Answer:
y = -0.5x - 3.5
Explanation:
Take two points: (1, -4), (3, -5)
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{-5-(-4)}{3-1} = -\dfrac{1}{2}[/tex]
Equation:
[tex]\sf y- y_1 = m (x - x_1)[/tex]
[tex]\rightarrow \sf y- (-4) = -\dfrac{1}{2} (x -1)[/tex]
[tex]\rightarrow \sf y+ 4 = -\dfrac{1}{2} x + \dfrac{1}{2}[/tex]
[tex]\rightarrow \sf y = -\dfrac{1}{2} x + \dfrac{1}{2} - 4[/tex]
[tex]\rightarrow \sf y = -0.5 x -3.5[/tex]
The formula of a line is:
[tex]f(x) = kx + b[/tex]
k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.
We can see 2 points:
A (1, -4)
B (3, -5)
We can make a system of equations:
[tex]k*1+b=-4\\k*3+b=-5\\[/tex]
From second equation:
[tex]b = -5 - 3k[/tex]
Let's put b in first equation:
[tex]k-5-3k=-4\\-2k=1\\k=- \frac{1}{2}[/tex]
Now we can find b:
[tex]b = -5 -3*- \frac{1}{2}\\b = -5 + 1.5\\b = -3.5[/tex]
The answer is:
-0.5x -3.5
Find the value of x.
5
X
11
y
The value of the variable is 4√5. Then the correct option is C.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The similar triangles are shown in the diagram.
16 / x = x / 5
x² = 16 × 5
x = 4 √5
Then the value of the variable is 4√5.
Then the correct option is C.
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The second number in an ordered pair that represents the position of a point relative to the vertical axis is called ______________.
It is called the y-coordinate
The point itself is called a coordinate, vertically, the vertical component of the coordinate is called the y-coordinate, while horizontally, the horizontal component of the coordinate is called the x-coordinate.
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please help this is so confusing
Answer:
f(x)=f(6)= 6^2 - 2*6=36-12= 24
Step-by-step explanation:
This is a function, so we replace x with 6. When we do this, we use it to replace x in the above equation, so instead of having x^2-2x, we have 6^2 -2x. Then we just solve the equation, leaving us with the final solution of 24.
Let f(x)=4x and g(x)=4x+1−2. Which transformations are needed to transform the graph of f(x) to the graph of g(x)? Use the drop-down menus to complete the statements.
horizontal transformation 1 unit left.
vertical translation 2 units down.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given:
f(x) = [tex]4^{x}[/tex]
g(x) = [tex]4^{x+1} -2[/tex]
As, we can see that g(x) is shifted left side by 1 unit
So, horizontal transformation 1 unit left.
Now, as 2 is subtracted
So, vertical translation 2 units down.
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Triangle ABC is a right triangle with CD | AB. Angle C is a right angle.
(BC)²+(AC)² = (AB)(BD + AD). Using
gives Blank space for answering Question.
(BC)²+(AC)=(AB) (AB), which simplifies to (BC)2 + (AC)2 = (AB)2
Possible answers
CPCTC
Side-Angle-Side Similarity Postulate
congruent
Side-Side-Side Similarity Postulate
segment addition postulate
proportional
First blank: Side-Angle-Side similarity postulate
Second blank: proportional
use your calc to work this out
What is 5 + 10^5 or what is 5 + 10 to the 5th power?
Answer:
5 + 10^5 = 100005 (I think its this one you are looking for
(5 + 10)^5 = 759275
Step-by-step explanation:
Answer:
100,005
Step-by-step explanation:
Original: 10 * 1 = 10
First, you need to do 10 * 10 which = 100.
Next, you need to do 100 * 10 which = 1,000.
Next, you need to do 1000 * 10 which = 10,000.
Next, you need to do 10000 * 100 which = 100,000.
Lastly, you need to add 5 to 100,000 and you get 100,005.
I Hope This Helped :D
For 1-3, consider an investment of $6000
that earns 4.5% interest. Use a graphing
calculator if needed.
1. Write an equation to describe the value
V(t) of the investment at time t if the
interest is compounded daily.
Answer:
See below
Step-by-step explanation:
Period = 1 day
Periodic interest = .045 / 365 (since there are 365 days in a year)
V(t) = 6000 * ( 1 + .045/365)^t where t is in days
V(t) = 6000 * (1+.045/365)^(t * 365) where t is in years
If the unit rate is 30 miles per hour, then how much miles is traveled in 9 hours?
I'm having a hard time doing inequalities, and I really need help with this question. Any help will be appreciated.
