y = -2
Explanation:
10y-(4y+8)= -20
Open the bracket:
10y - 4y - 8 = -20
Note: multiplication of opposite signs give a negative number
Collect like terms:
10y - 4y = -20 + 8
6y = -12
Divide through by 6:
[tex]\begin{gathered} \frac{6y}{6}=\frac{-12}{6} \\ y\text{ = -2} \end{gathered}[/tex]The answer is y = -2
suppose a bag if groceries costs $14.50 this year and the average annual rate of inflation over the last five years is 3%. if the inflation rate continues to be 3% per year, how much will the same bag of groceries cost 2 years from now? (round to the nearest $0.10)
Let:
Op = Original price = $14.50
r = rate of inflation = 3% = 0.03
After the first year, the cost of the bag of groceries will be:
[tex]\begin{gathered} P1=Or+r\cdot Or \\ P1=14.50+0.03\cdot14.50=14.935 \end{gathered}[/tex]After the 2nd year, the cost will be:
[tex]\begin{gathered} P2=P1+rP1 \\ P2=14.935+0.03\cdot14.935=15.38 \end{gathered}[/tex]A truck driver is allowed to drive amaximum of 7.5 hours each day. If thedriver’s average speed is 58 miles per hour,how many miles does the driver travel eachday
The speed can be described as:
[tex]speed=\frac{distance}{time}[/tex]then, if want to find the distance we can say that,
[tex]speed\times time=distance[/tex]if the driver has an average speed and a time limit,
[tex]\frac{58miles}{hour}\times7.5hour=435miles[/tex]Answer:
we can say that the driver can travel a maximum of 435 miles per day at an average speed of 58 miles per hour.
17. A company ships notepads in rectangular boxes that each have inside dimensions measuring 9 inches long, 9 inches wide, and 12 inches tall. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the maximum number of notepads that will fit in 1 closed box? A. 10 B. 11 C. 12 D. 22 E. 36
The volume of each box is:
[tex]V=\text{length}\cdot\text{width}\cdot\text{height}[/tex]Substituting with length = 9 in, width = 9 in, and height = 12 in, we get:
[tex]\begin{gathered} V=9\cdot9\cdot12 \\ V=972in^3 \end{gathered}[/tex]The volume of each notepad is:
[tex]V=\text{length}^3[/tex]Substituting with length = 3 in, we get:
[tex]\begin{gathered} V=3^3 \\ V=27in^3 \end{gathered}[/tex]The number of notepads that fit in 1 box is obtained dividing the volume of the box by the volume of each notepad, as follows:
[tex]\frac{972in^3}{27in^3}=36\text{ notepads}[/tex]A recipe requires \frac{1}{4}1414 cup of water for each \frac{1}{3}1313 cup of milk. How many cups of water are needed for each cup of milk?
1/4 cup of water----------------------->1/3 cup of milk
x cups of water------------------------> 1 cup of milk
using cross-multiplication:
[tex]\begin{gathered} \frac{\frac{1}{4}}{x}=\frac{\frac{1}{3}}{1} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=\frac{\frac{1}{4}}{\frac{1}{3}} \\ x=\frac{3}{4} \end{gathered}[/tex]Answer:
3/4
The function f(x) = x² - 6x+9 is shifted 5 units to the right to create g(x).What is g(x)?A. g(x) = (x - 5)^2 - 6(x - 5) +9B. g(x) = (x + 5)² - 6(x+5) +9C. g(x) = (x² - 6x +9) - 5D. g(x) = (x² - 6x + 9) + 5
Solution:
Given the function:
[tex]f(x)=x^2-6x+9[/tex]To create g(x), the function f(x) is shifted 5 units to the right.
Firstly, the graph of f(x) is shown below:
To create g(x), we have
[tex]g(x)=(x-5)^^2-6(x-5)+9[/tex]The graph g(x) is shown below:
Hence, the g(x) function is expressed as
[tex]g(x)=(x-5)^2-6(x-5)+9[/tex]The correct option is A
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S=0.50M+1\$.75 , where is the number of miles driven The company also offers an option to insure the car against damage. The insurance charge (in dollars) is given by the function I = 0.25M + 5.80 Let C be the total charge (in dollars) for a rental that includes insuranceWrite an equation relating C to M. Simplify your answer as much as possible.
