how much money would 12 yards of fabric cost?
Correct answer will get brainliest
The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The two points are (3, 5) and (6, 10).
Let 'x' be the number of yards of fabric and 'y' be the cost in dollars. Then the equation is given as,
(y - 5) = [(10 - 5) / (6 - 3)](x - 3)
y - 5= (5/3)x - 5
y = (5/3)x
The cost of the 12 yards of fabric is given as,
y = (5/3) × 12
y = 5 × 4
y = $20
The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.
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Evaluate 5² + 2(-8 ➗ 2)
Answer:
17
Step-by-step explanation:
Using PEMDAS:
5² + 2(-8 ÷ 2)
5² + 2(-4)
25 - 8
17
if sin (2x) = a and 0 < x < pi/2 then sin x is equal to which of the following and why?
a) a
b) a/2
c) 2a
d) a cos x
e) a sex x
explain pleaseee
The solution to the equation are x=a
How to determine the value of sin (2x) = a ?The given equation is sin (2x) = a and 0 < x < pi/2
Sin(2x) = sin x, 0≤x≤2п ........................... (eq. 1)
Using the trigonometrical formula,
sin(2x) = sin xcosx
Let us subtract the formula from equation 1
2sinxcosx = sinx
Therefore, 2sinxcosx-sinx = 0
Let us remove common terms to get
sinx(2cox-1)=0
Now, sinx=0
x= 0, [tex]\pi[/tex], [tex]2\pi[/tex]
Also, 2cos x =1
This means that cos x = 1/2
By implication, x=cos⁻¹(1/2)
That is to say that x= [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]
In conclusion, the value of [tex]\pi[/tex] is a as a single integer
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what is 10 less than the quotient of a number and five
(x/5)-10 where x is "number"
Liam deposits $3,500 in a saving account that pays 1.5% interest, compounded quarterly.
a.Find the balance after a year.
B. Compare the interest compounded annually.
Therefore the balance after a year comes out to be $3552.80 and the balance comes out to be after compounded annually is $3552.50
What is compound interest ?Compound interest is the interest on savings that is computed using both the original principal and the interest accrued over time.
It is believed that Italy in the 17th century was where the idea of "interest on interest" or compound interest first emerged. It will accelerate the growth of a sum more quickly than simple interest, which is only applied to the principal sum.
Money multiplies more quickly through compounding, and the higher the
Here,
The Liam deposits $3,500 in a saving account that pays 1.5% interest,
Thus rate=1.5% and principle amount =3500
Therefore it is compounded quartely ,
The balance after year=
C=P[tex]e^{rt}[/tex]
C=3500*[tex]e^{1.5*4}[/tex]
C=3552.80
Therefore the balance after a year comes out to be $3552.80
Therefore the balance comes out to be after compounded annually is
$3552.50
So there is only $0.30 difference between the amounts
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Carrie is trying to solve this inequality. After she solves it, she shows it to you, and asks you if she did it correctly. This is the work she completed.
2x-5 < 11+ 6x
Step 1: 2x<+16
Step 2 -4x < 16
Step 3 <-4
Part A In which step did Carrie make a mistake?
Part B: How would you explain to Carrie what her mistake was, so she won't make the mistake again on a future test?
Carrie made a mistake in her step 3.
She was suppose to change the inequality symbols to the opposite after dividing by a negative number.
How to solve inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Carrie is trying to solve this inequality.
2x - 5 < 11 + 6x
add 5 t both sides of the inequality
2x - 5 + 5 < 11 + 5 + 6x
2x < 16 + 6x
subtract 6x from both sides of the inequality
2x - 6x < 16 + 6x - 6x
-4x < 16
divide both sides by -4
-4x / -4 < 16 / -4
x > - 4
Therefore, She made a mistake in the step 3.
If she is dividing both sides of an inequality by a negative number, the inequality sign will change to the opposite.
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