Answer: Scott - 18, Kaitlin - 9, Bill - 54
Step-by-step explanation:
Let's view this as units. There are a total of 81 units. If we solve for Scott's orders:
Kaitlin served 9 fewer orders than Scott. We add 9 to 81 --> 9 + 81 = 90.
Now if we view Scott's orders as one unit:
Scott - 1 unit
Kaitlin (after adding 9) - 1 unit
Bill - 3 units (he served 3 times as many orders as Scott)
In total there are 3 + 1 + 1 = 5 units.
90 / 5 = 18.
Therefore, Scott served 18 orders.
18 - 9 = 9.
Kaitlin served 9 orders.
18 x 3 = 54.
Bill served 54 orders.
And to check our answer, 54 + 18 + 9 is 81.
write the expression 5x(x+9) -7(x+9) in complete factored form.
(5x-7)(x-9)
Step-by-step explanation:Factoring is the inverse of the distributive property. This means that we want to find the factors, not the product.
Partial Factoring
The expression we are given has already been factored to an extent. Both terms are split into 2 different factors. This was done by factoring out the greatest common factor (GCF) from both terms. In the first term, the GCF was 5x, and in the second, the GCF was -7.
Complete Factoring
Even though it was partially factored, we can factor it more. When given the situation:
a(x + y) - b(x + y)The expression can be factored into:
(a - b)(x + y)You can add (subtract in this case because 7 is negative) the values from outside the parentheses together. This term can then be multiplied by the value within the parentheses.
Thus, 5x(x+9) -7(x+9) can be factored into:
(5x-7)(x-9)Remember this trick only works when both terms share a factor like (x-9).
What is the radian measure of central angle AOB in the circles? Write down the answer in the lowest terms
5pi/12 radians
The arc measure is 75, so theta must also be the same. if theta is 75, and 75 in radians is 5pi/12 radians, then the answer is that.
NO LINKS!! Please help me with this problem
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given vertex and Focus are of a vertical parabola having an opening downward as the focus is in downward direction as the vertex.
Focus of the parabola can be written as :
[tex]\qquad \sf \dashrightarrow \: (h ,k+ a )[/tex]
where, h and k are coordinates of vertex
so,
k + a = -2 -1 + a = -2a = -1So, the equation of parabola can be written as :
[tex]\qquad \sf \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)[/tex]
plug in the values ~
[tex]\qquad \sf \dashrightarrow \: (x - 1) {}^{2} = 4(- 1)(y + 1) {}^{} [/tex]
[tex]\qquad \sf \dashrightarrow \: (x - 1) {}^{2} = - 4(y + 1)[/tex]
Answer:
[tex](x-1)^2=-4(y+1)[/tex]
Step-by-step explanation:
Standard form of a parabola with a vertical axis of symmetry:
[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]
Vertex = (h, k)Focus = (h, k+p)Directrix: y = (k-p)Axis of symmetry: h = kIf p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.Given:
vertex = (1, -1)focus = (1, -2)Comparing with the formulas:
⇒ h = 1
⇒ k = -1
⇒ k + p = -2 ⇒ -1 + p = -2 ⇒ p = -1
Substituting the values into the formula:
[tex]\implies (x-1)^2=4(-1)(y-(-1))[/tex]
[tex]\implies (x-1)^2=-4(y+1)[/tex]
Solve the proportion
12
8
=
7.5
x
Answer:
9.8 is the final anwser
Step-by-step explanation so easy
What is the center of the circle given the following equation? (x-h)² + (y-k)² = r²
Answer:
on a coordinates plane :
The point of coordinates (h , k) is the center of the circle.
Step-by-step explanation:
by definition the expression:
(x-h)² + (y-k)² = r²
is the equation of the circle (in standard form)
Where r is the radius and (h , k) is the center of the circle.
It is the general equation of a circle
Correct answer:
The general equation of a circle is [tex](x - h)^2 + (y - k)^2 = r^2,[/tex]where (h, k) represents the location of the circle's center, and r represents the length of its radius. if we take some entities as [tex]h=4,k=-3[/tex] first has the equation of [tex](x - 4)^2 + (y + 3)^2 = 29[/tex]. This means that its center must be located at (4, –3), and its radius is √29.
