Answer:
-1.83 (repeating decimal)
Step-by-step explanation:
Sureepan borrows 40 000 Bhat to buy a new computer. The bank charges 7.5% interest compounded yearly. Sureepan agrees to pay a half of the amount still owing at the end of each year after the interest has been compounded. Determine how much Sureepan would have paid back at the end of 4 years.
Answer:
$42,606.41Explanation:
year 1 (all the values are is $)
Initial debt 40,000Interest of the year (7.5%) 7.5% × 40,000 = 3,000Debt at the end of the year(including the interest) 40,000 + 3,000 = 43,000
Payment at the end of the year(half of the debt) 43,000 / 2 = 21,500
Debt after payment 21,500year 2 (all the values are is $)
Initial debt 21,500Interest of the year (7.5%) 7.5% × 21,500 = 1,612.50Debt at the end of the year(including the interest) 21,500 + 1612.50 = 23,112.50
Payment at the end of the year(half of the debt) 23,112.50 / 2 = 11,556.25
Debt after payment 11,556.25year 3 (all the values are is $)
Initial debt 11,556.25Interest of the year (7.5%) 7.5% × 11,556.25 = 866.72Debt at the end of the year(including the interest) 11,556.25 + 866.72 = 12,422.97
Payment at the end of the year(half of the debt) 12,422.97 / 2 = 6,211.48
Debt after payment 6,211.48year 4 (all the values are is $)
Initial debt 6,211.48Interest of the year (7.5%) 7.5% × 6,211.48 = 465.86Debt at the end of the year(including the interest) 6,211.48 + 465.86 = 6,667.35
Payment at the end of the year(half of the debt) 6,667.35 / 2 = 3,338.67
Amount paid back at the end of 4 years ($) :
21,500 + 11,556.25 + 6,211.48 + 3,338.67 = 42,606.41An auto repair shop charged a customer $280 to repair a car. The bill listed $80 for parts the remainder for labor. If the cost of labor is $50 per hour, how many hours of labor did it take to repair the car?
3x + 7y = -5
8x + 9y = 6
The question involves solving simultaneous linear equations, a high school level topic in mathematics. Methods like substitution or elimination can be used to find the values of the variables.
The student's question involves solving simultaneous linear equations, which is a topic in mathematics. To solve the given system of equations, one can use methods such as substitution, elimination, or matrix operations like determinants. The elimination method can be particularly efficient. For example, you can multiply the first equation by a number that will allow the x or y terms to cancel out when added or subtracted from the second equation. After simplifying, you're left with one equation in one unknown, which can be easily solved. Then, back-substitute the known value into one of the original equations to solve for the other variable.
Given the equations 3x + 7y = -5 and 8x + 9y = 6, we may choose to multiply the first equation by 3 and the second by 7 (to eliminate the x terms) or to multiply the first equation by 8 and the second by 3 (to eliminate the y terms). Once one variable is eliminated, we solve for the other and use it to find the value of the remaining variable.
A box of granola bars has a volume of 210 cubic centimeters. What could be the dimensions of the box?
Answer:
Few of the following CASES can be the solutions:
1. (7 cm , 3 cm, 10 cm) 2.(14 cm , 3 cm, 5 cm)
3.(35 cm , 3 cm, 2 cm) 4.(7 cm , 6 cm, 5 cm)
5.(7 cm , 15 cm, 2 cm)
Step-by-step explanation:
Here, the volume of the box of granola bars = 210 cubic cm.
Let us assume the length of the box = l
The width of the box = w
and The height of the box = h
Also, the box is in shape of a cuboid.
VOLUME OF A CUBOID = Length x Width x Height
⇒l x b x h = 210 .... (1)
Now, we need to find such combinations of (l,b,h) such that their product is 210 cubic centimeters.
There are many number of possible such combinations.
Few of the following CASES can be the solutions:
1. (7 cm , 3 cm, 10 cm)
2.(14 cm , 3 cm, 5 cm)
3.(35 cm , 3 cm, 2 cm)
4.(7 cm , 6 cm, 5 cm)
5.(7 cm , 15 cm, 2 cm)
There can be any other possible such solution as well.
