[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &2 \end{cases} \\\\\\ 8000=5000[1+(\frac{r}{100})(2)]\implies \cfrac{8000}{5000}=1+\cfrac{r}{50}\implies \cfrac{8}{5}=1+\cfrac{r}{50} \\\\\\ \cfrac{8}{5}-1=\cfrac{r}{50}\implies \cfrac{3}{5}=\cfrac{r}{50}\implies \cfrac{3(50)}{5}=r\implies 30=r[/tex]
What division problem does this area model represent?
Answer:
2,160 ÷ 36 = 60
Step-by-step explanation:
The division problem that this area model represents is,
2,160 ÷ 36 = 60
Graph the set {x|x≤-5} on the number line.
Then, write the set using interval notation.
The interval notation that defines this set is: (-∞, -5]
And the graph can be seen below.
How to graph the inequality?Here we want to graph the inequality:
x ≤ -5
This refers to all the values of x equal or smaller than -5.
To graph this, we need to graph a closed circle at -5, and we need to draw an arrow that points to the left (values smaller than -5). The graph is the one that you can see below.
The interval notation that defines this set is: (-∞, -5]
The first end is open, and the second is closed (because of the symbol ≤).
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Two exponential functions are shown in the table.
X
f(x)=2*
g(x) =
2
2
4
1
2
0
-1
-2
2
71111
4
141212
4
Which conclusion about f(x) and g(x) can be drawn
from the table?
O The functions f(x) and g(x) are reflections over the x-
axis.
O The functions f(x) and g(x) are reflections over the y-
axis.
O The function f(x) is a decreasing function, and g(x) is
an increasing function.
O The function f(x) has a greater initial value than g(x).
Based on the table, a conclusion which can be drawn about f(x) and g(x) is that: B. the functions f(x) and g(x) are reflections over the y-axis.
How to compare the functions f(x) and g(x)?In Mathematics, two functions are considered to be reflections over the y-axis under the following condition:
If, f(-x) = g(x).
Evaluating the given functions, we have:
f(x) = 2ˣ
f(-x) = 2⁻ˣ = ½ˣ = g(x).
Similarly, two functions are considered to be reflections over the x-axis under the following condition:
If, -f(x) = g(x).
Evaluating the given functions, we have:
f(x) = 2ˣ
-f(x) = -2ˣ ≠ g(x).
Therefore, we can logically conclude that the two functions f(x) and g(x) are considered to be reflections over the y-axis but not the x-axis.
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2/3(cx+1/2)-1/4=5/2 solve
Answer:
2/3(cx+1/2)-1/4=5/2. CX=29/8
6. Janet spent $25, $30, $10, and $8 for
recreation in the last four weeks. What
was her average weekly expense for
recreation?
A. $12.50
B. $18.25
C. $25.25
D. $36.50
Answer:
B
Step-by-step explanation:
Total money spent = 25 + 30 + 10 + 8 = 73
Per week = 73 / 4 = 18.25
An ordinary die is a cube with numbers 1 through 6 on the sides. Imagine that the die is rolled twice in sucession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
What is the probability that the sum is not divisible by 2 and not divisible by 4?
Answer:
1/2Step-by-step explanation:
NOTE : we have 6×6=36 possible outcome.
we can resume the set of outcomes in the table below :
Then
the probability that the sum is not divisible
by 2 and not divisible by 4 :
= 18/36
= 1/2
help me with this please
Answer:
A- 17/24 sugar all together
B- yes the bowl would be big enough because when you add all the ingredients together it equals 3 5/24 and it's less than 3 1/2.
A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has a y intercept of 6. What is the equation of the function described?
Equation of the function: f(x) = 4 sin (x/2) + 6.
What is sinusoidal function ?The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x).
Given: max value= 6, min value= -2, y-intercept= 6.
As, standard form f(x) = A sin (ωx +φ) + k,
where A is the amplitude, ω is the angular velocity with ω=2πf.
Now,
A = |6- (-2)/2|
A = |6 +2/2| = 8/2
A = 4
Also, ω:
The period of a sinusoidal is T = 1/f
so, f = 1 / T
ω = 2πf
ω = 2π ( 1/T) with T = 4π
ω = 2π (1/(4π) = 2π (2)
ω = 1/2
The y-intercept k = 6
So, equation with values A =4, ω = 1/2, k = 6, φ = 0.
f(x) = A f(x)
f(x) = A sin (ωx +φ) + k
f(x) = 4 sin (x/2) + 6.
Hence, equation of the function f(x) = 4 sin (x/2) + 6.
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I need a thorough explanation for question 4 please. It’s about Operations of Powers/Exponents.
Simplify
I need help for finals
Answer:
goto gauth maths and ask again
Select whether the pair of lines is parallel, perpendicular, or neither. x=−2, y=10
Answer:
perpendicular
Step-by-step explanation:
x = -2 is a vertical line at x = -2
y is a horizontal line the two lines are perpindicular
the lines x=−2, y=10 are perpendicular to each other.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Here, The given equations are :
x=−2 and y=10
First, consider x = -2 equation :
equation x = -2 is a vertical line, parallel to x = 0 line and perpendicular to line y = 0.
