Answers
As given by the question
There are given that the equation
[tex]y=-1-\frac{2}{5}x[/tex]Now,
The graph of the line is given below:
Related Questions
A) Find the points of intersection between the curve y = x(x - 1) (x - 2) and x-axis.
Answers
To find the intersection of the curve
[tex]y=x(x-1)(x-2)[/tex]And the x-axis, we first have to notice that the x-axis is the same as the line:
[tex]y=0[/tex]Now, we have a system of two equations.
If we substitute y = 0 into the first, we have:
[tex]x(x-1)(x-2)=0[/tex]Now, for this equation to be true, one of the factors, "x", "(x-1)" or "(x-2)" has to be zero.
So, we will have three solutions:
[tex]\begin{gathered} x=0 \\ x-1=0\leftrightarrow x=1 \\ x-2=0\leftrightarrow x=2 \end{gathered}[/tex]And since these are on the x-axis, we already know that the y values for them are all y = 0.
Thus, the points of intersections are:
[tex]\begin{gathered} (0,0) \\ (0,1) \\ (0,2) \end{gathered}[/tex]a/5 + 8<13 please help
Answers
We have the inequality
[tex]\frac{a}{5}+8<13[/tex]solving for a, we have
[tex]\begin{gathered} \frac{a}{5}+8<13 \\ \frac{a}{5}<13-8 \\ \frac{a}{5}<5 \\ a<5\cdot5 \\ a<25 \end{gathered}[/tex]Then a has to be less than 25. Written the solution in interval form we have:
[tex](-\infty,25)[/tex]1 5/6 - (-2 4/5)[tex]1 \frac{5}{6} - ( - 2 \frac{4}{5} )[/tex]
Answers
We have the following:
[tex]1\frac{5}{6}-(-2\frac{4}{5})[/tex]solving:
[tex]\begin{gathered} 1\frac{5}{6}=\frac{11}{6} \\ 2\frac{4}{5}=\frac{14}{5} \\ \frac{11}{6}+\frac{14}{5}=\frac{11\cdot5+14\cdot6}{30}=\frac{55+84}{30}=\frac{139}{30} \\ \frac{139}{30}=4\frac{19}{30} \end{gathered}[/tex]The answer is 4 19/30
Evaluate each expression using the graphs of y=f(x) and y = g(x) shown below.(a) (gof)(-1) (b) (gof)(0) (c) (fog) - 1) (d) (fog)(4)
Answers
Answer:
a) 5
b) 6
c) -2
d) -3
Explanation:
Given:
a) From the graph, we can see that f(-1) = 1 and g(1) = 5, so we'll have that;
[tex](g\circ f)(-1)=g(f(-1))=g(1)=5[/tex]b) From the graph, we can notice that f(0) = 0, g(0) = 6, so we'll have that;
[tex](g\circ f)(0)=g(f(0))=g(0)=6[/tex]c) From the graph, we can notice that g(-1) = 4 and f(4) = -2, so we'll have that;
[tex](f\circ g)(-1)=f(g(-1))=f(4)=-2[/tex]d) From the graph, we can see that g(4) = 3 and f(3) = -3, so we'll have that;
[tex](f\circ g)(4)=f(g(4))=f(4)=-3[/tex]What are the solutions to the following system?{-2x+y=-5y=-3x2 + 50 (0, 2)O (1, -2)o (12.-1) and (- 12.-1):o 15.-10) and (-75-10
Answers
Answer:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Explanation:
Here, we want to solve the system of equations
Since we have y in both equations, let us start by rewriting the second equation to look like the first
We have that as:
[tex]\begin{gathered} -2x^2+y\text{ = }-5 \\ y+3x^2\text{ = 5} \end{gathered}[/tex]Subtract equation ii from i
We have it that:
[tex]\begin{gathered} -5x^2=\text{ -10} \\ 5x^2=10 \\ x^2=\text{ 2} \\ \\ x\text{ = }\pm\sqrt[]{2} \end{gathered}[/tex]when x = positive root 2, we have it that:
[tex]\begin{gathered} -2x^2+y\text{ = -5} \\ -2(\sqrt[]{2\text{ }})^2+y\text{ = -5} \\ -4+y\text{ = -5} \\ y\text{ = -5+4} \\ y\text{ = -1} \end{gathered}[/tex]when x = negative root 2:
We will still get the same answer as the square of both returns the same value
Thus, we have the solution to the system of equations as:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Kevin went for a drive in his new car. He drove for 377.6 miles at a speed of 59 miles per hour. For how many hours did he drive ?
Answers
We know that the average speed (v) can be calculated as the quotient between the distance D and the time t.
As v = 59 mi/h and D = 377.6 mi., we can calculate the time as:
[tex]v=\frac{D}{t}\longrightarrow t=\frac{D}{v}=\frac{377.6\text{ mi}}{59\text{ mi/h}}=6.4\text{ h}[/tex]Answer: he drove for 6.4 hours.
What are all of the answers for these questions? Use 3 for pi. Please do not use a file to answer, I cannot read it.Question 8.
Answers
To calculate the area of the doughnut, we need to calculate the area of the larger circle and substract the area of the smaller circle.
The area of a circle can be calculated using its radius:
[tex]A=\pi r^2[/tex]The diameter of the larger circle is 6cm which meand that its radius is half as large, so the radius is 3 cm and the area of the larger circle is:
[tex]A_L=\pi3^2=9\pi[/tex]Area of 9π cm².
The smaller one have a diameter of 2 cm, so its radius is half as large, radius of 1 cm.
So, the area of the smaller circle is:
[tex]A_S=\pi1^2=\pi[/tex]Area of π cm².
The total shaded area is, then, the area of the larger minus the area of the smaller.
So, the shaded area is:
[tex]\begin{gathered} A=A_L-A_S \\ A=(9\pi-\pi)cm^2 \\ A=8\pi cm^2 \\ A\approx(9\cdot3)cm^2 \\ A\approx27cm^2 \end{gathered}[/tex]the sum of 2 numbers is 30. the sum of the squares of the two numbers is 468 what is the product of the two numbers
Answers
Take x and y as the 2 numbers
Define the equation that represents each situation
The sum of 2 numbers is 30
[tex]x+y=30[/tex]The sum of the squares of the numbers is 468
[tex]x^2+y^2=468[/tex]Complete the square in the second equation (don't forget to write
which of tje following proportion are true16/28=12/216/16=4/1430/40=24/3510/15=45/30
Answers
Notice that:
1)
[tex]\frac{16}{28}=\frac{4\cdot4}{7\cdot4}=\frac{4}{7}=\frac{4\cdot3}{7\cdot3}=\frac{12}{21}\text{.}[/tex]2)
[tex]\frac{6}{16}=\frac{2\cdot3}{2\cdot8}=\frac{3}{8}\ne\frac{2}{7}=\frac{2\cdot2}{2\cdot7}=\frac{4}{14}\text{.}[/tex]3)
[tex]\frac{30}{40}=\frac{10\cdot3}{10\cdot4}=\frac{3}{4}\ne\frac{2}{3}=\frac{12\cdot2}{12\cdot3}=\frac{24}{36}.[/tex]4)
[tex]\frac{10}{15}=\frac{5\cdot2}{5\cdot3}=\frac{2}{3}\ne\frac{9}{10}=\frac{5\cdot9}{5\cdot10}=\frac{45}{50}.[/tex]Answer: The only proportion that is true is the first one.
PLESSS HELP I NEED HELP PLESS HELP I NEEED HELP
Answers
For this exercise you need to remember that the area of a triangle can be calculated with the following formula:
[tex]A=\frac{bh}{2}[/tex]Where "b" is the base of the triangle and "h" is the height of the triangle.
Analyzing the information given in the exercise, you can identify that, in this case:
[tex]\begin{gathered} b=x=11units \\ h=7units \end{gathered}[/tex]Then, knowing these values, you can substitute them into the formula and then evaluate, in order to find the area of the triangle. This is:
[tex]\begin{gathered} A=\frac{(11units)(7units)}{2} \\ \\ A=\frac{77units^2}{2} \\ \\ A=38.5units^2 \end{gathered}[/tex]The answer is: Option B.
