What is the range of f(x) = (3/4)^x – 4
Answer:
{y | y > –4}
Step-by-step explanation:
The range of f(x) = (3/4)^x - 4 is (-∞, -4].
Explanation:The range of the function f(x) = (3/4)^x - 4 can be determined by finding the minimum and maximum values that the function can reach.
First, let's determine the minimum value of f(x). The base of the exponent, 3/4, is less than 1, which means that as x approaches positive or negative infinity, the function approaches negative infinity. Therefore, the minimum value of f(x) is negative infinity.Next, let's determine the maximum value of f(x). Since the base is less than 1, as x approaches positive or negative infinity, the function approaches 0. However, f(x) can never actually reach 0 because of the constant -4 subtracted from it. Therefore, the maximum value of f(x) is -4.Putting it all together, the range of f(x) is (-∞, -4].
15 POINTS
Is it possible for a system of equations to be both independent and inconsistent? Explain
When a system has one answer or in other words, the graphs of the equations intersect one time, the system is called a consistent system of linear equations and therefore the equations are independent.
When a system has no solution meaning, the graphs of the equations don’t interconnect at all, the system is known to be an inconsistent system of linear equations and the equations are independent.
So therefore, the answer is yes.
while driving with his father, Amit his guys breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds he good his breath, on average, for about 8 seconds. if his father drives the car at 60 miles per hour through the tunnel, according to the average time Amit his his breath, about how long is the tunnel? (there are 5280 feet in a mile)
Answer: 704 feet
Step-by-step explanation: speed of car is V= 60 miles per hour
First convert the speed from miles per hour to feet per second .
[tex]V=\frac{60\times 5280}{60\times 60} \frac{ft}{s} = 88 \frac{ft}{s}[/tex]
Now Length of tunnel , L= speed of car x time taken
Therefore [tex]L=88\times 8 feet=704 feet[/tex]
An Olympic sprinter runs 200 meters in 20.1 seconds. Calculate the runner's speed in miles per hour.
Which expression is equal to (5−2i)−(1+3i)?
4+3i
4+i
6−5i
4−5i
Which expression is equal to −2i(−9+6i) ?
−12+18i
18−12i
18+12i
12+18i
first one is 4-5i
second one is 12+18i
The expression (5−2i)−(1+3i) is equal to 4−5i option (d) is correct and the expression −2i(−9+6i) is equal to 12+18i option (c) is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
It is given that:
(5−2i)−(1+3i)
After using distributive property:
= 5 - 2i - 1 - 3i
= 4 -5i
−2i(−9+6i)
After using distributive property:
= 18i - 12(i)²
= 18i - 12(-1)
= 18i + 12 = 12 + 18i
Thus, the expression (5−2i)−(1+3i) is equal to 4−5i option (d) is correct and the expression −2i(−9+6i) is equal to 12+18i option (d) is correct.
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The Yoga class you wish to take is offering two price quotes: $108 for 5 weeks as (15 classes) or $125 for 8 weeks (24 classes). How much per class would you save by taking the 8 week class?
A $2.10
B $2.05
C $1.99
D $1.89
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Cost for 5 weeks i.e. 15 classes = $108
Cost of per class is given by
[tex]\frac{108}{15}=7.2[/tex]
Cost for 8 weeks i.e. 24 classes = $125
Cost of per class is given by
[tex]\frac{125}{24}=5.21[/tex]
Amount of saving of per class by taking the 8 week class is given by
[tex]7.2-5.21=\$1.99[/tex]
Hence, Option 'C' is correct.
What is 1.2+d+0.4=9.7?