Consider second line y = 10 :
line y = 10 is horizontal line and is parallel to line y = 0 and is perpendicular to line x = 0.
Therefore, the lines x=−2, y=10 are perpendicular to each other.
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Multiply
k+3/4K - 2 (12k2 +2k -4)
Answer:
-204kk+3+32k/4k
Hope this helps!!
Which equation could generate the curve in the graph below?
y=3x² - 2x + 1
y=3x² - 6x +3
y=3x² - 7x + 1
y=3x² - 4x-2
What causes the economy to move from its short-run equilibrium to its long-run equilibrium?
Answer:
Nominal wages, prices, and perceptions adjust upward to this new price level
Step-by-step explanation:
which expression is equivalent to 15n – 20
2(8n – 6)
6(2n – 9)
5(3n – 4)
5(4n – 3)
The Other Number Your first number was 8. Is the other one 0? How did we know that? Can we read your mind?
Answer:
???
Step-by-step explanation:
70 POINTS !!! Measure each angle and write the measure on the line.
Answer:
See below
Step-by-step explanation:
You will just need to use your protractor to measure the given angles..
Here is some gross guesses starting with top row
45 120 100 25 90 80 135 120 °
Lines RS, TV, and SW are shown.
10-
8-
R
S
6
4-
2-
-10-8-6-4-22-
2 4 6 8 10 x
T
-6
8
W
-10-
☎ do
N
Which statements are true about these lines? Select
three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
Answer:
b
Step-by-step explanation:
The statements true about the slopes and lines are
a) Line TV has a slope of 0.
b) Lines RS and TV are parallel.
c) Line SW has an undefined slope.
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be S ( 2 , 6 )
Let the second point be R ( -8 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - 6 ) / ( -8 - 2 ) = 0
So , the slope of line RS = 0
Let the point T = T ( -6 , -4 )
Let the point V = V ( 8 , -4 )
Slope m = ( -4 - (-4) ) / ( 8 - (-6) ) = 0
So , the slope of line TV = 0
And , the lines RS and TV are parallel as they have the same slope
Now , the x coordinate of the point S and W does not change
So , it has an undefined slope
Hence , the equation of line is solved
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The complete question is attached below :
Lines RS, TV, and SW are shown.
Which statements are true about these lines? Select
three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
A. 36
B. 52
C. 148
D. 168
Answer:
B) 52
Bodmas rule:
BracketsOrderDivisionMultiplicationAdditionSubtractionSolving Steps:
⇒ 2 × (3 - 1)⁴ + 5 × 4
⇒ 2 × (2)⁴ + 5 × 4
⇒ 2 × 16 + 5 × 4
⇒ 32 + 20
⇒ 52
Option B
Zahid started the construction of an equilateral triangle inscribed in a circle. Which segments need to be drawn to create the triangle?
To finish his construction, Zahid needs to draw segments df ,
, and
.
The rule for construction of Inscribed equilateral triangle
Draw 6 marks as per the picture.Then join one with next alternative leaving second .Means if marks are from 1 to 6 then
133551Or
244662Now
Here the rest two segments are
DFBFBDAnswer:
FB and DB
Step-by-step explanation:
got it right on the test
can someone help me on part B please? I've done the answer to the rest please thanks!
Answer:
84 circular tiles are needed to make pattern number 20
4(20+1)
Step-by-step explanation:The number of circular tiles is 1 more than the pattern number on each side of the square.
circular tiles = 4(n +1)
Write each expression in radical form
[tex]\sqrt[4]{6^5}[/tex]
Step-by-step explanation:
This expression in radical form :4√65 =2.838412A rifle is aimed horizontally at a target on a screen some distance away. The bullet hits the target 2.8 cm below the aim point. The initial velocity of the bullet is 750.0 m/s.
Find the flight time?
Answer:
0.03 second time the flight
If the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units, using integration find the value of a, where a > 0.
Answer:
a=2
Step-by-step explanation:
[tex]area=2\int\limits^a_b {y} \, dx =2\int\limits^a_b {\sqrt{4ax} } \, dx \\=2 \times 2\sqrt{a} \frac{x^{\frac{3}{2} } }{\frac{3}{2} } ~from~~b~to~a\\=\frac{8}{3}\sqrt{a} (a^{\frac{3}{2} } -b^{\frac{3}{2} } )\\=\frac{8}{3} \sqrt{a}( (4a)^{\frac{3}{2} } -0)\\=\frac{8}{3} \sqrt{a} ((4a)\sqrt{4a} -0)\\=\frac{32 a}{3} \times 2a\\=\frac{64}{3} a^2[/tex]
[tex]\frac{64}{3} a^2=\frac{256}{3} \\a^2=\frac{256}{3} \times \frac{3}{64} =4\\a=2 (a > 0)[/tex]
the curve is a right parabola.
here b=0,and a=4a for x
we are finding the area between x-axis and x from 0 t0 4a.
curve is symmetrical about x-axis so we multiply by 2.
