The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
What are the domain and range of a function?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
if you use the foil method it will come out to -(x^2+2x+1)+4. then distribute the negative and simplify the equation (add the four) the equation comes out to be -x^2-2x+3.
The vertex is at -b/(2A).
The vertex is at x=2/(2*-1), which is -1. plug -1 into the original equation to find y, (y=-(-1)^2-2*(-1)+3) which is y=4. so the vertex is at (-1,4).
since the parabola opens down (negative a value) and has a maximum at 4, y is always less than or equal to 4. x is all real numbers as it goes on forever. so b is your answer.
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the following table shows how a certain man spent his 1992 annual salary rent=18% savings=12% maintenance=25% food=30% taxes=5% others=10% a) represent this information on the pie chart b) find his savings at the end of the year if his annual salary was gh¢6,000.00
a) The pie chart that represents this information is given at the end of the answer.
b) The amount that represents his savings is of: gh¢ 720.
What is a pie chart?A pie chart is a graph in which the values of each measure in the data-set assume a percentage equivalent to the percentage of these values in the circular graph.
In the context of this problem, these percentages are given as follows, as stated from the text:
Rent: 18%.Savings: 12%.Maintenance: 25%.Food: 30%.Taxes: 5%.Others: 10%.All these percentages are inserted on the image given at the end of the answer, which represents the pie chart.
The percentage of savings is of:
12%.
Hence the amount of savings is given by the multiplication of 0.12 by 6,000. as follows:
0.12 x 6000 = gh¢ 720.
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Eva bought seven and one-half pounds of chocolate chips. She used three and three-fourths pounds in some cookies and two and five-sixths pounds in some muffins. How many pounds of chocolate chips were left?
three-twelfths pounds
eleven-twelfths pounds
one and two-twelfths pounds
one and seven-twelfths pounds
The pounds of chocolate chips that were left is B. eleven-twelfths pounds
How to calculate the fraction?Given that Eva bought seven and one-half pounds of chocolate chips. She used three and three-fourths pounds in some cookies and two and five-sixths pounds in some muffins
The fraction left will be:
= Total pounds bought - The amount used
= 7 1/2 - (3 3/4 + 2 5/6)
= 7 1/2 - (3 9/12 + 2 10/12)
= 7 1/2 - 6 7/12
= 11/12
In conclusion, the correct option is B.
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Given: <1 and <2 are complementary. <1 and <3 are complementary
Prove: 22 = 23
Complete the proof.
Answers:
1st box: [tex]\boldsymbol{90}[/tex]
2nd box: [tex]\boldsymbol{90}[/tex]
3rd box: [tex]\boldsymbol{\text{m}\angle 2 = \text{m}\angle 3}[/tex]
===============================================
Explanation:
Complementary angles form a corner. Note that "complementary" and "corner" both start with "C" to help remember the rule.
By "corner", I refer to a 90 degree angle.
Since [tex]\angle 1\text{ and } \angle 2[/tex] are complementary, we know that [tex]\text{m}\angle 1+\text{m}\angle 2 = 90[/tex] simply by the definition of what it means to be complementary.
---------------
Through similar logic, [tex]\angle 1\text{ and } \angle 3[/tex] are complementary which means [tex]\text{m}\angle 1+\text{m}\angle3 = 90[/tex]
We can then equate the left hand sides (LHS) of both equations since both LHS expressions equal 90. This is an example of the substitution property in action.
That's how we end up with [tex]\text{m}\angle 1+\text{m}\angle 2 = \text{m}\angle 1+\text{m}\angle 3[/tex]
After this point, subtract [tex]\text{m}\angle1[/tex] from both sides to cancel them out. We'll be left with [tex]\text{m}\angle 2 = \text{m}\angle 3[/tex], which concludes with [tex]\angle 2 \cong \angle 3[/tex] to show the two angles are congruent.
Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons. Select the equation that represents the given situation and find the number of hours of Sophia's lesson.
The equation to represent the situation is y = 15 + 30x.
The number of hours Sophia used for the guitar training after paying 75 dollars is 2 hours.
How to use equation to represent situations?Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons.
