Answer:
1. ) $6,734.30
2) 12 years
Step-by-step explanation:
1. we use the compound interest formula for this
Mathematically;
A = P( 1 + r/n)^nt
where P is the principal which is the amount deposited = $5,000
r = rate = 6% = 6/100 = 0.06
n = number of time per year we compound = 4 since it is quarterly
t = number of years = 5
Substituting all of these, we have;
A = 5,000( 1 + 0.06/4)^(4)(5)
A = 5,000( 1 + 0.015)^20
A = 5,000(1.015)^20
A = $6,734.28 which to the nearest cent = $6,734.30
2) For the money to double means that A becomes 2P
Thus;
2P = P( 1 + 0.015)^4t
divide both sides by P
2 = (1.015)^4t
Fine the ln of both sides
ln 2 = 4t ln 1.015
divide both sides by ln 1.015
4t = ln 2/ ln 1.015
4t = 46.56
t = 46.56/4
t = 11.63 which is approximately 12 years
If f(x) = 5x - 3, fill out the following table of values:
-2,-1,0,1,2,3
What type of function is this?
Answer:
Step-by-step explanation:
Given function is,
f(x) = 5x - 3
Where f(x) represents the output values and 'x' is the variable representing the input values.
For x = -2,
f(-2) = 5(-2) - 3
= -13
For x = -1,
f(-1) = 5(-1) - 3
= -8
For x = 0,
f(0) = 5(0) - 3
= -3
For x = 1,
f(1) = 5(1) - 3
= 2
For x = 2,
f(2) = 5(2) - 3
= 7
For x = 3,
f(3) = 5(3) - 3
= 12
Table for the input-output values will be,
x -2 -1 0 1 2 3
f(x) -13 -8 -3 2 7 12
Since the values of f(x) has a common difference of [-13 - (-8) = -5] negative five, given function will be a linear function.
Benjamin's age is 6 years less than twice Lucas's age. If Benjamin is 12 years old, how old is Lucas? Choose the answer below that is a viable solution to this problem
We can express Benjamin's age with x, we can express Luca's age as y.
x-6=2y
So, if x=12
2y=6
y=3
Therfore, Lucas is 3 years old
Find the x - intercept and y - intercept of 3x + 27= y
Answer:
x-intercept is (-9,0)
y-intercpt is (0,27)
Step-by-step explanation:
you have to subsitute x and y from zero then you go from there
Answer:
Y-intercept (0,27)
X- intercept (-9,0)
Step-by-step explanation:
To find X - intercept, substitute in 0 for y and solve for X. To find Y-intercept, substitute in 0 for x and solve for y.
Y= 3x plus 27
Y = 3(0) plus 27
Y = 0 plus 27
Y = 27 The Y-intercept (0,27)
Y = 3x plus 27
0 = 3x plus 27
0 - 27 = 3x
-27 = 3x
divide by boyh side to 3 and X will be -9
answer choices:
A- y=3x-8
B- y=-2x+1
C- y=-4x-1
D- y=2x-5
The linear equation plotted in the graph is y=4x-1
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The graph of a line that passes through the point (0,-1)
We know the slope intercept form of a line is given by
y=mx+c
Thus if the line passes through this point then
-1=m×0+c
c=-1
Again we can clearly observe that one of the points that lie on the line is (-1,3)
3=-m-1
m=4
∴ The required equation is y=4x-1
Hence, The linear equation plotted in the graph is y=4x-1
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Stumped on math question
Answer:
x = 11/2
Step-by-step explanation:
X-intercept(s) can be found when y = 0
Rearrange the equation
-3y = -2x + 11
y = 2x/3 - 11/3
Let y = 0
0 = 2x/3 - 11/3
Rearrange so that x is on one side
2x/3 = 11/3
x = 11/2
Answer:
5.5
Step-by-step explanation:
The x-intercept of a function is the value of x when y is equal to 0.
Therefore, we can just plug in 0 for y and solve for x:
2x-3(0)=11
2x=11
x=5.5
The x-intercept is 5.5
72 ounces in 6 steaks
Answer:
Each steak is 72/6 = 12 oz
Step-by-step explanation:
Unit rate = total ounces / total steaks:
72 ounces / 6 steaks = 12 ounces per steak
Unit rate = 12 ounces per steak.
