The distance between line y= -x-3 and the point (2,5) is 5√2units.
The distance(d) between the line ax+by+c=0 and point (x₁,y₁) is calculated using the formula
d= |ax₁+by₁+c|/√a²+b² , where a and b are the coefficients of x and y .
In the question ,
the equation of the line ℓ is given by y = -x-3
rewriting the equation in standard form x+y+3=0
So the distance between the line x+y+3 and the point (2,5) can be calculated by substituting the values in the formula, we get
d=|1(2)+1(5)+3|/√1²+1²
= |2+5+3|/√2
= 10/√2
Simplifying further , we get
= 5√2
Therefore , the distance between line y= -x-3 and the point (2,5) is 5√2 units.
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help a sister out with a polynomial and quadratic functions question
Answer:
when you multiply the exponents, you add the numbers
so it'll now be y^5
Find the value of x.
[tex]8x + 6 + 118 = 180 \\ 8x + 124 = 180 \\ 8x = 180 - 124 \\ 8x = 56 \\ \frac{8x}{8} = \frac{56}{8} \\ x = 7[/tex]
NOTE THAT DUE TO LACK OF LABELLING OF ANGLES IN THE DIAGRAM I COULDN'T GIVE YOU BRIEF EXPLANATION BUT I HOPE YOU UNDERSTAND.
I opened a grocery account at my bank with $150. Every week thereafter, I withdraw $55 from the account to pay for groceries.
If x is the number of weeks I've had the account, then y is the amount in the account.
Find an equation of a line in the form y = mx + b that describes my grocery account balance.
y=
If he opened a grocery account at my bank with $150 and every week thereafter he withdraw $55 from the account to pay for groceries, then the equation of the line in the form y = mx+b that describes the grocery account balance is y = -55x+150
The balance in the bank account = $150
The amount he withdraw from the account for groceries = $55
Consider the number of week he had the account as x
y is the amount in the account
Then the equation will be
y = 150-55x
Rearrange the term and make the equation in the form y = mx+b
y = -55x+150
Hence, If he opened a grocery account at my bank with $150 and every week thereafter he withdraw $55 from the account to pay for groceries, then the equation of the line in the form y = mx+b that describes the grocery account balance is y = -55x+150
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maths question to purely maths tutor
answer is here
some drawing:
cool
∉343
[tex]\sqrt[422\sin 242]{e}2424\begin{cases}x=24 \\ y=24242f(x)=\begin{cases}4242 \\ 4242 \\ 424224\lim _{n\to\infty}2424244224\end{cases}\end{cases}[/tex]Answer: Need a math question
Step-by-step explanation: x3+y3+z3= ?
A linear function passes through the points (-3.14) and (2,-1). What is the rate of change of the function?
Responses
-13
−17/3
-3
−3/17
The rate of change of the linear function is the third option that is -3.
It is given in the question that the linear function passes through the points (-3,14) and (2,-1).
We have to find the rate of change of the function.
We know that,
The rate of change of a linear function is the slope of the function.
Slope of a line
The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’.
Hence, slope of a line that passes through the points (-3,14) and (2,-1) is
(-1-14)/(2-(-3)) = -15/5 = -3.
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Decide whether perimeter or area should be considered when buying a frame needed around a door.
Step-by-step explanation:
yes its important because we need to know the measurements of the side
In AKLM, the measure of ZM=90°, ML = 55, KM = 48, and LK = 73. What ratiorepresents the cosecant of ZK?
Remember that
csc k=1/sin k
and
sin k=55/73
therefore
csc k=1/(55/73)
csc k=73/55Which pair of complex numbers has a real-number product?
The product of (1 + 3i)(1 – 3i) is a real number.
