Quiz 1 Write an addition equation or a subtraction equation (your choice!) to describe the diagram. _15 10 -5 0 5 Report a prob
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Each arrow represents a subtraction. The beginning of the arrow is the number where the subtraction should start and the point of the arrow is the point where the subtraction should end. The first arrow begins in "0" and ends in "-4", while the second arrow begins on the point of the second one and ends in "-13".
We should first represent the arrow number 1, which is shown below:
[tex]0\text{ -4}[/tex]Because the arrow starts at 0 and go "4" units to the left, therefore we need to subtract 4.
The second arrow starts from the first and goes 9 units to the left, so we have:
[tex](0\text{ - 4) - 9}[/tex]Related Questions
The scores of Janet in her math tests are 65, 78, 56, 73, 67, 92. Find themedian score of Janet.
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Answer
70
Explanations;
Given the following datasets that represents the scores of Janet in her math tests
65, 78, 56, 73, 67, 92.
The median is the middle value of the dataset after rearrangement. On rearranging in ascending order;
56, 65 (67, 73) 78, 92
Since there are 2 numbers at the middle, hence the median is the mean value of the data
[tex]\begin{gathered} Median=\frac{67+73}{2} \\ Median=\frac{140}{2} \\ Median=70 \end{gathered}[/tex]Hence the median scores is 70
a. angle addition postulate with angles forming a straight line angle.b. triangle sum theorem c. linear pair postulate
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A. angle addition postulate with angles forming a straight line angle
1) Examining that table, we can see that step 4 is a consequence of the third step, the triangle sum theorem.
2) Then in step 4, we have the following reason to state that the sum of those angles is 180º: Then as we can see below:
We have a Linear Pair between the angles ∠ABD, ∠DBE, and ∠CBE since those angles combined add up to 180º (a straight angle) in red.
3). Hence, the answer is A
*DUE TODAY* ANSWER ASAP Olivia has read 40 pages of a 70 page book, 60 pages of an 85 page book and 43 of a 65 page book. What is the percentage of pages Olivia has not read? PLEASE GIVE ME A STEP BY STEP EXPLANATION PLEASE!
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STEP2: turn all of the fractions you have just made into percentages ( divide the numerator by the denominator then, times by 100)
STEP 3: add all of the percentages up and put the sum of them all over 300 ( e.g each percentage added up / 300 )
STEP 4: turn that fraction you just made back into a percentage then that should be your answer!!!
If you need any more help just ask me!
A sequence is shown below.10, 12, 14, 16, ...Which function can be used to determine the nthnumber in the sequence?
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Answer:
The nth term of the given sequence can be determined using the function;
[tex]a_n=2n+8[/tex]Explanation:
Given the sequence;
[tex]10,12,14,16,\ldots[/tex]The sequence is an arithmetic progression with a common difference d and first term a;
[tex]\begin{gathered} d=12-10 \\ d=2 \\ a=10 \end{gathered}[/tex]Recall that the nth term of an AP can be calculated using the formula;
[tex]a_n=a+(n-1)d[/tex]substituting the given values;
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_n=10+(n-1)2 \\ a_n=10+2(n-1) \\ a_n=10+2n-2 \\ a_n=2n+10-2 \\ a_n=2n+8 \end{gathered}[/tex]Therefore, the nth term of the given sequence can be determined using the function;
[tex]a_n=2n+8[/tex]I just don't know how to indicate values on ration equations
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Solving the equation we have:
[tex]\begin{gathered} \frac{x+3}{x-3}=\frac{12}{3} \\ \frac{x+3}{x-3}=4\text{ (Simplifying the fraction)} \\ x+3=4(x-3)\text{ (Multiplying x-3 on both sides of the equation)} \\ x+3=4x-12\text{ (Distributing)} \\ x+3+12=4x\text{ (Adding 12 to both sides of the equation)} \\ 3+12=4x-x\text{ (Subtracting x from both sides of the equation)} \\ 15=3x\text{ (Adding)} \\ \frac{15}{3}=x\text{ (Dividing by 3 on both sides of the equation)} \\ 5=x\text{ } \end{gathered}[/tex]The solution is x=5 and it is valid as the result of replacing it in the denominator is not zero. ( 5 - 3 ≠ 0)
Parker has tangerines and apricots in a ratio of 12:95. How many apricots does hehave if he has 96 tangerines?On the double number line below, fill in the given values, then use multiplication ordivision to find the missing value.