. Which cross section is NOT possible when slicing a square prism with a plane?
A. rectangle
B. triangle
c. hexagon
D. octagon
The answer is D. octagon.
Therefore, the only shapes that can be formed by slicing a square prism with a plane from the given options are a rectangle, a triangle, and an octagon. A hexagon is not possible, making option C the correct answer.
The correct answer is C. A hexagon is not possible when slicing a square prism with a plane.
When slicing a square prism with a plane, the resulting cross section can take on various shapes depending on the angle and position of the cutting plane. Here are the possible cross sections:
- If the plane is parallel to one of the faces of the prism and intersects the prism, the cross section will be a rectangle (Option A).
- If the plane intersects two adjacent edges of the prism, the cross section will be a triangle (Option B).
- If the plane passes through the prism in such a way that it intersects all four edges of one face of the prism, the cross section will be an octagon (Option D), provided that the plane does not intersect the prism at the corners of the square base.
However, a hexagon (Option C) is not a possible cross section when slicing a square prism with a plane. This is because to create a hexagon, the plane would need to intersect three non-adjacent edges of the prism's base, which is geometrically impossible given the right angles of the square base. A hexagon has six sides, and a square prism's base has only four edges, which cannot be divided into three pairs of non-adjacent edges that a plane could intersect to form a hexagon.
-99 less than a number
Answer:
-99 is less than -98
-99 is less than -97
-99 is less than -96
.
.
.
-99 is less than -1
-99 is less than 0
-99 is less than (any posifive number)
Ashley is taking a road trip from California to Washington. Every 4 hours, she travels between 204 and 272 miles. Twelve hours ago, Ashley had traveled 118 miles from her starting point in California. Which is a reasonable measure of Ashley's distance from her starting point in California now? A. 238 miles B. 596 miles C. 832 miles D. 356 miles
Answer:
Option C. 832 miles
Step-by-step explanation:
Ashley travels between 204 and 272 miles in every 4 hours.
That means she travels between 51 [tex](\frac{204}{4}miles)[/tex] and 68 ([tex]\frac{272}{4}miles)[/tex] per hour.
Therefore, in 12 hours she will travel between 612 (51×12 miles) miles and 816 (68×12 miles).
Since she has already traveled 118 miles before 12 hours then the distance traveled by her till now will be between 730 (612+118 miles) and 934 (816+118 miles).
From the given options, Option C. 832 miles is the reasonable measure of Ashley's distance from the starting point.
In the function f(x) = 6x + b, what must be the value of b, if f(5) = 1?
=============================================
Work Shown:
f(x) = 6x + b
f(5) = 6(5) + b .... replace every x with 5
f(5) = 30 + b
1 = 30 + b ..... replace f(5) with 1, since f(5) = 1 was given.
1-30 = 30 + b - 30 .... subtract 30 from both sides
-29 = b
b = -29
-----------
The function f(x) = 6x+b turns into f(x) = 6x+(-29) which is equivalent to f(x) = 6x-29
Plugging in x = 5 leads to
f(x) = 6x-29
f(5) = 6(5) - 29
f(5) = 30 - 29
f(5) = 1
So we have confirmed the answer.
Answer:
Step-by-step explanation:
f(5) = 1
6*5 + b = 1
30 + b = 1
b = 1 - 30 = -29
b = -29
Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 5% syrup?
4.75 lbs of water and 0.25 lbs of sugar is needed to make 5% of syrup.
Solution:
Let us assume that x is the required pounds sugar to make 5% syrup
[tex]\Rightarrow\frac{x}{\text{total quantity}}=5\%[/tex]
which is [tex]\frac{x}{5}=5\%[/tex]
On solving we get,
[tex]\Rightarrow\frac{x}{5} =0.05 [5\%=\frac{5}{100}][/tex]
[tex]\Rightarrow x = 5\times0.05\rightarrow x=0.25[/tex]
If the required sugar to make 5% syrup is 0.25 lbs then the remaining quantity in the total sugar syrup would be water. That is,
[tex]5 \text{ lbs }-0.25 \text{ lbs }=4.75 \text{ lbs }[/tex]
So, the required amount is 0.25 lbs of sugar and 4.75 lbs of water.
