Start by applying the log on both sides wi
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 timesBrooke's age. How old is Darius now?
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 times
Brooke's age. How old is Darius now?
Let
x ------> darius's age
y -----> Brooke's age
we know that
x+y=78 ------> equation A
(x-7)=3(y-7) -----> equation B
solve the sytem of equations
isolate the variable x in the equation A
x=78-y -------> equation C
substitute equation C in equation B
78-y-7=3(y-7)
slve for y
71-y=3y-21
3y+y=71+21
4y=92
y=23
Find the value of x
x=78-y
x=78-23=55
therefore
Darius now is 55 year old
1. A bank account pays 0.5% monthly interest.a. If $600 is put in the account, what will the balance be at the end of one year, assuming no additionaldeposits or withdrawals are made?b. What is the effective annual interest rate?c. Is the effective annual interest rate more or less than 6% (the nominal interest rate)?
a. 637.007$
b. 0.5%
c. Less than the nominal interest rate
Explanation & Steps:
a.
[tex]600\cdot(1.005)^{12}\text{ }\cong637.006687\text{ }\cong\text{ 637.007\$}[/tex]b.
[tex]\begin{gathered} (1+(\frac{0.5\%}{12}))^{12}\text{ - 1 = x} \\ (1\text{ + (}\frac{0.005}{12}))^{12}\text{ - 1 = x} \\ (1+0.000417)^{12}-1\text{ = x} \\ (1.000417)^{12}\text{ - 1 = x} \\ 1.000502\text{ - 1 =x} \\ 0.00502\text{ = }0.5\text{ = x} \end{gathered}[/tex]c. 0.5% < 6%
Drag each tile to the correct box.Arrange the functions in ascending order, starting with the function that eventually has the least value and ending with the function thateventually has the greatest value.3x + 8+4+3x² + 63x4*
To answer the question we are going to graph the functions given:
From the graph we notice that the order will be:
[tex]\begin{gathered} 3x \\ 3x+8 \\ x^2 \\ x^2+6 \\ 4^x \\ 4^x+3 \end{gathered}[/tex]Ever NL OP N 2 PN, and is the midst of MO. PALUN APON STATEMENTS REASONS: 2. Nisthe MO 1. Gren Given the following proof, what is the 5th reason? 2 MZ - OP 2. Given 3. IN EN 3. Given 2 MIN ON 4. Definition of midpoint 5 5. ALMN 2 APON SAS CPCTC SSS ASA
In this case, we have to use the SSS Postulate for the congruency of the triangles, that is, if three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.
We have that all reasons are given congruent sides. The midpoint divides the segment into two equal parts, then the angles are congruent because of the reason: SSS ( SSS Postulate for congruency of triangles).
Carlos fills an aquarium to a depth of 4/5 meters in 8 minutes. What is the unit rate in minutes per meter?write the answer in the simplest form
Step 1. The information that we have is:
The aquarium is filled to a depth of 4/5 meters in 8 minutes.
Required: Find the unit rate in minutes per meter.
Step 2. First, we convert 4/5 meters to a decimal number:
[tex]\frac{4}{5}\text{ meters }=0.8\text{ meters}[/tex]Step 3. To find the unit rate, we need to divide the number of minutes by the number of meters:
[tex]\frac{8minutes}{0.8\text{ meters}}[/tex]The result is:
[tex]10\text{ minutes per meter}[/tex]The unit rate is 10 minutes per meter.
Answer: 10
Madison says that 579.8 x 0.001 is the same as 579.8 : 10? Is she correct? Explain your answer in 3-5 sentences
Step 1:
First, write the expression for each value
[tex]\begin{gathered} 579.8\text{ }\times\text{ 0.001 = 0.5798} \\ \\ 579.8\text{ }\times\text{ 10 = 5798} \end{gathered}[/tex]Final answer
The two are not the same because the value of 579.8 x 0.001 is less than the value of 579.8 x 10.
Which of the following expressions is equal to5 - 2(x + 2)?O -2x+1O 3x+6O -2x+2O 3x+2
Given:
an expression is given as 5 - 2(x + 2)
Find:
we have to simplify the expression and find correct expression from the options, which is equal to the given expression.
Explanation:
Now
5 - 2(x + 2) = 5 - 2x - 4 = - 2x + 1
Therefore, 5 - 2(x + 2) = - 2x + 1
help meeeeeee ok will you
∠ BCD has the same measure as ∠ CFG and ∠ FIJ.
