Answer:
k = 2Step-by-step explanation:
[tex]\text{Put the coordinates of the given point A(2, 3)}\\\text{to the equation of a line}\ kx-2y+k=0:\\\\A(2,\ 3)\to x=2,\ y=3\\\\(k)(2)-(2)(3)+k=0\\2k-6+k=0\qquad\text{add 6 to both sides}\\2k+k=6\\3k=6\qquad\text{divide both sides by 3}\\\boxed{k=2}[/tex]
The value of k will be 3.
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The point A(2,3) lies on the line given by equation kx- 2y + k = 0
Since, Point A is lies on the equation.
Hence, Point A(2,3) is satisfy by the equation;
The equation of line,
kx - 2y + k = 0
Substitute (x, y) = (2, 3) in above equation;
k × 2 - 2 × 3 + k = 0
2k - 6 + k = 0
3k - 6 = 0
3k = 6
k = 3
Thus, The value of k will be 3.
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On a train car there are 30 rows of seats and each row has 5 seats .find the total number of seats on 6 train cars .draw a model and write an equation to support the answer
Answer:
900
Step-by-step explanation:
30 x 5 = 150 and 150 x 6 = 900. You would make a model with 5 rows of 30, then make 6 of them
-13(v-6)=-5v+2(5v+12)
Answer:
v = 3Step-by-step explanation:
[tex]-13(v-6)=-5v+2(5v+12)\qquad\text{use the distributive property}\\\\(-13)(v)+(-13)(-6)=-5v+(2)(5v)+(2)(12)\\\\-13v+78=-5v+10v+24\qquad\text{cobine like terms}\\\\-13v+78=(-5v+10v)+24\\\\-13v+78=5v+24\qquad\text{subtract 78 from both sides}\\\\-13v+78-78=5v+24-78\\\\-13v=5v-54\qquad\text{subtract}\ 5v\ \text{From both sides}\\\\-13v-5v=5v-5v-54\\\\-18v=-54\qquad\text{divide both sides by (-18)}\\\\\dfrac{-18v}{-18}=\dfrac{-54}{-18}\\\\v=3[/tex]
A bicycle store costs $3250 per month to operate. The store pays an
average of $35 per bike. The average selling price of each bicycle is $85
How many bicycles must the store sell each month to break even?
Answer:
65 bikes
Step-by-step explanation:
The store buys the bikes that they sell for $35, and they sell them for $85, so in order to find the actual amount of money earned from one sale, you have to subtract how much they sell the bikes for by how much they bought them for, so:
85 - 35 = 50
Then, you divide the $3250 by the 50:
3250 / 50 = 65
So now we know that the store must sell 65 bikes a month to break even.
17 is added to a number, the result is 37 less than twice the number. Find the number
To find the number, subtract 37 from both sides of the equation and isolate 'x'. The number is 54.
Explanation:To find the number, let's represent it with the variable 'x'. The problem states that when 17 is added to the number, the result is 37 less than twice the number.
Mathematically, this can be represented as:
x + 17 = 2x - 37
To solve for 'x', we can start by subtracting 'x' from both sides of the equation:
17 = x - 37
Next, we can add 37 to both sides to isolate 'x':
54 = x
Therefore, the number is 54.
how many solutions are there to this equation 3(x-4)+5-x=2x-7
Cam has a piece of plywood that is 6 7/8 feet wide. He is going to cut shelves from the plywood that are each 1 1/6 feet wide. Which is the best estimate for the number of shelves Cam can make?
A. 1
B. 2
C. 4
D. 7
Answer:
C.
Step-by-step explanation:
So how I would estimate is by see that each piece is going to be 1 and 1/6 but you have 6 and 7/8 feet of plywood so 1 can go into 6 six times but since you got that 1/6 for each piece is lower it down do about 4, so he can make about four. lol
Answer: Cam can make 4 shelves.
Step-by-step explanation:
Dylan buys 3.2 pounds of grapes for $2.56. What is the price per pound of the grapes?
Answer:
$0.64/lb
Step-by-step explanation:
The price per pound of the grapes is $0.8/pound and this can be determined by using the unitary method.
Given :
Dylan buys 3.2 pounds of grapes for $2.56.
To determine the price per pound of the grapes, the unitary method can be used and in the unitary method single unit is evaluated first then the necessary unit by multiplying the single unit.
Given that Dylan buys 3.2 pounds of grapes for $2.56 so, through the unitary method the unit price per pound will be:
[tex]=\dfrac{2.56}{3.2}[/tex]
= $0.8 / pound
So, the price per pound of the grapes is $0.8/pound.