Which of the following are solutions to the equation below?Check all that apply.x2 – 6x + 40 = 6x + 5
a. -5 b. -6 c. 7 d. 5 e. 6
Answer:
c.7 and d.5
Step-by-step explanation:
Given the following equation :
[tex]x^{2}-6x+40=6x+5[/tex]
This equation is equivalent to the following equation :
[tex]x^{2}-6x+40=6x+5[/tex]
[tex]x^{2}-6x+40-6x-5=0[/tex]
[tex]x^{2}-12x+35=0[/tex]
Given an equation [tex]ax^{2}+bx+c=0[/tex] we can find the solutions using the quadratic equation (x1 and x2 are the solutions) :
[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
Using this equations :
[tex]x^{2}-12x+35=0[/tex]
[tex]a=1\\b=-12\\c=35[/tex] ⇒
[tex]x1=\frac{-(-12)+\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=7[/tex]
[tex]x2=\frac{-(-12)-\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=5[/tex]
Given the two solutions x1 and x2 we can write the equation :
[tex]ax^{2}+bx+c=0[/tex] ⇒ [tex]a.(x-x1).(x-x2)=0[/tex] ⇒
[tex]x^{2}-12x+35=0[/tex] is equivalent to
[tex](x-7).(x-5)=0[/tex]
The solutions for this equation are 7 and 5.
Therefore, c.7 and d.5 are the solutions for this exercise.
The graph shows the altitude of a helicopter over time. A graph measuring altitude and time. A line runs through coordinates (0, 10,000) and (15, 4000) and shows a decrease in altitude as time increases What is the slope of the line and what does it mean in this situation? The slope is –2000 . This means that the helicopter descends 2000 ft each minute. The slope is –400 . This means that the helicopter descends 400 ft each minute. The slope is 400. This means that the helicopter ascends 400 ft each minute. The slope is 2000. This means that the helicopter ascends 2000 ft each minute. 1 2 3 4 5
We can calculate for the slope of the line using the formula:
m = (y2 – y1) / (x2 – x1)
From the given values:
m = (4,000 – 10,000) ft / (15 – 0) min
m = -400 ft/min
This means that the altitude is decreasing by 400 ft per minute.
> The slope is –400 . This means that the helicopter descends 400 ft each minute.
What is the average speed of a person that travels 40 miles to their grandmothers house and then 40 miles back home in 6 hours?
A certain three three-cylinder combination lock has 65 65 numbers on it. to open it, you turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a three three-number lock combination has been affected. repetitions are allowed, and any of the 65 65 numbers can be used at each step to form the combination. (a) how many different lock combinations are there
I NEED THIS ANSWERED ASAP! PLEASE!!
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation h = -16t^2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t^2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
The time it takes the rock to reach the canyon floor is after 3.99seconds
Application of intercept to a functionThe intercept is the point where the axis is equal to zero. Give the quadratic equation that represents the height h (in feet) of an object t seconds after it is dropped expressed as:
h = -16t² + 255
The rock reaches the ground when h(t) = 0. Substitute
h = -16t² + 255
h = -16t² + 255 = 0
16t² = 255
t² = 255/16
t² = 15.9375
t = 3.99seconds
Hence the time it takes the rock to reach the canyon floor is after 3.99seconds
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REALLY NEED HELP I HAVE NO IDEA WHAT THE ANSWER IS
How could you confirm that a transformation is not a rigid motion by using a protractor
Final answer:
To confirm that a transformation is not a rigid motion, use a protractor to check for any changes in angles within a shape post-transformation. If the angles have changed, the transformation is not rigid. Corresponding side length changes further confirm this.
Explanation:
To confirm that a transformation is not a rigid motion using a protractor, you must look for changes in the shape's size or the angles between any two adjacent sides. A rigid motion, also known as an isometry, will preserve distances and angles between all points on a shape. Therefore, if after a transformation, using a protractor shows that the angles within the shape have changed, or that the corresponding sides are not congruent, then the transformation is not a rigid motion.
