1. The three lengths are B. 18cm, 12cm, and 9cm which cοuld be the lengths οf the sides οf a triangle.
2. The third side D. It must be greater than οr equal tο 6 and at mοst 24.
What is length?A physical measure οf distance between twο places in space is length. It is a fundamental quantity that is emplοyed in bοth engineering and physics. The Internatiοnal System οf Units (SI) uses metres as the unit οf length (m). In geοmetry, length plays a crucial rοle in describing the size and lοcatiοn οf geοmetrical shapes in space.
Accοrding tο the Triangle Inequality Theοrem,
The tοtal οf twο sides οf a triangle must be greater than the sum οf the third side, accοrding tο this theοrem. If all three cοmbinatiοns are true, yοu will have a true triangle.
1) Yοu must gο thrοugh each οf these οptiοns οne by οne tο ensure that the triangle is feasible. Cοnsider the triangle tο have the side lengths a, b, and c, and the theοrem tο be an inequality, which states:
a+b > c, a+c > b, and b+c > a.
As per οptiοn (B),
a = 18, b = 12, and c = 9
Here, Triangle Inequality Theοrem satisfies.
Thus, the three lengths are 18cm, 12cm, and 9cm which cοuld be the lengths οf the sides οf a triangle.
2. By the prοperties οf the triangle, the sum οf the square οf twο lengths is equal tο the third side length οf the triangle.
Always remember that when yοu add twο sides tο a triangle, the sum will cοme οut tο be higher than the third side’s length.
Hence, D. It must be greater than οr equal tο 6 and at mοst 24.
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interval notation for t - 1/3 >= -12/9
Answer: [-1, ∞)
Step-by-step explanation:
First, we will simplify the equation.
Given:
t - 1/3 ≥ -12/9
Add 1/3 to both sides of the equation:
t ≥ -1
Next, we know that a bracket is used when representing greater than or equal to and less than or equal to. Here, it's greater than or equal to so we will use a bracket on the left side.
Then, t can be any value to infinity above -1, so we will use ∞) on the right side.
[-1, ∞)
someone help step by step
Step-by-step explanation:
we know, the area of a rectangle is
length × width
so, we have here
length × (x - 5) = x² - 7x + 10
therefore,
length = (x² - 7x + 10) / (x - 5)
so, just by looking at it (with experience) I see that length is (x - 2).
but let's do the actual polynomial division, which seems to be the desired exercise here.
x² - 7x + 10 ÷ x - 5 =
it is very similar to actual number divisions.
we go from left to right.
we start with the first term (x²) and see how many times (x - 5) would fit into it. for that we look only at the first term in x - 5 (that is x).
x² / x = x
that is already our first term of the result (quotient) :
x² - 7x + 10 ÷ x - 5 = x
now, we multiply that result with the divisor (x - 5) and subtract that from the dividend.
x² - 7x + 10 ÷ x - 5 = x
- x² - 5x
--------------
0 - 2x
and now we pull down the next term from the dividend :
x² - 7x + 10 ÷ x - 5 = x
- x² - 5x
--------------
0 - 2x + 10
and we repeat the process with that new dividend :
-2x / x = -2
that is our next term of the quotient.
x² - 7x + 10 ÷ x - 5 = x - 2
- x² - 5x
--------------
0 - 2x + 10
we repeat the process of multiplying that term (-2) with the divisor (x - 5) and subtracting that result from the dividend :
x² - 7x + 10 ÷ x - 5 = x - 2
- x² - 5x
--------------
0 - 2x + 10
- -2x + 10
-------------
0 0
there is no remainder, and there is no more term to pull down. we are finished.
the result of the division is (as expected) : x - 2
the expression to describe the length is therefore
x - 2
8-9. If AG = 2, GF = 5, FE = 3, GB = 6, CD = 7 and GB || FC || ED, find the lengths of the missing sides?
AB=?
BC=?
FC=?
ED=?
