Answer:
i think its -412 but im not sure
Step-by-step explanation:
The value obtained by using the remainder theorem for the the f(x)=2x5−3x4−9x3+8x2+2 at x=−3 will be 2x⁴-9x³+18x²-46x+138-(412)/(x+3).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that,use the Remainder Theorem to evaluate f(x)=2x5−3x4−9x3+8x2+2 at x=−3
A method for Euclidean polynomial division is the remainder theorem. This theorem states that if we divide a polynomial, P(x), by a factor, (x - a), which isn't really an element of the polynomial, we get a smaller polynomial and a remainder.
[tex]=\frac{2x^5-3x^4-9x^3+8x^2+2}{\left(x+3\right)} \\\\ =2x^4+\frac{-9x^4-9x^3+8x^2+2}{x+3} \\\\ =2x^4-9x^3+18x^2+\frac{-46x^2+2}{x+3}\\\\ =2x^4-9x^3+18x^2-46x+\frac{138x+2}{x+3} \\\\ =2x^4-9x^3+18x^2-46x+138+\frac{-412}{x+3} \\\\ =2x^4-9x^3+18x^2-46x+138-\frac{412}{x+3}[/tex]
Thus, the value obtained by using the remainder theorem for the the f(x)=2x5−3x4−9x3+8x2+2 at x=−3 will be 2x⁴-9x³+18x²-46x+138-(412)/(x+3).
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What is the equivalent expression for 6(x-7)+50
Answer:
3x+4
Step-by-step explanation:
i need help on 1 & 2
Answer:
1 - Avenue A is perpendicular to South St.
2 - 70°
Step-by-step explanation:
1 - North, Center, and South St. are parallel lines. Therefore Ave A will be perpendicular to the three lines.
2 - Ave B and Center street forms a 70° angle. Since Center and South St. are parallel lines, they have corresponding angles. Therefore, Ave B and South St also form a 70° angle. The same is true for Ave B and North St.
Square root of -4 simplified by using the imaginary number i
Answer:
2i
Step-by-step explanation:
The square root of -4 is equal to 2i.
The square root of -4 can be simplified using the imaginary number i. Since the square root of a negative number is not defined in the set of real numbers, we use i to express it, where i is defined as the square root of -1. Thus, the square root of -4 is calculated as follows:
√-4 = √(-1*4)
= √(-1) * √(4)
= i * 2
= 2i
This result shows that 2i is the simplified form of the square root of -4 using the imaginary number i.
4 friends share 5 medium pizzas equally once a week after school when they study for their math quiz. James wants to know how much pizza he’s eaten this year. If they’ve been meeting for 14 weeks, how much pizza had James eaten while at his study group? Show your work.
Answer:
17 pies and one half pie
Step-by-step explanation:
If a circle has a diameter of 18cm, how long is the circumference?
Answer:
56.52
Step-by-step explanation:
C=3.14 * D
the sum of 4 numbers is 771. the ratio of the first to second number is 2:3. the ratio of the second to third is 5:4. the ratio of the third to the fourth is 5:6. find the value of the second number
Answer:
The second number is 225.
Step-by-step explanation:
Consider the provided information.
Let the first number is x.
Second number
[tex]\dfrac{x}{\text{Second number}} =\dfrac{2}{3}\\\\\text{Second number}=\dfrac{3}{2}x[/tex]
Third number is:
[tex]\dfrac{\text{Second number}}{\text{Third number}} =\dfrac{5}{4}\\\\\text{Third number}=\dfrac{3}{2}x\times\dfrac{4}{5}=\dfrac{6}{5}x[/tex]
Fourth number is:
[tex]\dfrac{\text{Third number}}{\text{Fourth number}} =\dfrac{5}{6}\\\\\text{Fourth number}=\dfrac{6}{5}x\times\dfrac{6}{5}=\dfrac{36}{25}x[/tex]
The sum of 4 numbers is 771.
