An analogous equation can be created by factoring a quadratic equation. 5x^2 = (x-2) * (x+2) + 488 can give integers 9, 11,13.
What is a quadratic equation?In algebra, quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as
[tex]{ax^{2}+bx+c=0}[/tex]
where a 0 and x denotes an unknown and a, b, and c denote known numbers, Since there is no ax2 term, the equation is linear (and not quadratic) if a = 0 (and b 0). The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient, linear coefficient, and constant or free term, respectively.
The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation. There can only be two solutions to a quadratic problem. One claims that a problem is a double root if there is just one solution. There are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or two real solutions if all the coefficients are real values. If complex roots are included, a quadratic equation will always have two roots; a double root counts as two. An analogous equation can be created by factoring a quadratic equation.
According to the formula, if 5x2 = x2 - 4 + 488, then 5x2 = x2 + 484.
For 4x2 = 484, subtract x2 from each side, resulting in x2 = 121.
For x = 11, square root each side.
TEST: 5*121 = 9*13 + 488, so 605 is equal to 117 plus 488.
The middle odd number, x, is equal to 11.
The figures are 9, 11, and 13.
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Isabelle's family raises honey bees and sells the honey at the farmers' market. To get ready for market day, Isabelle fills 24 equal sized jars with honey. She brings a total of 16 cups of honey to sell at the farmers' market. Use an equation to find the amount of honey each jar holds. To write a fraction, use a slash ( / ) to separate the numerator and denominator. cups
Answer:
2/3
Step-by-step explanation:
The amount of honey each jar holds is 2/3 cups.
Fraction
The fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 5/8 is a fraction where the upper part denotes the numerator and the lower part is the denominator.
Given that:-
Number of equal sized jars filled by Isabelle = 24 jars
Total amount of honey brought by Isabelle to the sell at the farmer's market = 16 cups
We have to find the amount of honey each jar holds.
From the data given in the question, we can write,
24 jars = 16 cups
Hence, using the equation, we can write the fraction,
1 jar = (16/24) cups
1 jar = 2/3 cups
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Add 0.74 and 0.19! How many tenths are in the sum?
Answer: 0.93
There are 9 tenths
Step-by-step explanation:
What is the length of segment BC? (4 points) A coordinate plane is shown. Point B is located at negative 3, negative 2, and point C is located at 0, 2. The points are connected by a line segment. a 4 b 5 c 6 d 7
By means of vector sum and Pythagorean theorem, the line segment BC has a length of 5 units.
What is the length of the line segment?
We find a line segment whose endpoints are known and set on Cartesian plane, the length of the line segment must be found by means of vector sum and Pythagorean theorem. First, determine the vector associated to the line segment:
[tex]\overrightarrow {BC}[/tex] = C(x, y) - B(x, y) = (0, 2) - (- 3, - 2) = (3, 4)
Second, determine the magnitude of the vector derived in the previous step:
BC = √(3² + 4²)
BC = 5
The length of the line segment BC is equal to 5 units.
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PLEASE HELP MATH QUESTION
Answer:
Proved below.
Step-by-step explanation:
Parallel lines and angles:
Given: p // q and ∠1≅ ∠2
Proof:
p //q, l is transversal,
∠3 ≅ ∠1 -----(I) {Corresponding angles are congruent}
∠1 ≅ ∠2 ---------(II) {Given}
From (II) & (I),
∠3 ≅ ∠2
∠3 and ∠2 are alternate interior angles. Alternate interior angles are congruent only if the lines are parallel.
⇒ l // m
PLEASE I NEED HELPNSMKSJSBW
Check the picture below.
[tex]\stackrel{\measuredangle U}{(3x-4)}~~ + ~~\stackrel{\measuredangle V}{(x+20)}~~ + ~~\stackrel{\measuredangle W}{(6x+6)}~~ = ~~180 \\\\\\ 10x+22=180\implies 10x=158\implies x=\cfrac{158}{10}\implies {\Large \begin{array}{llll} x=\cfrac{79}{5} \end{array}}[/tex]
A scientist is experimenting on a newly discovered virus. The ideal
temperature for this new virus to thrive is 20°C. The temperature can
vary by 15°C and the virus can still survive.
Write an absolute value linear inequality that represents the
acceptable temperatures for this virus to survive. Use t as your
variable.
The required absolute value linear inequality is 15 ≤ t ≤ 20.
