If Zachary purchased a computer for $1600 on a payment plan. five months after he purchased the computer, his balance was $900. eight months after his balance was $480. The equation that models the balance y after x months is: y = -140x + 1600.
EquationMonth Balance
0 1600
5 900
8 480
Slopes:
(1600 - 900) / 5 = 700 / 5 = 140
(1600 - 480) / 8 = 1120 / 8 = 140
(900 - 480 ) / - 3 = - 140
Hence,
y = -140x + 1600
Therefore the equation is y = -140x + 1600.
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Tyrone's bank account had a balance of -$72.04 last week. His paycheck of $335.67 was deposited this week. If there have been no
other transactions, which of the following is true?
OA. Tyrone's current account balance is $263.63.
is $263
OB. Tyrone's current account balance is
$263.63.
OC. Tyrone's current account balance is -$407.71.
OD. Tyrone's current account balance is $407.71.
Hello, the correct answer to the question should be [tex]263.63[/tex] dollars.
Tyrone does not have any money in his bank account. Also, his balance contains a negative symbol, which means that he owes money to the bank.
[tex]Balance=-72.04[/tex]When his paycheck arrives, money will come into his account. This means that Tyrone will pay off his debt to the bank.
[tex]335.67-(72.04)[/tex]Since the money coming into his account and his balance have different symbols, we will add the two values and get the result.
[tex]=263.63[/tex] dollars.The size P of a small herbivore population at time t (in years) obeys the function P(t) = 600e0.16t if they haveenough food and the predator population stays constant. After how many years will the population reach 3000?Round to the nearest hundredth.F) 10.06 yrG) 16,31 yrH) 48.65 yrD 19.86 yr
Given the function
[tex]P(t)=600e^{0.16t}[/tex]When P(t)=3000
[tex]\begin{gathered} P(t)=3000 \\ 600e^{0.16t}=3000 \end{gathered}[/tex][tex]\begin{gathered} \text{divide through by 600} \\ e^{0.16t}=\frac{3000}{600} \\ e^{0.16t}=5 \\ 0.16t=in5 \\ 0.16t=1.6094 \\ t=\frac{1.6094}{0.16} \\ t=10.05899yr \\ t=10.06yr(\text{nearest hundredth)} \end{gathered}[/tex]Hence, it will take 10.06yr for the population to reach 3000, option F
∠c and ​∠d​ are vertical angles with m∠c=−3x 58 and m∠d=x−2. what is m∠d? enter your answer in the box. ​ °
D has a value of 13 using vertical angles.
What is a vertical angle?
When two lines intersect, the angles that face each other are called vertical angles.Instead of referring to them as being up-down, "vertical" in this context denotes that they share a vertex (corner point).Assuming that C and D constitute vertical angles
The formula is C = (-3x) + 58 and D = x - 2.
We must ascertain what D's measurement is.
Vertical angles are really a pair of opposing angles created when two lines cross.
A and B in the figure represent vertical angles. C and D are also.
Angles vertically are always congruent. Accordingly, in this illustration, A, B, and C, D
Therefore, value of C = D (-3x)+ 58 = x – 2
By assembling,
(-3x )- x = (-2) - 58
By doing more math, 4x = 60 (-4x = - 60)
4 x = 60/4 x = 15 when both sides are divided.
So, ∠D = (x - 2) and
= 15 - 2
So, ∠D = (x - 2) and
Consequently, D has a value of 13 using vertical angles.
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A recipe book shows measurement conversions for cups to tablespoons. It shows that 0.5 cup equals 8 tablespoons and 1.5 cups equals 24 tablespoons.
Write an equation that shows the proportional relationship between cups and tablespoons where c represents cups and n represents tablespoons.
n = 0.0625c
c = 0.0625n
n equals 0.5 over 8 times c
c equals 8 over 0.5 times n
I have to submit this today pls hurry
AND THANK YOU SO MUCH
An equation that shows the proportional relationship between cups (c) and tablespoons (n) is: B. c = 0.0625n
What is a proportion?A proportion is an equation which is typically used to indicate the equality of two (2) ratios. Therefore, proportions can be used in mathematics to show that two (2) ratios are equivalent and then used to calculate or determine all of the unknown quantities.