Thanks
The solution to the given compound inequality 2x - 3 < x + 2 ≤ 3x + 5 is 5 > x ≥ -3/2
Compound inequality2x - 3 < x + 2 ≤ 3x + 5
solve differently
2x - 3 < x + 2
2x - x < 2 + 3
x < 5
x + 2 ≤ 3x + 5
x - 3x ≤ 5 - 2
-2x ≤ 3
x ≥ 3/-2
x ≥ -3/2
Therefore, the solution of the compound inequality is 5 > x ≥ -3/2
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Find the value of cos N rounded to the nearest hundredth, if necessary.
cos N = 14/20 = 0.70
como faltar a la escuela
Answer:
Como faltar a la escuela. Por favor, ¿cuál es el significado?
Please please help! translate the phrase into a variable expression. use the letter p to name the variable. if necessary, use the asterisk (*) for multiplication and the slash (/) for division
... the total number of parrots in the jungle and the 2 parrots your neighbor owns ...
The expression p+2 will denote the statement given
What is a Variable ?A variable is a unknown quantity in an equation , which is used to denote the parameter that needs to be determined.
It is given that
the total number of parrots in the jungle and the 2 parrots your neighbor owns
Let p be the total parrots in the jungle
p+2 will denote the statement given
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An unknown number b is 10 more than an unknown number k. The number b is also k less than 8. The equations to find k and b are shown below.
b=k+10
b=-k+8
Which is a correct step to find k and b?
O Write the points where the graphs of the equations intersect the x-axis.
O Write the points where the graphs of the equations intersect the y-axis.
O Add the equations to eliminate k.
O Multiply the equations to eliminate b.
Answer: Add the equations to eliminate k
Step-by-step explanation:
Adding the equations, you get 2b=18, which you can solve for b. Afterward, you can substitute this value of b back into either equation to solve for k.
To solve the equation ‐2x + 5 = 9 for x, what operations must be performed on both sides of the equation in order to isolate the variable x?
Answer:
b.) Subtracting 5 then dividing both sides by -2
Step-by-step explanation:
Given expression:
⇒ -2x + 5 = 9
To solve this equation, first we need to remove the 5 on the left side. Then divide both sides by -2.
When done so:
⇒ -2x = 9 - 5
⇒ -2x = 4
⇒ -2x/-2 = 4/-2
⇒ x = -2
Plot the foci of the hyperbola represented by the equation x^2/625 − y^2/3600 =1 100pts
The attached image represents the foci of the hyperbola
How to determine the foci?The equation of the hyperbola is given as:
[tex]\frac{x^2}{625} - \frac{y^2}{3600} = 1[/tex]
Rewrite as:
[tex]\frac{x^2}{25^2} - \frac{y^2}{60^2} = 1[/tex]
A hyperbola is represented as:
[tex]\frac{(x - h)^2}{b^2} - \frac{(y - k)^2}{a^2} = 1[/tex]
This means that:
h = 0
k = 0
b = 25
a = 60
Next, calculate c the distance from the center to the focus using:
[tex]c = \sqrt{a^2 -b^2}[/tex]
This gives
[tex]c = \sqrt{60^2 -25^2}[/tex]
Evaluate
[tex]c = \pm \sqrt{2975}[/tex]
This means that:
Foci = (0, -√2975) and (0, √2975)
See attachment for the hyperbola and the foci
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An unknown number b is 10 more than an unknown number k. The number b is also k less than 8. The equations to find k and b are shown below
b=k+10
b=-k+8
Which is a correct step to find k and b?
O Write the points where the graphs of the equations intersect the x-axis.
O Write the points where the graphs of the equations intersect the y-axis.
O Add the equations to eliminate k
O Multiply the equations to eliminate b.
Answer: Add the equations to eliminate k
Step-by-step explanation:
Adding the equations together, we get 2b=18.
Simplify 4^3/4^8 so that it is not in fraction form.
Answer:
[tex]4^{-5}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{4^{3} }{4^{8} }[/tex] = [tex]4^{(3-8)}[/tex] = [tex]4^{-5}[/tex]
I need this answer . I would be happy if I got it .
Answer:
15cm
Step-by-step explanation:
PC = 15
BR = 15
.
............................................
What are the zeros of f(x) = (x-7)(x - 3)(x - 2)?
07, -3, 2
07, -3, -2
07, 3, 2
07, 3, -2
Answer:
7, 3, 2
Step-by-step explanation:
Answer:
Option C,
07, 3, 2
Step-by-step explanation:
Set all zeros to 0
(x-7)=0
x= 7
(x-3)=0
x= 3
(x-2)=0
x= 2
7, 3, 2
A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters
The area of the swimming pool on the scale drawing will be 300 sq. centimeters.
What is the scale ratio?A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.
For the given scale drawing 1 centimeter represents 2 meters, therefore, the length of 40 meters in one scale drawing will be equal to,
40 meters = 40/2 centimeters = 20 centimeters
The width of 30 meters one scale drawing will be equal to,
30 meters = 30/2 centimeters = 15 centimeters
Now, the area of the swimming pool on the scale drawing will be,
Area= 20 centimeters × 15 centimeters = 300 sq. centimeters
Hence, the area of the swimming pool on the scale drawing will be 300 sq. centimeters.
