Expansion of (x + 3) (x + 5) [tex]=x^{2} +8x+15[/tex]
How is the expansion done?
Applying the Product of binomials rule,
(x+a) (x+b) = [tex]x^{2} +(a + b)x +ab[/tex]
Here, in the given expression:
a = 3 and b = 5
[tex](x + 3) (x + 5) =x^{2} +(3 + 5)x +15\\\\ =x^{2} +8x+15[/tex]
What is the product of binomials rule?
The FOIL (First Outer Inner Last)method is being applied to multiply binomials quickly. It is the arrangement of multiplying terms in a two-binomial product.The expression for the product of the sum and difference of two binomials is (x + y) (x- y) Assume that each binomial is a difference rather than a sum the the resultant expression is in (x- y) (x -y).To learn more about product of binomials, refer:
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6) Ray is in debt $32 right now. He used to owe more, but he has been paying $6 a month on his debt for the last five months.
a) How much was Ray in debt 5 months ago?
b) At his present rate, how much longer will it take Ray to pay off his debt? Explain your reasoning.
Answer:
a)62
b)6 months
Step-by-step explanation:
a) if he pays $6 every month then you would times $6 by 5 to find out how much he paid off which is 30 so you would add that to the current amount therefore $30+$32=$62
b) You would do $32 divided by 6 to find out how much hit would take to pay off which is 5 but there is 2 remaining so he can pay that off the next month, so it takes 6 months
The line y-5=9/7(x+4) is graphed in the coordinate plane. Complete the sentence below describing this process
By inspecting the equation, the graph of the line has a slope of what?
Answer:
the slope Is 9/7........
how do you solve 94 divided by 33 because when I tried solving it, it didn't make sense.
it's 2.84
step by step:
Start by setting it up with the divisor 33 on the left side and the dividend 94 on the right side.
The divisor 33 goes into the first digit of the dividend 9, 0 time(s). Therefore, put 0 on top.
Multiply the divisor by the result in the previous step (33 x 0 = 0) and write that answer below the dividend.
Subtract the result in the previous step from the first digit of the dividend (9 - 0 = 9) and write the answer below.
Move down the 2nd digit of the dividend 4
The divisor 33 goes into the bottom number 94, 2 time(s). Therefore, put 2 on top.
Multiply the divisor by the result in the previous step (33 x 2 = 66) and write that answer at the bottom.
Subtract the result in the previous step from the number written above it. (94 - 66 = 28) and write the answer at the bottom.
it's a repeating decimal so make sure to add a line on top of the last to digits to represent that it is repeating.
The Hobby Center has 3,590 seats. On Monday,
25
5
of the seats were sold. On Tuesday
2
3
of the remaining seats were sold. How many seats are left?
3312 seats were left at The Hobby Center which has 3,590 seats.
What is subtraction?Subtracting from a group or a number of objects in math indicates taking something away. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. In mathematics, subtraction involves removing anything from a group or a number of objects. What is left in the group gets smaller when you subtract. The following is an illustration of a subtraction issue: 5 - 3 = 2
Given Data
The Hobby Center has 3,590 seats. On Monday, 255 of the seats were sold. On Tuesday 23 of the remaining seats were sold.
Total = 3590
On Monday = 255
On Tuesday = 23
Remaining seats = Total - seats sold
Remaining seats = 3590 - 255 - 23
Remaining seats = 3312
3312 seats were left at The Hobby Center which has 3,590 seats.
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Hello, I need some assistance with this homework question please for precalculusHW Q41
Two consecutive whole numbers are n-1 and n
a) Simplify n-(n-1)
b) Multiply out n(n-1)
c) Simplify (n-1) + n
d) The two numbers are added.
The answer is
A always even B always odd C sometimes even, sometimes odd
a. n-(n - 1) = 1
b. n( n - 1) = n² - n
c. (n - 1) + n = 2n - 1
d. (n - 1) + n = 2n - 1
Solution:
General Rule for Equation Solving
Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.Given two consecutive numbers , (n - 1) , n
simplifying :
n - (n - 1)
= n -1(n - 1)
= n - n + 1
= 1
multiplying :
n( n -1)
= n² - n
simplifying :
(n-1) + n
= n - 1 + n
= 2n -1
by adding two numbers :
(n - 1) + n
= n -1 + n
= 2n - 1
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The following table gives the number of people on the Titanic by class and whether or not they survived.
