Answer:
x = -1/3 or x = -4
Step-by-step explanation:
Answer:
x= [tex]\frac{-1}{3}[/tex]
x= -4
Step-by-step explanation:
[tex]6x^2+28x-2=2x-10[/tex]
Subtract 2x - 10 from both sides.
[tex]6x^2+26x+8=0[/tex]
[tex]x= \frac{ -(26) +/ \sqrt{(26)^2-4(6)(8)} }{2(6)}[/tex]
x= [tex]\frac{-26 +/\sqrt{676-4(6)(8)} }{2(6)}[/tex]
x= [tex]\frac{-26 +/ \sqrt{676-192} }{2(6)}[/tex]
x= [tex]\frac{-26+/\sqrt{484} }{2(6)}[/tex]
x= [tex]\frac{-26+/22}{12}[/tex]
x= [tex]\frac{-26+22}{12}[/tex] = -0.33333333333333 = -1/3
x= [tex]\frac{-26-22}{12}[/tex]= -4
If f(x) = 5 + 3x and g(x) = 5 - 9x, find f(g(2)).
If the function f(x) = 5 + 3x and g(x) = 5 - 9x. The value of f(g(2)) is -34
The given functions are
f(x) = 5 + 3x and g(x) = 5 − 9x.
a. We plug-in 2 in the function g(x) and then the obtained image in the function
f(x)g(2) = 5 − 9 × 2
= 5 - 18
= -13
f(g(2)) = f(-13)
= 5 + 3 × (−13)
= 5 - 39
= -34
b. We find the composite function by replacing x in f(x) by
g(x) f(g(x)) = 5 + 3g(x)
= 5 + 3 × (5−9x)
= 5 + 15 − 27x
f(g(x)) = 20 − 27x
f(g(2)) = 20 − 27 × 2
= 20 − 54
= -34
Learn more about f(g(x)) at :https://brainly.com/question/29103939
#SPJ1
How do you solve an equation using the substitution method?
Solution of the equation using substitution method is given by following steps:
1. Get the value of one variable in the other variable form using one equation.
2. Substitute the value of that variable in the second equation and get the value of both the variables.
Let us consider the system of equation to explain the solution of substitution method:
x + y = 0 __(1)
2x + 3y = 6 ___(2)
Get the value of y in the x form and substitute the value of y in equation (2) we get,
y = -x
2x + 3(-x) = 6
⇒2x - 3x = 6
⇒ -x = 6
⇒ x = -6
Now substitute the value of x in equation (1) we get,
y = -( -6)
⇒ y = 6
Therefore, the solution of the equation using substitution method is given by following way:
1. Get the value of one variable in the other variable form using one equation.
2. Substitute the value of that variable in the second equation and get the value of both the variables.
Learn more about substitution method here
brainly.com/question/14619835
#SPJ4
During the day, a patient had her temperature measured at 37.3C, 38C, 37.8C and 38.5C. So what was her average temperature?
Help meeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Help meeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Help meeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Help meeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Help meeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Help meeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Help meeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
How do you prove 3x 1?
It is an iterated function also known as hailstone problem and can be solved on iterated steps.
Is it possible to solve 3X+1?Since then, the 3X + 1 issue has taken many different shapes. It is among the most infamous puzzles that have never been solved. For more than 40 years, prizes have been offered for its resolution, but nobody has totally and properly done so.
What are the rules for 3X+1?The 3x+1 Conjecture states that this function can be iterated through multiple times to eventually produce the value 1 starting from any positive integer n.
Take a positive integer X and divide it by 2 if it is even. If it is odd, multiply it by 3 and add 1 to the result to form the conjecture 3X + 1. The ends operate repeatedly according to the aforementioned criteria, and after a finite number of repetitions, the final end is always 1.
To learn more about hail storm visit the link:
https://brainly.com/question/14694010
#SPJ4
A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses. Choose the correct answer from the drop-down menu to complete the statement.
As per the concept of linear equation, the college student took 13 courses of 3 credit hours.
An equation in math is defined as a mathematical statement with an 'equal to' symbol between two expressions that have equal values
Here we have given that college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses
And we need to find number of students in each category.
