Answer:
He has 110
Step-by-step explanation:
5x20 = 100
100 + 10 = 110
The real solutions to the equation 3x5 + 25x4 + 26x3 – 82x2 + 76x = 48 are shown on the graph. What are the nonreal solutions? StartFraction 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus i StartRoot 5 EndRoot Over 3 EndFraction. StartFraction negative 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus i StartRoot 5 EndRoot Over 3 EndFraction. StartFraction negative 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus StartRoot 5 EndRoot Over 3 EndFraction. StartFraction 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
Using the Factor Theorem, the non-real solutions are given as follows:
[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
For this problem, the function is:
f(x) = 3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48.
The function can be written as:
f(x) = g(x)h(x).
In which:
g(x) is the polynomial with the real solutions.h(x) is the polynomial with the non-real solutions.Using a calculator, as the graph is not given, the real solutions are given as follows:
[tex]x_1 = -6, x_2 = -4, x_3 = 1[/tex]
Hence:
g(x) = (x + 6)(x + 4)(x - 1)
g(x) = (x² + 10x + 24)(x - 1)
g(x) = x³ + 9x² + 14x - 24.
f(x) is of degree 5, g(x) of degree 3, hence h(x) is of degree 2 and:
f(x) = g(x)h(x)
3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48 = (x³ + 9x² + 14x - 24)(ax² + bx + c)
Hence:
ax^5 = 3^5 -> a = 3.-24c = -48 -> c = 2.-24bx + 14cx = 76x
-24b + 28 = 76
-24b = 48
b = -2.
Then the equation with the non-real solutions is:
h(x) = 3x² - 2x + 2.
Which is a quadratic equation with coefficients a = 3, b = -2 and c = 2, thus:
[tex]\Delta = b^2 - 4ac = (-2)^2 - 4(3)(2) = -20[/tex][tex]x_1 = \frac{2 + \sqrt{-20}}{6} = \frac{2 + 2\sqrt{5}i}{6} = \frac{1 + \sqrt{5}i}{3}[/tex][tex]x_2 = \frac{2 - \sqrt{-20}}{6} = \frac{2 - 2\sqrt{5}i}{6} = \frac{1 - \sqrt{5}i}{3}[/tex]Hence the non-real solutions are:
[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]
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A recipe for oatmeal cookies calls for 5 cups of flour for every 8 cups of oatmeal. How much flour is needed for a big batch of cookies that used 16 cups of oatmeal?
Answer:
10 cups
Step-by-step explanation:
Since 16 cups is twice 8 cups, it needs twice 5 cups of flour which is 10 cups.
We can also use a proportion.
5/8 = x/16
8x = 5 × 16
x = 5 × 2
x = 10
Answer: 10 cups
write the function whose graph is the graph of y=x^2 but is translated 9 units to thre left
Answer:
y= (x+9)^2
Step-by-step explanation:
If h<0 ( negative) then it shifts to the right, if it is is h>0 ( positive number) then it shift to the left!
y = x2
Shift 2 units left: y = (x+2)2
Then, shift up 9 units: y = (x+2)2 + 9
Then, reflect in the x-axis: y = -(x+2)2 - 9
Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below.
f(-2) = ? f(2) = ?
The domain is ___. (use interval notation)
From the graph of the function, we have that:
a) The domain is all real values.
b) The range is y ≤ 4.
c) The x-intercepts are x = -4 and x = 1.
d) The y-intercept is y = 3.
e) f(-2) = 3, f(2) = -5.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, the domain is composed by the values of x.The range of a function is the set that contains all the values of the output. In a graph, the domain is composed by the values of y.Hence, for this problem:
a) The domain is all real values.
b) The range is y ≤ 4.
What are the intercepts of a function?The x-intercepts of a function are the values of x when f(x) = 0, that is, the values of x for which the function crosses the x-axis.The y-intercept of a function is the values of f(x) when x = 0, that is, the value of y for which the function crosses the y-axis.Hence:
c) The x-intercepts are x = -4 and x = 1.
d) The y-intercept is y = 3.
What are the numeric values?For the graph, when x = -2 y = 3 and when x = 2 y = -5, hence:
f(-2) = 3, f(2) = -5.
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(4x+2)+(x-2) can someone tell me its procedure
[tex] \green\star\:{\underline{\underline{\sf{\orange{Answer:}}}}}[/tex]
¡Hello :D!
