Answer:
x = 15
Step-by-step explanation:
Step 1: Distribute
3x - 5(x) - 5(2) = -40
3x - 5x - 10 = -40
Step 2: Combine like terms
-2x - 10 = -40
Step 3: Add 10 to both sides
-2x - 10 + 10 = -40 + 10
Step 4: Divide both side by -2
-2x / -2 = -30 / -2
x = 15
First: State the degree and tell which monomial (term) you determined to be the one as the greatest degree. Second: Classify each of the 2 polynomials. If it is NOT a polynomial, explain why you think it is not a polynomial. For example you may say: Polynomial # 4. has degree of 5 and is classified as a quintic polynomial of 4 terms. We covered this in class (see below). Explain in sentences how you determined degree and "name" or why it is NOT a polynomial: 1. 7x4 + 5x2 + x − 92. 7x6 − 4x3 + 1x
Step-by-step explanation:
The relationship between monomial, degree and polynomial
A monomial is basically an individual term. A polynomial is the sum of monomials. Any monomial (term) which contains the highest power of the variable would be considered as the degree of a polynomial. For example, [tex]2x^{2} + 3x + 1[/tex] is a polynomial of degree 3, as the first monomial (term) has the highest power (degree) of the variable x.Now, lets analyze the given algebraic expressions
Examining the first polynomial
Considering the first polynomial
[tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex]
Carefully notice that the first term [tex]7x^{4}[/tex] which is also called a monomial does have the highest exponent or power of a variable x, which is 4. Thus, it can be determined that the degree of [tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex] will be 4.Here is the summary of the classification of the first polynomial [tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex].
[tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex] is a polynomial of 4 terms.Its degree is 4.It can also be named as 'quintic' because its degree is 4Examining the second polynomial
Considering the expression
[tex]7x^6\:-\:4x^3\:+\:1/x[/tex]
It is easy to figure out that [tex]7x^6\:-\:4x^3\:+\:1/x[/tex] is not a polynomial as it does not fulfill the criteria to be a polynomial as its last term is [tex]\frac{1}{x}[/tex] has the variable x in the denominator.
Here are some important things that need to be fulfilled for any expression to be a polynomial.
The polynomial can not contain any variable having fractional or negative powers. For example, any expression containing [tex]2v^{-5}[/tex] in any of its terms can not be a polynomial as the variable v has a negative power of exponent. Similarly, the polynomial can not contain any square root of variables. For example, any algebraic expression with the term [tex]2\sqrt{v}[/tex] can not be a polynomial as the variable v is right inside the radical symbol.The polynomial can not have any variable in the denominator. For example, any expression that contains the term [tex]\frac{7}{v}[/tex] would not be treated as the polynomial as the variable v is in the denominator.Therefore, from the above discussion we can safely say that the expression [tex]7x^6\:-\:4x^3\:+\:1/x[/tex] can not be treated as as a Polynomial as its last term [tex]\frac{1}{x}[/tex] contains the variable x which is in the denominator.
Keywords: matrimonial, polynomial, exponent, degree
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Express the product in simplest form.
8/2x+8*x^2-16/4
A. (x + 4)
B. 2(x − 4)
C. (x − 4)
D. (x + 4)(x − 4)
The product in simplest form is (x - 4)
Solution:
Given expression is:
[tex]\frac{8}{2x+8} \times \frac{x^2-16}{4}[/tex]
We have to find the product in simplest form
In the given expression,
2x + 8 = 2(x+ 4)
We know that,
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Therefore,
[tex]x^2-16 = x^2-4^2 =(x+4)(x-4)[/tex]
Substitute these in given expression
[tex]\frac{8}{2(x+4)} \times \frac{(x+4)(x-4)}{4}[/tex]
Cancel the common factors,
[tex]\frac{8}{2(x+4)} \times \frac{(x+4)(x-4)}{4} = x - 4[/tex]
Thus the product in simplest form is (x - 4)
the cost of producing x laser printers is given by C(x)=325x + 2,300,000. Each printer can be sold for $450
Answer:
C(450)=2,446,250
Step-by-step explanation:
C(450)=325(450)+ 2,300,000
C(450)=146,250+2,300,000
C(450)=2,446,250
The profit from producing and selling x laser printers is given by the equation P(x) = 125x - 2300000.
