[tex]\bf \textit{exponential form of a logarithm} \\\\ log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=\log_4(0.25) ~\hfill 0.\underline{25}\implies \cfrac{025}{1\underline{00}}\implies \cfrac{1}{4}\implies 4^{-1} \\\\\\ y=\log_4\left( 4^{-1} \right)\implies 4^y=4^{-1}\implies y=-1[/tex]
Solve each of these systems using the substitution method. Make sure to check your answers !
2x + 3y = -4
x − 2y = 5
a. x = 1, y = -2
b. x = -1, y = 2
c. x = 1, y = 2
d. x = -2, y = -1
Answer:
a. x = 1, y = -2
Step-by-step explanation:
The given equations are 2x + 3y = -4 -------------(1)
x - 2y = 5 -----------------(2)
From the second equation, we get x = 2y + 5
Now plug in x = 2y + 5 in the first equation, we get
2(2y + 5) + 3y = - 4
4y + 10 + 3y = -4
7y + 10 = -4
7y = -14
y = -2
Now plug in y = -2 in x = 2y + 5 to find the x value.
x = 2(-2) + 5
x = -4 + 5
x = 1
Therefore, x = 1, y = -2
Thank you.
Bryan purchases a new boat. The expression below represents the value of the boat after x years. 22000(0.88)^(X+2)
Which statement is true?
The price of the boat decreases by 88% every year.
The price of the boat increases by 88% every year.
The price of the boat decreases by 12% every year.
The price of the boat increases by 12% every year.
None of the above. All the answers refer to price. The given equation refers to value. We imagine price may stay the same or actually increase year-to-year. The problem statement gives insufficient information to conclude anything about price.
Math is about attention to detail. The equation tells you ...
... The value of the boat decreases by 12% every year.
Step-by-step explanation:The value of the boat is multiplied by 0.88 each time X increases by 1. That means the value is 88% of what it was the year before, a decrease of 12%.
If m ABC is 53 degrees then m EDF is ?
Answer:
74°
Step-by-step explanation:
The triangle is isosceles and the congruent base angles are 53°. The sum of angles in a triangle is 180°, so the apex angle (∠EDF) will be ...
... 180° - 2×53° = 74°
Answer:
74* is the answer
Step-by-step explanation:
#PLATOFAM
#PLATOLIVESMATTER
#PLATOFAMILY
1/3(y+7)=(y-1) y= what?
Answer:
y=5
Step-by-step explanation:
1/3(y+7)=(y-1)
I will multiply by 3 on each side to get rid of the fractions
3*1/3(y+7)=(y-1)*3
y+7 = 3*(y-1)
Distribute the 3
y+7 = 3y -3
Subtract y from each side
y-y+7 = 3y-y-3
7 = 2y-3
Add 3 to each side
7+3 = 2y-3+3
10=2y
Divide each side by 2
10/2 = 2y/2
5 =y
f(x)=log5 (2x+12)+2 yeah this ome threw me off
Answer:
See below for a graph
Step-by-step explanation:
Let's call the parent function g(x) = log₅(x), which has a vertical asymptote at x=0, and goes through the points (1, 0), (5, 1), (25, 2).
Then this function is
... f(x) = g(2(x+6)) +2
That is, the function is horizontally compressed by a factor of 2, shifted left 6 units, and shifted up 2 units. This moves the points listed above to ...
... (-5.5, 2), (-3.5, 3), (6.5, 4)
The graph shows the parent function and the listed points in blue, then the transformed function and the corresponding points in red.
The sum of the measures of the angles shown is 63° . Which choice is the measure of angle y ?
Answer:
63
Step-by-step explanation:
Answer:
25 degrees.
Step-by-step If one of the angles is 38 degrees then in order for the sum to be 63, the answer is 25
In trapezoid ABCD with bases AB and DC , diagonals intersect at point O. Find the length of diagonal BD , if BO=6 cm and: AO/OC = 3/1
Answer:
8 cm
Step-by-step explanation:
... BO/OD = AO/OC = 3/1
Written another way, this is ...
