The given expression [tex]x^{2} +8x+15[/tex] , can be expressed in completely factored form as [tex](x+5)(x+3)[/tex] .
The expression that is to be written in factored form is [tex]x^{2} +8x+15[/tex] ;
we will use the split the middle term method to express it in factored form , in this method we split the middle term and then write down the common factors .
the middle term [tex]8x[/tex] can be written as [tex]3x+5x[/tex] ;
we get ; [tex]x^{2} +3x+5x+15[/tex] ;
taking "x" common from first 2 terms and "5" common from the next two terms ,
we get ;
⇒ [tex]x(x +3)+5(x+3)[/tex] ;
⇒ [tex](x +3)(x+5)[/tex] ;
So , we get that the expression [tex]x^{2} +8x+15[/tex] is equivalent to [tex](x +3)(x+5)[/tex] .
Therefore , the completely factored form is [tex](x +3)(x+5)[/tex] .
The given question is incomplete , the complete question is
What is the completely factored form of the expression [tex]x^{2} +8x+15[/tex] ?
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Which of the following is not a measure of variability of a data set?
a.
variance
b.
standard deviation
c.
median
d.
coefficient of variation
e.
Range
Median is not a measure of variability of a data set.
A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.
The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets can also be made up of a group of files or documents.
The information supplied in a public open data repository is measured in the open data discipline using data sets. Over one million data sets are collected through the European portal.
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Solve for the following proportion for u. U/9 =8/13 round your answer to the nearest tenth
Answer:
u ≈ 5.5
Step-by-step explanation:
[tex]\frac{u}{9}[/tex] = [tex]\frac{8}{13}[/tex] ( cross- multiply )
13u = 9 × 8 = 72 ( divide both sides by 13 )
u = 72 ÷ 13 ≈ 5.5 ( to the nearest tenth )
How do you solve for y varies inversely as x?
The relationship between y and x can be equation as y = k/x, where k is a constant that does not change.
The equation y varies inversely as x means that as the value of x increases, the value of y decreases, and vice versa. To solve for y, we can use the general equation y = k/x, where k is a constant. This equation states that the value of y is directly proportional to the reciprocal of x.
1. Start by understanding that when two variables are inversely proportional, they follow the equation
y = k/x.
2. The constant, k, is a number that will remain the same throughout the equation.
3. For example, if y varies inversely as x, and
y = 2 when x = 4, then k = 8.
4. Therefore, the equation
y = k/x becomes y = 8/x.
5. To solve for y when x = 5, substitute x = 5 into the equation and solve: y = 8/5
= 1.6.
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Look at the figure below. The area of the rectangle is 200 in².
What is the radius of the semicircle?
Answer:
r≈11 m or 1/2πr2 /=fraction
Step-by-step explanation:
too many fractions to put but yeah have fun with answer though i'm 1 hour late
The radius of the semicircle given in the given figure is 10in.
What is a semicircle?A semicircle is a half circle created by splitting a circle into two equal parts. It is created when a line pierces the circle's center and touches its two ends. The diameter of the circle is the name given to this line.
In the given figure, A semicircle is drawn on the base of the rectangle.
Since the Area of the rectangle is 200 inches square and the height of the rectangle is 10 inches.
Thus, the Base of the semicircle = 200/10 = 20in.
Since the Base of the rectangle is equal to the diameter of the semicircle that is 10.
Therefore, the semicircle's radius in the provided illustration is 10 inches.
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Complete question:
Need this solved! precal please help if you can Thx
Answer:
[tex]f(-1)=-11\\f(0)=16\\f(2)=22[/tex]
Step-by-step explanation:
[tex]\displaystyle f(-1)=3(-1)-8=-3-8=-11\\f(0)=3(0)+16=16\\f(2)=3(2)+16=6+16=22[/tex]
Let u=1nx and v=1ny. Write y^3x^5 in terms of u and v
The expression y³x⁵ in terms of u and v is [tex]e^{3u} e^{5v}[/tex]
what is the natural logarithm?The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x. The equation being [tex]e^{\ln x}=x[/tex]
Given here, the polynomial expression y³x⁵ where [tex]{\ln x}=u[/tex] and [tex]{\ln y}=v[/tex] thus, [tex]e^{v} =y[/tex] and [tex]e^{u} =x[/tex]
∴ , y³x⁵=[tex]e^{3u}e^{5v}[/tex]
Hence, The expression y³x⁵ in terms of u and v is [tex]e^{3u} e^{5v}[/tex]
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Why is it called secant line?
Secant line is the name given to any line that intersects a circle at two or more points. This line is called "secant" because it comes from the Latin word secare, which means to cut.