What is a complex number?Complex Numbers in Math. Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
We know that,
[tex]i^{2} = -1[/tex]
case A) [tex](1+3i)(6i)[/tex]
applying distributive property
[tex]6i+18i^{2}[/tex]
[tex]6i-18[/tex]
This is not a real number.
case B) (1+3i) (2-3i)
applying distributive property
[tex]2-3i+6i-9i^{2}[/tex]
[tex]11+3i[/tex]
This is also not a real number.
case C) [tex](1+3i) (1-3i)[/tex]
applying difference of square
[tex]1-9i^{2}[/tex]
1+9 = 10
This is a real number.
case D) [tex](1+3i) (3i)[/tex]
applying distributive property
[tex]3i+9i^{2}[/tex]
[tex]3i-9[/tex]
This is not a real number.
Hence, The product of (1 + 3i)(1 – 3i) is a real number
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←
At the Olympic Games, a runner won the 26.2-mile marathon race in 2 hr 5min and 4 second. What was his average speed in mph and
km/h?
Answer:
The average speed of the runner is 12.7 mph and 20.4 km/h
Step-by-step explanation:
Value of 0.3(1/4 - 1) + 0.35
The value of the expression is 0.125
Numerical expressions are sets of numbers that undergo mathematical operations with a pre-established order of operations. Numerical expressions are sets of numbers that undergo mathematical operations with a pre-established order of operations.
How to calculate the expression ?The expression is
0.3(1/4 - 1) + 0.350.3(0.25-1) + 0.35
solve by using BODMAS0.3(-0.75) + 0.35= -0.225 + 0.35= 0.125
Hence the value of the expression is 0.125
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Question 1 Describe the error in writing an equation of the line that passes through the point (3, 4) and is parallel to the line y = 2x+1. Responses The x- and y-coordinates are substituted for the wrong variables. The , x, - and , y, -coordinates are substituted for the wrong variables. The y-intercept b should be solved for instead of the slope m. The , y-intercept b should be solved for instead of the slope m, . To find m, standard form must be used instead of slope-intercept form. To find , m, standard form must be used instead of slope-intercept form. Once the new slope is found, the new y-intercept must also be found. Once the new slope is found, the new , y, -intercept must also be found. Question 2 Correct the error. The line y = is parallel to the line y = 2x+1 and passes through the point (3,4).
An error in writing an equation of the line is to use 1 as the y intercept, or to use the negative inverse of the slope which gives you a perpendicular line, not a parallel line
How to write a Line in slope Intercept form?
For a line to be parallel, it means that the line must have the same slope, but a different y-intercept because If it has the same y intercept, it means that it is the same line.
Now, we are told that the line passes through the point (3, 4) and is parallel to the line y = 2x +1. Thus;
The slope; m = 2
The coefficient of the x term, when the equation is solved for y is;
y = mx + c is the standard equation in slope intercept form with c as the y intercept
Plug in the coordinate point to solve for c;
4 = 2(3) + c
c = 4 - 6
c = -2
Thus, we conclude that the parallel line through the given point is gotten as; y = 2x - 2
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At a factory, there are 40 new cars produced every 8 hours. How many cars can be produced in a 40-hour week?
Answer:
200
Step-by-step explanation:
Multiplying by 5, we get 200 cars can be produced in 40 hours.
Choose the four expressions that are equivalent to 6^−2.
Answer:
y=-3/2x+4
Step-by-step explanation:
The expression 6⁻² can be written as -
6⁻² = 1/6²
6⁻² = 1/36
6⁻² = (1/6 x 1/6)
What is an expression? What is equation Modelling?A mathematical expression is a combination of terms separated by mathematical operators. For example : 2x + 3y + 6. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following expression -
6⁻²
We can write the expression 6⁻² in the following possible ways -
6⁻² = 1/6²
6⁻² = 1/36
6⁻² = (1/6 x 1/6)
Therefore, the expression 6⁻² can be written as -
6⁻² = 1/6²
6⁻² = 1/36
6⁻² = (1/6 x 1/6)
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Which inequality correctly compares 118%, 0.34, and 2 1/5?
