If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
we have
y=x+2
y=-2x+8
Solve the system of equations
equate both equations
x+2=-2x+8
x+2x=8-2
3x=6
x=2
Find the value of y
y=(2)+2
y=4
the solution is (2,4)
that means
(2,4) is a common point , that satisfy both equations
Find the value of b if it is known that the graph of y=-3x+b goes through the point_
M(-2, 4)
Answer:
b = -2
Step-by-step explanation:
y = mx + b; (-2, 4)
y = -3x + b (x₁, y₁)
m = -3
y - y₁ = m(x - x₁)
y - 4 = -3(x -( -2))
y - 4 = -3(x + 2)
y - 4 = -3x - 6
+4 +4
------------------------
y = -3x - 2
I hope this helps!
I am an even number.
I have three digits and they are all the same.
If you multiply me by 4, all of the digits in the product are 8.
What number am l?
Answer:
Step-by-step explanation:
The number is 2.
222x4=888
Hence, the number am I is [tex]888[/tex].
What is the even number?
A number that is divisible by [tex]2[/tex] and generates a remainder of [tex]0[/tex] is called an even number.
Here given that,
I am an even number. I have three digits and they are all the same.
If you multiply me by [tex]4[/tex], all of the digits in the product are [tex]8[/tex].
The number is [tex]2[/tex] sp ot would be
[tex]222[/tex]x[tex]4=888[/tex]
Hence, the number am I is [tex]888[/tex].
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through: (-5,4) perpendicular to x=5
First let's calculate the slope of the straight line
For slopes that are perpendicular to each other we can use the following formula
[tex]m1m2=-1[/tex]Where
m1 = original slope
m2 = perpendicular slope
[tex]\begin{gathered} m2=-\frac{1}{m1} \\ m2=-\frac{1}{5} \end{gathered}[/tex]Now for the intersection
[tex]\begin{gathered} b=y-mx \\ b=4-(\frac{-1}{5})\cdot(-5) \\ b=4-1 \\ b=3 \end{gathered}[/tex]The equation of the line that passes through the point (-5,4) with a slope of -1/5 is
[tex]y=-\frac{1}{5}x+3[/tex]Exercise 1: What's In2.Mark’s temperature goes 1.5°C higher from the normal body temperature. What is Marks temperature now?A. 38.5°CB. 37.5°CC. 36.5°CD. 36.5C
The normal body temperature of a human is 37°C.
If Mark's temperature goes 1.5°C higher than that temperature, his new temperature will be:
[tex]\Rightarrow37+1.5=38.5°C[/tex]OPTION A is the correct option.
How do I understand Standard Form of a Line? I don't know how to do it.
There are several forms in which one can write the equation of a line. Have in mind that TWO variables should be included in the equation. These two variables are: x and y.
If you type the equation in a form that looks like:
A x + B y = C
where the A, B, and C are actual numbers (like for example: 3 x - 2 y = 5)
This is the standard form of a line. to recognize it notice that bith variables x an y appear in separate terms on the LEFT of the equal sign., and a pure number (no variables) appears on the right of the equal sign.
Another form of writing the equation of a line is in the so called "solpe-intercept" form. This form looks like:
y = m x + b
Notice that in this case the variable ÿ" appears isolated on the left , and on the right of the equal sign you get a term with the variable x, and another constant (pure number) term (b). Like for example in the case of:
y = 3 x
Problem: A school has a student to teacher ratio of25:5. If there are 155 teachers at the school, howmany students are there?Mike's AnswerCarlos's Answer25 .5 1551552555x = 3875x=77525x = 775x=31There are 31 students at the school.There are 775 students at the scheel.Who is correct? Mike or Carlos? Explain the error thatwas made.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
ratio = 25:5 (students:teachers)
teachers = 155
students = ?
Step 02:
[tex]\begin{gathered} \text{students = 155 teachers }\cdot\text{ }\frac{25\text{ students }}{5\text{ teachers}} \\ \text{students = }775\text{ } \end{gathered}[/tex]Carlos is correct.
[tex]\frac{25}{5}=\frac{x}{155}[/tex]The answer is:
There are 775 students.
