Using the digits 1 to 9, without repeating, fill in the blanks to create a system of equations that intersect at x=1
Answers
The exponential function system that intersects as x = 1, is [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].
What is an exponential function?The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The d Here are two different exponential functions of the required form that intersect at x = 1 -
[tex]y = 3(1)^x[/tex]
[tex]y = \frac{6}{8} \times (4)^x[/tex]
In the first equation, a = 3, and b = 2.
Plugging in x = 1, we get -
[tex]y = 3(1)^1[/tex]
y = 3 × 1
y = 3
So the point of intersection of this equation with the x-axis is (1, 3).
In the second equation, a = 6/8 , and b = 4.
Plugging in x = 1, we get -
[tex]y = \frac{6}{8} \times (4)^1[/tex]
y = 3/4 × 4
y = 3
So the point of intersection of this equation with the x-axis is also (1, 3).
So, both of these equations intersect at x = 1 and are of the form [tex]y = a \times b^x[/tex].
Therefore, the equations are [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].
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Complete reference question:
Related Questions
20) Calculate the average rate of change of f(x) = −x² + 3x - 6 on the interval [1, 3].
Answers
Answer:
asdf
Step-by-step explanation:
If AB= 8x-5 and DC= 5x+4 Find AB+DC
Answers
The expression that represents the sum of the segments is:
AB + DC = 13x - 1
How to find the sum of the two segments?
Here we have two segments defined as functions of a variable x, and we can write them as:
AB = 8x - 5
DC = 5x + 4
We want to find an expression that represents AB + DC, we can just replace the two expressions (for each of the segments) in the sum above, then we willget:
AB + DC = 8x - 5 + 5x + 4
Now we can simplify that sum to get:
AB + DC = 8x + 5x - 5 + 4
= 13x - 1
That is the expression we wanted.
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HELP ASAP WILL GIVE BRAINLYEST AND 60 POINTS EACH
Answers
Answer: Reflection in the y -axis:
Explanation: The rule for a reflection over the y -axis is (x,y)→(−x,y) .\
Did it already but I don’t know if it is right.
Answers
Step-by-step explanation:
I'd say the association is linear, based on the first 3 options you chose
What's x if 23x = 253
Answers
Answer:
11
Step-by-step explanation:
11 x 23 is 253
On a field trip, the ratio of adults to students is 1:8. Which of the following statements about the field trip must be true? (A) A total of 9 people went on the field trip. B. The total number of people on the trip is a multiple of 8. C. There were 7 more students than adults on the field trip. D. There were 8 times as many students as adults on the field trip.
Answers
Answer:
B
Step-by-step explanation:
The correct answer is B. The total number of people on the field trip must be a multiple of 9 (1 adult and 8 students).
A is not true because if there were only 9 people, there could not be both an adult and 8 students, and the ratio would not be 1:8.
C is not necessarily true. It is possible that there were more adults than students on the field trip, or that the ratio was not an exact 1:8.
D is not true because if there were 8 times as many students as adults, the ratio would be 1:64, not 1:8
Fill in this table as you work through the lesson.
Answers
The completed text are:
Point of Tangency: A point of contact between a circle and its tangent line.
Secant segment: A segment that intersects a circle twice and has one endpoint on the circle and one endpoint outside of the circle.
Tangent Segment: A segment of a tangent line that has an endpoint at the point of tangency.
Why are the above concept relevant?The concepts of chord, point of tangency, secant segment, and tangent segment are relevant in geometry, particularly in the study of circles.
They provide the foundation for understanding the relationships and properties of circles and their associated segments.
These concepts are essential in various fields such as engineering, physics, and architecture, where circular shapes are commonly used. They are also relevant in solving real-world problems that involve circles, such as determining the area and circumference of a circle.
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1 1/2 = 2x
what is the answer?
Answers
Answer:
3/4
Step-by-step explanation:
In which quadrant does the terminal ray fall with an angle of rotation of 6 radians?
Answers
The angle is in the fourth quadrant.
What do you mean by quadrant?
The coordinate system's two axes (the x-axis and y-axis) constitute a region called a quadrant. The quadrants are the four areas generated when the x- and y-axes cross at a 90-degree angle.
Coordinate values, also known as x- and y-values, are present in both positive and negative directions in these locations.
What is a quadrant circle?
Any one of the four regions is a quadrant when a circle is uniformly divided into two perpendicular parts. In fact, anything that can be divided into four equal halves is said to be made up of quadrants. Hence, a quadrant of a circle is one-fourth of the entire circle.
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The terminal ray strikes the fourth quadrant at a rotational angle of 6 radians.
What are quadrants?Two-dimensional Cartesian axes separate the plane into four infinite regions known as quadrants, each of which is bordered by two half-axes.
