Find the point of intersection of the following pair of equations, then sketch your solutions indicating all point where the equations intersect both sets of axes: a) y = 2x – 1 and x + 2y = 5b) ^2 + ^2 = 4 and 3x + y = 2
Answers
Answer:
a) Intersection of the equations (1.4, 1.8)
b) Intersection of the equations (0, 2) and (1.2, -1.6)
Explanation:
Part a) y = 2x – 1 and x + 2y = 5
To find the intersection point, let's replace the first equation on the second one, so
x + 2y = 5
x + 2(2x - 1) = 5
Now, we can solve the equation for x
x + 2(2x) - 2(1) = 5
x + 4x - 2 = 5
5x - 2 = 5
5x - 2 + 2 = 5 + 2
5x = 7
5x/5 = 7/5
x = 1.4
Then, replace x = 7/5 on the first equation
y = 2x - 1
y = 2(1.4) - 1
y = 2.8 - 1
y = 1.8
Then, the graph of the lines is:
Where the intersection points with the axes for y = 2x - 1 are (0, -1) and (0.5, 0) and the intersection points with the axes of x + 2y = 5 are (0, 2.5) and (5, 0)
Part b) ^2 + ^2 = 4 and 3x + y = 2
First, let's solve 3x + y = 2 for y, so
3x + y - 3x = 2 - 3x
y = 2 - 3x
Then, replace y = 2 - 3x on the first equation and solve for x
x² + y² = 4
x² + (2 - 3x)² = 4
x² + 2² - 2(2)(3x) + (3x)² = 4
x² + 4 - 12x + 9x² = 4
10x² - 12x + 4 = 4
10x² - 12x + 4 - 4 = 0
10x² - 12x = 0
x(10x - 12) = 0
So, the solutions are
x = 0
or
10x - 12 = 0
10x = 12
x = 12/10
x = 1.2
Replacing the values of x, we get that y is equal to
For x = 0
y = 2 - 3x
y = 2 - 3(0)
y = 2 - 0
y = 2
For x = 1.2
y = 2 - 3(1.2)
y = 2 - 3.6
y = -1.6
Therefore, the intersection points are (0, 2) and (1.2, -1.6)
Then, the graph of the functions are:
Since ^2 + ^2 = 4 is a circle with radius 2, the intersection points with the axes are (2,0), (0, -2), (-2, 0) and (0, 2). Additionally, the intersections potins with the axis of the line 3x + y are (0, 2) and (0.667, 0)
Related Questions
The ratio of the measures of the three angles in a triangle are 3:4:6. Determine the measures of each angle of the triangle.
Answers
Given:
The ratio of the angles is 3:4:6.
Required:
We need to find the measure of each angle of the triangle.
Explanation:
Let the angles of the triangle be 3x, 4x and 6x.
We know that the sum of the angles is equal to 180 degrees.
[tex]3x+4x+6x=180\degree[/tex][tex]13x=180\degree[/tex]Divide both sides by 13.
[tex]\frac{13x}{13}=\frac{180\degree}{13}[/tex][tex]x=13.85[/tex]Substitute x values in 3x, 4x and 6x.
[tex]3x=3\times13.85=41.55[/tex][tex]4x=4\times13.85=55.4[/tex][tex]41.55+55.4+6x=180[/tex][tex]6x=83.05[/tex]Final answer:
The angles are 41.55, 55.40 and 83.05.
show 1.25 and -1.25 as points on the number line. what is the distance between the two points explain
Answers
The distance between 1.25 and -1.25 is computed as follows:
1.25 - (-1.25) = 1.25 + 1.25 = 2.5
Billy is solving the inequality 4x - 4 > 20:His work is shown:4x - 4 > 20+4+44x > 244 4X < 6Did Billy solve the problem correctly? If not, where did Billy make a mistake
Answers
He added 4 to both sides:
[tex]\begin{gathered} 4x-4+4>20+4 \\ 4x>24 \end{gathered}[/tex]He divided both sides by 4:
[tex]\begin{gathered} \frac{4x}{4}>\frac{24}{4} \\ x>6 \end{gathered}[/tex]However he got:
x < 6
He flipped the inequality sign which is incorrect since he is not dividing by a negative number
what us the value of x that makes the equation true?
Answers
Complete the sentence below. A rhombus is a rectangle. always sometimes never Submit
Answers
The correct answer is Never
There are 48 employees in a company. On a certain day, 36 were present. What percent showed up for work'
Answers
Answer:
75%
Step-by-step explanation:
Divide 48 by 36:
36/48=
(12*3)/(12*4)=
3/4=0.75
Multiply the decimal by 100 to get the percent:
0.75*100=75%
The workers present on the certain day given is 75%
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
Given that, There are 48 employees in a company. On a certain day, 36 were present.
To find the percentage of workers present = present/totalx100
= 36/48x100
= 75
Hence, The workers present on the certain day given is 75%
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Why is the product of two rational numbers always rational?Select from the drop-down menus to correctly complete the proof. Let ab and cd represent two rational numbers. This means a, b, c, and d are Choose... integers or irrationals number , and b and d are not 0. The product of the numbers is acbd, where bd is not 0. Both ac and bd are Choose... integers or irrationals numbers, and bd is not 0. Because acbd is the ratio of two Choose... integers or irrationals numbers, the product is a rational number.
Answers
a rational number is a type of real numbers, which is in the form of p/q where q is not equal to zero.
Let a/b and c/d represent two rational numbers. This means a, b, c, and d are integers, and b and d are not 0. The product of the numbers is ac/bd, where bd is not 0. Both ac and bd are integers, and bd is not 0. Because ac/bd is the ratio of two integers, the product is a rational number
Use the point-slope formula to write an equation of the line that passes through (-3, 2) and (-6, -2).Write the answer in slope-intercept form (if possible).
Answers
The equation of a line in the slope-intercept form is y = mx + b, where "m" is the slope and b is the y-intercept.
To find the equation of the line given two points (x, y), follow the steps below.
Step 01: Substitute the point (-3, 2) in the equation.
To do it, substitute x by -3 and y by 2.
[tex]\begin{gathered} 2=m\cdot(-3)+b \\ 2=-3m+b \end{gathered}[/tex]Isolate b by adding 3m to both sides of the equation.
[tex]\begin{gathered} 2+3m=-3m+b-3m \\ 2+3m=-3m+3m+b \\ 2+3m=b \end{gathered}[/tex]Step 02: Substitute b in the equation of the line.
Knowing that b = 2 + 3m. Then,
[tex]\begin{gathered} y=mx+b \\ y=mx+2+3m \end{gathered}[/tex]Step 03: Substitute the point (-6, -2) in the equation from step 02.
To do it, substitute x by -6 and y by -2.
[tex]\begin{gathered} -2=m\cdot(-6)+2+3m \\ -2=-6m+2+3m \\ -2=-3m+2 \end{gathered}[/tex]Isolate "m" by subtracting 2 from both sides.
[tex]\begin{gathered} -2-2=-3m+2-2 \\ -4=-3m \end{gathered}[/tex]Finally, divide both sides by -3:
[tex]\begin{gathered} \frac{-4}{-3}=\frac{-3}{-3}m \\ \frac{4}{3}=m \end{gathered}[/tex]Knowing "m", use the equation from step 1 to find "b".
Step 04: Find "b".
[tex]\begin{gathered} b=2+3m \\ \end{gathered}[/tex]Substituting m by 4/3 and solving the equation:
[tex]\begin{gathered} b=2+3\cdot\frac{4}{3} \\ b=2+\frac{3\cdot4}{3} \\ b=2+4 \\ b=6 \end{gathered}[/tex]Answer: The equation of the line is:
[tex]y=\frac{4}{3}x+6[/tex]A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 7 milliliters of compound B. If a chemist wants to make 1056 milliliters of the drug, how many milliliters of compound A are needed?what is the answer?
Answers
If the proportion of compounds A and B is 5 to 7, we can calculate the amount of each compound in the total of 1056 using the equations:
[tex]\begin{gathered} A=\frac{5}{5+7}\cdot1056 \\ A=\frac{5}{12}\cdot1056 \\ A=440 \\ \\ B=\frac{7}{5+7}\cdot1056 \\ B=\frac{7}{12}\cdot1056 \\ B=616 \end{gathered}[/tex]So the amount of compound A needed is 440 ml.
