❄ Hi there,
let us combine the like terms and create an equivalent expression –
[tex]\large\begin{gathered} \sf{9+a-5b-2} \\\sf{9-2+a-5b}\\\sf{7+a-5b} \end{gathered}[/tex]
That's as far as we can go.
❄
Amelia has a job baby-sitting for a neighbor. she is paid $20 plus $2.50 for each hour on the job. if amelia wants to earn $40 to buy a new sweater, how many hours would she need to work? a. 16 hours b. 9 hours c. 10 hours d. 8 hours please select the best answer from the choices provided a b c d
The correct option is option (d) 8 hours.
Amelia need to work for 8 hours to buy new sweater $40.
What is an equation and its solution?When two expressions are connected with the equals sign (=) in a math equation, it expresses the equality of the two expressions. A number that may be entered for the variable to produce a true number statement is the solution to an equation.
Let the hours Amelia need to work=h
Amalia paid=$20
Payment of each hour=$2.50
So, we can make an equation with given problem
40=20+2.50h
40-20=2.5h
20=2.5h
[tex]h=\frac{20}{2.5}[/tex]
h= 8
So, Amelia need to work for 8 hours to get $40.
To know more about equation, visit: https://brainly.com/question/14603452
#SPJ4
Geometry: Write the theorem or postulate for each of the following, ASAP!!!
The theorems or postulates for the given pair of angles are as follows:
2. ∠2 ≅ ∠8 → Alternate exterior angles are congruent;
3. ∠2 ≅ ∠4 → Vertically opposite angles are congruent;
4. ∠3 ≅ ∠5 → Alternate interior angles are congruent;
5. ∠3 is supplementary to ∠6 → Consecutive interior angles are supplementary;
6. ∠4 ≅ ∠8 → Corresponding angles are congruent;
What are the types of pairs of angles?Consider two lines m and n are parallel. A transversal t is intersecting the lines m and n.
So, it forms 8 angles with the lines m and n. They are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
Based on their position, they are paired into different categories. Such as:
Interior angles: ∠3, ∠4, ∠5, ∠6
Exterior angles: ∠1, ∠2, ∠7, ∠8
'Alternate interior angles' are the pair of interior angles on the opposite side of the transversal 't'. I.e., (∠3, ∠5), (∠4, ∠6) are congruent.'Alternate exterior angles' are the pair of exterior angles which are on the opposite side of the transversal 't'. I.e., (∠2, ∠8), (∠1, ∠7) are congruent.'Consecutive interior angles' are the pair of interior angles which are on the same side of the transversal 't'. I.e., (∠3, ∠6), (∠4, ∠5). These are also called "Supplementary angles" which mean they add up to 180°.'Consecutive exterior angles' are the pair of exterior angles on the same side of the transversal 't'. I.e., (∠2, ∠7), (∠1, ∠8). These are also called "Supplementary angles" which mean they add up to 180°.'Vertically opposite angles' are the pair of angles that are opposite to each other at the point of intersection. I.e., (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8)'Corresponding angles' are the pair of consecutive angles in which one of the angles is exterior and the other is interior. I.e., (∠1, ∠5), (∠2, ∠6), (∠4, ∠8), (∠3, ∠7)Theorems or postulates for the given pair of angles:Classifying the given pair of angles and their corresponding theorems:
2. ∠2 ≅ ∠8 → These angles belong to pair of Alternate exterior angles.
Theorem - "The alternate exterior angles are congruent"
3. ∠2 ≅ ∠4 → These belong to pair of vertically opposite angles.
Theorem - "The verticle angles are congruent"
4. ∠3 ≅ ∠5 → These belong to pair of alternate interior angles.
Theorem - "The alternate interior angles are congruent"
5. ∠3 is supplementary to ∠6 → These angles belong to pair of consecutive interior angles. Thus, they are supplementary.
Theorem - " The supplementary angles add up to 180°"
6. ∠4 ≅ ∠8 → These angles belong to pair of corresponding angles.
Theorem - " The corresponding angles are congruent".
Learn more about the pair of angles here:
https://brainly.com/question/18772057
#SPJ1
When you send out a resume, the probability of being called for an interview is 0. 40. what is the probability that the first interview occurs on the fifth resume that you send out?
The probability that the first interview occurs on the fifth resume that you sent is 0.2592.
According to the given question.
The probability of being called for an interview, p = 0.40.