What is absolute value linear inequality?
A variable enclosed by the absolute value sign of an inequality is known as an absolute value inequality.
Given highest temperature as 20°C and lowest temperature as 15°C
Given variable is t.
From the first condition we get t ≤ 20 ...........(1)
From the second condition we get 15 ≤ t .....(2)
From the inequalities (1) and (2), we get
15 ≤ t ≤ 20
Therefore, the required absolute value linear inequality is 15 ≤ t ≤ 20.
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the angle of elevation to a nearby tree from a point on the ground is measured to be 45 degrees. How tall is the tree if the point on the ground is 79 feet from the tree? Round your answer to the nearest hundredth of a foot
The tree is 79 feet tall if the ground is 79 feet from the tree and the angle of elevation is 45°.
Angle of elevation:
The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
Therefore, the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
Given,
The angle of elevation to a nearby tree from a point on the ground is measured to be 45 degrees.
Here we need to find how tall is the tree if the point on the ground is 79 feet from the tree and we have also need to round the answer to the nearest hundredth of a foot.
Here we know that
The angle of elevation = 45°
Distance of the point from the tree = 79 feet
Suppose h is the height of the tree.
Then the value of h is calculated as,
=> h / 79 = tan 45°
We know that, the value of tan 45° = 1,
So,
=> h/79 = 1
Then the value of h is,
=> h = 79
Thus, the height of the tree is 79 feet.
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What amount of pure acid must be added to 600 mL of a 50% acid solution to produce a 60% acid solution?
That indicates that in order to make a solution that is 60% acid, you will need to add a total of 300 milliliters of pure acid into the mixture.
This is further explained below.
What amount of pure acid must be added?In general, pure acid refers to an acid concentration of 100%. It is feasible to formulate the following equation if you assume that X represents the volume addition of the pure acid:
[tex]Va=100 \%X + 600 * 40 \%[/tex]
[tex]Va= (600+X)60 \% (M_1V_1=M_1 V_2)[/tex]
100X + 24000 = 36000 + 60x
X = 300.
In conclusion, That implies in order to generate a solution that is 60% acid, you will need to add 300 milliliters of pure acid.
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The points A, B and C are 3 corners of a rectangle. What are the coordinates of D, the 4th corner?
PLEASE HELP URGENTLY WILL MSRK BRAINLIEST! :D
Answer:
(5,7)
Step-by-step explanation:
Answer:
(5,7)
Step-by-step explanation:
Abscissa of D will be the abscissa of A. A(5,9)
Abscissa of D = 5
Ordinate of D will the ordinate of C. C(8,7).
Ordinate of D = 7
So, D(5,7)
distance in space is often written using a lightyear. A lightyear is the distance light travels in one year. It is equal to 6,000,000,000,000 miles. Write this measurement in scientific notation. PLS HELP ME ASAP!!!!!!!!!!!!!!!!!!!!!!!! >_
Answer:
Step-by-step explanation:
C
Leah has an account balance of -150 dollars. Which of the following represents a debt greater than -150 dollars? - 175 dollars - 150 dollars -125 dollars 0 dollars
Owing 175 dollars is more than owing 150 dollars.
Thereby, the correct answer is A) -175 dollars
need help y’all pls ♀️
In this Triangle, ΔUVW, UW is extended through point w to point x
∠ WUV = (3x - 4)°
∠ VWX = (6x + 6)°
∠ UVW = (x + 20)°,
the value of x is 5
According to the question, given that
∠ WUV = (3x - 4)°
∠ VWX = (6x + 6)°
∠ UVW = (x + 20)°
because ∠ VWX = ∠ WUV + ∠ UVW
⇒ (6x + 6) = (3x - 4) + (x + 20)
⇒ (6x + 6) = 4x + 16
⇒ 2x = 10
⇒ x = 5
{The sum of triangle's interior angles is 100°}
{The sum of supplementary angles is 180°}
Therefore, In ΔUVW, UW is extended through point w to point x, then the value of x is 5.
The interior angles of a triangle always add up to 180° while the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.
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Which statements would prove the lines are parallel?
The statements that would prove the lines are parallel are;
∠GHI ≅ ∠KJH
∠MJH + ∠NHJ = 180°
∠KJH + ∠IHJ = 180°
How to Identify Congruent Angles?