In mathematics, the secant line is used as a tool for finding the length of an arc, area of a sector, and other geometric measurements. The secant line is also used in calculus to calculate derivatives and integrals of functions.
The secant line is formed by two points on a circle’s circumference, and its slope is determined by those points. Its slope is calculated by the difference between the two points divided by the product of the radius of the circle and the angle made by the two points.
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Find the least common multiple of the given numbers. 5 and 8
Based on data collected by the National Center for Health Statistics and made available to the public, an estimate of the percentage of adults who at some point in their life have been told they have hypertension is 23.53%. If we select a simple random sample of 20 US adults and assume that the probability that each has been told that he or she has hypertension is 0.20, find the probability that the number of people in the sample who have been told that they have hypertension will be (a) exactly three (b) at least three (c) at most five (d) between six and ten, inclusive
The answer is (a) exactly three. The probability of selecting exactly three adults out of a sample of 20 who have been told that they have hypertension is calculated using the Binomial Distribution. The probability can be calculated using the formula:
P(X=3) = (20C3) * (0.20^3) * (0.80^17) = 0.1504The probability of selecting at least three adults out of a sample of 20 who have been told that they have hypertension is calculated using the Cumulative Binomial Distribution. The probability can be calculated using the formula:
P(X>=3) = 1 - P(X<3) = 1 - P(X<=2) = 1 - (20C0) * (0.20^0) * (0.80^20) - (20C1) * (0.20^1) * (0.80^19) - (20C2) * (0.20^2) * (0.80^18) = 0.9991The probability of selecting at most five adults out of a sample of 20 who have been told that they have hypertension is calculated using the formula:
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A bag contains 222 red marbles, 333 green marbles, and 444 blue marbles. If we choose a marble, then another marble without putting the first one back in the bag, what is the probability that the first marble will be green and the second will be red?
There is a 7.4% probability that the first marble will be green and the second will be red.
To calculate the probability, you will need to use the following formula:
P(A and B) = P(A) x P(B).
In this case, P(A) is the probability of picking a green marble on the first pick and P(B) is the probability of picking a red marble on the second pick. Using this formula,
we get P(A and B) = 333/999 x 222/998 = 0.074,
which is the probability of picking a green marble on the first pick and a red marble on the second pick.
So, there is a 7.4% chance of this happening.
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Jessica is trying to get a credit card. she has a credit score of 790. how is jessica’s lender likely to view this credit score?
The lender of Jessica viewed her credit score of 790 that shows lower risk and reimbursement of outstanding balances on time.
A credit card is an electronic card that enables someone to buy items in an emergency when they don't have enough cash to pay for them. This is a specific type of bank loan that must be returned with interest in the future.
The range of numbers that make up a credit score indicate how creditworthy a credit card holder is. This aids in understanding the risk and timing of credit card bill payments. The ideal credit score range is between 300 and 850, with many alternative ranges.
According to the circumstances, Jessica's credit score is 790, which is within the range of 740 to 799, which is considered to be an excellent credit score. This demonstrates that she pays the due balances on time and that there was less of a chance that she would default on the payments.
Any credit card can help you build good credit if you consistently use only a small portion of your available credit and make on-time payments.2 But some cards are designed to help you build credit.
Secured credit cards are secured by cash: You make a security deposit to the bank ($200 is usually the minimum) and get a credit card with a limit equal to that deposit. You then use the card and make payments toward your balance to show that you are a responsible borrower.
Thus, the lender of Jessica viewed her credit score of 790 that shows lower risk and reimbursement of outstanding balances on time.
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Answer:
✔️A) Jessica is low risk and will pay her outstanding balances on time.
Step-by-step explanation:
How many solutions exist for the given equation 12x 1 3 4x 1 2?
There are existing infinite solutions for the given equation 12s + 1 = 3 ( 4s + 1) - 2.
Solving the equation,
12s + 1 = 3 ( 4s + 1) - 2
12s + 1 = 12s + 3 -2
12s + 1 equals to (=) 12s + 1
Bringing constant to one side of the equation and variables to the other side of the equation so that equation could be solved
+ 12s - 12s = + 1 - 1
0 = 0
This shows that the given equation has infinite solutions because after solving it gives a solution where both sides are equal.
"
Complete question:
How many solutions exist for the given equation 2s + 1 = 3 ( 4s + 1) - 2?
"
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The probability that both of two tossed coins will come down heads (or tails) is: 1/4 x 1/2 or 1/8 1/2 x 1/2 or 1/4 1/4 x 1/4 or 1/16.
Answer:
B
Step-by-step explanation:
The probability that both the two tossed coins will come down heads (or tails) is 1/2 x 1/2 or 1/4.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
To calculate the probability of two independent events happening at the same time, you multiply their individual probabilities.
