ANSWER
x = 7
y = -7
EXPLANATION
Given:
- x - 8y = 49 ..........(equ 1)
- x - 2y = 7 ............(equ 2)
Desired Outcome
The values of x and y.
Multiply Equation 2 by -1
[tex]equ\text{ 2}\times-1\Rightarrow x+2y\text{ = -7 ............}(equ\text{ 3})[/tex]Add Equation 1 with Equation 3
[tex]\begin{gathered} -\text{ x - 8y = 49} \\ x\text{ + 2y = -7} \\ ------ \\ -6y\text{ = 42} \\ y\text{ = }\frac{42}{-6} \\ y\text{ = -7} \end{gathered}[/tex]Solve for x from equation 3
[tex]\begin{gathered} x\text{ + 2y = -7} \\ x\text{ + 2}(-7)\text{ = -7} \\ x\text{ - 14 = -7} \\ x\text{ = -7 + 14} \\ \text{x = 7} \end{gathered}[/tex]Hence, the values of x and y are 7 and -7 respectively.
A sequence is shown below.10, 12, 14, 16, ...Which function can be used to determine the nthnumber in the sequence?
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]The scores of Janet in her math tests are 65, 78, 56, 73, 67, 92. Find themedian score of Janet.
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
Convert repeating decimal 0.155….to fraction
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]15. Find the missing sides/angles.i=94jk=42k
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.
"Solve for all values of x on the given intervals. Write all answer in radians." I am stuck on number 4
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]Joseph deposited $60 in an account earning 10% interest compounded annually.To the nearest cent, how much will he have in 2 years?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Solution:
Using;
[tex]\begin{gathered} B=p(1+r)^t \\ \\ \text{ Where }p=60,r=10\text{ \%}=0.1,t=2 \end{gathered}[/tex][tex]\begin{gathered} B=60(1+0.1)^2 \\ \\ B=72.6 \end{gathered}[/tex]ANSWER: $72.6
How many solutions does the equation −5a + 5a + 9 = 8 have? (5 points)NoneOneTwoInfinitely many
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
a. angle addition postulate with angles forming a straight line angle.b. triangle sum theorem c. linear pair postulate
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
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
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).
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
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]
If x varies directly as y, and x=-30 when y=-6, find x when y=-4.
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.
Very confused on question 5 need help as soon as possible
To solve this, we can use the remainder theorem.
The theorem says:
Given a polynomial P(x), the remainder of
[tex]\frac{P(x)}{x-a}[/tex]Is equal to P(a)
This means, that we are looking for a value of x such as P(a) = 0
We need to find the roots of the polynomial. We can do this, by trying values of x.
Let's use:
x = 0, 1, 2, 3
[tex]x^3+3x^2-16x-48[/tex]Then:
[tex]\begin{gathered} x=0\Rightarrow0^3+3\cdot0^2-16\cdot0-48=-48 \\ x=1\Rightarrow1^3+3\cdot1^2-16\cdot1-48=1+3-16-48=-60 \\ x=2\Rightarrow2^3+3\cdot2^2-16\cdot2-48=8+12-32-48=-60 \\ x=3\Rightarrow3^3+3\cdot3^2-16\cdot3-48=27+27-48-48=-42 \end{gathered}[/tex]Let's try negative values,
x = -1, -2, -3
[tex]\begin{gathered} x=-1\Rightarrow(-1)^3+3(-1)^2-16(-1)-48=-1+3+16-48=-30 \\ x=-2\Rightarrow(-2)^3+3(-2)^2-16(-2)-48=-8+12+32-48=-12 \\ x=-3\Rightarrow(-3)^3+3(-3)^2-16(-3)-48=-27+27+48-48=0 \end{gathered}[/tex]We have found that the polynomial evaluated in x = -3 is equal to zero, which means:
[tex]\frac{x^3+3x^2-16x-48}{x+3}[/tex]has remainder zero.
The answer is (x + 3)
What is the least common denominator for the following rational equation?x/x+2 + 1/x+4 = x-1/x^2-2x-24
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)
[tex]4112 \div 5 = 822 remainder 2[/tex]drag each expression to a box to show whether it is a correct way to check the answer to this equation
given that
4112/5 = 822 remainder 2
to get the correct way and incorrect way.
so
For,
822 x 5 = 4110
For,
822 x 2 + 5 = 1649
For,
822 x 5 + 2 = 4112
therefore,
The correct way to check The incorrect way to way to check
822 x 5 + 2 822 x 5
822 x 2 + 5
Graph the line y = 3/2x + 7y=3/2 x + 2
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,
*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!
the cost of 9kg of rice is $111.24a)what is the cost of 10kg?b)what is the cost of 10.6kg?
