The given statement "The x-intercept of a function y = f(x) are the real solutions of the equation f(x) = 0." is True because the x-intercepts of a function y = f(x) are points on graph where function crosses x-axis.
At these points, the value of y (f(x)) is equal to 0. In other words, the x-intercepts are the real solutions of the equation f(x) = 0.
To find the x-intercepts of a function, we set f(x) equal to 0 and solve for x. The solutions to this equation will be the x-coordinates of the x-intercepts.
For example, given the function y = 2x - 6, to find the x-intercept, we set y (f(x)) equal to 0:
0 = 2x - 6
Now, solve for x:
2x = 6
x = 6 / 2
x = 3
The x-intercept is (3, 0) since at x = 3, the value of y (f(x)) is 0.
In conclusion, the statement is true. The x-intercepts of a function y = f(x) are the real solutions of the equation f(x) = 0.
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Find the center of the circle whose equation is (x-2)^2(y-4)^2=9.
A.(-2,-4)
B.(2,4)
C.(4,2)
Answer:
B.(2,4)
Step-by-step explanation:
The equation for a circle is written as
(x-h)^2 +(y-k)^2 = r^2
where (h,k) is the center and r is the radius
(x-2)^2+(y-4)^2=9.
Rewriting this equation
(x-2)^2+(y-4)^2=3^2
The center is at (2,4)
what decimal is equivalent to negative 3/8
Answer:
-6/16
Step-by-step explanation:
Step 1: Find equivalent to -3/8
(-3*2) / (8*2)
-6/16
Answer: -6/16
Answer:
-0.375
Step-by-step explanation:
If you have a scientific calculator just plug in [tex]-\frac{3}{8}[/tex] then switch it to decimal form
[tex]-\frac{3}{8} = -0.375[/tex]
If you need help going from fraction to decimal form all you need to do is divide -3 by 8 = -0.375
x + 5 = 2(7 + x) in sentence form
Answer:
x plus 5 equals 2 times brackets 7 plus x
Step-by-step explanation:
How many solutions are there to this equation 3x(x-4)+5-x=2x-7
Answer:
2 solutions
Step-by-step explanation:
I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...
x = 1x = 4__
To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:
3x(x -4) +5 -x -(2x -7) = 0
3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses
3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms
3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor
The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.
__
Alternate method
Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...
d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c
d = (-15)^2 -4(3)(12) = 225 -144 = 81
This positive value means the equation has 2 real solutions.
Solve x2 + 2x + 9 = 0. (2 points) x equals negative 2 plus or minus 4 I square root of 2 x equals negative 2 plus or minus 2 I square root of 2 x equals negative 1 plus or minus 4 I square root of 2 x equals negative 1 plus or minus 2 I square root of 2
Answer:
it is D (-1 + or - 2i square root of 2)
Step-by-step explanation:
just took test
The value of x obtained after solving the equation x² + 2x + 9 = 0 will be x = -1 ±2i √(2)(x equals negative 1 plus or minus 2 I square root of 2).Option D is correct.
What is a quadratic equation?Any equation of the form ax²+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
it is given that,
x² + 2x + 9 = 0
Rearrange the equation as
x² + 2x = - 9
Add 1 on both sides of the equation,
x² + 2x +1 = - 9 +1
x² + 2x +1 = - 8
(x+1)² = -8
Taking square root,
(x+1) = √ -8
Subtract 1 from both sides,
x+1-1 = -1 ±√(-8)
x = -1 ±√(-8)
√(-8) can be written as,
√(-8) = 2i√2
Substitute the values,
x = -1 ±2i sqrt(2)
Thus, the value of x obtained after solving the equation x² + 2x + 9 = 0 will be x = -1 ±2i √(2)(x equals negative 1 plus or minus 2 I square root of 2).Option D is correct.
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Solve -8(2z-3) Equivalent to -16z-3
Answer:
-16z + 24
Step-by-step explanation:
Apply the Distributive Property of Multiplication:
-8(2z-3) = -16z + 24
Answer:
-27
Step-by-step explanation:
-8 ( 2z - 3 ) = -16z - 3
distribute -8
-16z + 24 = -16z - 3
add 16z on right side
z + 24 = - 3
subtract 24 on left side
z = -27
Hopefully this helps :)
PLEASE be respectful and don't do this for the points!
