60 minutes will be taken by the older computer to send out the email on its own.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
one computer takes x minutes and the other takes 3x minutes
in 1 minute, they send (1/x) and (1/3x) of the total message
together, (15/x)+(15/3x)=1, the full message
multiply by 3x to clear fractions
45+15=3x
60=3x
Divide both sides by 3
20=x
So for older computer 60 minutes it take to send out the email on its own.
Hence, 60 minutes will be taken by the older computer to send out the email on its own.
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I need help with this Question.
Answer:
Step-by-step explanation:
a. 1 hectare = 2.471 acres
6 hectares x (2.471 acres / 1 hectare)
=14.826 acres
b. prices per acre: 150,000/14.826
=10,117.36 per acre
7v-7-4v-10=v+7-4v help now pleas
Answer:
v = 4
Step-by-step explanation:
[tex]collect \: like \: terms \: \\ 7v - 4v - v + 4v = 7 + 7 + 10\\ 3v - v + 4v = 14 + 10\\ \\ 2v + 4v = 24 \\ 6v = 24 \\ v = 4[/tex]
q(x) = -x-2
r(x) = x² + 2
Find the following.
(r∙q)(-5) =
(q∙r)(-5) =
Answer: 5q-5r -5q+5r
Please help me simplify
Answer: [tex]\frac{4\sqrt{x} }{t^2}[/tex]
Step-by-step explanation:
You can start by either applying the exponent to both the numerator and denominator (exponent rule), or make things simpler by dividing first. Doing the latter allows me to show both properties. Since the terms in the fraction are being multiplied, we can divide common terms which will leave us with [tex]\frac{16x}{t^4}[/tex] on the inside. Now that it is simplified, we can apply the exponent. We will end up with 4x^1/2 in the numerator and t^2 in the denominator. If the exponent seems daunting, it is also helpful to know that raising something to the exponent of 1/2 is basically taking the square root of it.
Gotta answer this quick this is timed please
Answer:
Step 1:subtract 5 from both sides
step 2: divide both sides by two
final answer: c= p-5/2
Answer:
Step 1: Subtract 5 from both sides.
Step 2: Divide 2 from both sides.
Final answer: C= p-5 / 2
Step-by-step explanation:
In a geometric sequence, the difference between each pair of consecutive terms must be the same.
The given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.
What is a Sequence?Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -
3, 6, 9, 12, 15
x, x + 2, x + 4, x + 6
Given is the following statement -
"In a geometric sequence, the difference between each pair of consecutive terms must be the same"
The given statement is false as the statement mentioned above is the definition of a arithmetic sequence. In geometric sequence, the ratio of each pair of consecutive terms must be the same. Mathematically -
a[n + 1]/a[n] = r {constant}
Therefore, the given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.
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cos(θ)=−2√5 / 5
If (θ) is an angle in quadrant ll what is the value of sin (θ)
The exact value of sin(θ) given that cos(θ) = -2√5/5 is √5/5
How to determine the value of sin(θ):The given trigonometry ratio is
cos(θ) = -2√5/5
By the trigonometry ratio, we have
sin²(θ) + cos²(θ) = 1
Substitute cos(θ) = -2√5/5 into the above equation
So, we have the following representation
sin²(θ) + (-2√5/5)² = 1
Evaluate the exponent
sin²(θ) + 4/5 = 1
Subtract 4/5 from both sides
This gives
sin²(θ) = 1/5
Take the square root of both sides
√sin²(θ) = √1/5
Evaluate the square root
sin(θ) = ±1/√5
Sin is positive in quadrant II
So, we have
sin(θ) = 1/√5
Rationalize
sin(θ) = 1/√5 * √5/√5
This gives
sin(θ) = √5/5
This gives the value of sin(θ)
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HELP.
This item has two parts: Part A and Part B. Use the function to complete Part A and Part B.
f(x) = (x – 5)(x + 3)(x – 1)2
Which of the following statements CORRECTLY identifies the degree and number of unique zeros of the function?
degree: 3; number of unique zeros: 4
degree: 4; number of unique zeros: 3
degree: 4; number of unique zeros: 4
degree: 3; number of unique zeros: 3
Part B
What is the end behavior of the function?
as x → –∞, f(x) → ∞ and as x → ∞, f(x) → –∞
as x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞
as x → –∞, f(x) → –∞ and as x → ∞, f(x) → ∞
as x → –∞, f(x) → –∞ and as x → ∞, f(x) → –∞
The degree and number of unique zeros of f(x) = (x – 5)(x + 3)(x – 1)² is:
Degree: 4; number of unique zeros: 3.
