Answer: You must put the highest exponent of the variable first, and then proceed in descending order.
Step-by-step explanation:
This is done to keep track of the powers much easier and also just looks nicer. ^^
Suppose that you borrow $15,000 for 4 years at 5% toward the purchase of your car. use pmt to find the monthly payments and the total interest for the loan
The formula for the monthly loan payment is given as
[tex]A\text{ = }P(\frac{r(1+r)^n}{(1+r)^n-1})[/tex]Where
P = loan amount ( initial principal) = $15000
A= Payment amount per period = ?
r = interest rate per period = (5/12) x (1/100) =0.0041667
n = total number of payments or periods = 4 years = 4 x 12 = 48 months
Substituting all these into the above equation gives
[tex]A\text{ =15000( }\frac{0.0041667(1+0.0041667)^{48}}{(1+0.0041667)^{48}-1})[/tex][tex]A\text{ = 15000(}\frac{0.0041667(1.0041667)^{48}}{(1.0041667)^{48}-1})[/tex][tex]\begin{gathered} A\text{ = }15000(\frac{0.0041667\text{ }\times1.2208973}{1.2208973\text{ - 1}}) \\ A=\text{ 15000(}\frac{0.005087112781}{0.2208973}) \end{gathered}[/tex][tex]\begin{gathered} A=15000(0.023029311) \\ A=\text{ \$345.4396759} \end{gathered}[/tex]So each month he pays $345.44 to the nearest cent
B)
The total interest for the loan is given by
Total amount paid over the total period of time - Original amount borrowed
Total amount paid over the total period of time = 345.44 x 48 months = $16581.12
The total interest of the loan hence = $16,581.12 - $15,000 = $1,581.12
The total loan interest to the nearest cent = $1,581.12
Harold filled his swimming pool over the weekend. The pool has a capacity of 540 gallons. Harold put in 180 gallons of water on Saturday. The garden hose that Harold used supplies 9 gallons of water per minute. How long did it take for Harold to fill the pool to capacity on Sunday? Define a variable for the unknown quantity. Write and solve an equation to answer the question.
Pool Capacity = 540 gallons
Saturday = 180 gallons
Hose water rate = 9 gallons per minute
540 = 180+9m
Where m is the number of minutes (independent variable)
Solve for m :
540-180 = 9m
360 = 9m
360/9= m
40 =m
It will take 40 minutes.
y=x-7
5x+2y = 7
Use the substitution method.
O (0, -7)
O (-1, -8)
O (7,0)
O (3, 4)
-
Answer:
(3, -4)
Step-by-step explanation:
To solve the system of equations by substitution, start by labelling the 2 given information.
y = x - 7 -----(1)
5x + 2y = 7 -----(2)
Substitute (1) into (2):
5x + 2(x - 7) = 7
Expand:
5x + 2x - 14= 7
7x = 14 + 7
7x = 21
Divide both sides by 7:
x = 21 ÷ 7
x = 3
Substitute into (1):
y = 3 - 7
y = -4
Thus, the solution to the equations is (3 , -4).
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Autumn has 55 cups of yogurt to make smoothies. Each smoothie uses 1/3
cup of yogurt. How many smoothies can Autumn make with the yogurt?
The total number of smoothies that Autumn can make with the yoghurt is 165.
We know that the total number of cups of yoghurt that Autumn needs to make smoothies is 55. Each smoothie uses 1/3 cup of yogurt. We need to calculate the total number of smoothies that Autumn can make with the yogurt.
Let the total number of smoothies be represented by the variable "N''. We will use the unitary method. The total number of smoothies that can be made is the ratio of the total number of cups of yoghurt to the fraction of a cup used to make one smoothie.
N = 55/(1/3)
N = 55*3
N = 165
Hence, Autumn can make 165 smoothies from 55 cups of yogurt.