Class Survived Died Total
First class 202 123 325
Second class 118. 167. 285
Third class 178. 528. 706
Crew class 215 698 913
Total 713 1516 2229
Which of the following interpretations are correct?
(A). If a person survived, it is more likely that the person was in the crew than any other individual class.
(b). Given that a person was in the crew, it was more likely that the person died than survived.
(c). If a person died, it is likely that the person was in the third class or crew.
Answer:
(A) correct
(B) correct
(C) correct
Step-by-step explanation:
(A) is correct
Total survived = 713
Out of the 713 passengers who survived, the number of crew members = 215, the highest. The ratio of 215/713 is higher than any other ratio. This means 30% of those who survived were crew members. The next higher group of survivors was First Class passengers with a survival rate of 202/713 ≈ 28%
(B) is correct
There were 913 crew members. Out of this, 698 died 215 survived.
So it is more likely that given a person was a crew member, the person died than survived. That comprises 698/913 or 76% of crew members who died with only 24% survival rate
(C) is correct
There were 1516 passengers who died
Out of these, 528 + 698 = 1,226 were either third class or crew members and comprised 1226/1516 or approximately 81 percent of people who died
what is (-3) (-2) +98
Answer:
104
Step-by-step explanation:
(-3) (-2) +98
= 6 + 98
= 104
heeeeeelpppp meehh pl.s
Answer:
1) d times c = n
2) 2A - a =b
3) F times R2 divided by m2G = m
Step-by-step explanation:
if you know what maps are they are like a guide so the map to your first answer would be times c on both sides of the = sign
your second map would be times 2 on both sides of the = sign then to also subtract a on both sides
a/12 = 30.1/12 i am trying to find a if someone could help me please. :)
The value of a is 30.1
Divide Fraction Definition
The denominators of fractions must match in order to divide them. The numerators' quotient will be the quotient.
The phrase provided is,
a/12 = 30.1/12
We can directly cut the values if the denominator is the same. Since there is a 12 in the denominator on both the right and left sides in this case, remove 12 from both sides.
Thus, a = 30.1
Likewise, you can act in such manner,
a = (30.1 * 12) / 12
a = 30.1
Here, we take the right side of the left side denominator 12 and cancel 12.
Hence, A has a value of 30.1
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If ST = 65, TR= 40, and WU = 16, find the length of VW. Round your
answer to the nearest tenth if necessary.
Answer:
162.5
Step-by-step explanation:
You can set up a proportion
[tex]\frac{vw}{st}[/tex] = [tex]\frac{tr}{wu}[/tex] plug in the numbers that you know and solve for vw
[tex]\frac{vw}{65}[/tex] = [tex]\frac{40}{16}[/tex]
I would simply [tex]\frac{40}{16}[/tex] by dividing the numerator (top) and the denominator (bottom) by 8 to get [tex]\frac{5}{2}[/tex] which would be easier to work with
[tex]\frac{vw}{65}[/tex] = [tex]\frac{5}{2}[/tex] Cross multiply
2vw = 5(65)
2vw = 325 Divide both sides by 2
vw = 162.5
which shows the opposite -1.2
the opposite of -1.2 is 1.2
I AM GROUNDED AND NEED A BETTER GRADE PLEASE AND THANK YOU IN ADVANCE
Answer:
y=90, x=56
Step-by-step explanation:
y has a 90 degree indicator, sum theory solves x
Answer:
x = 56
y = 90
Step-by-step explanation:
34 + 90 + x = 180
124 + x = 180
x = 56
y = 90
Find the coordinate of the image of B (4, 0) after a reflection over the y-axis.
We need to know reflection of point about axes to solve the problem. The image of B (4,0) after reflection about y-axis is (-4,0).
