After simplifying the expression, the value of y is 4.53.
In the given question,
We have to solve for y.
The given expression is 116° +15y - 4=180.
To solve for y we simplify the expression.
The expression is 116° +15y - 4=180
Now simplifying the expression.
Add 4 on both side
116° +15y - 4+4=180+4
116° +15y=184
Subtract 116 on both side
116° +15y-116°=184-116°
Simplifying
15y=184-116°
15y = 68
Divide by 15 on both side
15/15 y=68/15
y=4.53
Hence, the value of y is 4.53.
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shopping at savers mart, Lisa buys her children four shirts and three pairs of pants for $85.50. she comes back the next day and buys three shirts and five pairs of pants for $115. What is the price of each shirt and each pair of pants.
At which values of x does the function F(x) have a vertical asymptote? Check
all that apply.
F(x) =1/7(x + 2)(x+3)
The vertical asymptote of a given function is x = -2 and x = -3.
What is the vertical asymptote of a function?
A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. It appears at the x-value that is outside the domain of the function, therefore the graph can never cross it.
To find the vertical asymptotes, set the denominator equal to zero and solve for x.
For the given function,
[tex]F(x) = \frac{1}{7(x+2)(x+3)}[/tex]
To find the vertical asymptote, equate the denominator to zero.
7(x + 2)(x + 3) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 (or) x + 3 = 0
x = -2 (or) x = -3
Hence, The vertical asymptote of the given function is x = -2 and x = -3.
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math, pls help, will mark brainlest
Answer:
Step-by-step explanation:
3x + 3x equals 11x
Adela paid $64.25 for 5 tickets at the skating rink. Calculate the unit rate per ticket.
Answer:
12.85
Step-by-step explanation:
hope it helps, pls lmk if it is wrong in comments!
Answer:
12.85
Step-by-step explanation:
64.25÷5
f(x)=x^2-1, g(x)=x+2
The composite function ( f. g(x)) is x² + 4x + 3
What is a function?A function can be described mathematically as a rule, law or equation that explains, shows and elaborates the relationship between to variables.
The variables are known as;
The independent variableThe dependent variableFrom the information given, we have the functions as;
f(x)=x^2-1g(x)=x+2To determine the composite function ( f. g(x)), we have to substitute the value of g(x) as a function in the function f(x) as the variable 'x', we get;
( f. g(x)) = (x + 2)² - 1
Now, let's expand the square
( f. g(x)) = (x + 2) ( x+ 2) - 1
Expand the bracket
( f. g(x)) = x² + 2x + 2x + 4 - 1
Now, let's collect like terms, we get
( f. g(x)) = x² + 4x + 3
Thus, the function is x² + 4x + 3
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The complete question:
Find ( f. g(x)) if f(x)=x^2-1, g(x)=x+2
Eve and Patty swam fewer laps than Maureen. Patty swam more laps than Eve, and Maureen swam fewer laps than Raymond. Who swam the most laps?
Answer:
Raymond
Step-by-step explanation:
1 ) Eve and Patty swam fewer laps than Maureen so...
Eve and Patty < Maureen
2 ) Patty swam more laps than Eve...
Patty > Eve
3 ) Maureen swam fewer laps than Raymond...
Maureen < Raymond
4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...
Maureen and Raymond
5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.
Raymond
6 ) This mean that the one who swam the most laps is...
Raymond
Hope this helps! :)
Devontae claimed that the line y=-3/4x forms an angle of about 53.13° with the positive x-axis. Which statement proves his claim correct or incorrect?
a) Correct because arctan(4/-3) = -53.13
b) Correct because arccos(-3/4) = 53.13
c) Incorrect because arctan(-3/4) = -36.87
d) Incorrect because arccos(-3/4) = -138.59
The statement that proves the claim about the angle is incorrect is that;
c) Incorrect because arctan(-3/4) = -36.87
How to solve Trigonometric Ratios?The 6 main trigonometric ratios of a right angle triangle are;
Sine θ = length of the opposite leg / length of the hypotenuse
Cosine θ = length of the adjacent leg / length of the hypotenuse
Tangent θ = sine θ/cosine θ = opposite leg / adjacent leg.
cosecant θ = 1 / sine θ = hypotenuse / opposite leg
secant θ = 1 / cosine θ = hypotenuse / adjacent leg
cotangent θ= 1 tangent θ = adjacent leg / opposite leg.
