Answer:
x = - 2 or x = - 4
Step-by-step explanation:
Via completing the square:
x^2 + 6x + 8 = x^2 + 6x + (6/2)^2 - (6/2)^2 + 8
= (x + 3)^2 - 3^2 + 8
= (x + 3)^2 - 9 + 8
= (x + 3)^2 - 1
Since x^2+6x+8=0,
(x + 3)^2 - 1 = 0
(x + 3)^2 = 1
x + 3 = +- sqrt(1)
x + 3 = +- 1
x + 3 = 1 or x + 3 = -1
x = -2 or x = -4
Barrett earns $15 per hour cutting grass and $10 per hour tutoring reading. In one month, Barrett
needs to save at least $400 for a new lawnmower but does not want to work more than 35 hours.
Part A: Let x represent the hours cutting grass and y represent the hours tutoring. Given x ≥ 0 and
y ≥ 0, select all the inequalities that represent the situation.
A. x + y ≥ 35
B. 15x + 10y ≤ 400
C. x + y ≤ 35
D. 15x + 10y ≥ 400
E. 25x + 25y ≤ 400
F. 15x + 10y ≤ 35
Part B: Determine whether each point is a viable or nonviable solution according to the above scenario.
Viable Nonviable
(10, 25)
(10, 20)
(20, 12)
(35, 0)
(20, 20)
The inequalities that represent the situation are 15x + 10y ≥ 400 and x + y ≤ 35 and the viable solutions are (10, 25), (20, 12), (35, 0) and (20, 20)
The inequalities that represent the situation.From the question, we have the following parameters that can be used in our computation:
Earnings from cutting = $15Earning from tutoring = $10Number of hours = not more than 35Total earnings = At least $400These parameters above mean that
15x + 10y = Total earnings
x + y = Number of hours
So, we have
15x + 10y ≥ 400
x + y ≤ 35
The above represent the inequalities of the situation
The viable solutionsIn (a), we have
15x + 10y ≥ 400
x + y ≤ 35
Next, we test the options
(10, 25)
15 * 10 + 10 * 25 ≥ 400 ⇒ 400 ≥ 400
10 + 25 ≤ 35 ⇒ 35 ≤ 35
True
(10, 20)
15 * 10 + 10 * 20 ≥ 400 ⇒ 350 ≥ 400
10 + 20 ≤ 35 ⇒ 30 ≤ 35
False
(20, 12)
15 * 20 + 10 * 12 ≥ 400 ⇒ 420 ≥ 400
20 + 12 ≤ 35 ⇒ 32 ≤ 35
True
(35, 0)
15 * 35 + 10 * 0 ≥ 400 ⇒ 525 ≥ 400
35 + 0 ≤ 35 ⇒ 35 ≤ 35
True
(20, 20)
15 * 20 + 10 * 20 ≥ 400 ⇒ 500 ≥ 400
20 + 20 ≤ 35 ⇒ 40 ≤ 35
False
Hence, the viable solutions are (10, 25), (20, 12), (35, 0) and (20, 20)
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What is the value of k in the quadratic polynomial 3x2 2kx 3 if X − 12 is one of the zeroes of it?
The values of k are 3, – 3 for which roots of the quadratic equation are real and equal.
What is a quadratic equation?
An equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.
Given: 3x² + 2kx + 3 = 0
Comparing with standard quadratic equation ax² + bx + c = 0
a = 3 b = 2k c = 3
Given that the roots of the equation are real and equal
Thus, D = 0
Discriminant D = b² – 4ac = 0
(2k)² – 4.3.3 = 0
4k² – 36 = 0
4k² = 36
k² = 9 taking square root on both sides
k = 3 or k = – 3
Hence, The values of k are 3, – 3 for which roots of the quadratic equation are real and equal.
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What role does place value have in finding 10% and 1% of a number? Write at least two complete sentences.
The fractions of the numbers are found as follows:
10% of a number is found moving the decimal digit one unit right.1% of a number is found moving the decimal digit two units right.How to divide a number by powers of 10?To divide a number by the nth power of 10, the decimal digit in the number is moved n units to the right.
The fraction that represents 10% of a number is given as follows:
10/100 = 1/10.
Meaning that the number is divided by 10, which is the first power of 10, and thus the decimal digit is moved one unit right in the number.
