Answer & Step-by-step explanation:
(x² - 5x)(2x² + x - 3)
Multiply each term from the first expression into the second expression.
2x⁴ + x³ - 3x² - 10x³ - 5x² + 15x
Combine like terms.
2x⁴ - 9x³ - 8x² + 15x
So, after you multiply the expressions, your answer will be 2x⁴-9x³-8x²+15x.
(W^3 Z^2)^2 simplify
Answer: w^6 z^4
Step-by-step explanation:
w^6z^4
w^3^2 z^2^2
w^6 z^4
Answer:
[tex]w^6z^4[/tex]
Step-by-step explanation:
[tex]\text{Apply rule: }(a*b)^n=a^nb^n\\\\(w^3z^2)^2=\left(w^3\right)^2\left(z^2\right)^2\\\\\text{Apply rule: }(a^n)^m=a^{nm}\\\\(w^3)^2=w^{3*2}=\boxed{w^6}\\\\w^6(z^2)^2\\\\(z^2)^2=z^{2*2}=z^4\\\\\boxed{w^6z^4}[/tex]
John earns a total of t dollars mowing n lawns. He charges d dollars per lawn. Which equation shows the proportional relationship between the total John earns and the number of lawns he mows?
Answer:
[tex]t = dn[/tex]
Step-by-step explanation:
Given:
Total Earnings = t dollars
Charges per lawn = d dollars
Number of lawn = n
Required:
Find the equation that describes the above illustration
To get the equation of proportionality of this system; we simply multiply the charges by the numbers of lawn;
i.e.
[tex]Total\ Earnings\ (t) = Charges\ (d) * Number\ (n)[/tex]
This gives:
[tex]t = d * n[/tex]
[tex]t = dn[/tex]
What must be the factor of the polynomial function f(x) graphed on the coordinate plane below
Answer:
x = -1
Step-by-step explanation:
x is the in the left lower quadrant
Answer:A
Step-by-step explanation:
A great white shark swims 22 feet below sea level.
If the shark is 67.7 feet from the sailboat, what is the angle of
denression of the boat to the shark
Answer:
x = 18 degrees
Step-by-step explanation:
Use tan to find the value of x
tan x = 22/67.7 Simplify
tan x = 0.3298 Take the negative of tan to find x
tan^-1 x = 18
The required angle of depression of the boat to the shark is 18.96°.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
Applying trig ratios, to determine the angle of depression.
Sin x = 22 / 67.7
x = sin ⁻¹[22/67.7]
x = 18.96°
Thus, the required angle of depression of the boat to the shark is 18.96°.
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Solve
2/3x+4=8 whats x?
Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
[tex] \frac{2}{3} x + 4 = 8 \\ \frac{2x}{3} = 8 - 4 \\ \frac{2x}{3 } = 4 \\ 2x = 4 \times 3 \\ 2x = 12 \\ x= 6[/tex]
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
[tex]2/3x+4=8\\[/tex]
Subtract 4 from both sides
[tex]2/3x=4[/tex]
Multiply both sides by 3
[tex]6/3x=12\\2x=12[/tex]
Divide both sides by 2
[tex]x=6[/tex]
I NEED HELP BEFORE 1:40 P.M! Johanna uses 40 sheets of paper every 4 days. ( Part A and B are not here because they were pretty easy for me.) Part C: Johanna's sister uses twice as much paper as Johanna uses in half the number of days that Johanna does. How many times more does Johannna's sister use each day than Johanna?
Answer:
Johanna's sister uses 4x the amount of paper that Johanna uses each day.
Step-by-step explanation:
Johanna uses 10 pieces of paper each day. (40 divided by the 4 days = 10)
If Johanna's sister uses twice the amount that Johanna uses in half the days, then she would be using 80 pieces of paper in 2 days. (80 divided by the 2 days = 40) Johanna's sister uses 40 pieces of paper each day.
So now we know that Johanna uses 10 pieces of paper each day, and her sister uses 40 pieces of paper each day.
