The correct statement for the number of negative zeros and of positive zeros is given as follows:
The number of positive zeros is of 4, while the number of negative roots is of zero.
How to obtain the number of positive and negative roots?The number of possible positive and negative roots is obtained using Descartes' Rule.
The Descartes' Rule states that the number of positive roots is at most the number of sign changes in the sequence of polynomial's coefficients (disconsidering the zero coefficients), while the difference between these two numbers is always even.
The number of changes for this problem is given as follows:
4 changes.
The changes are given as follows:
x^4 to x^3.x^3 to x^2.x^2 to x.x to constant.As there are 4 changes, the number of positive roots is of 4, while the number of negative roots is of zero, as the polynomial is of the fourth degree.
Missing InformationThe answer was given in general terms, as the statements are not presented.
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Rewrite it in for y=a(1+r)^t
Answer:
I don't get it please elaborate!
Step by Step Explanation:
Thank you!
John i 7 year younger than jane. The um of their age i 10 year ago wa 55 year. How old are they now
John 38 years old and Jane 45 years old 10 years ago from the present age .
John: 48 years old
Jane: 55 years old
Jane is 55 years old and John is 7 years younger, so John is 55 - 7 = 48 years old.
John is 7 years younger than Jane, so if we subtract 7 years from Jane's age, we can find John's age. Jane is 55 years old, so if we subtract 7 years, we get 55 - 7 = 48. Therefore, John is 48 years old, and Jane is 55 years old. To find their age 10 years ago, we can subtract 10 years from each of their current ages. This would make John 38 years old and Jane 45 years old 10 years ago from the present age
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What is the measure of angle ACD?
Using the exterior angle theorem which involves the use of two interior angles in the polygon, the value of angle ACD in the triangle is 150 degrees
What is an Exterior AngleAn exterior angle of a polygon is an angle that is formed outside of the polygon by extending one of its sides. It is the supplementary angle of an interior angle.
Exterior angle theorem states that the sum of two interior angles is equal to one exterior angle.
Using that theorem in this problem;
∠ACD = 33 + 117
∠ACD = 150°
The value of angle ACD in the triangle is equal to 150 degrees
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Sally's class is raising money for charity with a goal of raising $2,000. They raise $997 at a bake sale and $961 at a car wash. Sally wants to see if they raised enough money to meet their goal. Complete the statements.
Sally's class haven't raised $2,000 as the amount made is $958. The estimated value is $1900. The amount needed is $42.
How to illustrate the value?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, Sally's class is raising money for charity with a goal of raising $2,000. They raise $997 at a bake sale and $961 at a car wash. Sally wants to see if they raised enough money to meet their goal. The amount made will be:
= $997 + $961
= $1958
They have not made $2000. The amount left is:
= $2000 - $1958
= $42
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Dante deposits $300 to open a savings account. He will earn 2% interest each year on his
money If he makes no deposits or withdrawals, how much money will Dante earn in interest
in 1 year? How much money will be in the account after 4 years?
Therefore , the solution to the given problem of interest comes out to be $324.
What is meant by interest?By dividing the original capital by the cost of borrowing, the time period, and other factors, simple interest is calculated. Simple return is calculated as follows: principal + interest + hours. This method of calculating interest is the simplest. The most typical method is to calculate it as a percent of the principal amount. For instance, if he took $100 from a buddy and promised to repay it with 5% interest, he would only be required to pay his proportion of the interest. $100 (0.05) = $5. When you make loans, you should pay interest, and you also need to when you lend money. Interest is often computed as a percentage of a loan.
Here,
Given: $300 is the principal amount
Time: 4 years,
2% interest rate
To discover the basic interest:
Using this formula
Simple interest equals
=> P*R*T/100,
=> 300*2*4/100
=> 24.
Total after four years equals 300 + 24 = 324
Therefore , the solution to the given problem of simple interest comes out to be $324.