[tex]x+\dfrac{3}{2}x+\dfrac{6}{5}x+\dfrac{36}{25}x=771[/tex]
[tex]50x+75x+60x+72x=38550[/tex]
[tex]257x=38550\\x=150[/tex]
First number is 150.
[tex]\text{Second number}=\dfrac{3}{2}\times150=225[/tex]
Hence, the second number is 225.
The value of the second number is 165.21.
Step 1: Understand the problem.
We have four numbers whose sum is 771. The ratios between consecutive numbers are given. We need to find the value of the second number.
Step 2: Construct equations using the provided ratios.
Let the four numbers be represented as 2x, 3x, 4x, and 5x respectively (using the smallest common multiple of the ratios).
Step 3: Create an equation using the total of the numbers.
2x + 3x + 4x + 5x = 771
Step 4: Solve for x.
[tex]\(2x + 3x + 4x + 5x = 771\)[/tex]
[tex]\(14x = 771\)[/tex]
[tex]\(x = \frac{771}{14}\)[/tex]
[tex]\(x = 55.07\)[/tex]
Step 5: Find the value of the second number.
The second number is 3x.
[tex]\(3x = 3 \times 55.07 = 165.21\)[/tex]
So, the value of the second number is 165.21.
What is the quotient 212,960\1000
The quotient of 212,960 divided by 1,000 is 212.960, achieved by moving the decimal point to the left by three places, reflecting the three zeros in 1,000.
Explanation:The question asks to find the quotient when 212,960 is divided by 1,000. To find the quotient, you essentially move the decimal point three places to the left. When dividing by powers of 10, each power of 10 represents the number of places you move the decimal to the left. Therefore, 212,960 divided by 1,000 gives us 212.960. This methodology is similar to the examples provided in the reference where dividing by 10, 100, and 1000 shifts the decimal point to the left by one, two, and three places respectively.
Remember that when multiplying or dividing by powers of 10, the decimal point is moved rather than actually performing the multiplication or division action. This is one of the reasons why working with decimals and powers of 10 is simpler compared to other numbers.
5) A stereo speaker in the shape of a triangular pyramid has a height of 6 inches. The area of the base of the speaker is 11 square inches. What is the volume of the speaker in cubic inches?
volume of the speaker= 22 cubic inches
Step-by-step explanation:
The formula to find this question is V= 1/3 BHWHERE H =6 INCHESArea of base = 11 square inchestherefore,v= 1/3 (11) (6)volume of the speaker= 22 cubic inchesSolve each inequality
X + 15 > 3
Answer:
It can be anything
Step-by-step explanation:
It just has to be grater.
What is the translation shown in the following graph?
(x + 3, y - 4)
(x - 3, y + 4)
(x + 4, y - 3)
(x - 4, y + 3)
Answer:
(x - 4, y + 3)
Step-by-step explanation:
This is because when you follow the movement of the individual points you can see that they have moved 3 spaces up which is shown as y + 3, and they have moved 4 spaces to the left which is shown as x - 4
Answer:
The correct answer is: D
Step-by-step explanation:
(x - 4, y + 3)
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please answer both with work,please use a paper and picture, thanks
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thanks
Answer:
a. [tex]$ \frac{\textbf{17}}{\textbf{4}} $[/tex]
b. [tex]$ \frac{\textbf{3}}{\textbf{8}} $[/tex]
Step-by-step explanation:
a. [tex]$ \textbf{3} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{1}\frac{\textbf{1}}{\textbf{4}} $[/tex]
A mixed fraction of the form [tex]$ a\frac{x}{y} = a + \frac{x}{y} $[/tex]
[tex]$ \therefore 3 + 1\frac{1}{4} = 3 + 1 + \frac{1}{4} $[/tex]
[tex]$ = 4 + \frac{1}{4} $[/tex]
[tex]$ = \frac{\textbf{17}}{\textbf{4}} $[/tex]
b. [tex]$ \textbf{2} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{1}\frac{\textbf{5}}{\textbf{8}} $[/tex]
A mixed fraction of the form [tex]$ -c\frac{a}{b} = - c - \frac{a}{b} $[/tex]
[tex]$ \therefore 2 - 1\frac{5}{8} = 2 - 1 - \frac{5}{8} $[/tex]
[tex]$ = 1 - \frac{5}{8} $[/tex]
[tex]$ = \frac{8 - 5}{8} $[/tex]
[tex]$ = \frac{\textbf{3}}{\textbf{8}} $[/tex]
Hence, the answer.