Answer:
4.75 lbs of water and 0.25 lbs of sugar is needed to make 5% of syrup.
Solution:
Let us assume that x is the required pounds sugar to make 5% syrup
which is
On solving we get,
If the required sugar to make 5% syrup is 0.25 lbs then the remaining quantity in the total sugar syrup would be water. That is,
So, the required amount is 0.25 lbs of sugar and 4.75 lbs of water.
Step-by-step explanation:
Excellent! Move on to the 7th (or 8th if you count 0)
Fibonacci number.
Answer:
The answer is 13 if you count 0.
Step-by-step explanation:
The sequence is as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
Also, have a great day and Happy Valentines! <3
Mr. Phillips is mixing paint for his art
class. How many 6-ounce bottles can
he fill with the quantities of paint shown
at the right? Explain.
Answer:
the question lacks the full information and is incomplete.
Step-by-step explanation:
What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 5. Base C B is labeled as 6. Segment A D is labeled as x. Segment B D is labeled as 4.2.
Answer:
The correct answer is indeed 3.5 :)
Step-by-step explanation:
just took the test <3 hopes this help
The value of x is 3.5.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Right triangle with vertices labeled as A, B, and C.
Side C B is the base and the top vertex is A.
Side A B contains a midpoint D.
A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D.
Side A C= 5.
Base C B = 6.
Line Segment A D = x.
Segment B D=4.2.
4.2/6=x/5
Apply cross multiplication
4.2×5=6x
21=6x
Divide both sides by 6
x=3.5
Hence, the value of x is 3.5.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ6
Write an inequality for x that would give this rectangle a perimeter of at least 300ft
Answer:
[tex] x\geqslant 300[/tex]
x is greater then or equal to 300
A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?
Area of the doghouse =- 32.5 sq. ft
Solution:
Given height = 5 ft, base1, [tex]b_1[/tex] = 5ft
Base2, [tex]b_2[/tex] = [tex]b_1+3=5+3=8[/tex] ft
Area of the trapezoid = [tex]\frac{1}{2}\times height\times (base1 +base2)[/tex]
[tex]=\frac{1}{2}\times 5\times (5+8)[/tex]
[tex]=\frac{1}{2}\times 5\times 13[/tex]
[tex]=\frac{1}{2}\times 65[/tex]
[tex]=32.5[/tex] sq. ft
Area of the trapezoid = 32.5 sq.ft
Hence the area of the doghouse is 32.5 sq. ft.
a number c increased 6 by is less than or equal to -26
Answer:
[tex]c\leq -32[/tex]
Step-by-step explanation:
Let
c ---> the number
we know that
The number c plus 6 must be less than or equal to -26
so
The inequality that represent this situation is
[tex]c+6\leq -26[/tex]
Solve for c
Subtract 6 both sides
[tex]c\leq -26-6[/tex]
[tex]c\leq -32[/tex]
The solution for c is the interval (-∞,-32]
All real numbers less than or equal to -32
In a number line, the solution is the shaded area at left of c=-32 (closed circle)
see the attached figure to better understand the problem
Mai and Tyler work on the equation 2/5b+1=-11 together. Mais soulution is b=-25 and Tyler’s is b=-28. Here is their work. Do you agree with their solutions? Explain or show your reasoning.
Mai’s work : Tyler’s work:
2/5b+1=-11 2/5+1=-11
2/5b=-10. 2b+1=-55
B=-10•5/2. 2b=-56
B=-25. B=-28
PLEASE HELLP ME
Answer:
No I don't agree with their solution; both their answers are wrong.
Correct answer is [tex]b=-30[/tex].
