The solution to the equation, −112 = 8x, is: x = -14.
How to Solve an Equation?To find the value of the variable in an equation, means to solve the equation.
To solve any given equation, we are to apply all necessary properties of equality in other to isolate, as much as possible, the variable of the equation to one side of the equation. Th value of the variable is the solution to the equation.
Given the equation:
-112 = 8x
Divide both sides of the equation by 8:
-112/8 = 8x/8 [division property of equality]
-14 = x
x = -14
Check: Plug in x = -14 into the equation:
-112 = 8(-14)
-112 = -112 [true]
Thus, the solution to -112 = 8x is: x = -14.
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PLEASEEE HELP ( ALOT OF POINTS)
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Greg bought a regular-sized box of his favorite cereal. A regular-sized box contains 12 servings.
Part A: If Greg eats 1 1/2 servings for breakfast every day, how many breakfasts can Greg eat from 1 box? Show all work.
Part B: The regular-sized box of cereal costs $4.29. How much does 1 breakfast from a regular-sized box of cereal cost Greg? Round to the nearest hundredth. Show all work.
Part C: If Greg purchased the family-sized box of cereal that contains 18 servings, how many more breakfasts could Greg eat from 1 box? Show all work.
The number of breakfast Greg can eat from a box of cereal if he eats 1 1/2 servings for breakfast everyday is 8 breakfast.
If a regular-sized box of cereal costs $4.29, the cost of 1 breakfast from a regular-sized box of cereal is $0.54The number of more servings of breakfasts Greg could eat from 1 family-sized box is 4 servings.How to find unit rate of Greg's breakfast?A regular-sized box of cereal = 12 servingsIf Greg eats 1 1/2 servings for breakfast every dayNumber of breakfast Greg can eat in a regular-sized box = A regular-sized box of cereal / servings of breakfast eaten everyday
= 12 ÷ 1 1/2
= 12 ÷ 3/2
multiply by the reciprocal of 3/2= 12 × 2/3
= 24/3
= 8 breakfast
Cost of regular-sized box of cereal = $4.29.
Cost of one breakfast from a regular-sized box of cereal = Cost of regular-sized box of cereal ÷ Number of breakfast Greg can eat in a box
= $4.29 / 8
= 0.53625
Approximately,
$0.54 per breakfast
If Greg purchased the family-sized box of cereal that contains 18 servingsNumber of breakfast Greg can eat in a family-sized box = A family-sized box of cereal / servings of breakfast eaten everyday
= 18 servings / 1 1/2
= 18 ÷ 3/2
= 18 × 2/3
= 36/3
= 12 servings
Therefore, the number of more servings of breakfasts Greg could eat from 1 family-sized box
= Number of breakfast Greg can eat in a family-sized box - Number of breakfast Greg can eat in a regular-sized box
= 12 servings - 8 servings
= 4 servings
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Answer:
= 4 servings
Step-by-step explanation:
triangle DEF and triangle CBD are similar right triangles which statement is slopes is DF and CDs true
We can calculate the slope of a line segment by using the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are two points of the line.
In this case the side DF goes from the point D(-2,-2) to the point F(1,7), then its slope is:
[tex]m=\frac{7-(-2)}{1-(-2)}=\frac{7+2}{1+2}=\frac{9}{3}=3[/tex]For the side, CD, it goes from D(-2,-2) to C(0,4), then its slope is:
[tex]undefined[/tex]Looking to receive help on the following problem, thank you!
olution
or this case we have the following vectors:
u= -3i +2j, w= 4j, v= 6i -4j
And we can do the following:
art a
u*v= -3*6 + 2*-4= -18 -8= -26
Part b
w*v= 0*6 + 4*-4 =-16
Multiply 4(Q+2) what's the answer
Given the expression:
[tex]4(Q+2)[/tex]Let's multiply the expression.
To multiply apply the distributive property of multiplication.
Distribute 4 to the values in the parentheses:
[tex]\begin{gathered} 4(Q)+4(2) \\ \\ =4Q+8 \end{gathered}[/tex]ANSWER:
[tex]4Q+8[/tex]Number 12 I don’t get it y’all know ?
Name the line of reflection used to map the preimage to its image.
Option E, the x-axis is the line of reflection used to map the preimage to its image.
The graph represents that if the graph is folded by an x-axis,
Point Y will cross-point Y', which is two coordinates away from the x-axis.