Answer:
ask your village people fowl
I’m confused on this and don’t know what to do
Answer:29
Step-by-step explanation:
3(3)^3+2(4)-6
3(9)+8-6
27+8-6
27+2
29
Solve the following compound inequality -24 ≤2x-10
-24 ≤ 2x-10
⇒ -24 + 10 < 2x
⇒-14 < 2x
⇒ 2x < 14
⇒ x < 7
What is Inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions unequally. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:The symbol a b indicates that and is smaller than b.When a > b is used, it indicates that and is bigger than b.a is not equivalent to b in any scenario. These relationships are referred to be stringent inequalities since either an or b is strictly bigger or less than the other. Equivalence is not considered.To learn more about Inequality, refer to:
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Create a hand drawn sketch of the quadratic function: h(x)= -2x^2 +5x-8To earn full credit be sure to identify the vertex, the axis of symmetry and all intercepts. Include all work, calculations and steps needed (as described in this lesson) to create the graph.Let your teacher know if you have any questions on how to upload or share your written work.
Hello!
We have the function below:
[tex]h\mleft(x\mright)=-2x^2+5x-8[/tex]The first step is to identify the coefficients a, b and c:
• a = -2
,• b = 5
,• c = -8
Just by analyzing these coefficients, we can say that the concavity of the parabola will be facing downwards because the coefficient a is negative
1st step: using the quadratic formula, we will find the interceptions in the x-axis. Look:[tex]x=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]As we know the coefficients, let's replace them in the formula:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4\cdot(-2)\cdot(-8)}}{2\cdot(-2)} \\ \\ x=\frac{-5\pm\sqrt[]{25^{}-64}}{-4}=\frac{-5\pm\sqrt[]{-39}}{-4}= \end{gathered}[/tex]Obs: as we obtained a negative square root, we can stop this step here. It means that
2nd step: let's identify the maximum point of it:[tex]\begin{gathered} x_V=\frac{-b}{2\cdot a}=\frac{-5}{2\cdot(-2)}=\frac{-5}{-4}=1.25 \\ \\ y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a}=-\frac{5^2-4\cdot(-2)\cdot(-8)}{4\cdot(-2)}=-\frac{-39}{-8}=-4.875 \end{gathered}[/tex]So, the vertex is at the point (x, y) = (1.25, -4.875).
The axis of symmetry is x = 5/4 or also x = 1.25.
Look at the graph below:
Note: if you solve this function when x = 0, you will obtain one interception in the y-axis, look:
[tex]\begin{gathered} h\mleft(x\mright)=-2x^2+5x-8 \\ h\mleft(0\mright)=-2\cdot0^2+5\cdot0-8 \\ h(0)=0+0-8 \\ h(0)=-8 \end{gathered}[/tex]So, the y-intercept is at (x, y) = (0, -8) as you can see at the graph.
Write a general rule for multiplying
help please
All multiplications must also be the same if to add the number over and over again.(if 9* 5 was 45, then 9+9+9+9+9 must also be 45.
Answer: Any number multiplied by zero equals zero. 4x0=0
If the area of a rectangular sign is approximately 4260 ft. and the width is approximately 60 feet what is the height of the sign
Answer:
The height is 71 feet.
Step-by-step explanation:
[tex]60h = 4260[/tex]
[tex]h = 71[/tex]
If the area of a rectangular sign is approximately 4260 square feet and the width of the sign is approximately 60 feet then, the height of the sign is approximately 71 feet.
To find the height of the given rectangular sign, let's put the given values in the formula for finding the area of a rectangle i.e.,
Area of rectangle = Height x Width
4260 = Height x 60
Solve the equation for the area of a rectangle where
Height (H) = Area of rectangle/Width
Height (H) = 4260/60
Height of the sign = 71 feet
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Parallelogram I is a scaled copy of parallelogram H.
What scale factor takes parallelogram H to parallelogram I?