If ∠ GFI measures x degrees, then the measure of HIK is (180 - x) degrees.
The sum of the measures of ∠ CFE and ∠ ACF is 180 degrees.
Given that:-
AD II EG II HJ and BK is the transversal.
As AD II EG
∠ BCD = ∠ CFG
As EG II HJ
∠ CFG = ∠ FIJ
Hence,
∠ BCD has the same measure as ∠ CFG and ∠ FIJ.
As ∠ GFI = x degrees
Hence, ∠ FIJ = (180 - x) degrees (Sum of internal angles is 180 degrees)
∠ FIJ = ∠ HIK (Vertically Opposite angles)
Hence,
∠ HIK = (180 - x) degrees.
As ∠ CFE and ∠ ACF are internal angles, hence their sum will be 180 degrees.
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Carol Wynne bought a silver tray that originally cost $150 and was advertised at 30% off. What was the sale price of the tray?The sale price was $(Type an integer or a decimal.)
The original price was $150
the discount was 30%
therefore, the final price is the following:
[tex]\begin{gathered} P_{final}=150*(1-0.3) \\ =150*0.7 \\ =105 \end{gathered}[/tex]Thus, the final price of the tray was $105
The values of bills for the last 12 months 338.28 328.93 341.03331.29356.01329.03328.46586.34401.23386.37388.43367.31A) Find the sample mean and sample standard deviation of your data.B) Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?C) Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.
step 1
Find out the mean
we have the data set
Mean=(338.28+328.93+341.03+331.29+356.01+329.03+328.46+586.34+401.23+386.37+388.43+367.31)/12
Mean=(4,482.71)/12
Mean=373.56
step 2
Find out the sample standard deviation
Subtract the mean from each data point and square it
(338.28-373.56)^2=1244.6784
(328.93-373.56)^2=1991.8369
(341.03-373.56)^2=1058.2009
(331.29-373.56)^2=1786.7529
(356.01-373.56)^2=308.0025
(329.03-373.56)^2=1982.9209
(328.46-373.56)^2=2034.01
(586.34-373.56)^2=45275.3284
(401.23-373.56)^2=765.6289
(386.37-373.56)^2=164.0961
(388.43-373.56)^2=221.1169
(367.31-373.56)^2=39.0625
Add the squared deviations
S=56,871.6353
Divide by the number of data sets minus 1
S/(n-1)
where
n=12
56,871.6353/(12-1)=5,170.14866
Take the square root
sample standard deviation=√(5,170.14866)
sample standard deviation=71.90
Part B
Remember that
z =(x - μ)/s
where
μ=373.56
s=71.90
I take the bills
jamie needs to find the height of the parallelogram. the base is three inches long and the area is 30 square inches. what is the height. step one of 2:choose the correct formula
10 inches
Explanation:Given:
base of parallelogram = 3 in
Area pf the paralllelogram = 30 square inches
height = ?
To find the height, we apply the formula for area of parallelogram:
[tex]\begin{gathered} \text{Area of parallelogram = Base }\times\text{ height} \\ \end{gathered}[/tex][tex]\begin{gathered} 30\text{ = 3 }\times\text{ height} \\ \text{divide both sides by 3:} \\ \frac{30}{3}\text{ = }\frac{\text{3height}}{3} \\ \text{height = 10 } \\ \\ \text{The hright of parallelogram is 10 in} \end{gathered}[/tex]The angle of elevation to the top of a 10-story skyscraper ismeasured to be 3° from a point on the ground 2000 feet fromthe building. What is the height of the skyscraper to thenearest hundredth of a foot?
ANSWER :
The height is 104.82 feet
EXPLANATION :
The angle of elevation to the top of the building is 3 degrees from a point that is 2000 feet away from the building.
Using tangent function :
[tex]\tan\theta=\frac{\text{ opposite}}{\text{ adjacent}}[/tex]The opposide side to the angle is H and the adjacent side is 2000 feet.
Then :
[tex]\begin{gathered} \tan3=\frac{H}{2000} \\ \\ H=2000\tan3 \\ H=104.816\sim104.82\text{ }ft \end{gathered}[/tex]The polynomial P(x) = 5x^3 + 2x^2- 42 has ___ local maxima and minima
SOLUTION:
Case: Local maxima and local minima
Given:
[tex]P(x)=5x^3+2x^2-42^{}[/tex]Required: To find the local maxima and minima
Method:
[tex]\begin{gathered} P(x)=5x^3+2x^2-42^{} \\ \text{ } \end{gathered}[/tex]First the find the first derivative:
[tex]\begin{gathered} P^{\prime}(x)=15x^2+4x \\ we\text{ make P'(x) = 0} \\ 15x^2+4x=\text{ 0} \\ x(15x+4)=0_{} \\ x=0\text{ or 15x+4 =0} \\ x=\text{ 0 or x= }\frac{-4}{15} \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = 0. The points are {-1, 1}.