So, the probability of not being called for an interview, q = 1 - 0.40 = 0.60
As we know that binomial distribution summarizes the number of trials, or observations when each trial has the same probability of attaining one particular value. The binomial distribution determines the probability of observing a specified number of successful outcomes in a specified number of trials.
Therefore, the probability that the first interview occurs on the fifth resume that you send out
= [tex]^{5} C_{1} (0.40)^{1} (0.60)^{4}[/tex]
= 5(0.40)(0.1296)
= 0.2592
Hence, the probability that the first interview occurs on the fifth resume that you sent is 0.2592.
Find out more information about probability here:
https://brainly.com/question/14210034
#SPJ4
PQRS is a cyclic quadrilateral.Chord RS is produced to T.K is a point on RS and W is a point on the circle such that QRKW is a parallelogram. PS and QW intersect at U. PST = 136° and Q₁ =100° Determine, with reasons, the size of: 8.1.1.R 8.1.2.P 8.1.3.PQW 8.1.4.U2
Answer:
Step-by-step explanation:
PS and QW intersect at U. PST = 136° and Q₁ =100°
Given: y varies directly with x and has a constant rate of change of 7. when the value of y is 12, then the value of x would be _____.
Answer:X=12/7
Step-by-step explanation:
Y [tex]\alpha[/tex] X
⇒Y=KX
Where K is the constant
From the question,k=7
⇒ When Y=12,
y=KX
12=7X
X=12/7
The base of each triangle varies inversely with the height. what are the possible base is 14 and height of a second triangle if the first triangle's base is 14 and its height 6 is ?
The possible base and height of a second triangle are:
B = 5 H = 12What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.To find the base and height of the triangle:
First, we must find the constant of variation (k).
The problem indicates that the base of each triangle varies inversely with the height.
So, this can be represented as below:
B = k/H
B is the base of the triangle (B=10). H is the height of the triangle (H=6). k is the constant of variation.When we clear "k", we obtain:
B = k/H k = BxH k = 10x6 k = 60Now, we have:
B = 60/HWe can give any value to "H" and you will obtain the base of the second triangle.
If H = 12, then:
B = 60/H B = 60/12 B = 5Therefore, the possible base and height of a second triangle are:
B = 5 H = 12Know more about triangles here:
https://brainly.com/question/17335144
#SPJ4
Use the graph to find the local minimum and the local maximum for the given function
The local minimum on the interval [-3, 0] is -16, the local maximum on the interval [0, 3] is 4 and the local minimum on the interval [0, 3] is -3
What is a local minimum?In a function, a point located at the local minimum is a point that is at a lower coordinate compared to the other neighboring points
What is a local maximum?In a function, a point located at the local maximum is a point that is at a higher coordinate compared to the other neighboring points
How to determine the local minimum and the local maximum?The complete question is added as an attachment
In the first interval, [-3, 0], the lowest point in the interval is located at (-16, -1.5)
This means that the local minimum on the interval [-3, 0] is -16
In the second interval, [0, 3], the highest maximum in the interval is located at (4, 1)
This means that the local maximum on the interval [0, 3] is 4
In the second interval, [0, 3], the lowest minimum in the interval is located at (0, -3)
This means that the local minimum on the interval [0, 3] is -3
Read more about local minimum and local maximum at:
https://brainly.com/question/9005728
#SPJ1
How to answer this problem
Answer:
m<C = 12.0 °
Step-by-step explanation:
Since we know that this is a non-right triangle, we must use either the law of sines or law of cosines to find m<C.
The information we now have only allows us to use the law of sines, which focuses on proportions:
[tex]\frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}[/tex]
Thus, we can use:
[tex]\frac{sin(98)}{19}=\frac{sinC}{4}\\ 4*sin(98)=19*sinC\\ \frac{4*sin(98)}{19}=sinC\\ sin^-1\frac{4*sin98}{19}=12.033=12.0[/tex]
The sin^-1 represents the sin inverse, which you must use to find angle measures.
Humood's house is (-5,7)
The school is (3,1)
If each unit in the graph is 50m, find the distance from Humood's house to the school.
The distance from Humood's house to the school is 500m
How to determine the distance from Humood's house to the school?The given parameters are:
Humood's house is (-5,7)
The school is (3,1)
The distance between both points is calculated using
[tex]d = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2[/tex]
Substitute the known values in the above equation
[tex]d = \sqrt{(-5 - 3)^2 + (7 - 1)^2[/tex]
Evaluate
d = 10
Each unit in the graph is 50m.
