Answers
Using long division:
Related Questions
7. Brian is packing boxes that can contain two types of items, board games and remote control cars. Board games weigh 3 pounds and remote controlled cars weigh 1.5 pounds, and the box can hold no more than 24 pounds. Also, in each box, the amount of remote control cars must be at least 4 times the amount of board games. Let x represent the number of board games. Let y represent the number of remote controlled cars.A. Write the system of inequalities that represents this situation. You should have 2 different inequalities that you wrote. B. Graph the system of inequalities on the coordinate plane below.
Answers
A)
[tex]\begin{gathered} 3x+1.5y\leq24\Rightarrow inequality(1) \\ y\ge4x\rightarrow inequality(2) \end{gathered}[/tex]Explanation
Step 1
Let x represents the number of board games
Let y represent the number of remote controlled cars
i)
a)Board games weigh 3 pounds
b) remote-controlled cars weigh 1.5 pounds
The box can hold no more than 24 pounds( in other words it must be equal or less thant 24),so
[tex]3x+1.5y\leq24\Rightarrow inequality(1)[/tex]ii) in each box, the amount of remote control cars must be at least 4 times the amount of board games( in other words, the number of remote control cars must be equal or greater than 4 times the amount of board games, so,
hence
[tex]y\ge4x\rightarrow inequality(2)[/tex]so,
A)
[tex]\begin{gathered} 3x+1.5y\leq24\Rightarrow inequality(1) \\ y\ge4x\rightarrow inequality(2) \end{gathered}[/tex]Step 2
graph the inequalities
a) set the sign = to convert the inequality in a funcion, isolate for y
b) fnd 2 coordinates of the line
C) draw the line
[tex]\begin{gathered} \leq\rightarrow\text{ continuous line} \\ \ge\rightarrow\text{ cointinuous line} \end{gathered}[/tex]i)
[tex]\begin{gathered} 3x+1.5y=24 \\ 1.5y=24-3x \\ y\leq\frac{24-3x}{1.5} \\ y=16-2x \\ \text{when x= 0} \\ y=16-0 \\ so,P1(0,16) \\ \text{when =3} \\ y=16-2(3) \\ y=16-6=10 \\ so\text{, P2(3,10)} \end{gathered}[/tex]draw a line(continuosus) that passes trougth P1 and P2
ii)
[tex]\begin{gathered} y\ge4x\rightarrow y=4x \\ \text{when x=0} \\ y=4\cdot0=0 \\ so\text{ , P3(}0,0) \\ \text{and when x= 2} \\ y=4(2)=8 \\ so,\text{ P4}(2,8) \end{gathered}[/tex]draw a line(continuosus) that passes trougth P3 and P4
I hope this helps you
35Todd forgot the first two numbers of his locker combination. The numbers can be any number 1 through 6. What istprobability that he will guess the first number correctly and the second number incorrectly?OAOB.olaroc.OD.ResetSubmit
Answers
Answer:
A. 5/36
Explanation:
The total number of possible number choice = 6
Only 1 out of 6 can be correct, thus:
[tex]P(\text{he will guess the first number correctly)}=\frac{1}{6}[/tex]There are 5 incorrect numbers, therefore:
[tex]P(\text{he will guess the }\sec ond\text{ number incorrectly)}=\frac{5}{6}[/tex]Therefore, the probability that he will guess the first number correctly and the second number incorrectly:
[tex]\begin{gathered} =\frac{1}{6}\times\frac{5}{6} \\ =\frac{5}{36} \end{gathered}[/tex]The correct choice is A.
write the letter of the table that corresponds with the graph.Explain your answer.
Answers
for the table X :
for the table R :
For tabel V :
For tabel Q :
Krissy owns a burger restaurant in Chicago, Illinois. The number of burgers sold at Krissy's restaurant was 605 in June. The number sold in July was 20% more than the number sold in June. How many burgers did Krissy's restaurant sell in July? burgers.
Answers
Answer:
100% ~ 605
20% ~ 121
120% ~ 726
The restaurant sells 726 burgers in July.