Now, we are told that the angle formed is 53.13°. Since the options are either arctan or arccos, we will use them to verify the angles;
cos 53.13° = 0.6
tan 53.13° = 1.33
They are both positive and it means both x and y values are positive since we are told that it involves the positive x-axis.
Thus, y/x cannot be negative or -3/4 as given.
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What is the domain of the following relation?
a. {-3, -1, 1, 4, 5}
b. {-5, 0, 2, 6}
c. {-3, -5, 0, 2, 4, 5, 6}
d. there is no domain
The domain of the relation in the diagram below is: a. {-3, -1, 1, 4, 5}.
What is the Domain of a Relation?A relation has a set of domain elements, which are all the inputs of the relation that are mapped to a set of range elements, which are all the corresponding outputs of the relation.
Given the relation as shown in the diagram that is attached below showing a mapping, the set of input values is {-3, -1, 1, 4, 5}, while the set of output values is {-5, 0, 2, 6}.
Therefore, {-3, -1, 1, 4, 5} is the domain of the relation because it is the set of all input values, while the range of the relation is {-5, 0, 2, 6}, because it is the set of all output values that corresponds to the input values.
The domain is therefore: a. {-3, -1, 1, 4, 5}.
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(−3,y) and (x,2).
y=4x+6
orderd pair
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials..
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a brown marble from the bag.
The theoretical probability, P(brown), is 50%, and the experimental probability is 25%.
The theoretical probability, P(brown), is 50%, and the experimental probability is 22.5%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 13.0%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
In this question, we have been given there are 10 brown, 10 black, 10 green, and 10 gold marbles in bag.
The theoretical probability of pulling a brown marble from the bag would be,
P = 10/40
P = 0.25
P = 25%
A student pulled a marble, recorded the color, and placed the marble back in the bag.
The frequency of each color pulled during the experiment after 40 trials is:
Brown 13
Black 9
Green 7
Gold 11
So, the experimental probability of pulling a brown marble from the bag would be,
P = 13/40
P = 0.325
P = 32.5 %
Therefore, the theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
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Answer: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Step-by-step explanation: :)
kayla used her cell phone for four days . her average calling time was 130 minutes each day .suppose that kayla used the phone for m minutes on fifth day . write an algebraic expression for the average number of minutes she spent on the phone over five days.
Answer:
130-60m
Step-by-step explanation:
simplify: 8x divided by 16+8 divided by 32
The value of 8x ÷ (16+8) ÷ 32 is x/96
What are basic operations?The four basic arithmetic operations in Maths, for all real numbers, are:
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
Discussing about division or quotient
The division is usually denoted by ‘÷‘ and is the inverse of multiplication. It constitutes two terms dividend and divisor.
To simplify
8x÷(16+8)÷32= 8x×1/24×1/32
= x/96
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00
Which could be the base shape of the cylinder?
Oline
O non-square rectangle
O circle
O square
Answer:
The answer is a D. a circle
The base shape of the cylinder can only be a circle.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A cylinder is a three-dimensional shape that has two congruent parallel circular bases connected by a curved surface.
The shape of the base determines the shape of the cylinder. If the base is circular, then the cylinder is called a circular cylinder.
A non-square rectangle and a square are not circular, and thus cannot be the base shape of a cylinder.
Hence, the base shape of the cylinder can only be a circle.
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You roll a fair six-sided die twice. Find the probability of rolling a 3 the first time and a number greater than 4 the second time.
The probability of rolling a 3 first time and a number greater than 4 thre second time is 1/18
What is probability?Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain. An example of a certain event is tomorrow being Friday if today is Thursday. This is definitely going to happen.
The possible outcomes of a fair die are : 1, 2, 3, 4, 5, 6. which is 6 in all
the required outcome for obtaining a 3 = 3 which is 1 outcome
the required outcome for obtaining a number greater than 4 : 5, 6. which is 2 outcomes.
probability of getting 3 first time = 1/6
probability of getting a number greater than 4 = 2/6 ( lowest term = 1/3)
Probability of rolling a 3 first time and a number greater than 4 second time is = 1/6 x 1/3 = 1/18
In conclusion, probability of obtaining a 3 and a number greater than 4 is 1/18.
