Answer:
Step-by-step explanation:
-4w
nkjiug kglkr fho'f v
Which statement is true for the function y = log3x
Answer:
Step-by-step explanation:
jack's age next year will be twice jill's age last year. their present ages total 45. how old is each no
We get the age of Jack is 29 years and the age of Jill is 16 years.
We are given that the sum of Jack's age and Jill's age is 45 years.
Let Jack's age be x.
Let Jill's age be y.
x + y = 45
x = 45 - y
Now, we are also given that jack's age next year will be twice Jill's age last year.
Jack's age next year = x + 1
Jill's age last year = y - 1
ATQ, We get the equation as:
x + 1 = 2( y - 1)
x + 1 = 2 y - 2
x = 2 y - 2 - 1
x = 2 y - 3
We get that:
45 - y = 2 y - 3
2 y + y = 45 + 3
3 y = 48
y = 48 / 3
y = 16 years.
x + y = 45
x + 16 = 45
x = 45 - 16
x = 29 years.
Therefore, we get the age of Jack is 29 years and the age of Jill is 16 years.
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Self balancing scooter travels 12 miles per hour, all terrain vehicle can travel 6 times as fast as the scooter,a go kart can travel 67 miles per hour,which vehicle can travel the fastest
The fastest vehicle is: the all terrain that can travel at a speed of 72 mi/h
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
v(scooter) = 12mi/hv(all terrain vehicle) = 6 * 12mi/hv(go kart) = 67 mi/hwhich is the faster=?Calculating the velocity of the all terrain vehicle we get:
v(all terrain vehicle) = 6 * 12mi/h
v(all terrain vehicle) = 72 mi/h
By ordering the velocities from highest to lowest we have:
(all terrain vehicle)72 mi/h >(go kart)67 mi/h >(scooter)12mi/h
Due to the all terrain vehicle has the highest velocity it is the faster vehicle.
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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The sum of two-thirds a
number and eighteen is twenty-three. What is the number?
number = x
2/3x + 18 = 23
2/3x = 5
x = 15/2 = 7.5
18% of the car inn the parking lot are blue . If there are 150 cars in the parking lot how many cars are blue
Answer:
27
Step-by-step explanation:
27
Explanation:
"Percent" or "%" means "out of 100" or "per 100", Therefore 18% can be written as
18 /100 .
When dealing with percentage, the word "of" means "times" or "to multiply".
Finally, lets call the number we are looking for "n".
Putting this altogether we can write this equation and solve for "n "
while keeping the equation balanced:
n = 18 /100 × 150
n = 2700 /100
n = 27
27 is 18% of 150
Solve for j in the literal equation
h - 10/j
=k.
The value of j from the equation h-10/j=k is equal to 10/(h-k).
Given that the equation is h-10/j=k.
We are required to find the value of j from the given equation.
Equation is a relationship between two or more variables that are expressed in equal to form. It may be a linear equation,quadratic equation, cubic equation and many more depending on the power of the variables present in that equation.
The equation is h-10/j=k.
-10/j=k-h
1/j=(k-h)/-10
j=-10/(k-h)
j=10/(h-k)
(We can eliminate the negative sign by taking negative out from the denominator.)
Hence the value of j from the equation h-10/j=k is equal to 10/(h-k).
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Given the numbers 1,2,3,4,5,6,7,8,9 use the operations +, -,/ and * to get the answer as 100 while leaving the numbers in their respective given order
Answer:
answer is ((1 × 2) + 3) × 4 × 5 + 6 - 7 - 8 + 9 = 100
Form linear equations in two variables using suitable variables for the unknowns.
The perimeter of a rectangle is 98 cm. [Take length as x and breadth as y.]
Answer:
2(x+y)=98 is the answer.
jamie is pedaling due south a 8 mi/hr. his sister, martha, is pedaling due west at 5 mi/hr. after 2 hours, how fast are the two cyclists moving apart?
Both cyclist are moving apart at a speed of 9.434 mi/hr.
What is velocity?Velocity is the direction at which an item is moving and serves as a measure of the rate at which its location is changing as seen from a certain point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a basic idea. A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of velocity; it is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI (metric system).
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(15y - 48)
(8r - 1)(11x - 25)
The measure of the angles ( 15y - 48 )°, ( 8x - 1 )°, and ( 11x - 25 )° are 165°, 15°, and 63° respectively.
The lines j and k are parallel and lines l and m are parallel.