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7 bees 5 cockroaches 8 spiders 4 deer 4 boars how many legs are there in total
There are total 168 legs.
Given, 7 bees 5 cockroaches 8 spiders 4 deer 4 boars.
We have to calculate the total number of legs.
Since, 1 bees has 6 legs, so 7 bees has in total [tex](7\times 6=42)[/tex] legs.
1 cockroach has also 6 legs, so 5 cockroach has in total of [tex](6\times 5=30)[/tex] legs.
1 spider has 8 legs so 8 spider has in total of [tex](8\times 8=64)[/tex] legs.
1 deer has 4 legs so 4 deer has in total of 16 legs.
1 boar has 4 legs so 4 boars has in total of 16 legs.
Hence the total number of legs the above animal has will be,
[tex]42+30+64+16+16=168[/tex] legs.
Therefore, There are total 168 legs.
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bernard ate part of a small pizza he started with 11/12 of a pizza but only ate 2/3 of it. Which is the best estimate of the amount bernard ate
Answer:1/4
Step-by-step explanation:
11/12 - 2/3
22/24 - 16/24 =6/24= 1/4
Assume the adults have IQ scores that are normally distributed with a mean of 105 in a standard deviation of 20 find the probability that a randomly selected adult has an IQ less than 145
Answer:
The correct answer is that the probability of a randomly selected adult has an IQ less than 145 is 97.8%
Step-by-step explanation:
According to the graphic of a standard distribution attached, we have:
68.3% of the population will have an IQ +/- one time the standard deviation plus the mean. It means that 68.3% (Rounding to one decimal place) of the adults will have an IQ between 85 and 125.
95.5% of the population will have an IQ +/- two times the standard deviation plus the mean. It means that 95.5% (Rounding to one decimal place) of the adults will have an IQ between 65 and 145.
The remaining 4.5% of the adults will have either an IQ below 65 or above 145. In this case, we only want to know the percentage below 65 because the question is about the probability of an IQ less than 145. For calculating the percentage of adults that have an IQ less than 65, we use this fraction:
4.5%/2 = 2.3% (Rounding to one decimal)
and we add this percentage to 95.5:
Probability that a randomly selected adult has an IQ less than 145 = 95.5 + 2.3 = 97.8%
Hope the moderator will not delete the answer because I'm uploading a graphic; this graphic is exclusively for academic purposes.
Mary and Lamar establish a tutoring service at a local mall. They tutor college students in math and English. They charge $40 per hour for tutoring. In the month of January they charged for 200 tutoring hours. The expenses of their business are given in the table below. Expense Amount/Month Rent of Space $4000 Electricity $325 Advertising $375 Using the formula Profit = $40(number of hours) – (expenses) , calculate their profit for the month of January.
Answer:
8000
Step-by-step explanation:
Answer: The profit is $3300
Step-by-step explanation:
The data we have is:
They charge $40 per hour.
In january, the charged for 200 hours.
The expenses are:
rent $4000
electricity $325
advertising $375
if we want to know the balance we must calculate:
The total expenses are: $4000 + $325 + $375 = $4700
The amount that they won is: $40*200 = $8000
Then the profit will be:
P = $40*200 - ($4000 + $325 + $375) = $8000 - $4700 = $3300
a bakery used 25% more butter this month than last month if the bakery use 240 kg of butter last month how much butter did he use this month
Answer: [tex]300\ Kg[/tex]
Step-by-step explanation:
Let be "x" the amount of butter (in kilograms) that the bakery used this month.
You need to divide the percentage by 100 in order to write it in decimal form. This is:
[tex]\frac{25}{100}=0.25[/tex]
According to the data given in the exercise, the total amount of butter they used last month is 240 kilograms.
Since 25% more butter was used this month than last month, you can write the folllowing equation:
[tex]x=240+(240 )(0.25)[/tex]
Evaluating, you get that the value of "x" is:
[tex]x=240+60\\\\x=300[/tex]
Therefore, the bakery used 300 kilograms of butter this month.
Final answer:
The bakery used 300 kg butter this month.
Explanation:
If a bakery used 25% more butter this month than last month and it used 240 kg of butter last month, then to calculate the amount of butter used this month, we need to add an additional 25% to the amount from last month. To find 25% of 240 kg, you multiply 240 kg by 0.25 (since 25% is the same as 0.25 when expressed as a decimal).
25% of 240 kg = 240 kg × 0.25 = 60 kg
Now, we add that 60 kg to the original 240 kg to find the total amount of butter used this month.
Total amount of butter used this month = 240 kg + 60 kg = 300 kg.
