The roots of the equation 2x² 5x 3 0 are the two values of x that make the equation equal to 0. In this case, the two roots are x = -3 and x = 0.5.
To find the solutions roots of 2x² 5x 3 0:
1. Rearrange the equation to make it equal to 0: 2x² 5x - 3 = 0
2. Use the quadratic equation to solve for x: x = (-b ± √(b² - 4ac)) / 2a
3. Substitute the coefficients of the equation: x = (5 ± √(25 - 4(2)(-3))) / 4
4. Simplify the equation: x = (5 ± √49) / 4
5. Calculate the two solution roots: x = -3 and x = 0.5
The solutions roots of 2x² 5x 3 0 can be found by rearranging the equation to make it equal to 0 and then using the quadratic equation to solve for x. The coefficients of the equation (2, 5, and -3) must be substituted into the equation to calculate the two solutions roots. When this is done, the two solutions roots are x = -3 and x = 0.5. This means that if x is equal to either -3 or 0.5, the equation 2x² 5x 3 0 will equal 0.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
What is a 15 degree angle called?
Answer:Acute Angle
Step-by-step explanation:
What is a 15 degree angle called? Acute Angle – Acute Angle An acute angle is an angle that is more than 0° but less than 90°. Common examples of acute angles include: 15°, 30°, 45°, 60°, etc.
What kind of system is involved when the solution of a system of equation is the intersection of two lines?
The unique solution system is given by the intersection of two lines .
When the line intersects at a point the value of the function becomes zero and also intersecting lines meet at only one point.
Hence this type of system have a unique solution.
The condition of the unique solution is
a1/a2[tex]\neq[/tex]b1/b2
Learn more about intersection,
https://brainly.com/question/4895104
Write the equation in Slope Intercept Form. y+
Pls help me on this
The angle-side connection theorem states that angle E in triangle DEF is equal to angle F.
what is triangle ?Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.
given
The length of every triangle side is proportional to the size of the angles that are directly across from them, according to the angle-side relationship theorem.
Thus,
Angle F = (61 + 58)/180 (sum of triangle)
F = 61 degree angle
Since mE = 61 degrees, F and E are therefore congruent to one another.
It follows that the sides that are perpendicular to each angle will also be parallel to one another.
The angle-side connection theorem states that angle E in triangle DEF is equal to angle F, which also implies that the sides that are opposite one other are congruent.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
Consider this equation
COS (θ)= -3/ -10
if θ is an angle in quadrant II, what is the value of tan(θ)?
A. -√91/10
B. √91/10
C. √91/3
D. -√91/3
Answer:
Option D
Step-by-step explanation:
As per your question, cos θ = 3/10
tanθ = √(sec²θ - 1) = √((1/cos²θ) - 1)
Put the value of cos θ, √(1/(9/100) - 1 = √(100/9 - 1) = ±√91/9 = -√91/3 (tan θ is negative in the third quadrant.)
So, option D is the correct answer.
9x
13x
20x+12
Solve for X
Helpppp
[tex]\it 13x+9x=20x+12 \Rightarrow 22x=20x+12\bigg|_{-20x} \Rightarrow \ 2x=12 \Rightarrow x=6[/tex]
Draw a square with side length 7 cm. Predict the perimeter and the length of the diagonal of the square
0 iq kid hshshisjsjsijsjsjsdj
A circle with a diameter of 32 inches is shown.
circle with diameter of 32 inches
What is the area of the circle using π = 3.14?
3,215.36 in2
803.84 in2
200.96 in2
100.48 in2
Answer:
Option B) 803.84in²
Step-by-step explanation:
We know the formula to find the area of a circle is listed as,
[tex]A = \pi r^{2}[/tex]
But over here the diameter is only given
that means we have to find the radius which is,
[tex]r = \frac{32}{2}[/tex]
[tex]r = 16in[/tex]
Now we can find the area of a circle which is,
[tex]A = 3.14X(16)^{2}[/tex]
[tex]A = 803.84in^{2}[/tex]
Hence , Option B) is the correct answer
Solve for X, Leave in simplest radical form.
When a number under the root sign contains no square factors, it is considered to be a radical in its simplest form. The number y = 2
Solve for y, Leave in simplest radical form ?The expression x = 2
The number y = 2
Trigonometry is the study of the correlations between triangle angles and side lengths.
Sine, cosine, tangent, cosecant, sec, and cotone are the six trigonometric functions.