Reflection about an axis means finding the point on the graph that is at an equal distance from the axis on the opposite side of the reflecting surface. The reflection can be about an axis or a line or origin. When a point is reflected about the x-axis, the sign of the y-coordinate of the point changes, when a point is reflected about y-axis the sign of the x-coordinate of the point changes and when a point reflects about the origin, the sign of both the coordinates change. Here in the question we need to find the reflection of point B (4,0) about y-axis, the image of point B will be (-4,0).
Therefore the image of point B(4,0) when reflected about y-axis is (-4,0).
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What principal will bring Birr 637 interest at a rate of 7% in 2 years?
The principal with the given simple interest, rate of interest and time period is $4550.
Given that, interest = $637, rate of interest = 7% and time period = 2 years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
We know that, simple interest = (P×R×T)/100
Put simple interest = $637, R=7% and T=2 years, we get
637 = (P × 7 × 2)/100
⇒ 14P=63700
⇒ P=63700/14
⇒ P= $4550
Therefore, the principal with the given simple interest, rate of interest and time period is $4550.
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please help me 15 points for helping
a. The rate of change in length of baby grace is 0.75.
b. The linear equation for Baby Grace growth rate in point slope form is y - 20 = 0.75(x - 4)
a. The slope of the line for baby Claire growth is 0.8.
b. Baby girl Claire growth rate is faster than baby girl Grace growth rate.
How to form linear equation and find slope?Let's solve for the growth chart of baby grace.
Therefore,
a.
The rate of change in length of baby Grace can be found as follows:
rate of change = y₂ - y₁ / x₂ - x₁
Hence, using (4, 20)(6, 21.5)
rate of change = 21.5 - 20 / 6 - 4
rate of change = 1.5 / 2
rate of change = 0.75
b . The linear equation in point slope form can be found as follows;
y - y₁ = m (x - x₁)
where
m = slopeTherefore,
y - 20 = 0.75(x - 4)
Let's tackle the growth chart for baby Claire,
a.
slope of the line = y₂ - y₁ / x₂ - x₁
Using (4, 22)(14, 30)
slope of the line = 30 - 22 / 14 - 4
slope of the line = 8 / 10
slope of the line = 4 / 5 = 0.8
b.
Therefore, Baby Claire growth rate is faster than baby Grace.
This is because bay Claire growth rate is 0.8 and baby Grace is 0.75.
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I need help with this
Step-by-step explanation:
71.5
....................
Question 4 of 6, Step 4 of 49/14CorrectConsider the following data representing the price of plasma televisions (in dollars).1387, 1135, 1352, 1220, 1202, 1217, 1176, 1268, 1150, 1182, 1222, 1391, 1163, 1168, 1282, 1250, 1201, 1225, 1403, 1175, 1371Copy DataPricePlasma Televisions (in Dollars)ClassFrequencyRelative FrequencyCumulative Frequency1077-11361137-11961197-12561257-13161317-13761377-1436Step 4 of 4: Compute the cumulative frequency of the fourth class.AnswerTablesKeypad
There are 21 televisions.
Class 1077-1136:
The frequency is how many of them cost in this range.
There is 1.
So frequency: 1
Relative frequency is 1/21 = 0.0476
Cumulative frequency is the previous cumulative plus the relative:
Previous cumulative: 0
Relative: 0.0476
Cumulative = 0 + 0.0476 = 0.0476
Class 1137-1196:
6 in this interval.
Frequency: 6
Relative frequency: 6/21 = 0.2857
Previous cumulative: 0.0476
Relative: 0.2857
Cumulative = 0.0476 + 0.2857 = 0.3333
Class 1197-1256:
7 in this interval.
Frequency: 7
Relative frequency: 7/21 = 0.3333
Previous cumulative: 0.3333
Relative: 0.3333
Cumulative: 0.3333 + 0.3333 = 0.6666
Class 1257-1316:
2 in this interval.
Frequency: 2
Relative frequency: 2/21 = 0.0952
Previous cumulative: 0.6666
Relative: 0.0952
Cumulative: 0.6666 + 0.0952 = 0.7618
Class 1317-1376:
2 in this interval.
Frequency: 2
Relative frequency: 2/21 = 0.0952
Previous cumulative: 0.7618
Relative: 0.0952
Cumulative: 0.7618 + 0.0952 = 0.857
Class 1377-1436:
3 in this interval.