For example, if you have a triangle and apply a transformation, such as dilation or shearing, the new angles can be measured with a protractor. If they are different from the original triangle's angles, this confirms the transformation was not a rigid motion. Additionally, if the distances between corresponding points on the figure have changed, which you can measure with a ruler, this also confirms that the transformation is not rigid.
describe two methods for adding and subtracting linear expressions
Identify the horizontal translation of the parent function f(x) = x^2
Y= (x+5)^2
there are 8 boxes, which contain a total of 56 sweaters, in a store warehouse. If the store needs 35 sweaters, how many boxes should they take. can you explain please thank you
Julio has a house worth $220,000. He has a $175,000 mortgage. Julio says that in this situation, his asset is really only $45,000. Which statement explains whether Julio is correct?
A. Julio is correct because the $45,000 equity in the house is the real asset.
B. Julio is correct because he can pay $45,000 and have no more liabilities.
C. Julio is not correct because the same item cannot represent both an asset and a liability.
D. Julio is not correct because the house cannot be worth more than the mortgage.
The statement that explains whether Julio is correct is: A .Julio is correct because the $45,000 equity in the house is the real asset.
What is asset?Asset is anything that add value to you or things that are valuable. Example of assets are:
BuildingEquipmentLand etcReal asset=House worth-- Mortgage
Real asset=$220,000-$175,000
Real asset=$45,000
Based on the information given we are told the asset was only $45,000 which means that the $45,000 equity in the house is the real asset.
Inconclusion the statement that explains whether Julio is correct is: A .Julio is correct because the $45,000 equity in the house is the real asset.
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15x+14y+3x+7y simplified is
a.39xy
b.29x+10y
c.29xy+10xy
d.18x+21y
The simplification form of the expression 15x+14y+3x+7y is 18x + 21y option (D) 18x + 21y is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
15x+14y+3x+7y
After simplification,
Adding like terms:
= 18x + 21y
Thus, the simplification form of the expression 15x+14y+3x+7y is 18x + 21y option (D) 18x + 21y is correct.
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What is the first step of adding 12.65 + 30.75?
Kite WXYZ is graphed on a coordinate plane.
What is the area of the kite?
a.7 square units
b.8 square units
c.14 square units
d.16 square units
Answer-
Area of the kite is 14.0 sq.units
Solution-
[tex]\text{Area}_{WXYZ}=\text{Area}_{WXY}+\text{Area}_{WZY}[/tex]
From the graph, in the triangle WXY
Base = WY=4 units,
Height = 3 units
[tex]\text{Area}_{WXY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 3=6\ sq.unit[/tex]
From the graph, in the triangle WZY
Base = WY=4 units,
Height = 4 units
[tex]\text{Area}_{WZY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 4=8\ sq.unit[/tex]
[tex]\therefore \text{Area}_{WXYZ}=6+8=14\ sq.units[/tex]
Simplify the expression 4(11 + 7) ÷ (7 – 5)
Write as a decimal: 203% 0.203 2.03 20.3 203
The decimal form of the given percent 203% is 2.03
What is percent?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction. The word "percent" means "per hundred." So, whenever you see a number with a percent sign (%), you can imagine it as a fraction,
Percent is from the Latin adverbial phrase per centum meaning “by the hundred.” The Latin phrase entered English in the 16th century.
Example: 10% means 10 out of every 100. So if 10% of 500 people have ice cream, then 50 people have ice cream.
Given that, what is decimal form for the 203 percent,
Since, the percent is any number in its 100th part,
Therefore, 203% = 203/100
Since, it is 100 in the denominator,
The decimal will be put after two digits in the numerator,
Therefore,
203% = 203/100 = 2.03
Hence, the decimal form of the given percent 203% is 2.03
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Mike collects toy cars. he decides to put all of his toy cars in a line so that he can count them. the 9th car in line ends up being exactly at the middle of the line. how many toy cars does mike have?
Answer:
17 cars
Step-by-step explanation:
Mike collects toy cars. He decides to put all of his toy cars in a line so that he can count them.
It is given that 9th car in the line ends up being exactly at the middle of the line.