The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What equation do you need to solve to find the selling price or prices that would generate $50 in daily profit? What method would you use to solve the equation? Justify your choice.
Answer:
x = 4 or x = 12
Step-by-step explanation:
Given:
y = -10x² + 160x - 430
When y = $50
50 = -10x² + 160x - 430
50 + 430 = -10x² + 160x
480 = -10x² + 160x
-10x² + 160x - 480 = 0
Divide through by -10
x² - 16x + 48 = 0
Solve the quadratic equation using factorization method
+48 = -12 × -4
-16 = -12 -4
Therefore,
-12 and -4 are both factors
x² - 16x + 48 = 0
(x - 4 )(x - 12 ) = 0
x - 4 = 0
x = 4
OR
x - 12 = 0
x = 12
Answer:
Replace y in the equation with 50: (50 = -10x2 +160x - 430) Use factoring to solve the equation. After writing the equation in standard form and dividing each side by -10, it is easy to factor as 0 = (x - 4)(x - 12).
Step-by-step explanation:
Evaluate the following expression.
3-2 x 33
3-1
A. 8
B. 9
C. 12
D. 15
Answer:
is -6x to the 33'd power tims 3 - 1. 3−2x33(3)−1
Step-by-step explanation:
Which lines are perpendicular to the line y - 1= 1(x+2)? Check all that apply
y2= -36% -4)
y-5=9(x - 11)
• y=-3x-2/
y = 1x-2
3x + y=7
) Intro
Done
Step-by-step explanation:
Given the line y-1 = 1(x+2), in order to know the line that is perpendicular to the given line, we will first find the slope of the known line.
The standard form of equation of a line is expressed as y = mx+c
m is the slope
c is the intercept
Rewrite the equation given
y-1 = 1(x+2)
y-1 = x+2
y = x+2+1
y = x+3
Comparing to the standard form, the slope m = 1.
For two lines to be perpendicular, the product of their slope must be -1 i.e mM = -1
Substitute
1(M) = -1
M = -1
For us to know the line that is perpendicular to the given line, its slope must be -1.
Since none of the equation has a slope of -1, hence none of the lines are perpendicular to the line y - 1= 1(x+2).
given the f(x)=5x-3 find x when f(x)=25
Answer:
28/5
Step-by-step explanation:
[tex]f(x) = 5x - 3 = 25 [/tex]
[tex]5x = 25 + 3[/tex]
[tex]5x = 28[/tex]
[tex]x = \frac{28}{5} [/tex]
I think this is the answer
Can you find the numbers as powers with the given bases as your clue? Example: the number is 64 and the base is 4. I test 4x4=16 Then 16x4=64 So my power must be 43 because 4x4x4=64. Now you try... 1. It has a value of 32; it has a base of 2 2. 81, base 9 3. 81, base 3 4. 100, base 10
Step-by-step explanation:
For 32:
The factors are as shown:
32 = 2*2*2*2*2
32 = 2²*2³
32 = 2²⁺³
32 = 2⁵ (Base of 2 and power of 5)
For 81:
factors
81 = 3*3*3*3
81 = 3²*3²
81 = 3²⁺²
81 = 3⁴ (Base of 3 and power of 4)
For 100:
factors
100 = 10*10
100 = 10² (Base of 10 and power of 2)
quickly, will mark brainliest
Answer: IDKDIKDIDKIKDI
Step-by-step explanation:
Find the value of a for which the solution of the inequality is all real numbers
a(x + 3) < 5x + 15 - X
Answer:
x = 3
Step-by-step explanation:
(3 • (5x - 15)) - 15 • (x - 3) = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
5x - 15 = 5 • (x - 3)
Equation at the end of step
3
:
15 • (x - 3) - 15 • (x - 3) = 0
STEP
4
:
Pulling out like terms
4.1 Pull out 15
Pulling out like terms :
4.2 Pull out x-3
After pulling out, we are left with :
15 • x-3 • ( 1 * 1 +( (-1) * (-1) ))
Equation at the end of step
4
:
30 • (x - 3) = 0
STEP
5
:
Equations which are never true
5.1 Solve : 30 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
5.2 Solve : x-3 = 0
Add 3 to both sides of the equation :
x = 3
One solution was found :
x = 3
The required value of a for which the solution of the inequality is all real numbers is a > 4.