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We know that if Parker has 12 tangerines he has 95 apricots, so to find how many apricots he has we need to do a rule of tree
[tex]\begin{gathered} x\text{ apricots }\cdot\frac{12\text{ tangerines}}{95\text{ apricots}}=96\text{ tangerines} \\ x\text{ apricots = 96 tangerines }\cdot\frac{95\text{ apricots}}{12\text{ tangerines}} \\ x\text{ apricots =}\frac{96\cdot95}{12}\text{ apricots = }\frac{9120}{12}\text{ apricots} \\ x=760 \end{gathered}[/tex]So the answer is that Parker has 760 apricots is he has 96 tangerines.
How many solutions does the equation −5a + 5a + 9 = 8 have? (5 points)NoneOneTwoInfinitely many
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ANSWER:
1st option: none
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]−5a\:+\:5a\:+\:9\:=\:8\:[/tex]We solve for a:
[tex]\begin{gathered} −5a\:+\:5a\:+\:9\:=\:8\: \\ \\ 0+9=8 \\ \\ 9=8\rightarrow\text{ false} \end{gathered}[/tex]Therefore, the equation has no solution, the correct answer is 1st option: none
-8, {0, -3, 1, -1}, {-1, 1, -2}, {3, -5, 4, -1}, {4, -2, 2}
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Solution
17. -8
18. 0, -3 ,1 , -1
19. -1 ,1 ,-2
20. 3, -5 ,4 ,-1
21. 4, -2. 2
3 view. writing simplity expressions The volume of a cube is calculated by multiplying all three side lengths. If a cube has a side of 16 cm, which expression can be used to calculate the volume? A. 161 B. 167 C. 162 D. 164 에 2y Click to add speaker notes
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If we have a cube with a side length of 16 cm, we can calculate the volume as the length side powered to the 3rd or multiplying the side length 3 times:
[tex]V=l\cdot l\cdot l=l^3=16^3[/tex]Answer: V = 16^3 (Option C).
Write the number 0.2 in the form a over b using integers
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We can express 0.2 in the form:
[tex]\frac{2}{10}[/tex]Find the degree and leading coefficient for the given polynomial.−5x^2 − 8x^5 + x − 40degree leading coefficient
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The given polynomial is
- 5x^2 - 8x^5 + x - 40
It can be rewritten as
- 8x^5 - 5x^2 + x - 40
The degree of the polynomial is the highest exponent of the variable in the polynomial. The highest exponent of x is 5. Thus,
degree = 5
The leading coefficient is the coefficient of the term with the highest variable. The coefficient of x^5 is - 8. Thus,
Leading coefficient = - 8
"Solve for all values of x on the given intervals. Write all answer in radians." I am stuck on number 4
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Answer:
[tex]x=\frac{2\pi}{3}+2\pi n,x=\frac{4\pi}{3}+2\pi n[/tex]Explanation:
Given the equation:
[tex]\sin x\tan x=-2-\cot x\sin x[/tex]Add 2+cot(x)sin(x) to both sides of the equation.
[tex]\begin{gathered} \sin x\tan x+2+\cot x\sin x=-2-\cot x\sin x+2+\cot x\sin x \\ \sin x\tan x+2+\cot x\sin x=0 \end{gathered}[/tex]Next, express in terms of sin and cos:
[tex]\begin{gathered} \sin x\frac{\sin x}{\cos x}+2+\frac{\cos x\sin x}{\sin x}=0 \\ \frac{\sin^2x}{\cos x}+2+\cos x=0 \\ \frac{\sin^2x+2\cos x+\cos^2x}{\cos(x)}=0 \\ \implies\sin^2x+2\cos x+\cos^2x=0 \end{gathered}[/tex]Apply the Pythagorean Identity: cos²x+sinx=1
[tex]2\cos x+1=0[/tex]Subtract 1 from both sides:
[tex]\begin{gathered} 2\cos x+1-1=0-1 \\ 2\cos x=-1 \end{gathered}[/tex]Divide both sides by 2:
[tex]\cos x=-\frac{1}{2}[/tex]Take the arccos in the interval (-∞, ):
[tex]\begin{gathered} x=\arccos(-0.5) \\ x=\frac{2\pi}{3}+2\pi n,x=\frac{4\pi}{3}+2\pi n \end{gathered}[/tex]The values of x in the given interval are:
[tex]x=\frac{2\pi}{3}+2\pi n,x=\frac{4\pi}{3}+2\pi n[/tex]please help with this question
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if each u it cube has edge's of length 1/2 foot, what is the volume of the blue-outlined prism
we have that
the volume of each cube is equal to
V=(1/2)^3
V=1/8 ft3
the rectangular prism volume is equal to
calculate the volume by the numbers of cube
so
V=(5)(2)(2)=20 cubes
Multiply by the volume of each cube
20*(1/8)=2.5 ft3
the volume of the rectangular prism is 2.5 ft3
[tex](x + 4)x + 5)[/tex]write the equivalente expression
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given that (x+4) (x+5) and they are asking for equivalent form.
