If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
If p(x) is a polynomial function with p ( 3/4 ) = 0
Then we need to find which of the given statements are true.
A. The function has a factor of (4x + 3).
If x=3/4 then 4(3/4)+3 which is not equal to zero
B. The function has a factor of (4x – 3).
If x=3/4 then 4(3/4)-3 which is equal to zero
C. The function has a factor of (3x + 4).
If x=3/4 then 3(3/4)+4 which is not equal to zero
D. The function has a factor of (3x – 4).
If x=3/4 then 3(3/4)-4 which is not equal to zero
Hence, If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).
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How do you know how many real solutions?
The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.
What are real solutions of an equation?A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.
How many real solutions does the discriminant have?When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.
So that we can find real solution of quadratic equation by finding discriminant of given equation.
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5 whole 1/7- 2 whole 5/21
The value of 5 1/7 minus 2 5/21 will be 2 19 / 21.
How to solve the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Based on the information, the value of 5 1/7 minus 2 5/21 will be:
= 5 1/7 - 2 5 / 21
= 5 3/21 - 2 5 / 21
= 2 19 / 21
The value is 2 19/21.
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A sookeeper weighted an African elephant to be 9 x 10 (to the 3rd power) pounds, and an African lion to be 4 x 10 (to the second power) pounds. Hiw many times greater is the weight of the elephant than the weight of the lion
2.25×10 times greater is the weight of the elephant than the weight of the lion.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a zookeeper weighted an African elephant to be 9 x 10³ pounds.
An African lion to be 4 x 10² pounds
We need to find how many times greater is the weight of the elephant than the weight of the lion
Now, Divide the weighed an African elephant with weighed an African lion to determine times greater is the weight of the elephant than the weight of the lion,
N=9×10³/4×10²
=2.25×10
Hence, 2.25×10 times greater is the weight of the elephant than the weight of the lion.
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During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large. What is the explanatory variable for this relationship
The number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.
The explanatory variable for this relationship is the number of seeds per square foot. The number of seeds per square foot is the variable that is being manipulated or changed by the farmers in order to observe the effect on the yield of the crop in pounds per square foot.
The farmers observed that the yields were the smallest when the number of seeds per square foot was either very small or very large, this means that there is an optimal number of seeds per square foot that yields the highest crop.
So, the number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.
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The points (-5, 5) and (5, u) fall on a line with a slope of 3/10 What is the value of u?
Thank you!
Answer:
u = 8
Step-by-step explanation:
calculate the slope of the line passing through the 2 give points using the slope formula, then equate to the given slope.
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 5 ) and (x₂, y₂ ) = (5, u )
m = [tex]\frac{u-5}{5-(-5)}[/tex] = [tex]\frac{u-5}{5+5}[/tex] = [tex]\frac{u-5}{10}[/tex] , then equating the 2 expressions gives
[tex]\frac{u-5}{10}[/tex] = [tex]\frac{3}{10}[/tex] ( cross- multiply )
10(u - 5) = 30 ( divide both sides by 10 )
u - 5 = 3 ( add 5 to both sides )
u = 8
Step-by-step explanation:
(u - 5)/(5 + 5)= 3/10
(u - 5)/10= 3/10
10u - 50 = 30
10u = 80
u = 8
Rob collects model planes one of his planes uses a sacks in which 1 inch represents 1. 5 feet if the length of the model airplane is 12 inches find the length of the actual airplane on feet
If 1 inch represents 1.5 feet, we can use this conversion factor to find the length of the actual airplane in feet. Thus 12 inches of model airplane represents an actual length of the actual airplane of 18 feet.
Therefore the answer is 18 feet.
To convert the length of the model airplane (12 inches) to feet, we can multiply it by the conversion factor (1 inch = 1.5 feet)
= 12 inches × 1.5 feet/inch
= 18 feet
So the length of the actual airplane is 18 feet.
