Answer:
Step-by-step explanation:
n = the number
n = 5m - 3
what is the value of h(2)
a) -2
b) -1
c) 0
d) 3
Answer:
(c) 0
Step-by-step explanation:
The answer to this question requires that you read a graph.
How to read a graphFinding the value of h(2) means finding the value of "y" that corresponds to x=2.
The x-axis of this graph is identified by the "x" at the right side, under the arrow at the end of the x-axis. The y-axis is similarly identified by the "y" to the right of the y-axis at the top of the graph.
Each axis is labeled with numbers.
To find the y-value associated with x=2, first find the vertical line labeled 2 on the x-axis. It is 2 grid squares to the right of the y-axis.
Follow this vertical line until you reach the point where it intersects the line segment(s) representing h(x). At one of these, you encounter a solid dot. At the other point of intersection, you see an open circle (empty dot). The open circle means the point is not included in the function graph.
The value of h(2) is the y-value at the point where the vertical line x=2 meets the defined point on the function graph, the solid dot. The y-value is found by following the horizontal grid line to the y-axis, and reading the y-value there.
The point on this graph where the axes cross, the "origin," has no markings indicating the x- and y-values are zero there. You must infer that from the markings that are shown.
Value of h(2)The point on the graph where x=2 lies on the horizontal line y=0. That is ...
h(2) = 0
Solve for x
x - 20 + 2x = 35
[tex] \sf{\red{ANSWER \: \: :}}[/tex]
x = 18 1/3
[tex] \sf{\purple{EXPLANATION \: \: :}}[/tex]
x - 20 + 2x = 35
- 20 + 3x = 35
3x = 35 + 20
3x = 55
x = 55/3
x = 18 1/3
Assume that P(E) = 0.471 and P(F) = 0.595. If E and F are independent, find P(E and F)
The value of the probability P(E and F) is 0.2802
Independent probabilityEvents are known to be independent if the occurrence of one does not affect the other.
Given the following parameters
P (E) =0.471
P(F) = 0.595
If E and F are independent, then;
P(E and F) = P(E)P(F)
P(E and F) = 0.471 * 0.595
P(E and F) = 0.2802
Hence the value of the probability P(E and F) is 0.2802
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solve (x - 3)^2 = 5 p
please help
Hello!
Let's solve !
⇒ (x - 3)² = 5
⇒ x² - 6x + 9 = 5
⇒ x² - 6x + 4 = 0
⇒ x = -(-6) ± √36 - 4(1)(4) / 2
⇒ x = 6 ± √20 / 2 = 6 ± 2√5 / 2
⇒ x = 3 ± √5
∴ The solutions are x = 3 + √5 and x = 3 - √5.
Answer:
p=(x−3)25
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x-3)^2-(5*p)=0
STEP1:
1.1 Evaluate : (x-3)2 = x2-6x+9
Equation at the end of step1:
x2 - 6x - 5p + 9 = 0
STEP2:
Solving a Single Variable Equation:
2.1 Solve x2-6x-5p+9 = 0
Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?
Choose the most logical value for the variable to represent.
Let x = .
3m = 15
9 + 15m = 12m – 1
3m = 18
9 + 6 – 15 = 15m – 12m
By solving a system of equations, we conclude that Kelli's speed on still water is 6.1km/h
How fast can Kelli swim in still water?Let's say that the speed of Kelli in still water is S. And we know that the speed of the river is 5km/h.
When she swims upstream, her velocity is:
(S - 5km/h)
When she swims downstream, her velocity is:
(S + 5km/h)
With the given information, we can write for a distance D:
(S - 5km/h)*1h = D
(S + 5km/h)*6min = D
First, let's rewrite 6 minutes into hours.
1 hour = 60min
6 min = 6/(60) hours = 0.1 hours
Then the system of equations that we need to solve is:
(S - 5km/h)*1h = D
(S + 5km/h)*0.1h = D
D is the same distance in both cases, then we can write:
(S - 5km/h)*1h = (S + 5km/h)*0.1h
Now we can solve this for S.