At the mission museum Mrs. Perez visited over break, there is a pond like the one below that has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle with a radius of 10 m. The inner edge of the sidewalk is a circle with a radius of 8 m.
(a) Write and simplify an expression for the exact area of the sidewalk. (4 points possible)
(b) Find the approximate area of the sidewalk. Use 3.14 to approximate π. (3 points possible)
Answer:
The formula for area of a circle is : A = PI x r^2
A) find the are of the two circles, subtract the two to find the area of the side walk:
Outside circle: A = PI x 10^2
Area = 100PI
Inner circle: A = PI x 8^2
Area = 64PI
Area of sidewalk:
100PI - 64 PI = 36PI
B) replace PI with 3.14:
Area = 36 x 3.14 = 113.04 square meters.
Step-by-step explanation:
Hope this helped.
Find the minimum value of
C = 4x + 3y
Subject to the following constraints:
x 20
y20
2x + 3y > 6
3x – 2y = 9
x + 5y = 20
Final answer:
To find the minimum value of C given the constraints, one must plot these constraints, find the feasible region's vertices, evaluate C at each vertex, and select the minimum value obtained. The minimum value of C = 4x + 3y, given the constraints and the corrected understanding of them, is 29.
Explanation:
To find the minimum value of C = 4x + 3y subject to the given constraints, we need to first correct the constraints provided, as it seems there might be a misunderstanding in how they were presented. Assuming the constraints meant to be:
1. [tex]\(x \geq 0\)[/tex]
2. [tex]\(y \geq 0\)[/tex]
3. [tex]\(2x + 3y \geq 6\)[/tex]
4.[tex]\(3x - 2y = 9\)[/tex]
5.[tex]\(x + 5y = 20\)[/tex]
We will solve the system of equations (4) and (5) to find the values of x and y that satisfy these conditions, and then we will check if these values satisfy all other constraints including (3). If they do, we'll use these values to find C.
Solving the equations simultaneously:
From equation (4): 3x - 2y = 9
From equation (5): x + 5y = 20
Multiplying equation (5) by 3 to eliminate x, we get:
3(x + 5y) = 3(20)
3x + 15y = 60
Now, subtract equation (4) from this result to eliminate x:
3x + 15y - (3x - 2y) = 60 - 9
3x + 15y - 3x + 2y = 51
17y = 51
y = 3
Substitute y = 3 into equation (5) to find x:
x + 5(3) = 20
x + 15 = 20
x = 5
Now, check if [tex]\(x = 5\) and \(y = 3\) satisfy the constraint \(2x + 3y \geq 6\):[/tex]
[tex]\[2(5) + 3(3) \geq 6\][/tex]
[tex]\[10 + 9 \geq 6\][/tex]
[tex]\[19 \geq 6\] - This is true.[/tex]
Since x = 5 and y = 3 satisfy all the constraints, we can calculate \(C\):
C = 4x + 3y
C = 4(5) + 3(3)
C = 20 + 9
C = 29
Therefore, the minimum value of C = 4x + 3y, given the constraints and the corrected understanding of them, is 29.
Translate six minutes less then bobs time in a algebraic expression
Answer:
B-6
Step-by-step explanation:
If (B) represents Bob's time, six minutes less than Bob's time is B-6=T where (T) represents the time six minutes less than Bob's time.
The phrase 'six minutes less than Bob's time' can be translated into the algebraic expression 'B - 6', where 'B' represents Bob's time.
Explanation:The given phrase 'six minutes less than Bob's time' can be written as an algebraic expression. Algebraic expressions are mathematical phrases containing numbers, variables (like 'Bob's time'), and operations. In this case, we can symbolize 'Bob’s time' as a variable, let’s choose 'B'. Then 'six minutes less than Bob's time' translates to 'B - 6' in an algebraic expression. That’s because 'less than' implies subtraction and it always means you subtract from the number or variable stated after the expression, in this case, 'Bob's time' or 'B'.
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An engineer scale model shows a building that is 3 inches tall. If the scale is 1 inch = 600 feet, how tall is the actual building in feet ?
The actual height of building is 1800 feet.