Consider the figure,
( 8x - 1 )° ≅ 1, corresponding angles
1 ≅ 9, corresponding angles
9 ≅ ( 11x - 25 )°, vertical angles
Therefore,
m∠ 1 = m∠ 9
m∠9 = ( 8x - 1 )°
So,
( 8x - 1 )° = ( 11x - 25 )°
Subtracting 8x from both sides of the equation.
11x - 25 - 8x = 8x - 1 - 8x
3x - 25 = - 1
Adding 25 on both sides of the equation.
3x - 25 + 25 = - 1 + 25
3x = 24
Dividing each side of the equation by 3
( 3x/3 ) = ( 24/3 )
x = 8
Now, the angle made by a straight line is 180°.
Therefore,
( 8x - 1 )° + ( 15y - 48 )° = 180°
( 8 × 8 - 1 )° + ( 15y - 48 )° = 180°
15° + 15y - 48° = 180°
15y - 33° = 180°
Adding each side of the equation by 33°.
15y - 33° + 33° = 180° + 33°
15y = 213°
Dividing each side of the equation by 15
( 15y/15 ) = ( 213/15 )°
y = 14.2°
So, the measure of the angles are:
( 15y - 48 )° = ( 15 × 14.2 - 48 )° = ( 213 - 48 )° = 165°
( 8x - 1 )° = ( 8 × 8 - 1 )° = 15°
( 11x - 25 )° = ( 11 × 8 - 25 )° = ( 88 - 25 )° = 63°
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Part A
JEWELRY Chloe makes necklaces and bracelets to sell at fundraisers to raise money for new band uniforms. She
has $18 to buy necklace and bracelet chains. Necklace chains cost $0.60 each, and bracelet chains cost $0.40
each. The number of bracelet chains she can purchase given the number of necklace chains that she buys are
shown in the table.
Necklace Chains
Bracelet Chains
What are the x and y intercepts of the function modeling the number of bracelet chains chloe can purchase given the number of necklace chains that she buys?
Using a linear function, it is found that:
The x-intercept is of 28.125.The y-intercept is of 45.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.From the table, we have that:
The input is the number of necklace chains.The output is the number of bracelet chains.Hence, we have that when x = 0, y = 45, meaning that:
The y-intercept is of 45.
When x increases by 5, y decays by 8, hence the slope is given as follows:
m = -8/5 = -1.6.
Then the function is:
y = -1.6x + 45.
The x-intercept is found as follows:
-1.6x + 45 = 0
1.6x = 45
x = 45/1.6
x = 28.125.
The x-intercept is of 28.125.
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olivia and yixing are volunteering at a cat rescue shelter. the shelter supervisor asks them to clean out kennels and haul bags of cat food from the donation area into storage. it takes olivia 6 minutes to clean out a kennel and 6 minutes to move a bag of food. it takes yixing 10 minutes to clean out a kennel and 12 minutes to move a bag of food. for the following questions, round each answer to the nearest tenth. a. has an absolute advantage in completing both tasks.
The correct option is A which is Yixing should clean out the kennels, and Olivia should move the food bags.
What is an expression?Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
All the parts will be solved below:-
a. Olivia has an absolute advantage as she takes less time for completing both the tasks
b. Olivia's opportunity cost of cleaning a kennel is
= 6 ÷ 6
= 1 bag of food moved.
c. Olivia's opportunity cost of moving one bag of food is
= 6 ÷ 6
= 1 kennel cleaned
d. Yixing's opportunity cost of cleaning a kennel is
= 10 ÷ 12
= 0.83 bags of food moved.
e. Yixing's opportunity cost of moving one bag of food is
= 12 ÷ 10
= 1.2 kennels cleaned
f. From the above calculations, we can see that the opportunity cost of kennel cleaning would be less sin Yixing so here Yixing should have a comparative advantage and Olivia should have moved the food bags
The complete question is given below:-
Olivia and Yixing are volunteering at a cat rescue shelter. The shelter supervisor asks them to clean out kennels and haul bags of cat food from the donation area into storage. It takes Olivia 6 minutes to clean out a kennel and 6 minutes to move a bag of food. It takes Yixing 10 minutes to clean out a kennel and 12 minutes to move a bag of food.