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Which of the following is degree 2 polynomial y2 y3 +2y8?A. 2B. -1c. 3D. 8
Answer:
Step-by-step explanation: .
The side of the quadrilateral are in the ratio 4:6:3:5. The perimeter of
the quadrilateral is 54 cm. What are the lengths of each side? Solution:
A quadrilateral is a four-sided shape. The perimeter of a quadrilateral is the sum of all its sides. If the perimeter of a quadrilateral is 54 cm, and we know that all four sides are equal, we can divide 54 by 4 to find the length of each side.
54 cm / 4 = 13.5 cmTherefore, the length of each side of the quadrilateral is 13.5 cm.
It's important to note that this is only one possibility, since quadrilaterals can have different shapes and different side lengths.
What value breaks 100 into 4 equal pieces?
Answer:
25 :)
Step-by-step explanation:
Are rectangles and squares similar polygons?
Yes, rectangles and squares are similar polygons.
Similar polygons are two or more polygons with the same shape but different sizes. This means that the sides of the polygons are proportional, and the angles are congruent. The formula to determine if two polygons are similar is A/a = B/b = C/c = D/d = …, where A, B, C, and D are the sides of one polygon and a, b, c, and d are the sides of the other polygon. For instance, if a rectangle has sides of 4 and 8, and a square has sides of 6 and 6, the ratio of the sides of the rectangle to the sides of the square is 4/6 = 8/6. This means that the two shapes are similar.
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Determine the type of dilation shown and the scale factor used.
Enlargement with scale factor of 1.5
Enlargement with scale factor of 2.5
Reduction with scale factor of 1.5
Reduction with scale factor of 2.5
The type of dilation and scale factor in the figure shown is
Enlargement with scale factor of 2.5How to find the type of dilationScale factors are used to increase or decrease image. The situation of increment is usually called magnifying or enlargement.
The given problem is enlargement since the preimage is smaller than the image. Also the scale factor will be greater than 1
Taking a point of reference say side 6 in the preimage and side 15 in the image and solve for the factor, assuming the factor is k
6k = 15
k = 15/6
k = 2.5
hence we say that the scale factor is 2.5
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Answer: Enlargement with scale factor of 2.5
Step-by-step explanation: I took the quiz so you don't have too!
Jon earns £90 one week. The next week, he receives a pay rise and earns £130. Write the amount of his pay rise as a fraction of his original pay. Give your answer in its simplest form.
PLEASE HELP I REALLY NEED IT FOR HOMEWORK
The fraction of Jon original pay is 4/10
How to calculate the fraction of Jon original pay?Jon earns £90 one week
The following week he earns £130
His pay rise is
130-90
= 40
The fraction of his original pay is
= 40/100
= 4/10
Hence the fraction of Jon original pay is 4/10
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How many grams are in 3.29 X 10²5 molecules of water (H₂O)?
Water molecules with a mass of 3.34 * (10 )23 weigh 9.911 grams.
What is the mass in grams of 3.34 x 1023 molecules of H2O?Firstly, you wish to transform the quantity of water molecules you have into the quantity of moles.
Undoubtedly, you are aware
Number of Particles = Mole Ratio x Avogadro's Constant
Avogadro's constant is equal to 3.34 * (10) 23 / 6.02 * (10) 23 when the number of moles is equal to the number of particles.
=0.55
so 0.55 moles
Consequently, mass/molar mass = number of moles.
Since we must determine the mass, we can use the formula Mass = Number of Moles x Molar Mass.
H 2 O's molar mass is calculated as H - 2(1.01) = 2.02 O- 16 18.02
Consequently, 18.02 g/mol is the molar mass.
We now possess the necessary values to determine the mass because of this.
Mass = 0.55 × 18.02
Mass = 9.911
As a result, the 3.34 mass
There are 9.911 grams in 3.34 * (10 )23 water molecules.