Point X will cross point X', which is five coordinates away from the x-axis.
Points W will cross-point W', which is eight coordinates away from the x-axis.
Points V will cross-point V', which is five coordinates away from the x-axis.
A mirror image is symmetric about the x or y-axis. Reflection is called "inverse geometry". A mirror reflector is a type of reflector. When the line reflects the image, the reflection line appears. A shape is said to reflect a different shape if a point on a shape is equidistant from a point on another shape.
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please hurry due today I will give you brainlest
Which numbers are solutions of 4p+6 < 3p? Choose exactly two answers that are correct.
6 and -6
please give brainliest
A square swimming pool is surrounded by a cement walkway with a uniform width. The swimming poa
has a side length of (x - 5) feet. The side length of the entire square area including the pool and the
walkway is (x+4) feet.
Enter an expression for the area of the walkway. Then find the area of the cement walkway when
x = 8 feet.
The area of the walkway is
ft².
When x = 8 feet, the area of the cement walkway
The expression of the square walkway is (x + 4)² - (x - 5)² and the area of the square cement walkway is 135ft².
Area of square:
The area of a square is refers the place covered by the square.
The formula to calculate the area of square is,
Area = s²,
where, 's' refers the side of the square.
Given,
A square swimming pool is covered by a cement walkway with a uniform width.
Length of swimming pool = (x-5) feet.
Length of square walkway including the swimming pool = (x+4) feet
Here we need to find the area of the cement walkway and when the value of x is 8 then the value of the cement walkway.
1) Here we have to write an expression for the area of the entire square minus area of the pool.
Remember the equation for the area of a square is , where
A = area of square and
s = side value of the square.
We are given that the side of the entire square including walkway and pool is s = (x+4)ft.
Apply the value of the side into the formula for the area of the square, then we get,
A = s²
A = (x + 4)² --------------(1)
We are also given that the side length of the swimming pool is s = (x-5)ft. Apply that into the equation for the area of a square to get the expression for the area of the pool:
A = s²
A = (x - 5)² --------------(2)
Now subtract the area of the pool (x - 5)² from the area of the entire square (x + 4)² to get your expression for the area of the walkway.
Expression for the area of the walkway:
=> (x + 4)² - (x - 5)²
2) Since you know that x = 8ft, you can solve your expression for the area of the walkway. Plug x into your expression:
=> (8 + 4)² - (8 - 5)²
=> (12)² - (3)²
=> 144 - 9
=> 135
The area of your walkway is 135ft².
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where we can use Adding and Subtracting Polynomials in real life??
Polynomials are utilized in management, business, farming, computer science, and math-related fields.Expressions defining known and unknown numbers are created using variables and constants in all professions that need proficiency with polynomials.
where we can use Adding and Subtracting Polynomials in real life?
Finance Loan computations and firm valuation utilize an assessment of present value.In order to determine an equal liquid value (present, cash, or in-hand), it uses polynomials that back interest accumulation out of hypothetical future liquid transactions.Fortunately, if the payment schedule is regular, many payments can be rewritten in a straightforward manner.Economic and tax calculations can frequently be expressed as polynomials as well.Electronics
Polynomials are widely used in electronics.The polynomial V=IR, which defines resistance, connects the resistance of a resistor to the current flowing through it and the potential drop across it.While many conductors (but not all) abide by Ohm's law, this is comparable to that law but not the same.It claims that on a graph, the relationship between voltage drop and current flowing through a resistor is linear.In the equation V=IR, resistance is therefore constant.Electronics also uses other polynomials, such as P=IV=IR2, which describes the relationship between voltage drop and power loss.Kirchhoff's loop rule and the Kirchhoff's junction rule, which both describe voltage drop around closed circuits and the current at junctions, respectively, are polynomials.Curve Fitting
In both regression and interpolation, polynomials are fitted to data points.Regression is the process of fitting a large set of data points with a function, typically a line: y=mx+b.Numerous linear regression is used when there are multiple dependent variables (or "x"s) in the equation.Chemistry
In chemistry, polynomials are frequently used.The ideal gas law, PV=nRT (where n is the mole count and R is a proportionality constant), is an example of a gas equation linking diagnostic parameters that can typically be represented as a polynomial.Molecule concentration equations at equilibrium can alternatively be expressed as polynomials.For instance, the equilibrium concentration equation can be stated in terms of the related equilibrium constant K: KC=AB if A, B, and C are the concentrations of OH-, H3O+, and H2O in solution, respectively.Engineering and physics
Proportionality is a key study in both physics and engineering.How much does the beam deflect when a stress is raised?How far will a trajectory land if it is shot at a specific angle?F=ma (from Newton's laws of motion), E=mc2, and F—-r2=Gm1—-m2 (from Newton's law of gravitation, though typically the r2 is put in the denominator) are well-known examples from physics.To learn more about polynomials refer
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The answer to one and two
Solution
(a) There are 9 students entering the school district science project:
medals for 1st, 2nd and 3rd
k1 = 1O ways to choose first person to be chosen from the group of 10.