The fraction that represents 1% of a number is given as follows:
1/100.
Meaning that the number is divided by 100, which is the second power of 10, and thus the decimal digit is moved two units right in the number.
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If Point B represents an alternate combination of flutternutters & blank books, then how much of each product could be produced?
From the given graph, at Point B a total of 8000 fluffernutters & 500 blank books could be produced.
The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this context, a graph is made up of vertices connected by edges.
In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.
Straight line graphs called linear graphs are used to show the relationship between two quantities. This graph makes it easier to show a result as a collection of straight lines. The term "linear" simply means a straight line; curves, dots, bars, etc. are not used.
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Chapter 3 Lesson 4 Arithmetic Sequence
Answer:
Step-by-step explanation:
1) 1,15,29,43,57,.....
here, 15-1 =14 and 29-15=14
therefore,it is an arithmetic sequence with common difference = 14
2) 3,6,9,15,17,....
here, 6-3=3, 9-6=3 , 15-9=6
therefore,it is not an arithmetic sequence.
3) 93,86,79,72,65,......
here, 86-93=-7 , 79-86=-7 and 72-79=-7
therefore,it is an arithmetic sequence with common difference = -7
4) 37,34,31,29,26,......
here, 34-37 = -3,31 - 34 = -3,29 - 31 =-2
therefore,it is not an arithmetic sequence.
96 - y = 161 solve for y
Answer: -65
Step-by-step explanation:
96 - y = 161
-y = 161 - 96
-y = 65
y = -65
How is the logarithmic function y log x defined?
The logarithmic function y log x is defined as
[tex]$\log_b \text x = \text y \leftrightarrow \text b^y= \text x[/tex].
What is logarithmic function?An exponent that is expressed in a unique way is called a logarithm. As an illustration, we are confident that the exponential formula 32 = 9 is correct. In this instance, the base is 3, and the exponent is 2. The formula will be written as log3 9 = 2 in the logarithmic form.
This is expressed as "9 divided by base 3 is 2" in words. The exponent has been effectively lowered to the mainline in this case. However, despite the fact that this was done to make division and multiplication easier, logarithms are still very useful in mathematics.
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I thought of a number, doubled it, then added 3. The result multiplied by 4 came to 52. What was the number I thought of?
The number you thought of is -1.
To solve this problem, you can use algebra to represent the unknown number as a variable (let's call it x) and the given information as equations. The first step is to determine what the problem is asking for. In this case, it is asking to find the original number before it was doubled and 3 was added. To do this, you can use the information given in the problem to set up equations.
The first equation is (2x+3)*4 = 52. You can then solve this equation for x. First, you can simplify the left side of the equation by distributing the 4 to the 2x and the 3: 4x + 12 = 52. Then, you can subtract 12 from both sides to get 4x = 40. Finally, you can divide both sides by 4 to get x = 10. however, this is not the solution, since the problem does have not a unique solution. x=-1 is also the solution.
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T h e r e a r e 235 seven t h - g r a d e st u d e n t s g o i n g o n a fi e l d t r i p . T h e sc h o o l h a s 5 b u se s t o t a k e t h e st u d e n t s. E a c h b u s h a s 22 se a t s, a n d 2 st u d e n t s c a n si t i n e a c h se a t . B a se d o n t h i s i n f o r m a t i o n , h o w m a n y st u d e n t s w i l l n o t b e a b l e t o r i d e o n a b u s f o r t h e fi e l d t r i p ?
The number of students who will not be able to ride on the bus for the school trip is given by the equation A = 15 students
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The total number of students for the trip = 235 students
The number of buses = 5 buses
The number of students in a bus be = B
Now , each seat on the bus can occupy = 2 students
So , 22 seats can occupy = 22 x 2 students
22 seats in the bus can occupy = 44 students
So , the number of students in a bus B = 44 students
And , the total number of students in 5 buses = 5 x number of students in a bus B
Substituting the values in the equation , we get
The total number of students in 5 buses = 5 x 44
The total number of students in 5 buses = 220 students
So , the remaining number of students A = total number of students for the trip - total number of students in 5 buses
Substituting the values in the equation , we get
The remaining number of students A = 235 - 220
The remaining number of students A = 15 students
Therefore , the value of A is 15 students
Hence , the number of students is 15 students
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at the same time that a 60 foot tall buidling casts s shadow hat is 21.5 feet long a nearby tree casts a shadow that is 18 feet long, Which measure is closest to the height of the tree
The height of the tree is closest to 40 feet.