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The biggest possible cube is taken out of a right solid cylinder of radius 15cm and height 25 cm respectively. what will be the volume of the cube
The volume of the biggest possible cube inside the right cylinder is approximately 1193.243 cubic centimeters.
What is the biggest possible cube that is taken out of a right solid cylinder?
Cubes are hexahedrons with one same side length and only right angles. In this case, the cube is constrained by cross area of right cylinder in accordance to image attached below. The maximum possible volume for a cube inside the cylinder is described by following expression:
V = (√2 / 2)³ · R³
Where:
V - Volume of the cube, in centimeters.R - Radius of the right cylinder, in centimeters.If we know that R = 15 cm, then the volume of biggest possible cube is:
V = (√2 / 2)³ · (15 cm)³
V ≈ 1193.243 cm³
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Is square root of 4 a polynomial?
Square root of 4 is not a polynomial. It is a quadratic function. Functions containing other operations like square root is not a polynomial.
A polynomial need not have any square root. polynomial is a finite sequence form. it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Polynomial are sums and differences of polynomial terms. For an expression to be a polynomial term, any variables in the expression must have whole number powers. It should not have any square root, cube root or any negative values. Quadratic function can have square root cube roots and fraction values.
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Line A pae through the point (1,5) and (5,7). Find the equation of the line perpendicular to A that pae through point (-1,7
The equation of the line perpendicular to the line A is given by the
x-4y +29=0
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Given is a Line A pass through the point (1,5) and (5,7).
Find the equation of the line perpendicular to A that pae through point (-1,7)
line A is y= 1/4 x+c
x-4y +4c=0
it passes through ( -1,7)
c= 29/4
equation becomes x-4y +29=0
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) Select the inequality that the number line represents. Use x as the variable.
The number line represents an inequality. The inequality is x ≥ -3.
What is a number line?
A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.
If a number line contains a close circle, then the number includes in the inequality.
If a number line contains an open circle, then the number does not include in the inequality.
In the graph, there is a close circle on -3.
The line represents all real numbers greater than -3.
Since there is a close circle on -3, thus -3 include in the inequality.
The given variable is x.
The graph represents all real numbers greater than or equal to -3.
The inequality is x ≥ -3.
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You are measuring the height of a spruce tree. You stand 45 feet from the base of the
tree. You measure the angle of elevation from the ground to the top of the tree to be
59. Find the height h of the tree to the nearest foot.
Provided the given distance and the angle of elevation, Using the trigonometry in the right angled triangle formed, The answer is 74.89 feet.
What is trigonometry?Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. Trigonometry is used to study properties such as lengths, angles, and areas of triangles and the relationships between them. It is also used in many fields, including physics, engineering, and navigation. Trigonometry is based on the study of the ratios of the sides of a right triangle. The three main ratios are sine, cosine, and tangent. These ratios are defined using the right triangle's angles and are often abbreviated as sin, cos, and tan. In addition to these three main ratios, there are also several other trigonometric functions, including cosecant, secant, and cotangent. These functions are the reciprocals of the sine, cosine, and tangent functions, respectively.
What is a right triangle?A right triangle is a type of triangle that has one angle that measures exactly 90 degrees. This angle is called the right angle and the two sides that form the angle are called the legs of the triangle. The side opposite the right angle is called the hypotenuse. A right triangle can also be defined as a triangle that has a 90-degree angle and two acute angles. The legs of the triangle are the sides that are opposite the acute angles, and the hypotenuse is the side that is opposite the right angle.
tan(A) = rise/run
tan(59) = height/45
height = tan(59)*45
=74.89 feet
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Please help quickly I have limited time!!!!!!
Cells share many cοmmon features, yet they can look wildly different. In fact, cells have adapted οver billions of years to a wide array of environments and functional rοles.
What Defines a Cell?The lοwest common element of life is a cell. Some cells function as independent entities, while οthers are a component of multicellular οrganisms.