99
k2 = 8 ways for the second person to be chosen from the remaining people(9–1).
k3 = 7 ways for the second person to be chosen from the remaining people(8–1).
then all you need to do is multiply these k1 * k2 * k3.
[tex]\begin{gathered} 1st\text{ 2nd 3rd} \\ 1st=9\text{ option} \\ 2nd=8\text{ }options \\ 3rd=7\text{ options} \end{gathered}[/tex][tex]\begin{gathered} 9\times8\times7 \\ =504 \end{gathered}[/tex](b) There are 7 unique names in a bowl. In how many orders can 2 names be chosen:
This is a permutation problem in order
There are 7 names, and the 2 name have to be in same order
[tex]\begin{gathered} 7P_2 \\ \frac{7!}{(7-2)!} \\ =\frac{7!}{5!} \\ =\frac{7\times6\times5!}{5!} \\ =42 \end{gathered}[/tex]Which recursive sequence would produce the sequence 2, -11, 54, ...
Answer:
[tex]n_{i+1} = -5n_i - 1[/tex]
Step-by-step explanation:
-5*2 - 1 = -11
-5*-11 - 1 = 54
4. Write a comparison statement for 9 x 3 = 27
Given the following expression:
[tex]\text{ 9 x 3 = 27}[/tex]Making a comparison statement out of this will be: 27 is 3 times more than 9.
3⁴-21÷7 use pemdas. to solve this
3⁴-21÷7
According to PEMDAS ( order of operations):
First, Do exponents before multiplying or dividing: 3^4
81-21÷7
Then, divide before subtracting (27÷7 )
81- 3
Finally, subtract
78
PLEASE HELP DUE SOON WILL GIVE 20 POINTS!!
Answer:
$5.19
Step-by-step explanation:
10.33 × $2.51 = $25.93
$25.93÷5=$5.19
Francis heard that a car stereo system was on sale for 30% off. If the sale price was 57.75, what was the original price of the stereo?
Answer:
$82.50
Step-by-step explanation:
82.5 times 0.7 = 57.75
doing 57.75 + 30% wouldn't work, so you have to increase the number (original price) being discounted until you get 57.75
also, the '0.7' is 70% which also means '30% off' because you took 30% away from the original price that was 100%
math calculator saves the day? dont use paper or it would take a long time (unless it was a test or teacher said no)
(-4, 2) and (5, 6) slope
In order to find the slope between those two points, we can use the following formula for the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where m is the slope between the points (x1, y1) and (x2, y2).
So using the points (-4, 2) and (5, 6), we have:
[tex]m=\frac{6-2}{5-(-4)}=\frac{4}{9}[/tex]So the slope is 4/9
Which statement is the most appropriate comparison of the spreads?A. The standard deviation for town A, 20", is greater than thestandard deviation for town B, 10°.B. The interquartile ranges (IQRs) for towns A and B are both 20°.C. The interquartile range (IQR) for town A, 30°, is less than the IQRfor town B, 46".D. The interquartile range (IQR) for town A, 20", is greater than theIQR for town B, 10".
We are given two box plots of a variable, for two different towns. Recall that the structure of a box plot is
where Q1 is the 25th percentile (or quartile 1), Q2 is the median and Q3 is the 75th percentile (or Quartile 3). This type of graphs tells us how the data is distributed, and more specially it can tell us how the data is spread across the different values the variable could take. So the way to analyze the spread from the graph is by considering the inter quartile range (IQR). This amount can be calculated by simply finding the difference between Q3 and Q1. If this range is really small, this would mean that the data is less spread and if this range is big, then this would mean that the data is more spread.
Using the given box plots, we can determine the following:
Town A: Q3 = 40, Q1 = 20, IQR = 40-20=20
Town B: Q3 = 45, Q1=35, IQR = 45-35 = 10
So, this would lead to option D.