Calculate the area of each figure. Which figure has the greatest area? 9 cm 6.8 cm 7 cm l-_- 10 cm 15 cm 6 cm 13 cm
Answers
For the frst one is: 63 cm^2
[tex]A_{F1}=\text{ 9cm}\cdot7\operatorname{cm}=63cm^2[/tex]For the second figure we have that the area is: 136cm^2
[tex]\begin{gathered} A_{F2}=2\cdot(6.8cm)(10cm) \\ =2(68cm^2)\text{ = 136}cm^2 \end{gathered}[/tex]And for the third one, the area is: 84cm^2
[tex]\frac{(15cm\text{ + 13cm)}\cdot6\operatorname{cm}}{2}=\frac{28\operatorname{cm}\cdot6\operatorname{cm}}{2}=\frac{168\operatorname{cm}^2}{2}=84\operatorname{cm}[/tex]factoring is writing an expression as the product of two factors; what are those factors ? 6(5+3)
Answers
Given the expression 6(5+3)
The expression shows that 6 was factored out from the bracket
evaluate the expression in parenthesis
= 6(5+3)
= 6(8)
This shows that the factors of the expression are 6 and 8
4. Jacob bought some tickets to see his favorite group, and it cost $76. The relationship between the adult tickets, a, and the student's tickets, s, can be expressed by the equation 10a + 8C = 76. If he bought 4 adult ticket, then how student's tickets did he buy? If he bought 2 student ticket, then how adult's tickets did he buy? Which equation shows the number of student tickets as a function of the number of adult tickets? A. C= 68 – 10a B.C=76 – 10a C. C= -4/5a +38/5 D. C=-5/4a+19/2
Answers
Given the equation:
[tex]10a+8c=76[/tex]If Jacob bought 4 adult tickets, then a = 4, so we can solve for c:
[tex]\begin{gathered} a=4 \\ \Rightarrow10(4)+8c=76 \\ \Rightarrow8c=76-40=36 \\ \Rightarrow c=\frac{36}{8}=\frac{9}{2}=4.5 \\ c=4.5 \end{gathered}[/tex]therefore, Jacob bought 4 or 5 students tickets.
Now, if Jacob bought 2 student tickets, then c=2 and for 'a' we have the following:
[tex]\begin{gathered} c=2 \\ \Rightarrow10a+8(2)=76 \\ \Rightarrow10a=76-16=60 \\ \Rightarrow a=\frac{60}{10}=6 \\ a=6 \end{gathered}[/tex]therefore, Jacob bought 6 adult tickets.
Finally, to find the equation that shows the number of student tickets as a function of adult tickets, we have to solve for 'c' to get the following:
[tex]\begin{gathered} 10a+8c=76 \\ \Rightarrow8c=76-10a \\ \Rightarrow c=-\frac{10}{8}a+\frac{76}{8}=-\frac{5}{4}a+\frac{19}{2} \\ c=-\frac{5}{4}a+\frac{19}{2} \end{gathered}[/tex]therefore, the function would be c = -5/4a +19/2
Just need a simple explanation.
Answers
QUESTION 1
The ingredients for Apple Crumble cost you $1.45 per serving. If your bakery menu lists a price of $4.95 for your Apple Crumble, then what percent
of the sale goes to the food cost?
Answers
The percentage of sale that goes to the food cost is 341.3%.
The ingredients for Apple crumble cost = $1.45 per serving.
The selling price of the Apple crumble = $4.95
percentage of the sale that goes to the food cost = ?
according to the question, we formulate:
% sale that goes to the food cost = cost of ingredients/selling price of the apple crumble×100
% sale = 4.95/1.45 × 100
% sale = 3.41 × 100
% sale = 341.3%
Hence the percentage of sale that goes to the food cost is 341.3%.
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I’m having trouble I need this answered, it is apart of my ACT prep guide
Answers
Question:
Solution:
According to the data of the problem, the series is given by the following expression:
[tex]\sum ^{\infty}_{n\mathop=1}\frac{n}{3^n}=\frac{1}{3^1}+\frac{2}{3^2}+\frac{3}{3^3}+\cdots[/tex]now, remember the ratio test:
Suppose we have the series
[tex]\sum ^{}_{}a_n[/tex]Define,
[tex]L\text{ =}\lim _{n\to\infty}|\frac{a_{n+1}}{a_n}|[/tex]Then,
if L<1, the series is absolutely convergent (and hence convergent).
if
L>1, the series is divergent.
if
L=1 the series may be divergent, conditionally convergent, or absolutely convergent.
Applying this definition to the given series, we obtain:
[tex]L\text{ =}\lim _{n\to\infty}|\frac{(n+1)3^n_{}}{n3^{n+1}_{}}|=\frac{1}{3}<1[/tex]then, the given series is absolutely convergent (and hence convergent). So that, we can conclude that the correct answer is:
The complex number w is given by w= p-4i/2-3i where p is a real constant. Express w in the form a+bi where a and b are real constants. give your answer in simplest terms of p.b) given that arg w= pi/4 find the value of p
Answers
Step 1
Given;
[tex]w=\frac{p-4i}{2-3i}[/tex]Required; To express w in the form of a+bi.