Answer:
AB = 4 2/3BC = 11 2/3FC = 21ED = 30Step-by-step explanation:
In the given triangle AED, segments GB and FC are parallel to base ED. Points G and F are on segment AE in that order. Lengths AG=2, GF=5, FE=3, GB=6, and CD=7 are given. You want the lengths of AB, BC, FC, and ED.
Proportional segmentsSegments of transversals crossed by parallel lines are proportional:
AG : GF : FE = AB : BC : CD
2 : 5 : 3 = AB : BC : 7
Multiplying the first ratios by 2 1/3 will give the second ratios:
2 : 5 : 3 = 4 2/3 : 11 2/3 : 7
This lets us conclude ...
AB = 4 2/3
BC = 11 2/3
Similar trianglesCorresponding segments of similar triangles are proportional:
AG : GB = FA : FC = AE : ED
2 : 6 = (5+2) : FC = (5+2+3) : ED
We notice the second number in the first ratio is 3 times the first number. That means these ratios are ...
2 : 6 = 7 : 21 = 10 : 30
This lets us conclude ...
FC = 21
ED = 30
The lengths of the missing sides are calculated to be
AB = 5BC = 12FC = 21ED = 30How to find the lengths of the missing sidesThe parallel lines in the figure created similarity between the dimensions, this makes the ratio of the dimensions equal
The given dimensions that is used to find the missing sides
Solving for AB
AB / CD = AG / FE
AB / 7 = 2 / 3
cross multiplying
3 * AB = 7 * 2
AB = 14/3 = 4.667
Using AB, GF is calculated
AB / BC = AG / GF
14/3 / BC = 2 / 5
cross multiplying
BC = (5 * 14/3) / 2
BC = 35/3 = 11.667
Solving for FC
GB / FC = AG / A'F
6 / FC = 2 / (2 + 5)
cross multiplying
2 * FC = 6 * 7
FC = 42/2 = 21
Solving for ED
GB / ED = AG / AE
6 / ED = 2 / (2 + 5 + 3)
cross multiplying
2 * ED = 6 * 10
ED = 60/2 = 30
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Kira and Hector each performed as soloists for a concert. Each person performed for the same amount of time. Kira sang three solos and played a piano piece. Hector sang 2 solos and played a piano piece that lasted twice as long as Kira's. Each of the solos Kira and Hector sang was 3.5 minutes long.
a. Define a variable and write an equation to represent the situation. Solve the equation and interpret the solution of your equation in the context of the situation.
b. How long did each student perform?
A variable can be any number or alphabet that may constantly vary and the equation to represent the given situation for Kira is (3x+y) and for Hector is (3x+z) where x is the time for solos and y and z are times for piano. The value of x and y is 3.5 minutes and that of z is 7 minutes.
According to the question,
We have the following information:
Each person performed for the same amount of time. Kira sang three solos and played a piano piece. Hector sang 2 solos and played a piano piece that lasted twice as long as Kira's. Each of the solos Kira and Hector sang was 3.5 minutes long.
Now, let's take time for solos to be x min and time for Kira's piano to be y min and that for Hector is z min.
So, we have the following equations:
Kira:
3x+y
Hector:
2x+z
Now, z = 2y
x = 3.5 minutes
Time is equal:
3x+y = 2x+z
3x+y = 2x+2y
3x-2x = 2y-y
x = y
y = 3.5 min
z = 2*3.5
z = 7 min
Hence, a variable can be any number or alphabet that may constantly vary and the equation to represent the given situation for Kira is (3x+y) and for Hector is (3x+z) where x is the time for solos and y and z are times for piano. The value of x and y is 3.5 minutes and that of z is 7 minutes.
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Pls Help I will give brainliest to whoever is first and correct. And answer all questions!
Answer:
Original equation
distributive property
subtract 5x from both sides
add 12 to both sides
Divide both sides by 14
Step-by-step explanation:
Kirsty changes $380.80 into pounds (£) when £1 = $1.19. Calculate the amount Kirsty receives.
