Answer:
a = 18
Step-by-step explanation:
The slopes of parallel lines are equal as
[tex]m_{2}=m_{1}[/tex]
We know that the slope formula is
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where y2, x2, y1, and y2 are any two points.
Thus, since the slopes are equal, we can use the slope formula to find the slopes of both lines and set them equal to each other to find a:
[tex]\frac{9-2}{4-a}=\frac{3-11}{(a+1)-3} \\\\\frac{7}{4-a}=\frac{-8}{a-2} \\\\7(a-2)=-8(4-a)\\7a-14=-32+8a\\7a=-18+8a\\-a=-18\\a=18[/tex]
If we plug in a for any of the two lines, we see that the slope is -1/2
Line 1 w/ (a, 2) & (4, 9):
[tex]\frac{9-2}{4-18}\\ \frac{7}{-14}\\ \frac{-1}{2}[/tex]
Line 2 w/ (3, 11) & (a+1, 3):
[tex]\frac{3-11}{18+1-3}\\ \frac{-8}{19-3}\\ \frac{-8}{16}\\ \frac{-1}{2}[/tex]
In September, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest. Jennifer plans to repay the loan in January. Assume this loan is a simple interest loan calculated monthly. What will be the total amount she will owe to the bank on January 31st? If necessary, round to the nearest cent.
Answer: The total amount Jennifer will owe to the bank on January 31st is $3,458.75
Step-by-step explanation: In September, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest for 4 months. As this loan is a simple interest loan calculated monthly, we need to calculate the total amount she will owe to the bank on January 31st.
We use the formula for simple interest which is:
Interest = Principal x Interest rate x Time
Interest = $2,500 x 11.75/100 x 4/12 = $958.75 (rounding to the nearest cent)
Now we can add the interest to the principal amount to get the total amount that Jennifer will owe to the bank on January 31st.
Total amount = Principal + Interest
Total amount = $2,500 + $958.75 = $3,458.75 (rounding to the nearest cent)
So, the total amount Jennifer will owe to the bank on January 31st is $3,458.75
One serving of Campbell Soup Company's Campbell's® Pork & Beans contains 5 grams of protein and 21 grams of carbohydrates.† A typical slice of white bread provides 2 grams of protein and 11 grams of carbohydrates per slice. The U.S. RDA (Recommended Daily Allowance) is 60 grams of protein each day.
(a)
I am planning a meal of "beans on toast" and wish to have it supply one-half of the RDA for protein and 139 grams of carbohydrates. How should I prepare my meal? (Fractions of servings are permitted.)
beans
serving(s)
bread
slice(s)
(b)
Is it possible to have my meal supply the same amount of protein as in part (a) but only 61 grams of carbohydrates?
Yes
No
The way we should prepare the meal to supply one half of the RDA for protein and 139 grams pof carbohydrates is 4 beans serving and 5 bread slices (answer A). It not possible to have the same amount of protein as in part A but only 61 grams of carbohydrates.
How to calculate the meal of point A?To calculate the meal of point A we have to consider the amount of grams of protein and carbohydrates in each food. In this case, we try with 4 servings of beans and 5 slices of bread, and it get the protein and carbohydrates required as shown in the following explanation:
Servings of beans
4 * 5 = 20 grams of protein
4 * 21 = 84 grams of carbohydrates
Slices of bread
5 * 2 = 10 grams of protein
5 * 11 = 55 grams of carbohydrates
Totals
20 + 10 = 30 grams of protein
84 + 55 = 139 grams of carbohydrates
According to the previous explanation the meal have to be composed by 4 servings of beans and 5 slices of bread. On the other hand, if we want to make a meal with the same amount of protein but only 61 grams of carbohydrates, it is imposible because the amount of carbohydrates of each food is bigger than we need.
Learn more about carbohydrates in: https://brainly.com/question/14614055
#SPJ1
Set up a ratio. If the ratio cannot be reduced to an equivalent ratio in terms of small integers, then express it as a ratio of decimal equivalents with the smallest term set at 1. Maintain three-figure accuracy.
Don, Bob, and Ron Maloney’s partnership interests in Maloney Bros. Contracting are in the ratio of their capital contributions of $78,000, $52,000, and $65,000, respectively.
What is the ratio of Bob's to Ron's to Don's partnership interest?
The ratio of Bob's to Ron's to Don's partnership interest is 26.6% : 33.3% : 40.0%.
What does partnership interest mean?A partnership interest is the percentage of a partnership that a specific member or individual owns. In this context, partnerships refer to a specific method of organizing business ownership in which each owner is a partner, with equal rights, privileges, and obligations to the company as a whole.
