NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 10z
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Answer:
(-2, 13)(1, 10)=====================
Given systemy = x² + 9 x + y = 11Substitute the value of y into second equationx + x² + 9 = 11x² + x - 2 = 0x² +2x - x - 2 = 0x(x + 2) - (x + 2) = 0(x + 2)(x - 1) = 0x + 2 = 0 and x - 1 = 0x = - 2 and x = 1 Find the value of yx = -2 ⇒ y = 11 - (-2) = 13x = 1 ⇒ y = 11 - 1 = 10Answer:
[tex](x,y)=\left(\; \boxed{-2,13} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{1,10} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\phantom{bbbb}y=x^2+9\\x+y=11\end{cases}[/tex]
To solve by the method of substitution, rearrange the second equation to make y the subject:
[tex]\implies y=11-x[/tex]
Substitute the found expression for y into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}y=11-x \implies 11-x&=x^2+9\\x^2+9&=11-x\\x^2+9+x&=11\\x^2+x-2&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2+x-2&=0\\x^2+2x-x-2&=0\\x(x+2)-1(x+2)&=0\\(x-1)(x+2)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=1 \implies 1+y&=11\\y&=11-1\\y&=10\end{aligned}[/tex]
[tex]\begin{aligned}x=-2 \implies -2+y&=11\\y&=11+2\\y&=13\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-2,13} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{1,10} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Related Questions
i don’t understand how to solve this promise and i need help.
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We have been given a figure and we need to find its area.
To determine the area we will divide the figure into known shapes. From the division into shapes, we have a square and a trapezoid.
[tex]Area\text{ of the figure = Area of the square + Area of the trapezoid}[/tex][tex]\begin{gathered} Dimensions\text{ of the square:} \\ length\text{ = 12 ft} \\ Area\text{ of the square = length}^2 \\ \\ Area\text{ of the square = 12}^2 \\ \\ Area\text{ of the square = 144 ft}^2 \end{gathered}[/tex][tex]\begin{gathered} Dimensions\text{ of the trapezoid:} \\ base\text{ 1 = 10 ft, base 2 = 12 ft} \\ height\text{ = 6 ft} \\ \\ Area\text{ of trapezoid = }\frac{1}{2}(10\text{ + 12\rparen}\times\text{ 6} \\ \\ Area\text{ of trapezoid = }\frac{1}{2}\times22\text{ }\times6\text{ = 11}\times6 \\ \\ Area\text{ of trapezoid = 66 ft}^2 \end{gathered}[/tex][tex]\begin{gathered} Area\text{ of the figure = 144 + 66} \\ \\ Area\text{ of the figure = 210 ft}^2 \end{gathered}[/tex]Hello, I am having trouble with this problem. Thank you so much.
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ANSWERS
• Graph:
• Interval notation: ,[-4, ∞)
EXPLANATION
The set is all x greater than or equal to -4. The value -4 is included in the interval, so we have to draw a dot and then a line from the dot to infinity.
When a value is included in the interval, we use the start or end bracket. For infinity or negative infinity, we always use parenthesis. To represent this set in interval notation we have to use a bracket, number -4, a comma, infinity, and a parenthesis: [-4, ∞)
Can you please help me out with a question
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Answer:
3 degrees
Explanation:
Using the theorem that states that the measure of the angle at the circumference is equal to the half of its intercepted arc. Hence;
31x+ 3 = 1/2(192)
31x + 3 = 96
Subtract 3 from both sides
31x + 3 - 3 = 96 - 3
31x = 93
Divide both sides by 31
31x/31 = 93/31
x = 3
Hence the value of x is 3 degrees
A QUESTION ON A PROFICIENCY TEST IS MULTIPLE CHOICE WITH 4 POSSIBLE ANSWERS, 1 OF WHICH IS CORRECT. ASSUMING THAT ALL RESPONSES ARE RANDOM GUESSES FIND THE PROBABILITY THAT AMOUNG 12 TEST SUBJECTS, EXACTLY 5 ANSWERS ARE CORRECT
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In this scenario, there are only 2 possible outcomes. It is either the answer is correct or wrong.Since the outcomes are independent, it means that it is binomial probability. We would apply the binomial distribution formula which is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n is the sample size
x is the number of successes
p is the probability of success
q = 1 - p = probability of failure
From the information given,
p = 1/4 = 0.25
q = 1 - 1/4 = 3/4 = 0.75
n = 12
x = 5
We want to find P(x = 5)
P(x = 5) = 12C5 * 0.25^5 * 0.75^(12 - 5)
P(x = 5) = 0.103
The probability that among 12 test subjects, exactly 5 answers are correct is 0.103
l
Write the equation of the line parallel to Y equals 2/3X +1 through the point (0,-4)  use slope intercept form
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Writing the slope-intercept form of a linear equation, we have:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Since parallel lines have the same slope, we can see that the slope of the line y = 2/3x + 1 is equal m = 2/3, so for our equation we also have m = 2/3.