Step-by-step explanation:
Given:
[tex]\frac{2}{5}b+1=-11[/tex]
Now given:
According to Mai [tex]b = -25[/tex] and According to Tyler [tex]b = -28[/tex]
Now we need to find which of them is correct.
So we will solve the given equation we get;
[tex]\frac{2}{5}b+1=-11[/tex]
Subtracting both side by 1 we get;
[tex]\frac{2}{5}b+1-1=-11-1\\\\\frac{2}{5}b =-12[/tex]
Now Multiplying both side [tex]\frac{5}{2}[/tex] we get;
[tex]\frac{2}{5}b\times\frac{5}{2}= -12 \times \frac{5}{2}\\\\b=-6\times 5\\\\b=-30[/tex]
Hence both of them are incorrect, correct answer is [tex]b=-30[/tex].
Both Mai's and Tyler's solutions are incorrect. Mai's solution is incorrect as the correct solution to b is -30, not -25. Tyler's work has several typos that lead to an incorrect solution. To correctly solve the equation, you should subtract 1 from both sides to get 2/5b = -12, then multiply by the reciprocal of 2/5 which gives b = -30.
Explanation:The original equation presented is 2/5b + 1 = -11. Let's verify both Mai's and Tyler's solutions:
Mai's work: In her work, she correctly subtracts 1 from both sides of the equation to isolate the term with b, which gives 2/5b = -12. Multiplying both sides by the reciprocal of 2/5 (which is 5/2) indeed gives b = -30, not b = -25. So, Mai's solution is incorrect.Tyler's work: Tyler's work has significant typos that prevent it from being a correct solution. He reformulated the equation to 2b + 1 = -55 which isn't equivalent to the original equation. So, Tyler's solution is incorrect as well.The correct procedure should be: Subtract 1 from both sides of the equation to get 2/5b = -12. Then multiply both sides by 5/2 to solve for b, which gives a correct solution of b = -30.
Learn more about Solving equations here:https://brainly.com/question/14410653
#SPJ11
PLEASE HELP
Solve 2^(x − 1) = 11 for x using the change of base formula log base b of y equals log y over log b.
A) −0.711
B) 1.289
C) 2.459
D) 4.459
Solved given expression for x using the change of base formula log base b of y equals log y over log b is 4.459
Answer: Option D
Step-by-step explanation:
Given Expression:
[tex]2^{x-1}=11[/tex]
To solve this, first convert the exponential form into log form
If [tex]a^{x}=b[/tex] then [tex]\log _{a}(b)=x[/tex]
So, when comparing the given expression with above, a = 2, x = x – 1 and b = 11 .
[tex]2^{x-1}=11[/tex] become [tex]\log _{2}(11)=x-1[/tex]
Now, apply change of base formula to remove base 3
[tex]\log _{a}(y)=\frac{\log y}{\log a}[/tex]
Hence,
[tex]\log _{2}(11)=\frac{\log 11}{\log 2}[/tex]
Substitute [tex]\log _{2}(11)=x-1[/tex] in above expression, we get
[tex]\frac{\log 11}{\log 2}=x-1[/tex]
[tex]\frac{1.0414}{0.301}=x-1[/tex]
x – 1 = 3.459
x = 3.459 + 1 = 4.459
Final answer:
To solve the equation 2^(x - 1) = 11 for x, one can use the change of base formula by taking the logarithm of both sides, rewriting the equation using logarithm properties, isolating x, and then simply calculating using a calculator, which results in x ≈ 1.289.
Explanation:
To solve 2(x − 1) = 11 for x using the change of base formula, take the logarithm of both sides of the equation and use the formula logb(y) = log(y) / log(b), where y is the number we want to take the logarithm of and b is the base of the logarithm.
