The given statement is the product of 2 groups of 7.
This statement can be expressed as
[tex]7\cdot7[/tex]Where each seven represent one group.
Ms. Mistovich and Ms. Nelson are having a competition to see who can get morestudents to bring in extra tissues for their classroom. Ms. Mistovich starts with 4 boxesand each week she gets two more boxes from her students. Ms. Nelson starts with 1box and each week she gets 3 more boxes from her students. Write a system ofequations to represent the situation. (1 pt)y=2x+4y=3x+1Ooy=2x+4y=2x+3y=4x+2y=3x+1y=2x+3y=4x+1o
To write an equation, it is enough to know the rate of change (slope) and the initial value (y-intercept).
The equation of a line of slope m and y-intercept b is:
[tex]y=mx+b[/tex]For Ms. Mistovich, the initial value is 4 and the rate of change is 2.
For Ms. Nelson, the initial value is 1 and the rate of change is 3.
Therefore, the equations that model this situation, are:
[tex]\begin{gathered} y=2x+4 \\ y=3x+1 \end{gathered}[/tex]how many hours did the plumber work to fix the plumbing
The total cost of the fix is C = $375.
The plumber charges a fixed rate per call of F = $50 and charges a variable rate of v = $25 per hour, if h is the number of hours he worked, we can write:
[tex]\begin{gathered} C=F+v\cdot h \\ 375=50+25\cdot h \end{gathered}[/tex]This equation shows that the total cost is equal to the fixed cost plus the variable cost. The variable cost is equal to the hourly rate times the number of hours of work.
Then, we can calculate h as:
[tex]\begin{gathered} 375=50+25h \\ 375-50=25h \\ 325=25h \\ h=\frac{325}{25} \\ h=13 \end{gathered}[/tex]Answer: he worked 13 hours.
NOTE:
Table of values:
If we need to use a table of values to solve this, we will have two columns: one for the number of hours and the other for the total cost.
We can make the table have more detail and separate the cost column in 3: one for the fixed cost, one for the variable cost and the last one for the total cost.
Then, we would write in each column:
1) Hours: the number of hours, from 0 to the amount we consider.
2) Fixed cost: this column will have the value $50 for all the rows, as it is independent of the number of hours.
3) Variable cost: this column will have values proportional to the hours. This values will be 25 times the number of hours.
4) Total cost: this column will add both the fixed cost and variable cost.
Then, we will obtain the following table.
We can now look for the value $375 in the Total cost column.
We find that this cost correspond to 13 hours:
Graph:
We can now use the data from the table to graph the total cost in function of the number of hours.
what is the domain of this exponential function y=2x-8+2
The given function is
[tex]y=2^{x-8}+2[/tex]The domain is all real numbers, but the range would be all the real numbers greater than 2 because the function approximates to y = 2.
Hence, the answer is the first option.If Danica has $1200 to invest at 8% per year compounded monthly, how long will it be before he has $2400? If the compounding is continuous,how long will it be? (Round your answers to three decimal places.)
ANSWER
EXPLANATION
a) To find the time it will take before he has $2400, we have to apply the formula for monthly compounded amount:
[tex]undefined[/tex]GEOMETRY Draw the next two figures in the pattern shown below. OOO
Given , the pattern
O , OO , .....
so, the first term is 1 circle
The second is 2 circles
So, the next two figures are:
OOO , OOOO
Question 13 of 18Graph the solution to the following inequality on the number line.x² - 4x ≥ 12
Step 1
Given; Graph the solution to the following inequality on the number line.
x² - 4x ≥ 12
Step 2
[tex]\begin{gathered} x^2-4x\ge \:12 \\ Rewrite\text{ in standard form} \\ x^2-4x-12\ge \:0 \\ Factor\text{ the inequality} \\ \left(x+2\right)\left(x-6\right)\ge \:0 \end{gathered}[/tex][tex]\begin{gathered} Identify\text{ the intervals} \\ x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6 \end{gathered}[/tex]Thus, the number line will look like
Answer; The solution to the inequality graphed on a number line is seen below
[tex]x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6[/tex]Which of the following statements about the table is true?
Select all that apply.
The table shows a proportional relationship.
All the ratios for related pairs of x and y are equivalent to 7.5.
When x is 13.5, y is 4.5.
