Jacob will need 7 months to spend all the money.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits into his savings account each week. when summer vacation is over, he plans to spend $180 per month.
The number of months will be calculated as:-
Total money in the account = 180 + 12(145-55)
Total money in the account = $1260
Total months = 1260 / 180
Total months = 7 months
Therefore, Jacob will need 7 months to spend all the money.
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help i don’t get it
answers pls
Answer: 13
Step-by-step explanation:
As the sum of the angles of a triangle is 180, we have that 39 + 90 + 3x+12 = 180.
3x = 180 - 39 - 90 - 12
3x = 39
x = 13
A store sells small notebooks for $6 and large notebooks for $10. If a student buys 6 notebooks and spends $48, how many of each size did he buy?
They could buy 8 small notebooks or 3 large notebooks and 3 small notebooks.
Answer: just one way to do it. You can buy 3, large books and 3 small books
Step-by-step explanation:
10x3=30
48-30=18
18 divided by 3 = 6
I'd appreciate some help here
Answer:
6.6 is the correct number
Step-by-step explanation:
The base is 2.2 inches. The height is 3 inches. So the area is 2.2 × 3 = 6.6 square inches.
the ratio of 26,000 bytes to 48,000 bytes can be written in fractional form as
Answer:
26000:48000
26000/48000
26/48(cancel the zeros)
13/24
fractional form=13/24
Identify the point corresponding to P.
P′ (−2, 0)
P′ (−4, 0)
P′ (−3, −1)
P′ (−5, −3)
Answer:
(-4,0)
ignore this line
8. Which best describes the relationship between the line that passes through (-1, -8) and (4,-4) and the line
that passes through (2, -9) and (7,-5)?
a. parallel
b. perpendicular
C.
same line
d. neither perpendicular nor parallel
Considering the expression of a line, the correct answer is option a.) the relationship between the line that passes through (-1, -8) and (4,-4) and the line that passes through (2, -9) and (7,-5) is parallel.
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 represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Relationship between lines in this caseIn this case, you can calculated in this case:
Being (x₁, y₁)= (-1; -8) and (x₂, y₂)= (4; -4), the slope m can be calculated as:
m= (-4 - (-8))÷ (4 - (-1))
m= (-4 + 8)÷ (4 + 1)
m= 4÷ 5= 4/5
Considering point 1 and the slope m, you obtain:
-8= 4/5× (-1) + b
-8= -4/5 +b
-8 + 4/5= b
-36/5=b
The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 36/5.
Being (x₁, y₁)= (2; -9) and (x₂, y₂)= (7; -5), the slope m can be calculated as:
m= (-5 - (-9))÷ (7 - 2)
m= (-5 + 9)÷ (5)
m= 4÷ 5= 4/5
Considering point 1 and the slope m, you obtain:
-9= 4/5× (-2) + b
-9= -8/5 +b
-9 + 8/5= b
-37/5=b
The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 37/5.
You can see that the lines y=4/5x - 36/5 and y=4/5x - 37/5 have the same slope of 4/5 and different ordinates to the origin. So, this lines are parallel.
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Answer the question in photo.
Answer: 1/4
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that A'D'=2 and AD=8, so the scale factor is 2/8 = 1/4.
Identify all the sets which each number belongs. 15,-5.075,and π
The sets of numbers which each of the numbers given belong to as required in the task content is as follows;
15; Real, rational and Integers.-5.075; Real, rational and decimal.π; Real, Irrational and decimal.To what sets do all three numbers as given belong?As evident in the task content, the sets to which the three numbers belong is to be determined.
Hence, taking the numbers one after the other; we have;
15 => The number 15 belongs to the set of real numbers, rational numbers and most particularly, integers.
-5.075 => The number -5.075 belongs to the set of real numbers, rational numbers, and most particularly, decimals.
π => The number represented by π belongs to the set of real numbers, irrational numbers and it's numerical value is a non-terminal and non-repeating decimal.
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Ethan’s family used 16.8 gallons of gas to drive 428.4 miles .How many miles did they drive on each gallon of gas.
Answer: 25.5 miles per gallon. 16.8 gallons x 25.5 miles = 428.4 miles
F(4) if f(x) = 3 x -1
Answer:
f(4) = 11
Step-by-step explanation:
f(x) = 3 x -1
Let x = 4
f(4) = 3*4 -1
= 12-1
= 11
f (x) = 3x - 1
f (4) = 3 × 4 - 1
f (4) = 12 - 1
f (4) = 11
Hope Helpful :-;
Use proof by contradiciton to prove that the sum of the squares of two odd integers cannot be a perfect square. HINT: you can use the fact that the sum of two odd numbers must be even without proof
Assume to contrary that the sum of the squares of two odd integers can be the square of an integer. Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.