Mathematically, a proportional relationship can be represented by the following equation:
y = kx
Where:
y and x represent the variables in a proportional relationship.k is the constant of proportionality.Let the cups be represented by c.
Let the tablespoons be represented by n.
Next, we would determine the constant of proportionality (k) as follows:
c = kn
Making k the subject of formula, we have:
k = c/n
k = 0.5/8 ≡ 1.5/24
k = 0.0625.
Substituting the parameters into the equation for a proportional relationship, we have;
c = kn
c = 0.0625n
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Answer:
C = (8/.5)n
Step-by-step explanation:
.5 = 8
1.5 = 24
C = (8/.5)n
Because
8 divided by .5 = 16
16 * .5 = 8
Ex.2
8 divided by .5 = 16
16 * 1.5 = 24
Use on of the equations:Bag Price ÷ Pounds in Bag = Cost/pound
Cost/pound x Pounds fed = Cost/day
Cost/day x # of Horses = Cost/head/day
Cost/head/day x # of days in month = Cost/head/month
1. You have 5 horses and you feed 4.5 pounds of grain to each in one day. What is the monthly cost per head to feed them if the grain you feed is $27.00 per 50lb bag?
2. You have 32 heads of horses, and each gets 1.5 pounds of grain per feeding. You feed grain twice a day, once in the morning and once in the evening. If you feed grain that costs $13 per 50lb bag, then is the cost per head per month?
3. You have 12 heads of horses, and each gets 2.5 pounds of grain per feeding. You feed grain twice a day, once in the morning and once in the evening. If you feed grain that costs $13 per 50lb bag, then is the cost per head per month?
Solving the questions from the given equations
1)the monthly cost per head to feed them if the grain you feed is $27.00 per 50lb bag is $16.2
2) The cost per head per month is $23.4
3) The cost per head per month is $39
What is Equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
1) The grains use feed for one horse = 4.5pound
The cost of 1 bag of grain = $27 per 50lb
The cost of 1lb grain = $0.54
Now the monthly cost of the grain will be:
Cost/head/day x # of days in month = Cost/head/month
$0.54 x 30 = $16.2
Hence, the monthly cost per head to feed them if the grain you feed is $27.00 per 50lb bag is $16.2
2) The amount of grain use to feed for one head = 1.5pound
If the grain is feed twice a day = 1.5 x 2
= 3.0
The cost of the grain = $13 per 50lb
The cost of 1lb grain = 13 / 50
= $0.26
The cost of grain feed in one day = 0.26 x 3
= $0.78
The cost of per head per month =
0.78 x 30 = $23.4
Hence, The cost per head per month is $23.4
3)The amount of grain use to feed for one head = 2.5pound
If the grain is feed twice a day = 2.5 x 2
= 5pounds
The cost of the grain = $13 per 50lb
The cost of 1lb grain = 13 / 50
= $0.26
The cost of grain feed in one day = 0.26 x 5
= $1.3
The cost of per head per month =
1.3 x 30 = $39
Hence, The cost per head per month is $39
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What is the difference of a number s and 6
An expression is
.
Answer:
s-6
both of them are elements
but s is a letter while 6 is a number so these can not subtract each other because they are different values
Help asap. 30 points
Answer:
The terms are rearranged, so the Commutative Property is correct.
