use inductive reasoning to find the remaining numbers in the pattern. 2,5,10,17,26,37, ?, ?
What is the value of a 3 - b 2 for a = 3 and b = ? A. 8 B. 8 3/4 26 3/4 26
Answer:
probably 26
Step-by-step explanation:
(3p3q)^3/4
What is the expression in radical form?
Answer:
[tex]p^2\sqrt[4]{27pq^3}[/tex]
Step-by-step explanation:
[tex](3p^3q)^\frac{3}{4}[/tex]
To get radical form , remove the fractional exponent
[tex](a^m)^n=a^{mn}[/tex]
multiply the exponent 3/4 inside the parenthesis
[tex]3^\frac{3}{4} p^{3 \cdot \frac{3}{4}} q^\frac{3}{4}[/tex]
[tex]3^\frac{3}{4} p^{\frac{9}{4}} q^\frac{3}{4}[/tex]
[tex]\sqrt[4]{27} \cdot p^2\sqrt[4]{p} \cdot \sqrt[4]{q^3}[/tex]
[tex]p^2\sqrt[4]{27pq^3}[/tex]
The radical form of the expression [tex]\rm \left (3p \times 3q \right )^{\frac{3}{4}}[/tex] will be [tex]\left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex].
How do convert the exponent into the simplest radical form?If the power of the variable "a" is b/c. Then the simplest radical form of the expression will be
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
[tex]\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}[/tex]
The expression is given below.
[tex]\rm \rightarrow \left (3p \times 3q \right )^{\frac{3}{4}}[/tex]
We know that (ab)ⁿ = aⁿ × bⁿ. Then the expression will be
[tex]\rm \rightarrow \left (3^{\frac{3}{4}} \times p^{\frac{3}{4}} \times 3^{\frac{3}{4}} \times q^{\frac{3}{4}} \right )[/tex]
Simplify the expression in the radical form. Then we have
[tex]\rm \rightarrow \left (3^{\frac{3}{2}} \times p^{\frac{3}{4}} \times q^{\frac{3}{4}} \right )\\\rightarrow \left ( \sqrt{3^3} \times \sqrt[4]{p^3} \times \sqrt[4]{q^3} \right ) \\\rightarrow \left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex]
The radical form of the expression [tex]\rm \left (3p \times 3q \right )^{\frac{3}{4}}[/tex] will be [tex]\left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex].
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Ali currently has $25. He is going to start saving $5 every week. Ali's Savings Function Rule: y = 5x + 25
The rate of change of this function is
The rate of change of Ali's saving function according to the first derivative is 5.
Given the saving function :
[tex]y = 5x + 25[/tex]
The rate of change is the first derivative of y
Therefore,
[tex] \frac{dy}{dx} = 5[/tex]
Therefore, the rate of change of the function is 5.
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A table is on sale for $403, which is 38% less than the regular price. what is the regular price
The regular price of the table is $650.
The student has asked to find the regular price of a table that is currently on sale for $403, which is 38% less than the regular price. To find the regular price, we can consider the sale price to be 62% (100% - 38%) of the regular price. Let's denote the regular price as R. Thus, we can set up the equation 0.62 * R = $403. Solving for R, we divide both sides by 0.62 to find the regular price:
R = $403 / 0.62
R = $650
Therefore, to find the regular price of a table on sale for $403 at 38% off, we determine that the sale price is 62% of the regular price. By dividing the sale price by 0.62, we discover that the regular price is $650.
what is y=2-3x in standard form?
The given equation of the line is in slope-intercept form. To convert it to standard form, simply rearrange so that all terms are on one side of the equation resulting in 3x + y = 2.
Explanation:The equation you're given is y=2-3x which is in the slope-intercept form i.e., y = mx + b, where m is the slope and b is the y-intercept. To convert this equation to a standard form, the general approach is to eliminate fractions and have the 'y' and 'x' terms on the same side of the equation.
Starting from y = 2 - 3x, add 3x to both sides of the equation to get it in the standard form. So, it becomes 3x + y = 2, which is the standard form of the given equation.
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a farmer has 268 cows. each cow has either one or two calves. if there are 335 calves in total, what fraction of the cows have two calves
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 5θ
Answer:
The graph is symmetric about the x-axis.
Step-by-step explanation:
1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point (r, -θ ) or (-r, π - θ ) also lies on the graph.
2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r, π - θ ) or (-r, -θ ) also lies on the graph.
3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.
The given polar equation is
[tex]r=2\cos (5\theta)[/tex]
Check the equation by (r, -θ).
[tex]r=2\cos (-5\theta)=2\cos (5\theta)=r[/tex]
Therefore, the graph is symmetric about the x-axis.
Check the equation by (-r, -θ).
[tex]-r=2\cos (-5\theta)=2\cos (5\theta)=r\neq -r[/tex]
Therefore, the graph is not symmetric about the y-axis.
Check the equation by (-r, θ).
[tex]-r=2\cos (5\theta)=2\cos (5\theta)=r\neq -r[/tex]
Therefore, the graph is not symmetric about the origin.
A 48 ounce container of juice costs $2.64 each. A 64 ounce container of the same juice costs $3.84.
a. Find the cost per ounce of each container.
b. Which size container costs less per ounce?
c. You want to buy 192 ounces of juice. How much do you save using the container size from your answer to part (b)?
How many solutions are there to the equation below? -46 = 3x + 7x
A man is 18 years older than his son. in 2 years, his age will be twice the the age of his son. how old is the son at this point in time?
If a cup of cereal has 12 grams of fiber, which is 40% of the recommended daily amount. What is the recommended daily amount?
For dinner, Abelita chooses the Italian salad that costs $3.99 before tax, and Franco chooses the fettuccini alfredo that costs $7.17 before tax. If the sales tax is 5 percent, explain how to find the total cost for their dinner.
Answer: The total cost of the dinner is found by adding the two prices together. Then this sum is multiplied by 1.05, which is 100% + 5%, to get a cost of $11.72.
Step-by-step explanation:
This is the sample answer.
To calculate the total cost including sales tax, convert the percent tax rate to a decimal, multiply it by the meal's cost, and add it to the original cost. In this case, a 5 percent tax on a $3.99 salad and a $7.17 fettuccini alfredo results in a final total cost of $11.72.
Explanation:Calculating Total Cost with Sales TaxFirst, to find the sales tax for Abelita's Italian salad and Franco's fettuccini alfredo, you convert the tax rate from a percent to a decimal. The tax rate is 5 percent, which as a decimal is 0.05. Next, add the cost of the Italian salad ($3.99) and fettuccini alfredo ($7.17) to get the total cost before tax, which is $11.16. Multiply this total by the tax rate to find the amount of sales tax: $11.16 × 0.05 = $0.558. Round this to the nearest cent, which gives us $0.56.
The next step is to add the sales tax to the total cost before tax to find the final total cost. Thus, $11.16 (meal cost) + $0.56 (sales tax) = $11.72. Therefore, the total cost for their dinner, including the 5 percent sales tax, is $11.72.
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There were 120 black birds sitting in a tree , but then some blackbirds flew after that there were 85 birds sitting in the tree if b=the number of blackbirds that flew away , which mathematical sentence expresses the information above?
Jillian has $50.45 to spend on hamburgers and drinks. Hamburgers are $2.25 each. What is the LARGEST number she can buy and still have at least $10 left over for drinks?
Point H is the circumcenter of triangle DEF.
Which must be true? Check all that apply.
Point H is the center of the circle that passes through points D, E, and F.
Point H is the center of the circle that passes through points L, M, and N.
HE=HD
LH=NH
MEH NEH
DLH FNH
Answer:
the correct answers are:
a. ) Point H is the center of the circle that passes through points D, E, and F.
c. ) HE=HD
Point H, being the circumcenter, ensures it is the center of the circle through D, E, and F and that HE equals HD; other statements regarding unrelated points cannot be confirmed.
Explanation:If Point H is the circumcenter of triangle DEF, then the following must be true:
Point H is the center of the circle that passes through points D, E, and F since the circumcenter is equidistant to all vertices of the triangle, forming the circumscribed circle.HE=HD since, by the definition of a circumcenter, it is equidistant from all vertices of the triangle.The other statements regarding points L, M, N cannot be determined to be true without additional information, as they are not related to triangle DEF and its circumcenter directly.
In summary, Point H as the circumcenter ensures it is at the center of the circumscribable circle through D, E, and F, and that HE equals HD.