While we looking into the given question, we have given the values like the following,
Here the total credits = 59
And the total courses = 18
Then let us consider the number of 3 credit hour courses is referred as x and the number of 4 credit hour courses referred as y
Then based on the given statement, we have written the equation as
=> x + y = 18 ----------------------------(1)
=> 3x+4y=59 --------------------------(2)
Here we have to eliminate y to find the number of 3 credit hour courses, by multiplying Equation 1 by 4
Then we get,
=> 4x + 4y = 72
Then we have to subtract Equation 2 from Equation 3
Then we get,
=> x = 13
Therefore, the resulting value is 13.
To know more about equation here.
https://brainly.com/question/10413253
#SPJ4
Solve the equation 6p=2(5-2p).
First, divide both sides by 2 and simplify.
6p=2(5-2p)
2p)
6p 2(5-2p)
2
2
p=5-2p
We will use the concept of Simplification of Equations . The value of p in the given equation is 1.
How can we simplify the given Equations?An Algerbraic equation in algebra is any equation that can be transformed in standard form like the following:
ax+bx+c=0 or ap+bp+cp+d=0 it can be of any form.
With a 0 and a, b, and c are known numbers, x is an unknown value, and a. The equation is linear, not quadratic, if a = 0 and b 0. The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient, linear coefficient, and constant or free term, respectively.
The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation. There can only be only solution to an Algebraic equation.
Calculation6p=2(5-2p) is the given equation
Divide by 2 on both LHS and RHS of the equation
6p/2 = 2(5-2p)/2
⇒3p=5-2p
⇒5p=5
∴p=1
We will use the concept of Simplification of Equations . The value of p in the given equation is 1.
To refer more about Simplification of Equations , visit :
https://brainly.com/question/432678
#SPJ1
How do you find the median on a calculator?
The median x˜ is the data value separating the upper half of a data set from the lower half.
Arrange data values from lowest to highest value
The median is the data value in the middle of the set
If there are 2 data values in the middle the median is the mean of those 2 values.
Median Example
For the data set 1, 1, 2, 5, 6, 6, 9 the median is 5.
For the data set 1, 1, 2, 6, 6, 9 the median is 4. Take the mean of 2 and 6 or, (2+6)/2 = 4.
Median Formula
Ordering a data set x1 ≤ x2 ≤ x3 ≤ ... ≤ xn from lowest to highest value, the median x˜ is the data point separating the upper half of the data values from the lower half.
To know more about median visit brainly.com/question/28060453
#SPJ4
Santa take 8 minutes to build 1 train and 6 minutes to built I car. How much minutes will it take him to build 100 train and 100 cars?
Answer:
800 and 600
Step-by-step explanation:
1 train = 8 minutes
100 trains =8×100
= 800 minutes
1 car= 6 minutes
100 cars = 6×100
= 600 minutes
Answer:
1400 minutes / 23 hrs
Step-by-step explanation:
How do you find the missing number in an integer array of 1 to 100?
The missing number in an integer array of 1 to 100 can be found by summing the numbers 1-100 and subtracting the sum of the given array. The difference between the two sums will be the missing number.
To find the missing number, first sum the numbers 1-100 to get the total sum. Then sum the given array and subtract this sum from the total sum. The difference between the two sums will be the missing number. This method works because the total of the array should be equal to the sum of 1-100 if all the numbers are present. By subtracting the sum of the given array from the total sum, any missing numbers will be accounted for in the difference.
Learn more about Arrays here:
https://brainly.com/question/26104158
#SPJ4
By what number must you multiply each side of the equation 45x=8 to produce the equivalent equation x = 10?.
Answer:
5
Step-by-step explanation:
For this case, we have the following equation:
4/5x = 8
We must find a number that when multiplied on both sides of the equation, as a result:
x = 10x
So, if we multiply 8 * 5 = 40
Now, the left side must also be multiplied by 5 to not alter the equation:
(4/5)x*5=4x
x∗5=4x
Finally we have 4x=40
Clearing "x":
\begin{gathered}x = 40/4
x=10
to know more equations
https://brainly.com/question/649785?referrer=searchResults
Did zero is prime number?