Now, using the point (0, -4), we have:
[tex]\begin{gathered} y=\frac{2}{3}x+b \\ (0,-4)\colon \\ -4=\frac{2}{3}\cdot0+b \\ b+0=-4 \\ b=-4 \end{gathered}[/tex]So our equation is:
[tex]y=\frac{2}{3}x-4[/tex]y = 2/3x - 4
find the sum of the first ten terms of an arithmetic series if the first term is 3 and the last term is 39a. 190b.210c.230d.275
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Given the first term is 3 and the last term is 39.
Recall that the sum is given as:
[tex]S_n=\frac{n}{2}(a_1+a_n)[/tex]Substituting in the above equation gives:
[tex]\begin{gathered} S_n=\frac{10}{2}(3+39) \\ S_n=5(42) \\ S_n=210 \end{gathered}[/tex]Therefore, option (a) is correct.
a bike rental service charges $19.70 initial flat rate and the an additional $5.60 per hour. in this situation, what is the value of the y-intercept
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The initial flat rate that bike rental service charges is $19.70
The additonal charges per hour is $5.60.
Let x be the number of hour.
The equation formed is
[tex]19.70+5.60x=y[/tex]The y-intercept is determined by substituting x=0.
[tex]19.70+0=y[/tex]Hence the y -intercept is 19.70 dollar.
Find anangle 0 coterminal to -560°, where 0° < 0 < 360°.
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Given the angle -560
The coterminal angle will be:
[tex]\theta=-560+360=-200+360=160[/tex]So, the answer will be 160
ginny is raising pumpkins to enter a contest to see who can grow the heaviest pumpkin. her best pumpkin weighs 22 pounds and is growing at the rate of 2.5 pounds per week. martha planted her pumpkins late. her best pumpkin weighs 10 pounds but she expects it grow 4 pounds per week. define the "let" statements for x and y. then write equations that represent the weight of ginny and martha's pumpkins.Let x=Let y=ginny's equations=Martha's equation:
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Let x=
1) Gathering the data
Ginny
Best pumpkin: 22 pounds
The growing rate of 2.5 pounds per week
Martha
Best pumpkin: 10 pounds
The growing rate: 4 pounds per week
Let x for the growing rate and y for the weight
2) Setting equations
Ginny's equation
2.5x=22
Martha's equation:
4x=10
5% annual interest rate for 30 years. This results in a monthly payment of $1100.48. If only the minimum payment is made in month one, how much of the first payment goes toward reducing her balance?First, let's find the amount of interest she paid in month 1.Then, find the amount toward reducing the balance. Round to the nearest cent.
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Given: Beth and Bryce sign on a $205,000 mortgage at a 5% annual interest rate for 30 years. This results in a monthly payment of $1100.48.
Required: To find the amount of interest she paid in month 1 and the amount toward reducing the balance.
Explanation: The monthly payment gets divided into two parts- One goes into the loan repayment and the other for the loan's interest.
The interest payment is based on the interest rate, which is 5%.
The monthly interest is:
[tex]\begin{gathered} I=205000\times5\%\times\frac{1}{12} \\ I=\text{\$}854.17 \end{gathered}[/tex]The amount that goes towards reducing her balance is:
[tex]\begin{gathered} =\text{ Monthly Payment-Interest Payment} \\ =1100.48-854.17 \\ =\text{\$}246.31 \end{gathered}[/tex]Final Answer: Interest in month 1 = $854.17
Their balance is reduced by $246.31
I'm having trouble figuring out this problem. Problem: Using the formula below, solve when s = 2.50. A = 6s²
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Given the formula:
[tex]A=6s^2[/tex]Let's solve for A when the value of s is = 2.50
To solve the equation, substitute 2.50 for s and evaluate.
Thus, we have:
[tex]\begin{gathered} A=6(2.50)^2 \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} A=6(2.50\ast2.50) \\ \\ A=6(6.25)^{} \\ \\ A=6\ast6.25 \\ \\ A=37.5 \end{gathered}[/tex]Therefore, when the value of s is 2.50, the value of A is 37.5
ANSWER:
37.5
Given Triangle XYZ, with Circumcenter O. If the distance from XO is 22mm. What is the distance of both YO and ZO?Required to answer. Single choice. 182022241313,
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Solution
Circumcenter Theorem
The vertices of a triangle are equidistant from the circumcenter.