Explanation:The question is about the calculation of profit in a business scenario. The calculation of profit involves finding the difference between the cost of production and the revenue obtained from selling the products. In this case, the cost function C(x) = 325x + 2300000 defines the cost of producing x laser printers. Each printer is sold for $450, which means the revenue function R(x) can be represented as R(x) = 450x.
To find the profit, we subtract the cost from the revenue. This gives us the profit function P(x) = R(x) - C(x) = 450x - (325x + 2300000). Simplifying this, we get P(x) = 125x - 2300000. This equation tells us the profit made from producing and selling x laser printers.
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When D is divided by 15, the result is 6 with a remainder of 2.what is the remainder when D is divided by 6?
When number D (which is 92) is divided by 6, the remainder is 2.
Explanation:Based on the information given, when D is divided by 15, the result is 6 with a remainder of 2, so we can express D as 15*6 + 2 = 92. Now let's find out what happens when D (92) is divided by 6. When we do, we find that 92 divided by 6 gives us 15 with remainder 2. So, the remainder when D is divided by 6 is 2.
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What is the solution set of the quadratic inequality 6x2+1 <0?
o {x|x€ R}
Answer:
In my opinion i think ur answer would be: B
Jeff bought a bottle of water for $2. He also
bought some hot dogs for $3 each. Jeff did
not spend more than $14 on the hot dogs
and the bottle of water. Write an inequality
statement that can be used to find h, the
number of hot dogs that Jeff could have
bought.
Final answer:
The inequality to determine the number of hot dogs Jeff could have bought is 3h + 2 ≤ 14, representing the cost of hot dogs and the bottle of water not exceeding the total amount of $14.
Explanation:
To find h, the number of hot dogs that Jeff could have bought, we can write an inequality statement based on the maximum amount Jeff can spend and the cost of the hot dogs and water. Jeff bought one bottle of water for $2 and some hot dogs for $3 each. Given that he did not spend more than $14 on everything, the inequality to represent this scenario can be written as:
Cost of water + Cost of hot dogs ≤ Total amount Jeff can spend
2 + 3h ≤ 14
This inequality suggests that when we multiply the number of hot dogs Jeff bought (h) by $3 and add the cost of the water ($2), it should not exceed $14. So the inequality demonstrating the number of hot dogs Jeff could have bought without spending more than $14, including the water, is 3h + 2 ≤ 14.
what is 7/21 in simplest form
Answer:
1/3
Step-by-step explanation:
simplifying fractions can be easy.
In this case you just need to find a common number.
The common number between 7 & 21 just happens to be 7.
7 goes into 7 one time.
7 goes into 21 three times.
Therefore the answer is 1/3.
I hope this was helpful!
About 42% of a paint mix is white. A painter orders 18 gallons of paint mix. How much of it is white
Answer:
7.56 liters
Step-by-step explanation:
Total amount of paint mix ordered by the painter = 18 gallons
42% of the paint mix is white.
Representing this as a fraction, [tex]\[\frac{42}{100}\] [/tex] of total paint mix is white.
To find the amount of white paint, we need to multiply this fraction with the total amount of paint mix.
[tex]\[= \frac{42}{100} * 18\] [/tex]
[tex]\[= \frac{756}{100}\] [/tex]
[tex]7.56 liters[/tex]
I need help finding the values of x and z
Answer:
z = 73
x = 15
Step-by-step explanation:
Since z and (5x +32) share a straight line, adding them would equal 180.
(5x+32) + z = 180
Since z is 73, we can replace z
(5x + 32) + 73 = 180
(5x + 32) = 107
(5x) = 75
x = 15
What is the output, or dependent variable or
quantity?
X
f(x)
Y
Answer:
y or f(x), depends on the context.
Step-by-step explanation:
When graphing a function, we input a value, x, and output a value, y. This is why we have a coordinate plane.
For example, if we have y = 2x and x=2, our input, then y = 4, our output.
However, if written in function notation, f(x) = 2x, our output will still be 4, except that our output is f(x)
Answer:
f(x)
Step-by-step explanation:
1. Annual sales for a fast food restaurant are $650.000 and are increasing at a rate of 4% per year.
Use an exponential function to find the annual sales after 7 years.