Answer:
320 pounds sterling
Step-by-step explanation:
All you have to do is $380.80 divided by $1.19 which is equal to one pound sterling. Hope this helps!
What is the area of trapezoid abcd? enter your answer as a decimal or whole number in the box. do not round at any steps. units²
The area of trapezoid ABCD is 37.5 units^2.
Trapezoid is a type of quadrilateral with at least one pair of parallel sides. The area of trapezoid is given by:
Area = ½(a + b)*h
Where a and b are the length of two parallel sides and h is the perpendicular length between the length of two parallel sides.
In the given trapezoid ABCD, which is defined by coordinates of A, B, C, and D, the distance of each side is given by: √((x2 – x1)^2 + (y2 – y1)^2)
The length of a (DA) = √((x2 – x1)^2 + (y2 – y1)^2) = √((-3 – 0)^2 + (2 – (-2))^2) = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5 units
The length of b (BC) = √((x2 – x1)^2 + (y2 – y1)^2) = √((7 – 1)^2 + (-3 – 5)^2) = √((6)^2 + (-8)^2) = √(36 + 64) = √(36 + 64) = √(100) = 10 units
The length of h (AB) = √((x2 – x1)^2 + (y2 – y1)^2) = √((1 – (-3))^2 + (5 – 2)^2) = √((4)^2 + (3)^2) = √(16 + 9) = √(25) = 5 units
Hence, the area of trapezoid:
Area = ½ (5 + 10) * 5 = 7.5 * 5 = 37.5 units^2
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pls helpp!! ixl is so frustrating and i can't get this question wrong itll drop me like 20 points i don't understand this question
Answer:
oof try adding dem
Step-by-step explanation:
hope you git 20 points
Katalin drove 300 miles on her vacation. she drove an average of 1.9 times faster on the second 150 miles of her trip than she did on the first 150 miles of her trip. which expression represents the time she spent driving?
The expression represents the time she spent driving is [tex]\frac{228.95}{x}[/tex]
The expression represent the time she spent driving can be calculated as follows:
We know that
Time = [tex]\frac{distance}{ speed}[/tex]
Let x be her speed on the first half of the trip.
Then for first half , the tiime she takes is
T1= [tex]\frac{150}{x}[/tex]
while in a second half the time taken by her is
T2= [tex]\frac{150}{1.9x}[/tex]
T2= [tex]\frac{78.95}{x}[/tex]
the total time she spent on driving is
T1 + T2 = [tex]\frac{150}{x}[/tex] + [tex]\frac{78.95}{x}[/tex] = [tex]\frac{228.95}{x}[/tex]
Hence, the expression represents the time she spent driving is [tex]\frac{228.95}{x}[/tex]
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Find the slope of the line graphed below.
Answer: -1
Step-by-step explanation:
Answer:
By counting, to go from one point to another, we go down 4, over 4. This means the slope is -4/4. This can then be simplified.
-4/4 = -1
So, the slope is -1
The function h(t) = -16t² + vt + 10 gives the height of a platform diver above the water, in feet, t seconds
after the diver leaves the platform with an initial velocity, U, in feet per second.
10 feet
On one dive, it takes the diver 1.42 seconds to reach the surface of the water.
• What was the initial velocity, U, in feet per second, of the diver?
. After how much time, in seconds, since leaving the platform did the diver reach the same height as the platform?
• What was the diver's maximum height, in feet, above the water?
Justify your answers. Enter your answers and justifications in the space provided.
The maximum height of the diver as calculated from the function is 14.54 feet.
The function that represents the position of the diver is
h(t) = -16t² + vt + 10
The diver is at a height of 10 feet.