... OD : BO = 1 : 3
Now, BD = OD + BO, so we have
... BD : BO = (OD +BO) : BO = (1 +3) : 3 = 4 : 3
That is, BD = 4/3 × BO
... BD = 4/3 × 6 cm = 8 cm
To find the length of diagonal BD in trapezoid ABCD, we set up an equation using the fact that the diagonals bisect each other. We solve for x and then substitute it into the equation for BD.
Explanation:To find the length of diagonal BD in trapezoid ABCD, we can use the fact that the diagonals of a trapezoid bisect each other. Let AO = 3x and OC = x. Since the diagonals intersect at point O, we can set up the equation (3x + 6) / x = 3 / 1. Solving for x, we find that x = 1.5. Therefore, BD = 2 * x + 6 = 2 * 1.5 + 6 = 9 cm.
Learn more about length of diagonal BD in trapezoid here:https://brainly.com/question/11848253
#SPJ3
You and your friend leave your houses at the same time to meet at a restaurant. The distance (in miles) your friend is from the restaurant is given by y=-70x+140,where x is the number of hours since your friend left home. You live 80 miles from the restaurant and arrive at the same time as your friend. Write a linear equation that represents your distance from the restaurant.
Answer:
y = 80 -40x
Step-by-step explanation:
The given equation shows the friend arrives at the restaurant (y=0) when x=2. That is, half the initial distance to the restaurant is covered in each hour of travel time.
If I take 2 hours to travel the 80 miles from my house, my distance will decrease at the rate of 40 miles per hour. My distance from the restaurant can be represented by ...
... y = -40x +80
Please help!!!!! I attached the picture of the full question
Drag each value to the correct location on the tree diagram. Not all values will be used.
$90 $27.84 $66.32 $46.8 $38.48 $29.12 $31.24
See the attachment
Step-by-step explanation:The expected value of store card transactions will be the product of their average value ($58) and their probability of occurrence (48%).
... $58 × 0.48 = $27.84
Transactions are either "store card" or "without a store card", so the probability of a transaction being made without a store card is
... 1 - 0.48 = 0.52
Using the same computatation as for store card expected value, the expected value of transactions made without a store card is ...
... $74 × 0.52 = $38.48
The expected value of the store's transactions is the sum of the expected values of the different ways transactions can be made:
... $27.84 +38.48 = $66.32
_____
The average value of transactions made without a store card is the weighted average of those made with another card and those made with cash or a gift card. Using c to represent the latter, this weighted sum is ...
... 74 = 0.80 × 70 + 0.20 × c
... 74 -56 = 0.20c . . . . . subtract 56
... 18/0.2 = c = 90 . . . . . divide by the coefficient of c
The average transaction made with cash or a gift card is $90.
Each expected value per transaction should be matched to the correct location on the tree diagram as shown in the image below.
How to determine the expected value per transactions?In this exercise, we would use probability to make each of the decisions. The expected value for transactions made with a store card can be determined by multiplying its probability of occurrence (48%) by the average value ($58) as follows;
Expected value per transaction = 58 × 0.48
Expected value per transaction = $27.84
Since transactions are either made with a store card or without a store card, the probability of a transaction being made without a store card is given by;
Probability (without a store card) = 1 - 0.48 = 0.52
In this context, the expected value per transactions made without a store card is given by;
Expected value per transaction = 74 × 0.52
Expected value per transaction = $38.48
... $74 × 0.52 = $
For the store's expected value transactions, we would add each of the expected values calculated above;
Store's expected value transactions = 27.84 + 38.48
Store's expected value transactions = $66.32.
The average transaction value for transactions that are made with cash or a gift card can be calculated by finding the weighted average of all transactions made without a card;
74 = (0.80 × 70) + 0.20 × m
74 = 56 + 0.20m
0.20m = 74 - 56
0.20m = 18
m = 18/0.20
m = $90.
Read more on probability here: brainly.com/question/25870256
#SPJ2
The formula for the area A of a trapezoid is A=1/2(b1+b2)h, where b1 and b2 represents the lengths of the bases and h represents the height. Which equation can be used to find the height of a trapezoid?
A. h=2A-b1-b2
B. h=2A/b1+b2
C. h=A(b1+b2)/2
D. h=A-2/b1-b2
Answer:
B. h=2A/(b1+b2) . . . . parentheses are needed
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of h. That coefficient is (b1 +b2)/2, so its inverse is 2/(b1 +b2). Parentheses are needed.