Carlos is correct.
Mike set the variables to find in the wrong way.
Express your answer as a polynomial in standard form.f(x) = x^2 + 6x +7g(x) = x + 2Find: g(f(x)
1) Firstly, let's find the composite function g(f(x)) plugging into the x variable in g(x) the function f(x):
[tex]\begin{gathered} g(f(x))=(x^2+6x+7)+2 \\ g(f(x))=x^{2}+6x+9 \end{gathered}[/tex]2) To write that as the standard form, let's replace g(f(x)) with "y" and write the polynomial orderly to the greatest coefficient to the least one.
[tex]y=x^2+6x+9[/tex]y = 2x - 4 Find the solution/root/zero.
The solution of the linear equation y = 2 · x - 4 is x = 2.
How to find the solution of a linear equationLinear equations are first order polynomials. In this problem we need to solve for x in a linear equation, this can be done by means of algebra properties. The complete procedure is shown below.
Step 1 - We find the find the following expression:
y = 2 · x - 4
Step 2 - We make y equal to zero and we use the symmetric property for equalities:
2 · x - 4 = 0
Step 3 - By compatibility with addition, existence of additive inverse, modulative, associative and commutative properties
2 · x = 4
Step 4 - By compatibility with multiplication, existence of multiplicative inverse and modulative, associative and commutative properties we get the following result:
x = 2
The solution of the linear equation is x = 2.
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Riley rented folding chairs and tables for an event.• She rented a total of 56 chairs and tables.• She paid $2.25 per chair and $8.50 per table and paid a total of $176.00.Write a system of equations to model this situation.Enter your equations in the space provided. Enter only your equations.+-Х.Iyx rr fr)而
Total rented= 56 chairs and tables
Chair= $2.25 (let's consider chairs as x)
Table = $8.50 (let's consider tables as y)
Total paid= $176.00
If she rented 56 chairs and tables, then the equation for that would be:
[tex]\begin{gathered} 56=\text{ x + y } \\ 56\text{ -x= y} \end{gathered}[/tex]Then the system of equations to model this situation is:
[tex]176.00=\text{ 2.25x + 8.50\lparen56-x\rparen}[/tex]Write the standard form of the equation and the general form of the equation of the circlewith radius r and center (h.k). Then graph the circle.r= 10; (h,k) = (8,6)The standard form of the equation of this circle isThe general form of the equation of this circle is(Simplify your answer.)Graph the circle.-20 -18Click toenlargegraph
To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be
[tex](x-h)^2+(y-k)^2=r^2[/tex]In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be
[tex](x-8)^2+(y-6)^2=10^2=100[/tex]The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that
[tex](a-b)^2=a^2-2a\cdot b+b^2[/tex]So, applying this to the standard equation we get
[tex](x-8)^2=x^2-16x+64[/tex][tex](y-6)^2=y^2-12y+36[/tex]So our equation becomes
[tex]x^2-16x+64+y^2-12y+36=100[/tex]Operating on the left side, we have
[tex]x^2-16x+y^2-12y+100=100[/tex]By subtracting 100 on both sides, we get
[tex]x^2-16x+y^2-12y=0[/tex]which the general form of the equation of the given circle.
Using a graphing tool, we have that the circle's graph would be
What's the volume of a cube with a side length of 3 inches?
ANSWER
27 in³
EXPLANATION
The volume of a cube is the cube of its side length, L,
[tex]V=L^3[/tex]So, if a cube has a side length of 3 inches, then its volume is,
[tex]V=3^3in^3=27\text{ }in^3[/tex]Hence, the volume of a cube with a side length of 3 inches is 27 cubic inches.
Evaluate: sin-¹(1)
A) 0
B) pi/3
C)pi/2
Answer:
The correct answer is C. Pi/2
Step-by-step explanation:
I got it wrong on edgen, and it told me the correct answer was C.
im doing math and im wondering when do i switch the inequality?