So, we have
Distance =10 * 50m
Evaluate the product
Distance = 500m
Hence, the distance from Humood's house to the school is 500m
Read more about distance at
https://brainly.com/question/1872885
#SPJ1
The sum of 10 consecutive integersstarting with 11, equals the sum of 5 consecutive integers, starting with
(A) 22
(B) 29
(C) 31
(D) 33
Answer: [tex]\large\boxed{29}[/tex]
Step-by-step explanation:
The sum of 10 consecutive integersstarting with 11
= 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
Lets try 29:
29 + 30 + 31 + 32 + 33 = 155
Therefore our answer is:
[tex]\large\boxed{29}[/tex]
PLEASE ITS MY LAST QUESTION
Answer:
[tex]y = - \frac{1}{4} x - 10[/tex]
Step-by-step explanation:
The negative reciprocal of 4 is -1/4.
Let's substitute in our values, to find the y-intercept:
[tex]y = - \frac{1}{4} x + c[/tex]
[tex] - 11 = - 1 + c[/tex]
[tex]c = - 10[/tex]
Finally, our full equation is:
[tex]y = - \frac{1}{4} x - 10[/tex]
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=10
There is a maximum value of 7/6 located at (x, y) = (5/6, 7).
The function given to us is f(x, y) = xy.
The constraint given to us is 6x + y = 10.
Rearranging the constraint, we get:
6x + y = 10,
or, y = 10 - 6x.
Substituting this in the function, we get:
f(x, y) = xy,
or, f(x) = x(10 - 6x) = 10x - 6x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = 10 - 12x ... (i)
Equating to 0, we get:
10 - 12x = 0,
or, 12x = 10,
or, x = 5/6.
Differentiating (i), with respect to x again, we get:
f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.
The value of y, when x = 5/6 is,
y = 12 - 6x,
or, y = 12 - 6*(5/6) = 7.
The value of f(x, y) when (x, y) = (5/6, 7) is,
f(x, y) = xy,
or, f(x, y) = (5/6)*7 = 7/6.
Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).
Learn more about maximum and minimum at
https://brainly.com/question/2437551
#SPJ4
Bryan's Boutique sells shirts, skirts, shoes and hats. If Bryan sells 3 types of shirts, 6 types of skirts, 8 types of bracelets and 2 types of hats, how many different outfits can a customer put together if an outfit must include one shirt, one skirt, one bracelet and one hat?
Using the Fundamental Counting Theorem, it is found that the customer can put together 288 different outfits.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Bryan sells 3 types of shirts, 6 types of skirts, 8 types of bracelets and 2 types of hats, hence the parameters are given as follows:
[tex]n_1 = 3, n_2 = 6, n_3 = 8, n_4 = 2[/tex]
Hence the number of different outfits is given as follows:
N = 3 x 6 x 8 x 2 = 288
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
#SPJ1
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]x = -7[/tex]
Step-by-step explanation:
Given the equation:
[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex],
to solve for [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] its subject.
[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex]
⇒ [tex]10x + 100 - 4 = 11 - 10x -55[/tex] [expand brackets]
⇒ [tex]10x + 96 = -44 - 10x[/tex]
⇒ [tex]10x + 10x + 96 = -44[/tex] [add [tex]10x[/tex] to both sides]
⇒ [tex]20x + 96 = -44[/tex]
⇒ [tex]20x = -44 - 96[/tex] [subtract 96 from both sides]
⇒ [tex]20x = -140[/tex]
⇒ [tex]x = \frac{-140}{20}[/tex] [divide both sides by 20]
⇒ [tex]x = \bf-7[/tex]
Answer:
B) x = -7
Step-by-step explanation:
Given equation: [tex]10(x+10)-4=11-5(2x+11)[/tex]
Step 1: Distribute [tex]10[/tex] and [tex]-5[/tex] through the parentheses.
[tex]\implies 10(x)+10(10)-4=11-5(2x)-5(11)[/tex]
[tex]\implies 10x+100-4=11-10x-55[/tex]
Step 2: Simplify (combine like terms).
[tex]\implies 10x+100-4=11-10x-55[/tex]
[tex]\implies 10x+96=-44-10x[/tex]
Step 3: Add [tex]10x[/tex] to both sides.