Write the numbers in order from greatest to least.
-5, 1 1⁄5, -5 3⁄4, 5⁄12
Answer:
-5 3/4, -5, 5/12, 1 1/5
Step-by-step explanation:
Negatives are opposite of positives when least to greatest
Which expression could be used to find the volume of the prism shown below?
A rectangular prism with length of 12, height of 10, and width of 4.
(4 times 12) times 10
(4 + 12) times 10
(10 + 4) times 12
(10 + 12) times 4
Answer:
The answer is A
Step-by-step explanation:
The volume is found by [tex]l*w*h[/tex]
Therefore you multiply, 4*12*10
Answer:
The answer is A
Step-by-step explanation:
which question represents a line that passes through (2,-1/2) and has a slope of 3?
Answer:
y=3x-13/2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1/2)=3(x-2)
y+1/2=3x-6
y=3x-6-1/2
y=3x-12/2-1/2
y=3x-13/2
Enter the value for x that makes the equation true
36(x-5)=9x-18
Answer:
x = 6
Step-by-step explanation:
Solve for x:
36 (x - 5) = 9 x - 18
Expand out terms of the left hand side:
36 x - 180 = 9 x - 18
Subtract 9 x from both sides:
(36 x - 9 x) - 180 = (9 x - 9 x) - 18
36 x - 9 x = 27 x:
27 x - 180 = (9 x - 9 x) - 18
9 x - 9 x = 0:
27 x - 180 = -18
Add 180 to both sides:
27 x + (180 - 180) = 180 - 18
180 - 180 = 0:
27 x = 180 - 18
180 - 18 = 162:
27 x = 162
Divide both sides of 27 x = 162 by 27:
(27 x)/27 = 162/27
27/27 = 1:
x = 162/27
The gcd of 162 and 27 is 27, so 162/27 = (27×6)/(27×1) = 27/27×6 = 6:
Answer: x = 6
x+13/2=4 what x equal
Step-by-step explanation:
x+13÷2×2=4×2
x+13=8
x+13-13=8-13
x=8-13
x=-5
Answer:-2.5
Step-by-step explanation:
13/2=6.5. 4-6.5 =-2.5
whats is 38.96×15.7
Solve the system of linear equations by substitution.What is the solution to x=2y+y and 3x+2y=3
Answer: the first one is 3y
Step-by-step explanation:
Go to the website mathpapa , type in the problem and it gives you the answer with steps
A shopper buys cat food in bags 4 lbs. her cat eats 3/4 lb each week. How many weeks does one bag last? Draw a diagram
Answer:
5 weeks
Step-by-step explanation:
2. A sweater costs $35. Find the total cost of the
sweater if the sales tax is 5%.
The total cost of the sweater will be $36.75.
What is Percentage?Percentage is a number or ratio which is a fraction of hundred.
Given,
Cost price of sweater =$35.
Sales tax= 5%.
The total cost of the sweater can be calculated as,
Total cost price = CP of sweater + sales tax
= 35 + (5/35)*100
=$36.75
Hence, The total cost price of sweater would be $36.75.
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A customer at the grocery store purchased 27 apples and an unknown number of bananas. The customer purchased a total of 58 apples and bananas. Write an equation with a variable that represents this situation. Explain your process for determining this equation, then solve for how many bananas the customer purchased.
Answer:
The equation is
(x+27)= 58
Therefore the customer purchased 31 bananas
Step-by-step explanation:
Given , A customer at the grocery store purchased 27 apple and unknown number of bananas. The customer purchased a total of 58 apple and bananas.
Let the number bananas be x
He purchased a total (x+27) apples and bananas.