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select
and test 54 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3
batteries do not meet specifications. A shipment contains 4000 batteries, and 3% of them do not meet specifications.
What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will
many be rejected?
The probability that this whole shipment will be accepted is
(Round to four decimal places as needed.)
The company will accept % of the shipments and will reject% of the shipments, so
(Round to two decimal places as needed.)
This probability of shipment being accepted is 84%.
And most similar deliveries will be allowed since the likelihood of receiving a sample with much more than three damaged batteries is extremely low.
If at least three batteries fail to satisfy standards, the delivery would be approved.
This may be described as a binomial distribution, with n = 54 samples as well as a p = 0.03 probability of not satisfying the parameters of any battery.
If n ≤ 3 the package will be accepted.
The probability of this event is:
P(D ≤ 3) = P(D = 0) + P(D = 1) + P(D = 2) + P(D = 3)
P(D = k) = (n! ÷ (k!(n-k)!)) × [tex]p^{k}[/tex] × [tex](1 - p)^{n - k}[/tex]
P(D = 0) = (54! ÷ (0!(54)!)) × [tex]0.03^{0}[/tex] × [tex](0.97)^{54}[/tex]
P(D = 0) = 1 × 1 × 0.110
P(D = 0) = 0.110
P(D = 1) = (54! ÷ (1!(53)!)) × [tex]0.03^{1}[/tex] × [tex](0.97)^{53}[/tex]
P(D = 1) = 54 × 0.03 × 0.205
P(D = 1) = 0.3321
P(D = 2) = (54! ÷ (2!(52)!)) × [tex]0.03^{2}[/tex] × [tex](0.97)^{52}[/tex]
P(D = 2) = 1431 × 0.0009 × 0.205
P(D = 2) = 0.264
P(D = 3) = (54! ÷ (3!(51)!)) × [tex]0.03^{3}[/tex] × [tex](0.97)^{51}[/tex]
P(D = 3) = 24804 × 0.000027 × 0.211
P(D = 3) = 0.141
Then,
P(D ≤ 3) = P(D = 0) + P(D = 1) + P(D = 2) + P(D = 3)
P(D ≤ 3) = 0.110 + 0.3321 + 0.264 + 0.141
P(D ≤ 3) = 0.8471
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HELP!! The table compares the average daily temperature and ice cream sales each day.
Temperature (°F) Ice Cream Sales
58.2 $112
64.2 $135
64.3 $138
66.8 $146
68.4 $166
71.6 $180
72.7 $188
76.2 $199
77.8. $220
82.8 $280
What is the slope of the line of best fit, where x represents the average daily temperature and y represents the total ice cream sales? (Round your answer to one decimal place.)
4.2
6.5
8.1
9.1
The slope of line of best fit is 6.47887 which is approximately 6.5.
Line of Best FitA line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points. It is an output of regression analysis and can be used as a prediction tool for indicators and price movements.
To calculate the slope of the equation, we need to solve for some parameters.
The sum of x = 703The sum of y = 1764Mean of X = 70.3Mean of Y = 176.4The sum of squares (SSx) = 490.24Sum of product (SP) = 3176.2The equation of regression is given as
[tex]y = bX + a[/tex]
let's solve for the unknown parameters b and a.
[tex]b = \frac{SP}{SS_x}=\frac{3176.2}{490.24} = 6.47887 = 6.5[/tex]
The slope of the line of best fit is given as 6.5.
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Answer: 6.5
Step-by-step explanation: i took the test
Find all solutions of the equation x^2+2x+6=0 and give your answer as a list of complex numbers, such as 3-4i, 5+i.
Given equation [tex]x^{2} +2x+6=0[/tex]
we use in Quadratic formula
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
So a=1, b=2, c=6
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {2^{2}-4*1*6}}}{2*1}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {4-24}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {20}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm 2i{\sqrt {5}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x= {-1\pm i{\sqrt {5}}}[/tex]
What is the Quadratic formula?
A second-degree equation is a quadratic equation. It implies that at least one term in which the variable is squared will be present. This equation's conventional form is:
ax²+ bx + c = 0
where a, b, and c are variables or coefficients.
X is also an unknowable variable.
The fact that the coefficient "a" cannot be 0 is one unbreakable law.
Two potential choices for its variable X will fulfill the equation because of the degree of 2. Quadratic equations may reflect a wide range of real-world scenarios, as is clear to observe. We'll now look at several solutions.