To solve the similar terms we must eliminate the parentheses and then put the parentheses back but this time it would be like this: (4 x + x) + ( 2 - 2)
Once we have done that we must restore the ones on the right side which gives us the result of 1 then as we see that there is + in the Parenthesis and another + outside the Parenthesis we do not care + since we are using the law of signs .
We proceed to solve:
[tex]\: \: \: \: \: \: \bold \: \bold \: \bold \: ( \bf4x+2)+(x-2)[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \bf \bold4x + 2 + x - 2[/tex]
[tex] \: \: \: \: \: \: \: \: \bf\tt( \bf4x + x) + (2 - 2)[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf5x[/tex]
So the result is 5x
I hope I've helped XD
Just 16 and 17 please!
Answer:
1(7-6)1/6
Step-by-step explanation:
Round 67536 to the nearest hundred
Answer:
67,500
Step-by-step explanation:
i think this is the answer.
Answer: 67500
This is because 536 is closer to 500 than it is to 600
The Taj Mahal is an enormous ivory-white marble monument in India that is known for
its architecture. More than 2 x 104 workers were involved in building the Taj Mahal.
Which number shows another way to express 2 x 10¹?
Answer:the iconic Indian building named Taj Mahal
Step-by-step explanation:
On a map , 1 inch represents 50 miles. You measure the distance on the map between two towns as 3 1 2 inches. How many miles apart are the towns?
The towns are 15600 miles apart.
WHAT IS MAP SCALE ?The term "map scale" refers to the proportion between a distance on a map and its corresponding distance on the ground. Lets see an example like, On a map with a scale of 1:100,000, one kilometer on the ground is equivalent to one centimeter. The scale of a map refers to the proportion between a distance on a map and its actual distance on the ground. This simple concept is complicated by the fact that scale must vary across a map due to the curvature of the Earth's surface. The concept of size is now important in two different ways as a result of this development.
The size of the producing globe is compared to the size of the Earth in the first technique. a theoretical globe known as the generating globe, upon which the map is projected and the Earth is compressed. The ratio of the size of the Earth to that of the generating globe is known as the nominal scale, also known as the major scale or representative fraction.
CALCULATION∵ 1 inch = 50 miles on the map
∴ 312 inches = 312 * 50 = 15600 miles .
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Given 4x=12x+22 prove x=-4
the required simplified value of given expression 4x = 12x + 32 is x = -4 (hence proved).
Given that,
An expression is given 4x = 12x + 32,
We have to prove x = -4 as of simplified solution.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
4x = 12x + 32
Taking 12x to the left side of the equal sign and it becomes -12x
4x - 12x = 32
Applying subtraction property between 4x and 12
- 8x = 32
Dividing both sides by -6
x = -4
Thus, the required simplified value of the given expression is x = -4 (hence proved).
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Candace bought a laptop for x dollars. She decided to sell it, after adding an $875 markup amount to the original price. If the markup rate used was 20%, then how much did she originally purchase the laptop for? Round your answer to the nearest dollar.
The original amount for the laptop that Candace bought when the markup rate is 20% will be $4375.
How to calculate the value?It should be noted that she added 875 markup amount to the original price and the markup rate used was 20%,
Therefore, 20% of x = 865
0.2x = 875
Divide
x = 875 / 0.2
x = 4375
Therefore, the original amount for the laptop is $4375.
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Pie/Circle Graph: As a wildlife biologist, one of your duties is to catch, tag, and
release different species of mammals found in Oak Mountain, Alabama. Use
the data provided below to determine the percentage of each mammal
species caught and then label the different sections found in the pie graph
provided. During a 24 hour period, six cotton mice were caught, nine Norway
rats, 17 pine voles, and two eastern chipmunks.
Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21% were taken in a 24-hour period from the pie chart.
Given that,
In the figure there is a chart pie chart with 4 parts and 4 colors.
Six cotton mice, nine Norway rats, 17 pine voles, and two eastern chipmunks were taken in a 24-hour period.
We have to find by use the information below to calculate the percentage of each species of captured mammal, and then use that information to name the various pie-shaped sections.
Each value must be converted into a circle's angle for the pie chart.
Total=6+9+17+2=34
Cotton mice=(6/34)×360°=64°
Norway rats=(9/34)×360°=95°
Pine voles=(17/34)×360°=180°
Eastern chipmunks=(2/34)×360°=21°
Therefore, Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21%.
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7 divide 161 step by step
this is what you need?if yes than look and write
Determine whether the given situation is best described by a linear model or an exponential model. What function models the situation?