S*1h - 5km = S*0.1h + 0.5km
S*1h - S*0.1h = 5km + 0.5km
S*(0.9h) = 5.5km
S = 5.5km/0.9h = 6.1km/h
Kelli's speed on still water is 6.1km/h
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In 2011, the maximum amount that you could have contributed to your RRSP (Registered Retirement Savings Plan) was
the lesser of $22,450 or 18% of your earned income from the previous year. How much income do you need to claim a
$22,450 contribution in 2011?
Using proportions, it is found that you need an income of $124,722.22 to claim a $22,450 contribution in 2011.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To claim a $22,450 contribution in 2011, this amount has to be 18% of your income, hence:
0.18x = 22450
x = 22450/0.18
x = $124,722.22.
You need an income of $124,722.22 to claim a $22,450 contribution in 2011.
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Hi- I need help please to get my HS diploma...did not graduate :(
For the inequality y+4x≤x2+2, where is the graph shaded and is the curve solid or dotted?
Answer:
B
Step-by-step explanation:
first for the easy one : the curve line is dotted, if the line points are NOT part of the solution. and it is solid, if the points are included.
you know what the curve line indicates ? it indicates the points for which there is equality.
so, if there is a ">=" or "<=" relation, then that includes equality, and the curve is solid.
if there is only a true inequality ("<", ">"), then the curve is dotted, as the equality is not included.
so, I how this is now really clear.
in our case here (I suspect it really looks like this)
y + 4x <= x² + 2
we have a "<=" sign, so, the curve is ..., well ? ... well ? ...
well ? ... well ? ... solid !
and we still treat inequalities as much as possible as regular equalities.
so,
y <= x² - 4x + 2 (after subtracting 4x from both sides).
and now you see it, right ?
all y values that are smaller or equal to the quadratic expression.
SMALLER ! so, BELOW the curve (as the smaller y values are represented by the lower part of the y-axis).
4. The following set of points belong to a specific function: {(-3,0)(-2,4), (-1,0 ), (0,-6),(1,-8), (2,0),(3,24)} Based on the set of points answers the following questions:
a) What type of function does the set of points produce? Justify your answer.
b) Write an equation for this function based on the set of points that have been given.
The type of function that these sets of points are known to produce is the cubic function.
What is a cubic function?This is a function that is known to be a polynomial of degree 3. This type of polynomial is one that the coefficients are known to be complex numbers.
This is a cubic function given that the x axis is known to go through these points (-3,0), (-1,0), (2,0).
b. Given the sets of pints that we have, we have the equation
f(x) = a(x+3)(x+1)(x-2)
Such that
f = -2 =
4 = a x 1 x -1 x -4
4 = 4a
a = 1
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Identify the underline place 75.733
Answer: Digit Place Value
7 Tens
5 Ones
.
7 Tenths
3 Hundredths
3 Thousandths
Step-by-step explanation: this should help its not the answer but it's support
write the equation of the line that is parallel to the y-axis and passes through the point (7,0)
The equation of the line is x = 7 which is parallel to the y-axis and passes through the point (7,0)
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
The line that is parallel to the y-axis and passes through the point (7,0)
As we know the line equation:
Parallel to the y-axis
x = c
Passes through the point (7,0)
x = 7
Thus, the equation of the line is x = 7 which is parallel to the y-axis and passes through the point (7,0)
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The doctor tells Evelyn that she needs to exercise enough to burn at least 700 calories each day. She prefers practicing yoga or jogging. While practicing yoga she burns 5 calories per minute, and while jogging she burns 8 calories per minute. Let x be the number of minutes she spend practicing yoga and let y be the number of minutes she spends jogging. Write an inequality that models this situation.
The inequality that can be used to model Evelyn situation is
x + y = 60
x + y = 605x + 8y ≥ 700
Inequalityx = number of minutes she spend practicing yogay = number of minutes she spends joggingCalories burnt practicing yoga = 5Calories burnt jogging = 8The inequality
x + y = 60
5x + 8y ≥ 700
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The next number in the series 0,7, 26, 63 is?
Answer:
124
Step-by-step explanation:
1^3-1=0
2^3-1=7
3^3-1=26
4^3-1=63
5^3-1=124
Hence the next one in the pattern is 124.