In this case, the two events are the two coin tosses coming up heads (or tails).
The probability of the first coin coming up heads (or tails) is 1/2, and the probability of the second coin coming up heads (or tails) is also 1/2, so the probability of both of them coming up heads (or tails) is (1/2) x (1/2) = 1/4.
Hence, the correct answer would be an option (B).
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kyle practices the piano trombone and violin. he dedicates one fourth of this practice time to piano, four ninths of his time to the trombone, and rest of his time to the violin. what fraction of kyle's practice time is spent playing the violin?
Answer:
Step-by-step explanation:
1/4 + 4/9 + n= total amount of time spent on all of the instruments.
1/4 + 4/9=
9/36 + 16/36= 25/36 (time on piano and trombone)
36/36- 25/36= 11/36- total time spent on violin
Please help as fast as you can
I think the answer is D (Day) ...........
Help aspp please thank you!!!
Answer:
YES ITS A DIRECT VARIATION
Step-by-step explanation:
explanation in the picture
How do you find the slope of a tangent line using a secant line?
To find the slope of a tangent line using a secant line, you can use the following formula:
Slope of tangent line = (y2 - y1)/(x2 - x1)where (x1, y1) and (x2, y2) are points on the secant line.
This formula works because the slope of a line is simply the change in y (the "rise") divided by the change in x (the "run"). When you use two points on a secant line to approximate the slope of the tangent line, the change in y (y2 - y1) represents the rise, and the change in x (x2 - x1) represents the run.
By taking the limit of this formula as x2 approaches x1, we can find the slope of the tangent line at the point where x = x1. This is known as the limit definition of the derivative.
For example, suppose we have a function f(x) and we want to find the slope of the tangent line at x = a. We can take two points on the secant line that pass through (a, f(a)) and (a + h, f(a + h)), where h is a small positive number. The slope of the secant line through these two points is (f(a + h) - f(a))/(a + h - a) = (f(a + h) - f(a))/h. As h approaches 0, this expression approaches the slope of the tangent line at x = a.
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Points A,B, and C are collinear Point B is between A and C. Solve for x
The required values of x in the collinear points A, B and C are -3, 1, -12 and 12
What are collinear points?Points that lie on the same line are called collinear points.
Given that, Points A, B, and C are collinear point B is between A and C.
We will use here segment addition postulate, to solve each part.
The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC.
1) AB = x+15, BC = x+13 and AC = 22
x+15+x+13 = 22
2x = 22-28
2x = -6
x = -3
2) BC = 2x-2, AC = 3x-3 and AB = 4
3x-3-(2x-2) = 4
3x-3-2x+2 = 4
5x = 5
x = 1
3) BC = x+28, AB = 2x+28 and AC = 12
x+20+2x+28 = 12
3x+48 = 12
3x = -36
x = -12
4) BC = x-8, AB = 9 and AC = 2x-11
x-8+9 = 2x-11
x+1 = 2x-11
x = 12
Hence, the values of x are -3, 1, -12 and 12
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solve 0 =3 x + 4 - x
Answer:
x = -2
Step-by-step explanation:
Combine like terms
0 = 2x + 4
-4 = 2x
-2 = x
Order the rational numbers from least to greatest
-3.11,-3.1,-3.01
Answer: -3.11, -3.1, -3.01
Explanation:
We are comparing:
-3.11
-3.10
-3.01
-3.11 < -3.10 < -3.01
what is the slope -intercept equation of a line that has a slope of 3 and passes through (0,-4)
Considering the definition of a line, the equation of the line that passes through the point (0, -4) and has a slope of is y=3x -4.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and always coincides with the value of y corresponding to the value of x= 0.Line in this caseIn this case, you know:
The line has a slope of 3.The line passes through the point (0, -4).Substituting the value of the slope and the value of the point, the value of the ordinate to the origin b can be obtained:
-4= 3×0 + b
-4= 0 + b
-4= b
-4= b
Finally, the equation of the line is y= 3x -4.
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A line passes through the point (-4, 3) and has a slope of -2.
Write an equation in point-slope form for this line.
Answer:
i agree
Step-by-step explanation:
A line passes through the point (-4, 3) and has a slope of -2 will be y = - 2x - 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is - 2. Then the equation of the line is given as,
y = - 2x + c
The equation passes through the point (-4, 3). Then the value of 'c' is given as,
3 = - 2(-4) + c
3 = 8 + c
c = - 5
The equation of the line is given as,
y = - 2x - 5
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Solve for m.
m+ < 1/4 < -1 2/5
O
0 m < -1 13/20
Om < -1 3/20
0 m > -1 3/20
O m > -1 13/20
The solution of the inequality m + 1/4 < -[tex]1\frac{2}{5}[/tex] is m < [tex]-1\frac {13}{20}[/tex].