What is inequality?
A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now the given inequality is,
a(x + 3) < 5x + 15 - x
or, a(x + 3) < 4x + 15
Now let us solve for x first,
⇒ ax + 3a < 4x + 15
Subtract 3a from both sides we get,
ax < 4x + 15 - 3a
Subtract 4x from both sides we get,
ax - 4x < 15 - 3a
or, (a - 4)x < 15 - 3a
Dividing both the side by (a - 4) we get,
x < (15 - 3a) / (a - 4)
Now for solutions to be real numbers,
a - 4 > 0
subtracting 4 both the side we get,
⇒ a > 4
this is the required value of a for which the solution of the inequality is all real numbers
Thus, the required value of a for which the solution of the inequality is all real numbers is a > 4.
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Kiran sells f full boxes and h half-boxes of fruit to raise money for a band trip. He earns $5 for each full box and $2 for each half-box of fruit he sells and earns a total of $100 toward the cost of his band trip. The equation 5f+2h=100 describes this relationship. Solve the equation for f.
Answer:
f = (100 - 2h) / 5
Step-by-step explanation:
Given:
5f + 2h = 100
Solve the equation for f.
5f + 2h = 100
Subtract 2h from both sides
5f + 2h - 2h = 100 - 2h
5f = 100 - 2h
Divide both sides by 5
5f / 5 = (100 - 2h) / 5
f = (100 - 2h) / 5
If f = 1 full box
h = 1/2 box
h = 1/2 of f
h = 1/2f
Substitute h = 1/2f into
f = (100 - 2h) / 5
f = {100 - 2(1/2f)} / 5
f = (100 - 2/2f) / 5
5f = 100 - f
5f + f = 100
6f = 100
f = 100 / 6
= 16.67
f = 16.67
The required value of f is 16.67.
Given that ;
Kiran sells full box of fruit cost for each box = f = $5
And Kiran sells half box of fruit cost for each = h = $2
According to the question ;
For full box cost + for half box cost = Total cost of his band trip
5f + 2h = 100
Solve the equation following equation for f .
5f + 2h = 100
Subtract 2h from both sides
5f + 2h - 2h = 100 - 2h
5f = 100 - 2h
Divide both sides by 5
[tex]\frac{5f}{5} = \frac{100}{5} - \frac{2h}{5}[/tex]
f = 20-2h
For full box f = 1 full box
For half box h = 1 half box
It means h = [tex]\frac{1}{2}[/tex] of f
h = [tex]\frac{1}{2}f[/tex]
Substitute the value of h
[tex]f = \frac{(100-2h)}{5} \\f = \frac{100-2(\frac{1}{2f} )}{5}[/tex]
[tex]f = \frac{100-f}{5}[/tex]
5f = 100 - f
5f + f = 100
6f = 100
[tex]f = \frac{100}{6}[/tex]
f = 16.67
The required value of f is 16.67.
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The scissor lift is a device that can lower and raise a platform. the scissor lift can raise the platform at a rate of 2.0 inches per second after t seconds is given by H=2.0t +35. after how many minutes will the lift be at least 50 feet off the ground
Answer:
i thank it is 25 seconds.
Step-by-step explanation:
Help!! Plss!!The Boone family is buying a new house that
was originally listed for $350,000. They were able
to purchase the house for $295,000. What was
the percent decrease in the cost of the house to
the nearest tenth of a percent?
Answer:
15.7% decrease
Step-by-step explanation:
Solve x^2 = 64, where x is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Answer:
x=8
Step-by-step explanation:
8 times 8 equals 64
1.what is the value of X
2. What is the value of the angle represented by(2x-10)?
Answer:
2x - 10=65-x
2x+x=65+10
3x=75
x=75/3
x=25 (1.)
2x - 10
2*25-10
50-10
40 (2.)
h(x)=−x−1, find h(6)
h(x) = -x-1
Then just substitute x =6
Then,
h(6) = (- 6-1)
=> h(6)= -7select the story problem that this this division problem represents 3/4 divided by 1/3
Answer:
3/4 divided by 1/3 would equal 2 1/4 or 2.25.