[tex]\begin{gathered} \text{when x=-1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(-1)=15(-1)^2+4(-1) \\ P^{\prime}(-1)=15(1)^2-4 \\ P^{\prime}(-1)=15^{}-4 \\ P^{\prime}(-1)=11 \\ \text{when x= 1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(1)=15(1)^2+4(1) \\ P^{\prime}(1)=15^{}+4 \\ P^{\prime}(1)=19 \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = -4/15. The points are {-1, 0}
[tex]\begin{gathered} \text{when x= 0} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(0)=15(0)^2+4(0) \\ P^{\prime}(0)=0^{}+0 \\ P^{\prime}(0)=0^{} \end{gathered}[/tex]Final answer:
The local minima is at x= 0 while the local maxima is at x= -4/15
Answer To this question so that we can move on to the next question so we can get all this homework done
A fuelling vehicle finished filling a plane with 12.40 tons of fuelat 10:35. If the fuelling rate is 0.20 ton of fuel per min, at whattime did the fuelling start? Give your answer in a 12-hour clockformat, such as 9:00.9:33xHmm, that wasn't the right answer. Let's give it one more try.
it f (x) = √ which equation describes the graphed function? y = f(-x+4)
y = -f(x+4)
y= -f(x-4) y=f(-x-4)
For the given equation f(x) = √x , the equation which help us defined the graphed function is given by y = f(-x +4).
As given in the question,
Given equation is equal to :
f(x) = √x
Equation which help us to defined the graphed function is as follow:
From the graph we have different values of x we get,
When x = 4, x=3 x=2
a. y = f(-x +4) y = f(-x+4) y = f(-x+4)
= √-x +4 = √-3+4 = √-2+4
= √-4 +4 = 1 = 1.414
= 0
Correct. Correct Correct
b. y = -f(x+4)
= -√x+4
= -√4+4
≠ 0
Incorrect.
c. y = -f(x-4) y = -f(x-4)
= -√x-4 = -√3-4
= -√4-4 = -√-1
= 0
Correct Incorrect
d. y = f(-x-4)
= √-x-4
=√-4-4
≠0
Incorrect
Therefore, for the given equation f(x) = √x , the equation which help us defined the graphed function is given by y = f(-x +4).
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"A quadrilateral is a square if and only if it has fourright angles."Which of the following terms provides acounterexample for why the biconditional statement is
Given statement: A quadrilateral is a square if and only if it has four right angles
Counterexample: A quadrilateral with four right angles can be also a rectangle. Then, not all quadrilaterals with four right angles are squares.
Answer: Rectangle
y^(3)-27=9y^(2)-27y. could you please show steps
The solution to the algebraic expression is y =3
Algebraic expressionThis algebraic expression contain variable and constant along with unknow variables.