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Solve the following equationX-3(x+2)=4 X - 3 ( x + 2 ) = 4
Given: X-3(x+2)=4X-3(x+2)=4
Find: the solution of the given equation
Explanation:
[tex]\begin{gathered} X-3(x+2)=4 \\ X-3x-6=4 \\ X-3x=10......................(1) \\ 4X-3(x+2)=4 \\ 4X-3x-6=4 \\ 4X-3x=10...........................(2)\text{ } \end{gathered}[/tex]on solving equation (1) and (2) , we get
Answer:
x = -5
Step-by-step explanation:
Solve for 'x':x - 3(x + 2)= 4
x - 3x - 3*2 = 4 {Distributive property}
x - 3x - 6 = 4
Combine like terms in LHS,
-2x - 6 = 4
Add 6 to both sides,
-2x = 4 + 6
-2x = 10
Divide both sides by (-2)
x = 10 ÷ (-2)
[tex]\sf \boxed{x= -5}[/tex]
A box contains four tiles numbered 1,4,5 and 8 as shown . Kelly randomly chooses one tile , places it back in the box, then choose a second tile. what is the probability that the sum of two chosen tiles is greater than 7? A. 1/4 B. 5/16 C. 2/3 D. 11/16
Since Kelly chooses one tile, places it back in the box, and then choose another tile, we have that the total outcomes are 4x4 = 16.
Now, we can write easily all the outcomes :
[tex]\begin{gathered} \Omega=\mleft\lbrace(1,1\mright),(4,1),(5,1),(8,1), \\ (1,4),(4,4),(5,4),(8,4), \\ (1,5),(4,5),(5,5),(8,5), \\ (1,8),(4,8),(5,8),(8,8)\} \end{gathered}[/tex]notice that on the first row, only the event (8,1) gives us that the sum is greater than 7.
On the second row,we have the same for events (4,4),(5,4) and (8,4)
On the third row only (1,5) gives us a sum lesser than 7, then here we have 3 more events that fit our criteria.
On the last row, all events gives us a sum greater than 7,then we have another 4 events.
Then, the probability that the sum of two chosen tiles is greater than 7 is:
[tex]\frac{1}{16}+\frac{3}{16}+\frac{3}{16}+\frac{4}{16}=\frac{11}{16}[/tex]Which expression is equivalent to the fraction below?
2/5
A. 2.2
B. 5.5
C. 5.2
D. 2.5
E. 2+5
F. 2 ÷ 5
Answer:F
Step-by-step explanation:
2/5=2 ÷ 5=0.4
8 squares and 10 triangles. What is the simplest ratio
The ratio for 8 squares and 10 triangles is 4:5.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, the ratio for 8 squares and 10 triangles will be:
= Number of square / Number of triangle
= 8/10
= 4/5
The ratio is 4:5.
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Solve two and one-third times four-fifths equals blank.
four-sixths
one and twelve-fifteenths
one and thirteen-fifteenths
four and four-sixths
The solution to the fraction two and one-third times four-fifths equals one and thirteen-fifteenths.
The correct answer option is option C
How to solve the product of a fraction?A fraction refers to a part of a whole, especially a comparatively small part. It is also the ratio of two numbers, the numerator and the denominator, usually written as one above the other and separated by a horizontal bar.
A numerator is the number above the horizontal bar while the denominator is the number below the horizontal bar in a fraction.
Two and one-third times four-fifths
= 2 1/3 × 4/5
= 7/3 × 4/5
= (7 × 4) / (3 × 5)
= 28 / 15
= 1 13/15
Therefore, the fraction two and one-third times four-fifths equals one and thirteen-fifteenths.
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Which sum or difference is modeled by the algebra tiles?-1OA (x2 - 2x + 3) - (-x2 - 4x - 2) = 2x - 1OB. (x2 - 2x - 3) + (x2 - 4x + 2) = 2x - 1OC. 02 - 2x - 3) - (x2 + 4x + 2) = 2x - 1OD. (x2 - 2x-3) + (-x2 + 4x + 2) = 2x - 1© 2021 Edmentum. All rights reserved.