Okay, here we have this:
Considering the provided information, we are going to find the requested equation, so we obtain the following:
Then we can see that we must find the function that represents the total cost, therefore we have
Total cost=Standard charge+ Insurance charge
Replacing:
C=0.50M+15.75+0.25M+5.80
C=(0.50M+0.25M)+(15.75+5.80)
C=0.75M+21.55
Finally we obtain that the equation for the total charge is C=0.75M+21.55
going to send you pictures
Answer: We have to find the probablity that a registered voter votted in the election
[tex]\begin{gathered} \text{Voters = 3072757} \\ \text{Not-Voted = 3481030 } \\ \text{Total registered=3,072,757+3,481,030=}6,553,787 \end{gathered}[/tex]Therefore, the probability that a registered voter voted is:
[tex]P_r=\frac{3072757}{6553787}=46.56\text{ percent}[/tex]Likewise, the probablity that a registered voter did not vote is:
[tex]53.11\text{ percent }[/tex]
What is the value of log4 16?
Answer:
[tex]\log_416=2[/tex]
Step-by-step explanation:
Given expression:
[tex]\log_416[/tex]
Rewrite 16 as 4²:
[tex]\implies \log_44^2[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies 2 \log_44[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies 2 \cdot 1[/tex]
Simplify
[tex]\implies 2[/tex]
Therefore:
[tex]\implies \log_416=2[/tex]
36. If the interest rate on a 30-year mortgage for $325,000 were changed from 2.9% to 2.6%, how much would you save over the life of the loan?
The formula to calculate the mortgage payment is as follows:
[tex]M=P\frac{\lbrack i(1+i)^n\rbrack}{\lbrack(1+i)^n-1\rbrack}[/tex]Where P is the principal loan amount $325,000
i is the monthly interest rate, divide the annual interest rate by 12 to find the monthly interest rate.
n is the number of payments over the lifetime of the loan (months) then as you have a 30-year mortgage n=30 years x 12 months per year=360 payment months.
a. For 2.9% interest rate:
i=2.9%/12=0.029/12=0.002417
Replace the known values:
[tex]\begin{gathered} M1=325,000\frac{\lbrack0.002417(1+0.002417)^{360}\rbrack}{\lbrack(1+0.002417)^{360}-1\rbrack} \\ M1=325,000\frac{\lbrack0.002417\cdot2.38441\rbrack}{\lbrack2.38441-1\rbrack} \\ M1=325,000\frac{0.005762}{1.38441} \\ M1=1352.75 \end{gathered}[/tex]This would be the monthly payment when interest rate is 2.9%
b. For 2.6% interest rate:
i=2.6%/12=0.026/12=0.002167.
[tex]\begin{gathered} M2=325,000\frac{\lbrack0.002167(1+0.002167)^{360}\rbrack}{\lbrack(1+0.002167)^{360}-1\rbrack} \\ M2=325,000\frac{\lbrack0.002167\cdot2.17963\rbrack}{\lbrack2.17963-1\rbrack} \\ M2=325,000\frac{0.004723}{1.17963} \\ M2=1301.1 \end{gathered}[/tex]Thus, to calculate how much would you save over the life of the loan, multiply each monthly payment by 360 payments, and the difference would be the money you save:
[tex]\begin{gathered} At\text{ 2.9\% interest rate:} \\ 1352.75\times360=486989.1 \\ At\text{ 2.6\% interest rate:} \\ 1301.1\times360=468397.5 \\ \text{Money saved: }486989.1-468397.5=18591.6 \end{gathered}[/tex]Answer: You save $18591.6 over the life of the loan if the interest changed from 2.9% to 2.6%
PHU ME Humber. Round to the nearest tenth if necessary. 26% of 13 is what number? * 50 O 338 0 3.4 0 200
3.38
Explanation
Step 1
remember the percentage is a ratio to 100,so
[tex]26\rightarrow\frac{26}{100}=0.26[/tex]so, to find 26 % of any number just multiply by 0.26
so
[tex]\begin{gathered} 26\text{ \% of 13}\rightarrow0.26\cdot13=3.38 \\ \end{gathered}[/tex]so, the answer is 3.38
is 0.6 reduction, enlargement or isometric
Since the scale factor is less than 1 this means that this is a reduction.
Which choices are equivalent to the expression below? Check all that apply.A.75B.C.D.E.F.
SOLUTION
We want to find the expression equivalent to
[tex]5\sqrt{3}[/tex]we have
[tex]\begin{gathered} 5\sqrt{3} \\ =\sqrt{25}\times\sqrt{3} \\ =\sqrt{25\times3} \\ =\sqrt{75} \\ =\sqrt{25}\text{ . }\sqrt{3} \end{gathered}[/tex]hence the answers are options B and F
88,826.564 The 6 in the ones place is ___ the value of the 6 in the hundredth place
Given the question:
88,826.564
The 6 in the ones place is 100 times (greater than) the value of the 6 in the hundredth place, since:
6/0.06 = 100.