[tex]\implies 10x+10x+96=-44-10x+10x[/tex]
[tex]\implies 20x+96=-44[/tex]
Step 4: Subtract [tex]96[/tex] from both sides.
[tex]\implies 20x+96-96=-44-96[/tex]
[tex]\implies 20x=-140[/tex]
Step 5: Divide both sides by [tex]20[/tex] to isolate [tex]x[/tex].
[tex]\implies \dfrac{20x}{20}=\dfrac{-140}{20}[/tex]
[tex]\implies \boxed{x=-7}[/tex]
A dealer bought digital watches at Rs 5,500 per piece and fixed the price of each watch to make 20% profit. How much should a customer pay for it with 13% VAT?
Answer:
A dealer bought digital watches at Rs 5500 per piece and fixed the price of each watch to make 20 profit. How much should a customer pay for it with 13 VAT? A trader purchased a laptop for Rs 45000 and marked its price to make 24 profit.
Step-by-step explanation:
Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables.
Michael
Lemons
Cups of Water
1
4
3
12
4
16
Sondra
Lemons
Cups of Water
2
6
4
12
6
18
Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?
Three-fourths and StartFraction 6 Over 4 EndFraction
StartFraction 3 Over 12 EndFraction and StartFraction 4 Over 12 EndFraction
StartFraction 16 Over 4 EndFraction and StartFraction 18 Over 6 EndFraction
StartFraction 1 Over 12 EndFraction and StartFraction 4 Over 18 EndFraction
The two ratios in the tables shown which have a common denominator you could use to compare is; 3/12 and 4/12
RatioMachael's ratio:
lemons to water = 1:4
Equivalent ratio
= 3 : 12
= 4 : 16
Sondra's ratio:
lemons to water = 2 : 6
Equivalent ratio
= 4 : 12
= 6 : 18
Therefore, the two ratios in the tables shown which have a common denominator you could use to compare is; StartFraction 3 Over 12 EndFraction and StartFraction 4 Over 12 EndFraction
Complete question
Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables. Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?
Learn more about ratio:
https://brainly.com/question/4301994
#SPJ1
Select all of the values of x that are solutions to 17-7x> 3(10x-4) + 61.
-2
-4
-1
2
5
0
Answer: -2, -4, -1
Step-by-step explanation:
[tex]17-7x > 3(10x-4)+61\\\\17-7x > 30x-12+61\\\\17-7x > 30x+49\\\\-32 > 37x\\\\x < -\frac{32}{37}[/tex]
So, the values of x are -2, -4, -1.
What is the solution to the equation
O x = -3
x = -3 and x=0
O x = 0 and x = 3
O x = 3
X+3
2 ?
2x²
The solution to the equation 1/x = x + 3/2x^2 is x = 0 or x = 3
How to determine the solution to the equation?The equation is given as:
1/x = x + 3/2x^2
Cross multiply in the above equation
2x^2 = x^2 + 3x
Evaluate the like terms
x^2 - 3x = 0
Factor out x
x(x - 3) = 0
Solve for x
x = 0 or x = 3
Hence, the solution to the equation 1/x = x + 3/2x^2 is x = 0 or x = 3
Read more about equations at:
https://brainly.com/question/2972832
#SPJ1
Answer:
The Answer Is "x=3"
Step-by-step explanation:
I just did it
PLS HELP IS IT TRUE OR NOT
Answer:
True
Step-by-step explanation:
All faces of a cube are the same.
Write down the equation for the following
i,Grade 7 students received a total of 88 books from world vision.they received 63 books on Monday and g books on Tuesday
ii,Solve the equation above
properties of intersection of sets
The intersection of the sets has the following properties: Commutative law – A ∩ B = B∩ A. Associative law – (A ∩ B)∩ C = A ∩ (B∩ C) φ ∩ A = φ
do mark brainliest
HEY PLS HELP IM STUCK
Using f(x), what is the equation that represents g(x)?
Og(x) = log5 (x) - 3
O
g(x) = log5 (x) +3
Og(x) = log5 (x-3)
Og(x) = logs(x + 3)
The equation that represents the function g(x) is g(x) = log₅(x - 3)
How to determine the equation that represents g(x)?The equation of the function f(x) is given as:
f(x) = log₅(x)
From the graph, we can see that the function g(x) is 3 units to the right of the function f(x)
This means that
g(x) = f(x - 3)
The function f(x - 3) is calculated as follows
f(x - 3) = log₅(x - 3)
Substitute f(x - 3) = log₅(x - 3) in g(x) = f(x - 3)
g(x) = log₅(x - 3)
Hence, the equation that represents the function g(x) is g(x) = log₅(x - 3)
Read more about function transformation at
https://brainly.com/question/1548871
#SPJ1
Identify the area of the figure rounded to the nearest tenth.