Now we divide 40 by 10 which gives us 4, to give us our answer. Johanna's sister uses 4x the amount of paper that Johanna uses each day.
Sorry for the later response; hope this helps!
HELP ME 20 POINTS + BRAINLEST GIVE ME THE CORRECT ANSWER
Select the correct answer from each drop-down menu.
This table represents a linear function.
x y
___
0 5
___
5 15
this graph represents another function.
the greater unit rate of the two function is ______. the greater y-intercep of the two function is ______.
Answer:
2 and 6...... im from the future too
Step-by-step explanation:
Answer:
2 and 6
Step-by-step explanation:
For the equations given below, which statement is true?
-21 = 14
6.1 = -42
A. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by -3.
B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by 3.
C. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by -4.
D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first
equation by any value.
Answer:
D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first
equation by any value
Step-by-step explanation:
-21=14 Equ(1)
6.1=-42 Equ(2)
Multiplying the first equation by -3 will give
-63= -42
Which is not equivalent to the second equation
Multiplying the first equation by 3, we have
-63=42
Not equivalent to the second equation
Multiplying both sides of the first equation by -4, we have
84=56
Not equivalent to the second equation
D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first
equation by any value
Match each statement with its corresponding value for the system below: y = (2) ^x and y = 3x
1. The y-intercept of the linear function. 0 2.The y-intercept of the exponential function. 1 3.The number of points of intersection. 2 4.The quadrant of the solution(s). 1/2
Answer:
1. The y-intercept of the linear function. 0
2.The y-intercept of the exponential function. 1
3.The number of points of intersection. 2
4.The quadrant of the solution(s). 1
Step-by-step explanation:
The given functions are
Exponential function : [tex]y=2^x[/tex]
Linear function : [tex]y=3x[/tex]
Substitute x=0 in the above functions to find the y-intercepts.
[tex]y=2^(0)=1[/tex]
The y-intercept of the exponential function is 1.
[tex]y=3(0)=0[/tex]
The y-intercept of the linear function is 0.
Plot the graph of both functions as shown below.
From the graph it is clear that both functions intersect each other at 2 points. So, the number of points of intersection is 2.
From the graph it is clear that both intersection points lie in first quadrant. So, the quadrant of the solution(s) is 1.
Determine whether quadrilateral ABCD is similar to quadrilateral EFGH. If so, give the similarity statement. answers: A) The quadrilaterals are not similar. B) Impossible to determine. C) ABCD ∼ FEHG D) ABCD ∼ EFGH
Answer: D) ABCD ∼ EFGH
Step-by-step explanation:
From the given picture,
In parallelogram ABCD, ∠A= 80° .
In parallelogram EFGH, ∠E= 100° .
Since the sum of two adjacent angles in a parallelogram is 180°.
So, ∠A + ∠B = 180°
⇒ ∠B = 180° -∠A = 180°- 80° = 100°
So, ∠B = 100°
Similarly in parallelogram EFGH, ∠ E= 80° .
Also, the opposite angles of a parallelogram are equal,
∠A =∠C= 80° and ∠B=∠D=100°
∠E =∠G= 80° and ∠F=∠H=100°
So, the corresponding angles of both parallelograms are equal.
That means they are similar.
So the required similarity statement : ABCD ∼ EFGH
Hence, the correct option is D.
Answer:
it is not D i got it wrong on the test
Step-by-step explanation:
Which of the ordered pairs below satisfy the following equation. Check all that apply!
Answer:
A, B, and C
Step-by-step explanation:
By substituting each of the ordered pairs into the equation you can determine that A, B and C all satisfy the equation.
Find the interquartile range (IQR) of the data in the dot plot below. 0,1,1,3,3,3,4,5,7
Answer:
3.5
Step-by-step explanation:
trust
me
=]
Solve this system of linear equations. Separate
the x- and y-values with a comma.