The distribution of the binomial random variable (x) has the following parameters: p = 0.3 and n = 9 Determine the P(X ≥ 2)
Answers
Answer:
Explanation:
The formula for calculating binomial probability is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n is the number of trials
x is the number of successes
p is the probability of success
q is the probability of failure
From the information given,
n = 9
p = 0.3
q = 1 - p = 1 - 0.3 = 0.7
By using a binomial probability calculator,
P(x ≥ 2) = 0.804
point (0,6) in which quadrant and axis
Answers
Given the point:
(0, 6)
Let's find the quadrant and the axis where the point is located.
We have:
(x, y) ==> (0, 6)
The x-coordinate of the point is 0, while the y-coordinate of the point is 6.
Here, the point (0, 6) lies on the y-axis.
Also, since the x-coordinate is 0, we can say the point lies in between quadrant I and quadrant II.
From the graph above we can see the point (0, 6) is between quadrant I and II, and the point lies on the y-axis.
ANSWER:
• The point is in beween Quadrant I and II
,• The point lies on the y-axis.
Can you please answer so I already have the answers on the side if you can see but can you show me how he did it
Answers
What is 0.023% of 2100?
Word "is" means = and the word "of" means times
So it is x = 0.023% * 2100
At first, change 0.023% to a normal number by dividing it by 100
[tex]x=\frac{0.023}{100}\times2100[/tex]Let us simplify the right side
[tex]x=0.023\times21[/tex]Now use your calculator to find the answer
x = 0.483
0.483 is 0.023% of 2100
Find AB. A =20B = 10C = 54 D = 12
Answers
Answer:
C. 54
Explanation:
The triangles ABD and ACD are congruent by SAS (Side - angle - side) becuase
AD is congruent to itself
∠ADB = ∠ADC
BD is congruent to CD
So, the length of AB is equal to the length of AC and we can write the following equation
AB = AC
4x + 6 = 5x - 6
Solving for x, we get:
4x + 6 + 6 = 5x - 6 + 6
4x + 12 = 5x
4x + 12 - 4x = 5x - 4x
12 = x
Then, the length of AB is
AB = 4x + 6
AB = 4(12) + 6
AB = 48 + 6
AB = 54
Therefore, the answer is
C. 54
F.28. 21 and 22 are vertical angles. If mZ1 =(6x + 11) and mZ2 = (10x - 9), find mZ1.mZ1 =
Answers
It is given that angle 1 and angle 2 are vertical angles.
It is known that the vertical angles are congruent.
Therefore it follows:
[tex]\begin{gathered} m\angle1=m\angle2 \\ 6x+11=10x-9 \\ 11+9=10x-6x \\ 20=4x \\ x=5 \end{gathered}[/tex]So the value of angle 1 is given by:
[tex]\begin{gathered} \angle1=6x+11 \\ =6\times5+11 \\ =41 \end{gathered}[/tex]Hence the angle is 41 degrees.
(-9,-5),(-6,1) and (5,8)What is the perimeter?
Answers
Answer
The perimeter of the triangle is 48.298 units
Explanation
The triangle has the vertices (-9, -5), (-6, 1) and (5, 8).
To find the perimeter of the triangle, we need to find the lengths of the sides of the triangle. The perimeter is the sum of all its sides.
Each side will be calculated from the distance between the vertices.
The distance between two points with the coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
The sides of the triangle will be between
(-9, -5) and (-6, 1)
(-9, -5) and (5, 8)
(-6, 1) and (5, 8)
(x₁, y₁) and (x₂, y₂) is (-9, -5) and (-6, 1)
x₁ = -9
y₁ = -5
x₂ = -6
y₂ = 1
d = √[(-6 - (-9))² + (1 - (-5))²]
d = √[(-15)² + (6)²]
d = √(261)
d = 16.155
(x₁, y₁) and (x₂, y₂) is (-9, -5) and (5, 8)
x₁ = -9
y₁ = -5
x₂ = 5
y₂ = 8
d = √[(5 - (-9))² + (8 - (-5))²]
d = √[(14)² + (13)²]
d = √(365)
d = 19.105
(x₁, y₁) and (x₂, y₂) is (-6, 1) and (5, 8)
x₁ = -6
y₁ = 1
x₂ = 5
y₂ = 8
d = √[(5 - (-6))² + (8 - 1)²]
d = √[(11)² + (7)²]
d = √(170)
d = 13.038
The perimeter of the triangle is thus given as
Perimeter = 16.155 + 19.105 + 13.038
= 48.298 units
Hope this Helps!!!