y^(3)-27=9y^(2)-27y
Add 27y to both sides
y^(3)-27 +27y =9y^(2)-27y +27y
Simplify
y^3-27 +27y =9y^2
Subtract 9y^2 from both sides
y^3-27 +27y-9y^2 =9y^2- 9y^2
y^3-27 +27y-9y^2= 0
Simplify
y^3 - 9y^2 + 27y - 27 =0
Factor by grouping y^3 - 9y^2 + 27y - 27 ; (y-3)^3
(y -3) (-y^2 + 6y -9) = 0
(y-3)^3 =0
Using the zero factor principle if ab = then a = 0 or b= 0
y-3= 0
Add 3 to both sides
y =3
Therefore, solution to the algebraic expression is y =3
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what is the H3O of a solution with a pH of 1.90
Given that
pH = 1.90
[tex]\begin{gathered} pH=-log(H^+_3O) \\ pH\text{ = 1.90} \\ \text{Take the log of both sides} \\ 1.90=-log(H^+_3O) \\ 10^{-1.9}=H^+_3O \\ H^+_3O\text{ = }1.26\cdot10^{-2}molL^{-1} \end{gathered}[/tex]3. Monthly Car Payment: The Mills' purchased a new car for $29,575. The tax on thevehicle was 3.25% and title and license fees were $210. They were able to get a trade-in of$4,500 on Jackson's old car. If they financed the remainder at 5.25% for 5 years, what wasthe monthly payment on the car loan?Select the correct answer for each dropdown menu.A. Total Purchase Price (including taxes and fees): [Select]B. Loan Amount (with down payment): (Select]C. Interest on Loan: [Select]D. Amount to be repaid: [Select]Select)E. Amount of each payment:
From the question;
Purchase price = $29,575
Tax = 3.25%
License fee = $210
A. We are to calculate the total purchase price
[tex]\begin{gathered} \text{Total Purchase price = \$29,575 + 3.25\% 0f \$29,575 + \$210} \\ \text{Total purchase price = \$29,575 + \$961.19 + \$210} \\ \text{Total purchase price = \$30,746.19} \end{gathered}[/tex]Therefore,
Total Purchase price = $30,746.19
B. Loan amount
[tex]\text{Loan amount = Total purchase - trade-in payment}[/tex]Trade-in payment = $4,500
Therefore,
[tex]\begin{gathered} \text{Loan amount = \$30,746.19 - \$4,500} \\ \text{Loan amount = \$26,246.19} \end{gathered}[/tex]Therefore,
Loan Amount = $26,246.19
C. Interest on loan
[tex]\text{Interest = }\frac{P\times R\times T}{100}[/tex]From the question
P = Loan amount =$26,246.19
R = 5.25
T = 5years
Therefore,
[tex]\begin{gathered} \text{Interest = }\frac{\text{\$26,264.19 }\times\text{5.25 }\times5}{100} \\ \text{Interest =}\frac{\text{\$688,957.5}}{100} \\ \text{Interest = \$6,889.6} \end{gathered}[/tex]Therefore,
Interest on loan = $6,889.6
D. Amount to be repaid
[tex]\begin{gathered} \text{Amount = Loan amount + Interest} \\ \text{Amount = \$26,246.19 + \$6,889.6} \\ \text{Amount = \$33,135.8} \end{gathered}[/tex]Therefore,
Amount to be repaid = $33,135.8
E. Amount of each repayment
since the repayment is on a monthly basis
[tex]\begin{gathered} \text{The loan is for 5 years} \\ \text{Hence, } \\ T\text{otal months = 5 }\times12\text{ months} \\ T\text{otal months = 60 months} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Amount of each payment = }\frac{Amount\text{ to be repaid }}{Total\text{ months}} \\ \text{Amount of each payment = }\frac{\text{\$33,135.8}}{60} \\ \text{Amount of each payment = \$552.3} \end{gathered}[/tex]Therefore,
Amount of each payment = $552.3
Hero and Lisa are photographers they take pictures of seniors for high school yearbooks they charge a standard fee for taking the pictures there’s also a charge for each set of prints ordered so the number sets of prints determine the total cost S stand for the sets of prints ordered right the rule that describes the students total cost
Given:
We get the points (0,30), (1,31),(2,32), and (3,33) from the table.
Required:
We need to find the total cost.
Explanation:
From the point(0,30).
There is an initial cost of $30 for print.
Let s be the number of sets of prints ordered.
Let k be the additional cost for each number of sets of print
The equation of the given model is
[tex]Total\text{ cost =ks+30}[/tex]Consider the point (1,31).
Substitute total cost =31 and s=1 in the equation.
[tex]31\text{=k\lparen1\rparen+30}[/tex][tex]31\text{=k+30}[/tex]Subtract 30 from both sides.
[tex]31-30\text{=k+30-30}[/tex][tex]1\text{=k}[/tex]Substitute k =1 in the equation.
[tex]Total\text{ cost =s+30}[/tex]Consider the point (2,32).
Substitute total cost =32 and s =2 in the equation.
[tex]32\text{ =2+30}[/tex]It is true, so the equation satisfies the values in the table,
Final answer:
[tex]Total\text{ cost =s+30}[/tex]I have two answers for the simplified quotient, I'm not sure which one it is
factor 2 on the denominator od the second one
What is the exact volume of the figure?5 om12 cm(The figure is not to scale.)cm3V=(Type an exact answer in terms of A.)