at first both terms are in multiplication form,so multiply x with (x+5) so we get that
[tex](x+4)(x+5)=x^2+5x+4x+20=x^2+9x+20[/tex]I kinda started it but I don’t know how to find the answer
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Solution
[tex]\begin{gathered} x^2+2x-16=0 \\ \\ \text{ using quadratic formula} \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=1,b=2,c=-16 \\ \\ \Rightarrow x=\frac{-2\pm\sqrt{2^2-4(1)(-16)}}{2(1)} \\ \\ \Rightarrow x=\frac{-2\pm\sqrt{4+64}}{2} \\ \\ \Rightarrow x=-1-\sqrt{17} \\ \\ \Rightarrow x=-1+\sqrt{17} \\ \\ \text{ since }x>0 \\ \\ \text{ Therefore the value of }x=-1+\sqrt{17} \end{gathered}[/tex]Convert repeating decimal 0.155….to fraction
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Given the repeating decimal 0.155...
We will convert it to a fraction as follows:
[tex]\begin{gathered} 0.1555.\ldots=0.1+0.055\ldots \\ \\ =\frac{1}{10}+\frac{5}{100-10} \\ \\ =\frac{1}{10}+\frac{5}{90}=\frac{9}{90}+\frac{5}{90}=\frac{14}{90}=\frac{7}{45} \end{gathered}[/tex]so, the answer will be:
[tex]0.1555\ldots=\frac{7}{45}[/tex]6y-(2y-5)=29 step by step
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The given expression is
[tex]6y-(2y-5)=29[/tex]First, we use the distributive property to solve the parenthesis, we have to multiply the negative sign with each term inside the parenthesis.
[tex]6y-2y+5=29[/tex]We reduce like terms, 6y and -2y are like terms in this case,
[tex]4y+5=29[/tex]Then, we subtract 5 on each side.
[tex]\begin{gathered} 4y+5-5=29-5 \\ 4y=24 \end{gathered}[/tex]At last, we divide the equation by 4.
[tex]\begin{gathered} \frac{4y}{4}=\frac{24}{4} \\ y=6 \end{gathered}[/tex]Therefore, the solution is 6.Which of these standard form equations is equivalent to (x + 1)(x - 2)(x + 4)(3x + 7)?
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The standard form equation that is equivalent to the expression is x⁴ + 16x³ + 3x² - 66x - 56
How to determine the standard form equation that is equivalent?From the question, we have the following expression that can be used in our computation:
(x + 1)(x - 2)(x + 4)(3x + 7)
The above equation is a product of linear factors
This means that the result of the equation is a polynomial with a degree of the number of factors in the expression
So, we have
(x + 1)(x - 2)(x + 4)(3x + 7)
Open the first two brackets
This gives
(x² + x - 2x - 2)(x + 4)(3x + 7)
Evaluate the like terms
So, we have
(x² - x - 2)(x + 4)(3x + 7)
Open the first two brackets
This gives
(x³ + 4x² - x² - 4x - 2x - 8)(3x + 7)
Evaluate the like terms
So, we have
(x³ + 3x² - 6x - 8)(3x + 7)
Open the remaining brackets
This gives
(x⁴ + 7x³ + 9x³ + 21x² - 18x² - 42x - 24x - 56)
Evaluate the like terms
So, we have
(x⁴ + 16x³ + 3x² - 66x - 56)
Remove the bracket
x⁴ + 16x³ + 3x² - 66x - 56
The expression cannot be further simplified
Hence, the result is x⁴ + 16x³ + 3x² - 66x - 56
Read more about equivalent expressions at
https://brainly.com/question/15775046
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A patient takes three 25 mg capsules a day. How many milligrams is he taking daily?
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Given:
A patient takes three 25 mg capsules a day.
[tex]3\times25\text{ mg=75mg}[/tex]Answer: A patient is taking 75 mg capsules every day.
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$.Find the rental cost for each movie and each video game.
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Given
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$. Find the rental cost for each movie and each video game.
