The expression is simplified to x - 147
What are algebraic expressions?Algebraic expressions are defined expressions made up of terms, factors, variables, constants , coefficients.
They are also made up of arithmetic operations such as addition, subtraction, multiplication, division, etc.
Given the expressions;
−3 (5x + 1) + 16(x − 9)
First, we have to expand the bracket
-15x -3 + 16x - 144
collect like terms, we have;
-15x + 16x - 144 - 3
Add or subtract like terms as seen in the expression
x - 147
Note that the expression is simplified to x - 147
Thus, the expression is simplified to x - 147
Learn more about algebraic expression here:
https://brainly.com/question/4344214
#SPJ1
If α =i+j−2k, β =−i+2j+3k andγ =5i+8k, then find c and d such that γ−cα−dβ is perpendicular to both α and β
If [tex]\hat\gamma-c\hat\alpha-d\hat\beta[/tex] is perpendicular to both [tex]\hat\alpha[/tex] and [tex]\hat\beta[/tex], then their dot products are zero.
Recall that for any vector [tex]\hat x[/tex], [tex]\hat x\cdot \hat x = \|\hat x\|^2[/tex].
Now, we have
[tex](\hat\gamma - c\hat\alpha - d\hat\beta) \cdot \hat\alpha = (\hat\gamma\cdot\hat\alpha) - c\|\hat\alpha\|^2 - d (\hat\beta\cdot\hat\alpha) = 0[/tex]
[tex]\hat\gamma\cdot\hat\alpha = 5 + 0 - 16 = -11[/tex]
[tex]\|\hat\alpha\|^2 = 1^2 + 1^2 + (-2)^2 = 6[/tex]
[tex]\hat\beta\cdot\hat\alpha = -1 + 2 - 6 = -5[/tex]
[tex]\implies 6c - 5d = -11[/tex]
and
[tex](\hat\gamma - c\hat\alpha - d\hat\beta) \cdot \hat\beta = (\hat\gamma\cdot\hat\beta) - c(\hat\alpha\cdot\hat\beta) - d \|\hat\beta\|^2 = 0[/tex]
[tex]\hat\gamma\cdot\hat\beta = -5 + 0 + 24 = 19[/tex]
[tex]\|\hat\beta\|^2 = (-1)^2 + 2^2 + 3^2 = 14[/tex]
[tex]\implies 5c - 14d = -19[/tex]
Solve for [tex]c[/tex] and [tex]d[/tex]. By elimination,
[tex]5(6c - 5d) - 6(5c - 14d) = 5(-11) - 6(-19)[/tex]
[tex]-25d + 84d = -55 + 104[/tex]
[tex]59d = 59[/tex]
[tex]\boxed{d=1}[/tex]
[tex]6c-5 = -11[/tex]
[tex]6c=-6[/tex]
[tex]\boxed{c=-1}[/tex]
What company has the absolute advantage when it comes to producing computers?
a. The G company Inc
b. Gonzalez and Bros. Inc
c. they both do
d. neither
Answer:
D neither
Step-by-step explanation:
Because they both don't have big numbers so the are unequal
Approximate -16+√40 to the nearest tenth.
A:9.7
B:6.3
C:-6.3
D:-9.7
Answer:
D. -9.7
Step-by-step explanation:
the square root of 40 is 6.32
-16 + 6.32 = -9.68
-9.68 rounded the nearest tenth is -9.7
Planes A and B intersect.
Which describes the intersection of line m and line n?
point W
point X
point Y
point Z
Answer:
Point W.
Step-by-step explanation:
Line [tex]n[/tex] is on plane [tex]A[/tex]. Line [tex]m[/tex], however, is not on any plane shown, but intersects plane [tex]A[/tex] and line [tex]n[/tex].
How do I solve this problem?
The algebraic solution for the variable x is as follows:
x = 9 / 2. How to find the variable x in the equation?The equation is represented as follows;
2 / 5 (2 - x) = - 1 / 3 x + 1 / 2
open the bracket on the left side
2 / 5 (2 - x) = - 1 / 3 x + 1 / 2
4 / 5 - 2x / 5 = - 1 / 3 x + 1 / 2
Add 1 /3 x to both sides
4 / 5 - 2x / 5 = - 1 / 3 x + 1 / 2
4 / 5 - 2x / 5 + 1 / 3 x = - 1 / 3 x + 1 / 3 x + 1 / 2
4 / 5 + 1 / 3 x - 2 / 5 x = 1 / 2
4 / 5 + 5x - 6x / 15 = 1 / 2
4 / 5 - x / 15 = 1 / 2
subtract 4 / 5 from both sides
4 / 5 - 4 / 5 - x / 15 = 1 / 2 - 4 / 5
- x / 15 = 5 - 8 / 10
- x / 15 = - 3 / 10
cross multiply
- x / 15 = - 3 / 10
-10x = - 45
divide both sides by -10
x = 45 /10
x = 9 / 2
Therefore, the algebraic solution for the variable x is 9 / 2.
learn more on variable here: https://brainly.com/question/15339510
#SPJ1
If a rectangle has a side that is 8 more than 4 times the length and the perimeter is
166 inches. What are the measures of the sides.