The equation that can be used to represent the given situation is as follows:
let
x = number of hours used for the training
y = total cost
Therefore,
y = 15 + 30x
Now, Sophia's mother spent 75 dollars for her daughters training. Let's find the hours Sophia used.
Therefore,
75 = 15 + 30x
75 - 15 = 30x
60 = 30x
divide both sides by 30
x = 60 / 30
x = 2
Therefore, she used 2 hours for the training.
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Find the area of the floor of a square room in square metres of which each side is 800 cm
Answer:
A = 64 m²
Step-by-step explanation:
Step 1: What is the question asking
A = ? m²Step 2: What is known
sides = 800 cmStep 3: Conversion
convert 800 cm to metersKilo, Hecto, Deca, Base, Deci, Centi, Milli800 cm = 8 mStep 4: Answer the question/solve for the area
Area of a square = s²A = s² = 8² = 64 m²HELP! ASAP!! 50 points if you help!
Heidi earned $30 in commission.
The amount of money that the store made from Heidi's sales is equal to $720.
How to calculate commission.In this exercise, you're required to determine the amount of money earned by the salesperson as commission based on the price at which she sold a jewelry.
Mathematically, the amount of commission earned on the sales of a product can be calculated by using this mathematical expression:
Commission = Percent commission × Sales price
Given the following data:
Percent commission = 4%
Sales price = $750.
Substituting the given parameters into the formula, we have;
Commission = 4/100 × 750
Commission = 0.04 × 750
Commission = $30.
Next, we would determine the amount of money that the store made from her sales:
Sales = $750 - $30.
Sales = $720.
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Anatoliy has a combination of 104 nickels and quarters totaling $22. Which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, anatoliy has? n = q = 22 0. 05n + 0. 25q = 104 n + q = 104 5n + 25q = 22 n + q = 104 0. 05n + 0. 25q = 22 n + q = 22 5n + 25q = 104.
The equation which is correct is :
n + q = 104
Since we have given that:
Number of nickels and quarters = 104
Total amount from them = $22
Let the number of nickels be 'n'
Let the quarters be 'q'
So, the equation will be
n + q = 104 -------------------------------------------- (1)
Since we know that
value of nickels = 0.05 dollars
Value of quarters = 0.25 dollars
So, the equation will be
0.05n + 0.25q = $22 ------------------------------------ (2)
So, there are two system of linear equation can be used to find the number of nickels and the number of quarters. i.e.
n + q = 104
0.05n + 0.25q = $22
Using elimination we can find the value of n and q :
0.05( n + q =104 )
⇒0.05n+0.05q=5.2-----------(3)
Now, from equation (2) and (3), we get,
0.05 n + 0.05q = 5.2
0.05 n + 0.25q = 22
(-) (-) (-)
------------------------------------
0 + 0.2q = 16.8
q = 16.8 ÷ 0.2
q = 84
Putting the value of q = 84 in equation (1),
n + q = 104
⇒ n + 84 = 104
⇒ n = 104 - 84
⇒ n = 20
Hence, n +q =104 equation is correct.
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Can someone tell me the answer to this question
Answer: option 2
Step-by-step explanation:
The leading coefficient is positive and the degree is odd, so the correct answer is option 2.
a major credit card company has determined that customers charge between $300 and $1500 per month. the monthly amount charged is uniformly distributed. find the standard deviation of the monthly amount charged. (round to four decimal places if needed)
The standard deviation of the monthly amount charged is 346.41
Step 1: Identify the values of a and b, where [a , b] is the interval over which the continuous uniform distribution is defined.
Since it takes between 300 and 1500 minutes to be seated at the restaurant, we have:
a = 300
b = 1500
Step 2: Calculate the variance using the formula Var(x) = [tex]\frac{(b-a)^{2} }{12}[/tex]
Using the formula for the variance and the values identified in step 1
(a = 300 , b = 1500), we have:
Var(x) = [tex]\frac{(b-a)^{2} }{12}[/tex]
= [tex]\frac{(1500 - 300)^{2} }{12}[/tex]
= 1440000/12
= 120,000
the variance is 120,000
Step 3: Calculate the standard deviation by taking the square root of the variance. σ = [tex]\sqrt{Var(x)}[/tex]
The standard deviation is the square root of the result from step 2 (variance = 120,000)
σ = [tex]\sqrt{Var(x)}[/tex]
σ = [tex]\sqrt{120000}[/tex]
= 346.41
The standard deviation of the monthly amount charged is 346.41
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Which is the equation in slope-intercept form
for the graph of the line shown?