What is a square?A quadrilateral with four equal sides is called a square. There are the numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about square's characteristics, mathematics, and design.
A square has four corners and is closed, two-dimensional (2D) object.
Assume to contrary that the sum of the squares of two odd integers can be the square of an integer.
Suppose that x,y,z∈Z such that [tex]x^{2} +y^{2} =z^{2}[/tex], and x and y are odd.
Let, x=2m+1 and y=2n+1.
Hence,
[tex]x^{2} +y^{2} =(2m+1)^{2} + (2n+1)^{2}[/tex]
=[tex]4m^{2}+4m+1+4n^{2}+4n+1[/tex]
=[tex]4(m^{2}+n^{2}) + 4(m+n)+2[/tex]
=[tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex]
Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.
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1. An elevator in a tall building starts at a floor of the building that is 80 meters above the ground. The elevator descends2 meters every 0.5 seconds for 4 seconds. Identify the domain and range using the following formats and then graph.Inequality:Set Notation:
Let's begin by listing out the information given to us:
The elevator starts at 80 m
The elevator descends 2 meters every 0.5 seconds for 4 seconds
The inequality is given by:
[tex]\begin{gathered} y=80-2x \\ where\colon x=every\text{ 0.5}seconds \end{gathered}[/tex]The set notation is given by:
[tex]undefined[/tex]What is the relationship between multiplying and factoring? You multiply numbers or expressions to produce a (select). You factor a product into the numbers or(select)that were multiplied to produce it.
Answer:
Factoring polynomials is the inverse process of multiplying polynomials. After factoring a polynomial, if we divide the polynomial with the factors then the remainder will be zero.
Which expression is equivalent to t
3(x+24)?
A-2/3x+24
B-2/3x+16
C -2/3x-16
D 2/3x-16
What is the smallest possible degree that the polynomial can have and why?
Check the picture below.
ygftlgvhbjknlkm;l,';
./m
You purchase a home for $200,000 which appreciates at 2.5%. How much is it worth in 7 years?
Answer: The answer I came up with is: $237,737
please give answer fast and provide explanation so I know how to do it
for a sequence of events in which the first event can occur n 1 ways, the second event can occur n 2 ways, the third event can occur n 3 ways, and so on, the events together can occur a total of n 1 times n 2 times n 3 times ... ways. this is called .
The most appropriate choice for Independent event and multiplicative counting rule will be given by
This is known as multiplicative counting rule.
What is Independent event and multiplicative counting rule?
Event that is not dependent on any other event is called independent event.
Let A and B be two independent events.
P(A∩B) = P(A) [tex]\times[/tex] P(B)
If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.
Here,
Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on
Also assuming that the events are independent
The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways
This is known as multiplicative counting rule.
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1) The compound interest of a sum of money is Rs 13310 and in 4 years is Rs 14641. Find the rate of interest and sum.
The rate of interest is 10% and the sum is Rs 10,1000.
What is compound interest?The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.
The compound interest formula is given by
Compound Interest = Amount – Principal
Here, the amount is
[tex]A=P(1+\frac{r}{100} )^{n}[/tex] where,
A = amount
P = principal
r = rate of interest
n = time (in years)
Given:
C.I. of a sum of money in 3 years = Rs 13310
C.I. of a sum of money in 4 years = Rs 14641
Let the principal be P and the rate of interest be r%
Then, according to the question,
For 3 years:
[tex]13310=P(1+\frac{r}{100} )^{3}[/tex] ..... (1)
For 4 years:
[tex]14641=P(1+\frac{r}{100} )^{4}[/tex] ..... (2)
Dividing equation (2) by (1), we obtain
[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]
⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]
⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]
⇒[tex]r=\frac{100}{10}[/tex]
⇒ r = 10%
Now, substituting r in equation (1),
[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]
⇒[tex]13310=P(\frac{1331}{1000} )[/tex]
⇒P = Rs 10,000
Therefore, the rate of interest is 10% and the sum is Rs 10,1000.
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You cut a 90-foot rope into 6 pieces of equal length. What is the length of
each piece?
Answer:
Length = 15
Step-by-step explanation:
The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation
90 feet / 6 pieces
Which equals
90 feet / 6 pieces = 15 feet/piece (15 feet per peice)
Hope this helps :)
How is the graph of each equation related to
standard form Ax + By = C?