According to the problem,
(x+27)= 58
⇔x= 58-27
⇔x = 31
Therefore the customer purchased 31 bananas
The perimeter of a rectangular atrium is 104 inches. The length of the atrium is three times the width. Find the length and the width.
Answer:
Length = 39 inches , breadth = 13 inches
Step-by-step explanation:
Given:
The perimeter of a rectangular atrium is 104 inches.
The length of the atrium is three times the width.
Question asked:
The length and the breadth of rectangular atrium = ?
Solution:
Let breadth of rectangular atrium = [tex]x[/tex]
Then, the length of rectangular atrium = [tex]3x[/tex] (given)
Perimeter of rectangle = [tex]2\times(length + breadth)[/tex]
[tex]104 = 2\times( 3x + x )[/tex]
[tex]104 = 2\times 4x[/tex]
[tex]104 = 8x[/tex]
Dividing both side by 8
[tex]13 = x[/tex]
breadth of rectangular atrium = [tex]x[/tex] = 13 inches
length of rectangular atrium = [tex]3x[/tex] = [tex]3 \times13 = 39[/tex] inches
Thus, length and the breadth of rectangular atrium are 39 and 13 inches.
How do u do this with a guess check revise graph?
Answer:
12 inches by 15 inches
Step-by-step explanation:
Let
Width of the painting = x inches, then
Length of the painting [tex]=1\dfrac{1}{4}x[/tex] inches
The area of the painting:
[tex]A=\\ \\=\text{Width}\times \text{Length}=\\ \\=x\times 1\dfrac{1}{4}x=\\ \\=\dfrac{5}{4}x^2\ in^2[/tex]
Hence,
[tex]\dfrac{5}{4}x^2=180\\ \\x^2=\dfrac{4}{5}\times 180=4\times 36=144\\ \\x=12\ inches\\ \\\text{Width}=12\ inches\\ \\\text{Length}=\dfrac{5}{4}\times 12=15\ inches[/tex]
Name the property the equation illustrates.
(ab)3 = a (63)
Accociative Property of addition
Name the property the equation illustrates
(ab)3 = a(b3)
A. Commutative property of addition
B. Associative property of Multiplication
C. Associative Property of Addition
D. Inverse Property of Multiplication
Answer:Associative property of Multiplication
Solution:From given equation
(ab)3 = a(b3)
We have to find the property used here
We find the brackets are interchanged
So here, given is a multiplication equation
Therefore, Associative property of Multiplication is used
Associative property of Multiplication:This property says that when we are multiplying it does not matter where you put the parenthesis
The result will be same wherever we put the parenthesis in multiplying two or more numbers
Which means,
[tex]a \times (b \times c) = (a \times b) \times c[/tex]
Therefore, from given,
[tex]a \times (b \times 3) = (a \times b) \times 3[/tex]
Thus associative property of multiplication is used
What is the answer to
10x+4=6x+9
Answer:
x = 5/4 or 1.25.
Step-by-step explanation:
10x + 4 = 6x + 9
10x - 6x = 9 - 4
4x = 5
x = 5/4.
Answer: x = 5/4 or 1.25 or 1 1/4
Step-by-step explanation:
Step 1: Subtract 6x from both sides.
10x+4−6x=6x+9−6x
4x+4=9
Step 2: Subtract 4 from both sides.
4x+4−4=9−4
4x=5
Step 3: Divide both sides by 4.
4x/4 = 5/4
Is 7% sales tax or 1/20 sales tax bigger
Answer: 7%
Step-by-step explanation:
A + 6 equals 3 a - 8
Answer:
7
Step-by-step explanation:
Let's solve your equation step-by-step.
a+6=3a−8
Step 1: Subtract 3a from both sides.
a+6−3a=3a−8−3a
−2a+6=−8
Step 2: Subtract 6 from both sides.
−2a+6−6=−8−6
−2a=−14
Step 3: Divide both sides by -2.
−2a
−2
=
−14
−2
a=7
Answer:
a=7
Mara spent 3/5 of her vacation in British Columbia. While in that province, she spent 1/2 of her time in Vancouver. What fraction of her vacation did Michaela spend in Vancouver? If her vacation lasted 20 days, how many days did she spend in Vancouver?