Ms. Juhal was making t-shirts. One of the designs had these coordinate points: A (-5, 5), B (-5, 3), C (-5, 1), and D (2, 1). Plot the points on graph paper in the order they are given and connect them. What shape is made?
Given data:
The given coordinates are A (-5, 5), B (-5, 3), C (-5, 1), and D (2, 1).
The below figure shown the graph of the above coordinate.
Thus, the above figure represents the right angle triangle.
Create an equation of a line that is perpendicular to y = 2 3 x − 3
Given data:
The given equation of the line is y= 2x/3 -3.
The standard equation of the line is,
[tex]y=mx+c[/tex]Compare the above equation with the given equation.
[tex]m=\frac{2}{3}[/tex]The equation of the line perpendicular to the given line is,
[tex]\begin{gathered} y-b=-\frac{1}{(\frac{2}{3})}(x-a) \\ y-b=-\frac{3}{2}(x-a) \\ y=-\frac{3}{2}x+\frac{3a}{2}+b \end{gathered}[/tex]Thus, the equation of the line perpendicular to the given line is y=-3x/2 +3a/2 +b.
Find the values of the variables. Then find the side lengths. square LMNO X + 7 M 3x + 1 N
We have the following:
A square has equal sides, therefore we make the following equality
[tex]\begin{gathered} x+7=3x+1 \\ 3x-x=7-1 \\ 2x=6 \\ x=3 \end{gathered}[/tex]now, replacing:
[tex]\begin{gathered} LM=3+7=10 \\ MN=3\cdot3+1=9+1=10 \end{gathered}[/tex]Therefore, the answer is option b
1) A ball is thrown downward from a window in a tall building. Its position at time t in seconds iss(t) = -16t2 + 32t + 55, where s(t) is in feet. How long (to the nearest tenth) will it take the ball to hit the ground?A)-1.2 secB) 1.2 secC) 2.9 secD) 3 sec
The equation for the position is,
[tex]s(t)=-16t^2+32t+55[/tex]When the ball hit the ground then value of height is 0 feet. So value of s(t)=0,
The equation for the time is,
[tex]-16t^2+32t+55=0[/tex]Determine the roots of the equation by using the quadratic formula.
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-32\pm\sqrt[]{(32)^2-4(-16)(55)}}{2(-16)} \\ =\frac{-32\pm\sqrt[]{4544}}{-32} \\ =\frac{-32\pm67.41}{-32} \\ =\frac{-99.41}{-32},\text{ }\frac{35.41}{-32} \\ =3.10,-1.10 \end{gathered}[/tex]The value of time can never be less than 0. so approximate value of time is 3 seconds. Correct option is D part.
Explain with definition and example of Cross Product of Vectors.
Given:
Cross product of vectors.
Required:
To define and explain the cross product of vectors.
Explanation:
Cross product is the binary operation on two vectors in three dimensional space. It again results in a vector which is perpendicular to both the vectors. Cross product of two vectors is calculated by right hand rule.
Right hand rule is nothing but the resultant of any two vectors is perpendicular to the other two vectors. Using cross product, we can also find the magnitude of the resulting vector.
Let
Vector A and Vector B is denoted by
[tex]\vec{A}\times\vec{B}[/tex]and its resultant vector is perpendicular to the vectors A and B.
Cross Product Formula :
[tex]\vec{A}\times\vec{B}=ab\sin\hat{\theta n}[/tex]where n is the unit vector.
Example:
Let
[tex]\begin{gathered} \vec{a}=2i+k \\ \vec{b}=i+j+k \end{gathered}[/tex]So,
[tex]\vec{a}\times\vec{b}=\begin{bmatrix}{i} & {j} & {k} \\ {2} & {0} & {1} \\ {1} & {1} & {1}\end{bmatrix}[/tex][tex]\begin{gathered} =i(-1)-j(2-1)+k(2-0) \\ =-i-j+2k \end{gathered}[/tex]Final Answer:
Cross product is the binary operation on two vectors in three dimensional space.
Teresa made $252 for 12 hours of work. At the same rate, how much would she make for 17 hours of work?
Given:
Amount earned, A=$252.
The number of hours of work, T=12.
