The total cost of a cake that serves 20 people is $35.
Step-by-step explanation:
Total cost = yNumber of additional servings = xThe number of additional servings = 20 - 12 = 8. (x=8)The equation can be formed as:
Total cost = basic cost + (No. of additional serving [tex]\times[/tex] cost per additional serving)y = 25 + x1.25Substitute x=8 in the above equationy = 25 + 8(1.25)y =25+10y = 35Therefore, the total cost of a cake that serves 20 people is $35.
PROBLEM
Write the equation of the line that passes through (0, -6) and (4, 10).
Answer:
y= 4x-6
Step-by-step explanation:
The equation of a line is usually written in the form of y=mx+c, where m is its gradient and c is its y-intercept.
Let's find the gradient, m, first.
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Using the above formula,
[tex]m = \frac{10 - ( - 6)}{4 - 0} \\ m = \frac{10 + 6}{4} \\ m = \frac{16}{4} \\ m = 4[/tex]
Subst. the value of m into the equation.
y=4x+c
To find c, substitute a coordinate into the equation.
When x=0, y= -6,
-6= 4(0) +c
c= -6
Thus, the equation of the line is y= 4x -6.
(x - 1)2 = 4
how do i do this
Answer:
x = 3
Step-by-step explanation:
(x - 1)2 = 4
how to get this solved is very simple.
first step to apply is the BODMAS RULE
B..................... bracket
O..................... of
D.....................Division
M.................... multiplication
A..................... addition
S.................... Subtraction
so (x - 1)2 = 4
we have,
2x - 2 = 4 ( by opening the bracket)
collect the like terms
2x = 4+2
divide both sides by 2
2x/2 = 6/2
x = 3
to check if your answer is correct put the value of x = 3 into the question and see if the right hand side will equal to the left handside
(x - 1)2 = 4
(3-1)2=4
2(2)=4
4=4.............................. proved
after five days in her new job, karen has $800 in her bank account. if she is adding exactly $50 to her account each day, when will her balance reach $1000? explain.
Answer:
After 4 more days
Step-by-step explanation:
The remaining amount of money needed to reach the goal is $200 this is because 1000-800=200
Now we divide the 200 by the amount Karen earns a day
200/50=4
That means after 4 more days Karen will have $1000
What's the sum of 6ft feet 10 in and 8 ft 9 inches
15 ft. 7 in is the sum of 6 feet 10 inches and 8 feet 9 inches.
6 feet 10 inches + 8 feet 9 inches
= 14 feet 19 inches
= 15 feet 7 inches
Solve the system of linear equations using elimination.
−2x − y = 3
−9x − y = 17
A)
(2, 1)
B)
(2, −1)
C)
(−2, 1)
D)
(−2, −1)
PLEASE HELP I NEED IT BY TODAY
Answer:
C (-2,1)
Step-by-step explanation:
−2x − y = 3 (1)
−9x − y = 17 (2)
(1) y = -2x - 3
(2) y = -9x - 17
-2x - 3 = -9x - 17
7x = -14
x = -2
y = -2(-2) - 3
y = 4 - 3
y = 1
what is the third angle of a triangle if two of the angles measure 29 ° and 87 °.
Answer:
64°
180°-29°-87°=64°
Write the equation of a line in y =mx+b
form that has a slope of 3/4 and a y-intercept of 0.
Answer:
y = ¾x
Step-by-step explanation:
y = mx + b, where
m = slope and
b = y-intercept
If slope = ¾ and y-intercept =0, the equation is
y = ¾x
The functions f(x) and g(x) are defined below.
f(x)= 2e^x + 1
g(x)= 1/2e^x + 5/2
Determine where f(x) = g(x) by graphing.