So at t=0 , h=10
Now we will find the rest of the solutions from the graph which follows the path of a parabola .
at t=1.42 , h(t)=0
Therefore 0 = -16(1.42)² + 1.42t + 10
or, V =15.68 ft/s
Again:
For h(t) to be maximum we have to find t for which h'(t)=0 , so we diff
h'(t) = -32t +15.68
or, t = -15.68 / 32
or, t = 0.49 seconds
Now h(0.49) = 16(0.49)² + 1.42 × 0.49 + 10 = 14.54 feet
Hence the maximum height of function is 14.54 feet
Therefore the diver has an initial velocity of 15.68 ft/sec and the diver reached a height of 14.54 feet at the maximum point.
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Brad and john met up for lunch when they were done brad traveled 6 blocks east and john traveled 4 blocks west how many blocks .away from brad was john
Answer:10 blocks
Step-by-step explanation: East And West are in a straight line
The midpoint of line AB is M(3,−3). If the coordinates of A are (2,−8), what are the coordinates of B?
Answer:
The coordinates of B are (4, 2)
Step-by-step explanation:
The coordinates of B can be calculated as follows ?
The midpoint of line AB is M(3,-3) is derived from the formula
[tex]M=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]
Where [tex]x_1[/tex] and [tex]y_1[/tex] are the coordinates of A and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the coordinates of B
Since the coordinates of A are (2, -8), then the value of [tex]x_1[/tex] is 2 and the value of [tex]y_{1}[/tex] is -8.
Since the [tex]x[/tex]-coordinate of M is 3, then the equation to follow is
[tex]\frac{x_{1}+x_{2}}{2}=3[/tex]
Substitute 2 for [tex]x_{1}[/tex], then it follows that
[tex]\frac{2+x_{2}}{2}=3[/tex]
Multiply both sides of the equation by 2
[tex]\frac{2+x_{2}}{2}\times 2=3\times 2[/tex]
Simplify both sides of the equation
[tex]2+x_{2}=6[/tex]
Substract 2 from both sides of the equation
[tex]2-2+x_{2}=6-2[/tex]
Simplify the equation
[tex]x_{2}=4[/tex]
Since the [tex]y[/tex]-coordinate of M is -3, then the equation to follow is
[tex]\frac{y_{1}+y_{2}}{2}=-3[/tex]
Substitute -8 for [tex]y_{1}[/tex], then it follows that
[tex]\frac{-8+y_{2}}{2}=3[/tex]
Multiply both sides of the equation by 2
[tex]\frac{-8+y_{2}}{2}\times 2=-3\times 2[/tex]
Simplify both sides of the equation
[tex]-8+y_{2}=-6[/tex]
Add 8 to both sides
[tex]-8+8+y_{2}=-6+8[/tex]
Simplify the equation
[tex]y_{2}=2[/tex]
Since the value of [tex]x_{2}[/tex] is 4 and the value of [tex]y_{2}[/tex] is 2, then the coordinates of B are (4,2).
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Solve for x with steps. Will mark brainliest.
x = 1.53347526
Take the log of both sides of the equation.
[tex]ln(2^{3x-1} ) = ln(3^{x-2} )[/tex]
Expand [tex]ln(2^{3x-1} )[/tex] by moving 3x-1 outside the logarithm
[tex](3x-1)ln(2)= ln(3^{x-2} )[/tex]
Move x-2 outside the logarithm [tex]ln(3^{x-2} )[/tex]
[tex](3x-1)ln(2) = (x-2)ln(3)[/tex]
Solve the equation for x
[tex]x = -[\frac{{2ln(3)-ln(2)}}{3ln(2)-ln(3)} ][/tex]
The value of x is 1.53347526(After applying the log values)
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Substitute 6 for the variable, n, using parentheses. Then simplify by multiplying 8 and 6. 8(6) = 48. So you have 56 = 48, which is not a true statement. 6 is not a solution to the equation.
The numeric value of the expression 8n at n = 6 is different of 56, hence n = 6 is not a solution to the expression 8n = 56.
How to verify if a number is a solution to an expression?A number a is a solution to an expression if the numeric value of the expression at input a generates an identity with the expression.
In this problem, the expression is given as follows:
8n = 56.