Answer:
2 of the sides are 15 inches and the other 2 sides are 68 inches
Step-by-step explanation:
2(8+4L)+2L=166
16+8L+2L=166
16+10L=166
10L=150
L=15
15(4)+8=68
The cost of Jake's cell phone bill is determined by how many megabytes of
data he uses each month, as shown in the graph below.
Jake's Cell Phone Bill
Cost ($)
70
60
50
40
30
20
10
0
5
10
Data Usage (megabytes)
15
Which equation represents the cost of Jake's cell phone bill, y, based on his
data usage in megabytes, x?
The equation that represents the cost of jake's cell phone bill is -
y = 2x + 40 . Option - B is the correct alternative.
We have a graph representing jake's cell phone bill.
We have to write a equation that represents the cost of jake's cell phone bill.
What is the general equation of a straight line ?The general equation of a straight line is given by -
y = mx + c
where -
m → slope of line.
c → y - intercept of line.
According to the question -
The y - intercept of the line is at the coordinates (0, 40). Now, we have to find the slope of this line. Consider the two coordinates -
A(0, 40) and B(10, 60)
Slope of a straight line is given by -
m = y₂ -y₁ / x₂ - x₁
m = 60 - 40 / 10 - 0
m = 20 / 10
m = 2
Now, substituting the values in the general equation of line, we get -
y = 2x + 40
Hence, Option B → y = 2x + 40 is the correct alternative.
To solve more questions on Equation modelling, visit the link below-
https://brainly.com/question/16829550
#SPJ1
AABC and AADE are similar. Find the length of of side DA
4
For the two similar triangles, the length of side DA = 4 units.
What is defined as the similar triangles?If two triangles get the same ratio of corresponding sides and then an equal pair of corresponding angles, they are similar.When two or more figures share a common shape but differ in size, they are referred to as similar figures.The three-sided polygon is the triangle. The following is the condition for triangle similarity:Both triangles' corresponding angles are equal, andBoth triangles' corresponding sides are proportional to one another.For the two triangles;
ΔABC ≡ ΔADE
The ratios of their side will be equal
Thus,
CB/ED = AB/DA
Put the values of the sides from given diagram.
2/4 = 2/DA
Cancel the common 2 and cross multiplying.
DA = 4 units.
Thus, the length for the side DA is 4 units.
To know more about the similar triangles, here
https://brainly.com/question/14285697
#SPJ9
triangles FIM and LAK below are similar, and LA= AK
Multiple choice
Based on the triangle similarity theorem, the length of AK is: A. 9.
How to Determine the Corresponding Side Lengths of Similar Triangles?Based on the triangle similarity theorem, the ratios of the corresponding side lengths of two triangles that are similar to each other are equal and their lengths are proportional to each other.
Given that triangle FIM and triangle LAK are similar triangles, therefore, the ratio is true:
FM/LK = IM/AK
Length of FM = 8 units
Length of LK = 12 units
Length of IM = 6 units
Length of AK = ?
Substitute
8/12 = 6/AK
8(AK) = (6)(12)
8(AK) = 72
Divide both sides by 8
8(AK)/8 = 72/8
AK = 9
AK = LA = 9
LA = 9 units
Therefore, based on the triangle similarity theorem, the length of AK is: A. 9.
Learn more about the triangle similarity theorem on:
https://brainly.com/question/21247688
#SPJ1
GEMDAS
26-6+ (0+3)
26-6 ÷
26- I need help whit this soon as possible
According to the GEMDAS rule the value of the 26-6+ (0+3)*26-6 ÷26- I:
= [tex]96\frac{10}{13}[/tex]
What is The GEMDAS rule ?The GEMDAS rule can be used to summarize or evaluate difficult numerical equations containing several binary operations. Important Information: 1. In a specific simplification, if you have simultaneous multiplication and division, perform the operations sequentially from left to right.
What is the significance of both the Gemdas ,Pemdas rule?If you mess up the order of parenthesis, exponents, multiplications, including addition and subtraction, the PEMDAS rule prevents you from getting the wrong result.