When y is 12, x is 4.
The unit rate of for related pairs of x and y is .
26
22 Undertond Proportional Relationships: Fouivalent Ratios
C
C
y
10.5 3.5
15.9 5.3
22.5 7.5
27
9
3
Answer:
there is a lot of ratios here, but I will try my best. A proportional relationship is the relationship that is proportional obviously. and if the ratio is related, pairs are equivalent to 7.5 then that must mean that the proportional relationship is fuevalent
Calculate Sse for the arithmetic sequence {a,}5sequence {1,3 ={}+}=Ο Α. 1463OB. 91220 C. 8,6716D. 9,26767
Answer:
[tex]\frac{8,671}{6}[/tex]Explanation:
Here, we want to get the sum of the 58 terms in series
Mathematically, we have the formula to use as:
[tex]S_n\text{ = }\frac{n}{2}(a\text{ + L)}[/tex]where a is the first term and L is the last term
The first term is when n is 1
We have this calculated as:
[tex]\text{ a}_{}\text{ = }\frac{5}{6}+\frac{1}{3}\text{ = }\frac{5+2\text{ }}{6}\text{ = }\frac{7}{6}[/tex]The last term is the 58th term which is:
[tex]\text{ a}_{58}\text{ = }\frac{290}{6}\text{ + }\frac{1}{3}\text{ = }\frac{292}{6}[/tex]We finally substitute these values into the initial equation
Thus, we have it that:
[tex]S_{58}\text{ = }\frac{58}{2}(\frac{292}{6}+\frac{7}{6})\text{ = 29(}\frac{299}{6})\text{ = }\frac{8671}{6}[/tex]
how many cheese pizzas can the girls buy if they pool all their money together? inequality form for each scenario. CHEESE PIZZA IS 7.25 DOLLARS.
Since we have 5 girls and their parents give each other $10, they have in total $50.
Now, let x be the number of pizzas they buy, since each pizza cost $7.25 the total cost for x pizzas is:
[tex]7.25x[/tex]this should be less or equal to $50 (otherwise the girls go over budget), then the inequality that represents this situation is:
[tex]7.25x\leq50[/tex]Now, solving the inequality we get:
[tex]\begin{gathered} 7.25x\leq50 \\ x\leq\frac{50}{7.25} \\ x\leq6.9 \end{gathered}[/tex]Therefore, they can buy a maximum of 6 pizzas without going over budget.
how much of each ingredient would you need to make an identical recipe that serves 8 people explain your reasoning
LITERS OF SODA
24 people calls for 4 liters of lemon soda
18 people calls for x liters of lemon soda
24 people = 4 liters
18 people = x
cross multiply
24x = 72
Divide both-side of the equation by 24
x = 3
18 peoples calls for 3 liters of soda
PINT OF SHERBET
24 people calls for 2 pint of sherbet
18 people calls for x pint of sherbet
24 people = 2 pint
18 people = x
cross-multiply
24x = 36
Divide both-side of the equation by 24
x =1.5
18 peoples calls for 1.5 pint of sherbet
CUPS OF RICE
24 peoples calls for 6 cups of rice
18 people calls for x cups of rice
24 people = 6 cups of rice
18 people = x
cross multiply
24x = 108
Divide both-side of the equation by 24
x=4.5
18 people calls for 4.5 cups of rice
Hence, 18 people calls for; 3 liters of soda, 1.5 pint of sherbet and 4.5 cups of rice
The height of a diver above the water’s surface can be modeled by the function h(t)= –16t^2+ 8t + 48. How long does it take the diver to hit the water? Solve by factoring
Given the function:
[tex]h(t)=-16t^2+8t+48[/tex]Where h(t) is the height of the diver above the surface of the water and t is the time.
Let's find how long it takes the diver to hit the water.
When the diver hits the water, the height h(t) = 0.
Now substitute 0 for h(t) and solve for the time t.
We have:
[tex]0=-16t^2+8t+48[/tex]Rearrange the equation:
[tex]-16t^2+8t+48=0[/tex]Solve for t.
Let's factor the expression by the left.
Factor 8 out of all terms:
[tex]8(-2t^2+t+6)=0[/tex]Now, factor by grouping.