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Represent each expression as a power of a, a cannot be equal to 0
Answer:
a^-27
Step-by-step explanation:
(a^3)^-3)^3)
(a^-9)^3)
a^-27
When we represent the expression ((a³)⁻³)³ as a power of a, the result obtained is a⁻²⁷
How to represent the expression as a power of a?The following data were obtained from the question:
Expression: ((a³)⁻³)³Representation as power of a =?We can represent the expression ((a³)⁻³)³ as a power of a by using the power law of indices as illustrated below:
((a³)⁻³)³
Recall
(Bᵐ)ⁿ = Bᵐⁿ (i.e multiply the power)
Thus,
((a³)⁻³)³ = (a⁻⁹)³
= a⁻²⁷
Thus, we can conclude from the above calculation that the representation of the expression ((a³)⁻³)³ as a power of a is a⁻²⁷
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Question 3(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following tables shows the correct steps to transform x2 + 6x +8=0 into the form (x-p)² =q?
[p and q are integers]
The correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;
x^2 + 6x +8 +1 = 0 + 1
x^2 + 6x +8 +1 = 1
x^2 + 6x + 9 = 1
(x+3)² = 1
Vertex form of a quadratic equationThe vertex form of a quadratic equation is expressed as:
a(x-h)² + k
Given the quadratic equation
x^2 + 6x +8=0
Subtract 8 from both sides
x^2 + 6x +8 - 8 = 0 - 8
x^2 + 6x = -8
Complete the square
(x^2+6x+3^2) = -8 + 9
(x+3)² = -8 + 9
(x+3)² = 1
Hence the correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;
x^2 + 6x +8 +1 = 0 + 1
x^2 + 6x +8 +1 = 1
x^2 + 6x + 9 = 1
(x+3)² = 1
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You are building a ramp for your grandparent’s house. The ramp will replace the steps that go to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the front door. How long will the ramp need to be?
Answer:
10.4403 or the square root of 109
Step-by-step explanation:
We do this by finding the height (3) and squaring it then the base (10) and squaring that, this sets up the Pythagorean theorem which is A^2+B^2=C^2 then you square C to find it's value
1. Which one of the following statements expresses a true proportion? A. 3:49:12 OB. 2:1 1:2 OC. 54:9 = 6:3 OD. 7:98:9
Answer:
3:4 9:12
Step-by-step explanation:
Rewrite the ratios as fractions. 3:4 becomes 3/4, and 9:12 becomes 9/12, which simplifies to 3:4. Therefore A is a true proportion.
Which of the following is the most accurate statement about Spatial Relations?
A- Children understand the spatial world watching movies about animals all over the world.
B- Children Need to know, use and be able to read spatial terms before they can demonstrate spatial awareness.
C-Spatial terms such as above, below, behind, and under are used to describe objects in space from different perspectives and are important for children to understand and express as they understand spatial relations.
Option C. The correct statement about spatial relationshipo is that Spatial terms such as above, below, behind, and under are used to describe objects in space.
What are spatial relationship?These are the types of relationships that are used to relate objects to the location of somethings else. It makes use of words like under, above etc.
It is one of the knowledge that children need in the preoperational stage to learn how to use logical operations.
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Please look at the attachment and answer my question :(
Answer:
AB / BC = 2 / 3
A equals 9 and C = 13
AC = 13 - 9 = 4
AB + BC = 13
A) AB + BC = 4
B) AB / BC = 2/3 Therefore BC = AB / (2/3)
B) BC = 1.5 AB
A) BC = 4 - A/B
Multiplying equation A) by -1
A) -BC = -4 + AB then we add equation B)
B) BC = 1.5 AB then adding both equations
0 = 2.5 AB -4
2.5 AB = 4
AB = 1.6
Since A = 9 then the number at B is 9 + 1.6
equals 10.6
Step-by-step explanation:
Answer:
The number at B is 10.6
Step-by-step explanation:
Let the number at B be x.
We know that distance between two points on the number line is the absolute value of the difference of numbers at those points.
Then distances representing the lengths of segments AB and BC are:
AB = x - 9BC = 13 - xWe are given the ratio of segments:
AB/BC = 2/3Substitute and solve for x:
(x - 9)/(13 - x) = 2/33(x - 9) = 2(13 - x)3x - 27 = 26 - 2x3x + 2x = 26 + 275x = 53x = 53/5x = 10.6Simplify the following expression.x-[tex]\frac{2}{3}[/tex] x[tex]\frac{6}{7}[/tex]
Keeping the bases and adding the exponents, the simplified expression is:
[tex]x^{\frac{4}{21}}[/tex]
How to solve a product of two terms with the same base and different exponents?We keep the bases and add the exponents.