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PLEASE HELP ME
Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
3x - 2 (2.3x + 2.5) = -1.6x -5
5 - 3 (-1.6x - 2.1) = 4.8x - 1.3
3x - 2 (2.3x + 2.5) = -1.6x-5 are equivalent expressions while 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3 are not equivalent expressions
How to determine if the linear expressions are equivalent?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)
Given: 3x - 2 (2.3x + 2.5) = -1.6x -5 and 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3
For 3x - 2 (2.3x + 2.5):
First, clear the parenthesis by using -2 to multiply what's in the parenthesis. Then add/subtract like terms:
3x - 2 (2.3x + 2.5) = 3x-4.6x- 5 = -1.6x-5
For 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3:
First, clear the parenthesis by using -3 to multiply what's in the parenthesis. Then add/subtract like terms:
5 - 3 (-1.6x - 2.1) = 5 + 4.8x + 6.3 = 4.8x + 11.3
Since 3x - 2 (2.3x + 2.5) is equal to -1.6x-5 and 5 - 3 (-1.6x - 2.1) is not equal to 4.8x - 1.3.
Therefore, 3x - 2 (2.3x + 2.5) = -1.6x-5 are equivalent expressions and 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3 are not equivalent expressions
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I rode my bike to my
grandparents' house in 1
hours and 15 minutes. My
grandparents live 33 blocks
from me, and each block is
560 feet. What was my
average speed in miles per
hour?
(Hint: 5,280 feet per mile)
By using the formula of average speed, it can be inferred that
My average speed is 14 miles per hour
What is average speed?
Speed of an object is the distance covered by the object per unit time
Average speed is calculated by dividing the total distance covered by the total time taken
Length of one block = 560 feet = [tex]\frac{560}{5280}[/tex] miles
Number of blocks = 33
Total distance = [tex]\frac{560}{5280} \times 33\\[/tex]
= [tex]\frac{7}{2}[/tex] miles
Total time = 15 minutes = [tex]\frac{15}{60}[/tex] hours = [tex]\frac{1}{4}[/tex] hours
Average speed = [tex]\frac{\frac{7}{2}}{\frac{1}{4}}[/tex] = [tex]\frac{7}{2} \times 4[/tex] = 14 miles per hour
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Current Attempt in Progress
Monty Corp. purchased a new machine on October 1, 2022, at a cost of $124,000. The company estimated that the machine will have
a salvage value of $15,000. The machine is expected to be used for 10,000 working hours during its 5-year life.
(a)
Compute the depreciation expense under straight-line method for 2022.
Depreciation expense $
2022
The depreciation expense under the straight-line method for 2022, for Monty Corp., is $5,450.
What is the straight-line depreciation method?Under the straight-line depreciation method, one of the cost-recovery methods, the depreciable amount of an asset is divided by its estimated useful life.
The quotient is the depreciation expense for each year. However, if the asset is not used for a full year, the depreciation expense is prorated according to the number of months or days that the asset is in use.
Note that the depreciable amount is the difference between the cost of the asset and its salvage value.
Cost of new machine = $124,000
Purchase date = October 1, 2022
Estimated salvage value = $15,000
Depreciable amount = $109,000 ($124,000 - $15,000)
Estimated useful life = 5 years
Estimated working hours = 10,000 hours
Depreciation method = Straight-line
Annual Depreciation Expense = $21,800 ($109,000/5)
October 1, 2022, to December 31, 2022, = 3 months
Depreciation expense for 2022 = $5,450 ($21,800 x 3/12)
Thus, using the straight-line method, Monty Corp. will record a depreciation expense of $5,450 for the new machine it purchased on October 1, 2022.
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Carlos goes out to lunch. The bill, before tax and tip, was $13.80. A sales tax of 3% was added on. Carlos tipped 23% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answer:i think its 13.70 or 14.00
Step-by-step explanation:
Answer:
$3.27
Step-by-step explanation:
$13.80 x 1.03 (which will add the 3% to the total, skipping a step) = $14.21
Then take $14.21 x .0.23 which will give you just the tip amount of $3.2683 or rounded to the nearest cent, $3.27
How many square inches are in a square mile?