The complete question is:
A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters. then what is the area of the swimming pool on the scale drawing?
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Select the two binomials that are factors of 49x^2 - 36
A. 7x + 12
B. 7x - 3
C. 7x + 6
D. 7x - 6
By definition of the subtraction of squares, the binomial 49 · x² - 36 have the following two factors: 7 · x + 6, 7 · x - 6 (Correct choices: C, D)
How to find the factors of subtraction of squares
A subtraction of squares is a binomial which satisfies the following property:
a² - b² = (a - b) · (a + b) (1)
If we know that a² = 49 · x² and b² = 36, then we have the following factors:
49 · x² - 36 = (7 · x - 6) · (7 · x + 6)
By definition of the subtraction of squares, the binomial 49 · x² - 36 have the following two factors: 7 · x + 6, 7 · x - 6 (Correct choices: C, D)
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please help mee, sketch the graph please (50 points will give brainliest!!!)
Values are given below as pairs (x,y) where x coordinate is x values in box and y coordinate is y values on box
(-5,9)(-4,4)(-2,0)(0,4)(1,9)Graph attached
what is the answer for this question much appreciated if you attempt to help me
Answer:
The surface area of the triangular prism is [tex]624cm^{2}[/tex]
Step-by-step explanation:
First find the area of the triangle.
The formula of the area of triangle is: [tex]\frac{1}{2} * h*b[/tex]
h=height
b=base or width.
[tex]\frac{1}{2}*16*12[/tex]
But, since we have two triangles we can skip the [tex]\frac{1}{2}[/tex] because [tex]2*\frac{1}{2} =1[/tex].
[tex]16*12=192[/tex], that is the area of the two triangles combined.
Now let's find the area of the rectangles. I'll start with the diagonal one.
The formula of the area of the rectangle is: [tex]h*b[/tex].
[tex]20*9=180[/tex].
The next rectangle.
[tex]9*16=144[/tex]
The final rectangle.
[tex]12*9=108[/tex]
Now combine all the areas to find the surface area of the triangular prism.
[tex]192+180+144+108=624[/tex]
The surface area of the triangular prism is [tex]624cm^{2}[/tex]
Hope this helps!
If not, I am sorry.
help me please number 8
Answer:
13
Step-by-step explanation:
square root of 12^2 + 5^2
Triangle ABC has vertices at A(1,2), B(4,0) and C(1,-4) Find the area of triangle ABC.
PLEASE EXPLAIN HOW YOU DID IT
The area of triangle ABC from the given vertices is gotten as; 7.5
How to find the area of a triangle?We are given the vertices of the triangle as;
A(1, 2)
B(4, 0)
C(1,-4)
The formula for area of a triangle with 3 vertices is;
Area = ¹/₂[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]
Thus;
Area = ¹/₂[1(0 + 4) + 4(-4 - 1) + 1(1 - 0)]
Area = ¹/₂(4 - 20 + 1)
Area = -7.5
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which function has a domain
Answer:
F(x) = - [tex]\sqrt[3]{x}[/tex]
Step-by-step explanation:
A square root can only have a positive input for the domain
(The domain is the input for the function)
The cube root can be either negative or positive as an input
F(x) = - [tex]\sqrt[3]{x}[/tex] can have inputs from negative infinity to infinity
help me solve this give steps as well please
The total cost of 6 wave pool tickets with the discount included would be $73.5.
How to calculate the total value of 6 tickets with the discount?To calculate the total cost we must multiply the value of each ticket by the number of tickets to be purchased, in this case there are 6:
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help me nowwwwwwwwww
The angle measurements the carpenter needs to cut the carpet to make it fit in his room are 144°, 144°, 144°, 144°, 144°, 90°, and 90°
Angles in a polygonFrom the question, we are to determine the angle measurements that the carpenter needs to cut the carpet to make it fit in his room
The diagram shows a heptagon with two of its angles, a right-angle each, and the remaining angles have equal values, x.
First, we will calculate the sum of angles in a heptagon
The sum of angles in a polygon is given by the formula
Sum of angles in a polygon = (n-2)180°
Where n is the number of sides
For a heptagon, n = 7
∴ Sum of angles in a heptagon = (7-2)180°
= 5×180°
= 900°
Now, considering the given diagram, we can write that
x + x + x + x + x + 90° + 90° = 900°
5x + 180° = 900°
5x = 900° - 180°
5x = 720°
x = 720°/5
x = 144°
Hence, the angle measurements the carpenter needs to cut the carpet to make it fit in his room are 144°, 144°, 144°, 144°, 144°, 90°, and 90°
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Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
D
Step-by-step explanation:
definitely