Therefore, the bakery used 300 kg of butter this month.
the numerator of a fraction is 9 and the denominator is6. all of the following numbers are equivalent except
Question is incomplete, complete question is given below.
The numerator of a fraction is 9 and the denominator is 6. All of the following numbers are equivalent except _____.
A) 2/3
B)3/2
C)1 1/2
D)18/12
Answer:
A) 2/3
Step-by-step explanation:
Given:
The fraction is [tex]\frac{9}{6}[/tex]
By solving the above fraction to its simplest form we get
[tex]\frac{9}{6}=\frac{3\times3}{2\times2}=\frac{3}{2}[/tex]
Now For Option A which is [tex]\frac{2}{3}[/tex]
Give fraction is [tex]\frac{3}{2}[/tex]
We can say that it is Not equivalent to given fraction.
Now For Option B which is [tex]\frac{3}{2}[/tex]
Give fraction is [tex]\frac{3}{2}[/tex]
We can say that it is equivalent to given fraction.
Now For Option C which is [tex]1\frac{1}{2}[/tex]
Solving above equation to simplest form we get,
[tex]1\frac{1}{2}= \frac{1\times2+1}{2}=\frac{3}{2}[/tex]
Give fraction is [tex]\frac{3}{2}[/tex]
We can say that it is equivalent to given fraction.
Now For Option D which is [tex]\frac{18}{12}[/tex]
Solving above equation to simplest form we get,
[tex]\frac{18}{12}= \frac{6 \times 3}{6 \times 2} = \frac{3}{2}[/tex]
Give fraction is [tex]\frac{3}{2}[/tex]
We can say that it is equivalent to given fraction.
Hence all answer B C and D are all equal to [tex]\frac{3}{2}[/tex] except A which is [tex]\frac{2}{3}[/tex]
Use prime factorization to find the GCF of 10, 45
Answer:
GCF(10, 45) = 5Step-by-step explanation:
[tex]10=2\cdot\boxed{5}\\\\45=3\cdot3\cdot\boxed{5}\\\\GCF(10,\ 45)=\boxed{5}[/tex]
Giselle pays $240 in advance on her account at the athletic club. Each time she uses the club, $5 is deducted from the account. Model the situation with a linear function.
A: b = 235 + 5x
B: b = 240 - 5x
C: b = 235 - 5x
D: b = 240 + 5x
Answer:
B) b = 240 - 5 x is the required expression to decipher the situation.
Step-by-step explanation:
The amount paid to the club in the advance = $240
Amount deducted in each visit = $5
Let us assume the number of times the club visited = x
So, the amount deducted in x visits = x ( $5) = 5x
Let b : amount Left after x visits
So, Amount left after x visits = Advance Amount - Deductions after x visits
⇒ b = $240 - 5x
or , b = 240 - 5x is the required expression to decipher the situation.
Answer:
Giselle pays $240 on advance
Each time she uses ,$5 is deducted
Let no of time she use be x
So, Amount deducted = 5x
As Giselle pays $240 in advance
So 5x amount will be deducted from $240 to get net amount
So b= 240-5x
B) is Correct
what is the value of n if n divided by 256 = 8 1/3 times 8 1/3?
The value of 'n' in the given mathematical equation n/256 = 8 1/3 * 8 1/3 is approximately 17766.4.
Explanation:The question asks what is the value of n if n divided by 256 = 8 1/3 times 8 1/3. To find the answer, first we need to calculate the value of 8 1/3 times 8 1/3. Converting 8 1/3 to a decimal result in approximately 8.33. Then, we multiply 8.33 by itself to get approximately 69.4.
Since n divided by 256 gives this value, to find n, we simply multiply 69.4 by 256. This results in approximately 17766.4. Therefore, given the condition in the problem, the value of n would be approximately 17766.4.
To find the value of n, we need to solve the equation: n/256 = 8 1/3 * 8 1/3. First, let's convert 8 1/3 to a fraction: 8 1/3 = 25/3. Next, multiply 25/3 by itself to get (25/3) * (25/3) = 625/9. Now we can solve for n by multiplying both sides of the equation by 256: n = (256 * 625/9).
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ALWAYS use significant figure rules. Remember that these rules apply to all numbers that are measurements. An object moves in uniform circular motion at 25 m/s and takes 1.0 second to go a quarter circle. What is the radius of the circle? R = _____ m 0.063 m 0.99 m 16 m 50. m
Answer: 16 m
Step-by-step explanation:
We have the following data:
[tex]V=25 m/s[/tex] is the velocity of the object moving in uniform circular motion
[tex]t=1 s[/tex] is the time it takes to the object to go [tex]\frac{1}{4}[/tex] of a complete circle
We need to find the radius [tex]r[/tex] of the circle, and this can be found by the following equation:
[tex]V=\frac{2 \pi r}{T}[/tex] (1)
Where [tex]2 \pi r[/tex] is the circumference of the circle and [tex]T=4 t=4(1 s)[/tex] is the period for a complete circle.