In congruency of angles formed in this type of scenario, we will make use of the following rules;
If two parallel lines are cut by a transversal, then, Alternate Interior Angles are congruent. If two parallel lines are cut by a transversal, then, Alternate Exterior Angles are congruent. If two parallel lines are cut by a transversal, then corresponding angles are congruent.Using the above congruency rules and applying them to our question, we can say that for lines HN and KM to be parallel to each other, then;
∠GHI ≅ ∠KJH because they are corresponding angles
∠MJH + ∠NHJ = 180° because they are supplementary angles
∠KJH + ∠IHJ = 180° because they are supplementary angles
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Which of the following statements must be true based on the diagram below? Select all that apply. (Diagram is not to scale.)
A. LN is a segment bisector
B. LN is an angle bisector
C. L is the vertex of a pair of congruent angles in the diagram
D. N is the vertex of a pair of congruent angles in the diagram
E. L is the vertex of a right angle
F. N is the vertex of a right angle
Answer: A
Step-by-step explanation:
A. True by the definition of a bisector.
B. False, this is an assumption based on appearances.
C. False, this is an assumption based on B.
D. False, this is an assumption that LN and JK are perpendicular.
E. False, assumption based on appeareances
F. False, assumption based on D.
Sarita bought eggs at rupees 8.40 at what price per 100must she sell them so as to earn a profit of 15 percent
Answer:
Cost per egg = 8.4/12 = 0.7
Cost per hundred egg =Rs70
Let selecting price per hundred be Rs.y
⇒ 70/y-70 ×100 = 15
⇒ 10y−700 = 105
⇒ y = 80.5RsThe function f(x) = 4x-6 is shown in the table below. Identify the domain and range of function f. Enter the numbers in order from least to greatest.
-5 -2 1
y -26 -14 -2
X
-26
domain:
range:
-14 -5
5
-14
-2
1 5
The domain and range of the function f(x) = 4x - 6 in order from least to greatest include the following:
Domain: -2, -6, 1, 5.Range: -26, -14, -2.What is a range?A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
In order from least to greatest, the range and domain of the given function f(x) = 4x - 6 are as follows:
Range: -26, -14, -2.Domain: -2, -6, 1, 5.Read more on range here: brainly.com/question/17295757
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Estimate the area covered by the drum picture. Pls help thanks
Answer:
Step-by-step explanation:
Area = L times w ( length times width.)
Your lengthyot Length is 4 units and width is 4. so what is 4 times 4?
your right, its 16. Answer A is correct.
You bring 1.5 dozen bagels to school.
A dozen bagels cost $5.98.
You used a coupon that took $1.00 off the total.
How much did you pay for the bagels?
Answer: You would pay $7.97 for the bagels.
Step-by-step explanation:
(Price per Dozen * Amount) - Coupon = Price of Bagels
(5.98 * 1.5) - 1 = Price of Bagels
8.97 - 1 = Price of Bagels
Price of Bagels = $7.97
Estimate 0.049127568 to the nearest hundredth. Express your answer as a single digit times a power of ten.
Please I need help
Casilde and Oziel walk from a restaurant in the same direction. If Casilde has walked five-eighths of a mile and Oziel has walked seven-tenths of a mile, how far apart are they?
For the first 4 home football games, the
concession stand sold 600 hotdogs. If
that ratio stays constant, how many
hotdogs will sell for all 10 home games?
Answer:
1500
Step-by-step explanation:
600 divided by 4 to see how much hotdogs are sold EACH home football game. This gives you 150 each game so you multiple it by ten in order to get the total for ten home games
24 in the ratio 1:2:3
Answer:
4:8:12
Step-by-step explanation:
To find the ratio of 24 in 1:2:3,
first add the ratios = 6 then divide each ratio as a fraction of the total
[tex] \frac{1}{6} \times 24 \\ = 4[/tex][tex] \frac{2}{6} \times 24 \\ = 8[/tex][tex] \frac{3}{6} \times 24 \\ = 12[/tex]Therefore, 24 in ratio 1:2:3 is 4:8:12
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify. The product of 7 and the square of a number.
Answer:
[tex]7 * x^2[/tex]
What is the graph if the function rule y = x+2 ?
Answer: This is the graph
help !!!!!!!!!!! please
Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).