It is important to pay attention to the units of measurement when performing conversions and make sure to use the correct conversion factor. And also it's a good practice to always check your answer to make sure it makes sense in the context of the problem.
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Is N2 the same as 2N?
Therefore, N2 and 2N are not equal, they are different mathematical expressions.
What are expressions?A finite collection of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
What are symbols?A mark, sign, or term that denotes, denotes, or is taken to denote a concept, an item, or a connection is known as a symbol. By connecting seemingly unrelated ideas and events, symbols let individuals look beyond the known and the visible.
No, N2 and 2N are not the same.
N2 is the square of N, which means it is N multiplied by itself. For example, if N = 5, then N2 = 5*5 = 25.
2N, on the other hand, is N multiplied by 2. For example, if N = 5, then 2N = 5*2 = 10.
So, N2 and 2N are not equal, they are different mathematical expressions.
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f(n) = 2n-1 find the arithmetic sequence ?
An arithmetic sequence is a sequence of numbers in which the difference between any two successive members of the sequence is a constant value. The general form of an arithmetic sequence is:
a, a + d, a + 2d, a + 3d, ...
where "a" is the first term of the sequence, and "d" is the common difference between successive terms.
Given the function f(n) = 2n - 1, we can see that the function outputs a sequence of integers, with a common difference of 2. So f(n) is not an arithmetic sequence.
Arithmetic sequence is a list of numbers in which each number is the sum of the previous number and a constant number.
Example: 1,3,5,7,9 is an arithmetic sequence because the constant difference is 2.
If you have any other question feel free to ask.
Find the inverse of y = √x + 8, y ≥ 8
To find the inverse of a function, you can follow these steps:
Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.
Solve the equation for y. In this case, you would get:
x = √y + 8
y = x - 8
Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:
f^-1(x) = x - 8
This is the inverse function of y = √x + 8.
Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.
After my salary was increased by $16\%,$ it was $\$52{,}200$. What was my salary before the increase
%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.
What is percentage?A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.
Considering the query
It was $52,200 after a 16% raise in my pay.
In light of the conditions stated, come up with
[tex]$=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$[/tex]
= $45000
Before the raise, I was making $45,000.
Therefore, the answer is $45,000.
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the survey is a research method in which: group of answer choices individuals are carefully observed in their natural environments. a representative, random sample of individuals are questioned regarding their attitudes or behaviors. an individual is studied in great depth. an investigator determines the extent to which two variables influence each other.
The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.
B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.
C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.
D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.
Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
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A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.
What are the odds against exactly 5 cars passing over the bridge in that time?
Answer: The odds against an event occurring are the ratio of the probability that the event will not occur to the probability that the event will occur. To find the odds against an event, you can use the formula:
Odds against = (1 - probability of event occurring) / probability of event occurring
In this case, the event is that exactly 5 cars will pass over the bridge in a 4-minute period. The probability that this event will occur is 0.16. Therefore, the odds against this event occurring are:
Odds against = (1 - 0.16) / 0.16
= 0.84 / 0.16
= 5.25
So, the odds against exactly 5 cars passing over the bridge in a 4-minute period are 5.25 to 1.
It means that there are 5.25 times more likely that it will not happen compare to happen.
Step-by-step explanation:
If f(x)=3x, g(x)=x+4, and h(x)=x2-1, find the value of h[f(5)]
Answer:
29
Step-by-step explanation:
Choose the equation that represents the line passing through the point (-3,-1) with a slope of 4.
y=4x-11
y = 4x + 11
y = 4x + 7
y=4x-7
On solving the provided question, we can say that - in the linear equation here the value will be
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
y = 4x + 11
x = 8
y = 32 + 11
y = 43
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How do u work this out ?
Answer:
[tex]\frac{d}{c}[/tex]
Step-by-step explanation:
[tex]\frac{cxcxdxdxd}{cxcxcxdxd}[/tex] You can cross out 2 c's from the top and the bottom and 2 d's from the top and the bottom. It now looks like this
[tex]\frac{d}{c}[/tex]
Is 10 12 15 a Pythagorean triple?