Step-by-step explanation:
Given,
Height of building in model = 3 inches
Scale used by engineer;
1 inch = 600 feet
Therefore;
Actual height of building = Height in model * Scale used
Actual height of building = 3 * 600
Actual height of building = 1800 feet
The actual height of building is 1800 feet.
A function, f, passes through the points (1,1), (2,7) and (3,25). A function, g, passes through the points (1,36), (2,43) and (3,50).
Select the correct answer.
Answer:
As the value of x increases, the value of f(x) will eventually exceed the value of g(x) is the correct option.
Step-by-step explanation:
A function, f, passes through the points (1,1), (2,7) and (3,25).
The equation of the function 'f' can be written as:
The f(x) is obtained by:
[tex]f\left(x\right)=3f\left(x-1_\right)+4[/tex]
[tex]f\left(4\right)=3f\left(3\right)+4=\left(25\times 3\right)+4=75+4=79[/tex]
A function, g, passes through the points (1,36), (2,43) and (3,50).
The g(x) is obtained by:
[tex]g\left(x\right)=g\left(x-1\right)+7[/tex]
[tex]g\left(4\right)=g\left(4-1\right)+7=g\left(3\right)+7=50+7=57[/tex]
So, value of f(x) at x = 4 exceeds the value of g(x) at x = 4.
Therefore, as the value of x increases, the value of f(x) will eventually exceed the value of g(x) is the correct option.
Kendra gets a paycheck of $300 after 5 days of work. At this rate, how much does she get paid for working 24 days?
Answer:
$1440
Step-by-step explanation:
First, find the unit rate by dividing 300 by 5, which equals 60. So, Kendra earns $60 in one day. Then, multiply 60 by 24, which equals 1440. So, Kendra makes $1440 in 24 days. Hope this helped!
Answer:1440 dollars earned In 24 hours
Step-by-step explanation: first divide 300 by 5 to get 60 then multiply 60 by 24 to get 1440
Multiplying Polynomials, Simplify with Work Shown.
3x^2 (4x^3 + 9x^2 - 8x + 4)
20 Point offer for real, complete answer.
Answer:
12x^5+27x^4-24x^3+12x^2:
Step-by-step explanation:
hope it helps
what is the P(T,H,T,H) on 4 flips of a coin?
i need help
Answer:
1/16
Step-by-step explanation:
Each coin flip is an independent event so the probabilities are independent
P(T,H,T,H) = P(T) P(H) P(T) P(H)
= 1/2 * 1/2 * 1/2 * 1/2
= 1/16
how to graph -5x + y = 1
Answer:
look on the graph i gave you
Step-by-step explanation:
A shoreline is eroding at a rate of 1/3 foot per 3 months. How many feet are eroding per year?
The number of feet the shoreline is eroding per year is 1 ⅓ feet.
How many feet are eroding per year?
Rate of shoreline eroding per 3 months = 1/3 foot
Number of 3 months in a year = 12 months / 3 months
= 4
Number of feets of the shoreline eroding per year = Rate of shoreline eroding per 3 months × Number of 3 months in a year
= 1/3 × 4
= 4/3 feet per year
Therefore, the shoreline erodes 1⅓ feet per year
Help show the work for
5.2 divide by 0.13
Answer:
40
Step-by-step explanation:
0.13 ⟌5.2 (We can move 0.13 over two spots)
13⟌520 (We move the decimal two spots because of previous)
We have
₄ ₀
13⟌520
- 52
______
0 0
- 0
______
0
So 40 is our final answer.
The value of (5.2/0.13) is 40 obtained by removing the decimals.
What are some alternative names for arithmetic operations?Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
Given, 5.2 is divided by 0.13, which is (5.2/0.13).
Now we can multiply both the numerator and the denominator by 100.
∴ (5.2/0.13)×(100/100).
= 520/13.
= 40.