12 divided by 11 in fraction form
Answer: if you are talking about mixed number form the answer is 1 1/11 the improper/exact form would just be twelve over eleven (12/11)
Step-by-step explanation:
1/2Hd=d^2 solve for b
The solution of the equation for b is b= 2d²/H
What is subject of formula?This involves taking a variable in an equation to stand alone
Note that this variable is different from the initial isolated variable
How to determine the equation for b?The equation is given as
1/2Hb = d²
Divide both sides of the equation by H
So, we have the following equation
1/2Hb/H = d²/H
Multiply both sides of the equation by 2
So, we have the following equation
2 * 1/2Hb/H = d²/H * 2
Evaluate the quotients and the products
b= 2d²/H
The above computation implies that:
We changed the subject of the formula in the equation 1/2Hb = d² from d² to b
This implies that solving for b is a concept of subject of formula
Hence, the solution is b= 2d²/H
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can u answer this, its for homework. Thx!
It is to be noted that the distance between P and ρ is: [tex]\approx[/tex] 15.52
This solution is arrived at using the Line Segment theorem. See further explanation below.
What is the line segment theorem?The length of the line segment connecting two points in a plane is defined as the distance between two points. The method for calculating the distance between two locations is often written as
[tex]d = \sqrt{((x_{2} – x_{1})² + (y_{2} – y_{1})²).} [/tex]
Hence, since we have ρ is to contain two points, we will solve as follows:
Distance between ρ and P where ρ is (0, -3) and (7,4)
we have to multiply the coordinates.
To multiply coordinates, you have to multiply the corresponding values.
That is
[tex]x_{1} \times x_{1} [/tex]
and
[tex]y_{1} \times y_{1}[/tex]
In this case:
x1 = 0
[tex]x_{1} = 0[/tex]
also
[tex]x_{1} = 7[/tex]
[tex]y_{1} = - 3[/tex]
also
[tex]y_{1} = 4[/tex]
Hence, for
[tex]x_{1} = 0 \times 7 = 0[/tex]
for
[tex]y_{1} = - 3 \times 4 = 12[/tex]
Hence, solving for the distance between P and ρ, we'd use coordinates of P as = (4, 3); and coordinates of ρ as = (0, -12)
Recall that distance is given as
[tex]d = \sqrt{((x_{2} – x_{1})² + (y_{2} – y_{1})²).} [/tex]
Hence,
d = √((0-4)² + (-12-3))²)
[tex]d = \sqrt{{(( {0 - 4}^{2} }) + { (- 12 - 3)}^{2} } [/tex]
Expand the brackets
[tex]d = \sqrt{ { - 4}^{2} + ( { - 15}^{2} } )[/tex]
[tex]d = \sqrt{16 + 225} [/tex]
[tex]d = \sqrt{441} [/tex]
d = 15.5241746963
Approximately,
d = 15.52
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Solve for x and y
35x-21y=10
5x-3y=2
Answer:
B. There is no solution
Step-by-step explanation:
35x - 21y = 10
5x - 3y = 2
---------------------
(5x - 3y = 2) × (-7)
= (-35x + 21y = -14)
---------------------------
35x - 21y = 10
-35x + 21y = -14
-------------------------
= (-4)
No Solution
I hope this helps!
The system of equation 35x - 21y =10 and 5x-3y=2 has no solution , Option B is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equation is 35x - 21y =10 and 5x-3y=2
We can use elimination method to solve for x and y.
First, we can multiply the second equation by 7 to get:
35x - 21y = 10
35x - 21y = 14
Next, we can subtract the second equation from the first equation to eliminate the x terms:
35x - 21y - (35x - 21y) = 10 - 14
0 = -4
This is a contradiction, so there is no solution for x and y that satisfies both equations. The system is inconsistent.
Hence, the given system of equation 35x - 21y =10 and 5x-3y=2 has no solution , Option B is correct.