Hence, isolating [tex]r[/tex] we have:
[tex]r=\frac{V T}{2 \pi}[/tex] (2)
[tex]r=\frac{(25 m/s)(4 s)}{2 \pi}[/tex] (3)
Finally:
[tex]r=15.9 m \approx 16 m[/tex] (4)
Carol wants to make a quilt using a scale of 1.5 inches=2 feet. Her scale drawing is 7.5 inches by 10.5 inches. What is the area of the actual quilt?
_[blank]_ square feet
I will mark the first one to answer my question brainleist
Answer:
140 ft
Step-by-step explanation:
write an expression where you multiply 0.035 times the power of ten so that the product is greater than 1 and less than 100 please help
Answer:
[tex]0.035\times 10^{3}[/tex]
Step-by-step explanation:
Given: The value of 0.035
Now, as we know 0.035 has three decimal place which mean if we multiply by 1000 then we have the product 35 which is greater than 1 and less than 100, however if we multiply 0.035 by 10000 then the output will be greater than 100, which is invalid.
Lets us use hit and trail method.
[tex]0.035\times 1000 = 35 < 100\\\\0.035\times 10000= 350 >100[/tex]
Now lets put the value in expression
[tex]0.035\times 10^{3}[/tex]
A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 85% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
50 gallos of 70%
100 gallons of 85%
Step-by-step explanation:
x = amount of 70% antifreeze
y = amount of 85% antifreeze
EQUATION 1: x + y = 150 (total of 150 gallons mixed)
EQUATION 2: .70x + .85y = .80(x + y)
Multiply second equation by 100 on both sides to remove the decimals 70x + 85y = 80(x + y)
70x + 85y = 80x + 80y (distributive)
70x - 80x + 85y - 80y = 0
-10x + 5y = 0
Now we have the following system of equations:
x + y = 150
-10x +5 y = 0
Multiply the first equation by 10 to get opposite coefficients for x; add the equations to eliminate x
10x + 10y = 1500
-10x + 5y = 0
------------------------------
15y = 1500
Solve for y 15y = 1500 y = 100
x+100=150 x=50
Mr Hays Bought a 5 gal. bucket of paint costing $175
Answer:
Nice! Uhh... What am I supposed to do with this info?
The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is ModifyingAbove y with caret equals negative 121 plus 3.38 x 1 plus 1.48 x 2, where x1 is the female athlete's height (in inches) and x2 is the female athlete's percent body fat, measured as x2%. Use the multiple regression equation to predict the total body weight for a female athlete who is 68 inches tall and has 21% body fat.
To predict the total body weight for a female athlete who is 68 inches tall and has 21% body fat, substitute the given value for each independent variable into the multiple regression equation.
Substitute the values for x1 and x2 into the multiple regression equation.
Answer:
do u still need help??
Step-by-step explanation:
A company ears a profit of $100 the first month it is in business. Every month after that, the
company ears a profit that is 1 1/2 the previous month's profit.
What will the company's profit be in the fifth month?
Good evening ,
Answer:
1318.75 $Step-by-step explanation:
Look at the photo below for the details.
:)
OMGGGGGGGGGG help me
Answer:
sin 39 = BS / 500
0.629320391 * 500 = BS
BS = 314.6601955 feet
ie. h = 314.66 feet
Answer:
404.9 m
Step-by-step explanation:
In the attached file
11. In 2010, the population in the United States will be about 3.09x10'. Spending for health care will be
about $8754 per person. About bow much will the US spend on health care in 2010? Write in scientific
notation and round to the ncarest hundredths.
Answer:
[tex]\$ 2.70\times 10^{12}[/tex]
Step-by-step explanation:
Complete question is here: In 2010, the population in the United States will be about 3.09x10^8. Spending for health care will be about $8754 per person. About how much will the US spend on health care in 2010? Write in scientific notation and round to the nearest hundred.
Given: Per person expenditure on healthcare is $8754.
Total population in 2010 is 3.09x10^8.
Now, lets find out total money U.S will spend on health care.
[tex]\textrm{Total population} \times amount\ spent\ per\ person\ on\ healthcare}[/tex]
= [tex]8754\times 3.09\times 10^{8} = 27049.96\times 10^{8}[/tex]
= [tex]\$ 2.705\times 10^{12}[/tex] ≅ [tex]\$ 2.70\times 10^{12}[/tex]
∴ In 2010, U.S will spend [tex]\$ 2.70\times 10^{12}[/tex] on health care.
