The system of equation x + 3y = 6 and 2x + 6y = -18 has no solution.
What is the solution to the given system of equation?Given the system of equation in the question;
x + 3y = 6
2x + 6y = -18
To find the solution to the system of equation, first solve for x in the first equation.
x + 3y = 6
Subtract 3y from both sides
x + 3y - 3y = 6 - 3y
x = 6 - 3y
Now, replace all occurrence of x in the second equation with 6 - 3y and solve for y
2x + 6y = -18
2( 6 - 3y ) + 6y = -18
Apply distributive property to remove the parenthesis
12 - 6y + 6y = -18
-6y and +6y cancels out
12 = -18
Since 12 equal -18 is not true, there is no solution to the system of equation.
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Ready for me for a quadratic function with vertex (3,9)
We have to write an equation of a quadratic function that has a vertex at (3,9) and pass through the origin.
We can use the vertex form of the quadratic equation:
[tex]y=a(x-h)^2+k[/tex]where the vertex has coordinates (h,k).
In this case, (h,k) = (3,9).
From the formula we can see that the parameter a that can take any value and still have the same vertex. We will use the parameter "a" to make it pass through the origin.
The vertex form of the equation is then:
[tex]y=a(x-3)^2+9[/tex]As it pass through the origin, then the equation should be satisfied when x = 0 and y = 0:
[tex]\begin{gathered} 0=a(0-3)^2+9 \\ 0=a(-3)^2+9 \\ 0=a\cdot9+9 \\ -9=9a \\ -\frac{9}{9}=a \\ a=-1 \end{gathered}[/tex]Then, as a = -1, we can write the equation as:
[tex]y=-(x-3)^2+9[/tex]Answer: An example of quadratic function with vertex (3,9) that pass through the origin is y = -(x-3)² + 9.
Find the quotient.8 / (1 1/3) (Type a whole number or a fraction.)
In order to calculate the result of this division, let's first convert the mixed number 1 1/3 into a fraction:
[tex]1\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}[/tex]Now, calculating the division, we have:
[tex]\frac{8}{\frac{4}{3}}=8\cdot\frac{3}{4}=2\cdot3=6[/tex]So the result is 6.
Sports Authority marks up New Balance sneakers $30 and sells them for $109. Markup is on cost. What are the cost and percent markup?
If Sports Authority marks up New Balance sneakers for $30 and sells them for $109, then the cost will be $79 while the percent markup will be 37.97%.
What is the cost and percent markup?The original cost of the product can be obtained by subtracting the markup price from the selling price as seen below.
Cost = selling price - markup
Cost = $109 - $30
Cost = $79
Thus, we arrive at the result that the cost of the product by Sports Authority is $79.
Next, we calculate the percent markup with the formula below:
Percent markup = Markup/cost × 100
Percent markup = 30/79 × 100
= 37.97%
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If 10 g of a radioactive substance are present initially and 9 yr later only 5 g remain, how much of the substance will be present after 18 yr?After 18 yr there will be g of a radioactive substance.(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as needed.)
Given:
The initial amount of substance, No=10 g.
The amount of substance left after 9 years, N=5 g.
Since 10 g of substance is present initially, and it became 5 g(half of the initial amount) in 9 years, the half life of the substance is, t =9 years.
Hence, the expression for the amount remaining after T years is,
[tex]N(t)=N_0(\frac{1}{2})^{\frac{T}{t_{}}}[/tex]To find the amount of substance remaining after 18 years, put T=18, N0=10 and t=9 in the above equation.
[tex]\begin{gathered} N(18)=10\times(\frac{1}{2})^{\frac{18}{9}} \\ N(18)=10(\frac{1}{2})^2 \\ =\frac{10}{4} \\ =2.5\text{ g} \end{gathered}[/tex]Therefore, after 18 years 2.5 g of the radioactive substance will remain.
name each angle pair as corresponding, alternate interior, alternate exterior, consecutive interior angle, or no relationship. identify the transversal that connects each angle pair.