A. ____has an absolute advantage in completing both tasks.
B. Olivia's opportunity cost of cleaning a kennel:___bags of food moved.
C. Olivia's opportunity cost of moving one bag of food:_____kennels cleaned.
D. Yixing's opportunity cost of cleaning a kennel:____bags of food moved.
E. Yixing's opportunity cost of moving one bag of food:____kennels cleaned.
F. Yixing says it does not matter which task each of them performs because Olivia is faster at both tasks. Is she correct?
A) No, Yixing should clean out the kennels, and Olivia should move the food bags.
B) No, Olivia should clean out the kennels, and Yixing should move the food bags.
C) Yes, Olivia should do both tasks because she is faster at both.
D) No, Yixing should do both tasks so that she can practice and become more efficient.
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an unreliable study can occur if the . a. survey is very clear b. survey yields consistent results c. test administration is inconsistent
An unreliable study can occur if the test administration is inconsistent
Consistency is the key to success in anything and it implies to the studies and surveys as well. If you want the results of the study to be reliable, then you must be consistent in test administration.
Inconsistency can lead to various issues like improper representation of the feedback which may alter the results. This can lead to various problems.
For example, test performed at certain time may have a different set of people and absence of periodic tests can accommodate feedback from irrelevant people.
Therefore, a proper set schedule must be followed for the tests with consistency.
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170% of what number is 40.8?
Answer: 24
Step-by-step explanation: first we can rewrite the expression as 170%*x=40.8 (x is your answer). By solving and simplifying it, you should get 24.
Yesterday Sarah read 15% of her entire book. Today she read another 17% of the entire book.
In lowest terms, what fraction of the book is left for her to read?
a) 7/25
b) 3/10
c) 17/25
d) 7/10
answer quick please!!!!
i think the answer is 3/10
The function h=−16t^2+1936 gives an object’s height h, in feet, at t seconds. When will the object be 912 feet above the ground?
A triangle has base 7 m and area 17.5 m². What is the height?
Answer: Height = 5m
Step-by-step explanation: To solve the height of the triangle we can use the Area formula and substitute the values given to solve for heigh.
A = ( b * h ) / 2
17.5 = (7 * h) / 2
17.5 (*2) = 7 * h
(Remember that everything done to one side has to be done to both. We can multiply by 2 on both sides to eliminate the 2.)
35 = 7 * h
35/7 = h
5 = h
The height of the triangle equals 5.
(5) Set up a system of equations and solve:
38 people are playing pickle-ball in a park. 13 matches are in progress. How many double and
how many single matches are being played?
Step-by-step explanation:
Assume the number of double matches is x (matches)
the number of single matches is y (matches)
(Condition: x > 0 and y > 0)
Because there are 13 matches in progress, so:
x + y = 13 (1)
Because there are 38 people playing (4 people on each double match and 2 people on each single match), so:
4x + 2y = 38 (2)
A system of equation is made by combining (1) and (2):
x + y = 13 (1)
4x + 2y = 38 (2)
Take (2) - 2×(1):
=> 2x = 12
=> x = 6
Substitute the result on (1)
=> y = 7
So there are 6 double matches and 7 single matches being played
A line segment has the endpoints K(0, 2) and L(0, 6). Find the coordinates of its midpoint M.
Write the coordinates as decimals or integers.
M =
A line segment has the endpoints as K and L that are (0,2) and (0,6).The midpoint M is (0,4).
Given that,
The line segment has the endpoints as K and L that are (0,2) and (0,6).
The Formula for the Midpoint of a Line Segment
Let the line segment's termination point be ([tex]a_{1}[/tex], [tex]b_{1}[/tex]) and ([tex]a_{2}[/tex], [tex]b_{2}[/tex]) respectively. The following is the midpoint formula for a line segment connecting these two points:
(a,b)=[tex](\frac{a_{1} -a_{2} }{2}, \frac{b_{1} -b_{2} }{2} )[/tex]
Where
[tex]a_{1} =0,b_{1} =2 \\and \\a_{2} =0,b_{2} =6[/tex]
[tex](a,b)=(\frac{0+0}{2},\frac{2+6}{2}) \\(a,b)=(0,4)[/tex]
Therefore, When the line segment with the endpoints k and L the midpoint M is (0,4).
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232x100 what is the answer
Answer:
23200
Step-by-step explanation:
Can somebody help wit this I’m failing geometry rn and it makes no sense .
By definition of vertical angles, the value of the variable x behind the geometric system is equal to 12. The measure of the labeled angle is 48°.
What is the measure of variable within a geometric system generated by two lines intersecting each other?