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4 = - 2/3 x whats the answer
hello
[tex]4=-\frac{2}{3}x[/tex]to solve for x, let's cross multiply both sides
[tex]\begin{gathered} 4=-\frac{2}{3}x \\ 4\times3=-2x \\ 12=-2x \end{gathered}[/tex]step 2
divide both sides by -2
[tex]\begin{gathered} 12=-2x \\ \frac{12}{-2}=-\frac{2x}{-2} \\ x=-6 \end{gathered}[/tex]x = - 6
Answer:
x = -6
Step-by-step explanation:
is 4 2/3 greater than 4 5/6
Answer:
4 [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Make them equivalent
4 [tex]\frac{2}{3}[/tex] if I multiply the numerator (top) and the denominator (bottom) by 2 I get
4[tex]\frac{4}{6}[/tex]
4 [tex]\frac{5}{6}[/tex] is greater than 4 [tex]\frac{4}{6}[/tex]
Environmentalists estimate an annual population decrease of giraffes in the wild of 3.5% due to development. This can be modeled by the function p(x) = 140,000(0.965)x, where x is the number of years of tracking the populations. Conservationists have developed a sanctuary that has shown the ability to increase the population by 0.85% per year. The increase can be modeled by the function S(p) = p(1.0085)x.
Which function represents S(p(x)), rounded to the nearest ten thousandth?
S(p(x)) = 135,100(0.9732)x
S(p(x)) = 135,100(1.9735)x
S(p(x)) = 140,000(0.9732)x
S(p(x)) = 140,000(1.9735)x
The equation of the function S(p(x)), rounded to the nearest ten thousandth is S(p(x)) = 140,000(0.9732)ˣ option (C) is corrrect.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The equation of the function:
p(x) = 140,000(0.965)ˣ
Which is the annual population decrease of giraffes in the wild of 3.5% due to development.
Plug x = 1.0085
[tex]\rm p(x) = 140,000(0.965)^{1.0085}[/tex]
S(p(x)) = 140,000(0.965)ˣ(1.0085)ˣ
S(p(x)) = 140,000(0.9732)ˣ
Thus, the equation of the function S(p(x)), rounded to the nearest ten thousandth is S(p(x)) = 140,000(0.9732)ˣ option (C) is corrrect.
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Solve this system of equations by eliminating.
5x + 7y=3
-5x + 7y=-17
The value of x is 2 is and y is -1 is after solving equation by elimination method
what is linear equation ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
What is elimination method ?To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
5x + 7y=3 .....(i)
-5x + 7y=-17......(ii)
Solve equation ii and iii
-5x + 7y=-17
5x + 7y=3
14y = -14
y = -1
put the value of y in equation 1
5x + 7y=3
5x + 7(-1)=3
5x - 7 = 3
5x = 10
x =2
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Part 2 - Find the error(s) and solve the problem correctly.
Simplify:
[tex](x^\frac{3}{5} )^\frac{7}{5}[/tex]
Answer:
[tex](x^\frac{3}{5} )^\frac{7}{5} = (x^\frac{10}{5} )=x^2[/tex]
The simplified expression is as follows;
[tex](x^{\frac{3}{5} } )^{\frac{7}{5} } = x^{\frac{21}{25} }[/tex]The error was made because you didn't multiply the powers.
How to simplify an expression?The expression can be simplified as follows;
[tex](x^{\frac{3}{5} } )^{\frac{7}{5} }[/tex]
Using the law of indices,
If a base variable is raised to a number (y) and the entire number raised to power (x), then it is equal to the base number raised to the multiplication of the two exponents (x × y) i.e.
Hence,
[tex](A^{x} )^{y} = A^{xy}[/tex]
Therefore, let's apply the rule,
[tex](x^{\frac{3}{5} } )^{\frac{7}{5} } = x^{\frac{3}{5}.\frac{7}{5} }[/tex]
Hence,
[tex](x^{\frac{3}{5} } )^{\frac{7}{5} } = x^{\frac{3}{5}.\frac{7}{5} } = x^{\frac{21}{25} }[/tex]
Therefore, using the law of indices,
[tex](x^{\frac{3}{5} } )^{\frac{7}{5} } = x^{\frac{21}{25} }[/tex]
The error was that he did not multiply the exponents.
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Isabella draws a mystery number from a bag with various integers inside and then describes it to the class read the clues below and then Circle all of the integers that it could be
1. The opposite of the integer is positive
2. The absolute value of the integer is positive
3. The integer is not zero
-8
11
15
-21
An integer exists a whole number that can be positive, negative, or zero and is not a fraction.