Answer:
When A = 0 and y = 1 and C = 2
0x + 1y = 2
y = 2 No matter what x is, y will always be 2 and this will create a horizontal line.
Step-by-step explanation:
0.3(6y + 15) = 1.8y + 4.5.
its hard
__________________________________________________________
Hello! In this question, we will be solving the given equation for the variable "y".
__________________________________________________________
Explanation:
In our question, we were given the following equation:
0.3(6y + 15) = 1.8y + 4.5To solve for our "y" variable, we will perform distributive property and simplify to get the value of "y".
__________________________________________________________
Solve:
[tex]0.3(6y + 15) = 1.8y + 4.5\\\\\text{Use the distributive property to distribute the "0.3"}\\\\1.8y+4.5=1.8y+4.5\\\\\text{Since both sides of the equal sign are equal, there will be infinite solutions}[/tex]
Proof:
[tex]\text{To prove that there are infinite solutions, we could continue to solve the}\\\text{equation:}\\\\1.8y+4.5 =1.8y+4.5 \\\\\text{Subtract 1.8y from both sides}\\\\4.5=4.5\\\\\text{Subtract 4.5 from both sides}\\\\0=0[/tex]
__________________________________________________________
Answer:
[tex]\boxed{\text{Infinite solutions}}[/tex]
__________________________________________________________
Find the area of the pool. Write as a polynomial.
Pool
6x
3x-5
Write the definition as a biconditional statement:
An equilateral triangle is a triangle with three congruent sides.
The term "if and only if" makes the sentence bi-conditional. A triangle is equilateral if and only if it has three congruent sides.
A conditional statement with its opposite expressed in the form of "if and only if," collectively known as a bi-conditional statement. Bi-conditional logic is the theory behind bi-conditional assertions.
This can be compared to the conditional sentence, "if this, then that." Due to the lack of a "if and only if," it is not bi-conditional. The reversal of a conditional statement's ability to produce a bi-conditional depends on whether it is also true.
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(ANSWER AT THE BOTTOM)A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular container costs the company $16, while the cylindrical container costs the company $15. If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs? Explain.
How many rectangular containers will be necessary to package 6,400 candles?
How many cylindrical containers will be necessary to package 6,400 candles?
Which container should the company use to minimize costs? Explain.
143,157,the rectangular containers,because it will cost the company $67 more to use the cylinder containers.
The number of rectangular containers will be necessary to package 6,400 candles is 143
The number of cylindrical containers will be necessary to package 6,400 candles is 157.
The container that would minimise cost is the rectangular container because it would $67 less to use the rectangular container.
Which container minimises costs?The first step is to determine the total cost of packing 6400 candles using the rectangular container.
Total cost = number of containers needed x cost of one rectangular container
Number of containers needed = total number of candles to be packages / number of candles the container can hold
6400 / 45 = 142.22 = 143 rectangular containers
Total cost = $16 x 143 = $2,288
The next step is to determine the total cost of packing 6400 candles using the cylindrical container.
Total cost = number of containers needed x cost of one cylindrical container
Number of containers needed = total number of candles to be packages / number of candles the container can hold
6400 / 41 = 156.1 = 157 cylindrical containers
Total cost = $15 x 157 = $2,355
Difference in costs = $2,355 - $2,288 = $67
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Hey could you help me make sure these are right . Thanks so much they points are at 50 and I’ll mark brainliest
Step-by-step explanation:
your answers are right in my pov
pls pls help whoever gets it right gets marked brainliest
Answer:
13 units
Step-by-step explanation:
[tex]d=√((x_2-x_1)²+(y_2-y_1)²) [/tex]
[tex] \sqrt{( - 2 - ( -14)^{2} } + ( - 4 - 1) {}^{2} [/tex]
[tex] \sqrt{12 {}^{2} } + ( - 5) {}^{2} [/tex]
[tex] \sqrt{169} [/tex]
= 13 UnitsPlease help me please
The equation y = 0.43x + 50 models the cost y of renting a car if the car is driven x
miles.
According to the model, what is the best estimate of the cost for renting a car if you
plan to drive 489 miles? Please round your answer to the nearest dollar.
By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.
What do we mean by equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.
Now, solve for y when the value of x is 489.
y = 0.43x + 5y = 0.43(489) + 5y = 210.27 + 5y = $215.27Rounding off: y = $215
Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.
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