The rate is 4% per year.
It is required to find the rate of interest.
What is simple interest ?Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Given that:
Let, principal is P,
so, interest is P/5 in 5 yrs.
As from the formula of simple interest,
So, P/5 = P× R ×5/ 100 (R = rate)Or, R = 4%
So, rate is 4% per year.
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The missing option is e. 4%
Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter .
Answer:
The height of the tree=8.42 m
Step-by-step explanation:
We are given that
Height of Joshua, h=1.45 m
Length of tree's shadow, L=31.65 m
Distance between tree and Joshua=26.2 m
We have to find the height of the tree.
BC=26.2 m
BD=31.65m
CD=BD-BC
CD=31.65-26.2=5.45 m
EC=1.45 m
All right triangles are similar .When two triangles are similar then the ratio of their corresponding sides are equal.
[tex]\triangle ABD\sim \triangle ECD[/tex]
[tex]\frac{AB}{EC}=\frac{BD}{CD}[/tex]
Substitute the values
[tex]\frac{AB}{1.45}=\frac{31.65}{5.45}[/tex]
[tex]AB=\frac{31.65\times 1.45}{5.45}[/tex]
[tex]AB=8.42m[/tex]
Hence, the height of the tree=8.42 m
Find p(0), p(1) and p(2) for the polynomial P(t) = 2 + t + 2t²-t³
p(0)=2
p(1)=2+1+2-1=4
p(2)=2+2+8-8=4
sketch the graph of xy = 3y² - 4
Answer:
xy = 3y² - 4
Step-by-step explanation:
Hope it is helpful....
In the file i have attached, you will find the equation graphed, hope this helps.
Find the equation of tangent to circle x^2+y^2 = 3 which makes angle of 60 ° with x-axis.
Step-by-step explanation:
hope it helps thnak you
brainliest pls ❤
Solve for x. Round to the nearest tenth, if necessary.
Answer:
11.3
Step-by-step explanation:
first we find angle F.
remember, all angles in a triangle always sum up to 180 degrees.
so,
F = 180 - 90 - 61 = 29 degrees
now we use the law of sines.
EF/sin(D) = ED/sin(F) = DF/sin(E)
DF = x
sin(E) = sin(90) = 1
5.5/sin(29) = x/1 = x
x = 11.3
Calculate the average rate of change of a function over a specified interval. Which expression can be used to determine the average rate of change in f(x) over the interval 2, 9?
Given:
The interval is [2,9].
To find:
The average rate of change in f(x) over the interval [2,9].
Solution:
The average rate of change in f(x) over the interval [a,b] is defined as:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
In the interval [2,9], the value of a is 2 and the value of b is 9.
Using the above formula, the average rate of change in f(x) over the interval [2,9] is:
[tex]m=\dfrac{f(9)-f(2)}{9-2}[/tex]
[tex]m=\dfrac{f(9)-f(2)}{7}[/tex]
Therefore, the required expression for the average rate of change in f(x) over the interval [2,9] is [tex]\dfrac{f(9)-f(2)}{9-2}[/tex], it is also written is [tex]\dfrac{f(9)-f(2)}{7}[/tex].
Answer:
D
Step-by-step explanation:
right on edge
Find the value of a if the line joining the points (3a,4) and (a, -3) has a gradient of 1 ?
Answer:
[tex]\displaystyle a=\frac{7}{2}\text{ or } 3.5[/tex]
Step-by-step explanation:
We have the two points (3a, 4) and (a, -3).
And we want to find the value of a such that the gradient of the line joining the two points is 1.
Recall that the gradient or slope of a line is given by the formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) is one point and (x₂, y₂) is the other.
Let (3a, 4) be (x₁, y₁) and (a, -3) be (x₂, y₂). Substitute:
[tex]\displaystyle m=\frac{-3-4}{a-3a}[/tex]
Simplify:
[tex]\displaystyle m=\frac{-7}{-2a}=\frac{7}{2a}[/tex]
We want to gradient to be one. Therefore, m = 1:
[tex]\displaystyle 1=\frac{7}{2a}[/tex]
Solve for a. Rewrite:
[tex]\displaystyle \frac{1}{1}=\frac{7}{2a}[/tex]
Cross-multiply:
[tex]2a=7[/tex]
Therefore:
[tex]\displaystyle a=\frac{7}{2}\text{ or } 3.5[/tex]
Answer:
[tex] \frac{7}{2} [/tex]
Step-by-step explanation:
Objective: Linear Equations and Advanced Thinking.