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. 0 is not a positive integer, so it is not considered a prime number.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
What is whole number?Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.
To learn more about prime numbers:
brainly.com/question/9315685
#SPJ4
Consider the original triangle and the reduction. A triangle has a base a and height 8 centimeters. Another triangle has a base of 3 centimeters and height of 4 centimeters. What is the length of side a in centimeters? one-sixth one-half 2 6.
So, the length of triangle side a in centimeters is 6.
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
We can use the fact that the ratio of corresponding sides in similar figures is constant to solve this problem.
Since the two triangles are similar, we know that the ratio of their sides is constant. Letting x represent the length of side a in centimeters, we have
(a/3) = (8/4)
We can solve this equation by multiplying both sides by 3 to get
a = (8/4) * 3
= 6
Therefore, the length of side a in centimeters is 6.
The answer is therefore 6.
To know more about Similarity of Figures visit; brainly.com/question/3426329
#SPJ4
Since the two triangles are similar, we know that the ratio of their sides is constant. Letting x represent the length of side a in centimeters, we have
(a/3) = (8/4)
We can solve this equation by multiplying both sides by 3 to get
a = (8/4) * 3
= 6
Therefore, the length of side a in centimeters is 6.
The answer is therefore 6.
If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is: (a)2 (b)-2 (c)1 (d)-1
Answer:
(a) 2
Step-by-step explanation:
We can assume this is a 3-4-5 triangle from the two given sides, 5 and 3(2--1) so then we know the y difference of the y coordinate should be + or - 4 from -2 giving us two solutions of 2 and -6 since this is a multiple choice and a is 2 he answer is 2
How do you find the nature of the roots of a quadratic equation using a graph?
The roots of a quadratic equation can be found by analyzing the shape of the parabola formed by the equation's graph. The number of roots is determined by the number of x-intercepts.
To find the nature of the roots of a quadratic equation using a graph, you can plot the graph of the equation and analyze the shape of the graph. The graph of a quadratic equation is a parabola which opens upward or downward depending on the sign of the coefficient of the x² term. If the coefficient is a positive number, the parabola opens upward and if the coefficient is a negative number, the parabola opens downward. The roots of the equation are the x-intercepts of the graph, and there may be zero, one, or two roots. If the graph intersects the x-axis at two distinct points, the equation has two real, distinct roots. If the graph touches the x-axis at one point, the equation has one real root. If the graph does not intersect the x-axis, the equation has no real roots.
To learn more about the quadratic equation, visit:
brainly.com/question/1863222
#SPJ4
How do you find the mean of 5?
The mean of given data is 5.
To find: Mean of the given data
Given data: 5
Mean: Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Mean=Sum of observations / Number of observationsHere sum of observation is 5
Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data
Total number of observation is 1
The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset
Now substitute the values in above formula
=[tex]\frac{5}{1}[/tex]=5
Therefore, the mean is 5.
For more questions on mean
https://brainly.com/question/29021104
#SPJ4
How many terms are there in the expression 3 }- 3p 2 }+ 4p 7?
There are four terms in the expression –2p³ – 3p² + 4p + 7. The first term is –2p³, the second term is –3p², the third term is 4p, and the fourth and final term is 7.
What is terms?Terms in math are individual components of equations or expressions, which can consist of constants, variables, and operators. A term can also be a single number or variable, or several numbers or variables multiplied together. Terms are separated by addition or subtraction operators. Terms can also be used to describe an algebraic expression such as the sum of two terms, or the product of two terms.
The expression can be written as –2p³ – 3p² + 4p + 7 = 0. This expression is a polynomial equation with degree three, meaning the largest exponent of the variables is 3.
To know more about terms click-
https://brainly.com/question/15894738
#SPJ4
What equation is perpendicular to Y =- 3x 4?
Equation y = -3x is perpendicular to Y =- 3x - 4.
Describe perpendicular.A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle. In every case, perpendicular lines cross or intersect. Any two perpendicular lines will always have an angle of 90 degrees.
Given
y = -3x - 4
Using slope intercept form.
y = mx + b
The reciprocal of the slope of the perpendicular line is negative.