Help pls
The annual sales after 7 years is $ 855.3556
Solution:
The growth function is given as:
[tex]y = a(1+r)^t[/tex]
Where,
y is the future value
a is the initial value
r is the growth rate
t is the number of years
From given,
a = 650
t = 7
[tex]r = 4 \% = \frac{4}{100} = 0.04[/tex]
Therefore,
[tex]y = 650(1 + 0.04)^7\\\\y = 650(1.04)^7\\\\y = 650 \times 1.315931\\\\y = 855.3556[/tex]
Thus the annual sales after 7 years is $ 855.3556
[Image Attached] Which equation is equivalent to 4^x+3=64
Answer: 2^2x+6 = 2^6
Explanation:
looking at the right of the equal since we can see:
64 is the same as 4^3
but since that answer isn't shown in the multiple choice but we can notice that 64 is the same as 2^6
Now that we know the left side is 2^6 we can see there is similar an answer in the multiple choice. But let's double check that the right side is the same.
Its pretty simple, just make 4 into 2^2 then distribute the exponent of 2 (times the 2 in the exponent to the rest to x+3)
2^2(x+3)
2^2x+6
Answer:
Option B
Step-by-step explanation:
The other guy is correct I'm just making it simpler on edge people. :>
What is the difference of the polynomials?
(8r⁶s³-9r⁵s⁴+3r⁴s⁵)-(2r⁴s⁵-5r³s⁶-4r⁵s⁴)
Answer:
8r⁶s³ - 5r⁵s⁴ + r⁴s⁵ + 5r³s⁶
Step-by-step explanation:
(8r⁶s³-9r⁵s⁴+3r⁴s⁵)-(2r⁴s⁵-5r³s⁶-4r⁵s⁴)
We need to combine like terms, take care the exponents of r and s
(8r⁶s³-9r⁵s⁴+3r⁴s⁵)-(2r⁴s⁵-5r³s⁶-4r⁵s⁴)
multiply the second parenthesis by -1
= 8r⁶s³-9r⁵s⁴+3r⁴s⁵-2r⁴s⁵+5r³s⁶+4r⁵s⁴
= 8r⁶s³ + (-9r⁵s⁴ + 4r⁵s⁴) + (3r⁴s⁵-2r⁴s⁵) + 5r³s⁶
= 8r⁶s³ - 5r⁵s⁴ + r⁴s⁵ + 5r³s⁶
Note: r⁶s³ is not like r³s⁶
Which of the following fractions is not equivalent to the others 24/36 8/12 12/16 4/6
Answer:
12/16
Step-by-step explanation:
because he 6 in 4/6 cant go into 16 and 16 from 12/16 c 36 so that is why the answer is 12/16
After simplifying each fraction to its lowest terms, it's clear that 12/16, which simplifies to 3/4, is not equivalent to the others since they all simplify to 2/3.
The question asks which of the following fractions is not equivalent to the others: 24/36, 8/12, 12/16, 4/6. To determine this, we need to simplify these fractions to their lowest terms.
24/36 simplifies to 2/3, by dividing both numerator and denominator by 12.
8/12 simplifies to 2/3, by dividing both numerator and denominator by 4.
12/16 simplifies to 3/4, by dividing both numerator and denominator by 4.
4/6 simplifies to 2/3, by dividing both numerator and denominator by 2.
Therefore, the fraction 12/16 is not equivalent to the others since it simplifies to 3/4, while the others simplify to 2/3.
Mick the monkey had 10 bananas he ate two fifth of them Mikey the monkey also had 10 bananas and he ate half of them which monkey ate more bananas step by step please
Answer: mikey ate more
Step-by-step explanation: mick ate 2/5 which is 4 out of ten mikey ate half which is 5 out of 10 so mikey ate more
brainliest plz
Final answer:
Mikey the monkey ate more bananas than Mick, consuming 5 compared to Mick's 4 bananas.
Explanation:
Let's calculate how many bananas each monkey ate. We'll start with Mick the monkey, who had 10 bananas and ate two fifths of them.
Calculate two fifths of 10 bananas: (2/5) × 10 = 4 bananas.
Mick therefore ate 4 bananas.
Now, let's calculate for Mikey the monkey, who also had 10 bananas and ate half of them.
Calculate half of 10 bananas: (1/2) × 10 = 5 bananas.
Mikey ate 5 bananas.