We want to verify if the number six is a solution to the presented expression.
The numeric value of the expression at n = 6 is found replacing the lone instance of n by 6, hence it is obtained as follows:
8n = 8 x 6 = 48.
(the product of 8 and 6 is 48).
Then the equality would be of:
48 = 56.
Which is a contradiction, hence n = 6 is not a solution to the expression 8n = 56.
Missing InformationThe problem is:
Explain how to determine if the number is a solution to the equation. 56 = 8n for n = 6
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the value of 1. 35⁷
Give your answer correct to 5 significant figures.
Answer:
1.35⁷ = 8.1722 (to 5sf)
In the accompanying diagram, parallel lines HE and AD are
cut by transversal BF at points G and C, respectively. If
mLHGF = 5n and m/BCD = 2n +66, find n.
The value of n is 22.
In this question, we have been given the parallel lines HE and AD are
cut by transversal BF at points G and C, respectively.
Consider the following diagram.
If m∠HGF = 5n and m∠BCD = 2n +66, we need to find n.
∠HGF and ∠BCD are alternate exterior angles.
We know that alternate exterior angles are congruent.
So, m∠HGF = m∠BCD
5n = 2n +66
5n - 2n = 66
3n = 66
n = 66/3
n = 22
Therefore, the value of n is 22.
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mmm nnn
333 212121
555 353535
888 565656
Write an equation to describe the relationship between mmm and nnn.
The equation that represents the relationship between m and n is written as: n = 7m.
How to Write a Proportional Relationship Equation?A proportional relationship between two variables have a slope of constant of proportionality, k, which is y/x.
The equation that represents a proportional relationship is expressed in slope-intercept form as y = kx.
In this situation m = x, and n = y.
The constant of proportionality, k = n/m.
Find the constant of proportionality, k, using a pair of values from the given table, say (3, 21):
k = 21/3
k = 7
To write the equation, substitute k = 7 into n = km:
n = 7m.
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Chicken and rabbit are placed in the ame cage. There are 35 head and 94 feet. How many rabbit are there?
Based on heads and feet of chicken and rabbits, there are 12 rabbits in the cage.
Let us represent chicken by x and rabbit by y. So, we all know that chicken and rabbit have 1 head each. We also know that chicken has 2 feet and rabbit has 4 legs. Now forming the equation accordingly.
Equation for head -
x + y = 35 : Equation 1
Equation for feet -
2x + 4y = 94 : Equation 2
Rewriting equation 1 according to x
x = 35 - y : Equation 3
Keep the value of x from equation 3 in equation 2
2(35 - y) + 4y = 94
Preforming multiplication on Left Hand Side
70 - 2y + 4y = 94
Performing subtraction
2y = 94 - 70
2y = 24
y = 24 ÷ 2
Performing division
y = 12
Thus, there are 12 rabbits in the cage.
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A rental car company charge $63. 25 per day to rent a car and $0. 07 for every mile driven. Ella want to rent a car, knowing that: She plan to drive 50 mile. She ha at mot $130 to pend
Answer:
it would be 66.75 for one day if ella plans to drive for 1 day with 50 miles, and if you need how much money she has left it is 63.25
Step-by-step explanation:
hope it helped:)
Delaney would like to make a 5 lb but mixture that i 60% peanut and 40% almond. He ha everal kind of peanut and everal kind of a mixture that i 20% peanut and 80% almond. Let p repreent the number of punt of peanut needed to make the mixture, and let m repreent the number of pound of the 80% almond-20% peanut mixture. What i the ytem that model thi ituation
The system that models the equation is m = 2.5 lb.
This is a mixed-up issue. The combination of
80% almonds and 20% peanuts make up combination A.
Completely peanuts in mixture B
both the
As a combination, use 60% peanuts and 40% almonds.
Since mixture C is created by combining mixtures A and B, we may calculate its combined weight in pounds to be 5 pounds.