Data
Partnership interests in Maloney Bros:
Don - $78,000
Bob - $52,000
Ron Maloney’s - $65,000
The total capital contribution is:
= $78,000 + $52,000 + $65,000
= $195,000
Bob's partnership interest is:
= $52,000/$195,000
= 0.266 or 26.6%.
Ron's partnership interest is:
= $65,000/$195,000
= 0.333 or 33.3%.
Don's partnership interest is:
= $78,000/$195,000
= 0.400 or 40.0%.
Read more about partnership interest
brainly.com/question/14835194
#SPJ1
2. In 2000, Social Security tax was 7.5%, to the maximum income of $53,000. If Mary earned $61,711 in 2000, how
much Social Security did she pay?
Mary paid Social Security tax of $4,378.325 in 2000. This is calculated by multiplying 7.5% by the amount of income over the maximum taxable income of $4,378.325.
How much Social Security did she pay?The theory used in this question is the marginal tax rate, which is the tax rate that applies to the income earned over the maximum taxable income. In this case, the marginal tax rate is 7.5%, which is the Social Security tax rate.
Step 1: Calculate the amount of income over the maximum taxable income.
Maximum taxable income: $53,000
Income earned: $61,711
Amount of income over the maximum taxable income: $8,711 ($61,711 - $53,000 = $8,711)
Step 2: Calculate the Social Security tax.
Social Security tax rate: 7.5%
Amount of income over the maximum taxable income: $8,711
Social Security tax paid: $4,378.325 ($8,711 x 0.075 = $4,378.325)
To learn more about marginal tax rate refer :
brainly.com/question/10798743
#SPJ1
k=3/2
y=kx
y=3/2x
what is the table of x and y
x -0 y-0
x___ y___
x___ y____
Using the proportionality relationship equation, y = 3/2x, the complete table is:
x | y
0 0
1 3/2
2 3
How to Complete a Table Using the Constant of Proportionality?The equation of a proportional relationship between x and y can be represented as y = kx, which means that the constant of proportionality, k, is y/x.
For example, if the constant of proportionality between two variables x and y is given as 4, therefore, the equation of the proportional relationship will be stated as y = 4x.
Given the following:
Constant of proportionality, k = 3/2.
The equation of the proportional relationship is: y = 3/2x
Use the equation, y = 3/2x to complete the table by substituting the values of x into the equation:
For x = 1:
y = 3/2(1)
y = 3/2
For x = 2:
y = 3/2(2)
y = 3
Therefore, the complete table is:
x | y
0 0
1 3/2
2 3
Learn more about the constant of proportionality on:
https://brainly.com/question/1835116
#SPJ1
Write and solve an inequality.
Please show work
Chris earns $8 per hour working on the weekends. He needs at least $320.00 for his class trip. How many hours, h, does Chris need to work on the weekends to be able to go on the class trip
We can start solving the problem by using the formula:
Hours worked = Total cost / Hourly wage
In this case, we know that Chris needs at least $320.00 for his class trip, and he earns $8 per hour working on the weekends. So, we can plug in these values into the formula:
Hours worked = $320.00 / $8.00
To solve this equation, we divide 320 by 8:
Hours worked = 40
So Chris needs to work 40 hours on the weekends to be able to go on the class trip.
I hope this helps :)
Answer:
Chris needs to work at least 40 hours.----------------------------------------
Chris earns $8 per hour and he needs at least $320.00 for his class trip.
If he works h hours, he will get 8h dollars.
Set up inequality:
8h ≥ 320Solving we get:
h ≥ 320/8h ≥ 40Chris needs to work at least 40 hours.
Marco budgets $1,600 a month for expenses.
According to the graph, how much does he pay
for his credit card, groceries, and rent?
$1,008
$908
$1,142
$1,029
Marco pays $1008 for for his credit card, groceries, and rent.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Marco budgets $1,600 a month for expenses.
According to the graph he pays 4% of credit card
Now let us find 4% of 1600
4/100×1600
0.04×1600
$64 Marco pays for credit card.
From graph, he pays 17% for groceries
17% of 1600
17/100×1600
0.17×1600=$272
$272 Marco pays for Groceries.
From graph, he pays 42% for rent
42/100×1600
0.42×1600=672
$672 Marco pays for Rent.
Hence, Marco pays $1008 for for his credit card, groceries, and rent.
To learn more on Percentage click:
brainly.com/question/28269290
#SPJ1
Diego brought 16candy bars $25. large candy bars cost $1.25 and regular candy bars cost $0.75. How many candy bars of each size did he buy? (with explanation if u can)
There are 10 and 26 candy bars of each size did he buy.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Diego brought 16 candy bars $25.