The coordinate system's two axes, the x-axis, and the y-axis constitute a region called a quadrant.
The quadrants are generated when the two axes, the x-axis, and the y-axis, cross at a 90-degree angle.
These areas include coordinates or positive and negative values of the x- and y-axes.
The terminal ray falls at a rotational angle of 6 radians in the fourth quadrant.
Therefore, the terminal ray strikes the fourth quadrant at a rotational angle of 6 radians.
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Resolve partially
3x+2/(x+1)(x²+x+2)
Answers
Answer:
The given expression is:
3x + 2 / (x + 1)(x² + x + 2)
To simplify this expression, we need to factor the denominator first:
x² + x + 2 = (x + 2)(x + 1)
So the expression becomes:
3x + 2 / (x + 1)(x + 2)(x + 1)
Next, we can use partial fraction decomposition to express the expression in terms of simpler fractions. Let's assume:
3x + 2 / (x + 1)(x + 2)(x + 1) = A/(x + 1) + B/(x + 2) + C/(x + 1)²
Multiplying both sides by the common denominator, we get:
3x + 2 = A(x + 2)(x + 1) + B(x + 1)² + C(x + 2)(x + 1)
Expanding the right side, we get:
3x + 2 = Ax² + 3Ax + 2A + Bx² + 2Bx + B + Cx² + 3Cx + 2C
Combining like terms, we get:
3x + 2 = (A + B + C)x² + (3A + 2B + 3C)x + (2A + B + 2C)
Since this equation holds for all values of x, the coefficients of each power of x must be equal on both sides. We can equate the coefficients of x², x, and the constant term to get a system of three equations for A, B, and C:
A + B + C = 0
3A + 2B + 3C = 3
2A + B + 2C = 2
Solving this system, we get:
A = 2/3
B = -1/3
C = -1/3
Substituting these values back into the partial fraction decomposition equation, we get:
3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²
Therefore, the simplified expression is:
3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²
Integers descending order
1.) +8,-4,-6,-2,+3
2.)+10,-11,-13,+8,+9
3.)-15,+5,+8,-11,-10
4.)+6,+9-14,-12,+1
5.)-10,+3,-4,+4,-3
Answers
Calculate the rate of power draining per hour if the capacity of the cell phone is 3 600mAh
Answers
(reposting because the one person that helped gotten their comment deleted so i couldnt see answer) PLEASE HELP ASAP WITH THIS
Answers
Answer:
64, 69, 88, 88, 91, 92, 93, 95, 97, 97, 100
Median= 92
Mode= 88, 97
Mean= 88.55
Range= 36
Quartile 1= 88
Quartile 2= 92
Quartile 3= 97
Interquartile range= 9
Minimum= 64
Maximum= 100
Not sure if this helped but I hope it did
mHJ
measure of arc HJ:
96
29°
1
Answers
Answer:
Step-by-step explanation:
To convert the mixed angle measure 96° 29' 1" to decimal degrees, we can use the following formula:
decimal degrees = degrees + (minutes / 60) + (seconds / 3600)
Using this formula, we have:
decimal degrees = 96 + (29 / 60) + (1 / 3600)
decimal degrees = 96.4836111
Therefore, mHJ = 96.4836111 degrees (rounded to seven decimal places).
Suppose we want to choose 2 objects, without replacement, from the 5 objects pencil, eraser, desk, chair, and lamp.
(a) How many ways can this be done, if the order of the choices is relevant?
(b) How many ways can this be done, if the order of the choices is not relevant?
PLEASE HELP
Answers
Step-by-step explanation:
(a) If the order of the choices is relevant, we can choose the first object in 5 ways, and the second object in 4 ways (since we cannot choose the same object again). Therefore, the total number of ways to choose 2 objects without replacement and with order being relevant is:
5 x 4 = 20 ways
(b) If the order of the choices is not relevant, we need to use the combination formula, which is:
nCk = n! / (k! * (n-k)!)
where n is the total number of objects, and k is the number of objects we want to choose.
In this case, we want to choose 2 objects out of 5, so n = 5 and k = 2. Therefore, the number of ways to choose 2 objects without replacement and with order not being relevant is:
5C2 = 5! / (2! * (5-2)!) = 10 ways
Therefore, there are 20 ways to choose 2 objects without replacement and with order being relevant, and 10 ways to choose 2 objects without replacement and with order not being relevant.
Find the range of the data below.(Help asappp please)
Answers
What is the distance between the two points?
A. 4 units
B. 5 units
C. 6 units
D. 7 units
Answers
Answer:
6 units the answer is C. just see it
What is the perimeter of the decks?
Answers
The perimeter of the decks is 120 feet
What is perimeter :
Perimeter is a mathematical term that refers to the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
Property of circles:The property of circles states that "the tangents drawn from the same point on a circle are equal in length". It means that if two tangent lines are drawn from an external point to a circle, the length of both tangents will be equal.