The image shows a geometric system generated by two non-parallel lines that intersect each other and consequently two pairs of vertical angles are therefore created. In geometry, two vertical angles are opposite to each other and have the same measure. Then, the following mathematical relationship is found:
4 · x = 48
In addition, we must clear the variable x within the equation:
4 · x = 48 Given
x = 48 / 4 Compatibility with multiplication / Commutative, associative and modulative properties / Existence of multiplication
x = 12 Definition of division / Result
The value of the variable x behind the geometric system is equal to 12.
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What are the first five terms of the following sequence a1=42, an=an-1-7
The first five term of the sequence are 42, 35, 28, 21 and 14.
According to the given question.
We have a rule for finding the terms of a sequence i.e. [tex]a_{n} = a_{n-1} -7[/tex].
Also, the first term of the sequence is a1 = 42
Therefore,
The second term of the sequence is given by
Second term [tex]a_{2}[/tex] = [tex]a_{1}[/tex] - 7
⇒ Second term = 42 - 7 = 35
Similarly,
The third term of the sequence, [tex]a_{3}[/tex] = [tex]a_{2}[/tex] - 7 = 35 - 7 = 28
Fourth term of the sequence = 28 - 7 = 21
Fifth term of the sequence = 21 - 7 = 14
Hence, the first five term of the sequence are 42, 35, 28, 21 and 14.
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Two angles are complementary. The measure of the larger angle is 14° less than 3 times the measure of the smaller angle.
The measure of the smaller angle is ____
degrees and the measure of the larger angle is ____ degrees.
Answer:
Step-by-step explanation:
Comment
2 angles are complementary means together they = 90 Degrees.
Let the smaller angle be x
The complement = 3*x - 14 It is the larger angle.
Givens
<1 = x
<2 = 3x - 14
<1 + <2 = 90
Solution
x + 3x -14 = 90 Combine the left
4x - 14 = 90 Add 14 to both sides
4x - 14+14 = 90 + 14 Combine
4x = 104 Divide both sides by 4
4x/4 = 104/4
x = 26
Answer
<1 = 26
<2 = 3*26 - 14
<2 = 78 - 14
<2 = 64
how to simplify 4x +5(-3x +6)
Answer:
-11x + 30
Step-by-step explanation:
distribute the 5 into the parenthesis
= 4x -15x + 30
combine like terms
= -11x + 30
Answer:
-11x + 30
Step-by-step explanation:
4x + 5(-3x + 6) Distribute the 5
4x + (5)-3x + (5)6
4x -15x + 30 Combine the x's
-11x + 30
Here is a rule that can be used to build a sequence of numbers once a starting number is chosen: Each number is two times three less than the previous number.
a. Starting with the number 0, build a sequence of 5 numbers.
b. Starting with the number 3, build a sequence of 5 numbers.
c. Can you choose a starting point so that the first 5 numbers in your sequence are all positive? Explain your reasoning.
Answer:
a. 0, -6, -18, -21, -90
b. 3, 0, -6, -18, -42
c. A starting point of any number ≥ 6 will result in a sequence of positive values
Step-by-step explanation:
Here the sequence is governed by the rule:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]
[tex]\textsf {where $a_n$ is the nth term and $a_{n-1}$ is the previous term}}[/tex]
1) Starting with a₁ = 0 we get
a₂ = 2(a₁ - 3) = 2(0 - 3) = -6
a₃ = 2(a₂ - 3) = 2(-6 -3) = 2(-9) = -18
a₄ = 2(a3 - 3) = 2(-18 - 3) = 2(-21) = -42
a₅ = 2(a₄ - 3) = 2(-42- 3) = 2(-45) = -90
So the first 5 numbers in the sequence starting with 0 are:
0, -6, -18, -21, -90
2) I will approach this slightly differently
We have the relationship:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]
Expanding the brackets we get
[tex]\sf a_{n} = 2a_{n-1} - 6[/tex]
We have a₁ = 3
a₂ = 2(a₁) - 6 = 2(3) - 6 = 6 - 6 = 0
a₃ = 2(a₂) - 6 = 2(0) - 6 = -6
a₄ = 2(a₃) - 6 = 2(-6) - 6 = -18
a₅ = 2(a₄ ) - 6 = 2(-18) - 6 = -42
The sequence starting with 3 is:
3, 0, -6, -18, -42
Both methods work exactly the same, some students find expanding the brackets easier to deal with
c. We can see that as a₁ increases, the number of negative numbers decreases by 2. So, in order for all numbers to be positive (> 0) we should start with a sufficiently large number so that all numbers are positive
The smallest such number is 6.