Step 2
Express w in the form of a+bi
Multiply the numerator and the denominator by the binomial conjugate of (2-3i)
The binomial conjugate of (2-3i) = (2+3i)
[tex]w=(\frac{p-4i}{2-3i})\times(\frac{2+3i}{2+3i})=\frac{2p+3pi-8i-12i^2}{4+6i-6i-9i^2}[/tex][tex]\begin{gathered} w=\frac{2p+3pi-8i-12(-1)}{4-9(-1)} \\ \text{Note; i}^2=(\sqrt[]{-1})^2=-1 \end{gathered}[/tex][tex]\begin{gathered} w=\frac{2p+3pi-8i+12}{4+9}=\frac{2p+3pi-8i+12}{13} \\ w=\frac{(2p+12)+(3p-8)i}{13} \\ w=\frac{(2p+12)}{13}+\frac{(3p-8)i}{13} \\ w=\frac{2(p+6)}{13}+\frac{(3p-8)i}{13} \end{gathered}[/tex]where;
[tex]\begin{gathered} a=\frac{2(p+6)}{13}_{} \\ bi=\frac{(3p-8)i}{13} \end{gathered}[/tex]a square base pyramid is shown below. find its surgace area. Round to the nearest tenth
Answers
Given data
Height = 16.8 ft
Slant height = 19.3 ft
First, you find the base of the right angle triangle in the daigram.
Opposite = 16.8 ft
Hypotenuse = 19.3 ft
Adjacent = b
[tex]\begin{gathered} \text{Appy pythagorus theorem} \\ \text{Opp}^2+Adj^2=Hypotenuse^2 \\ 16.8^2+b^2=19.3^2 \\ 282.24+b^2\text{ = 372.49} \\ b^2=372.49\text{ - 282.24} \\ b^2\text{ = 90.25} \\ b\text{ = }\sqrt[\square]{90.25} \\ b\text{ = 9.5} \end{gathered}[/tex]Next,
The side of the base of the pyramid = 2 x b
= 2 x 9.5
= 19
The square measure 19 ft
To find the surface area of the pyramid, sum the areas of the square base and the area of the four triangles.
Area of the square = 19 x 19 = 361
[tex]\begin{gathered} \text{Area of the four triangles = }\frac{1}{2}\text{ base x height} \\ \text{ = 0.5 x 19 x 19.3} \\ \text{ = 183.35} \\ \text{Area of the four triangle = 4 x 183.35 = 733.4} \end{gathered}[/tex]Toal surface area of the figure = 733.4 + 361
= 1094.4
Jane wants to make a a cake for her friend's birthday she had $9 and spent it on decoration with tax included a pack of 10 candles is $1.50 and which tube of of colored frosting is 2.75 if she has to bye two packs and candles how many tubes of frosting can she buy ?
Answers
Given:
Total money she had = $9
Cost of each pack of candles = $1.50
Cost of each tube of colored frosting = $2.75
Let's find the number of colored frosting she can buy.
Since she has to buy 2 packs of candles, the total cost she would spend on candles is:
Cost of candles = $1.50 x 2 = $3.00
Thus, we have the inequality:
2.75x + 3.00 ≤ 9
Where x represents the number of tubes of colored frosting she can buy.
Let's solve for x.
2.75x + 3 ≤ 9
Subtract 3 from bith sides:
2.75x + 3 - 3 ≤ 9 - 3
2.75x ≤ 6
Divide both sides by 2.75:
[tex]\begin{gathered} \frac{2.75x}{2.75}\le\frac{6}{2.75} \\ \\ x\le2.18 \end{gathered}[/tex]Since x is less than or equal to 2.18, this means Jane can buy no more than 2 tubes of colored frosting.
ANSWER:
No more than 2 tubes
ABC-DEF. what is the scale factor of triangle ABC to triangle DEF
Answers
in the given triangles the scale factor will be the ratio of the hypotenuse of DEF and the hypotenuse of ABC
so ratio = 30/10 = 3
thus the scale factor is 3
so the value of the sides of ABC is,
x = 27/3
x = 9
y = 18/3
y = 6
Solve the system of equation by substitution. x=7y+45x-4y=-11
Answers
Mila, this is the solution:
x = 7y + 4
5x - 4y = -11
_________________
Step 1: Let's substitute x in the second equation and solve for y, as follows:
Which of the following statements is NOT true regarding an expression written in scientific
notation in the form of ax10*?