Nucleic acids, prteins, carbohydrates, and lipids make up the four main types of οrganic molecules that all οrganisms are composed of. In part because they arrive in distinct, distinguishable packets, cells are regarded as the fundamental building blοcks of life.
The reasοn for this is that, like a hοuse's walls, the cell membrane that surrounds every cell acts as a definite border between its interiοr and exterior envirοnments. The plasma membrane is anοther name for the cell membrane. Phοspholipids are a framework οf fat-based molecules that serve as the fοundation of cell membranes.
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Y=x2+2x-2 graph each quadratic function
By evaluating the quadratic equation we can get some points, and with them we can estimate the graph.
The graph can be seen in the image at the end.
How to graph the quadratic equation?Here we want to graph the function:
y = x^2 + 2x - 2
To do so, we can evaluate the quadratic equation in some values of x to get points, and then just connect the points with a general parabola.
when x = 0
y = 0^2 + 2*0 - 2 = -2
So the point is (0, -2)
when x = 1
y = 1^2 + 2*1 - 2 = 1 + 2 - 2 = 1
So the point is (1, 1)
when x = -1
y = (-1)^2 + 2*(-1) - 2
y = 1 - 2- 2 = -3
So the point is (-1, -3)
when x = -2
y = (-2)^2 + 2*(-2) - 2
y = 4 - 4 - 2 = -2
So we have the point (-2, -2)
And so on..., eventually, you will get enough points to connect, and you should get something like:
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Using the cosine rule calculate the magnitude of angle B when dide b=20.8cm c= 14.5cm and a= 9.3cm
Using the cosine rule calculate the magnitude of angle B when did the b=20.8cm c= 14.5cm and a= 9.3cm is [tex]\approx 37.02364^{\circ}[/tex]
What is cosine rule?c = [a2 + b2 - 2ab cos C] is the cosine formula to get the side of the triangle. a, b, and c are the triangle's three sides. When attempting to link all three sides of a triangle to a single angle, the cosine rule can be applied. You need to know the other two sides as well as the opposing angle in order to determine the length of a side. Your objective is to locate side a. With the aid of the sine rule, one can determine an angle from three sides and an angle or a side from three angles and a side.Given,
b=20.8cm c= 14.5cm and a= 9.3cm
[tex]\gamma=\cos ^{-1}\left(\frac{a^2+b^2-c^2}{2 a b}\right)[/tex]
[tex]=\cos ^{-1}\left(\frac{9.3^2+20.8^2-14.5^2}{2 \cdot 9.3 \cdot 20.8}\right)[/tex]
[tex]\approx 37.02364^{\circ}[/tex]
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What is #6? Needhelp
Answer:
(-3,5)
Step-by-step explanation:
8x+3(23+6x)=-9
x=-3
y=23+6x(-3)
y=5
(-3,5)
HURRY PLEASE!!!!!!!
Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of an ounce per second. Diego starts with his usual 20 ounce milkshake and drinks at the same rate as before, an ounce per second.
What does the graph tell you about the situation? Specifically answer the following:
a.) How many solutions are there? (25 pts)
b.) Interpret the solution(s). (25 pts)
c.) Who finishes the milkshake first? (25 pts)
the other equation is missing, the solution cannot be found.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of an ounce per second.
Rate= 1/3 ounce milkshake per second
Initial = 20 ounces
Lin's condition is thus represented by the equation:
[tex]y = \frac{1}{3} x +20[/tex]
Since the other equation is missing, the solution cannot be found.
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How many images are formed If two plane mirror are position at an angle of 45â°?
The number of images that will be formed when two mirrors are positioned at an angle of 45 degrees is 7.
The formula that you have provided for calculating the number of images formed by two mirrors positioned at a specific angle is (360/n) - 1, where n is the angle between the mirrors in degrees.