The end behavior of the polynomial is:
As x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞.
How to obtain the degree of the function?The degree of the polynomial function is given by the sum of the multiplicities of the roots.
These roots are given as follows:
x = 5 with a multiplicity of 1.x = -3 with a multiplicity of 1.x = 1 with a multiplicity of 2.Hence the degree is:
1 + 1 + 2 = 4.
The unique zeros are the roots, hence there are three unique zeros, which is the same number of linear factors of the function.
What is the end behavior of the function?The end behavior is the limit of the function as x goes to negative infinity and to positive infinite, hence:
lim x -> -∞ f(x) = lim x -> -∞ x^4 = (-∞)^4 = ∞.lim x -> ∞ f(x) = lim x -> ∞ x^4 = (∞)^4 = ∞.Learn more about the end behavior of a function at brainly.com/question/1365136
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4. Daryll rides a bike 8 miles in 40 minutes. Isabella rides a bike 5 miles in 30
minutes. If they continue to ride at those speeds, who will bike the farthest
in 2 hours? How much father? Show your work.
5 A student sells 5 ears of corn for $2.00 how much will 9 ears cost show your work
6 A market sells 4 oranges for 2.45 how much will 8 oranges cost ? 12 oranges show your work
The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.
Which inequality can be used to determine the maximum number of hours h the
frozen yogurt machine can be used if the rental cost for the day will not exceed $300?
The inequality that can be used to determine the maximum number of hours h the frozen yogurt machine can be used if the rental cost for the day will not exceed $300 is 150+25h ≤300.
According to the question,
We have the following information:
The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.
And h represents the number of hours.
So, we have the following expression to find the total cost:
150+25h
Now, it is given that the total rental cost should not exceed $300.
So, we have the following inequality:
150+25h ≤300
Hence, the correct option is C.
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What is the size of angle x?
Write a justification for your answer.
The angle x will be 34°.
From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.
Supplementary angles are those which always sum to to 180°.
For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.
similarly ∠ROP + ∠RQP = 180°
∠RQP = 180° - ∠ROP
∠ROP is given to us 146°
After putting it in the equation above we get ∠RQP = 34°
Therefore x comes out to be 34°.
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You roll a fair six-sided die twice. Find the probability of rolling a 3 the first time and a number greater than 4 the second time.
The probability of rolling a 3 first time and a number greater than 4 thre second time is 1/18
What is probability?Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain. An example of a certain event is tomorrow being Friday if today is Thursday. This is definitely going to happen.
The possible outcomes of a fair die are : 1, 2, 3, 4, 5, 6. which is 6 in all
the required outcome for obtaining a 3 = 3 which is 1 outcome
the required outcome for obtaining a number greater than 4 : 5, 6. which is 2 outcomes.
probability of getting 3 first time = 1/6
probability of getting a number greater than 4 = 2/6 ( lowest term = 1/3)
Probability of rolling a 3 first time and a number greater than 4 second time is = 1/6 x 1/3 = 1/18
In conclusion, probability of obtaining a 3 and a number greater than 4 is 1/18.
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Last year, Dan had $ 10,000 into invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?
The amount invested in the account that yields 10% simple interest is $1,000.
The amount invested in the account that yields 7% simple interest is $9,000.
How much was invested in each account?The first step is to form a system of equations using the information provided in the question:
a + b = $10,000 equation 1
0.1a + 0.07b = 730 equation 2
Where:
a = amount invested in the account that yields 10% simple interest
b = amount invested in the account that yields 7% simple interest
The elimination method would be used to solve the equations
Multiply equation 1 by 0.1
0.1a + 0.1b = 1000 equation 3
Subtract equation 2 from equation 3
0.03b = $270
Divide both sides of the equation by 0.03
b = $270 / 0.03
b = 9,000
Substitute for b in equation 1
a + 9,000 = 10,000
a = 10,000 - 9,000
a = 1000
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Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15
The velocity function of a car is given by v(t) = -3t2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop.
