Write a quadratic function (f) whose zeros are −8 and 2.
in triangle RST, m∠R=(2x+10), m∠S=(2x+25), m∠T=(x-5)
what is the value of x
A. 30
B. 28
C. 26
D. 32
A Springer Spaniel weighs 20 kilograms 490grams. A Cocker Spaniel weighs 7,590 grams less than a Springer Spaniel. A Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. What is the difference, in grams, between the weights of the Newfoundland and the Springer Spaniel?
To find the difference in weight between the Newfoundland and the Springer Spaniel, subtract the weight of the Springer Spaniel from the weight of the Newfoundland.
Explanation:To find the difference in weight between the Newfoundland and the Springer Spaniel, we need to subtract the weight of the Springer Spaniel from the weight of the Newfoundland. The Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. So, we first need to find the weight of a Cocker Spaniel by subtracting 7,590 grams from the weight of the Springer Spaniel. We then add this weight to the weight of the Newfoundland to get the final answer. Let's calculate:
The weight of the Cocker Spaniel = Weight of Springer Spaniel - 7,590gThe weight of the Newfoundland = Weight of Cocker Spaniel + 52kg 656gFinally, the difference in weight between the Newfoundland and the Springer Spaniel is the weight of the Newfoundland - weight of the Springer SpanielWe can now substitute the given values into these equations and solve.
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Find (f - g)(x).
f(x) = -3x + 2
g(x) = x3
Answer:
[tex](f-g)(x) = -x^{3} - 3\cdot x + 2[/tex]
Step-by-step explanation:
The new function is:
[tex](f-g) (x) = -3\cdot x + 2 -x^{3}[/tex]
[tex](f-g)(x) = -x^{3} - 3\cdot x + 2[/tex]
Fifty randomly selected individuals were timed completing a tax form. the sample mean was 23.6 minutes; the sample standard deviation was 2.4 minutes. a 99% confidence interval for the mean time required by all individuals to complete the form is about:
I need help with this math question!!
Simplify 0.4i−i.
The simplification of the given expression is 0.6i.
What are complex numbers?Complex numbers are those numbers that contain the imaginary and the real part.
A Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
where r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Usually the simplification involves proceeding with the pending operations in the expression.
We need to simpify the 0.4i - i
= i(0.4-1)
= 0.6i
Therefore, the simplification of the given expression is 0.6i.
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An is planning a birthday party for her younger sister at a skating rink. the cost of admission is $3.50 per adult and $2.25 per child., and there is a limit of 20 people. jan has $50 to spend. how many adults and how many children can jan invite?
Which equation could generate the curve in the graph below?y=3x^2-2x+1
Javier wants to inscribe a circle inside of the triangle ABC shown in the following figure. He begins by constructing the angle bisectors of angles A and B and finding their intersection at point D.
If Javier is trying to inscribe a circle inside of triangle ABC in as few steps as possible, which of the following steps would be the best step for him to take next?
1) Construct the perpendicular line from point D to the line BC.
2) Find the altitude from point C.
3) Use the distance from D to any of the triangle's vertices to set the width of the compass.
4) Construct the angle bisector of angle C.
Thank you :)
Which property justifies this statement? If 4x=20, then x=5. Division Property of Equality Reflexive Property of Equality Substitution Property of Equality Subtraction Property of Equality
Answer:
Option 1 - Division Property of Equality
Step-by-step explanation:
Given : If [tex]4x=20[/tex], then x=5.
To find : Which property justifies this statement?
Solution :
The equation is [tex]4x=20[/tex]
To make variable separate we have to remove 4 which is in multiple of variable x.
So, We divide both side by 4,
Applying division property of equality,
We can divide both sides of an equation by the same number and preserve equality.
[tex]\frac{4x}{4}=\frac{20}{4}[/tex]
[tex]x=5[/tex]
Therefore, The property justifies the statement is 'Division Property of Equality'.
So, Option 1 is correct.
John has six more nickels than dimes in his pocket for a total of 2.25 write an equation to determine the number of dimes, x in his pocket
A variable is: an instruction for the compiler a location in memory where a value can be stored a description of a value (such as a number or character) none of the above.
Final answer:
A variable is a name assigned to a quantity that can take on various values, and is used by mathematicians, economists, and statisticians in different contexts to represent data or elements of an equation.
Explanation:
A variable is the name given to a quantity that may assume a range of values. Mathematicians and economists often use variables in equations to represent different aspects of a problem or scenario. For example, in the equation of a line, commonly expressed as y = mx + b, the variables are 'x' and 'y'. Here, 'x' typically represents values on the horizontal axis, and 'y' represents values on the vertical axis, while 'b' is the y-intercept, and 'm' is the slope of the line. To understand how an equation with variables functions, we can look at a numerical example.
In statistics, variables can also refer to characteristics or measurements that can be determined for each member of a population. These variables can be numerical or categorical. A numerical variable, such as 'X' representing the number of points earned by a math student, allows for mathematical calculations like averaging. A categorical variable, like 'Y' indicating a person's political party affiliation, places individuals into categories and doesn't lend itself to mathematical operations like averaging.
How many degrees are in each interior angle of a regular pentagon? 50 72 108 120
The answer 108 degrees.
Answer: [tex]108^{\circ}[/tex]
Step-by-step explanation:
The sum of all the angles in a regular polygon with sides n , is given by :-
[tex]S_n=180^{\circ}(n-2)[/tex]
Now, the sum of all the angles in a regular pentagon with 5 sides will be :-
[tex]S_5=180^{\circ}(5-2)=180^{\circ}(3)=540^{\circ}[/tex]
We know that all the interior angles of a regular polygon are equal .
Therefore, the measure of each interior angle in a pentagon is given by :-
[tex]x=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]
Hence, the measure of each interior angle in a pentagon=[tex]108^{\circ}[/tex]
What is the simplified form of the following expression?
(n5)(n2)
Change each fraction to a decimal. If the division doesn’t end, round your answer to the nearest hundredth. a. 3⁄4 b. 7⁄16 d. 3⁄5 e. 7⁄40 f. 51⁄20
Answer:
a = 0.75
b= 0.4375
d= 0.6
e=0.175
f= 2.55
Step-by-step explanation:
By simple division method, the following answers can be calculated:
a.
=[tex]\frac{3}{4}[/tex]
=0.75
b.
= [tex]\frac{7}{16}[/tex]
=0.4375
d.
= [tex]\frac{3}{5}[/tex]
=0.6
e.
= [tex]\frac{7}{40}[/tex]
=0.175
f.
=[tex]\frac{51}{20}[/tex]
=2.55
Thus, the answer are :
a = 0.75
b= 0.4375
d= 0.6
e=0.175
f= 2.55
Answer:
A.0.75 B.0.4375 C. 14.4 D. 0.6 E. 0.175 F. 2.55
Step-by-step explanation:
Jim’s fundraiser BBQ needs to make at least $1000 in sales on Saturday. He sells hot dogs for $2 each and hamburgers for $3 each, and he wants to sell at least twice as many hamburgers as hot dogs. He brought 300 hot dogs and 800 hamburgers to sell. The graph shows the feasible region, where x represents the number of hot dogs sold and y represents the number of hamburgers sold. Which ordered pairs meet all the constraints for a successful fundraiser and make sense in context of the situation?
Select each correct answer.
(275, 0)
(100.5, 800.5)
(0, 350)
(250, 700)
(200, 350)
Mr. Chen goes to the post office to buy small and large boxes. He needs at least 4 small boxes. Altogether, he will buy no more than 15 boxes. The post office has 10 small boxes and 9 large boxes in stock. The graph shows the feasible region, where x represents the number of small boxes and y represents the number of large boxes. Which ordered pairs meet all the constraints and make sense in context of the situation? Select each correct answer. (6, 9) (7,10) (8,6) (9,8) Graph of lines and a shaded region on a coordinate plane whose axes are labeled x and y. A solid vertical line passes through 4 comma 0. Another solid vertical line passes through 10 comma 0. A solid horizontal line passes through 9 comma 0. A solid diagonal line passes through 0 comma 15, 4 comma 11, 6 comma 9, and 10 comma 5. The polygon whose vertices are at 4 comma 9, 6 comma 9, 10 comma 5, 10 comma 0, and 4 comma 0 is shaded.
If you have $45 and they take 2.1% of it how much do you have left ?
If you have $765 and they take 2.1% of it how much do you have left ?
If you have $1300 and they take 2.1% of it how much do you have left ?
Find the geometric mean of 6/5 and 120. Show in simplest radical form.
Over the last 4 years, Michael has earned $240 interest on an initial investment of $2,000. What simple annual interest rate is the bank paying on this account?
If Michael has earned $240 interest on an initial investment of $2,000. , then simple interest is 3% for paying in bank.
What is simple Interest?Simple interest is a quick and easy method of calculating the interest charge on a loan.
Given that,
I = interest = $240
P = principal (investment)=2000
R = simple interest rate=?
T = years= 4 years
Formula: I = PRT
Plug into formula:
240 = 2000(R)4
Multiply right side 2000×4
240 = 8000R
Divide both sides by 8000.
R = 240/8000
R = 0.03
Now multiply with 100
The simple annual interest rate was .03 or 3%.
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A child rides around on a ferris wheel twice. Click on the graph until the graph that best represents the given statement appears.
Answer:
The second graph.
Step-by-step explanation:
When the time is 0, the ride has not yet begun. Therefore the height above ground is nearly nothing.
As time increases, the ride goes up until it hits the top. The ride then goes back down nearly to the ground. This is one time around.
The ride then goes back up to the top and back down to the starting point.
This is the motion of the second graph, so the second graph is correct.
The second graph is used to represent A child rides around on a ferris wheel twice.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points
In the given graphs, the relationship between the height above ground and times are represented.
The second graph given is best suited to represent "A child rides around on a ferris wheel twice"
When the time is 0, the ride has not yet begun. Therefore the height above ground is nearly nothing.
As time increases, the ride goes up until it hits the top. The ride then goes back down nearly to the ground. This is one time around.
The ride then goes back up to the top and back down to the starting point.
This is the motion of the second graph, so the second graph is correct.
Hence second graph is used to represent the given situation.
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How many times will he get heads and tails when flipped 8 times?
Keenan is checking his bicycle’s wheel. The wheel has a radius of 21 cm, and its center is 56 cm above the ground. Keenan is rotating the wheel at a constant speed of 165°/s. The height of a point on the tire as a function of time is given by h = 56 + 21 sin(165t), where h is the height in centimeters and t is the time in seconds. Find h when t = 17 s. Round your answer to the nearest tenth of a centimeter.
HELP!!! I GIVE LOTS OF POINTS!! THE ANSWER IS NOT 3!!!!!!!!
In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in.
the answer would be 6 i did my calculations on paper then misplaced it but checked answer and it said 6
What x-value makes the set of ratios equivalent? Tiles 2 : 3 = 6 : x ,4 : 7 = x : 42 , 2x : 48 = 3 : 12, 12 : 15 = x : 20
Pairs691624
The missing x-values are 9, 24, 12, and 16, ensuring proportions remain equal in each ratio set.
To find the missing values that make the sets of ratios equivalent, we can use proportions.
1. Tiles 2 : 3 = 6 : x
Cross multiplying, we get: 2x = 18
So, x = 9
2. 4 : 7 = x : 42
Cross multiplying, we get: 7x = 168
So, x = 24
3. 2x : 48 = 3 : 12
Cross multiplying, we get: 12x = 144
So, x = 12
4. 12 : 15 = x : 20
Cross multiplying, we get: 15x = 240
So, x = 16
Therefore, the x-values that make the sets of ratios equivalent are:
1. x = 9
2. x = 24
3. x = 12
4. x = 16
Twice the difference between 6 times h and 3 gives 30
Fresh side grocery sells 7 bagels for $4.41. value mart sells 5 bagels for $3.60. how do the unit rates compare?
The unit rate for a bagel at Fresh side is $0.09 cheaper than the unit rate at
Value mart for bagels.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Fresh side grocery sells 7 bagels for $4.41.
∴ The cost of one bagel at Fresh side is $(4.41/7) = $0.63.
Value mart sells 5 bagels for $3.60.
∴ The cost of one bagel at Value mart is
= $(3.60/5).
= $0.72
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Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth Decay
y=100(1−12)^t
y=0.1(1.25)^t
y=((1−0.03)12)^2t
y=426(0.98)^t
y=2050(12)^t
A function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).
[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].
We have the following equation:
[tex]y=100(1-12)^t[/tex]
That can be written as:
[tex]y=100(-11)^t[/tex]
Recall that the definition of exponential functions establishes that:
[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].
That is:
[tex]a \ \mathbf{must} \ be \ greater \ than \ 1[/tex]
In this problem, [tex]a=-11[/tex], therefore this is not an exponential function.
The function:
[tex]y=0.1(1.25)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=0.1 \ and \ a=1.25[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. This means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 1. This represents a growth.
The function:
[tex]y=((1-0.03)12)^{2t}[/tex] can be written as:
[tex]y=11.64^{2t}[/tex]
and is an exponential function because is a function of the form [tex]f(t)=a^{bt} \\ \\ where \ a>0 \ and \ b \ constant[/tex]
So [tex]a=11.64 \ and \ b=2[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]2t[/tex], the function increases. As in the previous exercise, this means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 2. This represents a growth.
The function:
[tex]y=426(0.98)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=426 \ and \ a=0.98[/tex]. Since [tex]a \ is \ less \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function decreases. Here this means that [tex]y[/tex] decreases as [tex]t[/tex] increases as illustrated in Figure 3. This represents a decay.
The function:
[tex]y=2050(12)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=2050 \ and \ a=12[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. So in this function [tex]y[/tex] also increases as [tex]t[/tex] increases as illustrated in Figure 4. This represents a growth.
Answer:
1. isn't an exponential function
2. growths
3. growths
4. decay
5. growths
Step-by-step explanation:
The exponential functions has the form: y = k1*k2^(k3*t), where k1, k2 and k3 are a constants, and k2>0. Graph of exponential functions always decrease or always increase. To know if a function growths or decay just evaluate the function in 2 points, for example t = 0 and t = 1, and compare their results.
1.
y = 100*(1−12)^x = 100*(−11)^x
Since (-11) is negative, then y is not an exponential function
2.
y(0) = 0.1*(1.25)^(0) = 0.1
y(1) = 0.1*(1.25)^(1) = 0.125
y(1) > y(0) -> growths
3.
y(0) =((1−0.03)12)^2(0) = 1
y(0) =((1−0.03)12)^2(1) = 135.4896
y(1) > y(0) -> growths
4.
y(0) = 426(0.98)^(0) = 426
y(1) = 426(0.98)^(1) = 417.48
y(1) < y(0) -> decay
5.
y(0) = 2050(12)^(0) = 2050
y(1) = 2050(12)^(1) = 24600
y(1) > y(0) -> growths
The apartments in Brian's apartment house are numbered consecutively on each floor. The sum of his number and his next-door neighbor's number is 1419. What are the two numbers?
Tristan jogs a route that is 7/10 mile. If he wants to jog between 2 and 3 miles, how many times should he plan to run the route? Circle the letter for all that apply.
A. 2 times
B 3 times
C. 4 times
D. 5 times
Answer:
B 3 times
C. 4 times
Step-by-step explanation:
For Tristan to jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.
Considering the options given
A. 2 * 7/10 = 1.4 miles (this is not within the range)
B. 3 * 7/10 = 2.1 miles (this is within the range)
C. 4 * 7/10 = 2.8 miles (this is within the range)
D. 5 * 7/10 = 3.5 miles (this is not within the range)