The solution of the given equation is -6 and 1.
What is Quadratic Equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Here, given equation:
(x+2)(x+3) = 12
x(x+3)+2(x+3) = 12
x² + 3x + 2x + 6 = 12
x² + 5x + 6 - 12 = 0
x² + 5x - 6 = 0
x² + 6x - x - 6 = 0
x(x+6) -1(x+6) = 0
(x+6)(x-1) = 0
Now, x + 6 = 0 or x - 1 = 0
x = -6 or x = 1
Thus, the solution of the given equation is -6 and 1.
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which of the following sets are discrete?!? check all that apply.
which of the following sets are discrete?
Answer: C. {2,4,6,8}
Step-by-step explanation:
because constituting a separate entity : individually distinct several discrete sections. 2a : consisting of distinct or unconnected elements : noncontinuous. b : taking on or having a finite or countably infinite number of values discrete probabilities a discrete random variable.
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.
The quotient of (x⁴+ 5x³ 3x - 15) and (x³ - 3) is a polynomial. What is the quotient?
a.x⁷+5x⁶-30x³9x+45
b.x-5
c.x+5
d x⁷+5x⁶+6x⁴+30x³+9x+45
Answer:
x+5 (under assumption you meant to do -3x
Step-by-step explanation:
you can use long division.
Take the leading coefficient x^4 and divide it by x^3. This results in x which is going to be the first part of you quotient. Now take that x and multiply it by the divisor (x^3 - 3). This gives you x(x^3 - 3) = x^4 - 3x. Now subtract that x^4 - 3x from the original polynomial and repeat this until you can't divide anymore
[tex]x^4+5x^3-3x-15 - (x^4-3x) = 5x^3-15\\x^3/5x^3=5\\5(x^3-3) = 5x^3-15\\5x^3-15-(5x^3-15) = 0\\\\x+5[/tex]
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.
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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como faltar a la escuela
Answer:
Como faltar a la escuela. Por favor, ¿cuál es el significado?
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.
Which is equivalent to
64 ^1/4?
O 24/4
O4
O 16
O 16/4
Answer: [tex]\sqrt[4]{64}[/tex]
Step-by-step explanation:
[tex]64^{\frac{1}{4} }= \sqrt[4]{64}[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′. The coordinates of point M are (2, 4), and the coordinates of point N are (3, 5).
The slope of is
The coordinates of point N are (3, 5).2 the answer is 2/1 but just write 2.
We have given that,
Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′.
What is the coordinate?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
The coordinates of point M are (2, 4), and the coordinates of point N are (3, 5)
Therefore we get,
2 the answer is 2/1 but just write 2.
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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.
Hope that helps!
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If the unit rate is 30 miles per hour, then how much miles is traveled in 9 hours?
Find the value of k for which the point (3k,k) lies on the line y = 3x +8.
Step-by-step explanation:
please mark me as brainlest
Please help me I am stuck
The width of a certain rectangle is 2 m greater than half its length. Four times its length is 26 m greater than its perimeter. What are the dimensions of the rectangle?
Answer:
Length = 30
Width = 17
Step-by-step explanation:
Let L = length of rectangle and W = Width
The first sentence gives the equation
W = L/2 + 2 ==>
2W = L +4 ==>
L = 2W - 4 .... (1)
The perimeter of the rectangle is 2(L+W) = 2L +2W
Second sentence gives us the equation
4L = 2L + 2W + 26 ===>
2L = 2W + 26 ...... (2)
(2) - (1) ==> L = 30 (2W cancels out)
From (1), W = 30/2 + 2 = 15 + 2 = 17
Check:
Using these values and substituting in equation 2 gives us
2 * 30 = 2* 17 + 26
60 = 34 + 26
which matches
(x+2)^2-3 evaluate and simplify the equation
Answer:
[tex](x^{2} +2)-3\\x^{2} +2-3\\x^{2} -1\\(x+1)(x-1)[/tex]
Answer:
x^2+4x+1
Step-by-step explanation:
(x+2)^2-3
(x+2)(x+2)-3
x^2+2x+2x+4-3
x^2+4x+4-3
x^2+4x+1
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
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
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
D
Step-by-step explanation:
definitely
Mark ran a mean distance of 13.2 km in five days. The next day, Mark ran 20 km.
Find the mean distance Mark ran in the six days.
Answer:
14.3 km (1 d.p.)