Answer:
about $2.70 × 1012
Step-by-step explanation:
$8754(3.09 × 108)
= $27,049.86 × 108
≈ $2.70 × 1012
E
What are the dimensions of the product?
2
4 -3 |x| -2
гу со
| 6 1 о| |
o1 x 2
O2 x 2
О 3x 2
o3х3
Answer:
The dimension of the product is 2×2.
Step-by-step explanation:
The given problem is based on Matrices and it is a matrix multiplication or Matrix product.
For any Two Matrix multiplication it is necessary, number of columns of matrix A must be equal to number of rows of matrix B.
Then only multiplication of matrix exist.
Then the product of multiplication i.e Matrix C will have the order number of rows of Matrix A by number of columns of Matrix B
Let A be the first Matrix multiplied by matrix B
Matrix A is of order 2×3
Rows=2, column =3
Matrix B is of order 3×2
Rows=3, column =2
So here number of columns of matrix A is equal to number of rows of matrix B i.e 3
And the product order will be number of rows of Matrix A by number of columns of Matrix B .i.e 2×2
Answer:
b on edge or 2x2
Step-by-step explanation:
Sherry invested some money at 7% interest Sherry also invested $242 more than four times that amount at 6% how much is invested at each rate if Sherry receives $427.13 in interest after one year
$1331 is invested at 7% and $5566 is invested at 6%
Step-by-step explanation:
The formula of the simple interest is I = P r t, where
P is the money investedr is the rate of interest in decimalt is the time of investmentAssume that Sherry invested $P in the first account
∵ Sherry invested $P in the first account at 7% interest for 1 year
∵ I = P r t
∴ The interest of the 1st account = P( [tex]\frac{7}{100}[/tex] )(1)
∴ The interest of the 1st account = 0.07 P
∵ Sherry also invested $242 more than four times that amount at
6% for 1 year
- Multiply P by 4 and add 242 to the product
∴ Sherry invested in the 2nd account (4P + 242)
∵ I = P r t
∴ The interest of the 2nd account = (4P + 242)( [tex]\frac{6}{100}[/tex] )(1)
∴ The interest of the 2nd account = 0.06(4P + 242)
- Simplify it
∴ The interest of the 2nd account = 0.24 P + 14.52
∵ Sherry receives $427.13 in interest after one year
- Equate the 1st interest and the 2nd interest and equate the sum
by 427.13
∴ 0.07 P + 0.24 P + 14.52 = 427.13
∴ 0.31 P + 14.52 = 427.13
- Subtract 14.52 from both sides
∴ 0.31 P = 412.61
- Divide both sides by 0.31
∴ P = 1331
∵ She invested (4P + 242) in the 2nd account
- Substitute P by 1331
∴ She invested in the 2nd account = 4(1331) + 242 = 5566
∴ She invested $1331 at 7% interest
∴ She invested $5566 at 6% interest
$1331 is invested at 7% and $5566 is invested at 6%
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-3x-4ya 2
Зr + 3y=-3
Answer:
x= -2 and y=1
Step-by-step explanation:
Given equations:
-3x - 4y = 2
3x + 3y = -3
Adding these two equations, we get:
3y - 4y = -1 ⇒ y=1
⇒ 3x + 3(1) = -3 ⇒ x=-2
In 2018, there were 238 Republicans, and 201 Democrats in the House of Representatives. Find the percentage of Republicans in the House of Representatives in 2018.
Answer:
54.2%
Step-by-step explanation:
The total number is 238 + 201 = 439. The percent that is Republican is:
238 / 439 × 100% = 54.2%
The percentage of Republicans in the House of Representatives in 2018 was approximately 54.21%, computed using the formula for percentage calculation - (number of Republicans/total number of representatives)*100.
Explanation:The subject of this question is Mathematics, specifically Percentage Calculation. To answer the question, we need to find the percentage of Republicans in the House of Representatives in 2018. Given that there were 238 Republicans and 201 Democrats, the total number of representatives is 238 + 201 = 439.
To find the percentage of Republicans, we divide the number of Republicans by the total number of representatives and multiply by 100. So, the calculation would be: (238/439) * 100, which gives approximately 54.21%. Therefore, the percentage of Republicans in the House of Representatives in 2018 was approximately 54.21%.
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Please help asap!!
Answer:
(4,-1)
Step-by-step explanation:
the graph goes up or down by 2 each time so 2x2=4
then half of -2 is -1