F. y=-3x - 2
G. y=-3x + 2
H. y = 3x - 2
I. y = 3x + 2
Please help me!
b) Simplify 18x³y³ + 2x³y
The GCF: 2x³y
answer: 2x³y2x³y(9y³+1)
Isaac works at a deli. He made a 30-cup batch of potato salad, and now he is filling 2.5-cup
to-go containers to sell to customers.
Write an equation that shows how the number of cups of potato salad remaining,y, depends
on the number of to-go containers Isaac has filled, x.
y =
Help
The equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.
Isaac made a 30-cup batch of potato salad, and now he is filling 2.5-cup
to-go containers to sell to customers.
Let y represent the number of cups of potato salad remaining,
And x represents the number of to-go containers Isaac has filled,
As per the given situation, we can write the equation as:
y = 30 - x ....(i)
Substitute the value of x = 2.5 in the above equation,
y = 30 - 2.5
y = 27.5
Thus, the equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.
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a store put dress shirts on sale for 2 for $27.00. How much will
someone pay if they buy 5 shirts?
Answer:
$67.50
Step-by-step explanation:
27(2) = 54
27/2 = 13.5
54+13.5 = 67.5
Answer:
67.5
explanation:
27/2= 13.5
5*13.5= 67.5
What is the solution to the equation 6x−5=15, given the replacement set {56, 53, 103} ?.
The solution of the given equation is x = 10/3
The replacement value is 10/3.
This is incorrect question
Correct question is :
What is the solution to the equation 6x−5=15, given the replacement set {5/6, 5/3, 10/3}
Given,
In the question:
The equation is given as:
6x - 5 = 15
To find the solution of the given equation.
Now, According to the question:
The equation is:
6x - 5 =15
Combine the like terms:
6x = 15 + 5
6x = 20
x = 20 /6
x = 10/3
Hence, The solution of the given equation is x = 10/3
The replacement value is 10/3.
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Answer the questions of the function below.
What is the slope of the line?
What is the y-intercept?
What is the x-intercept?
Answer:
slope and x-intercept is -1/2
y-intercept is 5
In the figure below, m1 equals (x-9) degrees, and m2 equals 8x degrees. Find the angle measures.
Answer: m1=2 and m2=88
Step-by-step explanation:
90=x-9+8x
99=9x
x=11
can someone please help asap !!!
Answer:
a = -1
b = -9
Step-by-step explanation:
when x = -2 put -2 for x in the equation:
a(3- (-2)) = -2*(-2) + b and then solve
a(3+2) = 4+b
5a = 4+b
then look at the numbers in the box and try for which number this equation will work. when you put a = -1 and b = -9 you will see it is equal on both sides because each side is -5
Sarah mailed her computer to Store B for repairs. Her bill was:
Initial Repair Cost = $1,350
Sales Tax of 7 percent = $94.50
Total Cost of Computer Repair = $1,444.50
Shipping = 2 percent of Total Cost
What is the cost to ship this computer from Store B?
$
Answer: $28.89
Step-by-step explanation: 2% of 1,444.50 is $28.89
Anyone ?. Need help
Step-by-step explanation:
it is a parallelogram.
that means both pairs of opposite sides are parallel and the sides of each pair are equally long.
the sum of all internal angles is 360°.
the opposing angles are equal.
and therefore neighboring angles are complementary angles (or a linear pair) : together they have 180°.
so,
76 = 4x - 8
84 = 4x
x = 21
-3z + 8 + 76 = 180
-3z + 84 = 180
-3z = 96
z = -32
-3z + 8 = -6y - 10
-3×-32 + 8 = -6y - 10
96 + 8 = -6y - 10
104 = -6y - 10
114 = -6y
y = -19
Nathaniel invested $2,900 in an account paying an interest rate of 5.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?