The population of rabbits in a forest is tripling every month.
At 0 months (the starting point) there was only one rabbit.
The model that best described the statement is an exponential model and the function that models the situation is A(t) = 4^t
How to determine whether the given situation is best described by a linear model or an exponential model.The statement is given as:
The population of rabbits in a forest is tripling every month.At 0 months (the starting point) there was only one rabbit.The above statement is a population function
Population functions are best represented by an exponential function
Hence, the model that best described the statement is an exponential model.
What function models the situation?Here, we have
Initial value, a = 1
Rate, r = 3
The function is represented as
A(t) = A * (1 + r)^t
So, we have
A(t) = 1 * (1+3)^t
Evaluate
A(t) = 4^t
Hence, the function that models the situation is A(t) = 4^t
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Convert the polar equation to rectangular form and identify the graph. Support your answer by sketching the graph. Show and explain your work.
The polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).
How to transform a polar expression into its rectangular formPolar and rectangular forms are related by this relation: (x, y) → (r · cos θ, r · sin θ), where r is the radial distance with respect to the origin and θ is the angle in standard position. We can use this fact to change the given expression into its rectangular form:
r = - 4 · (x / r)
r² = - 4 · x
x² + y² = - 4 · x
y² = - (x² + 4 · x)
y² - 4 = - (x² + 4 · x + 4)
y² - 4 = - (x + 2)²
(x + 2)² + y² = 4
(x + 2)² + y² = 2²
In a nutshell, the polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).
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Select all the correct answers.
If a figure is a square, its diagonals divide it into isosceles triangles.
p: A figure is a square.
q: A figure's diagonals divide into isosceles triangles.
Which represents the converse of this statement? Is the converse true?
0
0
0
The converse of the statement is sometimes true and sometimes false.
q+p
The converse of the statement is false.
The converse of the statement is true.
9-P
P-9
O ~p~9
Answer:
q arrow p, and p arrow q
Step-by-step explanation:
edmentum
Create a formula for a function f (x) that has f (9 )= 10. Do not give a simple constant function (like f (x) = 10 ) as your answer.
f(x)=x+1 is a formula for a function f(x) that has f(9)=10
What is a simple definition for function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
a constant function is a function whose (output) value is the same for every input value. For example, the function y(x) = 10 is a constant function because the value of y(x) is 10 regardless of the input value x
if we take f(x)= x+1
then put x=9 we get f(9)= 10
Hence , f(x)=x+1 is a formula for a function f(x) that has f(9)=10
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One number is six less than three times another number. If the sum of the numbers is 38, find the numbers
Answer:
consider the two number as x and y
first given condition
x-6 = 3y
i.e. x= 3y + 6 eqn 1
second given condition
x+ y = 38
i.e. x= 38-y eqn 2
solving eqn 1 and 2
3y + 6 = 38-y
3y + y = 38-6
4y = 32
y = 8
substituting the value of y in eqn 2
x = 38 - y
x= 38-8
x= 30
hence the required numbers are 8 and 30
Determine whether the relation is a function. Explain. x y 4 –5 –1 –10 0 –9 1 –7 9 1 Multiple choice question. cross out A) Yes; for each element of the domain, there is only one element of the range. cross out B) Yes; for each element of the range, there is only one element of the domain. cross out C) No; the element 1 is in both the domain and the range. cross out D) No; for each element of the domain, there is not only one element of the range.
It is not a function because: C) the element 1 is in both the domain and the range.
What makes a Relation a Function?A relation can be defined as a function if each of the domain values each has exactly one corresponding range value. This means that an element of the domain must not have two different elements from the range that it is related or corresponded to.
In the given function, 1 as an element of the domain is related to two different range elements, 10 and 7. This doesn't satisfy a function property.
Therefore, we can state that: it is not a function because: C) the element 1 is in both the domain and the range.
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[(10-9+8)-7] + [6-((5+4] ÷ 3)] ² - 1
Answer:
10
Step-by-step explanation:
1 Simplify 10-910−9 to 11.
1+8-7+{(6-(5+4)\div 3)}^{2}-1
1+8−7+(6−(5+4)÷3)
2
−1
2 Simplify 5+45+4 to 99.
1+8-7+{(6-9\div 3)}^{2}-1
1+8−7+(6−9÷3)
2
−1
3 Simplify 9\div 39÷3 to 33.
1+8-7+{(6-3)}^{2}-1
1+8−7+(6−3)
2
−1
4 Simplify 6-36−3 to 33.
1+8-7+{3}^{2}-1
1+8−7+3
2
−1
5 Simplify {3}^{2}3
2
to 99.