5x + 2y = 13
-9x + 7y = 19
Answer:
A) 5x + 2y = 13
B) -9x + 7y = 19 We'll multiply equation A) by -(7/2)
A) -35/2 x -7y = -(91/2) then we'll add equation B)
B) -9x + 7y = 19
-53/2x = -53/2
x = 1
2y = 13 -5
y = 4
Step-by-step explanation:
The midpoint between points (x, y) and (3, 7) is (4, 11). What is x?
Answer:
(3.5, 9)
Step-by-step explanation:
You can quickly find the midpoint by averaging the x and y values separately.
X coordinate: (3+4)÷2=7÷2=3.5
Y coordinate: (7+11)÷2=18÷2=9
The midpoint is then at (3.5,9).
Answer:
x=5Solution,
Midpoint between (X,y) and (3,7) is (4,11)
By using mid point formula:
[tex](4 ,11) = ( \frac{x + 3}{2} ,\frac{y + 7}{2} ) \\ 4 = \frac{x + 3}{2} \\ or \: 4 \times 2 = x + 3(cross \: multiplication) \\ or \: 8 = x + 3 \\ or \: - x = 3 - 8 \\ or \: - x = - 5 \\ x = 5[/tex]
hope this helps...
Good luck on your assignment..
The Locust Points idea allows you to define geometric objects just by determining whether or not two distance are equal.
A.) True
B.) False
Answer:
A. True
Step-by-step explanation:
The locus of points idea allows you to define objects in terms of points and given distances.
Answer:
True
Step-by-step explanation:
Which of the following statements about the distance formula is TRUE?
A. The distance formula only applies to points in one dimension
B. the distance formula can be derived from the Pythagorean Theorem
Answer:
The distance formula can be derived from the Pythagorean Theorem.
Step-by-step explanation:
The distance formula can be derived from the Pythagorean Theorem.
The distance formula can be derived from the Pythagorean Theorem. Option B is correct.
What is Distance?Distance is defined as the object traveling at a particular speed in time from one point to another. And distance is the measure of length between points.
Here,
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂- y₁]²],
In the above distance formula,
D = hypotenuse length between the points,
x₂ - x₁ = base length over the x-axis
y₂- y₁ = Perpendicular length over the y-axis.
So, the distance formula equivalent to the Pythagorean theorem
Thus, the distance formula can be derived from the Pythagorean Theorem. Option B is correct.
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Sarah correctly compares the values of the digits in 644.66. Select the comparison Sarah could have made. The value of the hundredths digit is 10 times the value of the tenths digit. The value of the ones digit is one over ten the value of the tens digit. The value of the tens digit is one over ten the value of the ones digit. The value of the hundreds digit is 100 times the value of the hundredths digit.
Answer:
10
Step-by-step explanation:
664.66 is right
Answer:
I think its right. ( 10) (644.66)
Step-by-step explanation:
if the sum of four times a number and four less than three times a number is seventeen
Answer:
13divided by 7
Step-by-step explanation:
[tex]4x + 3x - 4 = 17 \\ 7x - 4 = 17 \\ 7x = 17 - 4 \\ 7x = 13 \\ \frac{7x}{7} = \frac{13}{7 } \\ x = \frac{13}{7} or1 \times \frac{6}{7} [/tex]
The required number is 3 .
It is required to find the number.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given:
Let the number be x
According to given question we have,
4x+3x-4=17
Compare the like terms we get,
7x=17+4
7x=21
x=3
The number is 3 .
Therefore, the required number is 3 .
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Help idk how to do this ASAP please
Answer:
The area of ∆DEF = 4.5in²
Step-by-step explanation:
From the above diagram,
∆BAC ~∆DEF
It is important to note that if two triangles are similar, the ratio of their areas is equal or equivalent to the ratio of the areas of their sides
This means for the above question, that
We have the bigger triangle = ∆BAC has a side of 4 in and Area = 8 in²
The small triangle has a side of 3in
Finding the scale factor k = ratio of the sides of both Triangles
k = 4/3
k² = (4/3)²
k² = 16/9
Hence,
Area of ∆BAC/ Area of ∆DEF = 16/9
8in²/Area of ∆DEF = 16/9
We cross Multiply
8 in² × 9 = Area of ∆DEF × 16
Divide both sides by 16
Area of ∆DEF = 72/16
= 4.5in²
Therefore, the Area of ∆DEF rounded to the nearest tenth = 4.5in²
The following graph shows the cost c, in dollars, of p pounds of strawberries at a local grocery store.
Answer:
A. The ordered pair (5, 3.5) represents 5 lbs. of strawberries cost $3.50.
B. The cost per pound of strawberries is shown at (1, 0.7).
C. The relationship shown in the graph is a direct variation because as the pounds of strawberries increase, the cost also increases.
Explanation:
A. The coordinate is in (x,y). The x-axis represents the pound of strawberries and the y-axis represents the cost of the strawberries.
B. The cost for one pound of strawberries can be calculated to find the exact value of y (cost) when x is 1. The graph shows 5 lbs. of strawberries cost $3.50 so divide $3.50 by 5 lbs. to find the cost per pound of strawberries. 3.5 ÷ 5 = 0.7. On the graph, the cost for one pound of strawberries is at (1, 0.7)
C. A direct variation in a graph is shown when both x and y increase or decrease together. In this case, as the pounds of strawberries increase, the cost of the strawberries also increases.
Complete this item. State a definition for a polygon inscribed in a sphere.
Answer:
A polygon inscribed in a sphere has each vertex of the polygon on the outer figure of the sphere. this is a three dimensional shape, in which all the vertices must lie on the sphere. when they are joined with each other they form a closed 3d geometric shape.
Which is the correct rhyme scheme for this stanza?
o sabb
abcd
o abab
abcc
Answer:
option 2 ABab, ABCC wish you luck
Answer:
C- abab
Step-by-step explanation:
Trevor has been asked to analyze the rhyme scheme in Shakespeare’s “Sonnet 18.”
Sometime too hot the eye of heaven shines,
And often is his gold complexion dimm'd,
And every fair from fair sometime declines,
By chance, or nature's changing course untrimm'd:
Which is the correct rhyme scheme for this stanza?
A- aabb
B- abcd
C- abab
D- abcc
Jason went shopping he bought a watch and a pair of trainers for a total price of £53.55 this price includes a 15% loyalty discount. before the discount, the trainers were priced at £38 work out the price of the watch before the discount
please help me
I'm struggling
Answer:
£25
Step-by-step explanation:
Total price- £53.55
Pair of trainers cost- £38 before discount
Discount= 15%
Cost of pair of trainers after discount:
£38 - 15%= £38*0.85= £32.3Price of the watch after discount:
£53.55 - £32.3= £21.25Price of the watch before discount:
£21.25/0.85= £25FAST
Cecilia made an envelope to mail a letter. She colored the regular trapezoid flap on the bottom of the envelope blue, as shown. A trapezoid has a base of 9 inches, height of 2 inches, and top side length of 5 inches. What is the area of the blue flap of the envelope? 14 Inches squared 18 Inches squared 45 Inches squared 90 Inches squared
Answer:
The area is 14 inches squared.
Step-by-step explanation:
To find the area of a trapezoid the equation is...
a+b
------ x h (a and b equal the bases)
2
Seeing as we know all of the basses and heights lets plug it into the equation.
9+5
------- x 2
2
Well the 2 and the 2 cancel each other out in this scenario so what we would have to do now is ad 9 and 5 which would get us to 14.
Answer:
14in
Step-by-step explanation:
Apply the binomial theorem to 210 = (1 + 1)10 . Answer each question in the work area provided below. 1. Write out the equation using combination notation. 2. Simplify each term. Do not combine the terms. 3. In two or more complete sentences, describe the relationship between the terms of the equation and the number of combinations when flipping a coin 10 times. 4. What is the theoretical probability of getting exactly 5 heads in a sequence of 10 flips? 5. In two or more complete sentences, compare the theoretical probability of getting exactly 5 heads with the fraction in your histogram. Interpret any differences.