Step-by-step explanation:
To find the mean, divide the sum of all data values by the total number of data values.
If Mark ran a mean distance of 13.2 km in five days, we can use the mean distance for each of the 5 days in our calculation.
[tex]\begin{aligned}\implies \sf mean\:distance & = \sf \dfrac{13.2+13.2+13.2+13.2+13.2+20}{6}\\ & \sf =\dfrac{86}{6}\\\\ & = \sf 14.3\:km\:\:(1\:d.p.)\end{aligned}[/tex]
1 Select the correct answer from the drop-down menu. sinr O tant = cost. Therefore, tan(90-A) = COST. 1/tan(90-A) 1/sin A 1/cos(90 - A) 1/tan A . (All angle measurements are in degrees.) Reset Next 1 Select the correct answer from the drop - down menu . sinr O tant = cost . Therefore , tan ( 90 - A ) = COST . 1 / tan ( 90 - A ) 1 / sin A 1 / cos ( 90 - A ) 1 / tan A . ( All angle measurements are in degrees . )
[tex]\tan(90^{\circ}-A)\\ \\ =\frac{\sin(90^{\circ}-A)}{\cos(90^{\circ}-A)}\\ \\ =\frac{\cos A}{\sin A}\\\\=\boxed{\frac{1}{\tan A}}[/tex]
use your calc to work this out
Complete the table by converting from a fraction, a decimal, or a percent.
The value obtained by doing the operation are ,a=0.11,b=11,c=(111/250)d=44,e=(1/8),f=(83/500),h=0.375,i=37.5%,j=(111/125),k=0.888,i=(777/1000),m=77%,n=0.2,o=20%,p=(777/1000),q=66.6%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The procedure of changing the basis of a number is known as number conversion. A binary number is made up of only two numbers: 1 and 0. A decimal number is made up of ten digits ranging from 0 to 9.
The values obtained from the table the decimal and the percentage form are solved as;
[tex]\frac{1}{9} \\\\ 0.3111 \\\\\ 0.1111 \times 100 \\\\ 11.11 \%[/tex]
The other missing values are;
a=0.11
b=11
c=(111/250)
d=44
e=(1/8)
f=(83/500)
h=0.375
i=37.5%
j=(111/125)
k=0.888
i=(777/1000)
m=77%
n=0.2
o=20%
p=(777/1000)
q=66.6%
Hence all the missing values are given above.
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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
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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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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the answer choices is A. x B. z C. w D.y pls help me, I greatly appreciate all the help I'm getting
The graphed that represents the new function with the same slope and y-intercept is: graph Y.
What is the Slope and Y-intercept of a Function?Slope = rise/run along a line.
Y-intercept is the y-value of the point on the y-axis that the line intercepts.
Slope of the function given = rise/run = 2/1 = 2
2 multiplied by 1/2 = 2/2 = 1.
Y-intercept of the given function is: 1
1 increased by 3 units is: 1 + 3 = 4
The slope of graph Y = rise/run = 2/2/ = 1
The y-intercept is also 4
Therefore, the answer is: Graph Y
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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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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
Its about creating and Solving Linear Equations by writing linear equations from geometric figures please help
1. The value of x is 40
m ∠2x + 10 = 90
m ∠3x = 120
m ∠2x +5 = 85
m ∠2x -15 = 65
2. The value of x is 15
m ∠5x = 75
Calculating anglesFrom the question, we are to determine the value of x and the given angles
Since sum of angles is 360°
3x + 2x + 10 + 2x + 5 + 2x -15 = 360°
Collect like terms
3x + 2x + 2x + 2x = 360° - 10° - 5° + 15°
9x = 360
x = 360 / 9
x = 40
∴ x = 40
Then,
m ∠2x + 10 = 2(40) + 10
m ∠2x + 10 = 80 + 10
m ∠2x + 10 = 90
m ∠3x = 3(40)
m ∠3x = 120
m ∠2x +5 = 2(40) + 5
m ∠2x +5 = 80 + 5
m ∠2x +5 = 85
m ∠2x -15 = 2(40) - 15
m ∠2x -15 = 80 - 15
m ∠2x -15 = 65
Hence, the measure of angle 2x-15 is 65
2.
Since sum of angles is 180°
Then,
5x° + x° + 90° = 180°
6x° = 180° - 90°
6x° = 90°
x = 90/6
x = 15
m ∠5x = 5(15)
m ∠5x = 75
Hence, the measure of angle 5x is 75
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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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