1+8-7+9-1
1+8−7+9−1
6 Simplify 1+81+8 to 99.
9-7+9-1
9−7+9−1
7 Simplify 9-79−7 to 22.
2+9-1
2+9−1
8 Simplify 2+92+9 to 1111.
11-1
11−1
9 Simplify.
10
Find each sum 5/7+1/2
Answer: 17/14 or 1 3/14 simplified
Step-by-step explanation:
14 is the least common multiple of denominators 7 and 2. Use it to convert to equivalent fractions with this common denominator.
Need help with this asap
Answer: x=21, y=8
Step-by-step explanation:
18y+5=10x-61 ==> 18y+5 and 10x-61 are congruent angle, so they're equal
x+10+10x-61=180 ==> x+10 and 10x-61 are supplementary angles since they're on a straight line(a straight line measures 180 degrees and is called a straight angle), so they add up to 180 degrees.
x+10x+10-61=180
11x-51=180
11x=231
x=21
18y+5=10(21)-61
18y+5=210-61
18y+5=149
18y=144
y=8
6x + 4y = 36 when x = 3 and y = 4
Answer:
No solution.
Explanation:
Given expression:
6x + 4y = 36when x = 3, y = 4
Substitute these values inside expression:
6(3) + 4(4) = 36
18 + 16 = 36
34 = 36
As the statement "34 = 36" not true. The solution is false or no solution.
Answer:
The given values are wrong.
Step-by-step explanation:
Given information,
→ x = 3
→ y = 4
Solving the given equation,
→ 6x + 4y = 36
→ (6 × 3) + (4 × 4) = 36
→ 18 + 16 = 36
→ 34 ≠ 36
Hence, there is no solution.
find the median 2.5,2.3,2.3,1.8,2.3,1.5
Answer:2.1
Step-by-step explanation:
i added them then divided by 7
K
Monica's car will go 455 miles on 17.5 gallons of gasoline in highway driving.
a) How many gallons will it take to drive 2629 miles from her house to a friend's house?
b) How far can the car be driven on 139 gallons of gasoline?
***
Which graph is a parabola?
Step-by-step explanation:
THE THIRD GRAPH IS THE PARABOLA!
HOPE THIS HELPS!
solve for y -2(x + 3y) = 18
Answer:
[tex] \sf\large \: y = \frac{ - 1}{3} x - 3[/tex]
Step-by-step explanation:
Let's solve for y.
−2(x+3y)=18
Step 1: Add 2x to both sides.
−2x−6y+2x=18+2x
−6y=2x+18
Step 2: Divide both sides by -6.
−6y/−6 = 2x+18/−6
y= −1/3x−3
The width of a rectangle measures (10p - 9p) centimeters, and it’s length measures (7p + 8p) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
c
Step-by-step explanation:
Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms
The correct option is b. -30x + 32 = 182.
After combining the like terms, the equation that represents -8x + 23 - 22x + 9 = 182 is -30x + 32 = 182, where x = -5.
What is defined as equation?In its most basic form, an equation is a statement that demonstrates that 2 mathematical expressions have been equal.
3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are 2 expressions separated by a 'equal' sign.An equation is a formula in mathematics that conveys the equality of two expressions by linking them with the equal sign =.Now, as per the given question;
The stated equation in the question is is,
-8x + 23 – 22x + 9 = 182
Considering like terms together;
-8x – 22x + 23 + 9 = 182
Further simplifying;
– 30x + 32 = 182
Subtracting 32 from the both sides.
– 30x + 32 - 32 = 182 - 32
On solving;
– 30x = 150
⇒ x = -5
Therefore, the expression which defined the equation after taking alike terms is -30x + 32 = 182 for which the value of 'x' comes to be -5.
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The complete question is;
Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms?
-8x + 23 – 22x + 9 = 182
a. 14x + 32 = 182
b. -30x + 32 = 182
c. 14x + 14 = 182
d. -30x + 14 = 182
can anyone write out step-by-step directions and end up with the solution for this equation
2(3b - 2) = 2(2b + 12)
One way to solve is to follow these steps
2(3b - 2) = 2(2b + 12)
2*3b - 2*2 = 2*2b + 2*12
6b - 4 = 4b + 24
6b-4b = 24+4
2b = 28
b = 28/2
b = 14
Final answer: b = 14