Find the equation of the line that is perpendicular to y= -1 over 5x-3 and contains the point (1,2)
STEP - BY - STEP EXPLANATION
What to find?
Equation of a line.
Given:
Perpendicular equation; y=-1/5 x - 3
Point(1,2)
Step 1
Find the slope of the perpendicular line.
Comparing the line with y=mx + c
[tex]slope(m)=-\frac{1}{5}[/tex]Step 2
Determine thee slope of the new equation.
Slope of perpendicular lines have the following characteristic;
[tex]m_1m_2=-1[/tex]where m2 is the slope of the new equation.
[tex]\begin{gathered} -\frac{1}{5}m_2=-1 \\ \\ m_2=-1\times-\frac{5}{1} \\ \\ =5 \end{gathered}[/tex]Step 3
Find the intercept(c) using the formula below:
[tex]y=mx+c[/tex]Substitute x=1 y=2 and m=5
[tex]\begin{gathered} 2=5(1)+c \\ \\ c=2-5 \\ \\ =-3 \end{gathered}[/tex]Step 4
Form the equation of the line by substituting m=5 and c=-3 into the general equation.
[tex]y=5x+(-3)[/tex]ANSWER
y= 5x + (-3)
Hi, The area of a circle is 100 quare millimeters. The radius is 5.64 millimeters. what is the circumference?
The area A of a circle is given by
[tex]A=\pi r^2[/tex]where Pi is 3.1416 and r is the radius. In our case, we get
[tex]100\operatorname{mm}=\pi r^2[/tex]and we need to find r. In this regard, if we move Pi to the left hand side we get
[tex]\frac{100}{\pi}=r^2[/tex]then, r is given by
[tex]r=\sqrt[]{\frac{100}{\pi}}[/tex]Now, the circunference C is given by
[tex]C=2\pi\text{ r}[/tex]then, by substituting our last result into this formula, we have
[tex]C=2\pi\sqrt[]{\frac{100}{\pi}}[/tex]since square root of 100 is 10, we get
[tex]C=2\pi\frac{10}{\sqrt[]{\pi}}[/tex]we can rewrite this result as
[tex]\begin{gathered} C=\frac{2\pi\times10}{\sqrt[]{\pi}} \\ C=\frac{2\sqrt[]{\pi\text{ }}\sqrt[]{\pi}\times10}{\sqrt[]{\pi}} \end{gathered}[/tex]and we can cancel out a square root of Pi. Then, we have
[tex]C=2\sqrt[]{\pi}\times10[/tex]and the circunference is
[tex]C=20\text{ }\sqrt[]{\pi}\text{ milimeters}[/tex]What is the slope of the line shown below?(2,2), (-1,-4) A. 2 B-6. C.6. D-2
Solution
The slope is given by
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \Rightarrow m=\frac{-4-2}{-1-1}=\frac{-6}{-2}=3 \end{gathered}[/tex]Hence, the slope is 3
answer this question that stumbles tons of people around the world!!
The values of x and y in the angles formed by the straight lines are:
x = 18.5
y = 37
What are Angles on a Straight Line?If two or more angles lie on a straight line, they will have a sum of 180 degrees when added together. Therefore, all angles on a straight line have a sum of 180 degree.
Therefore:
16 + 90 + 2y = 180 [straight line angle]
Combine like terms
106 + 2y = 180
Subtract both sides by 106
106 - 106 + 2y = 180 - 106 [subtraction property of equality]
2y = 74
2y/2 = 74/2
y = 37
Also,
16 + 90 + 4x = 180
106 + 4x = 180
4x = 180 - 106 [subtraction property of equality]
4x = 74
4x/4 = 74/4
x = 18.5
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Which equation could result from
performing the distributive property
to
8.53 – 2 (2x + 8) =?
-
A
О
4.52 + 16 = 11.5
B
O
4.5x + 27 = -9
С
O
4.5x - 16 = 11
D
-4.52 +27 = 45
C
1) The distributive property allows us to rewrite some product in factors.