Let's start the process:
Apply logarithm to both sides of the equation: log(2(x - 1)) = log(11).By using logarithm properties, we know that log(ba) = a log(b), so we can rewrite the equation as (x - 1)log(2) = log(11).To isolate x, first, divide both sides by log(2), which gives us x - 1 = log(11) / log(2).Add 1 to both sides of the equation to solve for x, resulting in x = (log(11) / log(2)) + 1.Now, calculate the right side of the equation using a calculator:
x = (log(11) / log(2)) + 1 => x ≈ 1.289Hence, the correct answer is B) 1.289.
Please answer asap! will mark brainliest!
Describe the solution of f(x) shown in the graph
a parabola opening up passing through 0 comma 2, 1 comma zero and 2 comma zero
All real solutions is the answer
Which inequality is true?
A number line going from negative 1 to 1.
One-half less-than one-third
Three-fourths greater-than two-thirds
Negative one-fourth less-than negative two-thirds
Negative 1 greater-than three-fourths
Option C: Three-fourths greater-than two-thirds
Solution:
Option A: A number line going from negative 1 to 1.
Explanation: A number line is used to define a point in a given interval. And hence, a number line does not goes from negative 1 to 1.
Thus, this statement is false.
Option B: One-half less-than one-third
Explanation: The statement can be written as
[tex]\begin{array}{c}{\frac{1}{5}<\frac{1}{3}} \\{0.5<0.33}\end{array}[/tex]
which is not possible.
Hence, this inequality is false.
Option C: Three-fourths greater-than two-thirds
Explanation: The statement can be written as
[tex]\begin{array}{c}{\frac{3}{4}>\frac{2}{3}} \\{0.75>0.667}\end{array}[/tex]
which is true.
Hence, this inequality is true.
Option D: Negative one-fourth less-than negative two-thirds
Explanation: The statement can be written as
[tex]\begin{aligned}-\frac{1}{4} &<-\frac{2}{3} \\-0.25 &<-0.667\end{aligned}[/tex]
This is not possible.
Hence, this inequality is false.
Option E: Negative 1 greater-than three-fourths
Explanation: The statement can be written as
[tex]\begin{array}{l}{-1>\frac{3}{4}} \\{-1>0.75}\end{array}[/tex]
This is not possible.
Hence, this inequality is false.
Answer:
the person who answered this question is actually correct she just put option c when its actually option d people make mistakes its okay thats how u learn
Step-by-step explanation:
How many solutions in the equation y=x-3 and 4x-10y=6
Answer:
1
Step-by-step explanation:
These are two lines with different slopes and y intercepts so they will intersect once
Final answer:
Explaining how to find the number of solutions in a system of linear equations.
Explanation:
The given equations are:
y = x - 3
4x - 10y = 6
To find the number of solutions, we can solve these equations simultaneously.
Substitute y = x - 3 into the second equation and solve for x to find the value of y. If the solution leads to a valid pair of x and y that satisfies both equations, then there is one unique solution, otherwise there are no solutions.
What are the measures of the two angles in the figure? A. 125° and 55° B. 120° and 60° C. 100° and 80° D. 92° and 88°
Step-by-step explanation:
Know that the sum of angle A & B equal 180°In order to find the measures you must find X. Plug X's value into the equations for angle A and Bboth should equal 180°Answer:
Step-by-step explanation: You would do 5x+20+x+40=180
Then you would add 5x and x together and you would also add 20 and 40 together and then you get: 6x+60=180
You would then subtract 180-60 and then you should get 6x=120 and the you would divide from both sides and you should get x=20 you would then plug it into both angles So 5(20)+20 and you should get 120 for the left angle and then you would do the next angle which would be 20+40=60 for the right angle
Short version:
5x+20+x+40=180
6x+60=180
6x=120
X=20
I am really confused on this. It says find the value of x in each triangle.
2x-y=-1 in slope intercept form
Answer:
y = 2x + 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of a line in a standard form.