According to the food and nutrition service of the u.s. department of agriculture, in one school year, the national school lunch program (NLP) served 31.2 million school lunches. of these, 16.1 million were free lunches, 3.2 million were reduced-price lunches, and 11.9 million were full-price lunches. the federal government reimburses school districts $2.68 for each free lunch, $2.28 for each reduced-price lunch, and $0.25 for each paid lunch. in addition to cash reimbursements, schools are entitled to receive USDA foods called "entitlement" foods at a value of 19.50 cents for each lunch served. you are the administrator in charge of the school lunch program for your school district. last month, the schools in your district served 27,000 free lunches, 18,000 "reduced-price" lunches, and 54,000 regular-priced lunches. (a) calculate the amount of reimbursement (in $) you expect to receive from the nslp for last month. $____. (b) in addition to the lunch reimbursement, the nslp program pays your district $.035 per one-half pint of milk served with each meal. if each student averaged 1 one-half pint of milk per meal, calculate the total amount of milk reimbursement (in $) you expect for last month. $_____ . (c) the bottom line—what is the total amount of reimbursement (in $) your district will receive for last month? $_______. (d) red tape—the government paperwork you must submit requires that you report the average reimbursement (in $) per meal for both lunch and milk combined last month. calculate this amount. (round your answer to the nearest cent.) $________.
a) The amount of meal reimbursement (in $) you expect to receive from the NSLP for last month is $146,205.
b) The total amount of milk reimbursement (in $) you expect for last month is $103,950.
c) The total amount of reimbursement (in $) your district will receive for last month is $250,155 ($146,205 + $103,950).
d) The average reimbursement (in $) per meal for both lunch and milk combined last month is $2.53 ($250,155/99,000).
What is reimbursement?Reimbursement is a process by which an entity is compensated for the expenses it incurs under a stated program.
Examples of expenses under the reimbursement policy include business expenses, insurance costs, and overpaid taxes.
Data and Calculations:Annual NSLP lunches = 31.2 million
Lunches Free Reduced Price Full-Price Total
National Quantity 16.1 million 3.2 million 11.9 million 31.2 million
District Lunches 27,000 18,000 54,000 99,000
Reimbursement rate $2.68 $2.28 $0.25 $0.195
Reimbursement $72,360 $41,040 $13,500 $19,305
Total reimbursement = $146,205 ($72,360 + $41,040 + $13,500 + $19,305)
Amount for milk reimbursement = $103,950 ($0.35 x 1.5 x 2 x 99,000)
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PLEASE FIND THE COORDINATES!!!
The graph of the given equation is given below.
We have given the equation of the line is f(x)=-1/5x+4f(x)
We have to determine the coordination.
What are the coordinates of the line?line coordinates are used to specify the position of a line just as point coordinates (or simply coordinates) are used to specify the position of a point.
Therefore we get f(x)=y
y=-1/5x+4....(1)
Plug x=0 in (1) then y=4
Plug x=5 in (1) then
y=-1/5(5)+4
=-1+4
=3
Therefore we get the coordinates (0,4) and (5,3)
Therefore the graph is given below,
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Here are the ages (in years) of 10 professors at a college. 49, 43, 53, 41, 33, 67, 55, 34, 75, 55 What is the percentage of these professors who are younger than 55?
Answer:
60%
Step-by-step explanation:
There are 6 professors younger than 55 (49, 43, 53, 41, 33, 34).
6/10 = 60%
expressions is equivalent
to a(b-c)-b(a+c)-c(a-b)?
After solving the algebraic expression a(b-c)-b(a+c)-c(a-b) we get the equivalent answer as ₋2(ab ₊ ac).
What is equivalent of algebraic expression?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given the expression is a(b₋c)₋b(a₊c)₋c(a₋b)
The first step is to multiply the terms.
⇒(a×b ₋ a×c) ₋ (b×a ₊ b×c) ₋ (c×a - c×b)
= (ab ₋ ac) ₋ (ba ₊ bc) ₋ (ca ₋ cb)
Now open the brackets.
= ab ₋ ac ₋ ba ₋ bc ₋ ca ₊ cb
Now comes main step of combining the like terms.
Put similar terms together on both sides of the equation.The two phrases are equal if each of the terms in both of them is the equivalent.