We can use the proportion of similar triangles to determine the height of the tree.
Let h be the height of the tree and s be the length of the shadow cast by the tree.
We know that the height of the building is 60 feet and the length of its shadow is 21.5 feet. So:
(h/s) = (60/21.5)
We also know that the length of the shadow cast by the tree is 18 feet.
So we can substitute that into the proportion and solve for h:
h = (60/21.5) * 18
h = (60*18)/21.5
h ≈ 40
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If A=(7,9) and B=(3,12) what is the length of AB
The distance between two points A and B is 5 units.
There were 9 pieces of paper. Some of them were cut into 3 pieces. As a result, there
are now 15 pieces of paper. How many pieces of paper were cut?
6=3
6÷3
2 is the required answer for this question
In an amphitheater, eat are aranged in 50 emi-circular rowfacing a dome tate. The firt row contain 23 eat, and each row contain4more eat than the previou row. How many eat are in the amphitheater?
In an amphitheater, seat are arranged in 50 semi-circular row-facing a dome Tate. The first row contain 23 seat, and each row contain 4 more eat than the previous row. Therefore, there are 6050 seat are in the amphitheater.
Given that:
There are total 50 semi circular row.
In the first row there are 23 seats.
The given problem is AP series:
Arithmetic Series:
An arithmetic sequence is defined as an algebraic sequence in which each successive term has an equal difference. It is obtained by adding a constant to any preceding term. For the first term 'a' and the tolerance 'd' of the AP, here is a list of commonly used arithmetic progressions to solve various AP related problems:
Common Difference of AP: d = a2 - a1 = a3 - a2 = a4 - a3 = an - a(n-1) nth term of AP.AP: an = a + (n - 1)d of AP Sum of n terms: Sn = n/ 2( 2a+(n-1)d) = n/2(a + l),where l is the last term in the arithmetic progression.
Now,
Sum of n terms = n/2 [ 2a + (n-1)d]
= 50/2 [ 2× 23 + (50 -1)4]
= 25 [46 + 49×4]
= 25 × 242
= 6050
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Which of these equations is equivalent to the following: 8/12 divided by 7/8=
Plsssss help me
Answer: o.7619
Step-by-step explanation: i used the standard algorithm i am sorry i cant do a more in depth just hard to do with words ;)
Answer: 0.7619
:)
Step-by-step explanation:
9. A triangle with a height of 12 inches has an area of 36 square inches. How long is the base of the triangle?
If anyone knows this please tell me this is due tommorow!
Answer:
Step-by-step explanation
The triangle base would be 6
Write a multiplication expression using the following clues one factor is a two digit number between one and ten one factor is a two digit number between 1 and 10 but different from the first the product is greater than 8 but less than 10
first expression = 1×2, 1×1, 1×3, 1×4, 1×5, 1×6, 1×7, 1×8, 1×9, 2×2, 2×3, 2×4, 3×2, 3×3, 4×2 and second expression = 1×9
what is expression?In mathematics, an expression is a statement that represent the method of mathematical operation in a symbolic form. An expression is developed based on numerical terms or both numerical and variable terms along with operator or signs.
What is the multiplication expression stated in the question?it is stated that one factor is a two-digit number between one and ten.
the multiplication expression can be 1×2 , 1×1, 1×3, 1×4, 1×5, 1×6, 1×7, 1×8, 1×9, 2×2, 2×3, 2×4, 3×2, 3×3, 4×2
In the next, the multiplication expression for 2nd statement:
one factor is a two-digit number between one and ten and their product is greater than 8 and less than 10
1×9
the above is greater than 8 and less than 10.
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Jay wants to go paddleboarding at least 8 hours each week. If he averages 2 hours per day, write and solve an inequality to find how many days he will have to go kayaking.
An inequality to find how many days he will have to go kayaking. is; d ≥ 4
How to solve Inequality word problems?We are told that Jay wants to go paddle boarding at least 8 hours each week. This means greater than or equal to 8. That is the minimum number of hours each week is 8 hours.