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Which of the binomials below is a factor of this trinomial?
x2 + 14x+ 40
2 + 10
Β. χ+ 4
C. x-9
D. χ + 14
SUBMIT
Solution:
Given is:
[tex]x^2 + 14x + 40[/tex]
Factor the above polynomial
From given,
[tex]x^2 + 14x + 40[/tex]
[tex]Split\ the\ middle\ term\\\\x^2 + 4x + 10x + 40\\\\Break\:the\:expression\:into\:groups\\\\\left(x^2+4x\right)+\left(10x+40\right)[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\mathrm{:\quad }x\left(x+4\right)\\\\x(x + 4) + (10x + 40)\\\\\mathrm{Factor\:out\:}10\mathrm{\:from\:}10x+40\mathrm{:\quad }10\left(x+4\right)\\\\x(x + 4) + 10(x + 4)\\\\\mathrm{Factor\:out\:common\:term\:}x+4\\\\\left(x+4\right)\left(x+10\right)[/tex]
Thus, the binomials factor of given is (x + 4) and (x + 10)
the first term of an arithmetic sequence is -27. the common difference of the sequence is 6. What is the sum of the first 30 terms
Answer:
1800
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = - 27 and d = 6, thus
[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex] [ (2 × - 27) + (29 × 6) ]
= 15( - 54 + 174)
= 15(120)
= 1800
The sum of the first 30 terms of the arithmetic sequence, is 1800.
In an arithmetic sequence, the sum of the first n terms can be calculated using the formula:
Sum = n/2 × (2a + (n-1)d), where:
n is the number of termsa is the first termd is the common differenceGiven:
First term (a) = -27Common difference (d) = 6Number of terms (n) = 30Plugging in these values, we get:
Sum = 30/2 × (2(-27) + (30-1) × 6)
Calculating step-by-step:
Calculate the first part: 30/2 = 15Calculate inside the parentheses: 2(-27) + (30-1)6 = -54 + 29*629 × 6 = 174-54 + 174 = 120Final calculation: 15 × 120 = 1800Therefore, the sum of the first 30 terms of the arithmetic sequence is 1800.
On a container ship there were 30 small containers that each weighed 3 tons, 20 medium
containers that each weighed 5 tons, and 10 large containers that each weighed 8 tons.
Find the mean weight of the containers on this ship.
The mean weight of the containers on the ship is found by adding the total weight of all the containers (270 tons) and dividing by the total number of containers (60), giving a mean of 4.5 tons per container.
Explanation:In this problem, we are asked to find the mean weight of the containers on a ship. The mean is the average value of a set of numbers, found by adding all the numbers together and then dividing by the quantity of numbers.
First, let's compute the total weight of all the containers. The weight of the 30 small containers are 30 containers * 3 tons each = 90 tons. The weight of the 20 medium containers are 20 containers * 5 tons each = 100 tons. The weight of the 10 large containers are 10 containers * 8 tons each = 80 tons.
So, the total weight of all the containers is 90 tons + 100 tons + 80 tons = 270 tons. And the total number of containers is 30 + 20 + 10 = 60 containers.
So, the mean weight of the containers is 270 tons Total Weight / 60 = 4.5 tons/container. So, the mean weight of the containers on the ship is 4.5 tons.
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You buy a watch for $60. Your friend buys the same watch a month later. It is now sold at a discount of 15%. What is the new sale price?
Answer:
$9.00
Step-by-step explanation:
~~~~Hey there~~~~
1. Since it was 15% discount, that means you have to solve 15% of 60, which is equivalent to 0.15 x 60.
2. Since the product of 0.15 and 60 is 9, then 9 is your answer.
3. Your final answer is $9.00
Hope this helped!
~delightedsunrise8
Answer:
56
Step-by-step explanation:
You would first do 60 divide by 15 and get 4. Then you subtract 4 from 60 and get 56 as your answer.
» How many ounces are in 1 cup?
1)
The unit rate is
ounces per cup.
Answer:
8 oz. per cup
Step-by-step explanation:
15^1/5 rewrite in radical form
Answer:
[tex]\sqrt[5]{15}[/tex]
Step-by-step explanation:
A number to 1/5 is the [tex]\sqrt[5]{n}[/tex]
A number to 1/3 is the [tex]\sqrt[3]{n}[/tex]
So, since the number is 15 to the 1/5, it is [tex]\sqrt[5]{15}[/tex]
Answer: [tex]\sqrt[5]{15}[/tex]
Answer:
[tex]15^{\frac{1}{5} } = \sqrt[5]{15}[/tex]
Step-by-step explanation:
recall that
[tex]a^{\frac{1}{b} } = \sqrt[b]{a}[/tex]
if we apply this to our case,
[tex]15^{\frac{1}{5} } = \sqrt[5]{15}[/tex]
Kendra is babysitting her cousins, who are quintuplets. At snacktime, Kendra puts 5 plates on the table. She cuts apples into slices and places an equal number of slices on each cousin's plate. There is a total of 35 apples slices on the plates.