According to the given data:Applying the GEMDAS rule:
26-6+ (0+3)*26-6 ÷26- I
= 26-6+ (0+3)*26-6 ÷26- I
= 26-6+ 78 -6÷ 26-1
= 26-6+78- [tex]\frac{6}{26}[/tex] -1
= 1258/13
= [tex]96\frac{10}{13}[/tex]
According to the GEMDAS rule the value of the 26-6+ (0+3)*26-6 ÷26- I:
= [tex]96\frac{10}{13}[/tex]
To know more about GEMDAS rule visit:
https://brainly.com/question/1600356
#SPJ9
Use 3.14 for pie it’s __Units squared
The Area of the figure ≈ 19 units²
What is the Area of a Semicircle and a Triangle?Area of a semicircle = 1/2(πr²), where r is the radius.
Area of a triangle = 1/2(b)(h), where b is the base and h is the height of the triangle.
The figure can be decomposed into a semicircle and a triangle.
Area of the figure = 1/2(πr²) + 1/2(b)(h)
r = 1/2(7) = 3.5 units
π = 3.14
b = 7 units
h = 3 units
Substitute
Area of the figure = 1/2(3.14)(3.5²) + 1/2(7)(3)
Area of the figure ≈ 19 units²
Learn more about the area of semicircle on:
https://brainly.com/question/15822332
#SPJ1
a parallelogram has an area of 28 square feet and a height of 4 feet what is its base? yall help me please . i really appreciate it. :D
Identify the angle relationship and find the measure of the indicated angle.
(Alternate Interior, Alternate Exterior, Corresponding, Same-side Interior)
The angled relationship is the Same-side interior angle where x is 6 and ∠EFG is 102°
For the parallel lines ED and FG, where EF is the transversal,
The angle DEF and the angle EFG are same-side interior angles.
By the same-side interior angle theorem, we can say that the interior angles on the same side of the transversal are supplementary (the sum of the angles is 180°).
∠DEF = 13x°
∠EFG = 17x°
∠DEF + ∠EFG = 180°
13x + 17x = 180
30x = 180
x = 6
∠DEF = 13x = 13*6 = 78°
∠EFG = 17x = 17*6 = 102°
Therefore, the angles follow the same-side interior angles relationship, x = 6 and ∠EFG = 102°
For more parallel lines and transversal questions, check out,
https://brainly.com/question/19670823
#SPJ9
XY=3K-2,YZ=7K+4,XZ=4K+38
Answer:
6
Step-by-step explanation:
Due to the segment addition postulate, XY + YZ = XZ.
By substituting the values in, we get that [tex](3k-2)+(7k+4)=4k+38[/tex]
Simplifying gives us that [tex]10k+2=4k+38[/tex]
[tex]6k=36[/tex]
[tex]k=6[/tex]
How many times larger is (1.064 x 101) than (7 x 10−1)?
Answer:
177.464x−1
Step-by-step explanation:
How many times larger is (1.064x⋅101)+(7x⋅10−1)
Remove parentheses.
1.064x⋅101+7x⋅10−1
Simplify each term.
Multiply 101 by 1.064.
107.464x+7x⋅10−1
Multiply 10 by 7.
107.464x+70x−1
Add 107.464x and 70x.
177.464x−1
Find the sum of the first 8 terms of the
following series, to the nearest integer.
48, 60, 75
Answer:
952.32
Step-by-step explanation:
3. Mrs. Quinto is comparing the Calories in different types of bread. Wheat bread has 150 Calories for every 2 slices. The Calories in two other types of bread are shown in the table and graph. Which bread has the greatest ratio of Calories to slices?
options:
2 - 160
4 - 320
6 - 480 . (white bread)
Rye bread is 0 to 500 .
The bread that has the greatest ratio of Calories to slices is the Wheat bread
How to determine the bread that has the greatest ratio of Calories to slices?The table of values is given as
Wheat bread
Slice - Calories
2 - 160
4 - 320
6 - 480
The missing graph that represents the graph of rye bread is added as an attachment
On the graph, we have the following table of values
Rye bread
Slice - Calories
2 - 130
4 - 260
6 - 390
We start by calculating the rates of each table using
Rate = Calories/Slice
So, we have
Wheat bread = 160/2
Wheat bread = 80
Rye bread = 130/2
Rye bread = 65
80 is greater than 65
Hence, the bread that has the greatest ratio of Calories to slices is the Wheat bread
Read more about rate of change at
https://brainly.com/question/8728504
#SPJ1
Suppose you would like to deliver 20.6 terabytes data from Kansas City to Los Angeles. You have available a 1 Gbps dedicated link for data transfer. Would you prefer to transmit the data via this link or instead use USPS delivery knowing it will take them 2 days to complete the task? Explain.