Here we have
Tangents QR and QV from point Q
Tangents RS and ST from point S
Tangents VU and UT from point U
As we know,
The tangents drawn from the same point on a circle are equal in length
=> Tangent QR = QV --- (1) from point Q
=> Tangent RS = ST ----- (2) from point S
=> Tangent VU = UT ----- (3) from point U
From the figure,
The perimeter of decks = QR + RS + ST + TU + UV + VQ
From (1) (2) and (3)
=> QR + ST + ST + UV + UV + QR
=> 2QR + 2UV + 2RS
From the figure,
=> 2(24 ft) + 2(26 ft) + 2 (36 - 26) [ ∵ ST = US - TU ]
=> 48 ft + 52 ft + 20 ft
=> 120 ft
Therefore,
The perimeter of the decks is 120 feet
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A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 90 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.1 m3/min, how fast (in m/min) is the water level rising when the water is 10 cm deep?
Answers
Answer:
Let's start by finding the volume of water in the trough as a function of its depth.
At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:
V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm
Simplifying this expression, we get:
V(h) = (13/2000) h^2 m^3
Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:
dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)
At the moment when the water is 10 cm deep, we have:
h = 10 cm
dV/dt = 0.1 m^3/min
Plugging in these values, we get:
0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)
Solving for dh/dt, we get:
dh/dt = 0.1 m^3/min / (26/2000) / 10 cm
dh/dt ≈ 0.192 m/min
Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.
Using the figure below, ZFBD is 50%, which is
true regarding ZEBF?
09
C.
D.
A
A. ZEBF = 140°
B.
ZEBF = 90°
ZEBF = 50°
ZEBF = 40°
E
250°
B
F
Answers
Answer:
D. ∠EBF = 40°
Step-by-step explanation:
You want the measure of angle EBF in a diagram in which right angle EBD is split by ray BF to form angle FBD = 50°.
Angle addition postulateThe angle addition postulate tells you ...
∠EBD = ∠EBF +∠FBD
90° = ∠EBF +50° . . . . use the given values
40° = ∠EBF . . . . . . . subtract 50°
It must be true that ∠EBF = 40°.
What is the GCF in simplify form
Answers
So the Greatest Common Factor of The given expressions is -63x²y, 9x³y³, and 90x³y is 9x²y.
What is expression?In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a value or a quantity. Expressions can be simple or complex, and they can involve arithmetic operations, functions, and algebraic operations. Expressions can be evaluated, simplified, or manipulated using mathematical rules and techniques. They are used in many areas of mathematics, including algebra, calculus, and geometry, as well as in other fields such as physics, engineering, and economics.
Here,
To find the greatest common factor (GCF) of the given terms, we need to factor out any common factors of the coefficients and variables.
-63x²y = (-1) × 3² × 7 × x² × y
9x³y³ = 3² × x³ × y³
90x³y = 2 × 3² × 5 × x² × y
The common factors among these terms are 3², x², and y. Therefore, the GCF of the given terms is:
GCF = 3² × x² × y
= 9x²y
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Question:
A student is taking a quiz with one true/false question, one multiple-choice question with four choices, and one question where you must pick option 1 or 2. Each question has a single correct answer. What is the probability of getting all 3 answers correct?
Pls help.
Answers
The prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.
What is PrοbabiIity?PrοbabiIity is a measure οf the IikeIihοοd οr chance οf an event οccurring, expressed as a number between 0 and 1, with 0 indicating impοssibiIity and 1 indicating certainty. It is used in variοus fieIds such as mathematics, statistics, science, ecοnοmics, and finance.
The prοbabiIity οf getting the true/faIse questiοn cοrrect is 1/2 οr 0.5. The prοbabiIity οf getting the muItipIe-chοice questiοn cοrrect is 1/4 οr 0.25. The prοbabiIity οf getting the Iast questiοn cοrrect is 1/2 οr 0.5.
Tο find the prοbabiIity οf getting aII 3 answers cοrrect, we muItipIy the prοbabiIities οf getting each questiοn cοrrect:
0.5 * 0.25 * 0.5 = 0.0625
Sο the prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.
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Multiply the expression 23(13m-5)
Answers
Answer:
Step-by-step explanation:
294m
A road is inclined at an angle of 4°. After driving 4,813 feet along this road, find the driver's increase in altitude. Round to the nearest foot
Answers
Answer:
336 feet
Step-by-step explanation:
You want the change in elevation as a result of driving 4813 feet up a road with a 4° incline.