The perpendicular bisectors intersect in a point and that point is equidistant from the vertices.
Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.
Therefore, YO and ZO is 22mm( By the transitive property)
what is the value of b -a if a=18, b=27,and c= 11
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what is the value of b -a if a=18, b=27,and c= 11
we have
(b-a)
so
For a=18 and b=27
substitutte in the given expression
(27-18)=9
therefore
the answer is 9The coordinates of the focus are (2,-7/4), the coordinates of the endpoints of the latus rectum are (3/2,-7/4) and (5/2,-7/4). The equation of the directions is y=-9/4, and the equation of the axis of symmetry is x=2.
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General equation of a parabola:
[tex](x-h)^2=4p(y-k)[/tex]Equation of the axis of symmetry:
x = h
In this case, the axis of symmetry is x = 2, then h = 2.
Equation of the directrix:
y = k - p
In this case, the equation of the directrix is y = -9/4, then:
-9/4 = k - p (eq. 1)
Equation of the focus:
F(h, k+p)
In this case, the coordinates of the focus are (2,-7/4), then:
-7/4 = k + p (eq. 2)
Adding equation 1 to equation 2:
-9/4 = k - p
+
-7/4 = k + p
--------------------
-4 = 2k
(-4)/2 = k
-2 = k
Substituting this result into equation 2 and solving for p:
-7/4 = -2 + p
-7/4 + 2 = p
1/4 = p
Substituting with h = 2, k = -2, and p = 1/4 into the general equation, we get:
[tex]\begin{gathered} (x-2)^2=4\cdot\frac{1}{4}(y-(-2)) \\ (x-2)^2=y+2 \end{gathered}[/tex]
A water footprint is a measure of the appropriation of fresh water.The per capita water footprint (in mega gallons) in a certain countryfor a recent year can be approximated by a normal distribution, asshown in the figure.(a) What water footprint represents the 86th percentile?(b) What water footprint represents the 28th percentile?(c) What water footprint represents the third quartile?
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To answer this question, we can use the standard normal distribution to find the asked percentiles. We will need the z-scores to find the values for them.
The z-scores are given by the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where
• x is the raw value (the one we need to find here)
,• μ is the population's mean. In this case, μ = 1.75 Mgal.
,• σ is the population's standard deviation. In this case, σ = 2.82 Mgal.
Finding the 86th percentile
The 86th percentile represents the value for which 86% of the cases are less than this value, and, therefore, 14% are above this value.
Then we can find it, if we know the value for which, z, in the standard normal table, represents the cumulative probability (0.86) for the distribution. If we consult the table, we have:
[tex]P(z<1.08)=0.8599\approx0.86[/tex]Therefore, the value for z is, approximately, z = 1.08, and we can use this value to find the value for x (the 86th percentile, in this case):
[tex]\begin{gathered} 1.08=\frac{x-1.75}{2.82} \\ (1.08)(2.82)=x-1.75 \\ (1.08)(2.82)+1.75=x \\ x=4.7956 \end{gathered}[/tex]Therefore, the 86th percentile, if we round the value to two decimal places, is, approximately, x = 4.80.
Finding the 28th percentile
We can apply the same procedure as before. Then we have:
[tex]P(z<-0.58)=0.2809_{}[/tex]Then we have:
[tex]\begin{gathered} -0.58=\frac{x-1.75}{2.82} \\ (-0.58)(2.82)=x-1.75 \\ (-0.58)(2.82)+1.75=x \\ x=0.1144 \end{gathered}[/tex]If we round the result to two decimal places, we have that the 28th percentile is x = 0.11 (approximately).
Finding the footprint for the third quartile
The third quartile is equivalent to the 75% percentile. Then we can use the same process as before to find the value of z that represents it as follows:
[tex]P(z<0.675)=0.7502_{}[/tex]And we can apply the same formula as before:
[tex]\begin{gathered} 0.675=\frac{x-1.75}{2.82} \\ (0.675)(2.82)=x-1.75 \\ (0.675)(2.82)+1.75=x \\ x=3.6535 \end{gathered}[/tex]If we round this value to two decimal places, we have x = 3.65 (approximately).