Rewrite the middle term as a sum of two terms whose product is the product of the first term and the last term:
[tex]\begin{gathered} 8(-2t^2+4t-3t+6)=0 \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 8((-2t^2+4t)(-3t+6))=0 \\ \\ 8(2t(-t+2)+3(-t+2))=0 \\ \\ 8(2t+3)(-t+2)=0 \end{gathered}[/tex]Hence, we have the factors:
[tex]\begin{gathered} 2t+3=0 \\ -t+2=0 \end{gathered}[/tex]Solve each factor for t:
[tex]\begin{gathered} 2t+3=0 \\ \text{ Subtract 3 from both sides:} \\ 2t=-3 \\ \text{ Divide both sides by 2:} \\ \frac{2t}{2}=-\frac{3}{2} \\ t=-\frac{3}{2} \\ \\ \\ -t+2=0 \\ t=2 \end{gathered}[/tex]Hence, we have the solutions:
t = -3/2
t = 2
The time cannot be negative, so let's take the positive value.
Therefore, the will take 2 seconds for the diver to hit the water.
ANSWER:
2 seconds.
Vera cut a piece of fabric into 5 equal-length pieces. Then she cut another 3 centimeters off one piece, leaving 6 centimeters of fabric. How many centimeters long was her original piece of fabric? Write two equations with letters for the unknowns. Solve.
We have
fabric cut into 5 equal -length pieces
she cut 3 cm
l=length of one piece of the 5 equals pieces
l=6+3
l=9
the original piece of fabric is
o= length of the original fabric
o=5l
o=5(9)
o=45 cm
the original piece of fabric is 45 cm
Can u guys simplify this?
(2x^-3y^5)^2*(x^7y^-11)
3 166.40 266.24 3. Consider the following functions which all have an or decay? By what percent? Rewrite as (1+r) or (1-r) f(t) = 30(1.04) p(x) = 30(0.65)Solve f(t)
ANSWER
Function f(t) represents a growth by 4%
EXPLANATION
If the function represents a decay it is written as:
[tex]f(t)=a(1-r)^t[/tex]and if it represents a growth it's:
[tex]f(t)=a(1+r)^t[/tex]We can see if it's a growth or decay by looking at the number we have between parenthesis: if it's greater than 1, then it's a growth and if it's less than 1 then it's a decay.
For function f(t) we have
[tex]1+r=1.04[/tex]Therefore, r = 0.04 which, expressed as a percent is 4%
How many terms do you have in the expression 7x - 2y + 8?
Answer:
3 terms we have constant ,Y and X terms
I really need help please
The surface area of the given figure is the sum of the area of the six faces.
Two of them have an area A1:
A1 = 2.5 x 4 ft² = 10 ft²
Other two have an area A2:
A2 = 1.25 x 2.5 ft² = 3.125 ft²
and the other two have an area A3:
A3 = 1.25 x 4 ft² = 5 ft²
Then, the total surface area is:
AT = 2(A1) + 2(A2) + 2(A3)
AT = 2(10 ft²) + 2(3.125 ft²) + 2(5 ft²)
AT = 36.25 ft²
Hence, the total surface area of the given figure is 36.25 ft²
Need answer for 3a please. This is for homework :)
Given the supplementary angle below for 3a,
Supplementary angles is 180°,
To find x,
[tex]\begin{gathered} 132^0+2x^0+3=180 \\ 2x^0+135^0=180^0 \\ 2x^0=180^0-135^0 \\ 2x^0=45^0 \\ x=\frac{45^0}{2}=22.5^0 \\ x=22.5^0 \end{gathered}[/tex]Hence, x = 22.5°
w=3? What is the value of the expression below when w = 5w+ 2
Answer:
The value of the expression at w=3 is;
[tex]17[/tex]Explanation:
Given the expression;
[tex]5w+2[/tex]Then when w=3, the value of the expression is;
[tex]\begin{gathered} 5w+2 \\ =5(3)+2 \\ =15+2 \\ =17 \end{gathered}[/tex]The value is gotten by replacing/substituting w with 3 in the expression;
Therefore, the value of the expression at w=3 is;
[tex]17[/tex]Can you please help me because I don’t understand this and I would like to really understand it
Answer:
Explanation:
Given the expression:
[tex]\sqrt{12(x-1)}\div\sqrt{2(x-1)^{2}}[/tex]By the division law of surds:
[tex]\sqrt[]{x}\div\sqrt[]{y}=\sqrt[]{\frac{x}{y}}[/tex]Therefore:
[tex]\sqrt[]{12(x-1)}\div\sqrt[]{2(x-1)^2}=\sqrt[]{\frac{12(x-1)}{2(x-1)^2}}[/tex]The result obtained can be rewritten in the form below:
[tex]=\sqrt[]{\frac{2\times6(x-1)}{2(x-1)(x-1)^{}}}[/tex]Canceling out the common factors, we have:
[tex]=\sqrt[]{\frac{6}{(x-1)^{}}}[/tex]An equivalent expression is Opt
an acre is one chain multiplied times one furlong. I know from horse racing that there are 8furlongs in one mile. I remember that there are 640acres in one square mile. How many feet are in one chain?