Mikey the monkey ate more bananas than Mick because 5 is greater than 4.
carrie picked 7 red apples and 7 green apples
Answer:
she has 14 apples altogether
1 3/4 + 1/6 + blank =7 1/2
Answer:
5 7/12
Step-by-step explanation:
7/4 + 1/6 +x = 15/2
Lowest Common denominator =12
21/12 + 2/12 + x = 90/12
23/12 +x= 90/12
x= 90-23 = 67/12 = 5 7/12
what is the solution to this equation x-9=17
Answer:
26
Step-by-step explanation:
you add 17+9 and get 26.
The volume, V, of any cube with a side length, s. can be determined using the forma
V=s^3What is the volume, in cubic centimeters, of a cube with a side length
of 23 centimeters?
The volume of the cube is 12.167cm^3
Volume of a cubeThe formula for calculating the volume of a cube is expressed as:
V = s^3s is the side length of the cube
Given the following
side eof a cube = 2.3cm
Substitute into the formula
V = 2.3^3
V = 12.167cm63
Hence the volume of the cube is 12.167cm^3
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Answer:
dogs
Step-by-step explanation:
first you got a multiply the then you got to multiply the and then multiply me beautiful
find the value of two numbers if their sum is 11 and the difference is 3
Answer:
7
4
Step-by-step explanation:
7+4=11
7-4=3
To find the value of two numbers if their sum is 11 and the difference is 3, we can use a system of equations. The two numbers are 7 and 4.
Explanation:To find the value of two numbers if their sum is 11 and the difference is 3, we can use a system of equations.
Let's call the two numbers x and y. We can set up the following equations:
x + y = 11
x - y = 3
Now we can solve this system of equations by adding the two equations together:
(x + y) + (x - y) = 11 + 3
Simplifying, we get:2x = 14
Dividing both sides by 2, we get:x = 7
Now we can substitute this value of x back into one of the original equations to solve for y:7 + y = 11
Subtracting 7 from both sides, we get:y = 4
So, the two numbers are 7 and 4.
What is d,the common difference,in the arithmetic sequence 100,98,96,94,92...?
Answer: he is right the answer is -2
Step-by-step explanation:
The common difference (d) is -2.
In an arithmetic sequence, the common difference (d) is the constant value by which each term differs from the previous term.
To find the common difference in the sequence 100, 98, 96, 94, 92..., we can observe the difference between consecutive terms:
98 - 100 = -2
96 - 98 = -2
94 - 96 = -2
92 - 94 = -2
We see that each term is decreasing by 2. Therefore, the common difference (d) is -2.
Alex paid $17,520 for a new car.he will make equal payments each month for 4 years. What will be Alex’s monthly car payments?
Answer:
$365.00
Step-by-step explanation:
4 years times 12 months equals 48 months.
$17520.00 / 48=$365.00
The current rates for an 80/20 mortgage are 4.25% for the first mortgage and
9.75% for the second mortgage. On a $100,000 30-year mortgage, what is the
actual rate?
The actual rate of the mortgage is 5.27%.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Since, we're taking two mortgages for a total of $100,000 for 30 years,
Now, we can find the actual rate of the mortgage by finding the weighted average of the two rates.
Hence, The weights in this case will be the proportion of loan taken at each rate;
We have
Rates Weights Rates × Weights
4.15 0.80 4.15 x 0.80 = 3.32
9.75 0.20 9.75 x 0.20 = 1.95
Hence, The actual rate of the mortgage is,
⇒ 3.32 + 1.95
⇒ 5.27%.
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Answer:
mine was 5.45$
Step-by-step explanation:
Which of the following are solutions to the quadratic equation below?
Check all that apply.
X2 + 7x=8
The solutions to quadratic equation are x = 1 and x = -8
Solution:
Given quadratic equation is:
[tex]x^2+7x = 8\\\\x^2 + 7x-8 = 0[/tex]
We have to find the solutions of equation
[tex]\mathrm{Quadratic\:Equation\:Formula:}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{Compare the given } x^2 + 7x - 8 = 0 \text{ with } ax^2 + bx + c = 0\\\\We\ get\\\\a = 1\\\\b = 7\\\\c = -8[/tex]
[tex]x=\frac{-7\pm \sqrt{7^2-4\cdot \:1\left(-8\right)}}{2\cdot \:1}\\\\x =\frac{-7 \pm \sqrt{7^2+4\cdot \:1\cdot \:8}}{2\cdot \:1}\\\\x = \frac{-7 \pm \sqrt{49 + 32}}{2}\\\\Simplify\ the\ equation\\\\x = \frac{-7 \pm \sqrt{81}}{2}\\\\x = \frac{-7 \pm 9}{2}[/tex]
Thus we get two solutions:
[tex]x = \frac{-7+9}{2} \text{ and } x = \frac{-7-9}{2}\\\\x = 1 \text{ and } x = -8[/tex]
Thus the solutions to quadratic equation are x = 1 and x = -8
What geometric shape best describes the sun? triangular prism cube cylinder sphere
Answer:
A sphere.