Using proportions, it is found that the dedicated link would take 5.72 hours, which is significantly less time than the USPS delivery, hence the link should be used.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Each TB has 1000 GB, hence:
20.6 terabytes = 20,600 Gigabytes.
You have available a 1 Gbps dedicated link for data transfer, hence the time it would take for the transfer through the dedicated link is:
20,600/1 = 20,600 seconds.
Each hour has 3600 seconds, hence the time in hours is:
20600/3600 = 5.72 hours.
The dedicated link would take 5.72 hours, which is significantly less time than the USPS delivery, hence the link should be used.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
 Help please with my math
The monthly payment when Jack takes the loan will be B. $319.44
How to calculate the value?From the information, the interest will be:
= Principal × Rate × Time / 100
= ($10000 × 5 × 3)/100
= $1500
The total amount to be repaid will be:
= $10000 + $1500
= $11500
Therefore, the monthly payment will be:
= $11500 / 36
= $319.44
Learn more about interest on:
brainly.com/question/25793394
#SPJ1
Which of the following are factors of 96? Select ALL that apply.
18
06
04
012
014
Answer:
6, 4 and 12 are factors
Step-by-step explanation:
Divide 96 by each value. If the result is an integer then it is a factor
96 ÷ 18 = 6.333 ← not a factor
96 ÷ 6 = 16 ← factor
96 ÷ 4 = 24 ← factor
96 ÷ 12 = 8 ← factor
96 ÷ 14 = 6.857.. ← not a factor
The perimeter of the rectangle below is 166 units. Find the value of y.
4y + 2
Sy
The value of y is 9.
Perimeter is the total length of the boundary of any closed shape. It is basically the sum of all the sides of a given figure.
Perimeter of a rectangle is given by [ 2( l + b ) ] or (2 l + 2 b ) or
( l + l + b + b), here l and b represent the length and breadth of the given rectangle.
Perimeter of the given rectangle = 166 units ( given )
Length of the given rectangle = 5y ( given )
Breadth of the given rectangle = (4y + 2) ( given )
By putting values in the formula, we get
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
To learn more about perimeter
visit; https://brainly.com/question/18793958
#SPJ1
The value of y is 9.
The whole length of any closed shape's boundary is known as its perimeter. In essence, it is the total of a given figure's sides.
A rectangle's perimeter can be calculated using [2(l + b)] or (2 l + 2 b) or
(l + l + b + b), where l and b stand for the provided rectangle's length and width
The rectangle's perimeter is 166 units ( given )
The rectangle's length is 5y ( given )
Given rectangle's width equals (4y + 2) ( given )
When we enter values into the formula, we obtain
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
3.4/feet
5 feet
Find the area of the triangle pictured above.
h
square feet
Area =
Answer: answer is 3
Step-by-step explanation:
Is 1/2 and 9/3 integers, rationals or irrational numbers
In a survey of 292 professional athletes, it was found that 135 of them owned a convertible, 117 of them owned a giant screen TV, and 136 owned a sporting goods store. 29 owned a convertible and a store, 50 owned a TV and a store, and 57 owned a covertible and a TV. 10 owned all three items.
Using Venn sets, it is found that 30 athletes own none of the items.
What is the missing information?The missing information is the question, which asks how many athletes own none of the items.
What are the Venn Sets?For this problem, we consider the following sets:
Set A: athletes that have a convertible.Set B: athletes that have a giant screen TV.Set C: athletes that owned a sporting goods store.10 owned all three items, hence:
(A ∩ B ∩ C) = 10.
57 owned a convertible and a TV, hence:
(A ∩ B) + (A ∩ B ∩ C) = 57.
(A ∩ B) = 47.
50 owned a TV and a store, hence:
(B ∩ C) + (A ∩ B ∩ C) = 50
(B ∩ C) = 40.
29 owned a convertible and a store, hence:
(A ∩ C) + (A ∩ B ∩ C) = 29.
(A ∩ C) = 19.
136 owned a sporting goods store, hence:
C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 136
C + 19 + 40 + 10 = 136
C = 67.
117 of them owned a giant screen TV, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 117
B + 47 + 40 + 10 = 117
B = 20.
135 of them owned a convertible, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 135
A + 47 + 19 + 10 = 135
A = 59.
There were 292 athletes on the survey, hence the number who owned none is given as follows:
None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 292
None + 59 + 20 + 67 + 47 + 19 + 40 + 10 = 292
None + 262 = 292
None = 30.