Suppose the angle is such that
opposite/hypotenuse = sin
neighboring / hypotenuse = cos
tan = opposite or nearby
Tan equals sin and cos.
cosec = 1 / sin
Sec = 1 / Cos
Cot = 1 + Tan
given the data,
Let ABC be the triangle.
The angles inside the triangle ABC are 45°, 45°, and 90°. The triangle ABC is a right-angled triangle.
Now, based on the illustration,
trigonometric relationships
tan θ = x / √2
Now , θ = 45°
In this case, x = 2.
Moreover, using trigonometric relationships,
base2 plus length2 = hypotenuse2
y = √ ( √2 )² + ( √2 )²
y = √4
y = 2
Consequently, x has a value of 2.
The number y = 2
To learn more about radical form refer
brainly.com/question/16139901
#SPJ1
3. 05 polynomial identities and proofs
I have no idea how to do this assignment, since I’m doing home school now I don’t have anyone to help
SOMEONE PLEASE HELP!!
The polynomial identities and proofs are mathematical statements that show that two algebraic expressions are equal. They can be used to simplify equations or to prove certain properties of polynomials.
For example, to prove x^2 + 2x + 1 = (x + 1)^2, you can factor the left side and expand the right side. This will show that x^2 + 2x + 1 = x^2 + 2x + 1 and thus the two polynomials are equal.
x^2 + 2x + 1
= (x + 1) (x + 1)
= x^2 + 2x + x + 1
= x^2 + 3x + 1
= (x + 1)^2
To prove that x^2 + 2x + 1 = (x + 1)^2, we first factor the left side x^2 + 2x + 1 and expand the right side (x + 1)^2. This will give us two equations: x^2 + 2x + 1 and x^2 + 3x + 1. From here, we can observe that both equations are identical, and thus the two polynomials are equal. This can be further verified by noting that the left side is the result of squaring x + 1, and the right side is the square of x + 1. Therefore, x^2 + 2x + 1 is equal to (x + 1)^2.
Learn more about polynomial here
https://brainly.com/question/11536910
#SPJ4
What does K mean in quadratic equation?
The k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).
What is quadratic equation?We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. The formula (-b(b2-4ac))/(2a) is then used to enter these coefficients. A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible. To put it another way, if you have an equation with the form a squared by the expression after b plus b squared by the same expression but not squared plus c equal to 0, you have a quadratic equation.To learn more about quadratic equation refer to:
brainly.com/question/1214333
#SPJ4
What is log 10 called?
Common logarithmic functions are defined as logarithms with base 10 and natural logarithmic functions as those with base e. The common log function is primarily utilized.
The log's value can be expressed in either base 10 or base e. While the value of [tex]log_e 10[/tex] or ln(10) is 2.302585, the value of [tex]log_{10} 10[/tex] is 1. In general, there are two types of logarithmic functions, namely:
1. Frequently Used Logarithmic Function
2. Natural Logarithmic Function
If [tex]log_{a}b[/tex] = x, then axe = b is the definition of the logarithmic function.
Where x is a number's logarithm, "b," and "a" is the base of the log function, which might be either the value "e" or "10." Any positive number, other than 1, should be used as the variable "a," which should not be equal to 1.
To learn more about Common logarithmic functions link is here
brainly.com/question/30085872
#SPJ4
i-Ready
Dilations in the Coordinate Plane-Quiz - Level H
AJKL is dilated by a scale factor of with the center of dilation at the origin.
What are the coordinates of point J'?
7
4
1
C
...
8 9
5 6
3
(-)
2
?
X
+
+
X
1043
8
2
0
0
2
4
6
K
L
8
10
The coordinates of point J' are J'(-12,8)
How to determine the coordinates of point J'A dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
In this case, the point J (-3, 2) is transformed under a dilation of 4 with respect to the origin.
So the image point J' is (kx, ky) = (-3*4, 2*4) = (-12, 8)
So the image point of J(-3,2) under a dilation of 4 with respect to the origin is J'(-12,8)
Read more about transformation at
brainly.com/question/27224272
#SPJ1
Complete question
The triangle JKL is dilated by a scale factor of 4 with the center of dilation at the origin.
What are the coordinates of point J' if J = (-3, 2)?
What number is 10 times greater than 44,660?
Answer:
the answer 446600 ,nice to be of help to u
Are in the ratio 1 ratio 2 ratio 3 and the sum of their cubes is 4500 Find the numbers?
The three numbers which are in the ratio 1:2:3 and whose sum of the cubes is 4500 are 5, 10, and 15.
As given in the question,
Let us consider three number which are in the ratio 1: 2 : 3 be,
y, 2y , and 3y.