By doing this, you alter the slope's sign to the opposite, in this case to 3. The slope of the perpendicular line is then equal to 1/3 by finding the reciprocal by flipping the denominator and numerator.
Equation y = -3x is perpendicular to Y =- 3x - 4.
To learn more about perpendicular, visit:;
https://brainly.com/question/29268451
#SPJ4
How do you find the base area of a pyramid?
The base of a solid, three-dimensional, or shaped item. What the thing "rests" on is the base. Polygons, forms, and solids all employ base.
Explain the term base area of a pyramid?Any pyramid's surface area can be calculated by multiplying the base's surface area by the lateral faces' surface areas.
If you know how to calculate the area of the pyramid's base, you may use a formula to determine the surface area of a normal pyramid. Knowing how to calculate the area of forms like pentagons and hexagons is useful because the basis can be any polygon. However, when dealing with the usual, standard square pyramid, figuring out the total surface area is straightforward.Pyramid's slant height and the square base's side length.
Thus, base area of the square pyramid is length x width.
To know more about the surface area of a pyramid, here
https://brainly.com/question/29036343
#SPJ4
What is the slope of the equation y 10 4x?
The slope of the given equation y = 10 - 4x is equal to -4.
As given in the question,
Given equation is equal to y = 10 - 4x
Standard form in slope intercept form for the equation is given by :
y = mx + c
'm' is representing the slope of the given equation
'c' is representing the value of the y-intercept of the given equation.
Now after simplifying the given equation in the standard form we get,
y = 10 - 4x
⇒ y = -4x + 10 __(1)
Compare equation (1) with the standard form of slope intercept form we get,
Slope of the equation is equal to m = -2.
Therefore, the slope of the given equation y = 10 - 4x is given by m = -4.
The given question is incomplete , the complete question is:
What is the slope of the equation y = 10 - 4x ?
Learn more about slope here
brainly.com/question/3605446
#SPJ4
What are the 3 steps to finding an inverse function?
Rewrite f(x)= as y in step one, Swap X and Y in step one, then solve for y in step three.
What is multiplicative inverse ?A number that, when multiplied by a number x, produces the multiplicative identity 1, or 1/x or x1, is known as a multiplicative inverse or reciprocal in mathematics. B/a is the multiplicative inverse of the fraction a/b. Divide 1 by the real number to find its multiplicative inverse. As an illustration, the reciprocal of 5 is 1/5 (1/5 or 0.2), whereas the reciprocal of 0.25 is 1 divided by 0.25 (1 divided by 0.25 = 4) One of the most straightforward instances of a function that is its own inverse is the reciprocal function, or f(x), which transfers x to 1/x (an involution).Since no real number multiplied by 0 yields 1, zero does not have a reciprocal in the real numbers (the product of any number with zero is zero). The reciprocals of all real numbers, except zero, are real; the reciprocals of all rational numbers, except zero; and the reciprocals of all complex numbers, save zero.Hence, Rewrite f(x)= as y in step one, Swap X and Y in step one, then solve for y in step three.
To learn more about Multiplicative Inverse refer to;
https://brainly.com/question/1682347
#SPJ4
H(x)=3x^4+2x-5/x+9x^3-7 is it polynomial? If so write in standard form, degree, type, and leading coefficient. (20 points)
Answer:
yes its a polynomial espero te sirva
What are the two function used to form the rational function?
The two functions used to form the rational function are the ratio of two rational polynomial expression p and q.
A function is called a rational function if it can be expressed in terms of the ratio of p and q.
f( x ) = p( x ) / q( x )
They generally are made up of more than one part.
Each function has a domain and a co - domain , they generally tells us about the limits of the function. We can use the rational function to calculate the domain.
Rational function asymptotes are of 3 types which are known as ,
Horizontal AsymptotesVertical AsymptotesOblique AsymptoteTo learn more about functions
brainly.com/question/21145944
#SPJ4
William works at a tire shop and earns 6.75% commission on everything he sells. He also earns a base salary of $300 per week. How much will he earn for the week if he sells $5,385 worth of tires?
Answer: 363.49
Step-by-step explanation:
6.75%=.0675
5385*.0675+300=363.4875
round up
$363.49
Consider the following equation.