If a line connects two points (3a,4) and (a,-3) has a gradient of 1. This means that the slope formula has to be equal to 1
If we use the points to find the slope: we get
[tex] \frac{4 + 3}{3a - a} [/tex]
Notice how the numerator is 7, this means the denominator has to be 7. This means the denomiator must be 7.
[tex]3a - a = 7[/tex]
[tex]2a = 7[/tex]
[tex]a = \frac{7}{2} [/tex]
The width of a rectangle is only 15% of its length. If the perimeter of the rectangle is 46, what is the length
Answer:
20 units
Step-by-step explanation:
Let the length be x. According to the question,
Length = xWidth = 15% of the length➝ Width = 15% of the length
➝ Width = 15/100x
➝ Width = 3/20x
We have the perimeter of the rectangle that is 46 units.
[tex]\longrightarrow \sf {Perimeter_{(Rec.)} = 2(L + W) } \\ [/tex]
[tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]
[tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]
[tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{20x + 3x}{20} \Bigg \rgroup } \\ [/tex]
[tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{23x}{20} \Bigg \rgroup } \\ [/tex]
[tex]\longrightarrow \sf {\dfrac{46}{2}= \dfrac{23x}{20}} \\ [/tex]
[tex]\longrightarrow \sf {23= \dfrac{23x}{20}} \\ [/tex]
[tex]\longrightarrow \sf {23 \times 20 = 23x} \\ [/tex]
[tex]\longrightarrow \sf {460= 23x} \\ [/tex]
[tex]\longrightarrow \sf {\cancel{\dfrac{460}{23}} = x} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \bf {20\; units = x}}} \\ [/tex]
Therefore, length of the rectangle is 20 units.
Two cars started from a point and traveled in opposite directions; each
car has traveled some miles as shown on the number line. Find the
distance between the two cars.
Answer:
Hey, could you please add the number line to the question too
at the farmers market 8 apple cost $5.20 if each apple cost the samw amount what is the price per apple
[tex]\displaystyle\bf Solve:8\times p=5,2 \$ => p=\frac{5,2}{8} =\frac{5,2:\boxed{8}}{8:\boxed{8}} =0,65\$\quad She \:unit\: cost\:is\:\underline{ 0,65} \\\\Check :\:8\times\underline{0,65} =5,2\$ \\\\0,65=0,65 \\\\\rightarrow The\: price\:per \:apple \:is \: 0,65 \$[/tex]
Find the area of circle Q in terms of x
Answer:
The answer is C 100πcm^3
Write the equation of the line in Slope-Intercept Form given the information below.
Slope =−7/4
Y-Intercept =5
Answer:
y = -7/4 x + 5
Step-by-step explanation:
Mr. Tanaka is making Miso soup for his family. The recipe calls for 350 ml of Dashi. Mr. Tanaka plans to make a smaller batch using 280 ml of dashi. He wants to know what percent of the stock he will use compared to the original recipe. PLSS HELPPPPPPP Quick
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
14
x
х
12
Answer:
The answer is below
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are acute, obtuse, isosceles, equilateral, scalene and right angled triangle.
A right angled triangle is a triangle in which one of the angles is 90°. In a right angled triangle, the longest side is known as the hypotenuse and the side is opposite to the right angle.
Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given the question attached, using Pythagoras theorem:
18² = x² + 12²
324 = x² + 144
x² = 180
x = 13.42
can someone please help me solve this? thank you!:)
First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.
P = L + 2W
A = L * W
Now that we have our equations, we need to plug in what we know, which is the 40m of rope.
40 = L + 2W
A = L * W
Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.
L = 40 - 2W
Now, we can substitute the value for L into L in the area equation and get a quadratic equation.
A = W(40 - 2W)
A = -2W^2 - 40W
The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.
V = -b/2a
V = 40/2(2) = 40/4 = 10
Derivative:
-4w - 40 = 0
-4w = 40
w = |-10| = 10
To find the other dimension, use the perimeter equation.