A.
a = -6.46 m/s²
B.
a = -2.76 m/s²
C.
a = -0.46 m/s²
D.
a = 2.76 m/s²
Answer: In photo below
You're Welcome :)
The acceleration of the car three seconds before it comes to a stop is -2.76 m/s² (Letter B).
Derivative
Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.
In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.
For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x
The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you should solve this quadratic function:
Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]
[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]
[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]
[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]
Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].
The acceleration can be found from the derivative of the velocity function. See below.
a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]
a(t)= -6*[tex]2\sqrt{3}[/tex]t+18
a(t)= [tex]-12\sqrt{3}[/tex]t+18
a(t)=-2.76
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The velocity function of a car is given by v(t) = -3t^2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop. A. a = -6.46 m/s² B. a = -2.76 m/s² C. a = -0.46 m/s² D. a = 2.76 m/s²
The acceleration when the car comes to a full stop is 20.76 meters per square second.
How to find the acceleration?Here we have the velocity function:
v(t) = -3t^2 + 18t + 9
To find the acceleration we need to differentiate with respect to the variable t, so we will get the acceleration:
a(t) = 2*(-3)*t + 1*18
a(t) = - 6*t + 18
Now, the car will come to a stop when the velocity is equal to zero, so we need to solve:
-3t^2 + 18t + 9 = 0
Dividing all by -3 we get:
(-3t^2 + 18t + 9)/-3 = 0
t^2 - 6t - 3 = 0
The solutions are:
[tex]t = \frac{6 \pm \sqrt{(-6)^2 - 4*1*-3} }{2*1} \\\\t = \frac{6 \pm 6.92}{2}[/tex]
We only care for the positive solution:
t = (6 + 6.92)/2 = 6.46
The acceleration at that time is:
a(6.46) = - 6*6.46 + 18 = -20.76
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Find the average rate of change.
The average rate of change = 1.59 ≈ 2
The average rate of change can be calculated by
1) The first one = [tex]\frac{3 + 0}{2}[/tex] = 1.5
2 ) the second can also be solved by ; 8 + 2/ 2 = 5
3 ) the third one will be 20 + 6 / 2 = 13
4) 8.5
5) 12.5
To calculate the average rate of change
we will first add all the distance
Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51
The total time = 2 + 6 + 9 +15 = 32
Thus the average rate of change = 51 / 32 = 1.59
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Could you please help with this.
Answer:
[tex] \sqrt[2]{15} = 7.5[/tex]
Please help with this table. Not sure why this is difficult
A basketball player in a game makes x free throws worth 1 point and y 2-point baskets. The player needs to score at least 28 points to win the scoring title. What inequality represents the number and type of shots the player needs to win the title?
The inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have A basketball player in a game who makes [x] free throws worth 1 point and [y] free throws worth 2 point baskets. The player needs to score at least 28 points to win the scoring title.
The inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
Therefore, the inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
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Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 76 hours over the last two weeks and had a total of $1,790 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
A.
$953
B.
$371
C.
$684
D.
$269
The curved part of this figures is a semicircle.
What is the best approximation for the area of this figure?
Responses
28+16.25π units²
18 plus 16.25 pi, units²
14+16.25π units²
14 plus 16.25 pi, units²
14+8.125π units²
14 plus 8.125 pi, units²
28+8.125π units²
28 plus 8.125 pi, units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 4 comma negative 2 to negative 4 comma 2. Another segment extends from negative 4 comma 2 to 3 comma 2. A semicircle extends from 3 comma 2 to negative 4 comma negative 2.
The correct option regarding the area of the figure is given as follows:
14+16.25π units².
How to obtain the area of a figure?The figure, given with no scale at the end of the answer, is composed by:
A semi-circle.A right-triangle.The sides of the right-triangle are given as follows:
7, as 3 - (-4) = 7.4, as 2 - (-2) = 4.The area of a right triangle is given by half the multiplication of the sides, hence:
At = 0.5 x 7 x 4 = 14 units.