1 ÷ 3 is the scale factor that takes parallelogram H to parallelogram I.
If Parallelogram I is a scaled replica of Parallelogram H, then perhaps the figure in which every length in the initial estimate is multiplied by the exact number.
Scale factor = size of new shape ÷ size of the old shape.
The magnification ratio of a parallelogram I is significantly 3 times that of parallelogram H this ratio could be only assumed when the data is not given.
The polygon will be reduced if the magnification ratio would be between 0 and 1. The picture will be magnified if the zoom ratio is larger than one.
The scale factor refers to the ratio of the old thing's scale to the new object's scale. Although the size of these ratios varies, they are useful.
Use negative magnification to enlarge the picture. Whenever the scale factor is negative, the value diverges from the scale.
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The complete question is -
Parallelogram I is a scaled copy of parallelogram H. What scale factor takes parallelogram H to parallelogram I in the image?
The scaling factor that transforms parallelogram H into parallelogram I is 1/3.
If Parallelogram I is a scaled-down version of Parallelogram H, then it might be the result of multiplying each length in the initial estimate by a precise value.
Scale factor is equal to new shape's size minus old shape's size.
A parallelogram I's magnification ratio is noticeably three times greater than a parallelogram H's. Only in cases where no data is provided may this ratio be assumed.
If the magnification ratio is in the range between 0 and 1, the polygon will be smaller. If the zoom ratio exceeds one, the image will be enlarged. The scale factor is the ratio of the scale of the old thing to the scale of the new thing.These ratios are helpful despite the fact that their sizes differ.
Enlarge the image by applying negative magnification. The value deviates from the scale whenever the scale factor is negative.
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Find domain and range
Write the following inequality in s
19x + y ≤ -11
Write your answer with y first, fo
fractions, and improper fractions
The inequality in slope intercept form is –y≥19x+11
What is slope intercept?
Slope intercept form is defined as the graph of linear equation y=mx+b where m and b as the y-intercept.
What is inequality?
Inequality is an equation that is used to show the non equal comparison of two or more numbers and variables.
Given inequality is 19x+y≤-11
To solve this inequality in y form, we will subtract 19x from both side, we get
y≤-11-19x
Now, we will take minus sign common,
-y≥19x+11
Hence, the required answer.
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Write the expression 12-2 in simplest form
Answer:
Is it 6-1?
Step-by-step explanation:
Answer: 6-1
Step-by-step explanation:
is simplest form
Solve the application involving geometry. If necessary, refer to the geometry formulas listed in the inside back cover of the text.
The measure of one angle is 11 times the measure of another. If the two angles are supplementary, find the measures of the angles.
One angle's measurement is 11 times that of another. if the two angles supplementary one another. The measure of the angles area one is 165° and other angle is 15°.
Given that,
One angle's measurement is 11 times that of another. if the two angles supplementary one another.
We have to determine the angles' measurements.
The word "supplementary" refers to two angles coming together to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles. If two angles complement one another
It has an acute angle on one side and an obtuse angle on the other.
The angles are both right angles.
So, It follows that A + B = 180°.
Angle A is 11 times angle B means
A=11B
We get,
11B+B=180
12B=180
B=180/12
B=15°
Then angle A is
A=11×15
A=165°
Therefore, The measure of the angles area one is 165° and other angle is 15°.
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What is the rule for the pattern 1, 4, 7, 10,...?
A) Add 10
B) Multiply by 4
C) Add 3
D) Subtract 3
Answer:
C
Step-by-step explanation:
1+3=4
4+3=7
7+3=10
Wheras if you try to multiply by 4 it works on the first one, but 4×4=16 not 7. If you add 10 to 1 you get 11, which is not the next number. And if you subtract 1-3=-2, which is on the wrong side of 0.
Identify all extrema of this function: f(x) = 2/(3x-5).
Select one:
A. Max:2.52; Min: 1.23
B. Max:0.19; Min: -2.31;
C. No extrema
D. Max: 3; Min: -2
The correct option C. No extrema, is obtained for the given function.
What is defined as the extrema of the function?The term extremum (plural extrema) refers to a value that is the minimum or maximum among all function values.When a function changes from increasing to decreasing, it reaches its relative maximum as well as relative minimum (relative extrema).The absolute extremum (as well as global extremum) of the a function in a specified interval is the point at which the function's maximum or minimum value is obtained. The interval given is frequently the domain of the function, as well as the absolute extremum is the point that corresponds to the highest or minimum value for the entire function.For the given question;
The function is defined as ;
f(x) = 2/(3x-5)
First differentiate the function with respect to x using division rule.
f'(x) = -6/(3x - 5)²
Now, find the point of contraflexure for x by putting f'(x) equals to zero.
f'(x) = 0
-6/(3x - 5)² = 0
-6 = 0
But, -6 ≠ 0
As, x is getting eliminates, we don't have any point of contraflexure.
Thus,the will be no extrema for the given function.
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Need Help!!
Calculate the length x
Please explain to me on how to calculate this.
Answer: 55 cm
Step-by-step explanation:
a^2 + b^2 = c^2
X^2 + 48^2 = 73^2
X^2 + 2,304 = 5,329
X^2 = 3,025
X = 55
polynomial degree 3 root of multiplicity 2 at x=1 root of multiplicity 1 at x=-2 y-intercept is y =-1.6
By using the definition of a polynomial in product form is described by y = - 0.8 · (x - 1)² · (x + 2)
How to determine a least degree polynomial
According to algebra, polynomials are products of binomials of the form x - r, where r is a root of the polynomial. The product form of polynomials is described by the following formula:
p(x) = a · Π (x - r), for i = {1, 2, 3, n}, where n is the grade of the polynomial and a is the lead coefficient.
If we know that y(0) = - 1.6, r₁ = r₂ = 1 and r₃ = - 2, then the equation of the polynomial is:
- 1.6 = a · (0 - 1)² · (0 + 2)
- 1.6 = a · (- 1)² · 2
- 1.6 = 2 · a
a = - 0.8
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Which of the following IS a function?
A function connects an input to an output. It is analogous to a machine with an input and an output. And the output is somehow related to the input.
Option c is Example for the function.
Is all relation a function?The relationship depicts the connection between INPUT and OUTPUT. A function, on the other hand, is a relation that produces one OUTPUT for each given INPUT. It should be noted that all functions are relations, but not all relations are functions.A function has at least two variables: one for output and one or more for input. An equation expresses the equality of two expressions and can include any number of variables (none, one, or more). A function is frequently expressed as an equation, but not every equation is a function.
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For two events A and B, P(A) = 0.60, P(B) = 0.40, and P(B|A) = 0.60. Find P(A|B).
The value of P(A|B) will be;
⇒ 0.6
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
For the two events A and B;
⇒ P(A) = 0.60
⇒ P(B) = 0.40
And, P(B|A) = 0.60
Now,
Since, We know that;
⇒ P(A∪B) = P(A) + P(B) - P(A∩B)
Substitute all the values, we get;
⇒ P(A∪B) = 0.60 + 0.40 - P(A∩B)
And, P(A∩B) = P(A) P(B)
⇒ P(A∩B) = 0.60 × 0.40
⇒ P(A∩B) = 0.24
Hence,
⇒ P(A∪B) = 0.60 + 0.40 - P(A∩B)
⇒ P(A∪B) = 0.60 + 0.40 - 0.24
⇒ P(A∪B) = 0.76
Since, We know that the formula;
⇒ P(A|B) = P(A∩B) / P(B)
Substitute all the values we get;
⇒ P(A|B) = P(A∩B) / P(B)
⇒ P(A|B) = 0.24 / 0.40
⇒ P(A|B) = 0.6
Therefore,
The value of P(A|B) will be;
⇒ 0.6
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