A. x = 0
B. x = 0; x = 3
C. x = 1; x = 3
D. x= 3
Answer:
Answer : A x=0
Step-by-step explanation:
hello :
f(x)= 2e^x + 1 graph red
g(x)= 1/2e^x + 5/2 graph bleue
2e^x + 1
= 1/2e^x + 5/2
by graphic solution one solution x=0
Answer:
d) x=3
Step-by-step explanation:
Jamie recently started working as
manager at a company. He will be paid
an annual salary of $42,600 and will be
paid monthly. The company requires the
following deductions:
• Social Security (6.2%)
• Medicare (1.4%)
• State Income Tax (3%)
• Federal Income Tax (13%)
• Medical and Dental Insurance ($260 per month)
• Retirement ($280 per month)
How much should his monthly net paycheck be?
a $2587.55
b. $2172.20
$2667 20
$2712.40
d
Answer:
B
Step-by-step explanation:
From annual salary of 42,600, we have to subtract the following percentages:
Social Security:
0.062 * 42,600 = 2641.2
Medicare:
0.014 * 42,600 = 596.4
State Income Tax:
0.03 * 42,600 = 1278
Federal Income Tax:
0.13 * 42,600 = 5538
Total Deductions (from percentages) = 2641.2 + 596.4 + 1278 + 5538 = 10053.6
Now, remaining salary:
42,600 - 10053.6 = 32546.4 (annual)
Divided by 12 to get monthly:
32546.4 / 12 = 2712.2 (monthly)
Now, monthly deductions are:
260 + 280 = 540
Net Salary: 2712.2 - 540 =2172.2
Based on the information given his monthly net paycheck is: b. $2172.20.
Net paycheckDeduction
Social security=42,600×62%
Social security = 2641.2
Medicare=42,600×1.4%
Medicare = 596.4
State Income Tax= 42,600×3%
State Income tax = 1278
Federal Income Tax=42,600×13%
Federal Income Tax = 5538
Total Deductions = 2641.2 + 596.4 + 1278 + 5538
Total deduction= 10053.6
Net paycheck:
Net paycheck=(42,600 - 10,053.6)/12- (260 + 280)
Net paycheck=32,546.4/12-540
Net paycheck= 2712.2 - 540
Net paycheck=$2172.2
Therefore, his monthly net paycheck is: b. $2172.20.
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Write each function in vertex form, and identify its vertex.
14. h(x)=3x^2−24x+53
15. h(x)=x^2 +8x−10
16. g(x)=x^2 −3x+16
17. h(x)=3x^2 −12x−4
Answer:
its C or 16
Step-by-step explanation:
Which is the best estimate of the avarge rate of change for the quadratic function on the interval 0 ≤ x ≤ 4
Answer:
A) -1
Step-by-step explanation:
The missing graph is attached.
The possible answers were:
-1
-2
-3
-4
The average rate of change of a function f(x) on a≤x≤b is given by:
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
We want to find the best estimate of the average rate of change for the quadratic function on the interval 0 ≤ x ≤ 4.
From the graph, f(0)=0 and f(4)=-4
[tex] \frac{f(4) - f(0)}{4 - 0} = \frac{ - 4 - 0}{4 - 0} = \frac{ - 4}{4} = - 1[/tex]
What is the greatest common factor of the polynomial’s terms? 18x^2y^3-6xy^2+3x^3y
Answer:3xy
Step-by-step explanation:18x^2y^3= 3,6,x,x,y,y,y
6xy^2=. 3,2,x,y,y
3x^3y=. 3,x,x,x,y
All three have this in common a 3xy
The greatest common factor of the given polynomial's terms 18x^2y^3-6xy^2+3x^3y is 3xy. This is determined by factoring each term, and finding the greatest factor that occurs in all of the lists.
Explanation:In mathematics, the greatest common factor (GCF) of a set of terms in a polynomial, is the largest term that divides each term exactly. To find the greatest common factor for the given polynomial 18x^2y^3-6xy^2+3x^3y, first, we list the factors for each term.
The term 18x^2y^3 factors as 2*3*3*x*x*y*y*y, the term -6xy^2 factors as -2*3*x*y*y, and the term 3x^3y factors as 3*x*x*x*y.
The greatest factor that occurs in all three lists is 3*x*y, so 3xy is the greatest common factor of the polynomial’s terms.
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What is the range of the function
A square root can’t be a negative value, so the root would be greater than or equal to zero.
Range:
Y>=O
[O, infinity)
14+16+11+2+6+6+15+2+11
And round to the nearest tenth
Answer:
83
Step-by-step explanation:
Add the numbers together
Answer:
80
Step-by-step explanation:
14 + 16 = 30
30 + 11 = 41
41 + 2 = 43
43 + 6 = 49
49 + 6 = 55
55 + 15 = 70
70 + 2 = 72
72 + 11 = 83, which, rounded to the nearest tenth, is 80
Please help :( I don’t u derstand it
Answer:
[tex]\frac{3}{(2x+7)}[/tex]
Step-by-step explanation:
[tex]\frac{3x +3}{2x^2 + 9x + 7}[/tex]
[tex]\frac{3(x + 1)}{(2x + 7)(x + 1)}[/tex]
[tex]\frac{3}{(2x+7)}[/tex]
Answer: [tex]\frac{3}{(2x+7)}[/tex]
GRAPH BELOW:
find x when - 1/2 + x = - 21/4
Step-by-step explanation:
-1 / 2 + x = -21 /4
x = -21/4 + 1/2
x = (-21 + 2)/4
x = -19/4
A family of two adults and three children went to a water park. Admission to the water park costs $18 per person. Nora used the expression 2 (18) + 3 (18) to model the total cost for the family, and Alex used the expression 5 (18). Which property of operations makes both of their expressions correct?
associative property
commutative property
distributive property
identity property
Answer
Distributive Property.
Step-by-step explanation:
First you solve for the first equation by multiplying 2 by 18 which is 36. Then 3 times 18 which is 54. Then you add them together to get 90.
Next you solve for the second equation by multiplying 5 by 18 which is 90.
Both of these equations are solved by the distributive property because your distributing the number outside of the parenthesis.
find value of a and b in the triangle. (please help)
ErvIn bowled 7 games last weekend. his scorers are : 155,165,138,172,193,142. what is the range of ErvIn scores
The range of Ervin's scores is 55.
Range is the difference between the largest number and the smallest number.
To find the range of a set of values, first sort the values numerically (smallest to largest). With this set, it would look like this: 138, 142, 155, 165, 172, 193. Lastly, subtract 138 from 193 to find the range. By doing so, you will get 55 as an answer.
I hope this helps!
The range of ErvIn's scores is 55.
The range of ErvIn's scores is calculated by finding the difference between the highest and lowest scores.
Arrange the scores in numerical order: 138, 142, 155, 165, 172, 193.
Find the highest score: 193.
Find the lowest score: 138.
Subtract the lowest score from the highest score to find the range: 193 - 138 = 55.
A wise man once said,
“400 reduced by 3 times
my age is 244." How old is
the wise man?
The wise man's age can be calculated by solving the equation 400 - 3x= 244, leading to the solution that he is 52 years old.
To determine the wise man's age, we need to set up an equation based on the given statement:
Let's call the wise man's age x
The statement says, "400 reduced by 3 times my age is 244." This can be written as:
400 - 3x = 244
To find x, follow these steps
400 - 3x = 244
3x = 400 - 244
3x = 156
x = 156 / 3
x = 52
So, the wise man is 52 years old.
what is the half life formula
N = N₀* [tex](\frac{1}{2} )^{\frac{t}{h} }[/tex]
where N is how much you currently have
N₀ is the starting amount
t is the time
and h is the half life of the substance.
The half-life formula for a radioactive isotope is amount remaining = (amount initial) × e^(-t/t1/2), where e is the base of natural logarithms, t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. The formula can be used to calculate how much of a radioactive isotope remains after a certain amount of time.
Explanation:The half-life formula for a radioactive isotope is given by:
amount remaining = (amount initial) × e^(-t/t1/2)
Here, e is the base of natural logarithms (approximately 2.71828182), t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. To evaluate the exponential function, you may need to use a calculator or an inverse logarithm function. It is important to note that the length of time t does not need to be an exact multiple of half-lives.
∠ABC measures 124° and ∠MNO measures 56°. Therefore, the two angles are
Answer:
Supplementary
Step-by-step explanation:
Since the two angles add up to 180 degrees, they are supplementary
The table represents a function.
A 2-column table with 4 rows. The first column is labeled x with entries negative 6, negative 2, 0, 3. The second column is labeled f of x with entries 3, 1, 4, negative 2.
What is f(–2)?
f(–2) = 1
Solution:
The table represents a function.
x f(x)
–6 3
–2 1
0 4
3 –2
To find the value of f(–2):
f(–2) means the value of f(x) for the corresponding x value –2.