O The value of a must be greater than or equal to 1 and smaller than 10.
O The value of n must be an integer.
O Doubling n results in a doubling of the value of the expression.
O Doubling a results in a doubling of the value of the expression.
Answers
Step-by-step explanation:
not true is " doubling n results in a doubling of the value of the expression".
e.g.
2.3 × 10² = 230
now I double n :
2.3 × 10⁴ = 23,000
the value of the expression has increased much more than just doubling.
According to Greg, perfect cherry pies have a ratio of 240 cherries to 3 pies. How many cherries does Greg need to make 15 perfect cherry pies?
Answers
Answer: 1200 cherries.
Step-by-step explanation:
If 240 cherries are need for 3 pies, multiply 240 by 5 to get the answer.
Your answer is 1200 cherries.
Greg needs 1200 cherries to make 15 perfect cherry pies.
Question 15 of 15Taniah is trying to find the area of the following square whereWY=10. What is the area?
Answers
The area of a square given its diagonal (d) is computed as follows:
[tex]A=\frac{1}{2}d^2[/tex]In this case, the diagonal is 10 units long, then the area is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot10^2 \\ A=\frac{1}{2}\cdot100 \\ A=50\text{ square units} \end{gathered}[/tex]In a battle, Iceman beings to freeze iron man's suit. By the end of the battle, Iron Man's suit dropped to -4.5 deF. If Iceman was able to decrease Iron Man's suit by 73.2. What temperature did Iron Man's suit start at?
Answers
By solving a linear equation, we can see that the initial temperature of the suit is 68.7F
What temperature did Iron Man's suit start at?
We know that at the end of the battle, Iron Man's suit was at a temperature of -4.5 degrees Fahrenheit.
We know that Iceman decreased Iron Man's temperature by 73.2 F, so, if the initial temperature of the suit is T, then we can write the linear equation:
T - 73.2F = -4.5F
We can solve this equation for T.
T = -4.5F + 73.2F = 68.7F
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The approximate areas of Wisconsin and South Carolina are listed below:
Wisconsin: 1.7 x 105 square kilometers
South Carolina: 8.29 × 104 square kilometers
How much larger is Wisconsin? Express your answer using scientific notation.
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Step-by-step explanation:
you mean
1.7 × 10⁵ square kilometers (km²) and
8.29 × 10⁴ km²
1.7 × 10⁵ = 17 × 10⁴
how much larger is this than
8.29 + 10⁴ ?
(17 - 8.29) × 10⁴ = 8.71 × 10⁴ km²
so, Wisconsin is 8.71 × 10⁴ km² larger than South Carolina.
(4, -13) and (8,-8) slope formula
Answers
Point A (4, -13)
Point B (8, -8)
Slope formula
[tex]\begin{gathered} m=\frac{-8-(-13)}{8-4} \\ m=\frac{-8+13}{4} \\ m=\frac{5}{4} \\ \end{gathered}[/tex]The slope would be 5/4
A point is plotted on a coordinate grid at (-3, 4). How far is the point from point (0, 0)?
Answers
The point at (-3, 4) is at a distance of 5 units from the point (0, 0).
How far is the point from (0, 0)?For two points (x₁, y₁) and (x₂, y₂), the distance between them is given by the formula:
distance = √( (x₁ - x₂)² + (y₁ - y₂)²)
In this case, we want to get the distance between (-3, 4) and (0, 0), using the above formula we will see that the distance is:
distance = √( (-3 - 0)² + (4 - 0)²) = √25 = 5
The distance is 5 units.
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Stephanie was making chocolate chip cookies the recipe called for 9 chocolate chip cookie if Stephanie had a total of 108 chocolate chips how many cookies could she make
Answers
Given :
the recipe called for 9 chocolate chip cookie
The total chocolate chips = 108
So, the number of cookies = 108/9 = 12
For which value(s) of x will the rational expression below be undefined? Check all that apply
Answers
Given:
[tex]\frac{(x+3)(x+6)}{x+7}[/tex]Required:
We need to find the value of x that makes the given expression is undefined.
Explanation:
Recall that a rational expression is undefined when the denominator is equal to zero.
The denominator of the given expression is x+7.
Equate it to zero.
[tex]x+7=0[/tex]Subtract 7 from both sides of the equation.
[tex]x+7-7=0-7[/tex][tex]x=-7[/tex]Final answer:
[tex]x=-7[/tex]a. What is KL? __. b. What is the coordinate of the midpoint of KL? __?c. Point C lies between points K and L. The distance between points K and C is __ of KL. What is the coordinate of point C? __.