The radius of the semicircle is half the hypotenuse of the right triangle, hence, applying the Pythagorean Theorem:
h² = 7² + 4²
h = sqrt(7² + 4²)
r = 0.5sqrt(7² + 4²)
r = 4.03 inches.
The area of a semicircle of radius r is:
As = πr².
Hence:
As = π(4.03)² = 16.25 π.
The total area is obtained as the sum of the areas of each separate part, hence:
A = At + As = 14+16.25π units².
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Answer:
Step-by-step explanation:
14+8.125
C
Graph the solution to the equations below.
=1/4+2 and =−2−7
By graphing, the solution of the system of equations is: (-4, 1).
How to Solve a System of Equations by Graphing?The solution to the system of equations can be solved by graphing both lines of each equation on a coordinate plane, then find the coordinates of the point where both lines intersect each other.
Given the following equations:
y = 1/4x + 2
y = -2x - 7
The graph for y = 1/4x + 2 will intercept the y-axis at 2 and also has a slope of 2. The line for this equation is the red line.
The graph of y = -2x - 7 will also have a slope of -2. Its y-intercept would be -7. The line of the equation is the blue line.
The graph below shows the lines of both equations which intersect at (-4, 1), The solution is, (-4, 1).
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A rectangular patio has a length of 9 2/5 feet and an area of 81 3/8 square feet. What is the width of the patio?
Step-by-step explanation:
81 3/8 ÷ 9 2/5
81*8+3 = 651
651/8
9 2/5 = 9*5+2=47
47/5
651/8 ÷ 47/5 =
651/8 * 5/47 = 3255/376 =
8.65691489362
Solve the Inequality and graph the solution set.
-8-8(2x-4)>-5(4x-5)-21
Answer:
x > -5
Make a number line. Put a circle on the number line at -5 and then darken an arrow on the number line going to the right of -5
Step-by-step explanation:
-8-8(2x-4) > -5(4x -5) -21 Distribute the -8 and -5
-8 - 16x + 32 > -20x +25 -21 Combine like terms
-16x + 24 > -20x +4 Add 20x to both sides
4x + 24 > 4 Subtract 24 from both sides
4x > -20 Divide both sides by 4
x > -5
a ball is thrown up vertically. after t seconds, it's height (in feet) is given by the function h (t)=96t-16t^2 . after how long will it reach its maximum height
The time taken to reaches its maximum height is 3s.
In the question,
It is given that,
Height, h(t) = [tex]96t - 16t^{2}[/tex]
The maximum value of the function is obtained if the first derivative of the function h (t) = 0.
[tex]\frac{dh(t)}{dt} = 96 - 32t = 0[/tex]
⇒ [tex]t = 3[/tex]
So, time taken to reach its max height is 3 seconds.
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write an equation in slope-intercept form the table. help fast please
x: -4, 0, 4, 8, 12
y: 5, 6, 7, 8, 9
The linear equation in the table is written as:
y = (1/4)*x + 6
How to write the linear equation?The linear equation in slope-intercept form is written as:
y = m*x+ b
Where m is the slope and b is the y-intercept.
We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
m = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table:
(-4, 5) and (0, 6), so the slope is:
m = (6 - 5)/(0 + 4) = 1/4
And because of the point (0, 6) we know that the y-intercept is 6, then the line is:
y = (1/4)*x + 6
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Rewrite the equation in standard form from vertex form: y = -4(x - 3)² + 6
The equation of the parabola, in standard form is ______________
y = -4x²+24x-30 is the standard form of parabola whose equation is y = -4(x - 3)² + 6
What is Parabola?Parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
The given equation is y = -4(x - 3)² + 6.
We need to write this equation as standard form of parabola.
the equation of a parabola in standard form is.
y=ax² +bx+c
The given equation should be expanded y = -4(x - 3)² + 6.
y = -4(x²+9-6x)+6
Now apply distributive property
y = -4x²-36+24x+6
y = -4x²+24x+6-36
y = -4x²+24x-30
Hence y = -4x²+24x-30 is the standard form of parabola whose equation is y = -4(x - 3)² + 6
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i need help answering this question
Answer:
Step-by-step explanation:
there is no question?
Classify the following number: -22 Choose all that apply