Question:
Solve the following inequality:
[tex]12x+6<17[/tex]Solution:
Consider the following inequality
[tex]12x+6<17[/tex]solving for 12x, we get:
[tex]12x<17-6[/tex]this is equivalent to:
[tex]12x<11[/tex]solving for x, we get:
[tex]x<\frac{11}{12}[/tex]so that, the correct answer is:
[tex]x<\frac{11}{12}[/tex]2. Mr. Cole took a walk with his wife. They walked 4.4 miles in 1.4 hours. What was their average speed inmiles per hour?
Mr. Cole took a walk with his wife.
They walked 4.4 miles in 1.4 hours.
So we have
Distance = 4.4 miles
Time = 1.4 hours
We are asked to find the average speed in miles per hour.
The average speed is given by
[tex]S=\frac{D}{t}[/tex]Where D is the distance and t is the time.
[tex]S=\frac{4.4}{1.4}=3.142[/tex]Therefore, their average speed is 3.142 miles per hour.
The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 8lb stretches a certain spring 9in., how far will the spring stretch if the weight is increased to 37lb? (Leave the variation constant in fraction form. Round off your final answer to the nearest in.)
ANSWER
L = 42in
EXPLANATION
QUESTION 241 POINTFor a rectangular solid with length 14 feet, height 17 feet, and width 6 feet, find the a. volume and b. surface area.Provide your answer below:volume =cubic feet, surface areasquare feetFEE
The volume and surface area of a rectangular prism are given by the formulas below
[tex]\begin{gathered} V=l*b*h \\ A=2(lb+bh+hl) \\ l\rightarrow\text{ length} \\ w\rightarrow width \\ h\rightarrow\text{ height} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} l=14,w=6,h=17 \\ \Rightarrow V=14*6*17=1428 \\ and \\ A=2(14*6+6*17+17*14)=848 \end{gathered}[/tex]Thus, the answers are: Surface area=848ft^2, and Volume=1428ft^3
Converting between scientific notation and standard form in a real-world situation
Answer:
[tex]\begin{gathered} a)9.54\times10^6\text{square miles} \\ b)0.0061\sec onds_{} \end{gathered}[/tex]Explanations:
a) The scientific notation is generally expressed as;
[tex]A\times10^n[/tex]A is any real numbers between 1 and 10
n is an integer
Given that the total surface area of North America is 9,540,000 square miles. This is expressed in scientific form as;
[tex]9,540,000=9.54\times10^6mi^2[/tex]From the scientific notation, A = 9.54 and n = 6
b) Given the scientific notation as shown:
[tex]6.1\times10^{-3}\text{seconds}[/tex]Writing in standard form means writing in the normal way we write numbers/decimals. Hence;
[tex]6.1\times10^{-3}=0.0061\text{seconds}[/tex]In the diagram below, BS and ER intersect as show. Determine the measure of
please help me with this problem this question asks for the angle measure and if the lines are tangent
step 1
we have that
44=(1/2)[180-arc} ------> by exterior angle
solve for arc
88=180-arc
arc=180-88
arc=92 degrees
give me a minute to draw a figure with letters to better understand the problem
we have that
x+?=180 degrees -------> by form a linear pair (supplemenatry angles)
x=arc=92 degrees ------> by central angle
so
?=180-92
?=88 degrees
therefore
the missing angle is 88 degreesyour card gives you a bonus of 0.4%. what is your actual bonus if you charge $3,397.75 on your credit card?
Answer:
$13.591
Explanation:
To know your actual bonus, we need to find what is 0.4% of $3,397.75 as follows
[tex]3,397.75\times\frac{0.4}{100}=13.591[/tex]Therefore, your actual bonus is $13.591
3a^2 -3a - 36. solving quadratic by factoring. factor each expression. be sure to check for greatest common factor first.