What is meant by an integer?Unlike fractional numbers, integers can only be positive, negative, or zero. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. An integer is a whole number that can be positive, negative, or zero and is not a fraction.
Any number that exists a part of a collection of all the aforementioned number categories is considered an integer. Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
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pls help will mark brainliest
The value of n for a line that passes through point A(n, 4) and point B(6, 8) and is parallel to y = 2x - 5 is 6.
What is a parallel line?No matter how far we extend a parallel line, it will always remain straight. Take a look at the parallel lines in the following illustration. Lines "p" and "q" are parallel to each other as are lines "a" and "b."
We know that parallel lines have same slope, so the slope of y = 2x - 5 is 2 according the y intercept form, y = mx + b
Now using the point-slope form we will find the line parallel to Point B (6, 8)
y − y₁ = m(x − x₁)
Put m as 2, y₁ as 8 and x₁ as 6, and we wil get
y − 8 = 2(x −6)
y = 2x − 4 or
2 = (y + 4)/x (slope)
We will us point-slope form for point A(n, 4) too
y − 4 = 2(x −n)
y = 2x − 2n + 8 or
2 = (y - 8 + 2n)/x
As slope 2 is same in both points it means their equations are same too
(y + 4)/x = (y - 8 + 2n)/x
Lest solve for n
(y + 4)/x = (y - 8 + 2n)/x
y + 4 = y - 8 + 2n
4 = - 8 + 2n
4 + 8 = 2n
2n = 12
n = 12/2
n = 6
Thus, the value of n for a line that passes through point A(n, 4) and point B(6, 8) and is parallel to y = 2x - 5 is 6.
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Madison’s band used to practice for 50 minutes every Tuesday. Now they practice 130% as many minutes as they used to. How many minutes do they play on Tuesdays now?
Corey’s cat weighed 4 pounds. A year later, it weighed 175% of its previous weight
Answer: 65 min
7 pounds
Step-by-step explanation:
what is the value of x
Answer:
x = 70
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × 3 = 540°
sum the interior angles and equate to 540
x + 160 + 110 + 105 + 95 = 540
x + 470 = 540 ( subtract 470 from both sides )
x = 70
Can someone explain powers of imaginary numbers? (like i^2, i^3, i^4, and so on)
The powers of the imaginary number gives:
i² = -1i³ = -ii⁴ = 1i = i⁵i² = i⁶i³ = i⁷i⁴ = i⁸etc...
How the powers of imaginary numbers work?We know that the imaginary number is defined as:
i = √(-1)
If we square it, then we get:
i² = √(-1)² = -1
As the exponent 2 removes the square root.
With the exponent 3 we get:
i³ = √(-1)³ = √(-1)²*√(-1) = -1*i = -i
i³ = -i
Finally, the exponent 4 gives:
i⁴ = i²*i² = (-1)*(-1) = 1
And now the cycle repeats, we will have that:
i = i⁵
i² = i⁶
i³ = i⁷
i⁴ = i⁸
etc...
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given the system y=-1/2x-1 and -1/4x+y+4=0 write the solution to the system on the space provided below as an ordered pair
The solution to the system of equations as an ordered pair is (4, -3).
We are given a system of linear equations in two variables. The first equation is y = (-1/2)x-1. The second equation is (-1/4)x+y+4 = 0.
We need to find the solution of the system of equations. We will use the substitution method to solve for the values of "x" and "y".
y = (-1/2)x - 1
(-1/4)x + y + 4 = 0
Substitute the value of "y" from the first equation into the second equation.
(-1/4)x + (-1/2)x - 1 + 4 = 0
(-3/4)x+3 = 0
(3/4)x = 3
x = 4
Substitute the value of "x" back into the first equation to get the value of "y".
y = (-1/2)x - 1
y = (-1/2)4 - 1
y = -2 - 1
y = -3
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Pls help, What is X equal to?