Now, we are told that he averages 2 hours per day. If the number of days is given by d, then we have the inequality as;
2d ≥ 8
Divide both sides by 2 to get;
d ≥ 4
That is the domain of the number of days required to go kayaking
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Consider y =f(x)=-3x+2 . Using space below, determine the equation that represents the inverse f(x)
Answer: [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}[/tex]
Explanation:
Swap x and y, then solve for y to get the inverse.
[tex]f(\text{x}) = -3\text{x}+2\\\\\text{y} = -3\text{x}+2\\\\\text{x} = -3\text{y}+2\\\\\text{x}-2 = -3\text{y}\\\\\text{y} = \frac{\text{x}-2}{-3}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
What is the solution to the system of equations 3x 2y 7 and Y 3x 11?
The solution to the system of equations is x = 4 and y = 5.
3x + 2y = 7
y = 3x - 11
Substitute 3x - 11 for y in the first equation:
3x + 2(3x - 11) = 7
Simplify:
3x + 6x - 22 = 7
Combine like terms:
9x - 22 = 7
Add 22 to both sides:
9x = 29
Divide both sides by 9:
x = 29/9
x = 4
Change x in the second equation to 4:
y = 3(4) - 11
Simplify:
y = 12 - 11
y = 1
The solution to the system of equations is x = 4 and y = 1.
The solution to the system of equations 3x + 2y = 7 and y = 3x - 11 is x = 4 and y = 1. To solve this system, we first substituted 3x - 11 for y in the first equation. We then simplified the equation and combined like terms to get 9x - 22 = 7. We then added 22 to both sides, divided both sides by 9, and got x = 29/9 which is x = 4. We then substituted 4 for x in the second equation, simplified, and got y = 1. Thus, the solution to the system of equations is x = 4 and y = 1.
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Before taking his last test in a class, the arithmetic mean of Brian's test scores is 91. He has determined that if he scores 98 on his last test, the arithmetic mean of all his test scores will be exactly 92. How many tests, including the last test, does Brian take for this class
On solving the provided question, we can say that the mean that 6 tests including the last test brian took.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.
(91n + 98) / (n + 1) = 92
91n + 98 = 92(n + 1)
91n + 98 = 92n + 92
98 = n + 92
6 = n
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Find the total surface area of a cone with a base diameter of 7cm and height of 8cm
Answer: The formula for the surface area of a cone is S = π * r * s + π * r², where r is the radius of the base and s is the slant height of the cone.
To find the surface area of a cone, you first need to find the radius of the base. Since the base diameter is given as 7cm, you can divide this by 2 to find the radius of the base:
r = 7cm / 2 = 3.5cm
Next, you need to find the slant height of the cone. You can use the Pythagorean theorem to do this.
slant height = sqrt(r^2 + h^2) = sqrt(3.5² + 8²) = sqrt(12.25 + 64) = sqrt(76.25) = 8.766cm
Now you can substitute these values into the formula for the surface area of a cone and find the surface area of the cone.
S = π * r * s + π * r² = π * 3.5cm * 8.766cm + π * 3.5² cm² = 12.571 cm² + 38.485 cm² = 51.056 cm²
So the surface area of a cone with a base diameter of 7cm and height of 8cm is 51.056 cm²
Step-by-step explanation:
Could someone help me
[tex]\cfrac{6a^2 + 21a}{3a^2}\implies \cfrac{6a^2 }{3a^2}+\cfrac{21a}{3a^2}\implies 2+\cfrac{7}{a}[/tex]
A farmer took 2/3 of the trawberrie that he harveted to a market. At the the market, the farmer old 1/4 of the trawberrie. How can you find what part of the trawberrie the farmer harveted were old at the market?
There are 5/12 strawberries were left. This can be solved using the concept of fraction addition.
What is fraction?A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.
Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.
Given that,
A farmer took 2/3 of the strawberry that he harvested to a market.
At the market, the farmer sold 1/4th of the strawberry.
Now, the farmer has left no of strawberries were:
= (2/3) - (1/4)
= (8 - 3) / 12
= 5 / 12
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Don’t know need help
The meaning of adjoining is nearby or next to.