Okay, here we have this:
We will take as the first term the upper squares and as the second term the lower ones, and we obtain that:
[tex]\begin{gathered} (x^2-x-x-1-1-1)+(-x^2+x+x+x+x+1+1) \\ =(x^2-2x-3)+(-x^2+4x+2) \\ =2x-1 \end{gathered}[/tex]Here we obtain that the correct answer is the option D.
154= -4(8+6r)+24r I want to know the answer
The equation 154 = -4(8+6r) + 24r has no solution because the variable becomes 0.
How to solve equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
We have to find the variable r of the equation to solve the equation.
A variable is a number represented with letters in an equation.
Therefore, let's find the variable r in the equation.
154 = -4(8+6r) + 24r
open the brackets on the right side of the equation
154 = - 32 - 24r + 24r
154 = -32 + 0
Therefore, the equation cannot be solved.
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The sum of 3 consecutive evennumbers add up to 1002. Find the threenumbers.
Let the three consecutive even number be,
x, x+2, x+4
Sum of the numbers is 1002.
[tex]\begin{gathered} x+x+2+x+4=1002 \\ 3x+6=1002 \\ 3x=996 \\ x=332 \end{gathered}[/tex]Hence, the numbers are,
332, 332+2, 332+4
Hence, the answer is 332, 334, 336.
These two lines are parallel. Write an equation for each.
Answer:
Top: y = x
Bottom: y = 0.8x - 3.2
Step-by-step explanation:
I can see the question is asking to write the equation in Slope-Intercept form.
Slope-Intercept Form:
y = mx+b
M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.
Because these lines are parallel, we know they have the same form.
Lets look at the top line. When x increases by one, how much does y increase by?
1
What is the y value of when the line's x-value is 0?
0
Now, we have,
y = 1x + 0
Because adding 0 keeps the equation the same, we can remove it.
y = 1x
Because multiplying a term by 1 leaves it the same, we can remove one.
y = x
Now, for the bottom line.
How much does y increase by when x increases by 1? Because the slope will be a fraction and is not easy to see, I will use the slope formula.
Slope Formula:
[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
To find the slope, take any pair of points on the line and plug them in.
I'll use:
(0,-3.2)
(4,0)
Plug the y-values (the latter number, or the height of the point) into the formula. Do the same with the x-values. keep in mind it does not matter what y-value you plug in. For example, for [tex]y_2[/tex] and [tex]y_1[/tex] you can plug in -3.2 and 0 or vice versa. If you make [tex]y_2[/tex] -3.2, then make [tex]x_{2}[/tex] 0.
[tex]\frac{-3.2-0}{0-4}[/tex]
Simplify.
[tex]\frac{-3.2}{-4}[/tex]
Because a negative number multiplied or divided by another negative number is always a positive number, remove the negative signs.
[tex]\frac{3.2}{4}[/tex]
Divide.
3.2/4 = 0.8
Now we have m, the slope on the 2nd line, 0.8
y = 0.8x + b
What is the y-value of the line when the line has the x-value of 0? On the graph, it says -3.2.
y = 0.8x - 3.2
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: Width = 3.4 meters, Length = 6.4 meters
Step-by-step explanation:
If the width is [tex]w[/tex], then the length is [tex]w+3[/tex].
[tex]w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4[/tex]
Select the transformations of g(x) = |1-2x+6| in relation to the parent function. HURRY PLEASE!!!
Answer:
Translated right [tex]\frac{7}{2}[/tex] units and vertical stretch
OR
translated right 3.5 units and vertical stretch
bcz
[tex]\frac{7}{2} =3.5[/tex]
Step-by-step explanation:
The absolute function is given as:
[tex]g(x) = |1-2x+6|[/tex]
If we simplify the equation, then we have
[tex]g(x) = |1-2x+6|\\g(x)=|-2x+6+1|\\g(x)=|-2x+7|\\g(x)=2|x-\frac{7}{2} |[/tex]
Now we can say that the transformation of g(x) to the parent function will be translated right [tex]\frac{7}{2}[/tex] units and vertical stretch (bcz you have a number (2) multiplying the function).
If the sign of the number that adds to the independent variable is negative, the transformation will be translated to the right, and if it is positive, it will be translated to the left.