Hence, we
Let m be the weight in pounds of mixture A (20% peanuts, 80 % almonds).
and
50-m is the quantity of mixture B in pounds.
Consequently, the set of equations that models this circumstance is:
0.20m + 1(50-m) = 0.60(5) (5)
0.80m + 0(50-m) = 0.40(5)
Equation 2's solution for m gives us
m = 2.5 lb.
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Write a division equation that represents the question: how many 3/8s are in 5/4
The division equation is x * 3/8 = 5/4 and there are (10/3) times 3/8s there in 5/4.
Let's assume that x times 3/8 are in 5/4.
So, calculating a division equation for the value of x.
x * 3/8 = 5/4
=> x = 5/4 * 8/3
=> x = 40/12
Dividing the numerator and denominator by 4.
We get, the value of x equal to
=> x = 10/3
Division equation: A division equation is a mathematical expression containing a division operator. Division equations are useful not only in math class but also in everyday life.
For example, if we want to share a bundle of papers equally with our friends, we can use this solution to find the given question. 100 papers and we have 10 friends. To find out how many papers each person gets, divide 100 by 10. The solution is 10. This means that each friend receives 10 papers.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed by the debtor is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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Brianna is very good at keeping her school binder organized. Every time her teacher returns an assignment, Brianna puts it in the right section. Brianna has 113 assignments in the history, science, and art sections combined. The rest of her assignments are in the math section. Brianna has 182 assignments in total.
Using equation, the number of math assignment is 69 .
How to use equation to find the number of math assignment?Brianna has 113 assignments in the history, science, and art sections combined. The rest of her assignments are in the math section. Brianna has 182 assignments in total.
Using equation, the number of assignments in the math section of Brianna's binder can be calculated as follows:
She has 113 assignments in the history, science, and art sections combined.
Let x be the number of assignments that are in math section.
There are 182 assignments in total.
Therefore,
x + 113 = 182
subtract 113 from both sides of the equation
x + 113 = 182
x + 113 - 113 = 182 - 113
x = 69
Therefore, the number of math assignment is 69.
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consider the following graph. the x y coordinate plane is given. the curve begins at the origin, goes up and right becoming less steep, the curve changes direction at (1, 3), goes down and right becoming more steep, passes through (2, 2), goes down and right becoming less steep, changes directions at (3, 1), goes up and right becoming more steep, passes through the point (4, 3), goes up and right becoming less steep, passes through (5, 4) almost horizontally, goes up and right becoming more steep, passes through the approximate point (6, 4.2) and ends at (7, 6). (a) find the interval(s) on which f is increasing. (enter your answer using interval notation.) incorrect: your answer is incorrect. (b) find the interval(s) on which f is decreasing. (enter your answer using interval notation.) correct: your answer is correct. (c) find the interval(s) on which f is concave upward. (enter your answer using interval notation.) incorrect: your answer is incorrect.
A) The interval(s) on which f is increasing is; (1,3) ∪ (4,6).
B) The interval(s) on which f is decreasing is; (0,1) ∪ (3,4).
(C) The interval(s) on which f is concave upward is; (0,2) ∪ (3,5).
How to find the increasing or decreasing interval?
A) A function is said to be increasing on an interval if for every point on that interval we see that the first derivative is positive. Thus, from the attached graph, we see that the function is increasing on the intervals (1,3) and (4,6).
B) If the value of the derivative f' (x) ≤ 0 of the function, then we can say that the interval is a decreasing interval. From the graph, we can say that the function is decreasing on intervals (0,1) and (3,4).
C) The graph is concave upward on the intervals (0,2) and (3,5).
D) The graph is concave downward which means convex on the interval (3,4).
e) The points of inflection are defined as the points located on a smooth plane curve that the curvature changes sign. In this graph, the points of inflection are x=3 and x=5.
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Mari cella has a bag containing 35 nickels and quarters. The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions
From the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.