30 athletes own none of the items.
More can be learned about Venn sets at brainly.com/question/24388608
#SPJ1
You have the following information on Zip's Diner, Inc.: sales to working capital = 8 times, profit margin = 5 percent, net income available to common stockholders = $20 million, and current liabilities = $4 million. What is the firm's balance of current assets?
The balance of current assets of the firm is 54 million dollars.
The total of all current assets is the current asset balance. These include cash, cash equivalents, pre-paid expenses, inventories, and any other assets that are anticipated to be turned into cash throughout the course of the following year.
Any debts owed by your business to others, including bank loans, mortgages, unpaid bills, IOUs, and other sums of money, are referred to as liabilities.
We know that to calculate the balance of current assets we use the formula.
Current assets=working capital +current liabilities
Working capital=net income÷(profit margin × sales to working capital)
Now given the working capital=$20 million
Profit margin=5%
Working capital=20÷(8×5%)
or, working capital = 50
Now current assets=Working capital+liabilities
Hence balance of current assets= 50+4 million dollars
=54 million dollars
Therefore the firm's balance of current assets is 54 million dollars.
To learn more about current assets visit:
https://brainly.com/question/14287268
$SPJ9
In a certain federal prison, it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?
The probability that a prisoner selected at random from this prison is female and at least 25 years old is 1/64
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
GIven that 2/3 of the inmates are under 25 years of age also, that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older.
The number of mother inmates = 75% (100) = 75
The number of inmates, who are not mothers = 100 - 75 = 25
Selecting an inmate who is not a mother = 1/4
Selecting 3 female who are not mothers = 1/64
Therefore, the probability that a prisoner selected at random from this prison is female and at least 25 years old is 1/64
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ1
Player A finished first in a tournament at a golf club with a score of 8, or eight strokes under par. Tied for 46th place was Player B, with a score of +9, or 9 strokes over par. What was the difference in scores between Player A and Player B?
The difference in scores between Player A and Player B will be 17.
How to illustrate the information?From the information, Player A finished first in a tournament at a golf club with a score of 8, or eight strokes under par. Player B, had a score of +9, or 9 strokes over par.
Therefore, the difference in scores between Player A and Player B will be:
= 9 - (-8)
= 9 + 8
= 17
Therefore, the difference in scores between Player A and Player B will be 17.
Learn more about numbers on:
brainly.com/question/24644930
#SPJ1
The boxplot represents concert tickets sold on random days for a local venue. Find the interquartile range.
A. 143
B. 72
C. 36
D. 333
The interquartile range of the concert tickets sold is 72. (the second option).
What is the interquartile range?A box plot is a graph that is used to study the distribution and level of a set of scores. The box plot consists of two whiskers and a box. The first whisker represents the minimum number and the end of the second whisker represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
The interquartile range is the difference between the third quartile and the first quartile.
Interquartile range = third quartile - first quartile
369 - 297 = 72
To learn more about box plots, please check: https://brainly.com/question/27215146
#SPJ1
In a survey 738 of homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was 52.44 with standard deviation 10.98 . Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between 41.46 and 63.42. Round to the nearest whole number
The number of plans that cost between 41.46 and 63.42 is 504 to the nearest whole number
How to solve for the estimation of plansWe have the following data to solve this problem with
n = 738 home owners
standard deviation sd = 10.98
The number of plans is between 41.46 and 63.42
Such that we will have
p(41.46 < x< 63.42)
Then we would have
P(41.46 - 52.44 / 10.98) < z< (63.42 - 52.44 / 10.98)
= P (-1 < z < 1)
We have p(z < 1) = 0.8413
therefore p(z > 1) = 1 - 0.8413
= 0.1587
0.8413 - 0.1587 = 0.6826
This is the same as 68.26%
68.26% x 738 = 503.76
~ 504
Therefore we would have the conclusion that the number of plans that cost between 41.46 and 63.42 is 504 to the nearest whole number.
Read more on standard deviation here:
https://brainly.com/question/27894135
#SPJ1
Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and the range of the relation and determine whether the relation is a function.
Answer:
Domain: [-1, 0) U [2]Range: [0, 1)A functionStep-by-step explanation:
The domain is the set of x values and the range is the set of y values.
For the relation to the function, each value of x must map onto no more than one value of y.
Answer:
The Domain is -2 [is less than or equal to] x < 0
The Range is 0 [is less than or equal to] y < 2
This is NOT a function
Step-by-step explanation:
sry if this is a bit confusing:
[is less than or equal to] is just the sign that means what is said; this is bc you cant use that sign on keyboard