Evaluate with no calculator sin(sin^-1(3/8))
Answers
Since the sine ratio is opposite side/hypotenuse
Then in
[tex]\sin (\sin ^{-1}\frac{3}{8})[/tex]This means the angle has opposite side 3 and hypotenuse 8 in a right triangle
Then use this rule to evaluate without a calculator
[tex]\sin (\sin ^{-1}\frac{a}{b})=\frac{a}{b}[/tex]Because sin will cancel sin^-1
[tex]\sin (\sin ^{-1}\frac{3}{8})=\frac{3}{8}[/tex]The answer is 3/8
7/8 = X/16 X=how do I solve it
Answers
x= 14
1) Let's solve this equation considering that we're dealing with two ratios.
Then we can cross multiply and simplify them this way:
[tex]\begin{gathered} \frac{7}{8}=\frac{x}{16} \\ 8x=16\cdot7 \\ \frac{8}{8}x=\frac{16\cdot7}{8} \\ x=2\cdot7 \\ x=14 \end{gathered}[/tex]2) So the answer is x= 14
A regular plot of land is 70 meters wide by 79 meters long. Find the length of the diagonal and, if necessary, round to the nearest tenth meter
Answers
Given :
The length is given l=79 m and width is given w=70m.
Explanation :
Let the length of diagonal be x.
To find the length of diagonal , use the Pythagoras theorem.
[tex]x^2=l^2+w^2[/tex]Substitute the values in the formula,
[tex]\begin{gathered} x^2=79^2+70^2 \\ x^2=6241+4900 \\ x^2=11141 \\ x=\sqrt[]{11141} \\ x=105.55m \end{gathered}[/tex]Answer :
The length of the diagonal is 105.6 m.
The correct option is D.
HEL LE Maria has 36 episodes of Grey's Anatomy to watch with her friends. They watch 3 episodes each day. Which of the following equations represents the number days, d, it took for them to have 21 episodes left? 0210 - 3 = 36 O 21 - 3d = 36 36 - 3d = 21 36 + 3d = 21 LE
Answers
Total episodes: 36
Episodes watched per day: 3
Number of days: d
To represents the number of days, d, it will take for them to have 21 episodes left:
Subtract the episodes watched per day (3d) to the total episodes (36), and that expression must be equal to 21:
36-3d=21
Write an equation for the line that contains (-32, -12) and is perpendicularto the graph -8x + 10y = 40Can anyone that KNOWS the answer help?
Answers
The first step is finding the slope of the equation -8x + 10y = 40.
To do so, let's put this equation in the slope-intercept form: y = mx + b, where m is the slope.
So we have:
[tex]\begin{gathered} -8x+10y=40 \\ -4x+5y=20 \\ 5y=4x+20 \\ y=\frac{4}{5}x+4 \end{gathered}[/tex]Then, since the line we want is perpendicular to this given line, their slopes have the following relation:
[tex]m_2=-\frac{1}{m_1}[/tex]So, calculating the slope of the line, we have:
[tex]m_2=-\frac{1}{\frac{4}{5}}=-\frac{5}{4}[/tex]Finally, our equation has the point (-32, -12) as a solution, so we have:
[tex]\begin{gathered} y=mx+b \\ y=-\frac{5}{4}x+b \\ -12=-\frac{5}{4}\cdot(-32)+b \\ -12=-5\cdot(-8)+b \\ -12=40+b \\ b=-12-40 \\ b=-52 \end{gathered}[/tex]So our equation is y = (-5/4)x - 52
Convert Following expression in radical form into an exponential expression in rational form, multiply and simplify then divide you do not need to evaluate just put in simplest form
Answers
9.
[tex]\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}[/tex]Using the following properties:
[tex]\begin{gathered} x^a\cdot x^b=x^{a+b} \\ a^{-x}=\frac{1}{a^x} \\ \sqrt[z]{x^y}=x^{\frac{y}{z}} \end{gathered}[/tex][tex]\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}=5^{\frac{7}{2}}\cdot5^{\frac{6}{2}}\cdot5^{-\frac{3}{5}}=5^{\frac{7}{2}+\frac{6}{2}-\frac{3}{5}}=5^{\frac{59}{10}}[/tex]Answer:
5 7/5
Step-by-step explanation:
As you can see there is a divisions sign so you will start there.
The square root of 5^6 will turn into 5 6/2 divided by 5 3/5.
You want to find the LCD for the denominator. That will be 10, 6 divided by 3 equals 2 so you will have 5 7/2 times 5 2/10. You then change the two to a 10 and multiply the 7 and 2 which will become 5 14/10.
Once simplified the answer is 5 7/5.
Hope this helps :)
Part A: Show all work to solve the quadratic equation x2 − 12x + 35 = 0 by factoring.Part B: Using complete sentences, explain what the solutions from Part A represent on the graph.
Answers
Answer:
A) Notice that:
[tex]\begin{gathered} x^2-12x+35=x^2+(-5-7)x+(-5)(-7) \\ =x^2-5x-7x+(-5)(-7)=x(x-5)-7(x-5) \\ =(x-7)(x-5)\text{.} \end{gathered}[/tex]Therefore:
[tex]x^2-12x+35=0\text{ if and only if x=7 or x=5.}[/tex]B) The solutions from part A represent the x-coordinates of the x-intercepts of the graph of the function
[tex]f(x)=x^2-12x+35.[/tex]y = 3x ÷ 9 and x = -6 what is the output?
Answers
y = 3x ÷ 9 and x = -6
y = 3(-6) ÷ 9 = -18 ÷ 9 = -2
y = -2
Answer:
y = -2
Graph the following:X>y^2 + 4y
Answers
Solution:
Given the inequality;
[tex]x>y^2+4y[/tex]The graph of inequality without an equal sign is done with broken lines,
The y-intercept is;
[tex]\begin{gathered} 0>y^2+4y \\ \\ 0>y(y+4) \end{gathered}[/tex]Thus, the graph is;
Hi , i need help with this question: what is the anwser to the division problem. 9÷4590
Answers
Problem
what is the anwser to the division problem.
9÷4590
Solution
We have the following number given:
[tex]\frac{9}{4590}[/tex]The first step would be simplify the fraction and we can divide both numbers by 9 and we got:
[tex]\frac{9}{9}=1,\frac{4590}{9}=510[/tex]So then our fraction becomes:
[tex]\frac{1}{510}[/tex]And if we convert this into a decimal we got 0.00196.
If ST = x + 4, TU = 10, and SU = 9x + 6, what is ST?
Answers
Given:
[tex]\begin{gathered} ST=x+4 \\ \\ TU=10 \\ \\ SU=9x+6 \end{gathered}[/tex]Find-:
The value of "x."
Explanation-:
The line of property
[tex]SU=ST+TU[/tex]Put the value is:
[tex]9x+6=x+4+10[/tex][tex]\begin{gathered} 9x+6=x+14 \\ \\ 9x-x=14-6 \\ \\ 8x=8 \\ \\ x=\frac{8}{8} \\ \\ x=1 \end{gathered}[/tex]So, the value of "x" is 1.
The hallway of an apartment building is 44 feet long
and 6 feet wide. A landlord has 300 square feet of carpet. Does she have
enough carpet to cover the hallway? Explain.
Answers
Answer:
Yes, there is enough carpet to cover the hallway. We know this because the area of the floor is shown as 44 times 6, which equals 264 feet. With 300>264, there is enough feet of carpet to cover
Step-by-step explanation:
44 times 6 = 264
Hi I need help with this question please thank you!
Answers
To answer this question we will factorize each term.
Notice that:
[tex]20x^4y=5xy(4x^3),[/tex][tex]10x^3y^3=5xy(2x^2y^2),[/tex][tex]5xy^2=5xy(y).[/tex]Therefore, the greatest common factor of the terms is:
[tex]5xy\text{.}[/tex]Answer:
[tex]5xy\text{.}[/tex]
ubtract. - B the model to help
Answers
As you can see in the model
[tex]\frac{1}{2}=\frac{4}{8}[/tex]Then
[tex]\frac{5}{8}-\frac{1}{2}=\frac{5}{8}-\frac{4}{8}=\frac{5-4}{8}=\frac{1}{8}[/tex]This is the same as if you removed 4 pieces of 1/8 from the 5 pieces of 1/8, resulting in 1 piece of 1/8.
Therefore, the result of the subtraction is
[tex]\frac{1}{8}[/tex]What is the volume of this rectangular prism? 5/3 cm 1/4 cm 3/2 cm
Answers
The volume of the prism can be determined as,
[tex]\begin{gathered} V=\frac{5}{3}cm\times\frac{1}{4}cm\times\frac{3}{2}cm \\ V=\frac{5}{8}cm^3 \end{gathered}[/tex]Thus, the required volume is 5/8 cubic centimeters.