2) Let's then examine that equation:
[tex]\begin{gathered} 8.5x-2(2x+8)=\text{?} \\ 8.5x-4x-16= \\ 4.5x-16 \end{gathered}[/tex]3) Then examining the options, the only option that displays the correct application of the Distributive Property on the left side is: C
How many ounces of a 5% alcohol solution must be mixed with 17 ounces of a 10% alcohol solution to make a 6% alcohol solution?
Let x be number or ounces of a 5% alcohol solution, then:
[tex]x(0.05)+17(0.10)=(x+17)(0.06)[/tex]Solving the above equation for x, we get:
[tex]\begin{gathered} 0.05x+1.7=0.06x+1.02 \\ 0.01x=1.7-1.02 \\ 0.01x=0.68 \\ x=68 \end{gathered}[/tex]Therefore, you must add 68 ounces of the 5% alcohol solution.
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ≤ x ≤ 9.
The average rate of change is given by the rate of change of both variables.
"Rate" refers to a division. We want to divide the change of y, Δy, by the change of x, Δx:
Δy/Δx
("Δ" means "change").
We want to analyze the change over the interval 3 ≤ x ≤ 9.
Step 1: change of x (Δx)The change from x = 3 and x = 9 is
Δx = 9 - 3 = 6
Step 2: change of y (Δy)We observe the right column of the table. When x = 3, y = 28 and when x = 9, y = 4.
The change from y = 28 to y = 4 is
Δy = 4 - 28 = -24
Step 3: rate of changeThen, the average rate of change is:
Δy/Δx = -24/6 = -4
Answer: -4
[tex] log_{2 }(x - 6) + log_{2}(x - 4) = log_{2}(x) [/tex]x=8,3x=8No solution
Answer:
x=8,3
Explanation:
Given the expression:
[tex]\log _2\mleft(x-6\mright)+log_2\mleft(x-4\mright)=log_2\mleft(x\mright)[/tex]Applying the addition law of logarithm:
[tex]\log _2(x-6)(x-4)=log_2x[/tex]Next, cancel the logarithm operator on both sides:
[tex]\begin{gathered} (x-6)(x-4)=x \\ x^2-4x-6x+24=x \\ x^2-10x-x+24=0 \\ x^2-11x+24=0 \end{gathered}[/tex]We solve the resulting quadratic equation:
[tex]\begin{gathered} x^2-8x-3x+24=0 \\ x(x-8)-3(x-8)=0 \\ (x-3)(x-8)=0 \\ x-3=0\text{ or }x-8=0 \\ x=3\text{ or }x=8 \end{gathered}[/tex]The value of x is 3 or 8.
A crowbar 28 in. Long is pivoted 6 in. From the end. What force must be applied at the end in order to lift a 400-lb object at the short end?
What you are trying to do is balance the “moments" about the fulcrum (pivot).
We will calculate moment at the pivot (M1) due to weight (W):
• L1 = length of the bar = 6in
[tex]M1=W\times L1=400\cdot6=2400in\cdot lb_f[/tex]The moment (M2) at the pivot due to your applied force (Fa) on the other end of the bar must equal M1.
• LT = total lenght = 28in
,• L2 = LT - L1 = 28 - 6 = 22in
,• M2 = M1 = 2400in lbf
[tex]\begin{gathered} M2=Fa\times L2 \\ Fa=\frac{M2}{L2}=\frac{2400inlb_f}{22in}=109.09lb_f \end{gathered}[/tex]Answer: 109.09lbf
A force of 109.091 pounds would have to be applied to move the load.
what is the area of the following Circle R equals 7
Answer: Area is 153.94
Step-by-step explanation:
Area = π r 2
√64= A. 16 B. 8 C. 7 D. 9
Answer:
B. 8
Explanation:
[tex]64=8\times8[/tex]We can write this in index form as:
[tex]64=8^2[/tex]Therefore:
[tex]\sqrt[]{64}=\sqrt[]{8^2}[/tex]On the right-hand side, the square root sign cancels the square, so we have:
[tex]\sqrt[]{64}=8[/tex]The correct choice is B.