Convert to the slope-intercept form:
[tex]2x-y=-1[/tex] add y to both sides
[tex]2x-y+y=-1+y[/tex]
[tex]2x=-1+y[/tex] add 1 to both sides
[tex]2x+1=-1+1+y[/tex]
[tex]2x+1=y\to y=2x+1[/tex]
The slope intercept form of the given equation is y = 2x+1
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
(ii) 3x + 5 = 15
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given that, an equation of a line, 2x-y = -1, we need to convert this into slope intercept form,
The standard form of the equation of a line in slope intercept form, is given by :
y = mx+c
Where, m = slope of the line, c is the y-intercept,
So, the given equation is 2x-y = -1,
Add y both the side,
2x-y+y = -1+y
2x = -1+y
Add 1 in both sides,
2x+1 = y+1-1
y = 2x+1
Hence, the slope intercept form of the given equation is y = 2x+1
Learn more about equations, click;
https://brainly.com/question/29657992
#SPJ2
What is the answer?
Answer:
Step-by-step explanation:
141
Answer:
23
Step-by-step explanation:
I NEED HELP ASAP. PLZ HELP
Answer:
Y=x+1...written on the line between c and b
Step-by-step explanation:
CB is perpendicular to EF.
The slope is 1, the y intercept is 1
Therefore. Y =mx+B is y=1x+1
6 x 4237 solve using distributive property
Answer: 25422
Step-by-step explanation:
6(4000+237)
6(4000) + 6(237)
24000 + 1422
24000+1422=25422
Answer:
6·4237 = 25422
Step-by-step explanation:
This is the way multiplication by hand is usually done.
6(4237) = 6(4000 +200 +30 +7) = 6·4000 +6·200 +6·30 +6·7
= 24000 +1200 +180 +42
= 25200 +222 . . . . . add first two terms and last two terms
= 25422
vimesha drove 232 miles in 4 hours. at this rate, how far could she drive in 7 hours? what is her rate of speed in miles per hour?
Answer: distance = 406 miles
speed = 58 miles/hr
Step-by-step explanation:
4 hours - 232 miles
1 hr - 232/4
7 hours - 232/ 4 x 7 = 406 miles
Therefore , her distance is 406 miles for 7 hours.
Speed = distance / time
speed = 406/7 = 58 miles/hr
In 15 and 16, use the expression 1 + z/3 + 2w
15) Which part of the expression is a quotient? DESCRIBE its parts.
16) Which part of the expression is a product of two factors? DESCRIBE its parts.
We want to analyze the terms of the given expression.
15) second term, z/3
16) third term, 2*w
The given expression is:
1 + z/3 + 2*w
15) We want to find which part of the expression is a quotient.
A general quotient is something of the form a/b, so compared with the expression, the term that is a quotient is the second term; z/3.
Where the first number, z, is called the numerator and the second is called the denominator.
Notice that the variable z is on the numerator, so this would be a linear dependence with z.
16) We want to find which part of the expression is a product of two factors.
It is the third term, 2*w
Where the two factors are 2 and w.
Again, the variable si w, and we are multiplying it by a constant number, 2.
So we also have a linear dependence with w.
If you want to learn more, you can read:
https://brainly.com/question/7510157
In the expression 1 + z/3 + 2w, the quotient is z/3, where z is the numerator and 3 is the denominator. The product of two factors is 2w, with 2 and w being the factors.
Explanation:The student asked about parts of the expression 1 + z/3 + 2w.
15) Quotient in the Expression
The quotient refers to the result of division. In the expression given, the quotient is z/3. Its parts are the numerator z, which is the value being divided, and the denominator 3, which is the value by which z is divided.
16) Product of Two Factors in the Expression
The product refers to the result of multiplication. In the expression, the product is 2w. Its parts are the two factors being multiplied: the constant 2 and the variable w.
The radius of a circle is 4 millimeters. What is the circle's circumference?
Will give brainiest
Answer:25.12
Step-by-step explanation:
HELP FAST!!! Which angles could form an obtuse triangle? A. 62°, 39°, 79° B. 46°, 92°, 42° C. 40°, 40°, 100° D. 22°, 78°, 80°
Answer:
A. is Obtuse scalene triangle.
Step-by-step explanation:
Hope this help
Answer:
c i think
Step-by-step explanation: