Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. Hesets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections fothese graphs?noneonetwoinfinitely many
Answers
Given:
One side of the equation is a quadratic expression and the other side of the equation is linear.
sets the expressions equal to y and graphs the equations.
Required:
We need to find the greatest possible number of intersections of these graphs.
Explanation:
We know that the quadratic expression gives the parabola and the linea expression gives the line.
If the line crosses the parabola, then greatest possible number of intersections is two.
Final answer:
[tex]Two[/tex]
Related Questions
61.2 + 2x - 10 = -* - 71 + 4x
Answers
61.2 + 2x - 10 = - * - 71 + 4x
What do I have to do?
Find the equation of the line passing through the points (-2,3) and (1, -3). Write the equation in slope-intercept form. A) y = -2x + 3 B) y = 2x + 7 C) y = 2x - 5 D) y = -2x - 1
Answers
The coordinates are given (-2,3) and (1, -3).
The equation formed from the coordinates is
[tex]y-3=\frac{-3-3}{1+2}(x+2)[/tex][tex]y-3=\frac{-6}{3}(x+2)[/tex][tex]y=-2x-4+3[/tex][tex]y=-2x-1[/tex]Hence the correct option is D .
Enter the range of values for x using the picture shown
Answers
We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:
[tex]\begin{gathered} 3x+15<42 \\ 3x<27 \\ x<9 \end{gathered}[/tex]Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:
[tex]\begin{gathered} 3x+15>0 \\ 3x>-15 \\ x>-5 \end{gathered}[/tex]Now, we have our final range: -5 < x < 9
Given that lines b and care parallel, select all that apply.Which angles are congruent to 3?d123/4→b5/67/80 240270_226
Answers
We want to look which angles are congruent to 3 let's analyze the possible options:
Angle 4 is ot congruent since it's not a vertical angle respect to 3
Angle 7 is congruent since 7 and 3 are corresponding angles
Angle 2 is congruent since 2 and 3 are opposite angles
Angle 6 is congruent since 6 and 3 are consecutive interior angles
So
If g is a linear function and g(2)=7 and g(-2)=-1, find g(-5)
Answers
Since the function is linear, it can be written in slope intercept form which is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
From the information given,
g(2) = 7
This means that if x2 = 2, y2 = 7
Also,
g(- 2) = - 1
This means that if x1 = - 2, y1 = - 1
By substituting these values into the formula for calculating slope, we have
m = (7 - - 1)/(2 - - 2) = (7 + 1)/(2 + 2) = 8/4 = 2
We would find the y intercept, c by substituting x = 2, y = 7 and m = 2 into the slope intercept equation. We have
7 = 2 * 2 + c
7 = 4 + c
c = 7 - 4 = 3
By substituting m = 2 and c = 3 into the slope intercept equation, the linear function is
y = 2x + 3
Writing it as a function in terms of g, it is
g(x) = 2x + 3
To find g(- 5), we would substitue x = - 5 into g(x) = 2x + 3, we have
g(- 5) = 2(- 5) + 3 = - 10 + 3
g(- 5) = - 7
Write a rule to describe a transformation when a triangle hasbeen translated down 2 units and right 5 units.Using (x+10,y+10)
Answers
translated down 2 units and right 5 units.
The rule would be
(x + 5, y - 2)
Moving to the right is equal to adding 5 in the x-coordinate.
Translation down is equal to subtracting 2 in the y-coordinate.
In which direction does the left side of the graph of this function point?f(x) = 3x3 - x2 + 4x - 2Answer hereSUBMIT
Answers
The given function is expressed as
f(x) = 3x^3 - x^2 + 4x - 2
This is a cubic function which also means that it is an odd function.
The graph of the function is shown below
The perimeter of a rectangle measuring (2x + 2)cm by (3x -3) cm is 58cm. Calculate its area. 13. The perimeter
Answers
Given:
The length of the given rectangle is l =(2x+2) cm.
The width of the given rectangle is w =(3x-3) cm.
The perimeter of the given rectangle is P =58cm.
Required:
We need to find the area of the rectangle.
Explanation:
Consider the perimeter of the rectangle formula.
[tex]P=2(l+w)[/tex]Substitute l=2x+2, w =3x-3 and P=58 in the formula.
[tex]58=2(2x+2+3x-3)[/tex][tex]58=2(5x-1)[/tex][tex]58=10x-2[/tex]Add 2 to both sides of the equation.
[tex]58+2=10x-2+2[/tex][tex]60=10x[/tex]Divide both sides by 10.
[tex]\frac{60}{10}=\frac{10x}{10}[/tex][tex]x=6[/tex]Substitute x =6 in the equations l=2x+2.
[tex]l=2x+2=2(6)+2=12+2=14cm[/tex][tex]Substitute\text{ }x=6\text{ }in\text{ }the\text{ }equations\text{ }w=3x-3.[/tex][tex]w=3x-3=3(6)-3=18-3=15cm[/tex]The area of the rectangle is
[tex]A=lw[/tex]Substitute l=14cm and w =15cm in the formula.
[tex]A=14\times15[/tex][tex]A=210cm^2[/tex]Final answer:
The area of the given rectangle is 210 square cm.
Represent the following sentence as an algebraic expression, where "anumber" is the letter x.The difference of a number and 8.
Answers
Given,
The difference of a number and 8
Let the number be x
The result of subtracting one number from another is called the "Difference"
The difference of a number and 8 can be expressed below as
[tex]x-8[/tex]Hence, the algebraic expression of the difference of a number (x) and 8 is x - 8
One positive number is 5 more than another. The sum of their squares is 53. What is the larger number?
Answers
7
1) Let's write this
1st number: x
2nd number: y+5
So the positive number and the 1st number have the following relationship x = y +5
2) So we can write, and expand that binomial:
y² +(y+5)² = 53
y² + y² +10y +25 = 53 Combine like terms
2y² +10y -28 =0
We can now solve it:
[tex]\begin{gathered} y=\frac{-10\pm\sqrt[]{100-4(2)(-28)}}{2(2)} \\ y_1=2 \\ y_2=-7 \end{gathered}[/tex]3) As -7 is 9 units lower than 2, then it does not suits us. So let's use that prior relationship to find the other number
x =y+5
x = 2 +5
x=7
Hence, the larger number is 7 and the smaller one is 2
in circle C, BC = 6 and angle ACB = 120 degrees. what is the area of the shaded sector?
Answers
Area of sector = θ/360 × πr²
θ = m∠ACB = 120°
radius = r = 6
[tex]\text{Area of sector = }\frac{120}{360}\times\pi\times6^2[/tex][tex]\begin{gathered} \text{Area = }\frac{1}{3}\times\pi\times36 \\ Area\text{ = }\pi\times\frac{36}{3}\text{ } \end{gathered}[/tex][tex]\begin{gathered} Area\text{= }\pi\times12 \\ \text{Area of sector = 12}\pi\text{ (option C)} \end{gathered}[/tex]solve by substitution You are planning a birthday party. You buy a total of 50 turkey burgers and veggie burgers for $90.00 . Yo pay $2.00 per Turkey burger and $1.50 per veggie burger. How many of each burger did you buy?*use verbal model to write a system of linear equations. Let "x" representthe number of turkey burgers and let "Y" represent the number of veggie burgers
Answers
Let,
t = Turkey burgers
v = veggie burgers
t + v = 50
$2.00 per Turkey burger
$1.50 per Veggie burger
2t + 1.5v = 90
Now we have a system of two equations with two unknowns
[tex]\begin{gathered} t+v=50 \\ 2t+1.5v=90 \end{gathered}[/tex]First equation
[tex]t=50-v[/tex][tex]\begin{gathered} 2(50-v)+1.5v=90 \\ 100-2v+1.5v=90 \\ -2v+1.5v=-100+90 \\ -0.5v=-10 \\ v=\frac{10}{0.5} \\ v=20 \end{gathered}[/tex]20 Veggie burgers
[tex]\begin{gathered} t=50-v \\ t=50-20 \\ t=30 \end{gathered}[/tex]30 Turkey burgers
Statement: Using the figure, determine the following ratios. ∆RTS is a right triangle with a right angle at
Answers
By definition:
[tex]\text{tan(angle)}=\frac{\text{opposite side}}{adjacent\text{ side}}[/tex]From the picture:
[tex]\begin{gathered} \tan (S)=\frac{80}{18}=4.4444 \\ \tan (R)=\frac{18}{80}=0.225 \end{gathered}[/tex]What is 35/12 written as a Mixed Number?
Answers
Answer:
2 11/12
Explanation:
To write 35/12 as a mixed number we need to divide 35 by 12.
When we divide 35 by 12, we get 2 as a quotient and 11 as a remainder.
Additionally, 35 is the dividend, and 12 is the divisor:
Now, the mixed number can be written as:
It means that the mixed number is:
[tex]\text{quotient}\frac{\text{ remainder}}{\text{divisor}}=2\frac{11}{12}[/tex]Therefore, 35/12 written as a mixed number is 2 11/12
Sharma draws a floor plan of the local supermarket on a coordinate plane.
Answers
Solution
For this case we can do the following:
Coordinates
Dairy 1,0
Produce 3,3
Bakery 6,2
Frozen foods 2,6
Part A
B. (3,5)
Part B
D. (2,2)
Give each trig ratio as a fraction in simplest form. PQ is 48.
Answers
sin Q = 7/25
cos Q = 24/25
tan Q = 7/24
sin R = 24/25
cos R = 7/25
tan R = 24/7
Explanation:[tex]\begin{gathered} when\text{ Angle = Q} \\ \text{opposite = side opposite the angle= PR} \\ PR\text{ = 14} \\ \text{hypotenuse = 50} \\ \\ \sin \text{ Q = }\frac{opposite}{hypotenuse} \\ \sin \text{ Q = }\frac{14}{50} \\ \sin \text{ Q = 7/25} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ Q = }\frac{\text{adjacent}}{\text{hypotenuse}} \\ adjacent\text{ = PQ = ?} \\ \text{To get adjacent, we will apply pythagoras' theorem:} \\ \text{hypotenuse}^2=opposite^2+adjacent^2 \\ 50^2=14^2\text{ }+adjacent^2 \\ adjacent^2=50^2-14^2\text{ = 2500 - }196 \\ adjacent^2=\text{ 2304} \\ \text{adjacent = }\sqrt[]{2304}\text{ = 48} \\ \\ \cos \text{ Q = }\frac{48}{50} \\ \cos \text{ Q = 24/25} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ Q = }\frac{opposite}{adjacent} \\ \tan \text{ Q = }\frac{14}{48} \\ \tan \text{ Q = 7/24} \end{gathered}[/tex]when angle = R
opposite = side opposite the angle R = PQ
opposite = PQ = 48
adjacent = 14
hypotenuse = 50
[tex]\begin{gathered} \sin \text{ R = }\frac{opposite}{hypotenuse} \\ \sin \text{ R = }\frac{48}{50} \\ \sin \text{ R = 24/25} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ R = }\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{cos R = }\frac{14}{50} \\ \cos \text{ R = 7/25} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ R = }\frac{opposite}{hypotenuse} \\ \tan \text{ R = }\frac{48}{14} \\ \tan \text{ R = 24/7} \end{gathered}[/tex]help me graduate please the graph of each function is shown . write the function in factored format. do not include complex numbers
Answers
Given the function of the graph:
[tex]g(x)=2x^4+x^3-47x^2-25x-75[/tex]Let's factor the given function.
Regroup the terms:
[tex]g(x)=x^3-25x+2x^4-47x^2-75[/tex][tex]\begin{gathered} \text{Factor x out of x}^3-25x\colon \\ \\ g(x)=x(x^2-25)+2x^4-47x^2-75 \end{gathered}[/tex][tex]g(x)=x(x^2-5^2)+2x^4-47x^2-75[/tex][tex]g(x)=x(x+5)(x-5)+2x^4-47x^2-75[/tex][tex]\begin{gathered} \text{ Rewrite x}^4as(x^2)^2\colon \\ \\ g(x)=x(x+5)(x-5)+2(x^2)^2-47x^2-75 \end{gathered}[/tex][tex]\begin{gathered} Letu=x^2 \\ \\ g(x)=x(x+5)(x-5)+2u^2-47u^{}-75 \end{gathered}[/tex][tex]\begin{gathered} Factor\text{ by grouping:} \\ g(x)=x(x+5)(x-5)+(2u+3)(u-25) \end{gathered}[/tex][tex]\begin{gathered} \text{ Repalce u with x}^2\colon \\ g(x)=x(x+5)(x-5)+(2x^2+3)(x^2-25) \end{gathered}[/tex][tex]g(x)=x(x+5)(x-5)+(2x^2+3)(x^2-5^2)[/tex][tex]g(x)=x(x+5)(x-5)+(2x^2+3)(x+5)(x-5)[/tex][tex]\begin{gathered} \text{Factor out (x+5)(x-5)} \\ \\ g(x)=(x+5)(x-5)(x+2x^2+3) \\ \\ g(x)=(x+5)(x-5)(2x^2+x+3) \end{gathered}[/tex]ANSWER:
[tex]g(x)=(x+5)(x-5)(2x^2+x+3)[/tex]Harrison saved $38.97 from his first paycheck and $65.04 from his second paycheck. How much did he save from the paychecks?A.$26.07B.$94.01C.$94.91D.$104.01
Answers
Answer:
D.$104.01
Explanation:
Here is what we are told
Harrison got the following amount from his paychecks.
Paycheck 1: $38. 97
Paycheck 2: $65.04
Therefore total amount Harrison saved on his paychecks was
$38. 97 + $65.04 = $104.01
Now looking at the answer choices we see that choice D gives the correct answer.
Therefore choice D is the correct answer.
Answer:
it’s D sir =)
Step-by-step explanation:
I’m not sure if this correct is there no decimal? But it’s asking for a decimal format.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
1.6 x 10^7
decimal format = ?
Step 02:
decimal format:
10^7 ====> move decimal point 7 places right
1.6 x 10^7 = 16,000,000
The answer is:
16,000,000
John and Amber work at an ice cream shop. The hours worked and wages earned are given for each person.
Answers
John's wages are proportional to time if every time that we divide wages by time, we get a constant, so we can make the following table:
Time Wages Wages/Time (y/x)
2 18 18/2 = 9
3 27 27/3 = 9
4 36 36/4 = 9
Since Wages/Time is always equal to 9, John's wages are proportional to time.
Answer: John's wages are proportional to time.
The measure of angle a below is(Hint: Slide 3)42°78°
Answers
The measure of the angle = 78 - 42 = 36
The angle 78 is interior angle for the shown triangle
so, the angle 78 is the sum of the angles of the triangle except the adjacent angle to 78
17. Multistep The height of a trapezoid is 8 in. and its area is 96 in. Onebase of the trapezoid is 6 inches longer than the other base. What are thelengths of the bases? Explain how you found your answer.
Answers
The area of a trapezoid is computed as follows:
A = h*(a + b)/2
where h is the height, and a and b are the length of the bases.
One base of the trapezoid is 6 inches longer than the other base, then:
a = b + 6
Replacing with A = 96, h = 8, and a = b + 6, we get:
96 = 8*(b+ 6 + b)/2
96 = 8*(6 + 2b)/2
ET 170 ivel -47 1) 0> Erol Name Kuta Software - Infinite Algebra 2 Solving Absolute Value Equations Solve each equation. 1) |3x| = 9 2) |–3r\ = 3 ond -3 Rasm
Answers
Question:
Solution:
Consider the following equation:
To solve the above equation, split the equation up into two separate equations:
Equation 1:
[tex]-2n\text{ + 6 = 6}[/tex]Equation 2:
[tex]-2n\text{ + 6 =- 6}[/tex]now, solve each of the equation:
For equation 1 we have that:
[tex]-2n\text{ = 0}[/tex]then n = 0
and for equation 2, we have that:
[tex]-2n\text{ = -12}[/tex]then n = 6.
Then, the correct answer is :
n = 6 and n = 0.
In the similar triangles below, what is the length of AB?
Answers
Given:
There are given two triangles, ABC and DEF.
Where,
[tex]\begin{gathered} AC=6cm \\ BC=4cm \\ DE=15cm \\ DF=18cm \end{gathered}[/tex]Explanation:
To find the value of two congruent triangles, we need to use the ratio properties:
So,
From the given congruent triangle:
[tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex]Then,
Put the all values into the above ratio expression:
So,
[tex]\begin{gathered} \begin{equation*} \frac{AB}{DE}=\frac{AC}{DF} \end{equation*} \\ \frac{AB}{15}=\frac{6}{18} \\ \frac{AB}{15}=\frac{1}{3} \\ 3AB=15 \\ AB=\frac{15}{3} \\ AB=5 \end{gathered}[/tex]Final answer:
Hence, the correct option is D.