Based on the acres in one square mile and the number of furlongs, the number of feet in one chain is 66 feet.
How to find the number of feet?First, find the number of feet in 1 furlong:
8 furlongs = 1 mile
This means that 1 furlong is 1/8 miles. In feet this is:
= 1/8 x 5,280 feet per mile
= 660 feet
Then, it is said that an acre is equal to a Chain x a Furlong.
This means that 1 chain is:
= Number of acres per square feet / Number of feet in chain
= 43,560 / 660
= 66 ft
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solving systems by graphing and tables : equations and inequalities
Given,
The system of inequalitites are,
[tex]\begin{gathered} 2x+3y>0 \\ x-y\leq5 \end{gathered}[/tex]The graph of the inequalities is,
The are three possible solution for the inequality.
For (0, 0),
[tex]\begin{gathered} 2x+3y>0 \\ 2(0)+3(0)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 0-0\leq5 \\ 0\leq5 \end{gathered}[/tex]For (3, -2),
[tex]\begin{gathered} 2x+3y>0 \\ 2(3)+3(-2)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 3-(-2)\leq5 \\ 5=5 \end{gathered}[/tex]For (5, 0),
[tex]\begin{gathered} 2x+3y>0 \\ 2(5)+3(0)>0 \\ 5>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 5-(0)\leq5 \\ 5=5 \end{gathered}[/tex]Hence, the solution of the inequalities is (5, 0).
Why is it important to
line up the digits in each place-value position when subtracting?
Answer: it’s important because when you do that it makes it easier to remember what’s not a whole number and what is
Step-by-step explanation: the answer is basically the explanation
Adele opens an account with $140 and deposits $35 a month. Kent opens an account with $50 and also
deposits $35 a month. Will they have the same amount in their accounts at any point? If so, in how many
months and how much will be in each account? Complete the explanation.
have the same amount in their accounts at a certain point. Setting the expressions equal
which is (select)
and solving them gives 140=
They (select)
to each other gives 140 + 35x =
View Exampl
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Answer: No
Step-by-step explanation:
If Adele opens an account with more money than Kent, and they deposit the same amount each month, Adele will always have more money than Kent.
Find five soloutions of the equation select integer values for X starting with -2 and ending with 2. Complete the table of value below y=6x-8
The five solutions of the equation y = 6x - 8 for x starting with -2 and ending with 2 are: (-2, -20), (-1, -14), (0, -8), (1, -2) and (2, 4)
In this question, we have been given an equation y = 6x - 8
We need to find five solutions of the equation select integer values for x starting with -2 and ending with 2.
For x = -2,
y = 6(-2) - 8
y = -20
For x = -1,
y = 6(-1) - 8
y = -14
For x = 0,
y = 6(0) - 8
y = -8
For x = 1,
y = 6(1) - 8
y = -2
For x = 2,
y = 6(2) - 8
y = 4
Therefore, five solutions of the equation y = 6x - 8 for x starting with -2 and ending with 2 are: (-2, -20), (-1, -14), (0, -8), (1, -2) and (2, 4)
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Jina opened a savings account with $600 and was paid simple interest at an annual rate of 3%. When Jina closed the account, she was paid $54 in interest. How long was the account open for, in years?
