There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
The function f(x) = x³ +7x² - 5x + 19 is a polynomial function of degree 3, which means it has 3 roots (also known as zeros or solutions) that could be real or complex.
To determine the number of negative real roots, we can use the fact that a cubic function has at least one real root.
x³ +7x² - 5x + 19
the first coefficient is positive, the second is positive, the third is negative, and the fourth is positive.
There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"
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The average age of Elliot, Miya and Cara is 4 years more than the average
age of Elliot and Miya.
Cara is 9 years older than Elliot.
Four years ago, Elliot was double the age of Miya.
Work out the ages of Elliot, Miya and Cara.
Answer:
Elliot = 16 years old
Miya = 10 years old
Cara = 25 years old
Step-by-step explanation:
Define the variables:
x = Elliot's agey = Miya's agez = Cara's ageThe average age of Elliot, Miya and Cara is 4 years more than the average age of Elliot and Miya:
[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y}{2}+4[/tex]
[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y+8}{2}[/tex]
[tex]\implies 2(x+y+z)=3(x+y+8)[/tex]
[tex]\implies 2x+2y+2z=3x+3y+24[/tex]
[tex]\implies 2z=x+y+24[/tex]
[tex]\implies x=2z-y-24[/tex]
Cara is 9 years older than Elliot:
[tex]\implies z = x + 9[/tex]
Four years ago, Elliot was double the age of Miya:
[tex]\implies (x - 4) = 2(y - 4)[/tex]
[tex]\implies x - 4 = 2y-8[/tex]
[tex]\implies x +4 = 2y[/tex]
[tex]\implies y=\dfrac{1}{2}x +2[/tex]
Substitute the equations for z and y into the equation for x and solve for x:
[tex]\implies x=2z-y-24[/tex]
[tex]\implies x=2(x+9)-\left(\dfrac{1}{2}x +2\right)-24[/tex]
[tex]\implies x=\dfrac{3}{2}x-8[/tex]
[tex]\implies \dfrac{1}{2}x=8[/tex]
[tex]\implies x=16[/tex]
Substitute the found value of x into the equation for z and solve for z:
[tex]\implies z = 16 + 9[/tex]
[tex]\implies z = 25[/tex]
Substitute the found value of x into the equation for y and solve for y:
[tex]\implies y=\dfrac{1}{2}(16) +2[/tex]
[tex]\implies y=8+2[/tex]
[tex]\implies y=10[/tex]
Therefore, the ages of Elliot, Miya and Cara are:
Elliot = 16 years oldMiya = 10 years oldCara = 25 years oldWhich statements are true? Select three options.
and are parallel.
Answer: line AB and RS are parallel because their lines do not interact anywhere on the model, because it is 3D. this is the only one i am sure of, you may have to ask another person to get the other two.
Answer:
A. Line AB and Line CG are parallel, C. Line CG and Line RS are perpendicular, and E. Line CG lies in plane X
Step-by-step explanation:
A. Line AB and Line CG are parallel is true because the arrows are pointing in the same directions and do intersect or cross each other.
B. Line AB and Line RS are parallel is false because although they do not intersect, they also do not go in the same direction. These are also not perpendicular lines because they do not intersect other, even though they make a right angle.
C. Line CG and Line RS are perpendicular is true because these lines intersect at exactly 90° angle (as shown by the square).
D. Line AB and Line RS must intersect is false because Line AB does not intersect Line CG (which is the line that does intersect Line RS).
E. Line CG lies in plane X is true because point C and point G are in plane X.
F. Line RS lies in plane X is false because point r and point 2 are in plane Y.
what the answer to the math question?
The function f(x)= square root of x is translated using the rule (x,y) (x-7,y+2) to create f(x)what is the domain of f(x)?
The value inside the square root should be greater than or equal to zero. Then the domain of the function will be [7, ∞).
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
f(x) = √x
The function after the transformation, then we have
f(x) = √(x - 7) + 2
The value inside the square root should be greater than or equal to zero. Then the domain of the function will be given as,
x - 7 ≥ 0
x ≥ 7
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What is the domain of the function with the graph given below?
Answer:
(-∞, 1] or {x|x<=1}
Step-by-step explanation:
find the volume of the cylinder. use 3.14 for π. 5ft 10ft (10 is the radius) PLS HELP :(
Answer:
157[tex]ft^{3}[/tex]
Step-by-step explanation:
Volume = the area of the base times the height.
Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]
a = [tex]\pi[/tex][tex](5^{2})[/tex] I am going to use 3.14 for [tex]\pi[/tex]
a = 3.14(25)
a = 15.7
Volume = 15.7 x 10 = 157
Answer:
785 ft२
Step-by-step explanation:
volume =3.13*5२*10
=3.14*25*10
=785 ft२
Solve on the interval [0,2pi): 1- cos0= 1/2
Using an inverse trigonometric function, we will find that the solution is:
θ = 1.047
How to solve that equation?Here we want to solve the equation:
1 - cos(θ) = 1/2
Such that θ ∈ [0,2pi)
Now let's return to our equation:
1 - cos(θ) = 1/2
1 - 1/2 = cos(θ)
1/2 = cos(θ)
Now we could apply the inverse cosine function to both sides, then we will get:
Acos(1/2) = Acos(cos(θ))
1.047 = θ
That is the solution.
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Two tourists start walking across the Golden Gate Bridge at the same time but from opposite
ends. One of the tourists is walking at a leisurely rate of 0.9 meters per second, and the other
is walking at a rate of 1.1 meters per second. Given that the bridge is 2,738 meters in length,
how long will it take for the tourists to meet?
minutes and
seconds
Answer:
The tourists will meet at the midpoint of the bridge, which is 2738/2 = 1369 meters from each end.
At their respective walking speeds, it will take the first tourist 1369/0.9 = 1521.67 seconds to reach the midpoint, and it will take the second tourist 1369/1.1 = 1242.73 seconds.
Therefore, it will take them a total of 1521.67 + 1242.73 = 2764.4 seconds to meet.
Since there are 60 seconds in a minute, the time in minutes is 2764.4 / 60 = 46.07 minutes.
Therefore, it will take the tourists 46 minutes and 0.4 seconds to meet.
Uday Tahlan
When the function f(x) is divided by x + 2, the quotient is x² - 5x + 8 and the
remainder is 8. Find the function f(x) and write the result in standard form.
Step-by-step explanation:
this means :
f(x) / (x + 2) = (x² - 5x + 8) + 8/(x + 2)
f(x) = (x + 2)(x² - 5x + 8) + 8 =
= x³ - 5x² + 8x + 2x² - 10x + 16 + 8 =
= x³ - 3x² - 2x + 24
Moya is moving to a new house and packing up. She has 70 kilograms of books and 127 kg kilograms of clothing to send through the postal service. How much more do her clothes weigh than her books? How much is her shipping cost of sh has to pay $80 per kg of books and $200 per kg of clothing?
The amount that her clothes weigh more than her books would be = 57kg
The amount for the shipping cost for her school would be = 5600+25400 = $31000
What is postal service?Postal service is the type of service that helps.in the delivery of goods from one location to another when the goods are properly registered.
The mass of Moya's books = 70 kilograms
The mass of Moya's clothing = 127 kg
The difference between the bothe masses = 127 - 70 = 57kg
The cost per kg for books = $80 per kg
The cost per kg of clothing = $200
Therefore, the amount for the shipping cost for her school would be = (70×80) + (127 ×200)
= 5600+25400 = $31,000.
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Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
Opposite side = 14 in.
Adjacent side = 22 in.
cos θ = ?
Answer
Since this is a right triangle, we can use the inverse cosine function to solve for the angle θ.
cos θ = Opposite side / Adjacent side
cos θ = 14 / 22
cos θ = 0.6363
θ = cos^-1 (0.6363)
θ ≈ 45.9°
PLEASE HELP!!
I’m rlly struggling with my hw rn
There you have it, your answer
Step-by-step explanation:
Easy
y is equal to 5 less than the product of x and -2. If the output is -27, what is the input?
Answer: 27 over 2,5
Step-by-step explanation:
Locating Fractions on a Number Line
A B
Hot
-2
-1
Intro
C
D
+++++
0 1 2
Use the drop-down menus to label the points on the
number line.
Point A is at
Point B is at
Point C is at
Point D is at
<
Done
On solving the provided question we cans ay that - order when writing it on the number line: = -1.25, -0.75, 0.25, 1.5, 2
what is number line?A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.
The numbers on the number line must be
[tex]6/3 = 2\\-3/4 = -0.75\\1.5 = 1.5\\0.25 = 0.25\\-5.4 = -1.25\\[/tex]
In ascending order, t
[tex]-1.25 = -5/4\\-0.75 = -3/4\\0.25\\1.5\\2 = 6/3[/tex]
order when writing it on the number line:
-1.25, -0.75, 0.25, 1.5, 2
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Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now? Show your work.
The current temperature of the water is given as follows:
71.7 ºF.
How to obtain the current temperature of the water?The defining statement from the problem is given as follows:
He finds that the temperature changed by -0.6°F.