Quadratic is derived from the term "quad," which means square. Here, we'll create the formula for quadratic equations so that they may be solved.
The factorization approach fails to reduce a large number of equations. Such equations are solved using a more potent approach. Every quadratic problem may be solved using this technique. This is the formula for a quadratic equation in general.
This is how it is explained:
If ax2 + bx + c = 0, then
is a quadratic equation, then the following formula provides the value of x.
Simply enter the numbers for a, b, and c, and the computations will be performed.
The values of a, b, and c are extracted from the equation and entered into the quadratic equation formula.
A, B, and C in this case only numbers. These are the quadratic equation's numerical coefficients, which you must solve.
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
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Current Attempt in Progress
In a list of 15 households, 9 own homes and 6 do not own homes. Four households are randomly selected from these 15 households.
Find the probability that the number of households in these 4 who own homes is exactly 4.
Round your answer to four decimal places.
The most appropriate choice for probability will be given by:
Probability that the number of households in these 4 who own homes is exactly 4 = [tex]\frac{42}{455}[/tex]
What is Probability?
Probability of an event is the chance of occurance of that event.
Probability can be obtained by Number of favourable outcomes divided by the total number of outcomes
Probability varies from 0 to 1.
Here,
Total number of households = 15
No of households to be selected = 4
4 households can be selected from 15 households in [tex]15 \choose 4[/tex] ways
= [tex]\frac{15!}{(15-4)! \times 4!}\\[/tex]
= [tex]\frac{15!}{11! \times 4!}[/tex]
[tex]=\frac{15 \times 14 \times 13 \times 12}{1 \times 2 \times 3 \times 4}[/tex]
= [tex]1365[/tex] ways
Now,
Number of households who own homes = 9
4 households can be chosen from 9 households in [tex]9 \choose 4[/tex] ways
[tex]\frac{9!}{(9-4)! \times 4!}\\[/tex]
= [tex]\frac{9!}{5! \times 4!}[/tex]
[tex]=\frac{9 \times 8 \times 7 \times 6}{1 \times 2 \times 3 \times 4}[/tex]
= [tex]126[/tex]
Probability that the number of households in these 4 who own homes is exactly 4 = [tex]\frac{126}{1365}[/tex]
= [tex]\frac{42}{455}[/tex]
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pls help i dont get it
5/6x-5/12x-1/3+1/4x+1/12
(8x-3)/12
Step-by-step explanation:
The first four terms of a sequence are given below.
11, 9, 7, 5, ...
What is the seventh term of the sequence?
A. 5
B. -3
C. 1
D. -1
Answer: D:-1
Step-by-step explanation: 11,9,7,5,3,-1,-3,... => dãy số trên có quy luật là số lẻ
Suppose you earn 2% on $1000 for 2 years if this interest rate is doubled then the interest rate will be
When earn 2% on $1000 for 2 years if this interest rate is doubled then the interest rate will be 4% and the interest is $80.
How to illustrate the information?From the information, the person earns 2% on $1000 for 2 years and this interest rate is doubled, the interest rate will be: = 2% × 2 = 4%
It should be noted that simple interest is calculated as:
Interest = Principal × Rate × Time / 100
Interest = 1000 × 4 × 2 /100
Interest = 8000 / 100
Interest = $80
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Please help I’ll mark you as brainliest if correct!!
Answer:
it would be 29 five
Step-by-step explanation:
I can't do the small number so it's just typed big
math problem uploaded
From the graph provided, it can be seen that:
There is a maximum at (6,1)
Therefore, the answer is the following:
The function has a relative maximum of 1 at x = 6
2 X (6+ 2 + 8) -4 show your work pls
Answer:
Step-by-step explanation:
32
Absolute value |-6.809 > |-6.812 which is greater
Answer: 6.809 < 6.812. 6.812 is greater.
Step-by-step explanation:
If you mean if...
|-6.809| > |-6.812|
then, -6.812 will be bigger because when you absolute value an answer the number inside the | | will become positive. So the simplified equation will look like this:
6.809 > 6.812
So, the sign is wrong and should be flipped.
6.809 < 6.812
10. Using the two formulae, A=B/6.5 + 2.5, C= B/9A, obtain an expression for C in terms of A alone:
Answer:
43a + c = 13.25
Step-by-step explanation:
A = 9
C = 81