Hence:
[tex]x^{-\frac{2}{3}} \times x^{\frac{6}{7}} = x^{-\frac{2}{3} + \frac{6}{7}} = x^{\frac{-14 + 18}{21}} = x^{\frac{4}{21}}[/tex]
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How do i convert the follwing Powers Of Ten into standard numbers?
[tex]10^{7}[/tex]
[tex]10^{5}[/tex]
[tex]10^{8}[/tex]
[tex]10^{12}[/tex]
[tex]10^{6}[/tex]
The standard numbers are obtained from the given numbers as follows;
10⁷ → 1000000010⁵ → 10000010⁸ → 10000000010¹² → 100000000000010⁶ → 1000000Which method can be used to express the numbers in standard form?The standard form of numbers is obtained by expressing the number completely and not using powers of 10
The given numbers in powers of 10 can be expressed in standard form by writing the specified number of zeros next to 1 given by the power of 10 as follows;
Number → Standard form
10⁷ = 1000000010⁵ = 10000010⁸ = 10000000010¹² = 100000000000010⁶ = 1000000Learn more about standard form of numbers here:
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A race track is miles long. If the car race is 200 laps then how many miles will the drivers travel during the race?
The drivers will travel 200x miles during the race.
What is Unit of Measurement?A definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that A race track is miles long
The car race is 200 laps then we have to find the number of miles the driver travel.
If the race track is x miles long, then one lap around the track is x miles.
If the race is 200 laps, the total distance covered by the drivers is:
200 laps × x miles/lap = 200x miles.
Therefore, the drivers will travel 200x miles during the race.
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The real root of the equation x3 – 7x2 + 15x – 25 = 0 is 5. What are the nonreal roots?
–4i, 4i
2 – 4i, 2 + 4i
1 + 2i, 1 – 2i
–16i, 16i
Answer:
1±2i.
Step-by-step explanation:
1. if to evaluate the expression given, it can be written
(x-5)(x²-2x+5)=0;
2. where the nonreal roots are 1±2i.
Assignment
Slide the green dot from 0 to plot the number at the correct
location.
Plot-1.
-6 -5 4 -3 -2 -1 0 1
2
3 4
5
+
6
Use the interactive number line to find each sum to
complete the table.
A
1
-1
-4
-6
B
2
-2
1
-3
A + B
3
R
S
T
From the number line, the values which completes the sum in the table are:
R = -3.S = -3.T = -9.What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
How to find each sum?From the table of values (see attachment), the values on the number line are represented as follows:
a + b = a + b
R = -1 - 2
R = -3.
a + b = a + b
S = -4 + 1
S = -3.
a + b = a + b
T = -6 - 3
T = -9.
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Solutions greatest to smallest for function
=2+5−7
The greatest or maximum value for the given function = -8.25
The minimum or smallest value for the given function =-4
Calculation of greatest and smallest functionsThe maximum value of a function is the highest value of that function. To calculate the greatest function, the following equation is used,
Formula max = c - (b2 / 4a)
Where,
a = 2
b = 5
C = -7
Therefore maximum function
= -7 -(5*2/4*2)
= -7-(10/8)
= -7 - 1.25
= -8.25
The minimum value of a function is the least value of that function.
Formula for the minimum = c - b^2/4a.
= -7-5^2/4*2
= -32/8
= -4
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Sharon is planting tulip
bulbs in her garden. In the
catalog she sees a disclaimer that there is a 1/15 probability that a bulb will not flower. If Sharon plants 90 bulbs, how many tulips can she expect to see in her garden?
Answer:
84 flowers.
Step-by-step explanation:
We must multiply 90 by 1/15 to get 6 bulbs that will not flower. 90-6 is 84.
Two friends, Jamie and Devin, are working together at the Sparrowtown Cafe today. Jamie works every 2 days, and Devin works every 7 days. How many days do they have to wait until they next get to work together?
Answer:
14 days
Step-by-step explanation:
let assume they both work on Monday (today)
devin works every 7 days,that is devin works every Monday.
jamie has to work for 14 days inorder to work with devin again
Question 4 of 10
What should you substitute for y in the second equation (bottom equation) in
order to solve the system by the substitution method?