we have the expression
[tex]3a^2-3a-36[/tex]step 1
Factor 3
[tex]3(a^2-a-12)[/tex]step 2
equate to zero
[tex]3(a^2-a-12)=0[/tex]step 3
Solve
[tex](a^2-a-12)=0[/tex][tex]\begin{gathered} a^2-a=12 \\ (a^2-a+\frac{1}{4}-\frac{1}{4})=12 \\ (a^2-a+\frac{1}{4})=12+\frac{1}{4} \\ (a^2-a+\frac{1}{4})=\frac{49}{4} \end{gathered}[/tex]Rewrite as perfect squares
[tex](a-\frac{1}{2})^2=\frac{49}{4}[/tex]take the square root on both sides
[tex]\begin{gathered} a-\frac{1}{2}=\pm\frac{7}{2} \\ a=\frac{1}{2}\pm\frac{7}{2} \end{gathered}[/tex]the values of a are
a=4 and a=-3
therefore
[tex]3(a^2-a-12)=3(a-4)(a+3)[/tex]Please help 100 points
Answer:
y = - 6x² - 12x + 2======================
GivenVertex of parabola = (- 1,8),Point on the graph = (0, 2).To findThe equation of the parabola in standard form.SolutionWe can represent the quadratic equation in vertex or standard forms.
Vertex form:
y = a(x - h)² + k, where (h, k) is the vertex, a- coefficientStandard form:
y = ax² + bx + c, where a and b are coefficients and c- constantUse the vertex form with given coordinates of the vertex:
y = a(x - (-1))² + 8 ⇒y = a(x + 1)² + 8Use the other point to find the value of a:
2 = a(0 + 1)² + 82 = a + 8a = - 6The equation is:
y = - 6(x + 1)² + 8Convert it to standard form:
y = - 6x² - 12x - 6 + 8y = - 6x² - 12x + 2Answer:
[tex]y=-6x^2-12x+2[/tex]
Step-by-step explanation:
Vertex form of a quadratic equation:
[tex]y=a(x-h)^2+k[/tex]
where (h, k) is the vertex.
Given:
Vertex = (-1, 8)Point on the curve = (0, 2)Substitute the given values into the vertex formula and solve for a:
[tex]\implies 2=a(0-(-1))^2+8[/tex]
[tex]\implies 2=a(1)^2+8[/tex]
[tex]\implies 2=a+8[/tex]
[tex]\implies a=-6[/tex]
Substitute the vertex and the found value of a into the vertex formula, then expand to standard form:
[tex]\implies y=-6(x-(-1))^2+8[/tex]
[tex]\implies y=-6(x+1)^2+8[/tex]
[tex]\implies y=-6(x^2+2x+1)+8[/tex]
[tex]\implies y=-6x^2-12x-6+8[/tex]
[tex]\implies y=-6x^2-12x+2[/tex]
Therefore, the quadratic function in standard form whose graph has the given characteristics is:
[tex]y=\boxed{-6x^2-12x+2}[/tex]
[tex] \frac{x - 2}{x + 3} + \frac{10x}{x {}^{2 } - 9}[/tex]simplify the sum. state any restrictions on the variables.
We have
[tex]\frac{x-2}{x+3}+\frac{10x}{x{}^2-9}[/tex]first, we need to factorize the next term
[tex]x^2-9=(x+3)(x-3)[/tex]so we have
[tex]\frac{x-2}{x+3}+\frac{10x}{(x+3)(x-3)}[/tex]Remember in order to sum a fraction the denominator must be the same
[tex]\frac{(x-2)(x-3)+10x}{(x+3)(x-3)}[/tex]then we solve the multiplications (x-2)(x-3)
[tex]\frac{x^2-3x-2x+6+10x}{(x+3)(x-3)}=\frac{x^2+5x+6}{(x+3)(x-3)}[/tex]then we can factorize the numerator
[tex]x^2+5x+6=(x+3)(x+2)[/tex]so the simplification will be
[tex]\frac{x^2+5x+6}{(x+3)(x-3)}=\frac{(x+3)(x+2)}{(x+3)(x-3)}=\frac{(x+2)}{(x-3)}[/tex]the final result is
[tex]\frac{(x+2)}{(x-3)}[/tex]Which exponential function is represented by the table below? x –2 0 2 4 y 16 4 1 14
An exponential function which is represented by the table above is: f(x) = 4(1/2)^x
What is an exponential function?An exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled by using this equation:
f(x) = abˣ
Where:
a represents the initial value.b represents the rate of change.From the table above, we would calculate the value of a and b:
At x = 0 and y = 4; the value of a (initial value) is 4.