... 2A/(b1 +b2) = h
_____
Comment on the answer choices
As written, none of them are correct. The denominator can only be written without parentheses if the division bar is horizontal, and so serves also as a grouping symbol.
What is the apparent solution to the system of equations?
y=12x+2y=2x−1
y=12x+2y=2x−1
Graph the system of equations using the Line tool. Plot a point at the apparent solution to the system using the Point tool.
Answer:
(x, y) = (-0.3, -1.6)
Step-by-step explanation:
The graph below shows these equations graphed. Their point of intersection is (-0.3, -1.6).
_____
Analytical solution
You can equate the expressions for y to get ...
... 12x +2 = 2x -1
... 10x = -3 . . . . subtract (2x+2)
... x = -0.3 . . . . . divide by 10
... y = 2(-.3)-1 = -1.6 . . . . use the 2nd equation to find y.
You are tired at the end of the term and decide to borrow $500 to go on a trip to whatever land. You go to the bank and borrow the money at 11% for 2 years. A) find the interest you will pay on the loan. B) how much will you have to pay the bank at the end of the two years ?
Answer:
A)55
B)110
Step-by-step explanation:500 /11%=55
55*2=110
The interest is $110 and the amount paid to the bank is $610.
What is simple interest?Simple interest is calculated just on the loan's principal amount, whereas compound interest is calculated on both the principal and the cumulative interest.
It is given that you decide to borrow $500 to go on a trip to whatever land. You go to the bank and borrow the money at 11% for 2 years.
A. The simple interest is,
SI = ( Principle x rate x time ) / 100
SI = ( 500 x 11 x 2 ) / 100
SI = $110
B. The amount paid to the bank after 2 years is,
Amount = P + SI
Amount = $500 + $110 = $610
Therefore, the interest is $110 and the amount paid to the bank is $610.
To know more about simple interests follow
https://brainly.com/question/2294792
#SPJ2
Ally and Beth are at the grocery store. Ally buys a container of milk for $4 and 4.75 pounds of apples. Beth buys a box of cereal for $3 and 5.55 pounds of apples. If the girls spend the same amount, how much does 1 pound of apples cost?
Answer:
$1.25
Step-by-step explanation:
Please help if you can
Step-by-step explanation:
sqrt of 81 is 9 so rational
Sqrt of 89 is irrational
Sqrt of 121 is 11 so rational
Sqrt of 131 is irrational.
Suppose a fair six-sided is rolled three times in a row. The probability of rolling a number less than 3 three times in a row is __________ . Express the probability as a fraction.
Answer:
1/27
Step-by-step explanation:
The probabaility of rolling a number less than 3 is 2/6 = 1/3, since only two of the six numbers are less than 3.
Assuming the die rolls are independent, the probability of doing this 3 times is the product of the probabilities of doing it each time:
... (1/3)^3 = 1/27
Find a polynomial, which if substituted for M will make the equation an identity: (4c^2–7c^2+6)–M=0
Answer:
-3c^2 +6
Step-by-step explanation:
The equation will be an identity (0=0) when M is equal to the contents of the parentheses. That polynomial can be used directly, or it can be simplified by combining the c^2 terms.
The contents of parentheses simplify as follows:
... (4c^2 -7c^2 +6) = (c^2(4 -7) +6) = (-3c^2 +6)
Answer:
4c^4-7c^2+6
Step-by-step explanation:
Liam volunteers to help plan the event. The first month, he volunteered for x hours. The next month he volunteered for 1 2/3 times as many hours as he had the first month. If he volunteered for a total of 40 hours, how many hours did he volunteer during the first month? Write an equation to represent the situation and solve.
To find the number of hours Liam volunteered during the first month, we can set up an equation using the given information. By solving the equation, we find that Liam volunteered for 15 hours during the first month.
Explanation:To solve this problem, we can start by representing the number of hours Liam volunteered in the first month as x. The number of hours volunteered in the next month would be 1 2/3 times x, which can be written as (5/3)x. The total number of hours volunteered is given as 40, so we can write the equation: x + (5/3)x = 40. To solve for x, we can combine the like terms and solve the resulting equation.