This statement shows that before and after the middle car there were 8 cars.
So the cars in the line is 8 + 1(middle) + 8 = 17 cars
Mike have total 17 cars.
Find two numbers a a and b b whose sum a + b a+b is 0 and whose difference a − b a-b is 2. your answer is
To find two numbers a and b whose sum a + b is 0 and whose difference a - b is 2, we can set up a system of equations and solve for the values of a and b.
Explanation:To find two numbers a and b whose sum a + b is 0 and whose difference a - b is 2, we can set up a system of equations:
a + b = 0
a - b = 2
We can solve this system by adding the two equations:
(a + b) + (a - b) = 0 + 2
2a = 2
a = 1
Substituting the value of a back into one of the equations, we find that b = -1.
Therefore, the two numbers are 1 and -1.
There are (32)4 ⋅ 30 bacteria in a petri dish. what is the total number of bacteria in the dish? (1 point)
Answer:
[tex]3^{8}[/tex]
Step-by-step explanation:
[tex]3^{8}[/tex]x1 any expression multiplied by 1 remains the same
alternative form - 6561
Which of the following was a primary reason France sought to colonize North America?
A To reduce overpopulation in Europe
B To create communities founded on religious tolerance
C To profit from trading in furs and other goods
D To create joint ventures with other European powers
Answer: The answer is C on Quizizz.
Step-by-step explanation:
two parallel lines cut by a transversal. What is the value of x?
Which of the following equations has the solution x= all real numbers?
a. 4(3−x)+6x=x+12−3x
b. 4(3−x)+6x=3x+12+2x
c. 4(3−x)+6x=3x+12−x
d. 4(3−x)+6x=3x+10−x
Option (b) 4(3-x)+6x=3x+12+2x is the equation that has the solution x = all real numbers because it simplifies to an identity, which is true for any value of x.
Among the given equations, the one that has the solution x = all real numbers is essentially an identity, meaning that for any value of x you plug into the equation, the equation will hold true. To determine which equation is an identity, each equation must be simplified.
Let's take option (b) as an example:
4(3−x)+6x=3x+12+2x
4∙3 - 4∙x + 6∙x = 3∙x + 12 + 2∙x
12 - 4∙x + 6∙x = 3∙x + 12 + 2∙x
12 + 2∙x = 5∙x + 12
12 - 12 + 2∙x - 2∙x = 5∙x - 2∙x + 12 - 12
0 = 3∙x - 3∙x
After simplifying, we end up with 0 = 0, which is an identity and is true for all values of x, hence this is the equation where x is all real numbers.
2a7 – 16a6 + 18a5
Consider the degree of each polynomial in the problem.
The first factor has a degree of????? .
The second factor has a degree of ?????/ .
The third factor has a degree of ????? .
The product has a degree of ??????.
The first factor has a degree of 7, the second has a degree of 6, and the third has a degree of 5. The product has a degree of 7, the highest among them.
To determine the degree of each polynomial in the expression[tex]2a^7 - 16a^6 + 18a^5[/tex], we need to understand that the degree of a polynomial is the highest exponent of the variable in that polynomial.
The first factor is[tex]2a^7[/tex]. Here, the highest exponent of the variable 'a' is 7. So, the degree of the first factor is 7.
The second factor is[tex]-16a^6[/tex]. In this case, the highest exponent of 'a' is 6. So, the degree of the second factor is 6.
The third factor is [tex]18a^5[/tex]. Here, the highest exponent of 'a' is 5. So, the degree of the third factor is 5.
Now, to find the degree of the product of these three factors when added together, we need to find the highest degree among them. In this case, the highest degree is 7 (from the first factor). Therefore, the product has a degree of 7.
In summary:
The first factor has a degree of 7.
The second factor has a degree of 6.
The third factor has a degree of 5.
The product has a degree of 7.
These degrees reflect the highest power of 'a' in each term of the polynomial expression.
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