Step-by-step explanation:
The sun is a sphere.
The best geometric shape to describe the Sun is a sphere, as it appears as a circular disc in the sky and fits with observational data and theoretical models of its structure and the Earth's orbit around it.
Explanation:When considering the geometric shape that best describes the Sun, we assess its physical appearance and symmetry. The Sun is often depicted in diagrams as having a perfectly round, spherical shape, which aligns with our observations, as it appears as a circular disk in the sky. A sphere is a three-dimensional object where every point on the surface is the same distance from the center, which closely matches the Sun's observed shape. Unlike a triangular prism, cube or cylinder, a sphere has no edges, vertices, or faces, which makes it the best match for the Sun's shape.
Moreover, observations about the Sun, like those represented in figures discussing its structure as well as the Earth's orbit around the Sun, support the description of the Sun as being spherical. The orbit of the Earth itself is very close to a circle, which assumes central body - the Sun - of spherical form to exert a uniform gravitational pull. Additionally, the celestial sphere concept, although now known to be an incorrect model for the universe, also envisions stars, including our Sun, as points on a vast imaginary sphere, once more alluding to the spherical structure of these celestial bodies.
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As part of his retirement strategy, John plans to invest $210,000 in two different funds. He projects that the moderately high risk investments should return, over time, about 9% per year, while the low risk investments should return about 4% per year. If he wants a supplemental income of $11,400 a year, how should he divide his investments?
To achieve a supplemental income of $11,400 a year, John should allocate approximately $145,230 to the moderately high-risk investment and approximately $64,770 to the low-risk investment.
Explanation:To divide his investments and achieve a supplemental income of $11,400 a year, John can allocate a portion of his funds to the moderately high-risk investment and the remaining portion to the low-risk investment. Let's calculate the amounts:
Calculate the amount invested in the moderately high-risk investment:Therefore, John should allocate approximately $145,230 to the moderately high-risk investment and approximately $64,770 to the low-risk investment.
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3a + 3b is equivalent to 3(a + 2b).
A true
B false
Answer:
B-false
Step-by-step explanation:
It is false because where the 2 is, has to be 3, other wise it won't make sense. Because it will not equal the same thing.
Final answer:
The expression 3a + 3b is not equivalent to 3(a + 2b). The first results in 3a + 3b, while applying the distributive property to the second expression gives 3a + 6b, clearly showing the expressions are different.
Explanation:
The statement 3a + 3b is equivalent to 3(a + 2b) is false. To show this, we can apply the distributive property of multiplication over addition, which states that for any real numbers a, b, and c, a · (b + c) = a·b + a·c. Using this property, we can expand 3(a + 2b) to get 3·a + 3·2b, which simplifies to 3a + 6b. This is not the same as 3a + 3b since 3b is not equal to 6b. Therefore, the expressions are not equivalent.
what is the surface area of the pyramid in square inches? 17in 15in 16in
Answer:
so its gonna be
Step-by-step explanation:
2=2
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n)=5+(n-1)(1/6)
Answer:
First term: A(1) = 5
Fourth term: A(4) = 5 1/2
Tenth term: A (10) = 6 1/2
Step-by-step explanation:
Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:
A(n) = 5 + (n-1) (1/6)
First term:
A(1) = 5 + (1-1) (1/6)
A(1) = 5 + (0) (1/6)
A(1) = 5
Fourth term:
A(4) = 5 + (4-1) (1/6)
A(4) = 5 + (3) (1/6)
A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)
Tenth term
A(10) = 5 + (10-1) (1/6)
A(10) = 5 + (9) (1/6)
A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)
1. Find the geometric mean of 162 and 8.
46
Step-by-step explanation:
Geometric mean
[tex]= \sqrt{162\times 8}\\
=\sqrt{1296} \\
=36 [/tex]