When two mirrors are positioned at an angle of 45 degrees, n = 45. So, using the formula, the number of images formed would be: (360/45) -1 = 8 - 1= 7
It's important to note that this formula only gives you the approximate number of images that will be formed. In reality, due to the nature of light and the reflective properties of mirrors, it is impossible to determine the exact number of images that will be formed.
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3. The Lovely Day Fruit company makes two varieties of fruit drink, Fruit Delight and Heavenly Punch. The chart below shows how much juice goes into each type and the profit per can of juice. Each week, the company receives a shipment of 9000 ounces of pineapple juice, 24000 ounces of orange juice, and 14000 ounces of apricot juice. Fill in the question marks appropriately and then use the linear programming process to find how many cans of each should be made each week to maximize profit.
The optimal solution is x = 2000 and y = 4000, meaning that 2000 cans of Fruit Delight and 4000 cans of Heavenly Punch should be made each week to maximize profit.
Fruit Delight:
Pineapple juice: 3 oz
Orange juice: 6 oz
Apricot juice: 2 oz
Profit: $1.50
Heavenly Punch:
Pineapple juice: 6 oz
Orange juice: 2 oz
Apricot juice: 4 oz
Profit: $2.00
Linear Programming Process:
We can use linear programming to solve this problem. We will create two variables, x and y, to represent the number of cans of Fruit Delight and Heavenly Punch respectively. The objective is to maximize profit, which can be expressed mathematically as:
Maximize: 1.50x + 2.00y
subject to:
3x + 6y ≤ 9000
2x + 4y ≤ 14000
6x + 2y ≤ 24000
x ≥ 0
y ≥ 0
Using linear programming software, we can solve this problem and find that the optimal solution is x = 2000 and y = 4000, meaning that 2000 cans of Fruit Delight and 4000 cans of Heavenly Punch should be made each week to maximize profit.
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Can someone please solve this math problem? I can't use words, only numbers, infinity symbols, etc... The math problem is in the picture, Thanks!
Answer: 10
Step-by-step explanation:
What is the solution to the system of equations y equals one over 3x 10?
The solution to the given system of equations y = 1/3x - 10 and 2x + y = 4 is (6, -8).
y = 1/3x - 10 … (1)
2x + y = 4 … (2)
We can use the substitution method to determine the solution of the given system of linear equations.
Substituting (1) in (2), we get
⇒2x + (1/3 x - 10) = 4
⇒2x + 1/3 x - 10 = 4
⇒(6 + 1)/3 x = 14
⇒7/3 x = 14
⇒7x = 14 × 3
⇒7x = 42
Dividing both sides by 7
x = 6
Place the value of x in equation (1)
⇒y = 1/3 (6) - 10
⇒y = 2 - 10
⇒y = -8
--The given question is incomplete, the complete question is
"What is the solution to the system of equations y = 1/3x - 10 and 2x + y = 4?"--
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What is the symmetric of -15??
The symmetric of -15 is 15.
Step by step explanation:When we talk about symmetric, we must remember that it means the opposite of a number, that is, we take as a basis the number line where we have zero (0) as the central number, on one side the negative infinite numbers (-) and on the other, the positive infinite number (+), see the attached image.
In order to solve this type of exercise, just change the signs of the number in question, if it is negative it will become positive and vice versa.
[tex] \bold{- 15 = + 15}[/tex]
Molly jogged at a rate of 6 mph, what was her speed in feet per second?
Answer:
8.8 feet per second
Step-by-step explanation:
1 mile = 5280 feet
3600 seconds = 1 hour
6 mph = 5280(6)/3600 = 528/60 8.8 feet per second
please help im stuck like really stuck
Answer:
[tex]14v+7=7(2v+1)[/tex]
Step-by-step explanation:
break down the equation 14v +7
Answer:
7(2v+1)
Step-by-step explanation:
7 goes into 14 twice and into itself once so its factorised as 7(2v+1) you can do the multiplication to test it .
Alex made a table to record how many trees were in his yard for each day that the landscapers were working. Which equation represents the data?