And, large candy bars cost $1.25 and regular candy bars cost $0.75.
Now, Let number of large candy bars = x
And, Number of regular candy bars = y
Here, Diego brought 16 candy bars.
Hence, We get;
⇒ x + y = 16 .. (i)
And, large candy bars cost $1.25 and regular candy bars cost $0.75.
Hence, We get;
⇒ 1.25x + 0.75y = 25 .. (ii)
Multiply by 1.25 in (i) and subtract from (ii), we get;
⇒ 1.25y - 0.75y = 20 - 25
⇒ 0.5y = - 5
⇒ y = - 10
And, from (i);
⇒ x + y = 16
⇒ x - 10 = 16
⇒ x = 26
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Question 8
You decide to begin saving toward the purchase of a new car in five years. If you put
RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent
compounded annually, how much will you accumulate after 5 years?
If you save RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent compounded annually, the future value or the amount you will accumulate after 5 years is RM5,637.09.
What is the future value?The future value is the compounded present value of the periodic deposits.
The future value formula or FV table can determine the accumulated future value of periodic investments.
We can also use an online finance calculator to determine the future value.
N (# of periods) = 5 years
I/Y (Interest per year) = 6%
PV (Present Value) = RM0
PMT (Periodic Payment) = RM1,000
Results:
Future Value (FV) = RM5,637.09
Sum of all periodic payments = RM5,000(RM1,000 x 5)
Total Interest = RM637.09
Thus, in 5 years, you will have an accumulated future value of RM5,637.09 in the savings account.
Learn more about the future value at https://brainly.com/question/27979326
#SPJ1
2 people push a box from different directions, why doesnt the box move?
Answer:
Newton's 3rd law of motion
Step-by-step explanation:
Newton's 3rd law of motion states that for every force in nature there is an equal and opposite reaction.
So, assuming the people are both pushing with the same force, their forces are basically canceling each other out, and a net force of 0 is acting uponm the box, which explains why it is not moving.
pls help w geometry (see picture)
The given geometry of the figure does not show any of the options, so option D is correct.
What is a triangle?A polygon with three vertices and three sides is called a triangle. The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180 degrees.
Given a ΔSTU
a line from point T intersects at SU at point V and divides SU, given SV is 60 units and UV is 42 units.
The line TV is not a median, because a median divides the side into two equal halves, and the figure does not have SV equal to UV.
The line TV is not an attitude because the figure has not specified the angle of V in line SU, if given that the ∠TVU = ∠TVS = 90° then TV will be called altitude.
The line is not a perpendicular bisector because The line segment drawn from a vertex to the opposite side of a triangle, bisecting that side at a right angle, is known as the perpendicular bisector of the triangle.
Hence option D is correct.
Learn more about triangles;
brainly.com/question/2773823
#SPJ1
Match each of the equations with their corresponding graph.
a) y= x^3 +2x^2-1
b) 2x^2-x-3
c) 1/x +1
d) 2-3x^2 -x^3
Answer:
I think so the answer is a)y=x³+2x²-1
Mark plays field hockey. He makes a goal 55% of the time he shoots. A = the event Mark is successful on his first goal attempt. P(A) = 0.55. B = the event Mark is successful on his second goal attempt. P(B) = 0.55. Mark tends to make goals in streaks. The probability that he makes a second goal given that he made the first goal is 0.80.
If Mark attempts two goals, what is the probability that he makes both goals?
Answer:
We can use the formula for conditional probability to find the probability that Mark makes both goals:
P(A and B) = P(A) * P(B | A)
We know that:
P(A) = 0.55 (the probability that Mark makes a goal on his first attempt)
P(B | A) = 0.80 (the probability that Mark makes a goal on his second attempt given that he made the first goal)
So:
P(A and B) = 0.55 * 0.80 = 0.44
Therefore, the probability that Mark makes both goals is 0.44.
The diagram shows solid pyramid ABCDE.
The base BCDE of the pyramid is a horizontal square w side lengths 12cm
The vertex A of the pyramid is vertically above the midpoint of BD
The volume of the pyramid is 768cm3
Calculate the size of the angle between AB and the base of the pyramid.
Id the base BCDE of the pyramid is a horizontal square w side lengths 12cm . The size of the angle between AB and the base of the pyramid is 62 degree.