3.13 Which triangle congruence postulate or theorem proves that these triangles are congruent?
The triangle congruence postulate which proves that these triangle are congruent is SAS (Side Angle Side).
According to the SAS Postulate,
Two triangles are said to be congruent if their two sides and included angles are identical to those of another triangle's two sides and included angle.
According to the figures of the triangles, we can see
AC = XZ (Side)
∠ACB = ∠XZY (Angle)
BC = YZ (Side)
Hence, ΔABC ≅ ΔXYZ by SAS postulate.
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i need help on this math assignment
Answer: 3rd one is correct
Step-by-step explanation: got it right on the test
Which of the following values are in the domain of the function graphed below? Check all that apply. A. -4 B. -1 C. 4D. 0E. 5 F. -2
Checking the given graph, it can be seen that the range of values of x is
[tex]\begin{gathered} rangeofvaluesofx, \\ -2\leq x\leq4 \end{gathered}[/tex][tex]undefined[/tex]The range of values of x are the values of the domain of the graph function
A. -4; -4 does not satisfy the function of the graph
A ski resort rents snowshoes in the winter. the resort charges $1 per day and a flat fee of $3 to cover cleaning. write an equation that shows how the cost y, depends on the length of the rental in the day, x.
Answer:
3+ 1x = y
Step-by-step explanation:
a flat rebate means no matter how many days it will only be $3 so you add the 3 and you don’t know how many day you’ll rent the shoes so you put a variable next to the 1 and the 1 times however many days plus 3 will be your cost
How many solutions does this equation have?
4v = -6 + 5v
no solution
one solution
infinitely many solutions
Submit
4
Answer:
One Solution
Step-by-step explanation:
v can only equal 6
Find the value of X express each answer as a decimal rounded to the nearest 10th
x = 11.1
Explanations:Note that the Pythagora's theorem is applied in solving this exercise
The Pythagora's theorem states that "the square of the hypotenuse equals the sum of the squares of the other two sides"
Hypotenuse is the longest side of the right-angled triangle:
Hypotenuse = 22
[tex]\begin{gathered} 22^2=19^2+x^2 \\ 484\text{ = }361+x^2 \\ x^2\text{ = 484 - 361} \\ x^2\text{ = }123 \\ x\text{ = }\sqrt[]{123} \\ x\text{ = }11.1 \end{gathered}[/tex]Avenger uses 9.4 pints of white paint and blue paint to paint her bedroom walls 4/5 of this amount is white paint in the breast is blue paint how many pints of blue paint did you use to paint her bedroom walls
Avenger uses 9.4 pints of white paint and blue paint to paint her bedroom walls 4/5 of this amount is white paint in the breast is blue paint how many pints of blue paint did you use to paint her bedroom walls
Let
x ----> pints of blue paint
y ----> pints of white paint
we have
x+y=9.4 -----> equation A
y=(4/5)*9.4
y=7.52
Find the value of x
x=9.4-y
x=9.4-7.52
x=1.88
therefore
answer is
1.88 pints of blue paintThe graph of FX), shown below, has the same shape as the graph ofG(X) = x2, but it is shifted to the left 3 units. What is its equation?FX) ----A. F(x) = x² + 3B. FX) = (x - 3)2C. FX) = x2.3D. Rx) = (x + 3)?
We can represent the horizontal shift of a quadratic equation by adding or subtracting the constant h to the function
[tex]\begin{gathered} f(x)=a(x-h)^2+k \\ \text{where} \\ h\text{ is the horizontal shift} \end{gathered}[/tex][tex]\begin{gathered} \text{The function }f(x)\text{ has a default values of} \\ a=1 \\ h=0 \\ k=0 \\ \\ \text{A shift to the left of 3 units means that we will have }h=-3\text{ that means} \\ \\ F(x)=(x-(-3))^2 \\ \\ \text{Simplify},\text{ and we get} \\ F(x)=(x+3)^2 \end{gathered}[/tex]Hello could you please help me on questions 2 and 4 I don't understand them?