As per given condition:
Sum of their cubes = 4500
⇒x³ + (2x)³ + (3x)³ = 4500
⇒ x³ ( 1 + 8 + 27 ) = 4500
⇒36x³ = 4500
⇒ x³ = 4500/36
⇒x³ = 125
⇒ x = ∛125
⇒ x = 5
⇒2x = 10
⇒3x = 15
Therefore, three numbers which are in the given ratio are given by 5, 10, 15.
The above question is incomplete, the complete question is :
Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.
learn more about ratio here
brainly.com/question/13419413
#SPJ4
For what value of k will the following pair of linear equations have infinitely many solutions kx 3y?
The value k = 6 satisfies both equations Kx + 3y − (K − 3) = 0 and 12x + Ky − K = 0.
What is meant by linear equations?A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
An equation that depicts a straight line on a graph is said to be linear. The "line" in the name of the equation will help you remember this. Regular Form. Standard forms for linear equations look like this: Ax + By = C.
A linear equation has the form y = mx + b in the slope-intercept notation. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0. (b).
Given
Kx + 3y −(K − 3) = 0
Comparing with [tex]$a_1 x+b_1 y+c 1=0$[/tex]
[tex]$$\therefore \mathrm{a}_1=\mathrm{k}, \mathrm{b}_1=3, \mathrm{c}=-(\mathrm{k}-3)$$[/tex]
12x + ky - k = 0
Comparing with [tex]$a_1 x+b_1 y+c 1=0$[/tex]
[tex]$$\therefore a_1=12, b_1=k, c=-k$$[/tex]
Since equation has infinite number of solutions
So, [tex]$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$[/tex]
substitute the values in the above equation, we get
[tex]$\frac{\mathrm{k}}{12}=\frac{3}{\mathrm{k}}=\frac{\mathrm{k}-3}{\mathrm{k}}$$[/tex]
simplifying the equation, we get
[tex]$\frac{\mathrm{k}}{12}=\frac{3}{\mathrm{k}}$$[/tex]
[tex]$$\mathrm{k}^2=12 \times 3$$[/tex]
[tex]$$\mathrm{k}^2=36$$[/tex]
[tex]$$\mathrm{k}=\pm 6$$[/tex]
[tex]$\frac{3}{\mathrm{k}}=\frac{\mathrm{k}-3}{\mathrm{k}}$$[/tex]
simplifying the equation, we get
[tex]$$3 \mathrm{k}=\mathrm{k}(\mathrm{k}-3)$$[/tex]
[tex]$$\mathrm{k}=\pm 6$$[/tex]
[tex]$\frac{3}{k}=\frac{k-3}{k}$$[/tex]
[tex]$$3 \mathrm{k}=\mathrm{k}(\mathrm{k}-3)$$[/tex]
simplifying the equation, we get
[tex]$$3 k=k^2-3 k$$[/tex]
[tex]$$\mathrm{k}^2-3 \mathrm{k}-3 \mathrm{k}=0$$[/tex]
[tex]$$k^2-6 k=0$$[/tex]
[tex]$$\mathrm{k}(\mathrm{k}-6)=0$$[/tex]
k = 0, 6
Therefore, k = 6 satisfies both equations.
The complete question is:
For what value of K will the following pair of linear equations have infinitely many solutions?
Kx + 3y −(K − 3) = 0
12x + Ky − K = 0
To learn more about linear equations refer to:
https://brainly.com/question/2030026
#SPJ4
The value of a car is $21,000. It loses 11. 8% of its value every year. Find the approximate monthly decrease in value. Round your answer to the nearest tenth
If the value of a car is $21000 and it loses 8% of its value every year , then the approximate monthly decrease in value is $140 .
The value of the car is given as = $21000 ;
the percent decrease in the value of car is = 8% every year ;
So , in 1 year the value of car decreased is = [tex]0.08\times 21000[/tex]
= [tex]1680[/tex] .
So , in 1 year value of car decreased by $1680 ;
to find the monthly decrease , we divide the value by 12 ;
the monthly decrease is = [tex]\frac{1680}{12}[/tex] = $140 .
Therefore , The Approximate monthly decrease in the value of car is $140 .
Learn more about Percent here
https://brainly.com/question/12481192
#SPJ4
Please answer I need help
Answer: C- Opposite sides are parallel. (Same distance apart)
Hope this helps :)
Simplify the expression.
