Answer:
see explanation
Step-by-step explanation:
Given
2x² + 9x + 10 = 0
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × 10 = 20 and sum = + 9
The factors are + 4 and + 5
Use these factors to split the x- term
2x² + 4x + 5x + 10 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) + 5(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x + 5) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]
Answer:
1. x = 2
2. x = - 5/2
Step-by-step explanation: First put parenthesis around the equation
( 2x^2 + 4x ) + ( 5x + 10) = 0
2x ( x+ 2) 5 (x + 2),
when you have the same answer inside the parenthesis you know your right.
2x + 5 = 0
x + 2 = 0
Next preform basic algebra
2x = -5
x = -2x = - 5/2Is 3[g(x)] = x a linear function?
Answer: no
Step-by-step explanation:
Linear functions are straight lines and are also written in the form y=mx+b
The linearity of 3[g(x)] = x depends on the form of g(x). If g(x) is linear, such as g(x) = ax, then the equation is linear. Otherwise, if g(x) involves non-linear operations, the overall equation will not represent a linear function.
Whether or not the equation 3[g(x)] = x represents a linear function depends on the form of g(x). If g(x) is a linear function, then the equation represents a linear transformation. If g(x) is nonlinear, then the overall function is not linear.
For example, if g(x) = exp(3x), the relationship is non-linear due to the exponential function. However, if the g(x) function is a simple linear function like g(x) = a₁x, with a constant coefficient, the equation maintains its linearity. In this scenario, the function could even represent a constant multiple of the identity function, where g(x) = x/3.
It is important to note that in the context of mathematics, understanding whether a function is linear involves recognizing if it can be written in the form of g(x) = mx + b, where m and b are constants, and the function results in a straight line on a graph.
find f (-3) if f(x) = x^2
Konichiwa~! My name is Zalgo and I am here to help you out today. If f were to equal -3, first we need to put -3 into the equation. It would look like "f(-3)=x^2". The answer to that equation is 9.
I hope that this helps! :T
"Stay Brainly and stay proud!" - Zalgo
What is the definition of a base number
Answer:
main number
Step-by-step explanation:
Final answer:
A base number in mathematics is the number raised to a power, where in scientific notation it is always 10, whereas in economic terms, a base year is a reference year for economic measurements.
Explanation:
The definition of a base number in mathematics generally refers to the number that is being raised to a certain power. In the context of scientific notation, the base number is always 10. This is used to succinctly represent very large or very small numbers in the form N x 10^n, where N is a number greater than or equal to 1 and less than 10, and n is a positive or negative integer; for example, 10^0 = 1. However, the concept of a base extends beyond just the number 10; any number can act as a base in different mathematical contexts.
When discussing numbers in a positional numeral system, the base determines the value of each digit in the number and how those digits are combined to represent the overall number. For instance, in the base-10 system, the digits 0 through 9 are used, and the position of each digit indicates how many multiples of powers of 10 it represents. Finally, in the context of economic indexes, a base year is a reference year against which economic growth or inflation is measured.
Zed is making a centerpiece for his dining room table by putting sand in a cube-shaped vase. The vase is 0.25 meters in length, width, and height. He bought 25 kg of sand. Assume the density of dry sand is 1,602 kgm3. What is the volume of the sand that Zed purchased?
The volume of the sand is approximately __________ m3.
Enter your answer as the number that correctly fills in the blank in the previous sentence. If necessary, round your answer to six decimal places, like so: 42.536475
The answer is:
The volume of the sand is approximately 0.015605 m3
Why?To solve the problem, and find the volume of the sand that Zed purchased, we need to use the formula to calculate the density and isolate the volume from it.
So, solving we have:
[tex]density=\frac{mass}{volume}[/tex]
From the statement we know that:
The mass of the sand is 25 kg
The density of the dry sand is 1,602 kg/m3
So, substituting and solving we have:
[tex]density=\frac{mass}{volume}\\\\volume=\frac{mass}{density}\\\\volume=\frac{25kg}{1,602\frac{kg}{m^{3}}}=0.015605m^{3}[/tex]
Hence, the volume of the sand is approximately 0.015605 m3
Have a nice day!
Which of the following shows the polynomial below written in descending order
When it asks for descending order of the polynomial it wants you to put the exponents in order from largest to smallest like so...
C. [tex]x^{12} +3x^{7} + 4x^{3} -9x[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Option C
Step-by-step explanation:
In this question the given polynomial is 4x³ + 3x⁷ - 9x + x¹²
If we rewrite it in the descending order of the powers then the polynomial will be
x¹² + 3x⁷ +4x³ + 9x
This polynomial matches with option C.
Option C is the answer.
PLZ HURRY IT'S URGENT!
Jeff is buying an ice-cream sundae. There are 2 sizes of sundaes, 14 different ice-cream flavors, and 4 different toppings.