Answer:
-55
Step-by-step explanation:
Orenda opened a savings account with $4500 that earns 0.6% simple interest annually. After how many years will the balance of
the account be $4635? Round to the nearest tenth, if necessary.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$4635\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 0.6\%\to \frac{0.6}{100}\dotfill &0.006\\ t=years \end{cases} \\\\\\ 4635=4500[1+(0.006)(t)]\implies \cfrac{4635}{4500}=1+0.006t\implies \cfrac{103}{100}=1+0.006t \\\\\\ \cfrac{103}{100}-1=0.006t\implies \cfrac{3}{100}=0.006t\implies \cfrac{3}{0.6}=t\implies \boxed{5=t}[/tex]
How many 5-digit numbers can you form using the digits 8 and 9?
Answer:
88888
88889
88898
....
2^5 = 32
Approximately How many times greater is 1.7 x 10^6 then 3.5 x 10^5?
a = 86.4 rounded to 1 DP b = 2.81 rounded to 2 DP Find the maximum of a - b
83.59 is the solution of linear equation a- b .
What are examples of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5. It is rather simple to locate both intercepts when an equation is stated in this way (x and y).The expression on the left is known as a linear expression because it can be used to solve the equation y = 2x+4 with two variables, which has a graph that is in a straight line. Thus, we refer to 2x+4 as a linear equation (or, later, a linear function).a = 86.4
b = 2.81
So,
Substitute = 86.4 - 2.81
Calculate the sum or difference = 83.59
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A particle is moving on the x-axis and the position of the particle at time t is given by x(t), whose graph is shown above. Which of the following is the best estimate for the speed of the particle at time t=4 ? Responses 0
The speed of the particle at time t=4 is 5 units.
We are given the x(t) vs time curve.
To find:
Speed of particle at t = 4
We know that the slope of x-t curve represents the speed of the particle.
To calculate the speed of the particle at t = 4, We will calculate the slope of the curve at t = 4
Slope = y₂ -y₁ / x₂ - x₁
Slope = 40 - 10 / 6 - 0
Slope = 30 /6
Slope = 5
From here we can say that the slope of the curve between x = 0 and x = 6 is equal to 5.
So the value of speed is also 5 units.
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Tommy's weekly pay is directly proportional to the number of hours he works at the movie theater. His pay is $189 for 21 hours. Find the amount of pay for 40 hours of work.
We need to find the amount Tommy is paid per hour. This is simple:
r = 189/21
r = 9
Now, to find the amount he is paid, the equation is as follows:
y = rx
For 40 hours, the equation is:
y = 9(40)
y = 360
Answer:
Step-by-step explanation:
r = 189/21
r = 9
Now, to find the amount he is paid, the equation is as follows:
y = rx
For 40 hours, the equation is:
y = 9(40)
y = 360
A set of data is represented in the stem plot below.
Part A: Find the mean of the data. Show each step of work. Round answer to the nearest whole number. (2 points)
Part B: Find the median of the data. Show each step of work. (2 point)
Part C: Find the mode of the data. Show each step of work. (2 point)
Part D: Compare your values for mean, median, and mode from parts A, B, and C. Explain which value would best represent the data, and why? (4 points)
A. Mean = 71
B. Median = 75
C. Mode = 0
D. Mean is used to represent data, because mean measures central tendency.
What is mean , median and mode?From the given stem we have to write a data set ,
Data set = 35, 42, 43, 51, 55, 57, 62, 66, 68, 69, 74, 75, 76, 77, 78, 79 , 82, 84, 86, 88, 93, 94, 101
Mean = average
= sum of all numbers / total number of values .
= 1635 / 23
= 71.08 = 71
Median = middle term
Total there are 23 terms so middle term is the 12th term .
So median = 75
Mode = Most repeated term or term that has high frequency.
Here no terms are repeating so mode = 0
By comparing mean , median and mode ,
Mean is used to represent data .Because, the mean is the most commonly used measure of central tendency because it averages all of the values in the data set.
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