Rate of change, b = Δy/Δx
Rate of change, b = 1/2
Substituting the parameters into the formula, we have;
f(x) = abˣ
f(x) = 4(1/2)^x
Check:
f(x) = 4 × (1/2)^x f(x) = 4 * ( 1/2 )^x
f(x) = 4 × (1/2)² f(x) = 4 × (1/2)⁻²
f(x) = 4 × 1/4 f(x) = 4 × 4
f(x) = 1 f(x) = 16
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Can you help me please and thank you very much
Answer:
∠ FAE = 120°
Step-by-step explanation:
4x and 2x are a linear pair and sum to 180° , that is
4x + 2x = 180
6x = 180 ( divide both sides by 6 )
x = 30
then
∠ FAE = 4x = 4 × 30 = 120°
- A chemist mixes 2,362 milliliters of a solution. The solution must be divided equally among 8 beakers. How much solution should be poured into each beaker?
Answer:
295.25mm
Explanation:
If the chemist mixes 2362mm of a solution and needs to divide it equally into 8 breakers, to determine how much solution should be poured into each breaker, we have to divide 2362mm divide 8;
[tex]\frac{2362}{8}=295.25\operatorname{mm}[/tex]converting to slope intercept formmatch each equation to an equivalent equation written in slope intercept form.
Statement Problem: Match each equation to an equivalent equation written in slope-intercept form.
Solution:
A slope intercept form equation is written as;
[tex]y=mx+b[/tex](a)
[tex]2y-6=x[/tex]Add 6 to both sides of the equation;
[tex]\begin{gathered} 2y-6+6=x+6 \\ 2y=x+6 \end{gathered}[/tex]Divide each term by 2;
[tex]\begin{gathered} \frac{2y}{2}=\frac{x}{2}+\frac{6}{2} \\ y=(\frac{1}{2})x+3 \end{gathered}[/tex](b)
[tex]undefined[/tex]A cone with radius 6 feet and height 15 feet is shown.6ftEnter the volume, in cubic feet, of the cone. Round youranswer to the nearest hundredth.
EXPLANATION:
Given;
We are given a cone with the following dimensions;
[tex]\begin{gathered} Dimensions: \\ Radius=6ft \\ Height=15ft \end{gathered}[/tex]Required;
We are required to calculate the volume of the cone with the given dimensions.
Step-by-step solution;
To solve this problem, we would take note of the formula of the volume of a cone;
[tex]\begin{gathered} Volume\text{ }of\text{ }a\text{ }cone: \\ Vol=\frac{\pi r^2h}{3} \end{gathered}[/tex]We can now substitute and we'll have;
[tex]Vol=\frac{3.14\times6^2\times15}{3}[/tex][tex]Vol=3.14\times36\times5[/tex][tex]Vol=565.2[/tex]Therefore, the volume of the cone is,
ANSWER:
[tex]Volume=565.2ft^3[/tex]The picture below shows a pole and its shadow:
What is the height of the pole?
121 centimeters
220 centimeters
225 centimeters
231 centimeters
The height of the pole according to the attached image and parameters given is; 220 cm.
What is the height of the pole as required in the task content?It follows from the task content that the height of the pole is to be determined from the parameters given.
From observation, the triangle formed by the situation is a right triangle.
Hence, the height of the pole can be determined by Pythagoras theorem; where, c² = a² + b².
Therefore, we have;
221² = 21² + p²
p² = 48,841 - 21²
p² = 48,400
p = √48,400
p = 220.
On this note, the height of the pole is; 220 cm.
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A creative writing class compiled a list of their favorite superheroes. They listed each superhero's superpower and personality flaw. Fly Read minds Forgetful 6 11 Lazy 5 7 What is the probability that a randomly selected superhero is forgetful and can fly? Simplify any fractions.
The probability is given the following formula:
Probability = Favorable / total outcomes
In this case, there number of students that selected a forgetfull sperheroe that can fly is 6, the total number of outcomes is 6 + 11 + 5 + 7 = 29, then we get:
Probability = 6 / 29
Then, the probability of selecting a forgetful superheroe that can fly is 6/29