How to find the size of the angle between AB and the base of the pyramid?Side of square of base BCDE =12cm
Area of base =12² =144cm²
Volume of pyramid = 768cm³
1/3 a² × h= 768
1/3 × 144 × h =768cm³
h =768 × 3 /144
h =16 cm
BD² =BC² +CD²
BD² = 12² + 12²
BD² = 288
BD =√288 cm
BD = 16.97cm
BD = 17cm
So,
BF = 1/2 BD
BF = 1/2 × 17
BF =8.5cm
So since ΔABF is angle between AB and base of pyramid
tan <ABF = Tan-1 (16/8.5) = 62°
Therefore the size of the angle between AB and the base of the pyramid is 62 degree.
Learn more about angle between AB and the base of the pyramid here:https://brainly.com/question/6469233
#SPJ1
37 hundredths= ____ tenths + ____ hundredths
Answer:
30 TENTHS + 7 HUNDREDTHS
Step-by-step explanation:
Use z scores to compare the given values. In a recent awards ceremony, the age of the winner for best actor was 37 and the age of the winner for best actress was 52. For all best actors, the mean age is 45.2 years and the standard deviation is 8.3 years. For all best actresses, the mean age is 32.3 years and the standard deviation is 11.6 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
1.6982 is the actress age is more extreme when winning the award, the actor or the actress .
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.
Essentially, standard deviation is a measure of the degree of variability within a given data collection.
Z score for actor = ( 37 - 45.2 )/8.3
= - 0.9879
Z score for actress = ( 52 - 32.3 )/11.6
= 1.6982
since I - 0.9879 l < l 1.6982 l , the actress age is more extreeme .
Learn more about Z-score
brainly.com/question/15016913
#SPJ1
What are the dimensions of this matrix? I WILL MARK BRAINLIEST.
Answer:
1 * 3 ==> 4th option
Step-by-step explanation:
Matrix dimensions are:
number of rows by number of columns
The number of rows is 1 : ( -4 1/4 -1 is the row)
The number of columns is 3 : (-4, 1/4, and -1 are the columns)
Hence, the dimensions is 1 * 3.
Answer:
1 x 3
Last choice
Step-by-step explanation:
The dimensions of a matrix are represented by number of rows x number of columns
There is only one row here (don't be confused by the 1/4) and there are three columns
So 1 x 3
(last choice)
There is 25 pounds of dog food in a bag. There are approximately 2.2 kilograms in 1 pound. PLEASE HELP ME !! THANK YOU SMM!!
Which statement is true?
A. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/22.
B. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
C. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25
According to the given information, there is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/55
Conversion between units: Calculating kilograms of dog foodFrom the question, we are to determine the statement that is true
From the given information,
There is 25 pounds of dog food in a bag.
and
There are approximately 2.2 kilograms in 1 pound.
If there are 2.2 kilograms in 1 pound
Then,
There would be x kilograms in 25 pounds
x = 2.2 × 25
x = 55 kilograms
Hence, there are 55 kilograms
Learn more on Conversion of units here: https://brainly.com/question/17529194
#SPJ1
Please help, having trouble getting answer.
Answer:
C. 2 ≤ x
Step-by-step explanation:
EDGE
If P = 4s represents the square’s perimeter in terms of the square’s side length (in inches), write a formula that represents the perimeter’s side length 's' in terms of the square’s perimeter 'P.'
The side of the square in terms of the perimeter is P/4.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
P = 4s
Where s is the side of the square and P is the perimeter of the square.
Now,
The side of the square.
P = 4s
Divide 4 into both sides.
s = P/4
Thus,
The side of the square is P/4.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
PLEASE HELP ME IREADY DUE TODAY HELP NOW
simplify 7m-2(3m^2 +mn)
Answer: 7m-6m²-2mn
Step-by-step explanation:
Multiply each term in parenthesis by -2
Calculate product (2x3=6)
7m-6m²-2mn
PLS HELP ME PLSSS plsssss
Answer:
The circumference of a tire can be found by using the formula C = πd, where C is the circumference, and d is the diameter.
For the old bicycle with 12 inch diameter tires, the circumference is:
C = π * 12 = 12 * π inches
For the new bicycle with 16 inch diameter tires, the circumference is:
C = π * 16 = 16 * π inches
To find the difference in the circumference of the tires, we subtract the circumference of the old tire from the circumference of the new tire:
16π - 12π = 4π inches
So the difference in the circumference of the two tires is 4π inches.
It's around 12.56 inches.
. Descompuneti in factori:
a) 4x + 4x -35;
c) 4x2+ 20x - 11;
e) 4x2 + 12x - 16;
g) 16x7 + 24x - 40;
i) 25x + 10x - 48;
h ) 25x2 -
j) 16x2 + 40x - 39.