Combining the x terms, we get (8/3)x = 40. Solving for x, we divide both sides of the equation by 8/3: x = 40 / (8/3).
Simplifying, we have x = 40 * (3/8) = 15. Therefore, Liam volunteered for 15 hours during the first month.
Learn more about Equation here:https://brainly.com/question/17595716
#SPJ12
By representing the number of hours in the first month as x, we can find the value of x by using the given information and solving the equation. The solution shows that Liam volunteered for 15 hours during the first month.
Explanation:To solve this problem, we can set up an equation representing the total number of hours Liam volunteered. Let's represent the number of hours he volunteered in the first month as x. According to the problem, he volunteered for 1 2/3 times as many hours in the next month. So, the number of hours he volunteered in the next month is 1 2/3 x. The total number of hours is given as 40. Therefore, we have the equation:
x + 1 2/3 x = 40
To solve for x, we can simplify the equation by converting 1 2/3 to an improper fraction. This gives us:
5/3 x + 1 2/3 x = 40
Combining like terms, we get:
8/3 x = 40
To solve for x, we can multiply both sides of the equation by the reciprocal of 8/3, which is 3/8. This gives us:
x = (40)(3/8) = 15
Therefore, Liam volunteered for 15 hours during the first month.
Learn more about Volunteering here:https://brainly.com/question/40703235
#SPJ12
please help me asap!
Which postulate or theorem proves ∆MNQ ≅ ∆PNQ ?
SSS Congruence Postulate
AAS Congruence Postulate
ASA Congruence Postulate
AAS Congruence Postulate proves that ∆MNQ ≅ ∆PNQ
What is congruency?When two triangles have shape and sizes then the triangles are said to be congruent.There are 5 types of congruencies. They are SAS, AAS, ASA , SSS , RHS.How to know which postulate or theorem proves ∆MNQ ≅ ∆PNQ ?Considering ΔMNQ and ΔPNQ
∠QMN = ∠QPN (given)
∠QNM = ∠ QNP ( both are right angles)
Side NQ is common
∴ ΔMNQ and ΔPNQ are congruent by AAS congruency since two angles and a side are considered to prove the congruency.
The side is not included between the angles and hence ASA congruency is not the answer.The correct answer is option B. AAS congruency postulates.
Find out more details about "Congruencies" here: https://brainly.com/question/1675117
#SPJ2
Julie wants to make a handmade Valentines she buys 1/2 yard of red ribbon and 3/4 yard of pink if each Valentine needs 1/8 yards how many can she create please show you work will Mark rainiest and we'll add you to help suow work
Answer:
10 Valentines
Step-by-step explanation:
1/2 = 4/8
3/4 = 6/8
Julie has a total of 4/8 + 6/8 = 10/8 yards of ribbon. If color doesn't matter, she can make 10 Valentines.
_____
10/8 = 10 × 1/8
What is the fraction in decimal form?
21/6
Enter your answer in the box
Answer: Your answer would come out to be 3.5
Step-by-step explanation: it would be 3.5 due to the fact that you have to break these numbers down to the smallest one possible meaning simplify which would result in this equation 7 over 2
7 over 2 = 3 1 over 2 this equals 3.5
GUYS HELP PLEASE!!!! I NEED THIS ASAP!!!!!!!
Answer:
slope = .4
She ran .4 laps per min.
She ran 12 laps in 30 minutes
Step-by-step explanation:
The slope is the rate of change. It can be found by using the formula
slope = (y2-y1)/(x2-x1)
The given points are (11, 4.4) (5.5 ,2.2)
slope = (2.2-4.4(/ (5.5-11)
= -2.2/-5.5
.4
The slope represents .4 laps per min since y is in laps and x is in minutes.
If she ran 30 minutes, we multiply the time by the slope to calculate the laps.
30 * .4 = 12
She ran 12 laps.
A) The slope is the change in Y over the change in X.
Using the 2 points given on the graph (11,4.4) and (5.5, 2.2)
The first number in the parenthesis are the X value and the 2nd numbers are the Y values.
Slope = (4.4 - 2.2) / (11-5.5)
= 2.2 / 5.5
= 0.4
B) From the slope, she ran 0.4 laps per minute.