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 $131.02
I kinda started it but I don’t know how to find the answer
Solution
[tex]\begin{gathered} x^2+2x-16=0 \\ \\ \text{ using quadratic formula} \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=1,b=2,c=-16 \\ \\ \Rightarrow x=\frac{-2\pm\sqrt{2^2-4(1)(-16)}}{2(1)} \\ \\ \Rightarrow x=\frac{-2\pm\sqrt{4+64}}{2} \\ \\ \Rightarrow x=-1-\sqrt{17} \\ \\ \Rightarrow x=-1+\sqrt{17} \\ \\ \text{ since }x>0 \\ \\ \text{ Therefore the value of }x=-1+\sqrt{17} \end{gathered}[/tex]I just don't know how to indicate values on ration equations
Solving the equation we have:
[tex]\begin{gathered} \frac{x+3}{x-3}=\frac{12}{3} \\ \frac{x+3}{x-3}=4\text{ (Simplifying the fraction)} \\ x+3=4(x-3)\text{ (Multiplying x-3 on both sides of the equation)} \\ x+3=4x-12\text{ (Distributing)} \\ x+3+12=4x\text{ (Adding 12 to both sides of the equation)} \\ 3+12=4x-x\text{ (Subtracting x from both sides of the equation)} \\ 15=3x\text{ (Adding)} \\ \frac{15}{3}=x\text{ (Dividing by 3 on both sides of the equation)} \\ 5=x\text{ } \end{gathered}[/tex]The solution is x=5 and it is valid as the result of replacing it in the denominator is not zero. ( 5 - 3 ≠ 0)
Parker has tangerines and apricots in a ratio of 12:95. How many apricots does hehave if he has 96 tangerines?On the double number line below, fill in the given values, then use multiplication ordivision to find the missing value.
We know that if Parker has 12 tangerines he has 95 apricots, so to find how many apricots he has we need to do a rule of tree
[tex]\begin{gathered} x\text{ apricots }\cdot\frac{12\text{ tangerines}}{95\text{ apricots}}=96\text{ tangerines} \\ x\text{ apricots = 96 tangerines }\cdot\frac{95\text{ apricots}}{12\text{ tangerines}} \\ x\text{ apricots =}\frac{96\cdot95}{12}\text{ apricots = }\frac{9120}{12}\text{ apricots} \\ x=760 \end{gathered}[/tex]So the answer is that Parker has 760 apricots is he has 96 tangerines.
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$.Find the rental cost for each movie and each video game.
Given
One month Chris rented 8 movies and 4 video games for a total of 49$.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
A patient takes three 25 mg capsules a day. How many milligrams is he taking daily?
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.
Write the number 0.2 in the form a over b using integers
We can express 0.2 in the form:
[tex]\frac{2}{10}[/tex]21. What is the probability of getting an odd number? a.1/3b.2/3c.1/4d.1/5
The probability of getting an odd number from 1-10 is 1/5.
Given, we have numbers from1-10
The odd numbers ranging from 1-10 are 5
Hence we know the probability formula = Number of favourable outcomes/ totall number of outcomes.
Probability of getting an odd number = 1/5
Hence we get the answer as 1/5.
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Find the degree and leading coefficient for the given polynomial.−5x^2 − 8x^5 + x − 40degree leading coefficient
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
The circumference of a circle is 56.52 what is the diameter
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
[tex](x + 4)x + 5)[/tex]write the equivalente expression
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]Find the slope of the function 8x - 2y = 10.
Solve the equation in terms of y, so that it is in the slope-intercept form
[tex]\begin{gathered} 8x-2y=10 \\ -2y=10-8x \\ \frac{-2y}{-2}=\frac{10-8x}{-2} \\ y=-5+4x \\ y=4x-5 \end{gathered}[/tex]Since it is already in the slope-intercept form y = mx + b, where m is the slope. We find that m = 4.
Therefore, the slope of the function is equal to 4.
please help with this question
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
Which of these standard form equations is equivalent to (x + 1)(x - 2)(x + 4)(3x + 7)?
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
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