Answer: 4.014e+9 square inches
[(3^2)^6]^4
answer for thius
Answer: 7.9766443e+22 all added and multiplied correctly
Richard and two have a combined age of 26. Richard is 5 years old than twice Teos age. How old are Richard and Teo?
Answer:
R = 19 yr old; T = 7 yr old
Step-by-step explanation:
From the information given, we can create a system of equations to find both Richard and Teo's ages, letting R represent Richard's age and T represent Teo's age.
Thus we have:
[tex]R +T=26\\2T+5=R\\\\2T+5+T=26\\3T+5=26\\3T=21\\T=7\\\\R+7=26\\R=19[/tex]
When you plug in the numbers, you find that twice Teo's age is 14 as 7*2 = 14. 5 more than 14 is 19 as 14 + 5 = 19.
Plot a point that is in the solution region of this inequality.
y>x-3+8
The point (-6,6) is in the solution region of the inequality and is plotted in given below graph.
Given,
Equation -> y > x - 3 +8
y > x + 5
Lets take a point A(-6,6)
Putting the value in equation,
6 > -6 + 5
6 > -1
which is true.
Hence, A(-6,6) lies in the region of the inequality.
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Judy mom prepared 30 sandwiches for her friends. Her mom added chicken breast to 2/5 of the buns. How many chicken sandwiches did her mom make.
Please help me with these questions
The rate of change of the linear functions given in tabular form and equations are found as follows;
1. a. The rate of change of the function is 5
b. The rate of change of the function is 7
c. The rate of then function is 0.75
d. The function has a rate of change of -8
2. The rate of change of the function of -4, indicates that each unit increase in the input value results in 4 unit decrease in the output values
b. The number of days it took for the patients blood sample to have 360 antibodies is 13 days
c. The rate of change of the function is 20, which indicates that the antibody in the patients blood is increasing at a rate of 20 antibodies each day
The rate of change of a function is a measure of how much the output changes per unit change in the input.
1. The rate of change of the functions are as follows;
a. The first difference of the y-values is constant, therefore the function is a linear function
The formula for the rate of change of the linear function is presented as follows;
[tex]m = \dfrac{y_2-y_1}{x_2 - x_1}[/tex]
The rate of change of the function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{-3 - (-8)}{1 - 0} = 5[/tex]b. The first difference is constant and equal to 7, the rate of change of the straight line function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{49-42}{1-0} = 7[/tex]
The rate of change of the function is 7 unit changes in the y-value per unit change in the x-valuesc. The function is a linear function, as the first difference is constant and equal to 0.75
The rate of change of the function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{2.25-1.5}{-4-(-5))} = 0.75[/tex]
The rate of change of the function is 0.75d. The first difference is constant and equal to -8
The rate of change of the straight line function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{5 - 13}{1 - 0} = -8[/tex]
The rate of change of the function is -82. a. The rate of change of the function, y = -4·x + 1 is found by taking the slope of the function
The function is the equation of a straight line, of the form, y = m·x + c with the slope, m = -4
The rate of change of the function is -4, such that for each unit increase in the input value, the output value decreases by 4 units
b. When the number of antibodies is 360, we have;
360 = 20·d + 100
20·d = 360 - 100 = 260
d = 260 ÷ 20 = 13
It would take 13 days for the patients blood to have 360 antibodiesc. The rate of change of the function means that the number of antibodies the drug produces in the patients body each day is 20 antibodies.
3. The function that gives the amount of antibodies in the body is a = 20·d + 100
d = The number of days
a = The number of antibodies
a. The table is completed as follows;
Data for Medicine A
d [tex]{}[/tex] a
0 [tex]{}[/tex] 100
1 [tex]{}[/tex] 120
2 [tex]{}[/tex] 140
3 [tex]{}[/tex] 160
4 [tex]{}[/tex] 180
5 [tex]{}[/tex] 200
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Isabelle flips a fair coin and rells a fair six-sided dice.
Draw a sample space diagram to show all the possible outcomes.
Work out the probability that she gets an outcome of tails and 2.
Give your answer as a fraction in its simplest form.
When a six sided dice through with the coin all the possible outcomes are as follows
H-1 H-2 H-3 H-4 H-5 H-6
T-1 T-2 T-3 T-4 T-5 T-6
Probability that she gets an outcome of tails and 2 = 1 / 12
Isabelle flips a fair coin and rells a fair six-sided dice.