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
We have the inequality expression,
m + 1/4 < -[tex]1\frac{2}{5}[/tex]
Simplifying,
m + 1/4 < -7/5
Subtracting 1/4,
m < -7/5 - 1/4
m < (-28-5)/20
m < -33/20
m < [tex]-1\frac {13}{20}[/tex]
Therefore, the solution is m < [tex]-1\frac {13}{20}[/tex].
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Evaluate the expression if b=3 and c=1/3.
3c / (2b²)
After evaluation we get the above expression 1/18
What is mathematical expression?It is the mathematical statement that expresses the method of a mathematical operation in a symbolic way. An expression is developed based on two or more terms along with operator. The terms are variables and numbers. In a word, an expression is either combination of numbers, operators or numbers, variables, operators.
How to evaluate the above expression?we are given an expression
3c/ (2b²)
the value of b and c are also given, b= 3 and c = 1/3
The expression is written in fractional form that has 2 numbers and 2 variables. The number are 2 and 3, variables are c and b
The numerator 3c and the denominator 2b²
if we put the value of b and c
(3×1/3) / (2×9) =1/18
hence the result 1/18
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On Monday, jack rode 4 miles on a bike. On Tuesday, he rode 4 times more than he did Monday. On Wednesday, he rode an additional 5 miles.
How many miles has jack ridden so far this week?
Answer:
She has ridden 25 miles this week
Step-by-step explanation:
She rode 4 miles on monday to start off the week. Then she rode 4 times the amount he did on Monday, so multiply 4x4. Then he rode 5 more miles so add 5 and receive the answer of 25 miles.
Equation:
1. Write Equation: 4+(4x4)+5=
2. Solve for parenthesis: 4+16+5=
3. Solve: 4+16+5=25
-Hope this helped & Happy New Years
A rectangle has a length of 6cm and a breadth of 2m what is the height?
The height of the rectangle is 200 cm.
How to find the height of a rectangle?A rectangle is a quadrilateral that has two pairs of opposite sides equal to each other and two pairs of opposite sides parallel to each other.
The sum of angles in a rectangle is 360 degrees. Each interior angle is equal to 90 degrees .
The diagonals are also equal and they bisect each other.
The rectangle has a length of 6cm and a breadth of 2m.
Therefore, the height of the rectangle is the breadth of the rectangle.
The height of the rectangle is 2 meters and the length of the rectangle is 6 cm. Let's convert the height of the rectangle to centimetres.
Hence,
height of the rectangle = 2m
1 m = 100cm
2m = ?
cross multiply
height of the rectangle = 2 × 100
height of the rectangle = 200 cm
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Ms. Mayer's class has 8 students who are 5 feet or taller. That is 25% of the total number of students in her class. What is the total number of students in Ms. Mayer's class?
The total number of children in Ms. Mayer's class is 32.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:
Percentage = (value / total value) * 100%
Let Total number of student = X
Therefore;
25% of X = 8
(25/100)X = 8
Therefore;
X = 8 / (25/100)
X = 800/25
X = 32
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the area of a rectangular pool is 7980m^2. if the width if the pool is 84m what is its length?
Answer:
95 m would be the answer.
THIS IS THE 3.1.4 JOURNAL PROVING THE PYTHAGOREAN THEOREM ASSIGNMENT FULL ASSIGNMENT ANSWERS!!!
Determine if the TV will fit in the car.
a. Draw the rectangle that represents the height and width of the trunk including the diagonal. Label the dimensions on your sketch.
Answer:
Step-by-step explanation:
The dimensions of the rectangle are:
Height = 40 cm
Width = 30 cm
Diagonal = 50 cm
The sketch is given below.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
A rectangle with a height of 40 cm and a width of 30 cm is drawn.
Now,
The diagonal of the rectangle can be calculated using the Pythagorean theorem.
So,
Diagonal side = x
x² = 30² + 40²
x² = 900 + 1600
x² = 2500
x = 50 cm
Thus,
Rectangle:
Height = 40 cm
Width = 30 cm
Diagonal = 50 cm
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Find the algebraic representation of the reflection below.
The algebraic representation of the reflection in the image is the one in option A.
(x, y) → (-x, y)
What is the algebraic representation of the reflection?Here we have an image with two moons, such that one is the reflection of the other.
Notice that the reflection is across the vertical axis (it is the y-axis). So the y-values don't change after the reflection, only the x-values change.
So we will have a change of sign on the x-value, then the reflection must be written as:
(x, y) → (-x, y)
In this way we can conclude that the correct option is A.
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