I need help with this homework question please and thankyou
Answers
The formula for continuously compounded interest is
[tex]\begin{gathered} A=Pe^{rt} \\ \text{ Where }A\text{ is the Amount or future value} \\ P\text{ is the Principal, or initial value} \\ r\text{ is the interest rate, and} \\ t\text{ is the time} \end{gathered}[/tex]So, in this case, we have
[tex]\begin{gathered} A=\text{ \$}1,000 \\ P=\text{ \$}200 \\ r=4\text{\% }=\frac{4}{100}=0.04 \\ t=\text{ ?} \end{gathered}[/tex][tex]\begin{gathered} A=Pe^{rt} \\ \text{ Replace the know values} \\ \text{\$}1,000=\text{\$}200\cdot e^{0.04t} \\ \text{ Divide by \$200 from both sides of the equation} \\ \frac{\text{\$}1,000}{\text{\$}200}=\frac{\text{\$}200\cdot e^{0.04t}}{\text{\$}200} \\ 5=e^{0.04t} \\ \text{ Apply natural logarithm to both sides of the equation} \\ \ln (5)=\ln (e^{0.04t}) \\ \ln (5)=0.04t \\ \text{ Divide by 0.04 from both sides of the equation} \\ \frac{\ln(5)}{0.04}=\frac{0.04t}{0.04} \\ \boldsymbol{40.2\approx t} \end{gathered}[/tex]Therefore, it will take approximately 40 years for the account to reach $1,000.
Milanputting money into a savings account. He starts with $350 in the savings account, and each week he adds $60.Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Milan has been adding money. Write anequation relating S to W. Then use this equation to find the total amount of money in the savings account after 17 weeks.
Answers
We know that he starts with $650 in the savings account, and each week he adds $30.
If S represents the total amount of money and w the number of weeks, an equation that realtes S to w is compounded by:
1. An constant value that is the value which he starts
S = 650
2. Multiplying the number of weeks by the money he adds weekly
S = 650 + w30
So, the equation that relates S to w is
[tex]S=650+w30[/tex]Now, we must calculate the total amount of money after 19 weeks.
In order to calculate this value we must replace w = 19 in the equaton
[tex]\begin{gathered} S=650+(19)(30) \\ S=1220 \end{gathered}[/tex]So, after 17 weeks there are $1220
hey can you tell me how to find a domain of a function and what does real numbers mean
Answers
Solution
Basically the domain represent all the possible values that the function can assume on the x axis
And the real numbers represent all the possible numbers from - infinity to infinity
For example:
f(x)= 2x+1
The domain is all the real numbers since the function is defined for all the possible values of x
In the other hand:
[tex]g(x)=\frac{1}{x-1}[/tex]For this new function the domain is all the real numbers except x=1 since we can' divide by 0
A. Unfortunately, the precise data used by Eratosthenes was lost long ago. However, if Eratosthenes used a meter stick for his experiment today, then the stick’s shadow in Alexandria would be 127 mm long. Determine the angle 0 that the sunrays made with the meter stick. Remember that a meter stick is 1000 millimetres long.B. Assuming that the sun’s rays are essentially parallel, determine the central angle of the circle if the angle passes through Alexandria and Syene. How did you find your answer?
Answers
A
Answer:
Explanation:
The right triangle formed is shown below.
To find θ, we would apply the tangent trigonometric ratio which is expressed as
tan θ = opposite side /adjacent side
From the triangle,
opposite side = 127
adjacent side = 1000
tanθ = 127/1000 = 0.127
taking the tan inverse of 0.127
θ = tan^1(0.127)
θ = 7 degrees
A quality control inspector found 9 defective machine parts out of 500 manufactured.a) What percent of the machine parts manufactured were defective? b) What percent of the machine parts manufactured were NOT defective?
Answers
a) In order to calculate what percent of the machine parts manufactured were defective, you proceed as follow:
divide the defective machine between the total number of machines:
9/500 = 0.018
next, you multiply the previous result by 100:
0.018 x 100 = 1.8%
Hence, 1.8% of the total number of machines were defective
b) In this case you have:
subtract total machine and defective ones:
500 - 9 = 491
divide the previoues result by the number of toal machine:
491/500 = 0.982
multiply the previoues result by 100:
0.982 x 100 = 98.2
Hence, 98.2% of the total number of machine were NOT defective.
If f(x) = x^2 + 3x, find f(-3). *
Answers
Answer:
The value of f(-3) is;
[tex]f(-3)=0[/tex]Explanation:
Given that;
[tex]f(x)=x^2+3x[/tex]To get f(-3), we will substitute -3 for x in the given function f(x);
[tex]\begin{gathered} f(x)=x^2+3x \\ f(-3)=(-3)^2+3(-3) \\ f(-3)=9^{}-9 \\ f\mleft(-3\mright)=0 \end{gathered}[/tex]Therefore, the value of f(-3) is;
[tex]f(-3)=0[/tex]