A ferris wheel has a radius of 65 feet. How many feet will the feris wheel have turned after 10 rotations.
Answers
we need to calculate the perimeter of a circle of radius 65
perimeter=2pi*radius=2pi*65=130pi
then after 10 rotations the wheel have turned 10(130pi) feets= 1300pi feets
Assume five coins are tossed, and we're trying to figure out how many tails will appear. Let's use the letter T to denote the number of tails that will emerge. Find the values of a random variable called T.
Answers
The probability (P) can be gotten as follows:
[tex]P=\frac{number\text{ of favorable outcomes}}{total\text{ number of outcomes}}[/tex]Each coin has a 1/2 = 0.5 probability of getting a tail. Thus, to get the probability of the 5 coins is:
[tex]\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{32}=0.0313[/tex]Then the probability for a tail to emerge
What steps do you take in order to construct an equilateral triangle using a compass and a straight edge?
Answers
An equilateral triangle is one that has three equal sides, therefore it is more importante than with the rule to create 3 sides of the same length.
Chris had a new refrigerator delivered to his home for $950. He gave the delivery
person a $20 tip. What percent tip did he give the delivery person?
2.1%
21%
0.021%
0.21%
Answers
He give the delivery person a tip of 2.1%
What is delivery ?
Transporting items from a source point to a predetermined destination is known as delivery. Roads, railroads, shipping lanes, and airline networks all play major roles in the delivery of cargo (physical products). Specialized networks, such as pipelines for liquid products, power grids for electrical power, computer networks like the Internet, or broadcast networks for electronic information, may be used to distribute specific sorts of goods. [1] A specific subcategory is car transport, and an associated variation is autorack, which involves shipping cars through railroad.
Delivery, which comprises both transportation and distribution, is a crucial aspect of trade and commerce.Distribution is the overall process of providing things, while logistics is the study of efficient delivery and disposition procedures for both persons and materials. Distributors are companies that specialize in moving commercial items from their site of manufacture or storage to their point of sale, whereas delivery services are companies that focus on moving goods to consumers. Deliveries of goods for both commercial and private purposes are also made by postal, courier, and moving services.
According to the question
The new refrigerator delivered to his home for $950
tip he gave to the delivery person = $20
let tip he gave to the person in percentage be x
$20= [tex]\frac{x}{100}(950)[/tex]
x =[tex]\frac{20(100)}{950}[/tex]
x=2.1%
Thus the tip is 2.1%
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Eric and Sarah both have lemonade stands. The graph below represents how many cupsof lemonade Eric sells per day. The equation represents the rate at which Sarahmakes lemonade. Who sold more cups of lemonade in 5 days?
Answers
The graph indicates that Eric sells 60 cups of lemonade in 5 days.
Substituting x = 5 in the equation of Sarah, we get:
y = 10x
y = 10*5
y = 50
That is, Sarah sells 50 cups of lemonade in 5 days.
Then, Eric sells more cups.
Write the factored form of the least common denominator needed to simplify this expression.9419 + 3+g2 + 29- 15+5
Answers
ANSWER
[tex]g^2+2g-15=(g+5)(g-3)[/tex]EXPLANATION
Given:
[tex]\frac{g+1}{g^2+2g-15}+\frac{g+3}{g+5}[/tex]Desired Outcome:
The factored form of the least common denominator
Simplify the expression
[tex]undefined[/tex]Which geometric formulas describe functions that are nonlinear? Select all that apply. (A) P=3s 6) A=65² C) d=2r D C= 2tr E 4. V=
Answers
Answer:
B. A = 6s²
E. V = (4/3)πr³
Explanation:
A formula describes a function that is nonlinear if the exponent of the variable is greater than 1.
Therefore, the geometric formulas that describe functions that are nonlinear:
A = 6s²
V = (4/3)πr³
Because the variable s has an exponent equal to 2 for the first one and the variable r has an exponent equal to 3 for the second one.