Solution
Step 1
Let m represent the movies
And let v represent the video
Therefore,
[tex]\begin{gathered} 8m+4v=\text{ \$49}\ldots Equation\text{ 1} \\ 3m+2v=\text{ \$ 21 }\ldots Equation\text{ 2} \end{gathered}[/tex]Step 2
Use the circle graph below to answer each question. 1. What percent of the Milton's budget is for rent? 2. What percent of the Milton's budget is for clothes? 3. If the Milton's have a $2,000 budget, how much of that budget will go in savings? 4. If the Milton's have a $2,000 budget, how much of that budget will go towards food? 5. If the Milton's have a $2,000 budget, how much of that budget will go towards misc items?
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We are given the Pie chart of Milton's family budget with the following detail:
Food = 33%
Rent = 25%
Savings = 6%
Clothes = 15%
Misc = 21%
1. The percentage of the budget allocated to rent is 25%
2. The percentage of the budget allocated to clothes is 15%
3.
If the budget is $2,000, the amount allocated to Savings is:
[tex]\begin{gathered} Savings=6\text{\%}\times\text{\$}2,000 \\ Savings=\frac{6}{100}\times2,000 \\ Savings=\text{ \$}120 \end{gathered}[/tex]4.
If the budget is $2,000, the amount allocated to food is:
[tex]\begin{gathered} Food=33\text{\%}\times\text{\$}2,000 \\ Food=\frac{33}{100}\times2,000 \\ Food=\text{\$}660 \end{gathered}[/tex]5.
If the budget is $2,000, the amount allocated to Misc is:
[tex]\begin{gathered} Misc=21\text{\%}\times\text{\$}2,000 \\ Misc=\frac{21}{100}\times2,000 \\ Misc=\text{\$}420 \end{gathered}[/tex]18. What is the multiple zero and multiplicity of f(x) = (x - 1)(x - 1)(x + 7)?multiple zero = 2; multiplicity = 1multiple zero = 2; multiplicity = -1multiple zero = -1; multiplicity = 2multiple zero = 1; multiplicity = 2
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A polynomial written in factorized form is giving us the information we need about the roots or zeros.
In this case, the polynomial is:
[tex]f(x)=(x-1)(x-1)(x+7)=(x-1)^2(x+7)[/tex]In this case, we have two zeros: x=1 and x=-7.
NOTE: a zero "a" will be expressed in a factor (x-a). That is why the zeros are 1 and -7.
As x=1 appears 2 times as a factor, we can group the factor.
x=1 is a zero with multiplicity of 2.
Answer: the multiple zero is x=1 and has a multiplicity of 2.
multiple zero = 1; multiplicity = 2 [Fourth option]
What is the least common denominator for the following rational equation?x/x+2 + 1/x+4 = x-1/x^2-2x-24
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Least Common Denominator (LCD)
We are required to find the LCD for the expression:
[tex]\frac{x}{x+2}+\frac{1}{x+4}=\frac{x-1}{x^2-2x-24}[/tex]We need to have every denominator as the product of the simplest possible expressions.
Since x+2 and x+4 are already factored, we need to factor the expression:
[tex]x^2-2x-24=(x-6)(x+4)[/tex]Now we have the following prime factors:
x+2, x+4, x-6 and x+4
The LCD is the product of all the prime factors:
LCD = (x+2)(x+4)(x-6)
The circumference of a circle is 56.52 what is the diameter
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SOLUTION
We have been given the circumfeence of the circle as 56.52 and we are told to find the diameter
Circumference of a circle C is found as
[tex]\begin{gathered} C\text{ }=\pi d \\ \text{Where }\pi\text{ = 3.14 and d is the diameter. So from } \\ C\text{ }=\pi d \\ 56.52\text{ }=3.14d \\ d\text{ = }\frac{56.52}{3.14} \\ \\ d\text{ = 18} \end{gathered}[/tex]Therefore, the diameter is 18
Graph the line y = 3/2x + 7y=3/2 x + 2
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Given:
The equation of line is,
[tex]y=\frac{3}{2}x+2[/tex]Find the points on line.
[tex]\begin{gathered} y=\frac{3}{2}x+2 \\ \text{For x=2} \\ y=\frac{3}{2}\times2+2=5 \\ \text{For x}=-2 \\ y=\frac{3}{2}\times(-2)+2=-1 \\ \text{For x=0} \\ y=\frac{3}{2}(0)+2=2 \\ \text{ For x=4} \\ y=\frac{3}{2}(4)+2=8 \end{gathered}[/tex]So, the points are ( 2,5),(-2,-1),(0,2),(4,8).
The graph of the equation of line is,
the cost of 9kg of rice is $111.24a)what is the cost of 10kg?b)what is the cost of 10.6kg?