How many ways can Jeff choose a sundae?
A.
20
B.
56
C.
32
D.
112
Jeff can make his choices independently so there are a total of
[tex] 2 \times 14 \times 4[/tex]
different sundaes.
Answer: D. 112
Answer:
D 112
Step-by-step explanation:
Just multiply the number of different ways to choose things to come up with all your possibilities.
That is you just do 2(14)(4)=28(4)=112
Given x = wavelength and y = frequency, solve for the wavelength for the given type of radiation.
y= 3×10^8 m/s /x
Answer: 1 x 10^27 m
Step-by-step explanation:
The diagram below gives the dimensions of a swimming pool.
- 18 ft
What is the total area of the swimming pool? Show your work. (2 points)
b. What is the perimeter of the swimming pool? Show your work. (2 points)
Click or tap here to enter text.
Answer:
[tex]area = base \times hight 36 \times 18 \: ad perimeter \: base \times base \times hight \times hight36 \times 36 \times 18 \times 18[/tex]
Area is given by base * the Hight which gives the area of the pool
find a ordered pair to represent a in the equation a=b+c if b= (6,3) and c =(-4,8)
Answer:
So ordered pair a is (2,11)
Step-by-step explanation:
We are given
a = b+c
and ordered pair b =(6,3) and ordered pair c =(-4,8)
Putting values of b and c in the given equation and adding x and y coordinates of b and c we can find ordered pair a.
a=(6,3)+(-4,8)
a =(6-4,3+8)
a =(2,11)
So ordered pair a is (2,11)
14. Which of the following is the largest?
2^50 3^40 4^30 5^20
2. 3^40
3. 4^30
4. 5^20
1. 2^50
Convert the fraction to a mixed number
5/2=a b/2
Answer:
2 1/2
Step-by-step explanation:
5 is 2 more than 2 so the the first part would be 2.
[tex]\dfrac{5}{2}=\dfrac{2\cdot2+1}{2}=2\dfrac{1}{2}[/tex]
Use the net to find the surface area of the cylinder
give your answer in terms of pi
A 25pi yd2
B 70pi yd2
C 50pi yd2
D 120pi yd2
Answer:
D) 120pi yd2
Step-by-step explanation:
Use the properties of exponents to rewrite the expression
(-3yz)(-3yz)(-3yz)(-3yz)
[tex]\bf (-3yz)(-3yz)(-3yz)(-3yz)\implies (-3yz)^1(-3yz)^1(-3yz)^1(-3yz)^1 \\\\\\ (-3yz)^{1+1+1+1}\implies (-3yz)^4\implies (-3)^4 y^4 z^4\implies 81y^4 z^4[/tex]
The expression (-3yz) (-3yz) (-3yz) (-3yz) is (-3yz) ⁴
What is a number multiplicative?A multiplicative indicates how many copies of a number are multiplied together.negative multiplicative is the reciprocal of a number with a positive multiplicative which can be mathematically represented as. X ⁻¹ = 1/X⇒(-3yz)¹ (-3yz)¹ (-3yz)¹ (-3yz)¹=(-3yz)¹⁺¹⁺¹⁺¹
⇒ (-3yz)¹ (-3yz)¹ (-3yz)¹ (-3yz)¹ = (-3yz)⁴
Learn more about multiplication here:-https://brainly.com/question/1087373
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What is the greatest common factor of 8 and 36
Answer:
4
Step-by-step explanation:
When multiplying, the greatest common factor of each is four.
8= 4 x 2
36= 4 x 9
The greatest common factor (GCF) of 8 and 36 is 4. The correct option is B.
GCF stands for "Greatest Common Factor." It refers to the largest positive integer that divides evenly into two or more given numbers. In other words, the GCF is the largest number that is a factor of all the given numbers.
Finding the GCF is useful in various mathematical operations, such as simplifying fractions, finding equivalent fractions, or solving equations. It helps in identifying common factors and simplifying calculations.
To find the GCF, you can identify the common factors of both numbers and determine the largest one they share.
The factors of 8 are 1, 2, 4, and 8.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The largest factor that both 8 and 36 share is 4.
Therefore, the greatest common factor of 8 and 36 is 4.
To learn more about the greatest common factor click:
https://brainly.com/question/2352983
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2-digit numbers less than 91 which are 1 less than a multiple of 10
Answer:
{19, 29, ... , 79, 89}
Step-by-step explanation:
Multiples of 10 are {10, 20, 30, 40, ... , 90}
Numbers which are each 1 less than these multiples of 10 would be:
{9, 19, 29, ... , 79, 89}.
Note that the last number, 89, is less than 91.
We must omit 9 from this set, since 9 is not a 2-digit number. Then our final list is {19, 29, ... , 79, 89}.