Answer:
The following are the answer to this question:
Step-by-step explanation:
Binomial theorem Expression:
[tex]\bold{(x+y)^n= {^n}C_0x^ny^0+{^n}C_1x^{n-1}y^1+{^n}C_2x^{n-2}y^2+...+{^n}C_{\gamma}x^{n-\gamma}y^\gamma}+...+ {^n}C_nx^0y^n[/tex]Solution:
1)
[tex]\to 2^{10} = (1 + 1)^{10}[/tex]
[tex]= (1+1)^{10}= {^{10}}C_0\times 1^{10}\times 1^0+{^{10}}C_1\times 1^{9}\times 1^1+{^{10}}C_2\times 1^{8}\times 1^2+ \\ {^{10}}C_3 \times 1^{7}\times 1^3+{^{10}}C_4 \times 1^{6}\times 1^4+ {^{10}}C_5\times 1^{5}\times 1^5 \\+ {^{10}}C_6 \times 1^{4}\times 1^6+....+{^{10}}C_{10}\times 1^{0}\times 1^{10}[/tex]
[tex]= {^{10}}C_0. 1^{10}. 1^0+{^{10}}C_1.1^{9}. 1^1+{^{10}}C_2.1^{8}.1^2+\\{^{10}}C_3.1^{7}.1^3+{^{10}}C_4. 1^{6}. 1^4+ {^{10}}C_5.1^{5}. 1^5 + {^{10}}C_6 . 1^{4}. 1^6+ \\ {^{10}}C_7 . 1^{3}. 1^7 + {^{10}}C_8 . 1^{2}. 1^8+ {^{10}}C_9 . 1^{1}. 1^9+{^{10}}C_{10}. 1^{0}. 1^{10}\\[/tex]
2)
Simplify:
[tex](1+1)^{10}=[/tex]
[tex]{^{10}}C_0. 1^{10}. 1^0+{^{10}}C_1.1^{9}. 1^1+{^{10}}C_2.1^{8}.1^2+\\{^{10}}C_3.1^{7}.1^3+{^{10}}C_4. 1^{6}. 1^4+ {^{10}}C_5.1^{5}. 1^5 + {^{10}}C_6 . 1^{4}. 1^6+ \\ {^{10}}C_7 . 1^{3}. 1^7 + {^{10}}C_8 . 1^{2}. 1^8+ {^{10}}C_9 . 1^{1}. 1^9+{^{10}}C_{10}. 1^{0}. 1^{10}\\[/tex]
[tex]=1+10+45+120+210+252+210+120+45+10+1\\\\=1024[/tex]
3)
The [tex]r^{th}[/tex] word is the number of variations where a coin is redirected 10 times.
4)
Get the frequency of exactly five heads is: [tex]{^{10}}C_{5}[/tex] = 252
[tex]=\frac{252}{1024}\\\\=\frac{126}{512}\\\\=\frac{63}{256}\\\\=0.24[/tex]
5)
To Get 5 heads will be:
[tex]={^{10}}C_{5} \times (\frac{1}{2})^{10}\\\\=\frac{{^{10}}C_{5}}{2^{10}}\\\\=0.24[/tex]
A baby saw a toy and scooted closer, moving 1/3 of a meter in 1/4 of a minute.How fast was the baby moving
Answer:
1 1/3 meter a minute
Step-by-step explanation:
it pretty simple i just added
Answer:
1 1/3
Step-by-step explanation:
Part of a shape is drawn.
The line of symmetry of the shape is shown by a dotted line.
Complete the drawing of the shape and
then rotate it by 180° about the origin.