What is meant by adjoining?The terms neighboring, adjoining, contiguous, and juxtaposed denote close closeness. Adjacent may or may not indicate touch, but it always implies the lack of something like in between. A home with a garage attached. Adjoining means meeting and touching at some point or line. Two nearby dwellings are an example of adjacent. People on our block are typically considered our neighbors.
In the English language, “adjacent to” means “next to.” For two angles to be adjacent, they must meet the following three conditions: 1. The two angles must share (or have the same) side. 2. They must share a vertex (i.e. a common starting point for the sides).
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PS is the length of either segment multiplied by two ,PS is 38.
How to find PS?A line connecting the vertex with the middle of the other side forms the median angle. As a result, we may state that PR = QS for the provided.
By equating PR and QS, we can determine X's value.
PR = QS
5x-11 = 2x+7
Combine related terms to get 5x-2x = 7+11; divide both sides by 3 to get the x value; and last, multiply the result by 2 to get x = 6.
Find the value of PR and QS, and we'll demonstrate that two are equal as a result.
Correct: 5(6)-11 = 2(6)+7 19 = 19.
PS is the length of either segment multiplied by two, or simply the product of PR and QS.
PS = 19 x 2 = 19 + 19 = 38 (D) (D)
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Unit 1 geometry basics Homework 2
pls help! i’ll mark brainliest
The value of AB= 24 BD is congruent to BC. BD=BC
BD = 5x – 26, BC = 2x + 1, and AC = 43
How to find value of AB?From the diagram , AC=AB+BCTo find out , we need to find BC first . For that we have to find out xWE know that BD=BC, using that we solve for x5X-26=2X+1SUBSTRACT 2X3X-26=1ADD 263x=27x=9Now we plug in 9 for x and find out BCBC=2x+1BC=2(9)+1BC=19We know AC= 43AC=AB+BC43=AB+19subtract 19AB=24To learn more about find value of AB refers to:
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Convert 1.45454... into a ratio of two integers. Enter your answer as a fraction in lowest terms.
Answer:
16/11
Step-by-step explanation:
Let x = 1.45454...
Multiply both sides by 100:
100x = 145.454...
Subtract both sides by x:
100x - x = 145.454... - x
100x - x = 145.454... - 1.45454...
99x = 144
x = 144/99
The term can be simplified in lowest as 16/11. Hence, 1.45454... can be written as the ratio of two integers of 16/11
A line has a slope of – 1/7 and passes through the point (4,5). What is its equation in point-slope form?
Answer:
y-5=-1/7(x-4)
Step-by-step explanation:
The equation of the line in point-slope form is y-5=-1/7(x-4)
Answer:
y = -1/7 x + 39/7
Step-by-step explanation:
An equation in point slope form is
y = mx+b where m is the slope and b is the y intercept
We are given the slope
y = -1/7 x + b
Substitute in the point for x and y and solve for b
5 = -1/7(4) +b
5 = -4/7 +b
5 + 4/7 = b
5*7/7 + 4/7 = b
35/7 + 4/7 = b
39/7 = b
The equation is
y = -1/7 x + 39/7
what is -7 divided by 3/4 ?
Answer:
-9.333333333333333333333
Step-by-step explanation:
Answer-9 1/3
Step-by-step example
first, multiply 7x4 over 3 then next to that cross multiply that with 28 over 3
then simply that which’s gets to 28 over 3 then you get your answer 9.3333 then simplify that and you get 9 1/3
please help quickly
If UY=13p-1 and VX=20p-95 than what is UY
Viewing the given triangle, the information given helped to determine side UY to be 90
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
WX and WY, XV and YU
The solution is worked out using sides WX and XV, WY and YU
WX / WY = XV / YU
WX / WY = 1/2 since it is a mid segment
1 / 2 = (20p - 95) / (13p - 1)
13p - 1 = 2 * (20p - 95)
13p - 1 = 40p - 190
190 - 1 = 40p - 13p
189 = 27p
p = 7
solving for UY
= 13p - 1
= 13 * 7 - 1
= 90
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1. Marta walked 6 miles in 1.5 hours. At this rate how long will it take her to walk 16 miles?
2. Lionel typed 320 words in 4 minutes. At this rate, how long will it take him to type 800 words?
Answer for no.2: 800
Step-by-step explanation: