It looks like the given function is
[tex]f(x) = \begin{cases}-3x + 7 & \text{if }x < 0 \\ x^2+7 & \text{if }x \ge0\end{cases}[/tex]
The two pieces of f(x) are continuous since they are polynomials, so we only need to worry about the point at which they meet, x = 0. f(x) is continuous there if
[tex]\displaystyle \lim_{x\to0^-} f(x) = \lim_{x\to0^+} f(x) = f(0) = 7[/tex]
To the left of x = 0, we have x < 0, so f(x) = -3x + 7 :
[tex]\displaystyle \lim_{x\to0^-} f(x) = \lim_{x\to0} (-3x + 7) = 7[/tex]
To the right of x = 0, we have x > 0 and f(x) = x² + 7 :
[tex]\displaystyle \lim_{x\to0^+} f(x) = \lim_{x\to0} (x^2 + 7) = 7[/tex]
So f(x) is continuous at x = 0, and hence continuous for all real numbers.
322 children came to the summer carnival. if each child was given 3 free ride passes for attending, how many free ride passes were given away?
Answer: 996 free ride passes were given away
Step-by-step explanation:
If each child was given 3 free ride passes, then you have to do 332 x 3 which is 996
Solve the linear system:
y = 3 – 4x
y= 4+ 1/2x
· (3,5)
·(-0.22, 3,89)
·(3.2, 5.6)
·(-1,7)
The answer is:
(-2/9, 35/9) in rounded decimal form is (-0.22, 3.89)
x = - 2 / 9 which in decimal form as well as rounded is -0.22
y = 35 / 9 which in decimal form as well as rounded is 3.89
Hope this helps...
What is the solution to this system of equations?
3x + 2y = -10
y = -x - 4
A. (-2,-2)
B. (-2,2)
C. (-18,14)
D. No solution
3x + 2y=-10 equation 1
y=-x -4 equation 2
use the substitution method of elimination to get the answer to the question.
*using substitution
substitute equation 2 in one and we get
3x +2(-x-4)=-10
3x- 2x-8=-10
x=-2 and y=-2
Answer:
B
Answer: Choice A
(-2, -2)
=============================================================
Explanation:
I'll use the substitution method to solve this system.
Replace y in the first equation with -x-4. This is because y = -x-4 is mentioned in the second equation.
So,
3x + 2y = -10
3x + 2( y ) = -10
3x + 2( -x-4 ) = -10 .... substitution
3x - 2x - 8 = -10
x - 8 = -10
x = -10+8
x = -2
Then use this to find y
y = -x-4
y = -(x) - 4
y = -(-2) - 4
y = 2 - 4
y = -2
We have x = -2 and y = -2 pair up together
They form the ordered pair solution (x, y) = (-2, -2)
This shows why Choice A is the answer.
Another way to see this is to graph each equation given using a tool like Desmos. It's a free graphing app.
See below.
The two lines intersect at (-2, -2) which is the solution.
Given that f(x)=x3, find
Answer:
(f ∘ f)(–1) = –1
Step-by-step explanation:
To solve a composite function, rewrite using brackets and solve from inside to outside.
(f ∘ f)(x) is the same as: f[f(x)]
Given that x = –1 in (f ∘ f)(–1), we are solving for:
f[f(–1)] = ?
Solve for f(–1) inside the square brackets first.
f(x) = x³
f(–1) = (–1)³ Simplify.
f(–1) = –1 Solved the inside.
Substitute f(–1) = –1 into the square brackets.
f[f(–1)] = f[–1]
Now, we can solve the outside.
Solve with the equation of the function, x³.
f[–1] = x³
f[–1] = [–1]³ Substitute x = –1.
f[–1] = (–1)³ Simplify.
f[–1] = –1 Final answer
Am thinking of a number,l take away 3 the results is 14.what number is it
What is the rule for the following sequence of numbers: 2, 7, 17, 37, ?
Answer:
The rule is "add 5, add 10, add 20" and the rule keeps doubling.
PLS HELP ITS WORTH 20 points
Answer:
x=3, Aly is correct.
Step-by-step explanation:
a. angle YWZ
b. ZY = 9
c. the triangles are congruent so 7x-20=2x-5, 5x=15, and x=3
A map's scale is 1 inch equals 50 miles. if new york city is 4 inches away from chelsea, ma, about how many miles is it from chelsea to new york city?
Answer:
200 miles
Step-by-step explanation:
Each inch represents 50 miles, so 4 times 1 inch will represent 4 times 50 miles.
4(1 in) ⇔ 4(50 mi)
4 in ⇔ 200 mi
It is about 200 miles from Chelsea to New York City according to the map.
Rita wants to save her babysitting money to buy a $249.99 camera. she makes $64.33 a month, and her fixed expenses are $34.50 a month. how do you think she should budget for the camera?
The number of months in which Rita has a budget to buy a camera is 8 and a half months if Rita wants to save her babysitting money to buy a $249.99 camera.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Rita wants to save her babysitting money to buy a $249.99 camera. she makes $64.33 a month, and her fixed expenses are $34.50 a month.
Let x be the number of months in which Rita has a budget to buy a camera.
The linear equation in one variable can be framed as follows:
(64.33 - 34.50)x = 249.99
29.83x = 249.99
x = 8.38 = 8.5
Thus, the number of months in which Rita has a budget to buy a camera is 8 and a half months if Rita wants to save her babysitting money to buy a $249.99 camera.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ5
Using the properties of Integer exponents, match each expression with its equivalent expression.
The -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.
What is integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
5⁻³ = 1/5³ = 1/125
-5⁻³ = -1/5³ = -1/125
(-5⁻³)⁻¹ = (-1/5³)⁻¹ = (-1/125)⁻¹ = -125
(-5⁻³)⁰ = 1 [tex]\rm (a^0 = 1)[/tex]
Thus, the -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.
Learn more about the integer exponent here:
brainly.com/question/4533599
#SPJ1
Answer:
[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]
[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]
[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]
[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]
Step-by-step explanation:
Exponent Property Rules:
⟹ Zero Exponent Property - ex: x⁰ = 1
An integer (excluding 0) with an exponent of zero equals one.
⟹ Negative Exponent Property - ex: x⁻ⁿ = [tex]{\dfrac{1}{x^n}[/tex]
Any number raised to a negative power is equivalent to the reciprocal of the number's positive exponent.
⟹ Power of Product Property - ex: (xy)ⁿ = xⁿ × yⁿ
To find the power of a product, multiply the power of each factor.
[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]
[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]
[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]
[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]
Learn more here:
brainly.com/question/13429877
brainly.com/question/21222719
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
The square root of the quantity 2 x minus 7 end quantity equals 1.
Answer:
Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .
1x − 2+1x + 2=4(x − 2)(x + 2)
(x − 2)(x + 2)(x − 2)+(x − 2)(x + 2)(x + 2)=4(x − 2)(x + 2)(x − 2)(x + 2)
(x−2)+(x+2)=4
2x=4
x=2
But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed! . Therefore, it cannot be a root of the original equation. So, 2 is an extraneous solution. So, the equation has no solutions.
Step-by-step explanation:
An equal when substitute x = 4, the solution is not extraneous the solution x = 4 is valid for the original equation.
The equation is: √(2x - 7) = 1
Step 1: Square both sides of the equation to remove the square root:
(√(2x - 7))² = 1²
Simplify:
2x - 7 = 1
Step 2: Add 7 to both sides to isolate the term with "x":
2x - 7 + 7 = 1 + 7
Simplify:
2x = 8
Step 3: Divide both sides by 2 to solve for x:
2x / 2 = 8 / 2
Simplify:
x = 4
Now, we have found that the solution for x is 4.
To check if the solution is extraneous, we need to substitute the value of x back into the original equation and see if both sides are still equal:
Original equation: √(2x - 7) = 1
Substitute x = 4:
√(2(4) - 7) = 1
Simplify:
√(8 - 7) = 1
√1 = 1
1 = 1
To know more about equation here
https://brainly.com/question/29657983
#SPJ3
Plsss HELP ASAP WILL GIVE POINTS AND BRAILEST I WILL DO IT ASAP
Jayden wants to fence a rectangular area for his garden. The length of the garden should be at least 4 ft shorter than the width. And the distance around should be no more than 32 ft. Let x = length Let y = width Write two inequalities that model this problem and enter them below.
The two inequalities will be L>W-4 and (L x W) ≤ 32.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
It is given that:-
The length of the garden should be at least 4 ft shorter than the width
The distance around should be no more than 32 ft
The two inequalities will be as follows:-
a)The length of the garden should be at least 4 ft shorter than the width
L>W-4
b)The distance around should be no more than 32 ft
(L x W) ≤ 32.
Hence the two inequalities will be L>W-4 and (L x W) ≤ 32.
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ1
What is equal to 3 tons 2000 pounds 5000 pounds 6000 pounds 300 pounds
Answer:
6000 pounds or lbs.
Step-by-step explanation:
A ton=2000 lbs.
Hope this helps! ;-)
Determine the following for each sinsusoidal functions
Answer
whats the question
Step-by-step explanation:
Employees of the sports department at a television station want to measure the number of viewers for a particular exercise program. They call the homes of all the members of a nearby health club. Why might this be a biased sample?
A.The station does not include everyone in the viewing area.
B.The station does not include people all across the country.
C.People who belong to a health club may have many television sets in their homes.
D.People who belong to a health club may be more likely to watch an exercise program.
Answer:
d
Step-by-step explanation:
what is the GCF of 5 and 14
Answer:
1, because 5 and 14 are divisible by no other number except themselves in this instance only, and for this case, that only number is 1.
Your answer is 1.
Hope this helps
cuanto es: −2(−5n+6)+5(2−7n)
Answer:
here is the required answer hope it help u
Step-by-step explanation:
−2(−5n+6)+5(2−7n)
10n-12+10-35n
-25n-2
At Everyday Donuts, 3 of the last 6 donuts sold had sprinkles. Considering this data, how many of the next 10 donuts sold would you expect to have sprinkles?
__5___Sprinkles
THAT IS THE ANSWER
If 10 donuts are sold. Then the expected value of the number of sprinkles will be 5.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
The expected value will be given as
E(X) = np
At Everyday Donuts, 3 of the last 6 donuts sold had sprinkles. Considering this data.
If 10 donuts are sold.
Then the number of the sprinkles will be
The probability will be
p = 3/6
p = 0.5
n = 10
Then the expected value of the number of the sprinkles will be
E(x) = 10 x 0.5
E(x) = 5
Learn more about binomial distribution here:
https://brainly.com/question/13609688
#SPJ1
help me pls pls pls pls pls pls
Answer:
2.25 square inches
Step-by-step explanation:
SOLUTION,
HERE,
AREA OF SQUARE = L²
=(1.5)²
= 2.25 INCHES²
Answer:
2.25 inches
Step-by-step explanation:
The area of a square is two of its sides multiplied together. Each side is 1.5 inches. If you multiply 1.5x1.5, you get 2.25 inches.
The cost of 8 pounds of watermelon is $19.60. How many pounds of watermelon can a
person buy with $53.90?
Answer:
22 pounds of watermelon
Step-by-step explanation:
First find cost per pound
19.60/8=2.45
$2.45 per pound
Then divide $53.90 by $2.45 to determine how many pounds you can buy
53.90/2.45=22
22 pounds of watermelon
What number am i?7 times two digit number equals 4 times number with the digit reversed .the sum of the digits is 3.
Answer:
12
Step-by-step explanation:
7 times 12 is 84. 4 times 21 is 84. The digits have a sum of 3.
Find the approximate volume of a cylinder that has a radius of 4 inches and a height of 6 inches. Use 3.14 for Pie
150.72 cubic inches
163.28 cubic inches
301.44 cubic inches
452.16 cubic inches
Round this number to the nearest one.
87.6
ANWER:
rounded o the nearesr tens is 88.6
Answer:
88
Step-by-step explanation:
Because 6 is greater than 5 it will rounded off and 87.6 = 88
complete the process of solving the equation 5t+8=63 subtract 8 from both sides of the given equation
Answer:
t=11
Step-by-step explanation:
so to start we subtract 8 from both sides to get...
5t=63-8
5t=55
now we just divide 5 from both sides so we just have t
t=11
Answer:
t=11
Step-by-step explanation:
Subtract 8 from both sides to get 5t=55 then divide by 5 to get t=11
The volume of this cone is 140 cm3
Find the perpendicular height, c.
Give your answer rounded to 1 DP.
х
7 cm
Answer:
x = 10.9 cm
Step-by-step explanation:
Formula for a cone
Volume (cone) = 1/3 × π × (radius)² × heightHere, we are given :
Diameter = 7 cmVolume = 140 cm³Solving
140 = 1/3 × 22/7 × (7/2)² × (x)420 = 11 × 7/2 × (x)77x = 840x = 840/77x = 10.9 cm (1 DP)Answer:
x ≈ 3.6 cm
Step-by-step explanation:
the volume (V) of a cone is calculated as
V = πr²h ( r is the radius and h the perpendicular height )
here diameter = 7 , so r = 7 ÷ 2 = 3.5 , V = 140 and h = x , then
π × 3.5² × x = 140
π × 12.25x = 140 ( divide both sides by 12.25π )
x = [tex]\frac{140}{12.25\pi }[/tex] ≈ 3.6 cm ( to 1 dec. place )
Determine the equation of the circle graphed below.
Answer:
(x-6)^2+(y-5)^2=16
Step-by-step explanation:
Focus on the center point ONLY and change the signs of those numbers to negative for your equation. Count how much the outer circle moves back (which is 4) and times that as your radius
Which number has 3 significant
figures?
A. 15.233
B. 153.2
C. 5.24399
D. 57.2
Answer:
b because it is
Step-by-step explanation:
153.2 is a cool number
Find the constant of proportionality for the relationship plotted in the distance versus time graph shown below, and hence predict the distance covered at 10 seconds.
Answer: The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.
Step-by-step explanation:
what is this? please help
Answer:
4
Step-by-step explanation:
Mean is another way to say the average of a set of numbers. To find the average you need to add all the numbers in the set together, and then divide by the amount of numbers that where given.
In this case:
6 + 8 + 2 + 0 + 4 + 5 + 3 = 28
there are 7 numbers given in the set, so you divide 28 by 7 to get your mean.
28 / 7 = 4
Answer:
4
Step-by-step explanation:
To find the mean of a set of numbers, you add up all the numbers and then divide them by the amount of numbers there are.
So, let's add up these numbers.
6 + 8 + 2 + 0 + 4 + 5 + 3 = 28
Now, there are a total of 7 numbers, so we divide 28 by 7.
28 / 7 = 4
Therefore, the mean of this data set is 4. I hope this helps! Have a lovely day!!
Does anybody know the other two? QSRT is a Rectangle find the lengths of the following sides
Answer:
/TS/=12cm
/QP/=
/QR/²=16²+12²
/QR/²=256+144
/QR/²=400
/QR/=√400
/QR/=20
/QP/=20/2=10
let /PT/ be x
hyp²=opp²+adj²
16²=20²+x²
x²=400-256
x²=144
x=√144
x=12.