Answers
Given the graph of the line segment KL on the number line
As shown:
The coordinates of k = -9
The coordinates of L = 15
a. What is KL?
[tex]\begin{gathered} KL=15-(-9)=15+9=24 \\ KL=24 \end{gathered}[/tex]b. What is the coordinate of the midpoint of KL?
Let the midpoint = M
[tex]M=\frac{K+L}{2}=\frac{-9+15}{2}=\frac{6}{2}=3[/tex]So, the coordinates of the midpoint = 3
Explain the difference between the two different function transformations represented by
f(x+2)
f(x-2)
Include an example of each using the parent cubic equation,
f(x) = x³
For full credit, include the following:
1.
A description of each transformation including direction and number of units
2.
3 cubic equations and one graph showing the 3 curves: f(x), f(x+ 2), and f(x - 2)
Answers
The difference between the functions is explained below
What are functions?
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. The set of all pairs, also known as the function's graph, is the only way to express a function in a unique way. In science, engineering, and the majority of the branches of mathematics, functions are often utilized. Functions are allegedly "the principal objects of inquiry" in the majority of mathematical disciplines. Maps and mappings are other names for functions.
Two transformations of the function f(x) are given f(x+2) and f(x-2)
The first one increments the function by 2 and the next one decrements the function by 2.
Let us understand with the help of an example,
The function f(x) = x³
Then f(x+2) = (x+2)³ = x³ + 4x + 8
and f(x-2) = (x-2)³ = x³ - 4x + 8
We can clearly see that both functions expanded differently
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This figure has two intersecting lines and a ray. What is the value of x? What is the measure of the angles? I NEED FULL DETAIL
Answers
The value of x in the intersecting lines is 7 and the measure of the angles are 38 and 52 degrees respectively.
How to solve angles?The sum of angles on a straight line is 180 degrees.
Complementary angles are angles that sum up to 90 degrees.
Therefore,
3x + 17 + 6x + 10 = 90 (complementary angle)
combine like terms
3x + 17 + 6x + 10 = 90
3x + 6x + 17 + 10 = 90
9x + 27 = 90
subtract 27 from both sides of the equation
9x + 27 = 90
9x + 27 - 27 = 90 - 27
9x = 63
divide both sides by 9
9x / 9 = 63 / 9
x = 7
3(7) + 17 = 21 + 17 = 38°
6(7) + 10 = 52°
Therefore, the two angles are 38 degrees and 52 degrees respectively.
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Use f(x) = 5x − 4 and g(x) = 3 − x2 to evaluate the expression. (a) (f ∘ g)(−2) (b) (g ∘ f)(−2)
Answers
The composite functions are evaluated as:
a. (f ∘ g)(−2) = -9
b. (g ∘ f)(−2) = - 193
How to Solve Composite Functions?Given the functions,
f(x) = 5x − 4
g(x) = 3 − x²
a. To find the composite function, (f ∘ g)(−2), we will replace g(-2) instead of x in the function f(x).
Therefore, we would have:
(f ∘ g)(−2) = f(g(-2))
f(g(-2)) = 5(3 − (-2²)) − 4
f(g(-2)) = 5(3 − 4) − 4
f(g(-2)) = 5(-1) − 4
f(g(-2)) = -5 − 4
f(g(-2)) = -9
Therefore, (f ∘ g)(−2) = -9.
b. Also, the composite function (g ∘ f)(−2) would be evaluated by replacing f(-2) instead of x in g(x).
Therefore:
(g ∘ f)(−2) = g(f(-2))
g(f(-2)) = 3 − (5(-2) − 4)²
g(f(-2)) = 3 − (-10 − 4)²
g(f(-2)) = 3 − (-14)²
g(f(-2)) = 3 − 196
g(f(-2)) = -193
Therefore, (g ∘ f)(−2) = - 193
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The length of a rectangle i 5 centimeters more than the width. The area of the rectangle is 36 square centimeters. What is the length?
Answers
Answer: 9 cm
Step-by-step explanation:
l=length. A=area. w=width.
l*w=A
l*(l-5)=36 ==> w=l-5
l^2-5l=36
l^2-5l-36=0
l^2-9l+4l-36=0
l(l-9)+4(l-9)=0
(l+4)(l-9)=0
9*4=36
4=9-5 ==> w=l-5
l=9 cm
what is the answer to 2 3/5 if converted to a fraction greater than 1
Answers
Convert the mixed number into a simple fraction:
2 3/5 = (2x5+3) /5 = 13/5
13/5 > 1