C) To find the total laps, multiple laps per minute by total minutes:
30 minutes x 0.4 laps per minute = 12 laps.
please hurry thank you
Answer:
7.9 ft
Step-by-step explanation:
The hypotenuse is the side opposite of the right angle, hence the hypotenuse for this triangle is 11 ft.
Side [tex]x[/tex] is adjacent to the angle given. So we need adjacent and we have hypotenuse. Which trigonometric ratio relates adjacent and hypotenuse? It is COSINE.
Thus, we can write:
[tex]cos(A)=\frac{adjacent}{hypotenuse}\\cos(44)=\frac{x}{11}[/tex]
Cross multiplying, we can solve for [tex]x[/tex]:
[tex]cos(44)=\frac{x}{11}\\x=cos(44)*11\\x=7.91[/tex]
Rounding to nearest tenth, we have [tex]x=7.9[/tex] ft.
(2.)are NOT opposite reciprocals
(1.)are NOT equal
(2.) are NOT opposite reciprocals
REALLY NEED HELP WITH BOTH PLEASE FOR GRADE‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️
The slope of AB is ...
... slope = (change in y)/(change in x) = (-6-(-3))/(8-2) = -3/6 = -1/2
The slope of AD is ...
... slope = (change in y)/(change in x) = (0 -(-3))/(8 -2) = 3/6 = 1/2
We note that the differences have the same magnitudes in both cases (y changes by 6; x changes by 3). This tells us the line segments are the same length. (Each side of the figure is equivalent to the hypotenuse of a right triangle with legs 3 and 6.)
The opposite reciprocal of a number is found by dividing -1 by that number. Thus the opposite reciprocal of the slope of AB is ...
... -1/(-1/2) = (-1/1)·(-2/1) = 2
This value is not the same as the slope of AD, so the slopes are NOT opposite reciprocals.
_____
Plotting the points, we see that we have a rhombus, not a rectangle (or square).
Ben has $5. In order to have money for a new tablet computer, Ben is going to sell his collection of stamps for $3 per stamp. Ben has decided to graph a line showing the relationship between the number of stamps he sells and the total amount of money he has. Which will be the y-intercept of Ben's graph?
Answer:
5
Step-by-step explanation:
It is 5 because no matter how many stamps he sells, he has $5.
Answer:
The y-intercept of Ben's graph is [tex]y = 5[/tex].
Step-by-step explanation:
The function for Ben's amount of money y, depending on the number of stamps sold x, is as follows:
[tex]y = ax + b[/tex]
In which a is the price of each stamp and b is his initial money.
Building the function:
Ben has $5. This means that if he sells no stamps, he is still going to have $5. So [tex]b = 5[/tex].
For each stamp sold, he gains $3. So if sells 1 stamp, he will have $8, if he sells 2, he will have $11. So [tex]a = 3[/tex].
The function is:
[tex]y = 3x + 5[/tex]
Which will be the y-intercept of Ben's graph?
This is the value of y when x = 0.
So
[tex]y = 3*0 + 5 = 5[/tex]
The y-intercept of Ben's graph is [tex]y = 5[/tex].
please help me asap!
7. Law of cosines
a² = b² + c² - 2bc cos A
where a is the side opposite to ∠A and b and c are adjacent sides to ∠A.
Here, a=BC= 3.8
b=CA =4.8
c = AB = 3.2
Substituting the values in the formula,
3.8² = 4.8² + 3.2² - 2(4.8)(3.2) cos A
30.72 cos A =23.04 + 10.24 -14.44=18.84
cos A = 18.84/30.72 = 0.6133
∴ cos A =0.6133
8. It is a right angled triangle.
Pythagoras theorem
hypotenuse² = Perpendicular² + base²
Here, hypotenuse = 6.7, base = 5.4
Perpendicular² = 6.7² -5.4²=44.89 - 29.16 =15.73
Perpendicular = √15.73 = 3.966 = 3.97
∴ The length of the missing side is 3.97.
9. Given: Side of new cube = 5 * Side of original cube
Let the side of the original cube measure 1 unit.