Answer:
$5252.53============================
GivenInvested amount P = $2900,Annual interest rate r = 5.4% = 0.054,Time t = 11 years,Compound number = continuous.Find the balance after 11 yearsUse equation for continuous compound:
[tex]P(t) = P_0e^{tr}[/tex],where P(t) - final amount, P₀ - initial amount, t - time, r - interest ratePlug in the values and calculate:
[tex]P(11) = 2900e^{11*0.054}=5252.53 \ rounded[/tex]Answer:
$5,252.53 (nearest cent)
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amount.P = Principal amount.e = Euler's number (constant).r = Annual interest rate (in decimal form).t = Time (in years).Given values:
P = $2,900r = 5.4% = 0.054t = 11 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]
[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]
[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]
[tex]\implies \sf A=5252.53457...[/tex]
Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).
Someone please help me with this problem, thank uuu
Answer:
B
Step-by-step explanation:
Do You Understand?
1.8
? Essential Question How can you use
the properties of operations to multiply linear
expressions?
It is possible to multiply or divide an equation by the same number on each side of the equation without changing the answer, according to the "multiplication property" of the equation.
How can you use the properties of operations to multiply linear expressions?
According to the equation's "multiplication property," it is possible to multiply or divide an equation by the same number on each side of the equation without changing the equation's outcome. The result of multiplying two terms with two different signs will be negative, while the product of two factors with the same sign will be positive. If a and b are positive integers and x is a variable, then (xa * xb) = x(m + n). The identity, commutative, associative, and distributive properties of multiplications are four properties that can facilitate the process. They offer guidelines for solving multiplication problems quickly using properties that always hold true for particular equations.
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Question 1 (1 point)
The scatter plot shows the number of days since several people filled their cars with
gas and the gallons of gas in their tank. Which is the most reasonable estimate of the
gallons of gas in a tank if it has been 3 days since filling up?
GALLONS OF GAS
8875294
DAYS SINCE FILLING UP
10 gallons
13 gallons
23 gallons
17 gallons
Answer:
D) 17 gallonsStep-by-step explanation:
Estimated line of best fit added to the graph (see attached).
The most reasonable value of y corresponding to x = 3 is approximately 18 gallons.
The matching answer choice is D.
Answer:
(D) 17 gallons
Step-by-step explanation:
A, B, C, D, E, F, G and H form a cuboid. AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm. Find ED rounded to 1DP.
According to the Pythagoras theorem, the value of ED is 8.4 cm
Pythagoras theorem:
Pythagoras theorem defines that the right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given,
A, B, C, D, E, F, G and H form a cuboid.
AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm.
Now, we need to find the value of Ed and round off it into 1 decimal place.
Here we have the cuboid with the edges named as A, B, C, D, E, F, G and H.
Now, we have to use the value of BC and CG to find the value of hypotenuse of BG.
Because, BG and ED are opposite to each other.
Which means both have the same hypotenuse value.
So, according to the Pythagoras theorem,
=> BG² = BC² + CG²
=> BG² = (2.3)² + (8.1)²
=> BG² = 5.29 + 65.61
=> BG² = 70.9
So, the value of BG is 8.42.
Therefore, the value of ED is 8.4 When we round off this into one decimal place.
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For each situation below, find the unit rate
Drag each situation on the left to the unit rate on the right
Questions: Choices:
Ricky spent $15.00 on 4 pizzas $8.00
William paid $20.00 for 2 1/2 pounds of blackberries $13.50
$3.75
The unit rate of Ricky purchase is $3.75 per pizza.
The unit rate of William purchase is $8 per pounds of blackberries.
What is unit rate?Unit rate is the ratio of two different units, with denominator as 1.
In other words, a unit rate is a rate where the second quantity is one unit , such as $10 per pound, 30 miles per hour, 22 Indian Rupees per Nigerian naira, etc.
Let's find the unit rate of the situations.
Ricky spent $15.00 on 4 pizzas
unit rate = 15 / 4
unit rate = 3.75 dollars per pizza
William paid $20.00 for 2 1/2 pounds = 5 / 2 pounds of blackberries.