Explanation
The volume of a cone is one third the area of the base multiplied by the height of the cone:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]This cone has a radius of 5cm and a height of 12cm. The volume is
[tex]\begin{gathered} V=\frac{1}{3}\pi(5\operatorname{cm})^2(12\operatorname{cm}) \\ V=\frac{1}{3}\cdot\pi\cdot5^2\cdot12\cdot cm^{2}cm \\ V=\pi\cdot\frac{1}{3}\cdot25\cdot12\operatorname{cm}^{3} \\ V=\pi\cdot\frac{300}{3}cm^{3} \end{gathered}[/tex]Answer
The volume of the figure is:
[tex]V=100\pi cm^{3}[/tex]Finding the multiplier to give a final amount after a percentage increase or decrease
(a) The function with which the new price can be found in terms of the original price is; New price = 0.86 × Original price
(b) New price: $34, 056
What is a function in mathematics?A function is a relationship that maps the elements of a set A to the elements of another set B, such that each element of A is mapped to only one element of the set B.
The original price of the car = $39,600
The percentage by which the price of the car is decreased = 14%
The equation that can be used to find the new price in terms of the original price is therefore;
New price = (1 - 0.14) × Original price = 0.86 × Original price
Therefore;
New price = 0.86 × Original price(b) The value of the new price is obtained by plugging in the value of the original price in the equation above, as follows;
New price = 0.86 × 39,600 = 34,056
The new price is; $34,056
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Do these coordinate pairs represent a function?: *{(2, 4), (2,5), (3,6), (3, 7) }
Given,
The coordinate pairs are
{(2, 4), (2,5), (3,6), (3, 7) }
Here the argument 2 returns to both 4 and 5 while 3 returns to both 6 and 7.
This violates the defination of function.
Thus the coordinate pairs doesnot represent a function.
The answer is No.
What is the measure of ZBDC?What is the measure of arc length BC?
SOLUTION
Step 1:
To find the measure of
Step 2:
The angle subtended by an arc at the centre is twice the angle subtended at the circumference. More simply, the angle at the centre is double the angle at the circumference.
Step 3:
Dividing both sides by 2, we have;
[tex]\begin{gathered} <\text{BDC = }\frac{BOC}{2}\text{ = }\frac{138}{2} \\ \\Step 4:
We are to find the measure of arc length BC;
Angle BOC is given as 138
[tex]\begin{gathered} \frac{\theta}{360}\text{ x 2 }\pi\text{ r} \\ \\ \frac{138}{360}\text{ x 2 x 3.14 x r } \\ \\ 2.407r \end{gathered}[/tex]Note: Since the value of the radius was not given so we need to express our answer in term of r.
The measure of arc length BC is 2.407r, where r is the radius.
whstbis the area in square inches of the shaded part of the retangle below
The shaded area is trapezium with parallel sides as a = 10, b = 5 and height of trapezium is h = 18 in.
The formula for the area of trapezium is,
[tex]A=\frac{1}{2}\cdot(a+b)\cdot h[/tex]Determine the area of the tapezium.
[tex]\begin{gathered} A=\frac{1}{2}\cdot(10+5)\cdot18 \\ =15\cdot9 \\ =135 \end{gathered}[/tex]So area of shaded region is 135 square inch.
Manuel is planting grass seed in a rectangular lot that is 156 inches long and 228 inches wide. How wide is the deck in feet?
1 foot = 12 inches
The width of the rectangular lot = 228 inches
To change it to feet divide it by 12
The wide of the deck = 228/12 = 19 feet
The answer is 19 feet
Factor out the greatest common factor. Simplify the factors, if possible.6x4 - 42x3 + 12x2Select the correct choice below and fill in any answer boxes in your choice.O A. 6x4 - 42x3 + 12x2 =(Type your answer in factored form.)OB. There is no common factor other than 1.ih
You have to find the greatest common factor first.
To do so, do as follows:
[tex]6x^4-42x^3+12x^2[/tex]Factors of 6 are: 1, 2, 3, 6
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The greates common factor is the greatest common factor shared by all values, in this case is 6
Now to factor it out you have to divide each term of the equation by it.
[tex](\frac{6x^4}{6})=x^4[/tex][tex](\frac{42x^3}{6})=7x^3[/tex][tex](\frac{12x^2}{6})=2x^2[/tex]The expression with the GCF factorized is then:
[tex]6(x^4-7x^3+2x^2)[/tex]if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<14=?
According to the diagram, angles 10 and 14 are supplementary, so they sum 180°.
[tex]\begin{gathered} m\angle10+m\angle14=180 \\ 77+m\angle14=180 \\ m\angle14=180-77 \\ m\angle14=103 \end{gathered}[/tex]Hence, angle 14 measures 103°.