So, volume of original cube = side³ = 1
The side of new cube = 5 * 1 =5 units
So, volume of new cube = side³ = 5³ =125
The volume of the bigger cube is 125 times larger than the original cube.
10. Given : Height of the cone = 7 in
Radius of the base of the cone = 2 in
Volume of cone = (1/3) πr²h
=(1/3)π(2²)(7)
=29.32 cubic inches
∴ Volume of the cone is 29.32 cubic inches.
11. The given equation is:
x² -18x +10 =0
(x² -18x + 9²) +10 -9² =0
(x-9)²-71 =0
(x-9)² =71
x-9 =√71
x = 9 + √71
∴ x = 9+√71
What is the best approximation of the length of segment QS? (Note: cos 80° = 0.17)
(Round your answer to the nearest tenth.)
Answer: [tex]QS=11.8cm[/tex]
Step-by-step explanation:
1. You have the following information:
- The lenght of [tex]RS[/tex] is 2 centimeters.
- The angle m∠S=80°.
- Cos80°=0.17
2. Therefore, you can calculate the lenght of the segment [tex]QS[/tex] as following:
[tex]cos80=\frac{adjacent}{hypotenuse}[/tex]
[tex]adjacent=2cm\\hypotenuse=QS\\cos80=0.17[/tex]
3. Substitute values and solve for [tex]QS[/tex]:
[tex]0.17=\frac{2cm}{QS}\\QS=\frac{2cm}{0.17} \\QS=11.76cm[/tex]
4. To the nearest tenth:
[tex]QS=11.8cm[/tex]
1# Find the missing variable (s). Round to the nearest tenth.
Answer:
7.9
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship of the hypotenuse and the side opposite an angle:
... Sin = Opposite/Hypotenuse
For your geometry, this is ...
... sin(21°) = x/22
Multiplying by 22 gives ...
... x = 22·sin(21°) ≈ 7.9
The equation C = 5/9(F - 32) is used to convert between Fahrenheit temperatures and Celsius temperatures. The temperature in Augusta on a summer day is 33° C.
Rounded to the nearest whole number, what is the temperature in Fahrenheit?
A) 55°F
B) 68°F
C) 79°F
D) 91°F
Answer:
D) 91 °F
Step-by-step explanation:
C = 5/9(F - 32)
33 = 5/9 (F – 32) Multiply each side by 9
9×33 = 5(F- 32) Divide each side by 5
9×33/5 = F – 32 Add 32 to each side
F = 9×33/5 + 32
F = 59.4 + 32
F = 91 °F
Answer:
Its D
Step-by-step explanation:
USA TP
Camacho is buying a monster truck. The price of the truck is xx dollars, and he also has to pay a 13\%13% monster truck tax.
how much Camacho pays in total for the truck?
Answer:
[tex]1.13x[/tex]
Step-by-step explanation:
We have been given that Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13% monster truck tax. We are asked to find the total amount paid by Camacho for the monster truck.
The total cost of monster truck would be x plus 13% of x.
[tex]\text{The total cost of monster truck}=x+\frac{13}{100}x[/tex]
[tex]\text{The total cost of monster truck}=x+0.13x[/tex]
[tex]\text{The total cost of monster truck}=1.13x[/tex]
Therefore, Camacho paid [tex]1.13x[/tex] dollars in total for the truck.
Final answer:
To find the total cost of the monster truck, convert the 13\% tax to decimal form (0.13), multiply it by the price of the truck (xx dollars), then add the result to the original price to get the total cost, which is 1.13xx.
Explanation:
To determine the total amount Camacho will pay for the monster truck, we need to calculate the sales tax and add it to the original price of the truck. The sales tax is 13\%, which can be converted to a decimal for calculation purposes. First, convert 13\% to a decimal by dividing by 100, which gives us 0.13. Then multiply 0.13 by the price of the truck (xx dollars) to find the amount of tax Camacho will have to pay.
After calculating the tax, you can find the total cost by adding the tax to the original price of the truck.
Step 1: Convert 13\% to a decimal = 0.13
Step 2: Multiply the price of the truck (xx dollars) by 0.13 to find the tax = 0.13 * xx
Step 3: Add the tax to the original price to find the total cost: xx + (0.13 * xx).
Total cost = xx + 0.13xx = 1.13xx