Therefore,
unit rate = 20 ÷ 5 / 2
unit rate = 20 × 2 / 5
unit rate = 40 / 5
unit rate = 8 dollars per pounds of blackberries
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What is the additive inverse of the complex number 13 â€"" 2i? â€""13 â€"" 2i â€""13 2i 13 â€"" 2i 13 2i
The additive inverse of the mentioned complex number is -13 + 2i.
The additive inverse of any number is defined as the number, which on addition to the original number, gives the sum zero. In order to make possible this situation, the additive inverse will have opposite signs for each value.
In the question, 13 has positive sign and 2i has negative sign. To cancel them out, the additive inverse will be 13 with negative sign and 2i with positive sign. Thus, third option is correct additive inverse.
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The complete question is -
what is the additive inverse of the complex number 13 - 2i?
-13 - 2i
-13 + 2i
13 - 2i
13 + 2i
What is the slope of the line that passes through the points(7,-4) and (11, –4)? Write your answer in the simplest form.
differentiative
2x-3
2x+1
The differential equation is 8x-4 when the equation is (2x-3)(2x+1).
Given that,
The equation is (2x-3)(2x+1)
We have to find the differentiative equation.
Calculus differentiates the process of locating a function's derivatives. A derivative is the pace at which one function changes in relation to another. Sir Isaac Newton set the foundations for the laws of differential calculus. Numerous scientific disciplines make use of the limits and derivatives ideas. The essential ideas of calculus are differentiation and integration.
Differentiation is the rate at which one quantity changes in relation to another.
Take the equation
(2x-3)(2x+1)
We can do in two ways
1st way
Multiply
4x²+2x-6x-3
Subtraction
4x²-4x-3
Differentiation
8x-4
The equation is 8x-4.
2nd way
We have a formula in differentiation that is
u.v=uv'+vu'
Take u as 2x-3 and v as 2x+1
(2x-3)(2)+(2x+1)(2)
4x-6+4x+2
8x-4
Therefore, The differential equation is 8x-4 when the equation is (2x-3)(2x+1).
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what is the 60th percentile of breaking strength for this type of fishing line? round your answer to 2 decimal places.
the 60th percentile of breaking strength for this type of fishing line is
k= 6.64
assume that k pounds is the both percentile of breaking strength for this type of finishing line
p( x<k) = 0.60
p( x- 6.44/0.75 < k- 6.44/0.75)= 0.60
then k-6.44 /0.75 = 0.26
thus k= 6.64
Hence , the 60th percentile of breaking strength for this type of fishing line is 6.64
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Randy is installing PVC tiles to cover his garage floor. The width of the garage is 6 feet more than half the length, l . The perimeter of the garage is 313 times the length. If the PVC tiles cost $2.75 per square foot, what is the total cost of the materials? Enter your answer in standard form.
To cover the area of floor, we will spend $0.65 for the entire 0.23 squared feet
Perimeter of RectanglePerimeter of Rectangle could be considered as one of the important formulae of the rectangle. It is the total distance covered by the rectangle around its outside. A rectangle is a quadrilateral that has two pairs of parallel sides equal and all the four angles at the vertices are right angles.
The formula of perimeter of a rectangle is given as
P = 2(L + W)
P = Perimeter of rectangleL = length w = width.But the width the rectangle is 6 feet more than half it's length.
W = 6 + 1/2L
If the perimeter is 313 times the length;
P = 2(L + W)
P = 2(L + 6 + 1/2L)
But P = 313L
313L = 2(L + 6 + 1/2L)
313L = 2L + 12 + L
313L = 3L + 12
310L = 12
L = 12 / 310
L = 0.039 ft
The length of rectangle is 0.039ft
The width of the rectangle is 6 + 1/2(0.039) = 6.0195ft
The perimeter of the rectangle = 2(L + w)
Perimeter = 2 (0.039 + 6.0195)
Perimeter = 12.117ft
The area of the rectangle is L * w
A = L * W = 0.039 * 6.0195
A = 0.234ft^2
The cost of the materials will be 2.75 * 0.234 = $0.65
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