40 = L + 2(10)
40 = L + 20
L = 20m
Therefore, the dimensions of the area are 10m by 20m.
Hope this helps!
Answer:
Width: 10 m
Length: 20 m
Step-by-step explanation:
Hi there!
Let w be equal to the width of the enclosure.
Let l be equal to the length of the enclosure.
1) Construct equations
[tex]A=lw[/tex] ⇒ A represents the area of the enclosure.
[tex]40=2w+l[/tex] ⇒ This represents the perimeter of the enclosure. Normally, P=2w+2l, but because one side isn't going to use any rope (sandy beach), we remove one side from this equation.
2) Isolate one of the variables in the second equation
[tex]40=2w+l[/tex]
Let's isolate l. Subtract 2w from both sides.
[tex]40-2w=2w+l-2w\\40-2w=l[/tex]
3) Plug the second equation into the first
[tex]A=lw\\A=(40-2w)w\\A=40w-2w^2\\A=-2w^2+40w[/tex]
Great! Now that we have a quadratic equation, we can do the following:
Solve for its zeros/w-intercepts.Take the average of the zeros to find the w-variable of the vertex. (The area (A) in relation to the width of the swimming area (w) is what we've established in this equation, and the area (A) is greatest at the vertex. Finding the value of w of the vertex will tell us what the width needs to be for the area to be at a maximum.)Plug this w value into one of the equations to solve for l4) Solve for w
[tex]A=-2w^2+40w[/tex]
Factor out -2w
[tex]A=-2w(w-20)[/tex]
For A to equal 0, w=0 or w=20.
The average of 0 and 20 is 10, so the width that will max the area is 10 m.
5) Solve for l
[tex]40=2w+l[/tex]
Plug in 10 as w
[tex]40=2(10)+l\\40=20+l\\l=20[/tex]
Therefore, the length of 20 m will max the area.
I hope this helps!
Ryan was traveling by car at an average speed of 40.3 miles per hour.
He will cover 322.4 miles in hours.
Answer:
your answer is 8
Step-by-step explanation:
If you divide 322.4 by the speed 40.3 you would get 8 the amount of hours traveling the given distance.
If you dont think the answer is correct you can simply mutiply 40.3 by 8 to ensure that 322.4 miles is in fact how far you will go in that time
hope this help. Have a good day!
\
Bye
Miguel's scores on his first three math
PACE Tests were 95, 92, and 90. What
score does he need on his next test to
have a 94 average?
Answer: 99
Step-by-step explanation:
Fourth PACE Test = xSince the average of all four tests is 94:
[tex]\frac{95+92+90+x}{4} =94\\\\(4)\frac{277+x}{4} =(4)94\\\\277+x=376\\\\x=376-277=99[/tex]
Given : AB = BC and BC = CD, AB = 3x - 1 and CD = 2x + 3 Prove: BC = 11 plz help me
Answer:
Given
Given
Transitive
Substitution
Subtraction
Addition
Substitution
Multiplication
Hard to see list of options. But this should help.
Given
Given
Transitive
substitution property of equality
Subtraction property of equality
Addition property of equality
multiplication property of equality
Simplify
simplify
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression.
What is transitive property?The transitive property states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”
What is addition and subtraction property of equality?The addition and subtraction property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
What is multiplication property of equality?The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.
According to the given question.
AB = BC and BC = CD ( Given)
AB = 3x - 1 and CD = 2x + 3 ( Given)
Since,
AB = BC and BC = CD
⇒ AB = CD (transitive)
Substitute the value of AB and CD in AB = CD
⇒ [tex]3x - 1 = 2x + 3[/tex] (substitution property of equality)
⇒ [tex]x -1= 3[/tex] (subtraction property of equality)
⇒ [tex]x = 4[/tex] (Addition property of equality)
Since,
AB = BC
⇒ AB= 3x -1
⇒ [tex]AB = 3(4) - 1[/tex] ( multiplication property of equality)
⇒ [tex]AB = 11[/tex] (simplify)
Therefore,
BC = 11 (simplify)
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In the history of Major League Baseball, the most valuable player award has been won by players from 7 different countries. which countries were they
Answer:
United States, Canada, Dominican Republic, Cuba, Venezuela, Japan, Panama
Step-by-step explanation:
Taking a look at a list of Major League Baseball most valuable players, the countries are:
United States(most players are US-born).