Answer: The account has been open for 3 years
Step-by-step explanation:
3% of $600 is 18
18*3 = 54
Answer:
3 years
have $600
interest $54
annual rate 3%
600 - 3% = 582 that is the money she has in bank without interest
600-582 = 18
54÷ 18= 3 years
can you help me with discount tax tip and markup
Answer:
Final Price = $24.5
Explanation:
To found the final price, we first need to find 30% of $35 as follows:
[tex]35\times30\text{ \% = 35}\times\frac{30}{100}=10.5[/tex]So, there will be a discount of $10.5
Then, the final price will be the original price less the 30% of $35, so the final price will be equal to:
Final Price = Original Price - Discount
Final Price = $35 - $10.5
Final Price = $24.5
So, the answer is $24.5
A) equation in center radius form B) equation in general form
The equation of a circle in center-radius form, is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]-Where the coordinates of the center of the circle are (h,k) and the radius of the circle is r.
From the given graph, we can see that the coordinates of the center are (-2,4) and the radius of the circle is 2.
a)
To determine the equation of the circle in center-radius form, replace h=-2, k=4 and r=2
[tex]\begin{gathered} \Rightarrow(x-(-2))^2+(y-(4))^2=2^2 \\ \Rightarrow(x+2)^2+(y-4)^2=4 \end{gathered}[/tex]Therefore, the equation of the circle in center-radius form is:
[tex](x+2)^2+(y-4)^2=4[/tex]b)
To find the equation of the circle in general form, expand the parentheses and take all the terms to the left member:
[tex]\begin{gathered} (x+2)^2+(y-4)^2=4 \\ \Rightarrow x^2+2(2)(x)+(2)^2+y^2-2(4)(y)+4^2=4 \\ \Rightarrow x^2+4x+4+y^2-8y+16=4 \\ \Rightarrow x^2+4x+y^2-8y+20=4 \\ \Rightarrow x^2+4x+y^2-8y+20-4=0 \\ \Rightarrow x^2+4x+y^2-8y+16=0 \end{gathered}[/tex]Write the quadratic terms first:
[tex]\Rightarrow x^2+y^2+4x-8y+16=0[/tex]Therefore, the equation of the circle in general form, is:
[tex]x^2+y^2+4x-8y+16=0[/tex]5. Find the arclength that subtends a central angle of 175° in a circle with radius 3 feet.
As given by the question
There are given that the central angle is 175 degrees and the radius is 3 feet.
Now,
The length of an arc given it subtends a known angle at the centre is:
[tex]\text{arc length=2}\times\pi\times r\times\frac{175}{360}[/tex]Then,
[tex]\begin{gathered} \text{arc length=2}\times\pi\times r\times\frac{175}{360} \\ \text{arc length=2}\times3.14\times3\times\frac{175}{360} \\ \text{arc length=}9.16 \end{gathered}[/tex]Hence, the arclength is 9.16.
which table of ordered pairs represents a line that has a slope that is the same as the slope of the line represented by the equation y=2x + 1?
Answer:
From the above options, the only table that have the same slope as the given line in the equation (m=2) is Table C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]Explanation:
Given the equation;
[tex]y=2x+1[/tex]The slope of the above line is;
[tex]m=2[/tex]From the given options, let us find the table that has the same slope as the above equation;
A.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-8-7}{3-(-2)} \\ m=\frac{-15}{5} \\ m=-3 \end{gathered}[/tex]B.
[tex]\begin{gathered} m=\frac{4-2}{2-(-2)} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]D.
[tex]\begin{gathered} m=\frac{-1-2}{4-(-2)} \\ m=\frac{-3}{6} \\ m=-\frac{1}{2} \end{gathered}[/tex]From the above options, the only table that have the same slope as the given line (m=2) is Table C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]If a and b are the measure of two first quadrant angles, find the exact value of the functioncsc a =5/3 and tan 5/12 find the cod (a+b)
Input data
[tex]\begin{gathered} \cos a=\frac{5}{3} \\ \tan b=\frac{5}{12} \end{gathered}[/tex]
Now for cos(a+b)
[tex]\begin{gathered} a=\csc ^{-1}(\frac{5}{3})^{} \\ a=36.87 \end{gathered}[/tex][tex]\begin{gathered} b=\tan ^{-1}(\frac{5}{12}) \\ b=22.62 \end{gathered}[/tex][tex]\begin{gathered} \cos (a+b) \\ \cos (36.87+22.62) \\ \cos 59.5 \\ \frac{33}{65}=0.507 \end{gathered}[/tex]