= ab ₋ ba ₋ ac ₋ ca ₋ bc ₊bc
Since, bc is a like term with opposite sign, therefore bc gets cancelled.
= ab ₋ ba ₋ ac ₋ ca
= ₋2ab ₋ 2ac
Take 2 as a common term from both the terms.
= ₋2(ab ₊ ac)
Hence we get the required equivalent of a(b-c)-b(a+c)-c(a-b) as
₋2(ab ₊ ac)
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Consider the graph of the function f(x) = 10^x
Which statement describes a key feature of function g if g(x) = f(x + 4)
The statement that describes a key feature of g if g(x) = f(x + 4) and f(x) = 10ˣ is "horizontal asymptote of y = 0". (Correct choice: B)
How to analyze a function resulting from a transformation rule
According to the statement, we have an original function f(x) = 10ˣ and a transformation rule for horizontal translation g(x) = f(x + 4). By applying this rule, we have that g(x) = 10ˣ ⁺ ⁴, which have these features:
The y-intercept of g(x) is located at (0, 10000).Horizontal asymptote of g(x) is y = 0.There are no x-intercepts.Therefore, the statement that describes a key feature of g if g(x) = f(x + 4) and f(x) = 10ˣ is "horizontal asymptote of y = 0". (Correct choice: B)
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Solve the following equation:
30= |- 4y + 2|
Suppose [tex]-4y+2\ge0[/tex]. Then by definition of absolute value,
[tex]|-4y+2| = -4y+2 \implies 30 = -4y+2 \implies -4y = 28 \implies \boxed{y=-7}[/tex]
On the other hand, suppose [tex]-4y+2<0[/tex]. Then
[tex]|-4y+2| = -(-4y+2) \implies 30 = 4y - 2 \implies 4y = 32 \implies \boxed{y=8}[/tex]
Recall the definition,
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
A bus can reach from Kathmandu to Lumbini in 15 hours when the speed is 40 km per hour. I how many hours it reaches when the speed of the bus is 50 km per hour.
Answer:
12 hours
Step-by-step explanation:
1) Find the distance using: Distance = speed × time.
Distance = 40 × 15
= 600 km
2) Use the time formula to find the time taken. The formula is Time = distance / speed.
Time = 600 / 50
= 12 hours
4. A triangle has vertices A(4, 2), B(3, 7), and C(–4, –5).
a) Explain HOW you would draw the median of the triangle from vertex A. Then draw it on the grid provided.
B). Calculate the length of the median from C to AB
To draw the median of the triangle from vertex A, the mid point of BC must be determined. The median of the vertex A is given at (-1/2, 1). See explanation below.
How you would draw the median of the triangle from vertex A?Recall that B = (3, 7)
and C = (-4, -5).
Note that when you are given coordinates in the format above, B or C = (x, y)Hence the mid point of line BC is point D₁ which is derived as:Connecting D' and A gives us the median of the vertex A. See attached graph.
What is the length of the median from C to AB?
Recall that
A → (4, 2); and
B → (3, 7)
Hence, the Midpoint will be
[tex][(\frac{4+3}{2} )[/tex], [tex](\frac{2+7}{2} )][/tex]
→ [tex](\frac{7}{2}, \frac{9}{2} )[/tex]
Recall that
C → (-4, 5)
Hence,
[tex]\overline{C D_{2} }[/tex] = [tex]\sqrt{[(-4 -\frac{7}{2} })^{2} + (-5-\frac{9}{2} )^{2} ][/tex]
Simplified, the above becomes
= √(586)/2)
= 24.2074/2
= 12.1037
The length of the Median from C to AB ≈ 12
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The average early morning temperature in Churchill, Manitoba is "-4°C" in October. In January, it is 27°C colder. What is the average early morning temperature in January?
Answer:
-31 degrees
Step-by-step explanation:
-4-27=-31
Analyze the diagram below and complete the instructions that follow.
Find m
A. 15°
B. 30°
C. 75°
D. 150°
Please select the best answer from the choices provided
A
B
C
D
Answer:
I believe the answer to be c 75°
Step-by-step explanation:
a 4 sided shape is 360 total degrees
Which of the following is a valid probability distribution? Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2. Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1. Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1. Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Considering the given probability distribution, distribution D is valid.