Which equation can you use to find the number of apple slices s on each plate?
Answer:
Kendra is watching over 5 children. She wants to be sure that they each have an even number of apple slices. There are 35 apple slices total. She wants to take 35 and put it equally into 5 groups.
Your equation would be 5s=35, where s would be the total amount of apple slices on each plate.
To solve this equation you would divide both sides by 5 to get 7. s=7 (35/5=7)
Each quintuplet would be 7 apple slices.
Hope this helps ;)
Two lines intersect to form the angles shown.
Which statements are true?
Select each correct answer.
m<1=100 degrees
m<3=80 degrees
m<2= 80 degrees
m<3=m<1
Answer:
m∠3=80 degrees
m∠3=m∠1
Step-by-step explanation:
When two lines intersect, the opposite angles are equal. They are called vertical angles. That means for this problem:
m∠1 = m∠3 *Last option is true
m∠2 = 100° *Third option is false
A straight line is always 180°. When it is cut up, the sum of the angles is 180°. They are called suppementary angles. These are supplementary:
100° + m∠3 → m∠3 = 80° *Second option is true
m∠1 + 100° → m∠1 = 80° *First option is false
m∠1 + m∠2 → One or the other is 100° and 80°
m∠2 + m∠3 → One or the other is 100° and 80°
A certain forest covers an area of 8.25%. Suppose that each year this area decreases by 4800km^2. What will the area be after 5 years?
Solution:
The decreasing function is given as:
[tex]y = a(1-r)^t[/tex]
Where,
y is future value
a is initial value
r is decreasing rate
t is number of years
From given,
a = 4800
t = 5
[tex]r = 8.25 \% = \frac{8.25}{100} = 0.0825[/tex]
Therefore,
[tex]y = 4800(1 - 0.0825)^5\\\\y = 4800 \times 0.9175^5\\\\y = 4800 \times 0.6501\\\\y = 3120.841[/tex]
Thus the area after 5 years is 3120.841 square kilometer
Decimal equivalent to 11/44
Answer:0.25
Step-by-step explanation:
11/44 is equal to 1/4
1/4 is 0.25
First, we need to figure out how much you want to borrow. You said you wanted to spend $5,000, and you will put $500 down. Based on that, we can estimate your taxes to be $340. Put those numbers to see how much money you will need for your loan.
Answer: You will need $4,160 for the loan.
The money that will need for the loan is $4160.
What is down payment?A down payment is a sum of money the buyer pays at the outset of a large transactions. The down payment represents a portion of the total purchase price, and the buyer will often take out a loan to finance the remainder.
For the given situation,
The total amount wanted to spend = $5000
Down payment = $500
Tax amount = $340
Money that will need for the loan can be calculated as
⇒ [tex]5000-(500+340)[/tex]
⇒ [tex]5000-840[/tex]
⇒ [tex]4160[/tex]
Hence we can conclude that the money that will need for the loan is $4160.
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3) Paul bought 2 muffins, 2 brownies and I cookie at a bake sale. The muffins cost $1.30
each, the brownies cost $0.75 a piece and the cookie was $0.50. If he paid with a twenty
dollar bill, how much change should he get back?
Answer:
$15.40
Step-by-step explanation:
1.30 × 2 = 2.60
0.75 × 2 = 1.50
2.60 + 1.50 + 0.50 = 4.60
20 - 4.60 = 15.40
4 is to 6 as 10 is to what
Answer:
x = 15
Step-by-step explanation:
Step 1: Make an expression
4/6 = 10/x
Step 2: Cross multiply
4/6 = 10/x
4x = 60
Step 3: Divide both sides by 4
4x / 4 = 60 / 4
x = 15
Answer: x = 15
Answer:
15
Step-by-step explanation:
4 is to 6 as 10 is to what
Represent the unknown number as x and write as a ratio
4:6 = 10:x
Write as fractions
4/6 = 10/x
Cross-multiply
4x = 60
Divide both sides of the equation by 4
x = 15
15
Hope this helps :)