Answer:
The points of the rotated shape are: (4, 1), (5, 3), (4, 4), (2, 1), (1, 3), (2, 4)
Step-by-step explanation:
From the part of the shape we can see and the symmetry, the missing points are:
(-2, -1)
(-1, -3)
(-2, -4)
Rotation 180° about the origin transforms the point (x, y) into (-x, -y). Applying this rule to our figure, we get:
(-4, -1) -> (4, 1)
(-5, -3) -> (5, 3)
(-4, -4) -> (4, 4)
(-2, -1) -> (2, 1)
(-1, -3) -> (1, 3)
(-2, -4) -> (2, 4)
A same side interior angle of two parallel lines is three times the other same side interior angle. Find the measures of these two angles.
Answer:
45 and 135
Step-by-step explanation:
The sum of any interior angles will be 180 so you divide 180 by 4. And you get 45 then you multiply that by 3 and you get 135
Make m the subject of the formula
check the photo and if u feel I made any mistakes pls do let me know
Select the three expressions that are equivalent to 6^{2}6 2 6, squared. a: (6^9/6^8)^2 b: 6 times 6 times 6 times 6 times 6 times 6 times 6 / 6 times 6 times 6 c: 6^4/6^2 d: 6^5 times 6^7/6^10
Question:
Select the three expressions that are equivalent to [tex]6^2[/tex]:
a: [tex](\frac{6^9}{6^8})^2[/tex]
b: [tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }[/tex]
c: [tex]\frac{6^4}{6^2}[/tex]
d: [tex]\frac{6^5 * 6^7}{6^{10}}[/tex]
Answer:
a: [tex](\frac{6^9}{6^8})^2[/tex]
c: [tex]\frac{6^4}{6^2}[/tex]
d: [tex]\frac{6^5 * 6^7}{6^{10}}[/tex]
Step-by-step explanation:
Given
[tex]6^2[/tex]:
Required
Find equivalent expressions
To solve this question; we'll simplify options a to do, one after the other
a: [tex](\frac{6^9}{6^8})^2[/tex]
From laws of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This implies that;
[tex](\frac{6^9}{6^8})^2 = (6^{9-8})^2[/tex]
[tex](\frac{6^9}{6^8})^2 = (6^{1})^2[/tex]
From laws of indices;
[tex]{a^m}^n = a^{m*n} = a^{mn}[/tex]
This implies that
[tex](\frac{6^9}{6^8})^2 = (6^{1*2})[/tex]
[tex](\frac{6^9}{6^8})^2 = 6^{2}[/tex]
Hence, [tex](\frac{6^9}{6^8})^2[/tex] is equivalent to [tex]6^2[/tex]
b. [tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }[/tex]
From laws of indices;
[tex]a^m * a^n = a^{m+n}[/tex]
This implies that
[tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{1+1+1+1+1+1}}{6^{1+1+1}}[/tex]
[tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{6}}{6^{3}}[/tex]
From laws of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This implies that
[tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{6-3}[/tex]
[tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{3}[/tex]
Hence; [tex]\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }[/tex] is not equivalent to [tex]6^2[/tex]
c. [tex]\frac{6^4}{6^2}[/tex]
From laws of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This implies that
[tex]\frac{6^4}{6^2} = 6^{4-2}[/tex]
[tex]\frac{6^4}{6^2} = 6^{2}[/tex]
Hence, [tex]\frac{6^4}{6^2}[/tex] is equivalent to [tex]6^2[/tex]
d. [tex]\frac{6^5 * 6^7}{6^{10}}[/tex]
From laws of indices;
[tex]a^m * a^n = a^{m+n}[/tex]
This implies that
[tex]\frac{6^5 * 6^7}{6^{10}} = \frac{6^{5+7}}{6^{10}}[/tex]
From laws of indices;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This implies that
[tex]\frac{6^5 * 6^7}{6^{10}} = 6^{5+7-10}[/tex]
[tex]\frac{6^5 * 6^7}{6^{10}} = 6^{2}[/tex]
Hence, [tex]\frac{6^5 * 6^7}{6^{10}}[/tex] is equivalent to [tex]6^2[/tex]