The factors of the expression 16x²+40x-39 are (4x-3)(4x+13).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
A) 4x+4x-35
= 8x-35
C) 4x²+20x-11
= 4x²+22x-2x-11
= 2x(2x+11)-1(2x+11)
= (2x+11)(2x-1)
E) 4x²+12x-16
= 4x²+16x-4x-16
= 4x(x+4)-4(x+4)
= (4x-4)(x+4)
= 4(x-1)(x+4)
G) 16x⁷+24x-40
= 8(2x⁷+3x-5)
I) 25x+10x-48
= 35x-48
J) 16x²+40x-39
= 16x²-12x+52x-39
= 4x(4x-3)+13(4x-3)
= (4x-3)(4x+13)
Therefore, the factors of the expression 16x²+40x-39 are (4x-3)(4x+13).
To learn more about the factorisation of polynomial visit:
https://brainly.com/question/16789195.
#SPJ1
Borrowed 600$ from the bank. Interest is $14.25 for 90 days. What is interest rate?
Answer:
0.01 %
Step-by-step explanation:
The interest rate is the percentage of the principal (the amount borrowed) that is charged as interest over a certain period of time.
To find the interest rate, we can use the formula:
Interest Rate = Interest / Principal x Number of days / 365
We know that the principal is 600$, the interest is 14.25$ and the number of days is 90
so we can substitute the values into the formula:
Interest Rate = 14.25 / 600 x 90 / 365
Interest Rate = 0.02375 * 90 / 365
Interest Rate = 0.0104
Rounded to the nearest thousandth, the interest rate is 0.010 or 0.01 %
A Man bought 5 Crates of 60 of drinks. On his way home, he drank 5 bottles and broke 25 bottles what percentage of the bottles are left?
Answer:50%
Step-by-step explanation:
Use the parallelogram to find m
m
The angles in the parallelogram are as calculated below
How to find the angles in the parallelogram?
A parallelogram is a quadrilateral with opposite sides parallel. This means that both pairs of opposite sides are parallel and of equal length. The opposite angles of a parallelogram are also equal in measure.
m ∠BEA = 60° (alternate angles)
m ∠BAE = 42° (alternate angles)
m ∠DAE = 40° (alternate angles)
m ∠ABE = 180 - m ∠BEA - m ∠BAE = 78° (angle in a triangle)
m ∠CBE = 78° (vertically opposite angles)
m ∠ABD = 180 - m ∠ABE = 102° (angle on a straight line)
m ∠CBE = 102° (vertically opposite angles)
m ∠BEC = 180 - m ∠CBE - m ∠BEC = 38° (angle in a triangle)
m ∠ADB = 38° (alternate angles)
Learn more about parallelogram on:
brainly.com/question/24587399
#SPJ1
One aircraft has a capacity of 64 more seats than a second aircraft. A third aircraft has 152 seats less than twice the seating capacity of the second aircraft. If their total number of seats is 1900, find the number of seats for each aircraft.
The number of seats in the first, second and third aircraft are 561 seats, 497 seats and 842 seats respectively
How to find the number of seats for each aircraft?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Let F, S and T represent number of seats in the first, second and third aircraft respectively
We can set up three equations to represent the situation:
F = 64 + S --- (1)
T = 2S - 152 --- (2)
F + S + T = 1900 --- (3)
Put (1) and (2) in (3):
F + S + T = 1900
(64 + S) + S + (2S - 152) = 1900
64 + S + S + 2S - 152 = 1900
4S - 88 = 1900
4S = 1900 + 88
4S = 1988
S = 1988/4
S = 497 seats
F = 64 + S
F = 64 + 497 = 561 seats
F + S + T = 1900
561 + 497 + T = 1900
1058 + T = 1900
T = 1900 -1058 = 842 seats
Learn more about word problems on:
brainly.com/question/1781657
#SPJ1
Please look at the picture and answer the question thank you
The respective answers are 5 and 4
What is addition in math?Addition in math is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.
Given: 5 means 5+0+0 which equals to 5
4 means 4+0+0+0 which equals 4
Hence the respective answers are 5 and 4
Learn more about addition here:
https://brainly.com/question/29560851
#SPJ1
I question below and select the best answer choice. *
What property was used to simplify the expression?
12 × 47 = 12 × (40 + 7)
= 12 X 40 + 12 × 7
= 480 + 84
= 564
The property used to simplify the expression is 12 × 47 = 12 × (40 + 7) is distributive property.
What is distributive property?The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.
In other words, distributive property is a rule that states that you can distribute the terms of an expression.
Therefore, let's check the property used on the expression as follows:
12 × 47 = 12 × (40 + 7)
12 × 40 + 12 × 7
480 + 84
564
Hence, the property used on the expression is distributive property.
learn more on distributive property here: https://brainly.com/question/5637942
#SPJ1