The change by the negative amount of -0.6ºF means that the current temperature of the water is obtained subtracting the previous temperature of the water by 0.6 ºF.
The previous temperature of the water is given as follows:
72.3°F.
Hence the current temperature of the water is obtained subtracting 72.3ºF and 0.6ºF, as follows:
72.3 - 0.6 = 71.7 ºF.
Missing InformationThe previous temperature of the water is given as follows:
72.3°F.
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multiply the sum by the difference of 19 and 57
Answer:2009#73
Step-by-step explanation:
3939+373
Ie,ek
if you had had a dog and a cat how many horses would u have
Answer: a lot
Step-by-step explanation:
Answer:
ummmm none? maybe
Step-by-step explanation:
The following equations define a system. −2x + y = 10 x + 2y = 5 Which graph represents the system? The graph shows a line that passes through negative 5 comma 0 and 0 comma 2.5. There is a second line that passes through 0 comma 10 and 5 comma 0. The lines intersect at 3 comma 4. The graph shows a line that passes through negative 5 comma 0 and 0 comma 10. There is a second line that passes through 0 comma 2.5 and 5 comma 0. The lines intersect at negative 3 comma 4. The graph shows a line that passes through negative 5 comma 0 and 0 comma negative 2.5. There is a second line that passes through 0 comma negative 10 and 5 comma 0. The lines intersect at 3 comma negative 4. The graph shows a line that passes through negative 5 comma 0 and 0 comma negative 10. There is a second line that passes through 0 comma negative 2.5 and 5 comma 0. The lines intersect at negative 3 comma negative 4.
The graph of the system of linear equations is attached with the answer.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the system of linear equations as given -
- 2x + y = 10
x + 2y = 5
The given system of linear equations is -
- 2x + y = 10
x + 2y = 5
Refer to the graph of the system of linear functions attached. The point (-3, 4) is the solution set of this system of equation.
Therefore, the graph of the system of linear equations is attached with the answer.
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Please help - How many whole months will it take for a motorbike valued at £2550 to depreciate to less than £1200 if depreciation is at a rate of 5% per month?
Therefore the answer is 27 or more months to depreciate to less than £1200 at a rate of 5% per month.
What is depreciation?Depreciation is a phrase that covers two different elements of the same idea: first, the real decline in an asset's fair value, such as the annual decline in the worth of industrial equipment.
What is asset and liabilities?Your balance sheet may be broken down into two categories, assets and liabilities, in its most basic form. A company's assets are any possessions that have the potential to provide future financial gain. Your debts to other people are called liabilities. In other words, assets increase your wealth while obligations decrease it.
The value of the motorbike will decrease by 5/100 = 0.05 (or 5%) each month. So, to find out how many months it will take for the value of the motorbike to decrease from £2550 to less than £1200, you need to solve the following equation:
£2550 - (0.05 * x) < £1200
where x is the number of months.
You can re-arrange the equation to solve for x:
x > (2550 - 1200) / 0.05
x > (1350) / 0.05
x > 27
So it will take the motorbike 27 or more months to depreciate to less than £1200 at a rate of 5% per month.
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solve number 13 please
Therefore , the solution of the given problem of domain is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.
Describe Domain.A function's domain is the set of values that can be sent into it. This collection represents all x values in a function like f. (x). A function's range is the set of possible values that it can accept. This collection includes the values that the return statement when we enter an x value. Assume that x and y are indeed the independent and dependent variables of a function with the formula y = f(x). If a function f provides a way to generate a single value y successfully while using a value of x .
Here,
In this case, f(x)=-3x-2 x < 4
3/4x-1 x≥ 4
Domain
This range, which is the range of -3x-2 (-14,), is a subset of the range of f(x).
Therefore , the solution of the given problem is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.
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The positive number a is 2,352% of the sum of the positive numbers b and c, and b is 84% of c. What percent of b is a?
Answer: We can start by using the information given to set up an equation. We know that:
a = 2,352% of (b + c)
b = 84% of c
We can express the first equation in terms of percentages by dividing both sides by 100:
a = 23.52(b + c)
We can also express the second equation in terms of percentages by dividing both sides by 100:
b = 0.84c
Now we can substitute the second equation into the first equation:
a = 23.52(0.84c + c)
a = 23.52(1.84c)
So a = 43.1184c
To find the percentage of b, we divide b by a and multiply by 100:
percentage of b = (b / a) * 100
Now we substitute values of a and b
percentage of b = (0.84c / 43.1184c) * 100
percentage of b = (0.84 / 43.1184) * 100
Which simplify to
percentage of b = 1.9425 %
Step-by-step explanation:
Please screenshot and write the answer on the photo.