No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.
To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.
In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.
10^2 + 12^2 = 100 + 144 = 244
244 ≠ 15^2
Therefore, 10 12 15 is not a Pythagorean triple.
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The sides of a triangle are 68, 61, and 46. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answer: Acute
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex]. A and b are legs while c is hypotenuse. Hypotenuse is also the longest side. Let's plug them in and see if they are equal to each other.
[tex]46^2+61^2=68^2[/tex] [exponent]
[tex]2116+3721=4624[/tex] [add]
[tex]5837\neq4624[/tex]
Since they are not equal, then it is not a right triangle.
To tell is a triangle is acute, if the sum of the two shorter sides squared is greater than the longest side squared, then the triangle is acute.
At the end of the Pythagorean Theorem, we got 5837≠4624. 5837>4624, so that tells us that the triangle is acute.
Molly and Liza are exercising. Molly does
10 push-ups at the same time
as Liza
does 15 push-ups. When Molly does
40 push-ups, how many push-ups does
Liza do?
Answer:
25
Step-by-step explanation:
so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.
Angle AOB is a central angle with a measure of 110 degrees.
What is the measure of its arc AB?
The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
Given that,
In the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
We have to find the measure of the ACB arc.
We know that,
Suppose that AB is the minor arc that is m(arc AB) = 110°
We know that measure of the major arc is 360°- measure of minor arc.
m(arc ACB)= 360- m(arc AB)
m(arc ACB)= 360-110
m(arc ACB)= 250°
Therefore, The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
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Question 1 : (2.3 × 10^4) × (1.5 × 10^-2)
Question 2: (3.6 × 10^-5) ÷ (1.8 × 10²)
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expressions are given below.
(2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
Simplify the expression (2.3 × 10⁴) × (1.5 × 10⁻²), then the value of the expression will be given as,
⇒ (2.3 × 10⁴) × (1.5 × 10⁻²)
⇒ 345
Simplify the expression (3.6 × 10⁻⁵) ÷ (1.8 × 10²), then the value of the expression will be given as,
⇒ (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
⇒ 2 × 10⁻⁷
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
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7(3n + 2) - 3n - 5 i need to factor it tysvm!!
The answer to the Linear expression 7(3n + 2) - 3n - 5 is 18n + 11
What is a linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
From the expression 7(3n + 2) - 3n - 5
By expanding the bracket, we have
21n + 14 - 3n - 5
By collecting like terms, we have
21n - 3n + 14 - 3
18n + 11
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What linear equation means?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1 or 0. A linear equation is an algebraic equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
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A regular pentagon is a pentagon with five sides of the same length. If the length of one side of the pentagon is represented by 2X -1, what expression would represent the perimeter of this pentagon
Step-by-step explanation:
one side : 2x - 1
so, 5 sides (the perimeter is the sum of all sides) :
5 × (2x - 1) = 10x - 5
30 PTS: Please help me
You can earn money by shoveling your neighbors' driveways in the winter and get paid $10 per hour. What is a function that would define this situation? Define the domain and range of this function and describe reasonable values for each.
The function that will define the situation is y = 10x
The domain: {0, ∞)
The range: {0, ∞)
How to write the functionThe function that will define the situation is a linear function of the form
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function as as follows
c = there is no condition defined here hence = 0
m = cost of per hour = $2.50
x = time in hours
y = amount paid in hours
y = 10x
The domain in this case is time from 0 to infinity {0, ∞)
The range is also {0, ∞)
there are no limitations to hep set the range and domain
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When Edna's phone is fully charged, it can operate for up to 18 hours before running out of battery. It has been 6 hours since Edna's phone was fully charged. Let x represent how many more hours Edna's phone can operate without running out of battery. Which inequality describes the problem? 6 + x < 18 6 +xs 18 Solve the inequality. Then, complete the sentence to describe the solution. Edna's phone can operate for up to more hours without running out of battery.