When a probability distribution is valid?A probability distribution is valid if:
There are no negative probabilities.,The sum of all probabilities is of 1.In this problem:
For distribution A, the sum is of 1.2, hence it is not valid.For distribution B, the sum is of 1.2, hence it is not valid.For distribution C, the sum is of 0.9, hence it is not valid.For distribution D, the sum is of 1, hence it is valid.More can be learned about probability distributions at https://brainly.com/question/23670007
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What is the measure of 2 if 1 is (4x - 4) and 2 is (4x)?
The measure of <2 is 92 degrees
How to solve for 2?The complete question is in the attached image
The angles are given as:
<1 = 4x - 4
<2 = 4x
The sum of angles on a straight line is
<1 + <2 = 180
So, we have:
4x - 4 + 4x = 180
Evaluate the like terms
8x = 184
Divide by 8
x = 23
Substitute x = 23 in <2 = 4x
<2 = 4 * 23
Evaluate
<2 = 92
Hence, the measure of <2 is 92 degrees
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John and 2 friends are going out for pizza for lunch. They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10. Write an equation to model this situation, and find the cost of one large drink.
Answer:
$2.55
Step-by-step explanation:
2d + $14.00 – $7.00 = $12.10; $2.55
Use the function below to find F(3).
)(
F(x)=(1/4)^x
Answer:
1/64
Step-by-step explanation:
F(3) means to use 3 in place of x in the given equation.
f(x) = (1/4)^x
f(3) = (1/4)^3
Either use exponents rules:
= 1^3 / 4^3
= 1 / 64
or just use the meaning of exponents
= 1/4 × 1/4 × 1/4
= 1/64
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.8 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Using the normal distribution, the probabilities are given as follows:
a) 0.6517 = 65.17%
b) 0.0823 = 8.23%.
c) 0.6109 = 61.09%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8.9, \sigma = 2.8[/tex]
Item a:
The probability is the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 8.9}{2.8}[/tex]
Z = 0.39
Z = 0.39 has a p-value of 0.6517.
0.6517 = 65.17% probability that the time is less than 10 minutes.
Item b:
The probability is the one subtracted by the p-value of Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.9}{2.8}[/tex]
Z = -1.39
Z = -1.39 has a p-value of 0.0823.
0.0823 = 8.23% probability that the time is more than 5 minutes.
Item c:
The probability is the p-value of Z when X = 15 subtracted by the p-value of Z when X = 8, hence:
X = 15:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 8.9}{2.8}[/tex]
Z = 2.18
Z = 2.18 has a p-value of 0.9854.
X = 8:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 8.9}{2.8}[/tex]
Z = -0.32
Z = -0.32 has a p-value of 0.3745.
0.9854 - 0.3745 = 0.6109 = 61.09%.
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Alexander Efland has a savings account that earns 5.5% interest compounded daily. On May 5, the amount in the account was $28,214.35. How much interest will the money earn in the next 90 days?
Using compound interest, it is found that $390.6 was earned in interest in the next 90 days.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.In this problem, the parameters are:
P = 28214.35, r = 0.055, n = 365, t = 3/12 = 0.25.
Hence the amount after 90 days is:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(90) = 28214.35\left(1 + \frac{0.055}{365}\right)^{365 \times 0.25}[/tex]
A(90) = $28,604.95
28604.95 - 28214.35 = $390.6 was earned in interest in the next 90 days.
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AB = 8x + 3, BC =2x + 7 and AC = 80 Find value of AB and BC
Answers:
1) The value of AB is: " 59 units."
2) The value of BC is: "21 units."
_______
3) The value of AB + BC ;
= 59 units + 21 units ;
= [the value of AC ] ;
= {" 80 units ".}.
_______
Step-by-step explanation:
Given the following—and based on the assumption that we are dealing with: "geometric lines"—and/or: "geometric line segments"—we are asked to:
"Find the value of: " AB and BC" .
{Given: " AB = (8x + 3) ; BC = (2x + 7) ; AC = 80 ".}.