Approximate the measure in degrees of angle in a right triangle given that the side adjacent to angle is 5 and the hypotenuse of the triangle is 9 units. (Round your answer to one decimal place.)
Measure of perpendicular side for the given right triangle with adjacent side 5units and hypotenuse 9 unit is equal to 7.5 units(Upto one decimal place).
As given in the question,
In a right triangle,
Measure of a adjacent side = 5units
Measure of a hypotenuse = 9units
Let x be the measure of the perpendicular side
Using Pythagoras theorem we get,
(Hypotenuse)² = (Adjacent side)² +(perpendicular side)²
⇒ (9)² = (5)² + (x)²
⇒ (x)² = (9)² - (5)²
⇒x² = 81 -25
⇒ x = √56
⇒ x= 7.4833..
⇒x = 7.5 units(round upto one decimal)
Therefore, measure of perpendicular side for the given right triangle with adjacent side 5units and hypotenuse 9 unit is equal to 7.5 units(Upto one decimal place).
The complete question is :
Approximate the measure in degrees of angle in a right triangle given that the side adjacent to angle is 5 and the hypotenuse of the triangle is 9 units. Find the measure of perpendicular side.(Round your answer to one decimal place.)
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Please help me step by step
Answer:
f(0) = -1
Step-by-step explanation:
to find this out we must first plug in 0 to the equation
f(0) = -0^2 + 4(0) - 1
now solve it
f(0) = 0 + 0 - 1
f(0)= - 1
that is your answer
recommend using graph paper bcuz u can see ur answer that way w/o solving :)
Which point is on the circle centered at the origin with a radius of 5 units?Distance formula: Vx2 - xy)2 + (V2 - y2)?(2, 721)(2, 23)(2, 1)O (2,3)
To know if the point is on the circle, we mus calculate the distance between the point and the origin.
For the first option, we have:
- (2, √21)
and the origin
- (0, 0)
Then, we must replace the two points in the distance formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(0-2)^2+(0-\sqrt[]{21})^2} \\ d=\sqrt[]{4+21}=\sqrt[]{25}=5 \end{gathered}[/tex]Knowing that the distancie is 5 we can affirm that the point is on the circle because the radius is 5.
Finally, the answer is
[tex](2,\text{ }\sqrt[]{21})[/tex]Watch help videoA group of friends wants to go to the amusement park. They have no more than $305to spend on parking and admission. Parking is $19, and tickets cost $26 per person,including tax. Write and solve an inequality which can be used to determine p, thenumber of people who can go to the amusement park.<
p = number of people who can go to amusement park
Amount they want to spend is no more than $305. This means there expenses will be less than or equals to $305.
parking = $19
cost per person = $26
Therefore,
[tex]19+26p\leq305[/tex][tex]\begin{gathered} 26p\leq305-19 \\ 26p\leq286 \\ p\leq\frac{286}{26} \\ p\leq11 \end{gathered}[/tex]Which of the following polygons has reflective symmetry but not rotational symmetry?
a) square
b) regular decagon
c) kite
d) equilateral triangle
A kite has reflective symmetry but not rotational symmetry.
Define symmetry.In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more exact meaning of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.
Given,
A kite has reflective symmetry but not rotational symmetry.
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what is the the measure of each base angle of an isosceles triangle if it’s vertex angle measure is 44°?
An isoceles triangle has one vertex angle and two congruent base angles, that is,
how do I write down the values of each letters without measuring it?