The amount earned for one hour work is,
[tex]E=\frac{A}{T}=\frac{252}{12}=21[/tex]Now, the amount earned for t=17 hour work is,
[tex]A^{\prime}^{^{\prime}}=E\times t=21\times17=357[/tex]Therefore, Teresa would make $357 for 17 hour work.
sarah is putting her sweaters in boxes to organize her closet.seven sweaters can fit in each box. sarah will fill as many boxes as possible, and the remaining sweaters will stack on the shelf in the closet. if sarah has 38 sweaters, how many sweaters will go in her closet? Solve the problem. draw a tape diagram to represent the problem.
Given: Sarah can fit 7 sweaters in a box
She has 38 sweaters
the remaining sweaters will stack on the shelf in the closet.
By dividing 38 by 7 we will get:
[tex]\frac{38}{7}=\frac{35+3}{7}=\frac{5\cdot7+3}{7}=5\frac{3}{7}[/tex]So, she will need 5 boxes, she will put 35 sweaters in 5 boxes
The remaining sweaters = 38 - 35 = 3 sweaters
So, the answer is: 3 sweaters will go in her closet
What is the intermediate step in the form (x+a)^2=b(x+a) 2 =b as a result of completing the square for the following equation?
For this problem, we are asked to provide the intermediate step we obtain while completing the square for the following expression:
[tex]-6x^2-235=-48x+11[/tex]Completing the square means to transform the function into a expression such as:
[tex](a+b)^2=a^2+2\cdot a\cdot b+b^2[/tex]For this we will first change all the terms to the left side, as shown below:
[tex]\begin{gathered} 6x^2-48x+235+11=0 \\ 6x^2-48x+246=0 \end{gathered}[/tex]Since all three terms are divisible by 6, we need to use factorization to isolate the 6 from the equation:
[tex]6\cdot(x^2-8x+41)=0[/tex]Now, we need to rewrite the expression inside the parenthesis, such as we will obtain a form that is roughly equal to the perfect square we're looking for.
[tex]\begin{gathered} 6\cdot(x^2-2\cdot4\cdot x+41)=0 \\ 6\cdot(x^2-2\cdot4\cdot x+16+25)=0 \end{gathered}[/tex]Now, we need to remove the "25" from the parenthesis, for that we need to multiply the 6 by 25.
[tex]\begin{gathered} 6\cdot(x^2-2\cdot4\cdot x+16)+6\cdot25=0 \\ 6\cdot(x^2-2\cdot4\cdot x+16)+150=0 \\ 6\cdot(x^2-2\cdot4\cdot x+16)=-150 \end{gathered}[/tex]Now we can transform the parenthesis to the sum of two squares, where the term "a" is equal to x, and the "b" is equal to 4.
[tex]6\cdot(x^{}-4)^2=-150[/tex]Any help finding the 0th term? I have a guess but want to know if its correct.
Given series is:
100,50,25....
so the first term is a=100
and the common ration is: r=1/2
So the nth term of GP is calculated as:
[tex]T_n=ar^{n-1}[/tex]So for 0th term:
[tex]\begin{gathered} T_0=(100)(\frac{1}{2})^{0-1} \\ T_0=100\times(\frac{1}{2})^{-1} \\ T_0=100\times2 \\ T_0=200 \end{gathered}[/tex]So the oth term of given GP is 200.
Roofers describe the steepness of a roof by it's pitch, the number of inches of rise for each 12 inches of run. A "3 in 12" roof rises 3 inches for every 12 inches of run.a. What is the slope of a "3 in 12" roof?b. A roof rises 100 inches over a run of 20 feet. Find the slope of the roof.
It's pitch, the number of inches of rise for each 12 inches of run.
A "3 in 12" roof rises 3 inches for every 12 inches of run.
a. What is the slope of a "3 in 12" roof?
ratio 1: 12
1/ 12 = 3/ x
x= 36
b. A roof rises 100 inches over a run of 20 feet. Find the slope of the roof.
which value of k makes the inequality 11+2k>19 true?
Answer:
k>4
Explanation:
Given the inequality
[tex]11+2k>19[/tex]First, subtract 11 from both sides.
[tex]\begin{gathered} 11-11+2k>19-11 \\ 2k>8 \end{gathered}[/tex]Next, divide both sides by 2
[tex]\begin{gathered} \frac{2k}{2}>\frac{8}{2} \\ k>4 \end{gathered}[/tex]The value of k that makes the inequality true is any value of k greater than 4.