Canada(Joey Votto in 2010).
Dominican Republic(Albert Pujols and Vlad Guerrero Sr. for example).
Cuba(last Jose Abreu in 2020)
Venezuela(last Jose Altuve in 2017)
Japan(Ichiro in 2001).
Panama(Rod Carew)
Which of the following is an extraneous solution
Answer:
3 or
C
Step-by-step explanation:
(45 - 3x)^1/2 = x - 9 Square both sides
45 - 3x = x^2 - 18x + 81 Switch sides
x^2 - 18x + 81 = 45 - 3x Add 3x to both sides
x^2 - 15x + 81 = 45 Subtract 45 from both sides
x^2 - 15x + 36 = 0 Factor
(x - 12)(x - 3) =0
The answers are
x = 12
x = 3
Now the question asks which is extraneous. The answer will be which ever number won't solve the original equation. Looking at it right now, both look OK.
(45 - 3*12)^1/2 = 12 - 9
(45 - 36)^1/2 = 3
(9)^1/2 = 3
So 12 is a proper solution.
What about 3?
(45 - 3*3)^1/2 = 12 - 3
(45 - 9)^1/2 = 9
36^1/2 = 9
6 does not = 9
The extraneous solution is x = 3
2a is five times bigger than B.
Circle the ratio a:b.
A. 10:1
B. 1:10
C. 5:2
D. 2:5
Answer:
The answer is 2:5
Step-by-step explanation:
The ratio of the variable a over b will be 5/2. Then the correct oprion is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
2a is five times bigger than b. Then the equation is given as,
2a = 5b
The ratio of the a: b is given as,
2a = 5b
a / b = 5 / 2
The ratio of the variable a over b will be 5/2. Then the correct option is C.
More about the solution of the equation link is given below.
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Which is equivalent to 2^5?
Answer:
Are there certain options?
Step-by-step explanation:
2^5 is in other words 2x2x2x2x2
the answer to this is 32
Hope I helped?
Answer:
32
Step-by-step explanation:
(iii) If a, b, c are rational numbers, then
a x (b-c) #ax b-ax c. true or false
Answer:
false
Step-by-step explanation:
answer:ab-ac=ab-ac
Which ones ARE in scientific notation?
a. 3.5X10^-2
b. 21.2X10^3
c. 1.4X10^5
d. 9.9432X10^-4
Answer:
C
Step-by-step explanation:
Cause C met the rules of scientific notation which is:
(First digit of the number) followed by (the decimal point) and then (all the rest of digits of the number) times (10 to an appropriate power)Can someone help me with this math homework please!
Answer:
The first one is X=4
the second one is 5n - 300= 1,500
Step-by-step explanation:
Juan compró un led TV en cuotas que costó $ 76.000=. Si le falta pagar 3 cuotas y ya pagó $ 47.000, ¿Cuál es el valor de cada cuota fija?
Respuesta:
$ 9666. 67
Explicación paso a paso:
Costo de TV = $ 76,000
Número de cuotas = 3
Monto ya pagado = $ 47000
Amontof cada cuota fija = Cantidad que queda por pagar / 3
Cantidad que queda por pagar = Costo de TV - Cantidad ya pagada
Cantidad que queda por pagar = $ (76000 - 47000) = $ 29000
Monto de cada cuota fija = $ 29000/3 = $ 9666. 67
Write the solution set of the equation x2 – 4=0 in roster form
Answer:
Step-by-step explanation:
x²-4=0
(x+2)(x-2)=0
x=-2,2
solution is x∈{-2,2}
Henri bought a swim suit at a cost of $8. Which statements are true regarding the cost of the suit?
Answer:
What are the statements?
Step-by-step explanation:
Let u = <-7, -2>. Find 4u.
Answer:
<-28, -8>
Step-by-step explanation:
you multiply the values by 4 because that's what the question tells you to do.
if <-7,-2>=u and it's asking for 4u, then the answer is the solution to the equation 4(<-7,-2>)
Determine the value of x
2.12 units
2.02 units
12.38 units
0.49 units
Answer:
2.02
Step-by-step explanation:
Hello, I took the quiz. The correct answer is 2.02