In the table, if the x value is –2, then f(x) is 1.
See the value of f(x) which correspond to x = –2.
Hence f(–2) = 1.
Which of the following is the solution to | x | +5 <= 1
Answer:
NO SOLUTION
Step-by-step explanation:
Step 1: Subtract 5 from both sides
|x| + 5 - 5 ≤ 1 - 5
|x| ≤ -4
x ≤ NO SOLUTION
Answer: NO SOLUTION
Joshua and his friend Maxine want to buy charcoal pencils to add to their growing collection of art
supplies. They go to store A and find out that a 10 pack is worth $16.25. But at store B a 10 pack is worth
$7.65 but of lesser quality. Find out how much one pencil is worth at store A and store B.
Janet has three coins.
One coin has a value
that is 5 times another
coin. The third coin has
a value that is 2 times
another coin. She has
404 altogether. What
coins does she have?
Write an equation to
represent your work and
solve.
Answer:
Janet has coins worth 252.5, 101, and 50.5.
Step-by-step explanation:
Let us call the three coins [tex]a,b[/tex], and [tex]c[/tex].
The first coin [tex]a[/tex] is 5 times another coin (let's say [tex]b[/tex]); therefore,
[tex]a = 5b[/tex],
and the third coin is 2 times the value of another coin (it's coin [tex]b[/tex]):
[tex]c =2b[/tex].
The total worth of all coins is 404; therefore,
[tex]a+b+c =404[/tex]
or
[tex]5b+b+2b =404[/tex]
[tex]8b =404[/tex]
[tex]\boxed{b = 50.5}[/tex]
with the value of [tex]b[/tex] in hand, we find [tex]a[/tex] and [tex]c[/tex]:
[tex]a = 5b = 5(50.5)[/tex]
[tex]\boxed{a = 252.5}[/tex]
and for [tex]c:[/tex]
[tex]c = 2 b = 2 (50.5)[/tex]
[tex]\boxed{c = 101}[/tex]
Thus, Janet has 3 coins worth 252.5, 101, and 50.5.
Help with this question
Answer:
158
Step-by-step explanation:
20 + 60 + 40 = 120 + 38 = 158
I think this is right. (I tired)
X/4 < -1.5 for a million dollars and Brainliest. Send cash app too
Answer:
x < -6
Step-by-step explanation:
X/4 < -1.5
Multiply each side by 4
X/4*4 < -1.5*4
x < -6
Help plzzzz I don't understand how to do this
Mercury's distance = 5.8 x 10¹⁰
Venus' distance = 1.86 farther or more than Mercury's, namely 1.86(5.8 x 10¹⁰)
Earth's distance = 2.58 farther or more than Mercury's, namely 2.58(5.8 x 10¹⁰)
[tex]\bf \stackrel{\textit{venus' distance}}{1.86(5.8\times 10^{10})}\implies \begin{cases} 1.86(58000000000)\\ 107880000000\\ 1.0788\times 10^{11} \end{cases} \\\\\\ \stackrel{\textit{earth's distance}}{2.58(5.8\times 10^{10})}\implies \begin{cases} 2.58(58000000000)\\ 149640000000\\ 1.4964\times 10^{11} \end{cases}[/tex]
about how many meters farther is Earth's than Venus? well, we can simply get their difference, we know the Earth is farther than Venus, so we can just subtract Venus' distance from Earth's to get the difference, namely 149640000000 - 107880000000.
[tex]\bf \stackrel{earth}{149640000000} - \stackrel{venus}{107880000000}~~ = ~~41760000000\implies \stackrel{\textit{rounded up}}{4.2\times 10^{10}}[/tex]
The equation 4 + 9 = 4 + 9 is an example of which property of equality? *
Transitive
Symmetric
Substitution
Reflexive
Answer:
Reflexive
Step-by-step explanation:
The reflexive property of equality says that a given real number is always equal to itself.
For example :
[tex]y = y[/tex]
[tex]a = a[/tex]
[tex]b = b[/tex]
[tex]5 = 5[/tex]
are all examples of reflexive properties of equality.
[tex]4 + 9 = 4 + 9[/tex]
can be simplified to
[tex]13 = 13[/tex]
Which is explains why it is the reflexive property.