Answer:
91.5[tex]cm^{2}[/tex]
Step-by-step explanation:
The area of the rectangle:
a = lw
a =(21)(3) = 63
The area of the square:
a = lw
a = (5)(5) = 25
The area of a half circle:
a=[tex]\frac{\pi r^{2} }{2}[/tex]
a= [tex]\frac{3.14(1.5^{2}) }{2}[/tex]
a = [tex]\frac{3.14(2.25)}{2}[/tex]
a = [tex]\frac{7.065}{2}[/tex]
a = 3.5 rounded to the nearest tenth
63 + 25 + 3.5 =91.5
Lee wants to fence off a rectangular area that is 36 feet squared in size for a vegetable garden. He is considering three garden lengths of 6 ft, 9 ft, and 12 ft. He wants to determine which garden would require the least amount of fencing.
Determine the dimensions of the garden that would require the least amount of fencing.
tried my best to show the steps!! all i did was isolate to find the missing widths attached to the respective lengths (divided surface area by width) and then multiply both sides by two and add them together to find the perimeter.
The dimensions of the garden that would require the least amount of fencing are 6 ft in length and 6 ft in width.
The dimensions are the sides of a geometric shape.
The lengths of the three gardens are given as 6 ft, 9 ft, and 12 ft respectively.
If the area of the garden is 36 feet squared, then the widths for the three lengths will be as follows:
The width of the garden with a length of 6 ft [tex]= \dfrac{36}{6} = 6\ ft[/tex]
The width of the garden with a length of 9 ft [tex]= \dfrac{36}{9} = 4\ ft[/tex]
The width of the garden with a length of 6 ft [tex]= \dfrac{36}{12} = 3\ ft[/tex]
The parameters are calculated as:
The parameter of the garden with dimensions (6 ft, 6 ft) = 2(6 + 6) = 24 ft
The parameter of the garden with dimensions (9 ft, 4 ft) = 2(9 + 4) = 26 ft
The parameter of the garden with dimensions (12 ft, 3 ft) = 2(12 + 3) = 30 ft
The least of the parameter is of the garden with dimensions (6 ft, 6 ft).
Thus, the garden with dimensions (6 ft, 6 ft) would require the least amount of fencing.
Learn more about Dimensions here:
https://brainly.com/question/31209488
#SPJ3
A test consists of section A and section B. Section A has 15 questions and section B has 10 questions. The number of questions in section A is ____% if the questions in the test.
Solve For x :
[tex] \color{purple}{ \pmb{ \frak{2x \: = 100 \red { \: ?}}}}[/tex]
[tex] \\ \\ \\ \\ \\ [/tex]
[tex] { \color{yellow}\bigstar}\underline{ \pmb{ \frak{Thank \: uh }} \color{purple}{ \hearts} !!\: }[/tex]
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given ,
[tex]2x = 100[/tex]
To find ,
value of x
Now ,
[tex]\longrightarrow{2x = 20}[/tex]
Dividing both sides by 2 , we get
[tex] \frac{2x}{2} = \frac{100}{2} \\ \\ \longrightarrow\boxed{ \: x = 50} [/tex]
nikal -,- xD
Answer:
[tex]\bf x=50[/tex]Step-by-step explanation:
[tex]\bf 2x=100[/tex]
Divide both sides by 2:-
[tex]\bf \cfrac{2x}{2}=\cfrac{100}{2}[/tex]
Simplify:-
[tex]\bf x=50[/tex]
___________________
Which line of best fit accurately represents the given scatter plot?
what is 2^c=8 (please help)
Answer:
c=3.
Step-by-step explanation:
∵2*2*2=8,
∴2^3=8.
∵2^c=8,
∴c=3.
What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?
Answer:
[tex]y=-\frac{1}{3}x+7[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is -1/3.
Substituting into point-slope form and converting to slope-intercept form,
[tex]y-5=-\frac{1}{3}(x-6) \\ \\ y-5=-\frac{1}{3}x+2 \\ \\ y=-\frac{1}{3}x+7[/tex]