Frequency: 3
Relative frequency: 0.143
Previous cumulative: 0.857
Relative: 0.143
Cumulative: 0.857+0.143 = 1
Gustavo applied the distributive property to the expression 9(w+5) . He then used the commutative property.
Drag and drop expressions to the boxes to correctly complete the statements.
The values of the expression after each property are as follows:
Distributive property: 9w + 45.Commutative property: 45 + 9w.Distributive propertyFor the distributive property, the outer term multiplies each of the inner terms of the expression.
In this problem, the expression is:
9(w + 5).
After the distributive property, the expression is represented as follows:
9 x w + 9 x 5 = 9w + 45.
(the outer term 9 multiplies each of the inner terms, of w and 5, and then they are added, due to the plus sign).
Commutative propertyThe commutative property of addition states that the order of the terms of the addition is not important, hence:
9w + 45 = 45 + 9w.
(the two terms just exchanged places).
Missing informationThe problems asks for the algebraic expression after each property is applied.
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a 57-inch pipe is cut into two pieces. One piece is two times the length of the other. Find the length of the shorter piece
It is divided into two sections, a 57-inch piece. The length of one component is double that of the other. The length of the shortest piece wound be 29.
Given that,
It is divided into two sections, a 57-inch pipe. The length of one component is double that of the other.
We have to calculate the shorter piece's length.
Let us take the length of shortest piece as x
The length of longest piece wound be 2x
We can write as,
x+2x=57
3x=57
x=57/3
x=29
The length of largest piece will be 2×29=58
Therefore, The length of the shortest piece wound be 29.
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The angle of the rook on Kaya's dollhouse is 56 degrees. She built a scale model of the dollhouse with a scale ratio of 1:4. What is the measure of the angle of the roof of the model?
The measure of the angle of the roof of the model is 56 degrees.
Given:
The angle of the rook on Kaya's dollhouse is 56 degrees. She built a scale model of the dollhouse with a scale ratio of 1:4.
From the statements given:
That a dilation is being performed that is the original figure is similar to the scale mode she made.
When two figures are similar then the angle of the two figures are same.
This means angle of the rook on Kaya's dollhouse and the built a scale model of the dollhouse with a scale ratio of 1:4 is same.
Therefore the measure of the angle of the roof of the model is 56 degrees.
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PLEASE ANSWER OFFERING 50 POINTS.
lines a and b are parallel and are cut by transversal t to for interior angles 7, 8, 9, and 10. 7 and 8 are consecutive interior angles, and m7 = 94 degrees. 8 and 10 are alternate interior angles. FInd the measure of each angle.
1. angle 10
2. angle 9
3. angle 8
There are two lines a and b, Which are parallel lines and a line that cut the parallel lines a and b is transversal t.
1. Angle 8 is 86°
2. Angle 9 is 94° and
3. Angle 10 is 86°.
Given that,
There are two lines a and b, Which are parallel lines and a line that cut the parallel lines a and b is transversal t.
The interior angles are 7,8,9 and 10.
The angle 7 and 8 are consecutive angles and angle 7= 94°.
The angle 8 and 10 are alternative angles.
We have to find the angles 8,9 and 10.
We take,
The angle 7 and 8 are consecutive angles and angle 7= 94°.
Consecutive angles condition is Sum of the pair of consecutive angles is equal to 180°.
Now,
∠7+∠8=180°
94°+∠8=180°
∠8=180°-94°
∠8=86°
We got angle 8 as 86°.
Now, we take
The angle 8 and 10 are alternative angles.
Alternative angles condition is The pair of alternative angles are always equal if the two lines are parallel lines.
Now,
∠8=∠10
86°=∠10
∠10=86°
We got angle 10 as 86°.
Then we can say that the angle 7 and 9 are alternative angles.
Then,
∠7=∠9
94°=∠9
∠9=94°
We got angle 9 as 94°.
Therefore, The angle 7 is 94°, ∠8 is 86°, ∠9 is 94° and ∠10 is 86°.