SineThe sine function relates an angle to the ratio of the opposite side and the hypotenuse in a right triangle:
Sin = Opposite/Hypotenuse
In this application, we have ...
sin(4°) = (elevation change)/(distance along the road)
elevation change = (4813 ft)·sin(4°) ≈ 336 ft
The driver's increase in altitude is about 336 feet.
From his tent, Mario can see a tree 120m away on a bearing of 056°. He can also see a rock that is due east of his tent and due south of the tree.
a) Sketch and label a diagram showing this information.
b) Hence find the distance from the rock to the tree.
Answers
The distance from rock to tree is approximate 99.48 m.
What is bearing in navigation?The bearing in navigatiοn refers tο the path between twο pοints, calculated in clοckwise rοtatiοns arοund nοrth. It is frequently emplοyed tο indicate the directiοn οf travel between twο places οr the οrientatiοn οf a landmark with respect tο a ship οr aircraft.
The azimuth, which is the angle between a reference directiοn (οften nοrth) and the directiοn tο an οbject οr pοint, is distinct frοm the bearing.
A. check the attachment given.
B. Let the distance from rock to tree be = H meter
Now, [tex]$ \rm \frac{Sin(056^{\circ})}{1} = \frac{H}{120}[/tex]
H = Sin(056°) × 120
H = 99.48 m
Thus, The distance from rock to tree is 99.48 m.
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Isabella and her children went into a restaurant and will buy drinks
and tacos. Each drink costs $2.75 and each taco costs $2. Isabella has a
total of $40 to spend on drinks and tacos. Write an inequality that
would represent the possible values for the number of drinks
purchased, d, and the number of tacos purchased, t.
Answers
Answer:
2.75d+2t <= 40
Step-by-step explanation:
i may be wrong but I tried
Jenna's Tea Shop has caffeinated tea and decaffeinated tea. The tea shop served 36 caffeinated teas and 39 decaffeinated teas. What percentage of the teas served were caffeinated?
Answers
According to the solution we have come to find that, 48% of the teas served were caffeinated.
What is percentage?A percentage is a way of expressing a proportion or a fraction as a number out of 100. The symbol used for percentage is the "%" sign. For example, if you have 10 apples and you want to express how many of them are red, you can say that 20% (or 2 out of 10) of the apples are red.
To find the percentage of caffeinated teas served, we need to divide the number of caffeinated teas by the total number of teas served, and then multiply by 100 to get the answer as a percentage.
Total number of teas served = 36 + 39 = 75
Percentage of caffeinated teas served = (36/75) x 100%
= 48%
Therefore, 48% of the teas served were caffeinated.
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Write the equation of the line that passes through the points ( -2,9 ) and ( 2,6). put your answer in fully simplified point slope form, unless it is a vertical or horizontal line
Answers
Answer:
Equation: y= -3/4x+15/2
Step-by-step explanation:
The points given: (-2,9) and (2,6)
Slope ,m=y2-y1/x2-x1=6-9/2-(-2)= -3/(2+2)
slope ,m= -3/4
Equation: y-y1=m(x-x1)
Equation: y-6= -3/4(x-2)
y-6= -3/4x+3/2
y= -3/4x+3/2+6
y= -3/4x+15/2
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This graph shows the solutions to the inequalities y > 3x + 14 and y < 3x + 2.
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
C
Answers
This graph in the figure shows the no solutions to the inequalities
Define inequalitiesinequalities can be defined as if two real numbers or the algebraic expressions can be related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called inequalities.
For example, x>3 (x should be greater than 3)
given:system of inequalities y>3x+14 and y<3x+2
the system of inequalities have solutions only when the shaded part satisfies the given inequalities
We are given with the graph of inequalities . The given inequalities have 'and' in between.
so we look at the graph where both inequalities intersects
From the graph we can see that there is no intersection part of both shaded portions
So , we conclude that there is no solution.
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The complete question is:
This graph shows the solutions to the inequalities. does the system of inequalities y>3x+14 and y<3x+2. Does the system of inequalities have solutions? If so, which region contains the solutions?
The design dept is planning a new model of tent in the shape of a triangular pyramid. They intend to make two sizes of the new model
Answers
By taking these factors into account, they can create a product that meets the needs of potential customers and is a success in the market. the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.
What is the design dept is planning a new model ?Triangular Pyramid Tent Design:
The triangular pyramid tent design is a unique shape that could potentially offer better stability against wind and other weather conditions. However, it may also require more complex construction and assembly than a traditional rectangular tent.
The design department should consult with engineers and experienced tentmakers to ensure that the triangular pyramid tent can be manufactured in a cost-effective and user-friendly manner.
Size options:
The design department has decided to make two sizes of the triangular pyramid tent. They should consider the intended use of the tents and the needs of potential customers when determining the size options.
For example, a smaller size might be suitable for backpackers or solo campers, while a larger size could accommodate families or groups.
Therefore, the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.
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