Question 10 of 25Which of the following are roots of the polynomial function below?Check all that apply.F(x) = 2x³-²-9x+6OA. 9-√55B. 2□ C. -3-√33D.9+√√554-3+√33E.SUBMIT
Answers
Given
F(x) = 2x³-²-9x+6
Find
roots of the polynomial function below
Explanation
we have to find the roots of the polynomial function.
[tex]\begin{gathered} f(x)=2x^3-x^2-9x+6 \\ f(x)=(x-2)(2x^2+3x-3) \end{gathered}[/tex]now solve quadratic equation ,
[tex]\begin{gathered} 2x^2+3x-3=0 \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-3\pm\sqrt{(3)^2-4\times2\times(-3)}}{4} \\ \\ x=\frac{-3\pm\sqrt{9+24}}{4} \\ \\ x=\frac{-3\pm\sqrt{33}}{4} \end{gathered}[/tex]Final Answer
Therefore , the correct options are B , C and E
An electric guitar costs $790, with a $235 full-replacement warranty. If the manufacturer sells 598,274 warranties andhas to honor 11% of them, how much profit did the manufacturer gain from the warranties? Show work
Answers
What is the slope of a line that is parallel to the line y = 3/4x + 2?
-4/3
-3/4
3/4
4/3
Answers
Answer:
The slope of this line is 3/4.
Select all the equations on which the point (10,0) lies. O 5x + 2y = 15 O 2x + 4y = 20 O x + y = 10 O 3x + 3y = 13 4x + 2y = 20 O 6x + y = 50
Answers
2x + 4y = 20
when y = 0
2x + 4(0) = 20
2x = 10
Divide both-side of the equation by 2
x = 10
Hence, it lies on the point 2x + 4y = 20
Perform the indicated operation and express the result as a simplified complex number in the form a+bi. Do not put any spaces between your characters.(-2-4i)+(1+6i)simplifies to Answer
Answers
Given the expression:
(-2 - 4i) + (1 + 6i)
Let's simplify the expression.
To simplify the expression, let's combine the real and imaginary parts.
• Remove the parentheses:
[tex]-2-4i+1+6i[/tex]• Combine the like terms:
[tex]\begin{gathered} -2+1-4i+6i \\ \\ -1+2i \end{gathered}[/tex]ANSWER:
[tex]-1+2i[/tex]Regular pentagon HIJKL is shown below. What is the measure of ANGLE HIK? (image attached)A. 36 degreesB. 54 degreesC. 72 degreesD. 108 degreesthank you ! :)
Answers
Given a regular pentagon HIJKL.
We are asked to find the measure of Angle HIK
To find the measure of a central angle of a regular pentagon, we make a circle in the middle of the pentagon. We know that a circle is 360 degrees around.
Now, we will divide the 360 by the five angles. Now, the measure of each central angle is equal to:
360/5
So,
Angle HIK = 360/5
Angle HIK = 72˚
Therefore, the correct option is C, which is 72˚.
find the equations of the line those pass through (2/3, -3/5) and have slope 5/3
Answers
Slope intercept form (general)
y = mx + b
Where:
m= slope
b= y-intercept
m = 5/3
y = 5/3x + b
Replace ( x,y ) by the given point (2/3,-3/5) and solve for b.
-3/5 = 5/3 (2/3) + b
-3/5 = 10/9 + b
-3/5 - 10/9 = b
b = -77/45
y = 5/3x - 77/45
7. Tres hermanos tienen una bolsa de golosinas. Quieren regalarle a su padre un trozo de twizzler cada uno. Si cada trozo de twizzler que regalan tienen 100 mm, ¿cuántos centímetros de twizzler tendrá en total el padre?
Answers
Como cada uno de los hermanos le regalará un trozo de twizzler a su padre, ékl tendra tres twizzlers. En milímetros eso es
[tex](3)(100)=300\text{ mm}[/tex]Ahora tenemos que convertir los milimetros a centímetros. Recordemos que un centímetro tiene 10 milímetros. Entonces, tenemos que dividir la cantidad total de milímetros entre 10.
[tex]\frac{300}{10}=30[/tex]Por lo tanto el padre tendrá 30 cm de twizzler en total.