When a₁ = 6, the sequence is all 6s because
a₂ = 2(6) - 6 = 12 - 6 = 6
So the next number is a₃ = 12(6) - 6 = 6 and so on
So any starting point ≥ 6 will yield positive values. At 5 the sequence would be: 5, 4, 2, -2, -10 so starting point of 5 will not work
An equation and some of the steps used to solve the equation are shown below. One step is missing:
2(x-3) + 10x = 5(3 + x)
?
2x-5x + 10x = 15 + 6
7x = 21
x=3
Which set of statements is most likely the missing step and the property that justifies the step?
Answer choices listed in picture(Sorry for quality, taken from my laptop) (Will mark brainliest)
Answer 5795
Step-by-step explanation:
What are the values of b and c?
J
b =
C=
C
O
O
b
H
74°
I
Jason considered two similar televisions at a local electronics store. the cheaper version was 12 inches by 24 inches. the more expensive version was \large \frac{8}{3} the size of the cheaper one. what are the dimensions of the expensive television? a 4.5 inches by 9 inches b 28 inches by 56 inches c 7.5 inches by 15 inches d 32 inches by 64 inches
The dimensions of expensive television is 32 inches through 64 inches.
This trouble may be solved if we understand the idea of fraction and a way to calculate the part of a fragment.
right here it is for the reason that the inexpensive tv is 12 inches by means of 24 inches.
Also it is given that the expensive television is [tex]\frac{8}{3}[/tex] of the cheaper one.
Now taking the length into consideration the length of the television is
=[tex]\frac{8}{3}*12[/tex]
= 32 inches
Now taking the width into consideration the width of the television is
=[tex]\frac{8}{3}*24[/tex]
= 64 inches
So, the dimension of the expensive television is 32 inches by 64 inches.
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a cup of coffee at 160 degrees is placed in a room where the temperature of 70 degrees. after 5 minutes, the coffee’s temperature is 112.5 degrees.
The coffee reaches t ≈ 12 minutes a temperature of 150◦F.
(t) = Ts + (T0 - Ts)e-kt, according to Newton's Law of Cooling.
T(t) = temperature of the coffee cup t minutes after being placed in the roomTs is the ambient temperature.T0 indicates the coffee cup's beginning temperature.
(a). Using the given information, we have T(t) = 70 + (160 - 70)e-kt
= 70 + 90e-kt
T(5) = 70 + 90e-k(5) = 112.5
So, 90e-5k = 42.5
e-5k = 0.47222222
-5k = ln(0.47222222)
k = 0.15 Temperature after 10 minutes = T(10) = 70 + 90e-0.15(10)
≈ 90.1
-------------------------------------------------------------------------------------
(b). When will the temperature of the coffee reach 85°?
Find t so that T(t) = 85: 70 + 90e-0.15t = 85
90e-0.15t = 15
e-0.15t = 0.16666666
-0.15t = ln(0.166666666)
t ≈ 12 minutes
what do you mean by newton's law of cooling?According to Newton's law of cooling, a body's rate of heat loss is inversely related to the temperature difference between it and its surroundings. The law is frequently qualified to state that the tiny temperature differential and the consistency of the heat transmission mechanism must exist. As a result, it is the same as asserting that the heat transfer coefficient, which mediates between heat losses and temperature variations, is constant. Due to the fact that the thermal conductivity of the majority of materials very slightly depends on temperature, this requirement is typically satisfied in heat conduction (where it is guaranteed by Fourier's law). Newton's Law is applied in convective heat transfer for forced air or pumped fluid cooling.
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Find the value of the variable(s).
the variable(s) x have a value of 13.
What in mathematics is a variable?A variable is any property, amount, or number that can be measured or counted. A data item is another name for a variable. Age, sex, business income and expenses, place of birth, capital expenditures, class grades, eye color, and car kind are only a few examples of variables.
A variable is a value that could change based on the details of an experiment or the parameters of a mathematical problem. A variable is typically identified by a single letter. The letters x, y, and z are the universal symbols for variables that are most frequently employed.
According to given value ;
4x+(7x+37)=180
sum of three angle equal to 180
4x+7x+37=180
4x+7x=180-37
11x=143
x=143/11
x=13
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