As given,
Given measures of the triangle ABC are
Angle A=(18 +18)°
=36°
Consider side opposite to ∠A=a ,∠B=b ,∠C=c
Given side length
AC=b
=20
AB=c
=12
BC=c
=x+12
Using cosine law
cos A= (b²+c²-a²)/2bc
⇒cos36°= [20²+12²-(x+12)²]/2(20)(12)
⇒(1+√5)/4=(544-x²-24x-144)/480
⇒x²+24x-280+120√5=0
⇒x²+24x-11.7=0
Now, x = [-24±√24²-4(1)(-11.7)]/2(1)
= (-24±24.955)/2
≈ (-24 ±25)/2
Hence, x = (-24+25) /2
= 1/2
or x = -24.5 side length cannot be negative.
Therefore, Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).
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How many extra flowers did they order?
Answer:
B
Step-by-step explanation:
To find the number of extra flowers ordered, we can start by forming an equation based on the total amount paid by the customer.
Let the number of extra flowers be n.
Total paid
= cost of standard arrangement +(number of extra flowers)(cost per additional flower)
= $25 +n($1.25)
Given that the customer paid $45,
25 +1.25n= 45
Now that we have formed the equation, let's solve for n.
Subtract both sides by 25:
1.25n= 45 -25
1.25n= 20
Divide both sides by 1.25:
n= 20 ÷1.25
n= 16
You bike 14 1/4
miles from your house to a state park. You travel 1/3
of that
distance in the woods. You bike along the bank of a stream for the last 1/2
of
the woods. On how many miles of your trip do you bike along the bank of
the stream?
By taking some products between fractions and mixed numbers, we will see that your trip along the bank has a length of (2 and 9/24) miles.
How many miles do you travel along the bank of the stream?Here we know that the total distance of the travel is (14 + 1/4) miles.
In this case, we know that 1/3 of that distance is traveled in the woods, so the total distance traveled in the woods is given by the product:
D = (1/3)* (14 + 1/4) mi = (14/3 + 1/12) mi
Now we know that 1/2 of the distance traveled in the woods is traveled along the bank of a strem, then the distance that we are looking for is given by the product:
D' = (1/2)*(14/3 + 1/12) mi = (7/3 + 1/24)mi
Now we can simplify that mixed number as:
(7/3 + 1/24)mi = (6/3 + 1/3 + 1/24) mi = (2 + 8/24 + 1/24)mi = (2 + 9/24) mi
Your trip along the bank of the stream has a length of (2 + 9/24) miles.
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Tell whether x and y are proportional x: 4,6,12,16 y: 6,8,16,20
Check the picture below.
Which graph Represents a function
The first graph from the right as shown in the reference image attached hereby alongside the question statement, represents a function.
As per the question statement, we are provided with 4 distinct graphs attached hereby alongside.
We are required to determine, which of the above-mentioned graphs represent a function.
To solve this question, we need to know about the characteristics of a function, which we can match against our provided graphs and identify our required function.
A function is an operator, and hence, there will be a fixed pattern or sequence among it's outputs, which we can only find in the first graph from the right as shown in the reference image, since it is a straight line parallel to the Y-axis at (x = 1).
Therefore, the first graph from the right as shown in the reference image attached hereby alongside the question statement, represents a function.
Function: In Mathematics, a function is an operator, which when provided with a certain input, performs a pre-determined set of operations on the input and then produces a fixed output.To learn more about Functions, click on the link below.
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In the diagram below, the man on the diving board is 6 ft. tall and the angle of elevation from the man in the water (angle 4) to the man on the diving board is 40. How far apart are the two men? Round your answer to the nearest tenth.
A picture of a swimming pool with a lifeguard sitting on an elevated chair on the right side of the pool. There is a person on a diving board on the left side of the pool who is lower than the lifeguard. The lifeguard is looking down at the person on the diving board and there is a solid line showing his line of sight. A dotted line is drawn from the lifeguard’s eyes horizontally. The angle between these two lines is labeled 1.
The distance between the two men is 7.2 ft. That is, they are 7.2 ft apart
Calculating DistanceFrom the question, we are to determine the distance between the two men
Let the distance between the men be x
From the given information,
The man of the diving board is 6 ft tall
and
The angle of elevation from the man in the water to the man on the diving board is 40°
Considering the triangle formed, we can write that
Opposite = 6 ft
Adjacent = x
Angle = 40°
From SOH CAH TOA, we have that
tan (angle) = opposite / adjacent
∴ tan 40° = 6 / x
x = 6 / tan 40°
x ≈ 7.2 ft
Thus,
The men are 7.2 ft apart
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