If the area of the region bounded by the curve [tex]y^2 =4ax[/tex] and the line [tex]x= 4a[/tex] is [tex]\frac{256}{3}[/tex] Sq units, then the value of [tex]a[/tex] will be [tex]2[/tex] .
What is area of the region bounded by the curve ?An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.
Area bounded by the curve [tex]=\int\limits^a_b {x} \, dx[/tex]
We have,
[tex]y^2 =4ax[/tex]
⇒ [tex]y=\sqrt{4ax}[/tex]
[tex]x= 4a[/tex],
Area of the region [tex]=\frac{256}{3}[/tex] Sq units
Now comparing both given equation to get the intersection between points;
[tex]y^2=16a^2[/tex]
[tex]y=4a[/tex]
So,
Area bounded by the curve [tex]= \[ \int_{0}^{4a} y \,dx \][/tex]
[tex]\frac{256}{3} =\[ \int_{0}^{4a} \sqrt{4ax} \,dx \][/tex]
[tex]\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \][/tex]
[tex]\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \][/tex]
[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}[/tex]
[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}[/tex]
[tex]\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}[/tex]
On applying the limits we get;
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} \left[\begin{array}{ccc}(4a)^{\frac{3}{2} \end{array}\right][/tex]
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }[/tex]
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} * 8 *a^{2} \sqrt{a}[/tex]
[tex]\frac{256}{3}= \frac{4}{3} * 8 *a^{3}[/tex]
⇒ [tex]a^{3} =8[/tex]
[tex]a=2[/tex]
Hence, we can say that if the area of the region bounded by the curve [tex]y^2 =4ax[/tex] and the line [tex]x= 4a[/tex] is [tex]\frac{256}{3}[/tex] Sq units, then the value of [tex]a[/tex] will be [tex]2[/tex] .
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9. Find the area:
25
19
13
Answer:
162.5
Step-by-step explanation:
25=height
13=base
to find the area of a triangle you do (h(b)b)/2
Rebecca rolls a 6-sided number cube 1290 times. How many of the rolls are expected to show a factor of 6?
Answer:
215
Step-by-step explanation:
1/6 chance to roll a 6
1/6 * 1290
Which function has the same domain as y= 2√x?
Oy= √2x
O y=2³√x
0₁y = √x-2
O y=³√x-2
The option first is correct because y= 2√x and y= √2x have same domain which is x ≥ 0.
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.
We have a function:
y= 2√x
From the above function the domain should be:
x ≥ 0 (because square root of negative values does not exist)
The function:
y = √(2x)
2x ≥ 0
x ≥ 0
Thus, the option first is correct because y= 2√x and y= √2x have same domain which is x ≥ 0.
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a wall contains a rectangular window. the area (in square feet) of the window is represented by x^2-4x+3. write a bionominal that represents the height of the window. find the permiteter when the wall is 10 feet. the square on the inside is (x-3) ft
The height of the wall would be x - 1 and the perimeter of the wall is 32 feet
How to determine the height?The area of the window is given as:
A = x^2 - 4x + 3
Expand
A = x^2 - 3x - x + 3
Factorize
A = x(x - 3) - 1(x - 3)
Factor out x - 3
A = (x - 1)(x - 3)
The width of the wall is given as: x - 3
So, the height of the wall would be x - 1
How to determine the perimeter?
The perimeter is calculated using:
P = 2 *(Width + Height)
This gives
P = 2 * (x - 1 + x - 3)
When x = 10, we have:
P = 2 * (10 - 1 + 10 - 3)
Evaluate
P = 32
Hence, the perimeter of the wall is 32 feet
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Help help help help help help help help
why do some numerical expressions contain parentheses
The most basic and common reason to use parentheses, brackets, and braces is to control the order of operations.
What are parentheses?In mathematics, parenthesis is used to arrange numbers in the sequence of operations, clarify numbers, and denote multiplication.
Suppose you have an expression as:-
E = { ( 5-2 )8} 6
In this case, you would calculate 5 minus 2 first (parentheses), then multiply by 8 (brackets), then complete the part inside the curly braces, and finally multiply by 6.
Therefore the most basic and common reason to use parentheses, brackets, and braces is to control the order of operations.
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T=mv^2/L
Write an equation that shows the given formula solved for V
Answer:
v = √(LT/m)
Step-by-step explanation:
Given :
T = mv²/LMultiply both sides with L :
T × L = mv²/L x LLT = mv²Divide both sides by m :
LT × 1/m = mv² × 1/mLT/m = v²Take the square root on each side :
√v² = √(LT/m)v = √(LT/m)Answer:
[tex]v = \sqrt{ \frac{tl}{m} } [/tex]
Step-by-step explanation:
[tex]t = \frac{mv {}^{2} }{l} \\ making \: v \: the \: subject \\ t \times l = mv {}^{2} \\ dividing \: bothsides \: by \: m \\ \frac{tl}{m} = \frac{mv {}^{2} }{m} \\ v {}^{2} = \frac{tl}{m} \\ finally \\ v = \sqrt{ \frac{tl}{m} } [/tex]