As given in the question,
Let x represents the number of nickels
And y represents the number of quarters
Total number of nickels and quarters are 35
Total value of given coins = $2.50
Required equation for the given condition is:
x + y = 35 ___(1)
1 nickel = 0.05 dollars
1 quarter = 0.25 dollars
0.05x + 0.25y <2.50 ___(2)
Substitute x = 35 - y in (2) we get,
0.05 ( 35 - y ) + 0.25y < 2.50
⇒1.75 - 0.05y + 0.25y < 2.50
⇒ 0.2y < 2.50 - 1.75
⇒ 0.2y < 0.75
⇒ y < 3.75
Maximum number of quarters for the given condition is equal to 3.
Therefore, for the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.
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write expression in terms of log of x , and z
log x√z
The equation in terms of log(x) and log(z) is, [tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].
What is logarithmic expression?
A logarithmic equation is one in which a variable-containing expression's logarithm is used as a solution. If you can write both sides of the equation as powers of the same number, that will help you answer exponential equations.
Consider, the given logarithmic expression,
[tex]logx\sqrt{z}[/tex]
By using the logarithmic rule: log(ab) = log(a) + log(b)
So,
[tex]logx\sqrt{z} = log(x) + log\sqrt{z}[/tex] ..(1)
Replace [tex]\sqrt{z}[/tex] by [tex]z^\frac{1}{2}[/tex].
So,
[tex]log\sqrt{z} = logz^\frac{1}{2}[/tex]
Apply the rule: [tex]loga^b = b log(a)[/tex]
Therefore, [tex]log(\sqrt{z}) = \frac{1}{2}log(z)[/tex]
Substitute this value in equation (1).
[tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].
Hence, the expression in terms of x and z is, [tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].
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A new soup recipe contains 33\%33%33, percent less sodium per serving than the old soup recipe. The old soup recipe contained xxx milligrams of sodium per serving.
Which of the following expressions could represent the amount of sodium per serving, in milligrams, in the new soup recipe?
The expression that could represent the amount of sodium per serving, in milligrams, in the new soup recipe is y = 0.67x
How to get the expression?From the information, the new soup recipe contains 33% less sodium per serving than the old soup recipe.
Let's say Sodium in an old soup recipe per serving = x mg
Let's say Sodium in a new soup recipe per serving = y mg
The new soup recipe contains 33% less sodium per serving than the old soup recipe
y = x - (33/100)x
100y = 100x - 33x
100y = 67x
Divide through by 100
y = 0.67x
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Determine the distance between the points (−6, −3) and (0, 5).
22 units
10 units
8 units
5 units
By using the distance formula, The distance between the points (−6, −3) and (0, 5) is 10 units.
In geometry, we use the distance formula to evaluate the distance between two points whose coordinates are given,
The coordinates of the points are given as [tex](x_{1} ,y_{1})( x_{2} ,y_{2} )[/tex]
Then, the distance (D) between them is given by :
[tex]D = \sqrt{(x_{1} -x_{2} )^{2} -(y_{1} -y_{2} )^{2} }[/tex]
Now, the given points are (−6, −3) and (0, 5).
Putting these values in the distance formula, we have
[tex]D = \sqrt{(-6-0)^{2}+ (-3 -5)^{2} }\\ \\D = \sqrt{36 +64 \\\\ \\D = 10[/tex]
Hence, the distance between the points (−6, −3) and (0, 5) is 10 units.
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Answer: 10 units
Step-by-step explanation: i took the test and got it right
Which of the following graphs represents the solution(s) of the following system?
X^ - y = -2, 4y - 8 = x
The graph that represents the solutions of the given system of equations is attached below.
We are given a system of equations. The first equation is a quadratic polynomial. The second equation is linear in nature. The equations are given below.
x² - y = -2
4y - 8 = x
We need to find the solution to the equations using a graph. The graph of the equations is attached below. The graph of the first equation is represented by an upward parabola. The graph of the second equation is represented by a straight line. The intersection points of the two curves are the solutions to the given system of equations.
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