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What number is between these 2 numbers 6,534 and 6,565
I need help. It is just one question
Jason knows that AK←→⊥KB←→ , AK←→∥EF←→ , and AK←→∥CB←→ .
Which other facts can Jason conclude are true?
Select each correct answer.
m∠EJM=90°
KB←→⊥CB←→
m∠JFB=90°
KB←→∥DM←→−
The corresponding angles between parallel lines and their common transversal are congruent
The other facts Jason can conclude are true are:
1) [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
2) m∠JFB = 90°
The reason why the above selected options are correct are:
The relationships between the lines Jason knows are:
Segment AK is perpendicular to KB: [tex]\underset{AK}{\leftrightarrow}[/tex] ⊥ [tex]\underset{KB}{\leftrightarrow}[/tex]
Segment AK is parallel to EF: [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex]
Segment AK is parallel to CB: [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex]
m∠DKF = 90°
The required information:
The facts that Jason can conclude are true
Method:
Find the other relationships between the lines based on the relationships Jason knows
Solution:
We have;
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{EF}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex], and [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{EF}{\leftrightarrow}}[/tex] ║ [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex]
The relationship, [tex]\underset{EF}{\leftrightarrow}[/tex] ⊥ [tex]\underset{KB}{\leftrightarrow}[/tex], gives m∠JFB = 90°
Therefore;
The correct options for the facts Jason can conclude are;
1) [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
2) m∠JFB = 90°
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The ratio of the radii of two circles is 4:5. What is the ratio of the circumferences of the two circles?
Which is the graph of a quadratic equation that has a positive discriminant?
Answer:
D. Last gragh
Step-by-step explanation:
PLEASE HELP ME
The base of a triangle measures (2x + 7) units and the height measures (4x + 6) units. Part A: What is the expression that represents the area of the triangle? Show your work to receive full credit. (4 points) Hint: Area = 0.5bh Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Marni danced in a contest to raise money for an animal shelter. Marni raised $30 plus $1.80 per minute that she danced. She raised a total of $264. Let x equal the number of minutes Marni danced. What expression completes the equation to determine the total amount of minutes Marni danced? How many minutes did Marni dance? Enter the answers in the boxes.
Answer: 1: 30+1.8x=264
2: 130 min
Step-by-step explanation:
A square pyramid has a base edges 10 in long and a height of 4 in sketch the pyramid and find the surface area round your answer to the nearest tenth
Which statement describes how to solve sqrt3x+4 = sqrt3x+4?
A. Square both sides once and then solve the resulting linear equation.
B. Square both sides once and then solve the resulting quadratic equation.
C. Square both sides twice and then solve the resulting linear equation.
D. Square both sides twice and then solve the resulting quadratic equation.
NEED IT ASAP
since both equations are the same, you would square it one and solve for the linear equation
Answer is A
Answer:
A
Step-by-step explanation:
Sparky had room for 16 rows in his garden. He planted 3 rows of tomatoes for every 5 rows of onions. How many rows of tomatoes did he plant?
Answer: 6 rows - tomatoes
Step-by-step explanation:
1. Given △PQR≅△STU, m∠R=80°, and m∠S=70°, what is the measure of ∠Q?
2. What is m∠AEB?
(image is for this question)
Given that there are eight ounces in a cup and four cups in a quart , which quaintity below is equal to 128 ounces
A- 256
B- 64
C- 16
D- 2
The answer is D- 2.
128 ounces is equivalent to 1 quart in the English system. Knowing that 1 quart equals 4 cups and 1 cup equals 8 ounces, we can calculate that 128 ounces is equal to 1 quart.
A - 256B - 64C - 16D - 2A text font fits 12 characters per inch.Using the same font how many characters can be expected per yard of text?
1 foot = 12 inches
1 yard = 3 feet = 36 inches
36*12 = 432 characters
if p is the midpoint of xy, xp=8x-2 and py=12x-30, find the value of x
To find the value of x, we can use the midpoint formula which is 16/9.
Explanation:To find the value of x, we can use the midpoint formula. According to the formula, the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the same applies to the y-coordinate.
Given that XP = 8x - 2 and PY = 12x - 30, we can set up the equation:
(8x - 2 + 12x - 30) / 2 = x
Simplifying the equation, we get:
(20x - 32) / 2 = x
Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
20x - 32 = 2x
20x - 2x = 32
18x = 32
x = 32/18
x = 16/9