----------------------------------------------------------------------------------------------=-
Note: The following "line graphs" are "Not Drawn to Scale."
| (8x + 3) | (2x + 7) |
|<--------------->|<------------------->|
<----·|----------------->|<------------------->| {Note: "Not drawn to scale."}.
A B C
<-----|----------------->|<------------------->|
A C
<-----|<--------------------------------------->|
<-----|----------------------------------------->|
A {"AC = 80 ".} C
<---|------------------------------------------>|
A {"AC = 80 ".}. C
| (8x + 3) ; + (2x + 7) = 80 ;
<-----|----------------->|<--------------------->I
A B C
So: We have to find the value of:
1) AB ; which is: (8x + 3) ; And:
2) BC ; which is: (2x + 7) .
To get these values; we need to find the value for "x".
So: (8x + 3) + (2x + 7) = 80 ;
➝ 8x + 3 + 2x + 7 = 80 ;
➝ Now, Let us combine the "like terms" on the "left-hand side" of the equation:
+8x + 2x + 3 + 7 ;
➝ to get: + 8x + 2x = + 10x ; and:
+3 + 7 = 10 ;
To get: "10x + 10" ;
Now, we can rewrite the equation:
{" 70 ÷ 10 = 7 ."}. " 10x + 10 = 80 ;
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To solve for "x" ; there are many ways:
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Method 1) We have: " 10x + 10 = 80 " ;
➝ Now, subtract "10" from each side of the question;
10x + 10 − 10 = 80 − 10 ;
to get: 10x = 70 ;
➝ Now, divide each side of the equation by: "10" ; to isolate "x" on one side of the equation; & to solve for "x" ;
10x /10 = 70 /10 ; to get: " x = 7 "
Method 2)
At the moment above in which we have:
" 10x = 70 " ; we know that "10x ÷ 10 = 1x" ; and then "70 ÷ 10 = 7 ".
{Note that any value; divided by "10" ; is equal to:
{"that value" moved Back by: "One" decimal space.}.
So: " 1x = 7 " ; ↔ " x = 7 ".
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Method 3) :
When we have: " 10x /10 = 70 /10 " ; we have " 1x " on the "left-hand side" of the equation; and: "{ 70 /10 }" = {" 70 ÷ 10 = 7 ."}.
Note that: {" 70 ÷ 10 = 7 "} ; can be determined in many ways;
For instance: {" 70 ÷ 10 = ? "} ;
➝ The zeros for Both the numerator and denominator "cancel out"—
and we have: " [tex]\frac{70}{10}[/tex] " ;
➝ Cancel out each of the two (2) "zeros" ; and we have: " [tex]\frac{7}{1} = 7.[/tex] "
➝ This is assuming that we figure out that: " [tex]\frac{10x}{10}=1x =x[/tex] ."
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Now; let's find the correct values for this Brainly Question:
1) AB = 8x + 3 ;
Substitute our calculated value for "x" ; and solve:
➝ AB = 8x + 3 ; ↔ 8(7) + 3 = 56 + 3 = 59 .
➝ BC = 2x + 7 ; ↔ 2(7) + 7 = 14 + 7 = 21 .
Note:
➝ AC = 80 = AB + BC ≟ 59 + 21 ≟ 80 ? Yes!
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Answers:
1) The value of AB is: " 59 units."
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2) The value of BC is: "21 units."
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3) The value of AB + BC ;
= 59 units + 21 units = {The value of AC } = "80 units".}.
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Hope this answer—along with explanations—is helpful to you.
Best wishes in your academic pursuits!
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In which quadrants do solutions for the inequality y≤x-4 exist?
OI, III, and IV
OI, II, and III
OI and IV
All four quadrants
Answer:
(a) I, III, and IV
Step-by-step explanation:
We want to identify areas on a graph where the solutions to an inequality might be found.
Boundary lineThe boundary line for the inequality y ≤ 2/3x -4 has a positive slope and a negative y-intercept. That means it must pass through quadrants I, III, and IV.
Solution setQuadrant II is above the line, but the y ≤ () inequality tells you the shading is below the line, where y-values are less than those on the line. There can be no solutions in quadrant II.
Solutions are found in quadrants I, III, and IV.
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For reference, the second attachments shows the quadrant numbering.