Edna's phone can operate for up to 12 more hours without running out of battery.
In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
fully charged
T = 18Hr
It has been 6 hours since Edna's phone was fully charged.
remaining battery =18- 6= 12Hr
x=12Hr
6 + x < 18
6 +x > 18
neither nor.
both equations are wrong.
6 +x = 18
Edna's phone can operate for up to 12 more hours without running out of battery.
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In δfgh, g = 64 cm, ∠f=131° and ∠g=47°. find the length of f, to the nearest centimeter.
The length of f = 66 centimeters
What is the sine rule for triangle?It is a law that express a relationship between side length of triangle and their opposite angles.
If ABC is triangle, then sine rule can be expressed as
BC/ sin A = AB /sin C = AC /sin B
How can we determine the length of f of the above triangle?Given, a triangle fgh where angle ∠ f = 131° and ∠g = 47°
also, side length, g = 64 cm
the remaining angle ∠ h = 180° - (131°+47°)
∠h = 2°
this is because angle sum of three angle for a triangle is 180 degrees.
what is the length of f?
we know that Δf g h has three side f g, g h and f h.
we denote the side f g = h, side g h = f and side f h = g
according to the sine rule for a triangle
h/ sin h = f /sin f = g /sin g
f/ sin f = g/ sin g
f / sin 131° = 64 / sin 47°
f = (64 × sin 131°) / sin 47°
f = 66 cm
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How do you find the sides of an acute triangle?
To find the missing side length of the acute angled triangle apply the cosine law as follow:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
As given in the question,
Given triangle is acute angled triangle.
Let us consider the measure of two sides and its included angle of the acute angled triangle is given.
Let the triangle be ABC,
Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.
Apply cosine law to find the measure of the missing side in the acute angled triangle:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.
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In right triangle ABC,b is the right angle and m2C -30°, If AC - 10, what is AB?
The value of AB after solving the triangle is 10√3.
Since angle C is the right angle in triangle ABC, we know that angle A = 90 - m2C = 90 - 30 = 60. And since triangle ABC is a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse, AB.
The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So in this case,
AB^2 = AC^2 + BC^2 = 10^2 + BC^2 = 100 + BC^2.We know that angle A is 60, so we can use the trigonometric function sine to find the value of BC/AB. We know that
sin(A) = BC/AB. So BC/AB = sin(60) = √3/2.We can then square both sides of this equation to get
(BC/AB)^2 = (√3/2)^2 = 3/4.Since we know that BC/AB = 3/4, we can substitute this value into the equation
AB^2 = 100 + BC^2 to get
AB^2 = 100 + (BC^2) = 100 + (3/4)AB^2.
Solving this equation for AB, we get AB = 10√3
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Find the length of the third side. If necessary, round to the nearest tenth
Answer:
6.3
Step-by-step explanation:
This is a right triangle, so in order to solve you can use the Pythagorean theorem; which is a² + b² = c² (The hypotenuse, or the longest side, equals C. A and B equal the legs, or the shorter sides.) So once you plug in the values, your equation should look like this:
3² + b² = 7²
Square each side, or in other words multiply it by itself.
9 + b² = 49
Subtract 9 from both sides.
b² = 40
Take the square root of 40 and your done!
b = 6.3
I hope this helped you! :)
Cheese pizza was preferred by 40 students pepperoni pizza was preferred by 28 based on the results how many of the 340 students can be expected to prefer cheese pizza?
The number of students expected to prefer cheese pizza from the 340 students is 200 stduents.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Cheese pizza = 40 students
Pepperoni pizza = 28
The ratio of cheese and Pepperoni pizzas.
= 40:28
= 10:7
Now,
Cheese pizza = 10x
Pepperoni pizza = 7x
The number of expected students who prefer cheese pizza.
= (10x)/(17x) x 340
= 10/17 x 340
= 10 x 20
= 200
Thus,
The number of expected students preferring cheese pizza is 200.
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