Answer:
The numbers are 19,29,39,49,59,69,79,89
Step-by-step explanation:
2 digit numbers starts from 10 and ends on 99.
2 digit numbers less than 91 starts from 10 and ends at 90.
2 digit numbers less than 91 and multiple of 10 are 10,20,30,40,50,60,70,80,90.
2 digit numbers less than 91 and which are 1 less than a multiple of 10 are 19,29,39,49,59,69,79,89.
The numbers are 19,29,39,49,59,69,79,89
Rewrite the equation below in standard form y=-4x-2
Answer:
4x + y = - 2
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Given
y = - 4x - 2 ( add 4x to both sides )
4x + y = - 2 ← in standard form
Answer:
4x + y = -2
Step-by-step explanation:
Find the lateral area of a rectangular prism with l=6, w=4, h=2
Answer:
40 square units
Step-by-step explanation:
The surface area is given by
LA = 2(wh+lh)
where h is the height l is the length and w is the width
We do not include the top or bottom
We know l=6 w=4 and h=2
LA = 2 ( 4*2 + 6*2)
lA = 2( 8+12)
= 2 (20)
= 40
Solve 4x+2=12 for using the change of base formula logby=logy over logb
Answer:
log₄ 10 = log₁₀ 10 / log₁₀ 4
Step-by-step explanation:
Taking the x to be a power then;
[tex]4^x +2 =12[/tex]
[tex]4^x = 12-2[/tex]
[tex]4^x=10[/tex]
Introduce log on both sides
x log 4= log 10
x= log 10/log 4
log₄ 10 = log₁₀ 10 / log₁₀ 4
Answer: x = log₄(3/4) = -0.207
Step-by-step explanation:
when you have the equation:
n^x = b
whe have that:
Logₙ(b) = x
in this case we have the equation:
4^(x+2) = 12
(4^x)*(4^2) = 12
16*4^x = 12
4^x = 12/16 = 3/4
x = log₄(3/4) = -0.207
A 700 4/7 meter long cloth is cut into equal pieces measuring 1 2/5 meter each how many such small pieces are there?
Step-by-step explanation:
(700 4/7) ÷ (1 2/5)
Write the fractions in improper form:
(4904/7) ÷ (7/5)
To divide by a fraction, multiply by the reciprocal:
(4904/7) × (5/7)
24520/49
500 20/49
There are 500 pieces.
Answer:
(700 4/7) ÷ (1 2/5)
Write the fractions in improper form:
(4904/7) ÷ (7/5)
To divide by a fraction, multiply by the reciprocal:
(4904/7) × (5/7)
24520/49
500 20/49
There are 500 pieces.
Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 1.5% syrup?
Answer:
He needs 0.075 lbs of sugar and 4.925 lbs of water.
Step-by-step explanation:
Let x lbs be the amount of sugar in the syrup. Then 5-x lbs is the amount of water in this syrup.
Note
5 lbs - 100%
x lbs - 1.5%
Write a proportion:
[tex]\dfrac{5}{x}=\dfrac{100}{1.5}[/tex]
Cross multiply:
[tex]100x=5\cdot 1.5\\ \\100x=7.5\\ \\x=\dfrac{7.5}{100}=0.075[/tex]
So, he needs 0.075 lbs of sugar and 5 - 0.075 = 4.925 lbs of water.
Please help me with question 5
Answer:
99x +84 ≤ 1,150
Step-by-step explanation:
Her budget is $1,150, this means that the price of all her purchases cannot exceed it. In other words, the sum of all her purchases must be less or equal to 1,150.
To find how many watches she can buy, you need to multiply it by the price of the watches, which is $99, so it will be 99x.
As for the shirts, she spent $84.
So the inequality equation you will need will be the sum of the price of watches and shirts is less than or equal to 1,150.
99x + 84 ≤ 1,150
Identify an equation in point slope form for the Line perpendicular to y=-4x-1 that passes through (-2,7)
Answer:
[tex]y - 7 = \frac{1}{4}(x + 2)[/tex]
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are. Plus, perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES] so −4 becomes ¼.
I am joyous to assist you anytime.
which of the following is an arithmetic sequence?
Answer:
B
Step-by-step explanation:
And arithmetic sequence is a sequence in which the difference between each of the numbers are constant.
It is not A, because the difference between 3 and 9 is positive 6, and the difference between 9 and 81 is positive 72.
It is not C, because the difference between 4 and 1 is -3, and the difference between 1 and 4 is positive 3.
It is not D, because the difference between 2 and -2 is -4, and the difference between -2 and 2 is positive 4.
And it is B because the numbers maintain a constant difference between each other, which is -3.
Answer:
B
Step-by-step explanation:
An arithmetic sequence has a common difference (d) between consecutive terms.
The only sequence with a common difference is B
1 = 4 = - 3
- 2 - 1 = - 3
- 5 - (- 2) = - 5 + 2 = - 3
What is the sum of 4ft 4 in and 1 ft 11in
Answer:
6ft 3in
Step-by-step explanation:
4ft + 1ft = 5ft
4in +11in= 15in
15in =1ft and 3in
5ft+ 1ft 3in= 6ft 3in
Solve the following equation for x: 2x + 5y = 8.
Answer:
x = -5/2 y +4
Step-by-step explanation:
2x+5y = 8
Subtract 5y from each side
2x+5y -5y = -5y+8
2x = -5y+8
Divide each side by 2
2x/2 = -5y/2 +8/2
x = -5/2 y +4
Find the volume of the solid generated when the region bounded by y= x and y= 4√x is revolved about the x-axis
The volume of the solid is:
(Type an exact answer
cubic units)
Check the picture below, that enclosed area is pretty much our "washer".
now, to get the outer radius, or "farther" radius from the axis of rotation, what I usually do is, use the f(x) - g(x) to get the area under the curve, using the axis of rotation for g(x).
[tex]\bf \stackrel{\textit{top, f(x)}}{4\sqrt{x}}~~-~~\stackrel{\textit{bottom, g(x)}}{(0)}\implies \stackrel{\textit{farthest radius}}{4\sqrt{x}-0\implies 4\sqrt{x}} \\\\\\ \stackrel{\textit{top, f(x)}}{x}~~-~~\stackrel{\textit{bottom, g(x)}}{(0)}\implies \stackrel{\textit{closest radius}}{x-0\implies x} \\\\[-0.35em] ~\dotfill\\\\ 4\sqrt{x}=x\implies \stackrel{\textit{squaring both sides}}{16x=x^2\implies }16x-x^2=0[/tex]
[tex]\bf x(16-x)=0\implies x= \begin{cases} 0\\ 16 \end{cases}\qquad \qquad \impliedby \textit{these are the bounds} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int\limits_{0}^{16}~\pi [(4\sqrt{x})^2-(x)^2]dx\implies \pi \int\limits_{0}^{16}[16x-x^2]dx\implies \pi \int\limits_{0}^{16}16x~~-~~\pi \int\limits_{0}^{16}x^2[/tex]
[tex]\bf \pi \left. 16\cdot \cfrac{x^2}{2} \right]_{0}^{16}-\left. \cfrac{\pi x^3}{3} \right]_{0}^{16}\implies \left. \pi 8x^2 \cfrac{}{}\right]_{0}^{16}-\left. \cfrac{\pi x^3}{3} \right]_{0}^{16} \\\\\\ \left( \pi [2048]-\pi [0] \right)-\left(\left[ \cfrac{4096\pi }{3} \right]-[0] \right)\implies 2048\pi -\cfrac{4096\pi }{3} \implies \cfrac{2048\pi }{3}[/tex]
Which scatterplots display an example of a cluster ? Check all that apply
Answer:
1st and 3rd options
Step-by-step explanation:
We have been given three scatter plots. We are asked to choose the plots with cluster.
We know that cluster in a dot plot is formed when many data points lie in a small interval.
We can see that graphs represented by 1st option and 3rd option have many data points in a small interval, therefore, 1st and 3rd options are correct choice.
Answer:
Step-by-step explanation:
What is the volume of the sphere shown below with a radius of 6
Answer:
[tex]\large\boxed{V=288\pi}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{W have the radius}\ R=6.\ \text{Substitute:}\\\\V=\dfrac{4}{3}\pi(6^3)=\dfrac{4}{3}\pi(216)=4\pi(72)=288\pi[/tex]
The midpoint M of CD has coordinates (6, 6). Point D has coordinates (10, 4). Find the coordinates of point C.
Write the coordinates as decimals or integers.
Final answer:
To find the coordinates of point C when given the midpoint M and point D, we find the average of the endpoints' coordinates. Solving the equations, we find that the coordinates of point C are (2, 8).
Explanation:
The student is asking to find the coordinates of point C given that the midpoint M of line segment CD is at (6, 6), and point D is at (10, 4). To find point C, we use the concept that the midpoint's coordinates are the average of the coordinates of the endpoints of the segment. That means:
The x-coordinate of C can be found by the equation 6 = (xC + 10) / 2 which leads to xC = 2(6) - 10,
The y-coordinate of C can be found by the equation 6 = (yC + 4) / 2 which leads to yC = 2(6) - 4.
Solving for xC and yC, we find:
xC = 12 - 10 = 2,
yC = 12 - 4 = 8.
Therefore, the coordinates of point C are (2, 8).
Which is 6 3/4 (2/9) simplified?
Answer:
3/2
Step-by-step explanation:
6 3/4 (2/9)
(27/4)(2/9)
4 divided by 2 is 2.
27 divided by 9 is 3.
Answer: 3/2