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SOLUTION:
Case: Unit rates
Given: 9kg of rice cost $111.24
First we calculate the cost per kg
Since 9kg cost $111.24
1kg will be:
[tex]\begin{gathered} 1kg\text{ of rice =}\frac{111.24}{9} \\ 1kg\text{ of rice = 12.36} \end{gathered}[/tex]1kg costs $12.36
a) the cost of 10kg
The cost of 10kg will be:
[tex]\begin{gathered} 10kg\text{ of rice will be} \\ =\text{ 10 }\times12.36 \\ =\text{ 123.60} \end{gathered}[/tex]The cost of 10kg of rice is $123.60
b) the cost of 10.6kg
The cost of 10.6kg will be:
[tex]\begin{gathered} 10.6kg\text{ of rice will be} \\ =10.6\text{ }\times12.36 \\ =\text{ 131.0}2 \end{gathered}[/tex]The cost of 10.6kg of rice is $131.02
Final answer:
a) The cost of 10kg of rice is $123.60
b) The cost of 10.6kg of rice is $131.02
10.6 kg cost will be 131.016
How do I go about solving it. What would the answer be?
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The given sum is
[tex]\sum ^9_{k\mathop=4}(5k+3)[/tex]This means we have to replace k = 4, 5, 6, 7, 8, 9, and then we sum
[tex]\begin{gathered} (5\cdot4+3)+(5\cdot5+3)+(5\cdot6+3)+(5\cdot7+3)+(5\cdot8+3)+(5\cdot9+3) \\ 20+3+25+3+30+3+35+3+40+3+45+3=213 \\ \end{gathered}[/tex]Hence, the sum is equal to 213. The right answer is C.15. Find the missing sides/angles.i=94jk=42k
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From the figure given,
[tex]\begin{gathered} j=\text{opposite}=\text{?} \\ k=adjacent=\text{?} \\ hypotenuse=94 \\ \theta=42^0 \end{gathered}[/tex]Let us solve for 'j'
To solve for j, we will employ the method of Sine of angles.
[tex]\begin{gathered} \text{ Sine of angles=}\frac{opposite}{\text{hypotenuse}} \\ \sin \theta=\frac{j}{hypotenuse} \end{gathered}[/tex][tex]\begin{gathered} \sin 42^0=\frac{j}{94} \\ \text{cross multiply} \\ j=94\sin 42^0 \\ j=94\times0.6691 \\ j=62.8954\approx62.9units(nearest\text{ tenth)} \end{gathered}[/tex]Let us solve for k
To solve for k, we will employ the method of Cosine of angles.
[tex]\begin{gathered} \text{ Cosine of angles=}\frac{k}{\text{hypotenuse}} \\ \cos \theta=\frac{k}{hypotenuse} \\ \cos 42^0=\frac{k}{94} \\ \text{cross multiply} \\ k=94\cos 42^0 \\ k=94\times0.7431 \\ k=69.8514\approx69.9units(nearest\text{ tenth)} \end{gathered}[/tex]Hence, the value of j=62.9units,
k=69.9units.
If x varies directly as y, and x=-30 when y=-6, find x when y=-4.
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Let us now introduce a constant 'k' inorder to get the relationship between x and y,
[tex]\begin{gathered} x\propto ky \\ x=ky \end{gathered}[/tex]Let us substitute x = -30 and y = -6 inorder to get the relationship,
[tex]\begin{gathered} -30=k\times-6 \\ -30=-6k \\ \text{divide both sides by -6} \\ \frac{-30}{-6}=\frac{-6k}{-6} \end{gathered}[/tex][tex]\begin{gathered} k=5 \\ \text{The relationshiop betw}een\text{ x and y is,} \\ x=5y \end{gathered}[/tex]Let us now solve for x when y = -4,
[tex]\begin{gathered} x=5y \\ x=5\times-4 \\ x=-20 \end{gathered}[/tex]Hence, x is -20.
A rectangular prism has volume 10,878 cubic feet, length 7 feet, and height 42 feet. Find its width, in feet.
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Answer: The width is 37 feet
Given data
Volume = 10, 878 cubic feet
Length = 7 feet
Height = 42 feet
width = ?
Let width = w
Volume of the rectangular prism = l x w x h
10, 878 = 7 x 42 x w
10, 878 = 294 x w
10, 878 = 294w
Divide both sides by 294
10, 878 /294 = 294w/294
w = 10, 878 / 294
w = 37 feet
Therefore, the width is 37 feet