Given:
2. (2, 4), slope 2
we will write the equation of the line that passes through the point (2, 4) and has slope = 2
We will write the equation of the line using the point-slope form which is:
[tex]y-k=m\cdot(x-h)[/tex]where (m) is the slope and the point (h, k)
so,
m = 2
h = 2
k = 4
So, the equation will be:
[tex]\begin{gathered} y-4=2(x-2) \\ y-4=2x-4 \\ y=2x \end{gathered}[/tex]so, the answer will be the equation of the line is:
[tex]y=2x[/tex]Need some help with this question I’ve been stuck on it for a bit
Answer: L BOZO
Step-by-step explanation:
L+RATIO=BOZO
Which of the following is the equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5?
The equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is; (x - 1)²/25 + (y + 3)²/49 = 1
What is the equation of the ellipse?The general format for equation of an ellipse with center (h, k) and vertical major axis is;
(x - h)²/b² + (y - k)²/a² = 1
We are given the following;
center at (1, -3)
a = 7
b = 5
Thus;
Equation of ellipse with given parameters is;
(x - 1)²/5² + (y + 3)²/7² = 1
This simplifies to;
(x - 1)²/25 + (y + 3)²/49 = 1
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What is the answer to this problem?
Answer:
see explanation
Step-by-step explanation:
solving the inequality
3 ≤ 4x - 13 ≤ 7 ( add 13 to each interval )
16 ≤ 4x ≤ 20 ( divide each interval by 4 )
4 ≤ x ≤ 5
the solution lies between 4 and 5 and can be equal to 4 and 5
this is indicated on Graph A
Two ships leaving the same marina at the same timeare 3.2 miles apart after sailing 2.5 hours. If theycontinue at the same rate and direction, how farapart will they be 2 hours later?2.56 miles3.52 miles5.76 miles6.08 miles
To answer this question, we need to take into account that the two ships continue sailing at the same rate and direction, and we can solve this using the unit rate concept, as follows:
[tex]\frac{3.2}{2.5}\frac{miles}{h}=1.28\frac{miles}{h}[/tex]If they continue sailing at this same rate, then, after two hours they will be:
[tex]1.28\frac{miles}{h}\cdot2h=2.56miles[/tex]They will have 2.56 miles more distance between them.
Then, they will be separated by a distance of:
[tex]3.2\text{miles}+2.56\text{miles}=5.76\text{miles}[/tex]In summary, we have that the answer is 5.76 miles.
How do you answer this? I am so confused! Please help me
The coordinates of a slope triangle that could be on the line shown include
8) (10, 13), 15. 1) and (5, 4)C) (5, 4), (10, 4), and (10, 7)What is slope triangle?A slope triangle is a hypothetical triangle that aids in determining a line's or line segment's slope.
The line whose slope you are interested in learning is the triangle's hypotenuse (the diagonal). The slope formula's "rise" and "run" values are the two "legs" of the triangle.
With this idea, the slope triangle is drawn and the image is attached.
The coordinates should be able to form a right triangle which is used in slope calculation
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A right circular cone with a radius of 3 cm has a slant height of 5 cm. A right cylinder with a radius of 4 cm has a height of 6 cm. What is the number of full cones of water needed to completely fill the cylinder with water?.
About 3 full cones of water are needed to be added to the cylinder to completely fill it.
The radius of the right circular cone is 3cm and the slant height is 5 cm.
The height of the cone can be found as,
H = √(5)²- (3)²
H = 4cm
The volume of the cone is given by,
V = πR²H/3
R is the radius and H is the height of the cone,
Putting values,
v = π x 5 x 5 x 4/3
v = 104.71 cm³
Now, the height h of cylinder is given to be 6 cm and the radius r of the cylinder is 4cm.
The volume of the cylinder is given as,
V = πr²h
V = π x 4 x 4 x 6
V = 301.59
Let us assume that we have to add n full cones of water to completely fill the cylinder, so, we can write,
nv = V
Putting values,
n104.71 = 301.59
n = 2.85
So, we have to add roughly three full cones of water to completely fill the cylinder.
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