1] Answer: y = -[tex]\frac{1}{2}[/tex]x + 3
Step-by-step explanation:
➜ This line is going down from the top left to the bottom right, so it will have a negative slope.
➜ Using rise over run, we get a slope of -2/4. This simplifies to -1/2.
➜ The line intercepts the y-axis at 3.
2] Answer: y = 3x
Step-by-step explanation:
➜ This line is going down from the bottom left to the top right, so it will have a positive slope.
➜ Using rise over run, we get a slope of 3/1. This simplifies to 3.
➜ The line intercepts the y-axis at 0.
3] Answer: y = x - 4
Step-by-step explanation:
➜ This line is going down from the top left to the bottom right, so it will have a negative slope.
➜ Using rise over run, we get a slope of 2/2. This simplifies to 1.
➜ The line intercepts the y-axis at -4.
There are 8 boxes of erasers in the supply closet. Each box contains 9 erasers. How many erasers are there in all?
Answer:
each box contain 8 x 9 = 72
Target buys a pair of shoes for 20, but they sell it to the public for 35. what is the percent of change that target marks the shoes up for
Answer:
75%
Step-by-step explanation:
To find the percent of change that Target marks the shoes up for, you need to calculate the difference between the cost of the shoes to Target and the price at which they sell it to the public, and then divide that difference by the cost of the shoes to Target. Finally, you need to multiply the result by 100 to express the answer as a percentage.
Using this formula, the percent of change that Target marks the shoes up for is:
(35 - 20) / 20 * 100 = 15 / 20 * 100 = 0.75 * 100 = 75%
This means that Target marks the shoes up by 75% of their cost.
gavin painted 14 pictures last week. he painted some more pictures this week. he painted 25 pictures in all. how many pictures did gavin paint this week
Answer:
11
Step-by-step explanation:
Based on the given conditions, formulate: 25 - 14
Calculate the sum or difference: 11
get the result: 11
PLEASE HELP!! ALGEBRA 1 HW! I WILL GIVE BRAINLYEST
Answer:
(0.5, 3)
Step-by-step explanation:
Just entered it into a desmos graphing calculator online
1. Convert the following improper fractions to mixed numbers; a. 55
2
b. 43 3
2. Convert the following mixed numbers to improper fractions; a. 72
5
b. 121 2
[1]
[1]
[1]
7½
7×2+1/2
14+1/2
15/2
212½
12×2+1/2
24+1/2
25/2
What is the equation of this graph in slope intercept form
The slope-intercept form of the equations presented on the graph are;
y = 4
y = 3
What is the slope-intercept form of the equation of a line?The slope-intercept form of the equation of a line is; y = m·x + c, where;
m = The slope of the graph
c = The y-intercept of the graph
The equation of the lines in the graphs (blue line, and red line) are found as follows;
The slope of the blue line is found using the points on the graph as follows;
The coordinates of points on the blue line graph are; (0, 4), (2, 4), (4, 4)
The slope is therefore; m = (4 - 4)/(4 - 2) = 0
The y-intercept, obtained from the graph is; c = 4
The value of the slope, m = 0, indicates that the graph is an horizontal line with an equation y = c
c = 4
The equation of the blue line graph in slope-intercept form is therefore;
y = 4
The coordinates of points on the red line graph are; (0, 3), (2, 3), (4, 3)
The slope of the red line graph is therefore;
m = (3 - 3)/(4 - 2) = 0
The y-intercept of the red line graph is; c = 3
The value of the slope, m = 0, and the y-intercept, c = 3, indicates that the equation of the red line graph is therefore;
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Given csc 0=17/15, determine the values for “a” and “b” in cos 0=a/b
If cosec (tetha) = 17/15 then cos (tetha) = 8/17
What are trigonometry ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
cosec , sine, cotangent, cosine , secant and tangent are trigonometry function.
cosec( tetha) = 1/sin(tetha)
tangent (tetha) = 1/ cot ( tetha)
sec (tetha) = 1/ cos(tetha)
cosec (tetha) = 17/15
therefore 1/sin ( tetha) = 17/15
sin( tetha ) = 15/17 = opp/ hyp
therefore using Pythagoras theorem adj² = 17²-15²
adj² = 289-225
adj² = 64
adj = √64 = 8
cos ( tetha) = adj/hyp
therefore cos ( tetha) = 8/17
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"describe the domain and range for f(x)=3^x-1"
Answer:
Domain: All real numbers
Range: All real numbers greater than or equal to -1