-2³
Answer:
-8
Step-by-step explanation:
suppose we have a system of 5 equations with 3 variables. how many pivot columns can the corresponding matrix problem have? for any number of pivot columns that you claim is possible, give an example of a linear system where this happens. for any number of pivot columns that you claim is not possible, explain why this is the case.
Suppose we have a linear system that consists of 5 equations with 3 variables, then the maximum number of pivot columns is 3. In this case, the solution exists and unique.
A pivot is defined as the position of the leading entry in a matrix. For example in the matrix below:
1 0 *
0 1 *
0 0 0
The pivot positions are the ones with bold entries.
If we have a system of 5 equations with 3 variables, then the maximum pivot columns is 3.
If we have a system of 5 equations with 3 variables and the number of pivot columns is 3, then the system consists of 3 linearly independent equations. Moreover, the system is consistent. Hence, the solution exists and unique.If we have a system of 5 equations with 3 variables and the number of pivot columns is less 3, and there is a pivot position in the corresponding augmented column, then the system is inconsistent. Hence, the solution does not exist. Example:0 1 * | *
0 0 0 | 1
0 0 0 | 0
0 0 0 |0
The last column is an augmented column
If we have a system of 5 equations with 3 variables and the number of pivot columns is less 3, and there is no a pivot position in the corresponding augmented column, then the system is consistent but has less than 3 linear independent equations. Hence, the solution exists but not unique. It has many solutions.Learn more about linear system here:
https://brainly.com/question/30192137
#SPJ4
a tomato has a mass of 100 grams the mass of the ant is 4.0x10x^{3} gram the of the tomato is how much greater than the mass of the ant
Note that if a tomato has a mass of 100 grams and the mass of the ant is 4.0x10⁻³gram, then the mass of the tomato is 25,000 times greater than the mass of the ant.
What is the justification for the above result?The expression for finding the extent to which the Mass of the tomato is greater than that of the ant is given as follows:
100/4.0x10⁻³
= [100 x 10³] / 4.0x10⁻³ x 10³
= 100,000/4
= 25,000
Therefore, the tomato is 25,000 times the mass of the ant.
Learn more about mass;
https://brainly.com/question/19694949
#SPJ1
Answer:yes 2.5* 10-2
Step-by-step explanation:
latoya swam kilometers against the current in the same amount of time it took her to swim kilometers with the current. the rate of the current was kilometers per hour. how fast would latoya swim if there were no current?
Latoya swims 7 kilometers per hour if there were no currents.
Latoya's speed without the current can be calculated by adding the speed she swam against the current (S-c) to the speed of the current (c). Since she swam the same distance at the same time in both cases, we know that (S-c) * t = S * t. Therefore, S = (S-c) + c. We know that the rate of the current is c = 2 Km/h and she swam 5 Km against the current, so (S-c) = 5 Km/t and S * t = 15 Km.
By substituting the values, we get S = (5 + 2) Km/t = 7 Km/t.
Complete question :
Latoya swam 5 kilometers against the current in the same amount of time it took her to swim 15 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Latoya swim if there were no currents?
Read more about Speed and distance:
https://brainly.com/question/26046491
#SPJ4
What is the product 7x?
7x is equal to 7 times x, so the answer is 7 times whatever x is. if x is equal to 6, then 7x would be equal to 7 multiplied by 6, which is 42. Therefore, the product of 7x is 7 times whatever x is.
7x is an expression that is asking for the product of 7 and x. The product is the result of multiplying two or more numbers together. Therefore, 7x is equal to 7 times whatever x is.
7x is an expression used to calculate the product of 7 and x. The product is the result of multiplying two or more numbers together, so 7x is equal to 7 multiplied by whatever x is. It is important to remember that the product of two or more numbers is the answer you get after multiplying them together. For example, if x is equal to 6, then 7x would be equal to 7 multiplied by 6, which is 42. Therefore, the product of 7x is 7 times whatever x is.
learn more about product here
https://brainly.com/question/29775042
#SPJ4
What is the scale factor from AXYZ to AUVW?
60
/56⁰
X
83
90
75
41
O A. 1/
OB. 5
1
O C. //
OD. 4
Z
12
56°
U
-83⁰
15
18 /W
41°
The triangles are similar triangles. and the scale factor of triangle UVW to triangle XYZ is 7
What is triangle ?
triangle can be defined in which it contains three sides , three angles and the sum of three angles is always is 180 degrees.