Round 463,751 to the nearest hundred.
Answer:
463,800
Step-by-step explanation:
:) watch this be wrong lol
PLEASE HELP ME I NEED THIS DONE TODAY!!!
Taylor swam 3 different heats in the 100m freestyle. The first heat was 29.1 seconds,the second heat was 28.7 seconds, and the third heat was 27.2 seconds. What was the difference between her best time and her worst time?
Answer:
16.5 you have to add the divde
Round 433,321 to the nearest ten thousand.
Answer:
430,000
Step-by-step explanation:
Answer: 430,000
Step-by-step explanation: hope this helps
What’s 19,975 divided by 25 show your work
the answer to the question is 799
Hi hope your having a good day please answer this
17. Name the word that matches the definition given: Figures that have the same shape but not necessarily the same size.
A. similar figures
B. scale factor
C. scale
D. congruent figures
Answer:
A
Step-by-step explanation:
For each problem, select the answer from the two choices.
1. The value of 25 · (8.5) is:
a. More than 205
b. Less than 205
2. The value of (9.93) · (0.984) is:
a. More than 10
b. Less than 10
3. The value of (0.24) · (0.67) is:
a. More than 0.2
b. Less than 0.2
Answer:
a. More than 20b. Less than 10b. Less than 0.2Step-by-step explanation:
212.59.70.1608Hope it helped you
Answer:
1. [A] More than 205
2. [B] less than 10
3. [B] less than 0.2
Step-by-step explanation:
1. The value of 25 · (8.5) is:
a. More than 205
b. Less than 205
Solve:
25 · (8.5) = 212.5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2. The value of (9.93) · (0.984) is:
a. More than 10
b. Less than 10
(9.93) · (0.984) = 9.77112
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3. The value of (0.24) · (0.67) is:
a. More than 0.2
b. Less than 0.2
(0.24) · (0.67) = 0.1608
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~lenvy~
In the figure, the measure of angle 9 is 80 degrees and the measure of angle 5 is 68. Find the measure of each angle.
Answer/Step-by-step explanation:
Given:
m<9 = 80°,
m<5 = 68°
Lines w and v are parallel to each other.
m<1 = m<9 (corresponding angles theorem)
m<1 = 80°
m<2 + m<1 = 180° (linear pair)
m<2 + 80° = 180° (substitution)
m<2 = 180° - 80°
m<2 = 100°
m<3 = m<1 (vertical angles are congruent)
m<3 = 80°
m<4 = m<2 (vertical angles are congruent)
m<4 = 100°
m<6 + m<5 = 180° (linear pair)
m<6 + 68° = 180° (substitution)
m<6 = 180° - 68°
m<6 = 112°
m<7 = m<5 (vertical angles)
m<7 = 68°
m<8 = m<6 (vertical angles)
m<8 = 112°
m<10 = m<2 (corresponding angles)
m<10 = 100°
m<11 = m<9 (vertical angles)
m<7 = 80°
m<12 = m<10 (vertical angles)
m<12 = 100°
m<13 = m<5 (corresponding angles)
m<13 = 68°
m<14 = m<6 (corresponding angles)
m<14 = 112°
m<15 = m<13 (vertical angles)
m<15 = 68°
m<16 = m<14 (vertical angles)
m<16 = 112°
numerical expressions:(I need help)
1.) x-27=(-14) x=?
2.) x-72=12 x=?
3.) x*12=60 x=?
1). Add 27 to each side of the equation.
2). Add 72 to each side of the equation.
3). Divide each side of the equation by 12.
URGENT! 10 points
Solve for x then find DE
Answer:
14
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
x+7+7=4x+2 simplify
Can somebody please help with this?
Answer:
x=8°
y= 96°
z= 96°
Step-by-step explanation:
Solve for z first. The whole circle is 360° so if you only count half the angles it will add up to 180°.
Solve for z:
48+36+z=180°
84+z+180°
z=96°
Now that you have z you can solve for x by using only the bottom half of the circle.
z+36+6x=180° *remember z=96
96+36+6x=180
132+6x=180
6x=48
x=8°
Now you can solve for y by either plugging x into an equation or by knowing that opposite angles are equal.
y=96°