Hello I need help with this here please, I was studying but I can’t get this
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ANSWER
B. False
EXPLANATION
The Pythagorean Theorem states that the sum of the squares of the two legs of a right triangle, a and b, is equal to the square of the hypotenuse, c:
[tex]c^2=a^2+b^2[/tex]And this theorem is true for all right triangles.
Hence, this statement is false.
Bring the standard form of the equation of the line through the pair of points (5,2) and (5,-7)
Answers
The equation is
x = 5
Explanation:The equation of a line is given as:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Given the points (5, 2) and (5, -7)
The slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-2}{5-5}=-\frac{9}{0}=\infty[/tex]The slope is infinite, then the equation is:
[tex]x=5[/tex]verify the following trigonometric identity (1+tanx)^2=sec^2x+2tanx
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Verify the equation :
[tex](1+\tan x)^2=\sec ^2x+2\tan x[/tex]solve:
[tex]=(1+\tan x)^2[/tex]Use the formula :
[tex](a+b)^2=a^2+b^2+2ab[/tex][tex]\begin{gathered} =(1+\tan ^{}x)^2 \\ =1^2+(\tan x)^2+2(1)(\tan x) \\ =1+\tan ^2x+2\tan x \end{gathered}[/tex]Use the formua:
[tex]1+\tan ^2x=\sec ^2x[/tex][tex]\begin{gathered} =1+\tan ^2x+2\tan x \\ =\sec ^2x+2\tan x \end{gathered}[/tex]find the values of x and y
Answers
From the given figure
Since every two opposite sides are parallel
AB // DC
AD // BC
Then the given quadrilateral is a parallelogram
ABCD is a parallelogram
From the properties of the parallelogram,
Every 2 opposite sides are equal in length, then
AB = DC
AB = x + 2, and DC = 13, then
x + 2 = 13
Subtract 2 from both sides to find x
x + 2 - 2 = 13 - 2
x = 11
Since the opposite angles in the parallelogram are equal in measures
Since
m
Since m
y = 70
The value of x is 11 and the value of y is 70
It’s polynomial operations I need the answer and all the work written out.
Answers
Answer:
[tex]x^2+14x^3y^2-6x[/tex]Explanation:
Given the below polynomials expression;
[tex](4x^2+7x^3y^2)-(-6x^2-7x^3y^2-4x)-(10x+9x^2)[/tex]The 1st step to solving the above is to clear the brackets while minding the signs as shown below;
[tex]4x^2+7x^3y^2+6x^2+7x^3y^2+4x-10x-9x^2[/tex]The 2nd step is to group like terms;
[tex]4x^2+6x^2-9x^2+7x^3y^2+7x^3y^2+4x-10x[/tex]Let's go ahead and evaluate;
[tex]x^2+14x^3y^2-6x[/tex]How to fine the volume and surface are in a cone
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PROJECT WORK:
Assumption:
For the given cone, assuming
[tex]\begin{gathered} r\text{ = 10 m} \\ h\text{ = 12 m} \end{gathered}[/tex]Slant height of cone is calculated as,
[tex]\begin{gathered} l^2\text{ = r}^2\text{ + h}^2 \\ l^2\text{ = 10}^2\text{ + 12}^2 \\ l^2\text{ = 100 + 144} \\ l^2\text{ = 244} \\ l\text{ = 15.62 m} \end{gathered}[/tex]Required:
Surface area and volume of cone.
Explanation:
The surface area of cone is given as,
[tex]\begin{gathered} Surface\text{ area = }\pi r(l+r) \\ Surface\text{ area = 3.14}\times\text{ 10\lparen15.62 + 10\rparen} \\ Surface\text{ area =3.14}\times\text{ 10\lparen25.62\rparen} \\ Surface\text{ area = 3.14}\times\text{ 256.2} \\ Surface\text{ area = 804.468 m}^2 \end{gathered}[/tex]Volume of cone is calculated as,
[tex]\begin{gathered} Volume\text{ = }\frac{1}{3}\pi r^2h \\ Volume\text{ = }\frac{1}{3}\times3.14\times10\times10\times12 \\ Volume\text{ = }\frac{3768}{3} \\ Volume\text{ = 1256 m}^3 \end{gathered}[/tex]Answer:
Thus the volume of the cone is 1256 cu.m.
The surface area of the cone is 804.468 sq.m.
2.3= p + 0.6What does p equal?