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If one card is drawn from a deck, find the probability of getting these results.Enter your answers as fractions or as decimals rounded to 3 decimal places.(a) A black 4P (black 4) =
A deck has a total of 52 cards.
The probability of getting a black 4 is then:
[tex]\begin{gathered} P(\text{black 4)= }\frac{1}{52} \\ P(\text{black 4)= }0.019 \end{gathered}[/tex]Customers of a beauty salon were surveyed to see which type of service they had during their visit (hair, nails, or skin) and their age (18 years or younger or over 18 years old). The results of the survey were displayed in a joint relative frequency table.
Which of the following describes this data set?
Numerical and univariate
Numerical and bivariate
Categorical and univariate
Categorical and bivariate
The characteristics that describe the following data-set are given as follows:
Categorical and bivariate.
How to classify the variables?First, we classify the variable as either numerical or categorical, as follows:
Categorical variable: The possible values assumed by the variable are labels, such as yes/no, good/bad, hairs, nails, and so on...Numerical variable: The values assumed by the variable are numbers.In the context of this problem, the variables are as follows:
Type of service: Hairs, nails or skin, the three of which are labels.Age: 18 years or younger, or over 18 years old, hence assuming a yes/no format.Thus the variable is categorical.
Additionally, there are two variables in this problem, the ones stated above, the type of service and the age, hence the data set is classified as bivariate.
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What is the slope-intercept equation for this line?
Enter the correct
symbol, + or -
y =[]
Substitute the length of the sides (8in, 15 in, z) into the Pythagorean Theorem. Then, find the length of the missing side z.
The length of the sides (8in, 15 in, z) into the Pythagorean Theorem. Then, find the length of the missing side z.
z = 17
This is further explained below.
What is Pythagorean Theorem.?Generally, In the field of mathematics, the Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic connection in Euclidean geometry among three sides of a right triangle.
Pythagoras is credited with developing this theorem. It indicates that the total of the areas of the squares on the other two sides is equal to the area of the square whose side is the hypotenuse.
This signifies that the size of the square whose side is the hypotenuse is equal to that amount.
In conclusion,
a² + b² = c²
8² + 15² = z²
64 + 225 = 289
z² = 289
z = 17
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For f(x) = 2x + 1 and g(x) = x2 – 7, find (f + g)(x).
x^2 + 2x + 8
2x ^2– 15
2x^3 – 6
x^2 + 2x – 6
Answer:
x^2 + 2x - 6.
Step-by-step explanation:
(f + g)x
= f(x) + g(x)
= 2x + 1 + x^2 - 7
= x^2 + 2x - 6.
What is the product?
Enter your answer as
a fraction, in simplified form, in the box.
-1/4 . (-6/11)
The most appropriate choice for r=fraction is [tex]\frac{3}{22}[/tex].
What is fraction?Suppose there is a collection of objects and a part of the collection are taken. Fraction represents that part of the object which are taken. In other words it can be said that fraction represents part of a whole collection of objects.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator of the fraction
Here,
Product of [tex]-\frac{1}{4}[/tex] and [tex]-\frac{6}{11}[/tex] =
[tex]-\frac{1}{4} \times -\frac{6}{11}\\= \frac{3}{22}[/tex]
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Given the equation negative 24 equals y over 8, solve for y.
−192
−3
3
192
Answer:
Y= -192
Step-by-step explanation:
-24X8= -192
I hope this helps! If you don't mind could you please mark me brainliest?
need help asap!!!!!
Using the quadratic formula, the values in the form a + bi is 1 + 4i.
What do we mean by quadratic formula?The quadratic formula is a formula used to solve quadratic equations in elementary algebra. There are alternatives to using the quadratic formula to solve quadratic equations, including factoring, completing the square, graphing, and others.Quadratic formula: [tex]D = \frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]So, represent in the form a + bi:
Given equation: [tex]\frac{4+\sqrt{16 - (4)(5)} }{2}[/tex]
From the equation, we can assume that the value of b is 4 and the value a must be 1.When the value of a will be 1, then only the denominator can be 2 as 2(1) = 2.Hence, 1 + 4i.
Therefore, using the quadratic formula, the values in the form a + bi is 1 + 4i.
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