Answer:
6 days
Step-by-step explanation:
Data given:
Vancouver is in the British Columbia
3/5 of the vacation was spent in British Columbia
1/2 of the time spent in British Columbia was spent in Vancouver.
The whole vacation was 20 days long
total days spent in British Columbia = 3/5 *20
total days spent in British Columbia = 12
Since the 1/2 of the time in British Columbia was spent in Vancouver then
time spent in Vancouver = 1/2 * 12
time spent in Vancouver =6 days
Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver. If her vacation lasted 20 days, she spent 6 days in Vancouver.
Mara spent [tex]\(\frac{3}{10}\)[/tex]of her vacation in British Columbia. While in British Columbia, she spent [tex]\(\frac{1}{2}\)[/tex] of her time in Vancouver.
To find the fraction of her entire vacation that Mara spent in Vancouver, we multiply the two fractions:
[tex]\[ \text{Fraction of vacation in Vancouver} = \frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10} \][/tex]
So, Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver.
Next, to find out how many days she spent in Vancouver, we take the total number of days of her vacation, which is 20 days, and multiply it by the fraction of the vacation spent in Vancouver:
[tex]\[ \text{Days in Vancouver} = 20 \times \frac{3}{10} \][/tex]
[tex]\[ \text{Days in Vancouver} = 6 \][/tex]
Therefore, Mara spent 6 days in Vancouver.
What’s the distributive property of 12(x+5)?
Answer:
12x+60
Step-by-step explanation:
12 gets multiplied with x
12 gets multiplied with 5
Which gives 12x + 60
Given: a ∥ b and ∠1 ≅ ∠3
Prove: e ∥ f
Horizontal and parallel lines e and f are intersected by parallel lines a and b. At the intersection of lines a and e, the bottom left angle is angle 1. At the intersection of lines b and e, the uppercase right angle is angle 2. At the intersection of lines f and b, the bottom left angle is angle 3 and the bottom right angle is angle 4.
We know that angle 1 is congruent to angle 3 and that line a is parallel to line b because they are given. We see that __________ by the alternate exterior angles theorem. Therefore, angle 2 is congruent to angle 3 by the transitive property. So, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem.
Which information is missing in the paragraph proof?
∠2 ≅ ∠4
∠1 ≅ ∠2
∠2 ≅ ∠3
∠1 ≅ ∠4
Answer:
∠1 ≅ ∠2
Step-by-step explanation:
As shown in the figure:
We need to prove e ∥ f using the congruent angle.
So, check the options:
A) ∠2 ≅ ∠4 ⇒ (Wrong)
B) ∠1 ≅ ∠2 ⇒ (True) because a ∥ b (Given)
C) ∠2 ≅ ∠3 ⇒ It is required to prove that to prove e ∥ f , it can't be used.
D) ∠1 ≅ ∠4 ⇒ (Wrong)
The complete sentence will be:
We see that ∠1 ≅ ∠2 by the alternate exterior angles theorem.
Therefore, angle 2 is congruent to angle 3 by the transitive property.
The missing information in the paragraph proof is: ∠2 ≅ ∠4.
In the given proof, it is correctly established that angle 1 is congruent to angle 3 because lines a and b are parallel, and this is due to the alternate exterior angles theorem.
Furthermore, it is correctly deduced that angle 2 is congruent to angle 3 through the transitive property.
However, to conclude that lines e and f are parallel using the converse alternate exterior angles theorem, it is essential to establish that angle 2 is congruent to angle 4.
Without this information, the proof is incomplete because it doesn't demonstrate the congruence between the corresponding angles on lines e and f at their intersection with line b.
To complete the proof, you would need to show that ∠2 ≅ ∠4, thereby demonstrating that all pairs of corresponding angles between lines e and f are congruent.
This additional congruence statement would justify the application of the converse alternate exterior angles theorem, allowing you to conclude that e ∥ f.
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