We can write this in interval notation as:
[tex](4,\infty)[/tex]Which expression is equivalent to 3V 45 – 7V20? -20-630 – 20/5-5/5
Answer:
[tex]-5\sqrt{5}[/tex]Explanation:
Here, we want to simplify the given expression
We have that as follows:
[tex]\begin{gathered} 3\sqrt{45}\text{ = 3}\times\sqrt{45}\text{ = 3}\times\sqrt{9\times5}\text{ = 9}\sqrt{5} \\ 7\sqrt{20}\text{ = 7}\times\sqrt{20}\text{ = 7}\times\text{ }\sqrt{4\text{ }}\text{ }\times\sqrt{5\text{ }}\text{ = 14}\sqrt{5} \end{gathered}[/tex]Thus, we have the difference as:
[tex]9\sqrt{5}\text{ - 14}\sqrt{5}\text{ = -5}\sqrt{5}[/tex]17. Is the parallelogram in #15 a rectangle, rhombus, or square?
This parallelogram is called RHOMBUS
Explanation:In the given shape, all sides have equal lengths, and opposite angles are equal. This parallelogram is called RHOMBUS.
Jade this information to answer the questions below. If not enough information is given to answer a question, write not enough information
Answer
• a) 3
,• b) 21
,• c) Not enough information
Explanation
Given
• 28 seniors
,• 24 students went to the trip, where 7/8 were seniors.
Procedure
• a)
We are given the proportion of seniors, if we want to know the proportion of juniors we have to subtract it from 8/8 (whole):
[tex]\frac{8}{8}-\frac{7}{8}=\frac{1}{8}[/tex]Next, we have to multiply the students that went times the proportion:
[tex]24\cdot\frac{1}{8}=3[/tex]3 juniors went on the trip.
• b)
Now we have to multiply the proportion given times the students that went:
[tex]24\cdot\frac{7}{8}=21[/tex]Thus, 21 seniors went on the trip.
• c)
As we are not given the juniors that are in the class, we cannot answer this one.
You know 3 angles, angle one at the top has an equation of (y+x)° angle two has the equation (y-x)° angle three at the bottom is blank and angle 4 at the left has the equation 2x° you need to figure out what each angle measures to. angle one at the top and angle four to the left are a linear pair, same with angle 1 and 2 at the right, and 2 and 4 are vertical angles and angles 1 and 3 are vertical angles angle 1 and 3 are obtuse while angle 2 and 4 are acute.
2x° = 2(30) = 60°
(y+x)° = 90° + 30° = 120°
(y-x)° = 90 - 30 = 60°
Explanation:
2x° and (y-x)° are vertical angles.
Vertical angles are equal.
equating both:
2x = y - x
2x+x = y
3x = y
Also 2x° + (y+x)° = 180° (angles on a straight line)
2x + x + y = 180
3x + y = 180°
recall, 3x = y
Insert the value of y in the equation: 3x + y = 180°
y + y = 180
2y = 180
y = 180/2
y = 90°
y = 3x
x = y/3 = 90/3
x = 30°
One of the angle: 2x° = 2(30) = 60°
(y+x)° = 90° + 30° = 120°
(y-x)° = 90 - 30 = 60°
Solve for p in the equation 7p = -63.
Use the following property of equations to solve the given equation.
Let a, b and c be real numbers, such that c is different from 0. Then:
[tex]a=b\Leftrightarrow\frac{a}{c}=\frac{b}{c}[/tex]On the given equation:
[tex]7p=-63[/tex]Divide both sides of the equation by 7 (as the property says):
[tex]7p=-63\Leftrightarrow\frac{7p}{7}=\frac{-63}{7}[/tex]Simplify the fraction 7p/7:
[tex]\begin{gathered} \frac{7p}{7}=p \\ \Rightarrow p=\frac{-63}{7} \end{gathered}[/tex]Divide -63 by 7. Since -63 is negative and 7 is positive, the result should be negative. Additionally, 63/7 = 9, so:
[tex]\begin{gathered} \frac{-63}{7}=-9 \\ \therefore p=-9 \end{gathered}[/tex]Therefore, the solution for the equation 7p=-63 is p=-9.
can someone help me please
In this problem we have the price of many utilities, and the quantity consumed of each one. We must compute the total bill of a month.
The cost of each service is:
• Electricity: $0.15/kWh * 2,000 kWh = $300,
,• Gas: $1/(100 ft³) * 4,300 ft³ = $43,
,• Water: $0.03/(10 gal) * 8,000 gal = $24,
,• Phone: $30/line * $10 lines = $300,
,• Phone: $0.10/int min * 500 int min = $50,
,• Internet: $200.
The total bill of the services, is the sum of each individual cost:
• Total bill = $300 + $4,300 + $24 + $300 + $50 + $200 = $917
Answer: A. $917.00