Given the graph of parallel lines and a transversal
There is an angle = 90
This means the transversal is perpendicular to the parallel lines
So, All the angles are right angles
So, the measure of all angles = 90
So,
[tex]\begin{gathered} m\angle g=90\degree \\ m\angle h=90\degree \\ m\angle i=90\degree \end{gathered}[/tex]2. (02.01 LC)While researching the industry she is interested in, Charlize sees that the average employment rate is 97.3%. How many people, out of every 250, are employed? (1point)24.33O 234.66Ο Ο243.25O 256.93
EXPLANATION
We can compute the average by multiplying the average by 0.973, as shown follows:
[tex]\text{Amount of people}=250\cdot0.973=243.25[/tex]In conclusion, the amount of people is equal to 243.25
I have to find cars a speed in miles per hour
The graph in the picture shows the relationship between the distance traveled (y-axis) and the time (x-axis) that car A traveled.
The slope of the line represents the speed at which the car traveled. To determine the said speed you have to calculate the slope of the line.
-The first step is to determine two points of the line:
(x₁,y₁) → (2,80)
(x₂,y₂) → (0,30)
-The second step is to calculate the slope using the following formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]Where
(x₁,y₁) represent the coordinates of one point of the line
(x₂,y₂) represents the coordinates of a second point of the line
Replace the formula with the coordinates of the points and calculate the slope:
[tex]\begin{gathered} m=\frac{(80-30)mi}{(2-0)hr} \\ m=\frac{50mi}{2hr} \\ m=25\frac{mi}{hr} \end{gathered}[/tex]The slope of the line, which represents the speed of the car, is 25 miles per hour
which number is divisible by "644532"
Answer:
2
Step-by-step explanation: 2 can be divided by 644532
1/10+1/2=____ options 3/5
we are given the sum of the following fractions:
[tex]\frac{1}{10}+\frac{1}{2}[/tex]To sum these fractions we may multiply the numerator and denominator of the second fraction by 5, like this:
[tex]\frac{1}{10}+\frac{5}{10}[/tex]Since now they have the same denominator we can add the numerators and leave the same denominator, like this:
[tex]\frac{1}{10}+\frac{5}{10}=\frac{1+5}{10}=\frac{6}{10}[/tex]Now we can simplify the resulting fraction by dividing the numerator and denominator by 2:
[tex]\frac{6}{10}=\frac{3}{5}[/tex]Therefore, the sum of the two fractions is 3/5
The point (2, 4) is reflected over the x-axis. What are its new coordinates?Use the blank grid below it it helps.-6-54-321-6ch-4-3-2.-1O3N56-1-2-3--4--5-6O (2,-4)O (-2,-4)O (4,2)O (-2,4)
Let:
[tex]\begin{gathered} A=(x1,y1)=(2,4) \\ A^{\prime}=(x1^{\prime},y1^{\prime}) \end{gathered}[/tex]After a reflection over the x-axis:
[tex]A\to(x,-y)\to A^{\prime}=(2,-4)[/tex]Answer:
(2,-4)
8. A certain virus infects one in every 700 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (a) Find the probability that a person has the virus given that they have tested positive. (b) Find the probability that a person does not have the virus given that they have tested negative.
Part a
Find the probability that a person has the virus given that they have tested positive
Probability in fraction form
p=(1/700)*(90/100)=90/70,000
simplify
P=9/7,000Part b
Find the probability that a person does not have the virus given that they have tested negative
Probability in fraction form
P=(699/700)*(10/100)
P=6,990/70,000
simplify
P=699/7,000A hairdresser is considering ordering a certain shampoo. Company A charges $5 per 8 ounce bottle plus a $5 handling fee per order. Company B charges $2 per 8 ounce bottle plus a $23 handling fee per order. How many bottles must the hairdresser buy to justify using Company B?
For the shampoo:
Company A charges $5 per ounce bottle + $5 handling fee.
Company B charges $2 per ounce bottle + $23 handling fee.
Let C represent the total cost for the shampoo and x represent the number of bottles of shampoo then you can express the total cost for both companies as equations:
[tex]\begin{gathered} C_A=5x+5 \\ C_B=8x+23 \end{gathered}[/tex]For the hairdresser to justify using the shampoo of company C, the cost must be less than for company A, so that:
[tex]\begin{gathered} C_BNow