5x+y=10
3x-2y =6
A. -0.2y+2
B. -5x+10
C. 5x-10
D. 1.5x+3
Answer:
B
Step-by-step explanation:
5x+y=10
-5x -5x
y= -5x+10
evaluate f(x)=4|x|+3 for x=-5
x-4[x-2(x+6)]=5x+3
[tex]x - 4 [ x - 2(x + 6)] = 5x + 3[/tex]
The equivalence of the equation is 5x + 48 = 5x + 3.
Since 48 cannot be equal to 3, hence there are no solution.
What is the value of x?Given the equation; x-4[ x - 2( x + 6) ] = 5x + 3
We remove the parentheses
x-4[ x - 2( x + 6) ] = 5x + 3
x-4[ x - 2x - 12 ] = 5x + 3
x - 4x + 8x + 48 = 5x + 3
5x + 48 = 5x + 3
We can go further and collect like terms
5x - 5x + 48 = 3
48 ≠ 3
Since 48 cannot be equal to 3, hence there are no solution.
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Gene is tossing a normal quarter. He tosses the quarter 12 times and it lands on heads 9 times. If Gene tosses the quarter again, what is the probability that it lands on tails? Input your answer in fraction form.
Answer:
1/2
Step-by-step explanation:
This is an independent event. It does not matter what happened before the chances of getting a tail on one toss will always be what I want/all outcomes. There are only 2 outcomes: heads or tails. I am only looking for one of those outcomes, so 1/2.
What are the domain and range of g(x)=√x+4?
OD: [4, ∞) and R: [0, ∞)
OD: (-4, ∞) and R: (-∞, 0)
OD: [-4, ) and R: [0, ∞)
OD: (4,) and R: (-∞, 0)
Answer:
Domain [-4 , +∞)
Range [0 , +∞)
Step-by-step explanation:
the function g such that g(x)=√(x+4) ,is defined
for the values of x that verify :
x + 4 ≥ 0
⇔ x ≥ -4
Then
The domain of g is [-4 , +∞)
………………………………………………
Let x ∈ [-4 , +∞)
then x ≥ -4
then x + 4 ≥ 0
then g(x) = √(x+4) ≥ 0
Therefore, we can affirm that the range of g is [0 , +∞)
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 316 people entered the park, and the admission fees collected totaled 924.00 dollars. How many children and how many adults were admitted
Answer: pretty sure
There were 108 children and 175 adults.
a map has a scale of 2in: 6mi. if a two twons on a map is 10 in apart then how far apart are the real twons
Answer:
Step-by-step explanation:
You buy almond milk in 1 gallon containers. One portion of waffles requires 2.5 ounces of almond milk. How many portions can be made with one container
Answer:
61 portions
Step-by-step explanation:
First, the conversion between gallon and ounces is:
1 Gallon = 153.722 ounces (oz)
GIven 1 portion of waffles requires 2.5 ounces of milk
Number of portions of waffles = Total amount of milk / milk required per portion of waffles
= 153.722 / 2.5
= 61.489 portions
Of course, we are unable to make part portions in this case, so we will take the highest possible whole number, which is 61 portions.
Use the table to the right to answer the following question.
Compare the energy released by fission of 1 kilogram of element B to that released by burning 1 kilogram of element A.
The energy is compared based on the information given below.
How to illustrate the energy?Energy released by burning 1 kilogram of element A = EA = 5.1 * (10)8
Energy released by fission of hydrogen in 1 kilogram of element B = EB = 1.3 * (10)10
Therefore,
Ratio = EB / EA = 1.3 * (10)10 / 5.1 * (10)8 = 25
Thus, the fission of 1 kg of element B releases 25 times as much energy as burning 1 kilogram of element A.
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The other part of the question:
Energy released by burning 1 kilogram of element A = 5.1 times 10 Superscript 8
Energy released by the fission of hydrogen in 1 kilogram of element B = 1.3 times 10 Superscript 10
Which person has a dept ratio that is higher the 18%
the person with the debt ratio that is higher than 18% can be found by dividing the person's debt by their income .
what is the debt ratio?the necessary information is not given so a general explanation will be given.
the debt ratio is found by the formula:
= monthly debt payment / monthly gross income
this figure allows creditors to see if a person can affort to incur more debt based on how much of their gross monthly income is being used to service debt.
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Use properties of operations to find the quotient. -10.2/6
A. 1.7 B. -1.7 C. 4.2 D. -4.2
Answer:
B, -1.7
Step-by-step explanation:
-10.2 divided by 6 is -1.7.
I hope this helps!