Coin has two face H or T
Dice has six face hat is 1, 2, 3, 4, 5, 6
When a six sided dice through with the coin all the possible outcomes are as follows
H-1 H-2 H-3 H-4 H-5 H-6
T-1 T-2 T-3 T-4 T-5 T-6
So there are total 12 outcomes possible when a six sided dice through with the coin.
Probability that she gets an outcome of tails and 2 = event occur / total number of events = 1 / 12
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216. Factor and then calculate the value of the expression
a) a² + ab with a = 6.6, b = 3.4;
b) x2 - xu at x = 0.5, y = 2.5;
c) —5a² — 5ah at a = 4, x = -3
Answer:
a) 66, b) - 1, c) - 20Step-by-step explanation:
Solve as below
a) a² + ab with a = 6.6, b = 3.4;
a² + ab = a(a + b) = 6.6(6.6 + 3.4) = 6.6(10) = 66b) x² - xu at x = 0.5, y = 2.5;
x² - xu = x(x - u) = 0.5(0.5 - 2.5) = 0.5(- 2) = - 1c) -5a² - 5ah at a = 4, h = -3;
-5a² - 5ah = - 5a(a + h) = - 5(4)(4 - 3) = - 20(1) = - 20Answer:
a) 66b) -1 c) -20Step-by-step explanation:
a) a² + ab = ?
→ (6.6)² + (6.6 × 3.4)
→ 43.56 + 22.44
→ 66
So, the answer is 66.
b) x² - xu = ?
→ (0.5)² - (0.5 × 2.5)
→ 0.25 - 1.25
→ -1
So, the answer is -1.
c) -5a² - 5ah = ?
→ -5(4)² - 5(4 × -3)
→ (-5 × 16) - (5 × -12)
→ -80 + 60
→ -20
So, the answer is -20.
If a lumber yard sells plywood at $1,240/M, what is the price per square foot?
The price of the lumber per square foot is $115.
What is a unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that the cost of the lumber yard plywood per square meter is $1240.
The cost of the lumber plywood per square foot is calculated as,
Cost = $1240 per square meter
The square meter is equal to 1 m = 3.28 ft. The cost will be calculated as,
Cost = $1240 / m²
Cost = $1240 / (3.28)² ft²
Cost = $115 per square feet
Therefore, the price of the lumber per square foot is $115.
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Write an expression that has only one term and is equivalent to the expression below (f × g²) + 5 - (g² × f)
The expression that is equivalent to (f × g²) + 5 - (g² × f) is 5
How to determine the equivalent expression?The expression whose equivalence is to be determined is given as
(f × g²) + 5 - (g² × f)
To start with, we need to remove the brackets in the expression
So, we have the following representation
(f × g²) + 5 - (g² × f) = f × g² + 5 - g² × f
Evaluate the products
This gives
(f × g²) + 5 - (g² × f) = fg² + 5 - fg²
Next, we collect the like terms
So, we have
(f × g²) + 5 - (g² × f) = fg² - fg² + 5
Lastly, we evaluate the like terms
So, we have
(f × g²) + 5 - (g² × f) = 5
The above expression cannot be further simplified
Hence, the equivalent expression is 5
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A certain number is multiplied by 7, and 4 is taken from the product. Finally, the difference is divided by 9, resulting in 5. Find the initial number.
If the sum of two numbers is 10 and the difference of their squares is also 10, find the numbers?
The two numbers with sum is 10 and difference of their squares is 10 are 5.5 and 4.5.
What is square of numbers?
A square number, sometimes known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number since it equals 3^2 and is represented by the symbol 3 x 3.
Suppose x and y are the two numbers with sum is 10 and difference of their squares is 10.
As sum of two numbers is 10.
So, x + y = 10 ..(1)
As difference of their squares is 10.
So, x^2 - y^2 = 10 ..(1)
From equation (1), x = 10 - y
Plug value of x in equation (2)
(10 - y)^2 - y^2 = 10
100 - 20y + y^2 - y^2 = 10
100 - 20y = 10
20y = 100 + 10
2y = 110
y = 5.5
Plug y = 5.5 in equation (1)
x + 5.5 = 10
x = 10 - 5.5
x = 4.5
Therefore, The two numbers with sum is 10 and difference of their squares is 10 are 5.5 and 4.5.
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