How to determine the scale factor
From the given figure, we have the following corresponding side lengths:
UW = 2
XZ= 14
The scale factor of UVW to XYZ is then calculated using:
Scale factor = XZ/UW
Substitute known values
Scale factor = 14/2
Divide
Scale factor = 7
Hence, the scale factor of triangle UVW to triangle XYZ is 7
To learn more about Triangle from the given link.
https://brainly.com/question/2773823
#SPJ1
50 psychology students took a standardized test. the scores are summarized in the gfdt below. scores frequency 180 - 199 11 200 - 219 6 220 - 239 8 240 - 259 11 260 - 279 14 you would like to build a relative frequency distribution for this data set to easily compare it to another class of students. what is the relative fequency for the fourth class, 240 - 259? enter answer as a percent (but do not include the percent symbol).
The relative frequency for the fourth class, 240 - 259 is 22.
The number of times a specific value for a variable (data item) has been seen to occur in relation to the overall number of values for that variable is referred to as the relative frequency. By dividing the absolute frequency by all possible values of the variable, the relative frequency is derived.
To calculate the relative frequency,
Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency.
Below you can see a distribution table to compare the relative frequencies of other class of students to better understand it.
Learn more about Relative frequency:
https://brainly.com/question/26177128
#SPJ4
When Yoni jumps as high as he can, the function h (t) = -16t2 + 10t models his height above the ground, in feet, where t is the number of seconds since he left the ground. Yoni needs to jump 2.5 feet in the air to be able to dunk a basketball. Which statement BEST explains why Yoni can or cannot dunk the basketball?
A Yoni CAN dunk the basketball because the discriminant of 0 = -16t² + 10t-2.5 is positive.
B Yoni CAN dunk the basketball because the discriminant of 0= -16t² + 10t - 2.5 is negative.
C Yoni CANNOT dunk the basketball because the discriminant of 0= -16t² + 10t - 2.5 is positive.
D Yoni CANNOT dunk the basketball because the discriminant of 0 = -16t2 + 10t-2.5 is negative.
The correct statement is D. Yoni CANNOT dunk the basketball because the discriminant of 0 = -16t² + 10t - 2.5 is negative.
How to determine the correct statementThe discriminant of a quadratic equation is the value that is inside the square root sign of the equation,
in this case: b²-4ac.
If the discriminant is positive, it means that the equation has two distinct real roots.If the discriminant is zero, it means that the equation has one real root.If the discriminant is negative, it means that the equation has no real roots.Given that
h(t) = -16t² + 10t
Height = 2.5
We have
-16t² + 10t = 2.5
This gives
0 = -16t² + 10t - 2.5
In this case, the discriminant of the equation 0 = -16t² + 10t - 2.5 is negative, which means that there are no real roots.
This means that Yoni will not reach the height of 2.5 feet because the equation has no real solutions, so he cannot dunk the basketball
Read more about discriminant at
https://brainly.com/question/27839846
#SPJ1
Given the following table, find the domain and range of the function.
=======SELECT ALL THAT APPLY PLEASE =======
A) domain: {2, 4, 5, 9}
B) range: {2, 4, 5, 9}
C) range: {-3, 1, 5, 7}
D) domain: {-3, 1, 5, 7}
SELECT ALL THAT APPLY
Solve.
524 people watch the town parade. 178 of them
are children. How many people watching the parade
are adults? For 3rd grade math
To find out how many people watching the parade are adults, we can subtract the number of children from the total number of people.
524 people - 178 children = 346 adults
So, 346 people watching the parade are adults.
Answer:
To find out how many people watching the parade are adults, we have to subtract the number of children from the total number of people.
Total number of people watching the parade: 524
Number of children watching the parade: 178
524 - 178 = 346
Therefore, 346 people watching the parade are adults.
The ratio Tim spends on math homework to science homework is 5 to 4. If he spends 40 minutes on math homework, how many minutes does he spend on science homework?
A.20 minutes
B.32 minutes
C.60 minutes
D.90 minutes
Please explain how you got your answer.Thank you.
According to the ratio presented, he spends 32 minutes on his science homework.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, The ratio Tim spends on math homework to science homework is 5 to 4.
thus,
(time on math)/ (time on Science) = 5/4
Since he spends 40 minutes on math homework,
From equation 1
Time spent on science = 4/5 * (time on math)
Time spent on science = 4/5 * 40
Time spent on science = 32
therefore, 32 minutes he spends on science homework as per the given ratio.
Learn more about ratios here:
https://brainly.com/question/13419413
#SPJ1
annual sales for a company are $149,999 and are increasing at a rate of 5% per year. write an exponential growth function to model this situation. then, find the annual sales after 7 years.