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The given equation is
[tex]2.3=p+0.6[/tex]First, we subtract 0.6 on each side
[tex]\begin{gathered} 2.3-0.6=p+0.6-0.6 \\ 1.7=p \end{gathered}[/tex]Therefore, p is equal to 1.7.A tour bus is traveling at a constant speed. The relationship between it's time and distance is shown in the graph Which statement is correctA) The origin (0, 0) is the independent quantity and the time values are the dependent quantities.B) The time values are the independent quantities and the distance values are the dependent quantities.C) The distance values are the independent quantities and the time values are the dependent quantities.D) The rate of 50 miles per hour is the independent quantity and the distance values are the dependent quantities.
Answers
Jahna, this is the solution:
As you can see in the graph, the independent variable (Time) belongs on the x-axis and the dependent variable (Distance) belongs on the y-axis.
Therefore, the statement that is correct is:
B. The time values are the independent quantities and the distance values are the dependent quantities.
Please help us in figuring out this math problem so that we can move onto the next one thank you very much
Answers
All numbers in scientific notation or standard form are written in the form
[tex]m\cdot10^n[/tex]where m is a number between 1 and 10 and the exponent n is a positive or negative integer.
To convert 64500 into scientific notation, follow these steps:
1. Move the decimal 4 times to left in the number so that the resulting number, m = 6.45, is greater than or equal to 1 but less than 10
2. Since we moved the decimal to the left the exponent n is positive
n = 4
3. Write in the scientific notation form, m × 10^n
= 6.45 × 10^4
consider the cube shown at the right. All the side lengths of the cube have been marked with the variable s. the firmula firvthe surface area of a cube is given by SA=6s2. explain where this equatiin comes from
Answers
The explanation goes as contained below.
The shape is a cube and for a cube all sides are equal,
from the question the Area of just one side is :
[tex]\begin{gathered} S\times S=S^2 \\ \text{Then for 6 sides we have 6 }\times S^2=6S^2 \end{gathered}[/tex]Solve the inequality, then select the graph that matches the solution.x +5 ≥ 5
Answers
Answer:
Explanation:
Given the inequality:
[tex]x+5\geqslant5[/tex]Subtract 5 from both sides of the inequality.
[tex]\begin{gathered} x+5-5\geq5-5 \\ x+0\geq0 \\ x\geq0 \end{gathered}[/tex](a)The solution to the inequality is x ≥ 0.
(b)Since the inequality sign is "greater than or equal to", the circle at 0must be shaded and the arrow pointing towards the right.
The correct graph is attached below:
The second and third options are correct.
Which expression is equivalent to one sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x?
negative one eighteenth times x minus three
negative one eighteenth times x plus 3
one eighteenth times x minus 3
one and seven eighteenths times x plus three
PLS HURRY 30PTS
Answers
The equivalent expression will be;
⇒ ''negative one eighteenth times x plus 3''
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''Sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x''
Now,
Since, The algebraic expression is,
''One sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x''
Hence, The mathematical expression is,
⇒ 1/6 (4x + 18) - 13/18x
⇒ 4/6x + 3 - 13/18x
⇒ 12/18x - 13/18x + 3
⇒ - 1/18x + 3
Thus, The equivalent expression is,
''negative one eighteenth times x plus 3''
Learn more about the mathematical expression visit:
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expression and assume that X, y, and z denote any positive real numbers
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a) given equation is,
[tex]\begin{gathered} \sqrt[8]{x^8y^4z^{4\:}} \\ =\sqrt[8]{x^8}\sqrt[8]{y^4z^4} \\ =x\sqrt[8]{y^4z^4} \end{gathered}[/tex]b) the given equation is
[tex]\begin{gathered} \sqrt[3]{\sqrt{64x^6}} \\ =\sqrt[3]{8x^3} \\ =2\sqrt[3]{x^3} \\ =2x \end{gathered}[/tex]48 ounces of juice are required to make 3 gallons of punch. How many ounces of juice are required to make 9 gallons of punch?
Answers
If we need 48 onces of juice for making 3 gallons of punch we can write our problem like:
[tex]\begin{gathered} 48\to3 \\ x\to9 \end{gathered}[/tex]where x is the juice needed to made 9 gallons of punch, so we can made a rulo of 3 to find x
[tex]x=\frac{48\cdot9}{3}=144[/tex]So we need 144 ounces of juice to made 9 gallons of punch
Round 14.235 to the nearest tenth, hundredth, one and ten
Answers
The number 14.235 would round down to 14.2
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We need to round 14.235 to the nearest tenth, hundredth, one and ten
We can see that the 35 is below 50 so it goes down, and it rounds down to 14.2 instead of, 14.62 then that would round up to the decimal is higher than 50.
Since it is 235, then it rounds down to 14.2
Learn more about rounding numbers here:
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