Which of the following functions best describes this graph?O A. y=x2- 8x+15O B. y=x+8x+15O c. y = x + x - 12O D. y=x2-5x+6
Answers
We will investigate how to best represent a parabolic graph using a function description.
All parabolas are denoted as either a " U " or inverted " U ". There are two principal parameters of a parabola. The vertex i.e the maximum or minimum point attained by the parabola. The line of symmetry or focus point: The line of symmetry can either be vertical or horizontal but it always passes through the focus point.
We are given a graph of a parabola that has two zeros which can be read off from the plot.
We will locate these zeros and write them down:
[tex]\begin{gathered} x\text{ = 3} \\ x\text{ = 5} \end{gathered}[/tex]All parabolas are expressed by a quadratic polynomial function. The quadratic polynomial can be expressed in factorized form as follows:
[tex](\text{ x - }\alpha\text{ )}\cdot(x\text{ - }\beta\text{ )}[/tex]Where,
[tex]\begin{gathered} \alpha\text{ = 3 ( First Zero )} \\ \beta\text{ = 5 , ( Second Zero )} \end{gathered}[/tex]We will express our located zeros in the factorized quadratic expressed above:
[tex](\text{ x - 3 )}\cdot(x\text{ - 5 )}[/tex]Then we will try to solve the parenthesis and expand the factorized form as follows:
[tex]\begin{gathered} -5\cdot(x\text{ - 3 ) + x}\cdot(x\text{ - 3 )} \\ -5x+15+x^2\text{ - 3x} \end{gathered}[/tex]Group the similar terms and simplify:
[tex]x^2\text{ - 8x + 15 }[/tex]Therefore the function that best describes the given plot is:
[tex]y=x^2\text{ -8x + 15 }\ldots\text{ Option A}[/tex]Determine if each of the following relationships form a function.(1,1), (3,2), (5,4), (-9,6)
Answers
Determine if each of the following relationships form a function.
(1,1), (3,2), (5,4), (-9,6)
we know that
A relationship between x and y form a function, if for one value of x there is only one value of y
In this problem we have that
for one value of x there is only one value of y
therefore
Yes, form a function
Third-degree, with zeros of -3,-1, and 2 and passes through the point (3,6)
Answers
Since the polynomial must have zeroes at x=-3, x=-1, x=2, then, we can write it as a combination of the factors (x+3), (x+1), (x-2):
[tex]p(x)=k(x+3)(x+1)(x-2)[/tex]The constant k will help us to adjust the value of the polynomial when x=3:
[tex]\begin{gathered} p(3)=k(3+3)(3+1)(3-2) \\ =k(6)(4)(1) \\ =24k \end{gathered}[/tex]Since p(3) must be equal to 6, then:
[tex]\begin{gathered} 24k=6 \\ \Rightarrow k=\frac{6}{24} \\ \Rightarrow k=\frac{1}{4} \end{gathered}[/tex]Therefore, the following polynomial function has zeroes at -3, -1 and 2, and passes through the point (3,6):
[tex]p(x)=\frac{1}{4}(x+3)(x+1)(x-2)[/tex]Which of the following statements about the Real Number System is always true?A Rational numbers include irrational numbers.B A number that is an integer is also a whole number and a natural number.C A number that is a whole number is also an integer and a rational Fimber.Tmber.D A number that is a whole numbers is also a natural number.
Answers
C
1) Let's draw a sketch to better understand this:
2) So, based on that we can say that
A number that is a Whole number is also an integer and a Rational Number.
Whole numbers are counting number with the 0 included
Integers numbers are whole numbers and the negative numbers
Rational numbers are any number that can be written as a ratio like 2, (2/1), 3/2, 5, 6/7, etc.
So whole numbers are integer numbers and rational ones simultaneously.
For example 2, 3, etc.
Below is a model of the infield of a baseball stadium. How long is each side of the field Hurry pleaseee
Answers
We have the following:
[tex]\begin{gathered} A=s^2 \\ s=\sqrt{A} \end{gathered}[/tex]A = 81, replacing:
[tex]A=\sqrt{81}=9[/tex]therefore, each side measures 9 in