-16p + 37 =49 - 21 the equation that has the same solution
The equation that has similar equation with the one given is D. 3/2p - 5 + 9/4p = 7 - 5/4p
We are given the equation;
-16p + 37 = 49 - 21p
We are supposed to identify the equation that has similar solution with the equation given;
The solution for the equation given is;
-16p + 37 = 49 - 21p
Combining the like terms;
-16p + 21p = 49 - 37
5p = 12
p = 2.4
Solution for the choices given;
A. -14 + 6p = -9 - 6p
6p + 6p = -9 +14
12p = 5
p= 0.417
B. -55 + 12p = 5p + 16
12p - 5p = 16 + 55
7p = 71
p = 10.14
C. 2 + 1.25p = 3.75p + 10
1.25p - 3.75p = 10 - 2
-2.5p = 8
p = -3.2
D. 3/2p - 5 + 9/4p = 7 - 5/4p
3/2p +5/4p +9/4p = 7 + 5
5p =12
p = 2.4
Therefore, the equation that has similar equation with the one given is D. 3/2p - 5 + 9/4p = 7 - 5/4p
Learn more about Similar Equations at :
https://brainly.com/question/2972832
#SPJ1
What ratio does the point 1 a divided the join of (- 1/4 and 4 1 )? Also find the value of a?
Using the provided values for the points and the slope, With the formula of slope we can calculate the value of a = 14/5 =2.8 and the ratio as
1:1.49 .
What do you mean by slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.
What do you mean by ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the total amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
point (1,a) divided line joined by (-1,4) and (4,1).
Since, The slope between these points are same as they all line in a single line, we can ,
[tex]\frac{a-4}{1+1} = \frac{1-a}{4-1}[/tex]
3a-12=2-2a
5a=14
a=14/5 =2.8.
distance between (-1,4) and (1,2.8),
[tex]d1 = \sqrt{(1--1)^2 +(2.8-4)^2}\\=\sqrt{5.44}\\=2.33[/tex]
distance between (1,2.8) and (4,1),
[tex]d2= \sqrt{(4-1)^2 + (1-2.8)^2}\\=\sqrt{12.24}\\=3.49\\\\[/tex]
ratio = d1/d2
= 1: 1.49
To learn more about lines visit:
https://brainly.com/question/24524587
#SPJ4
Saha ue 3 teapoon of hot chocolate mix for every 8 ounce of milk. How many teapoon of hot chocolate mix doe he need for 48 ounce of milk?
Saha uses 3 teaspoons of hot chocolate mix for every 8 ounces of milk. for 48 ounces of milk, he needs 18 teaspoons of hot chocolate.
The problem can be solved using unitary method or using ratio.
- Unitary method
Using this method, first, compute how many teaspoons of chocolate needed for 1 ounce of milk.
8 ounces of milk need 3 teaspoons of hot chocolate. Hence,
1 ounce of milk need 3/8 teaspoons of hot chocolate
48 ounce of milk need 3/8 x 48 = 18 teaspoons of hot chocolate
- Using ratio
Let p = number of teaspoons of hot chocolate needed for 48 ounces of milk. Then,
3 : 8 = p : 48
8p = 3 x 48
p = 3 x 48/8 = 3 x 6 = 18 teaspoons
Learn more about ratio here:
https://brainly.com/question/26460724
#SPJ4
What is the best approximation of the solution to the system to the nearest integer values?
(7, 1)
(7, 0)
(1, 7)
(0, 6)
Answer:
7,0
Step-by-step explanation:
Which of the following statements about dilations are true? Select all that apply.
The true statement on dilations are that :
A. Dilations have the same shape as the original shape C. Dilations can be reductions of the original image What are dilations ?Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.
Dilation therefore allows for the same shape as the original shape, but it is a reduction of the original shape and so cannot be the same size.
Find out more on dilations at https://brainly.com/question/3457976
#SPJ1
What is the value of g 0?
Answer:
Step-by-step explanation:
The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by ɡ0 or ɡn, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined by standard as 9.80665 m/s2 (about 32.17405 ft/s2).