Answer:
The product of 2x + y and 5x – y + 3 is 10x^2+ 3xy + 6x - y^2 + 3y
Step-by-step explanation:
The product of the two expressions can be expressed mathematically as;
(2x +y) (5x -y +3)
To obtain the product of these expressions, we simply expand the brackets as follows;
2x(5x -y +3) + y(5x -y +3)
= 10x^2 - 2xy + 6x + 5xy - y^2 + 3y
= 10x^2- 2xy + 5xy + 6x - y^2 + 3y
= 10x^2+ 3xy + 6x - y^2 + 3y
The product of 2x + y and 5x – y + 3 is thus 10x^2+ 3xy + 6x - y^2 + 3y
Answer: 10x^2 +3xy + 6x + -1y^2 + 3y
Step-by-step explanation:
The area of a square can be represented by the expression x^10. The side of the square can be written in the form xn. What is the value of n?
ANSWER
n=5
EXPLANATION
The area of a square is given by
[tex] {l}^{2} [/tex]
where l is the length of the sides.
If the area is
[tex] {x}^{10} [/tex]
then we can rewrite this as
[tex]( { {x}^{5}) }^{2} [/tex]
This implies that:
[tex] {l}^{2} = ( { {x}^{5}) }^{2} [/tex]
Hence,
[tex]l = {x}^{5}[/tex]
Therefore n=5
The area of the trapezoid
The area of that trapeziod is 28 inches.
Answer:
Step-by-step explanation:
The area is a+b/2
so the answer is 28
What are the numbers???
Answer:
In: 5, 4, 2, 3, 1, and 10.
Out: 40, 32, 16, 24, 8, and 80
Step-by-step explanation:
The first step you should do is to take notice of the pairs that have their "in" and "out" both answered.
The second step is to find out what you must multiply the "in" by to get the "out". In this answer, you must multiply the "in" by 8 to get the "out".
The third step is to do the same thing for all of the values until the chart is completely filled with values.
The fourth step is to check your work!
If you have any questions, please let me know!
The rule is 8
Bc 5 times 8 is 40
32/8 is 4
Either divide or multiply when needed
Find the later area of the figure
Answer:
[tex]\large\boxed{60\pi\ sq.in.}[/tex]
Step-by-step explanation:
The formula of a lateral area of a cone:
[tex]L.A.=\pi rl[/tex]
r - radius
l - lateral height
We have the radius r = 6in and the height H = 8in.
Use the Pythagorean theorem to calculate the lateral height:
[tex]l^2=6^2+8^2\\\\l^2=36+64\\\\l^2=100\to l=\sqrt{100}\\\\l=10\ in[/tex]
Substitute:
[tex]L.A.=\pi(6)(10)=80\pi\ in^2[/tex]
What property is shown in the equation? a(b × c) = (a × b)c
Answer:
Commutative Property
Step-by-step explanation:
"Changing the order but not the result"
Which is the equation of the given line in point- slope form?
y - 0 = 1(x+8)
y - 0 = -1(x-8)
y = - x + 8
y - 8 = -1(x+0)
Answer:
[tex]y-0=-1(x-8)[/tex]
Step-by-step explanation:
The given line passes through (0,8) and (8,0).
The slope of this line is [tex]m=\frac{8-0}{0-8} =-1[/tex].
The point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the slope and the point (8,0) to get:
[tex]y-8=-1(x-0)[/tex]
We substitute the slope and the point (0,8) to get:
[tex]y-0=-1(x-8)[/tex]
Which pair of points is in the solution set for the system of linear inequalities below?
2x + y < 2
6x + 3y > 2
a.) (0, 3/2) and (3/4, 1/4)
b.) (1/2, 1) and (1/2,1/2)
c.) (-1,-1) and (0,-3)
d.) (0,2) and (1/3,0)
Final answer:
The correct pair of points that is in the solution set for the given system of linear inequalities is option a) (0, 3/2) and (3/4, 1/4). Each point in this pair satisfies both of the inequalities when substituted into them.
Explanation:
The question asks which pair of points is in the solution set for the given system of linear inequalities:
2x + y < 2
6x + 3y > 2
To verify if the points provided are solutions, we plug them into the inequalities to see if they satisfy both conditions.
Let's test each pair:
For pair a) (0, 3/2), the first inequality becomes 2(0) + (3/2) = 3/2, which is less than 2, so it satisfies the first inequality. For the second inequality, 6(0) + 3(3/2) = 9/2, which is greater than 2, so it satisfies the second inequality as well. Therefore, (0, 3/2) is a solution. However, for the second point (3/4, 1/4), the first inequality becomes 2(3/4) + (1/4) = 3/2 + 1/4 = 7/4, which is less than 2, satisfying the first inequality. But for the second inequality, we get 6(3/4) + 3(1/4) = 9/2 + 3/4 = 21/4, which is greater than 2, satisfying the second inequality, so (3/4, 1/4) is also a solution.
For pair b), to be brief, one point does not satisfy both inequalities.
For pair c), one point does not satisfy both inequalities.
For pair d), one point does not satisfy both inequalities.
Therefore, the correct pair of points is option a) (0, 3/2) and (3/4, 1/4), as they both are solutions to the system of inequalities.
ABCDEF and EHG are regular polygons. If mHGJ=220* on the exterior of the polygon, mEGJ is congruent to mGED, and mCDJ=136* on the exterior of the polygon, what is the measure of GJD?
Answer:
96 deg
Step-by-step explanation:
Polygon ABCDE is a regular hexagon. The sum of the measures of the interior angles is (n - 2)180 = (6 - 2)180 = 4(180) = 720. Since it's a regular hexagon, each interior angle measures 720/6 = 120 deg.
For the interior angle, m<CDE = 120
On the exterior of the polygon, m<CDJ = 136
m<CDE + m<CDJ + m<EDJ = 360
120 + 136 + m<EDJ = 360
m<EDJ + 256 = 360
m<EDJ = 104 deg
Triangle EHG is regular. The sum of the measures of the angles of a triangle is 180. For a regular triangle, each angle measures 60 deg.
m<EGH = 60
For exterior angle m<HGJ = 220
m<HGJ(exterior) + m<EGH + m<EGJ = 360
220 + 60 + m<EGJ = 360
m<EGJ + 280 = 360
m<EGJ = 80
m<EGJ = m<GED, so
m<GED = 80
Polygon DEGJ is a quadrilateral. The sum of the measures of its interior angles is 360 deg.
m<EGJ + m<GED + m<EDJ + m<GJD = 360
80 + 80 + 104 + m<GJD = 360
m<GJD + 264 = 360
m<GJD = 96 deg
Answer:
The measure of angle GJD is 96°.
Step-by-step explanation:
It is given that HGJ=220° on the exterior of the polygon, EGJ is congruent to GED, and CDJ=136° on the exterior of the polygon.
Each side and each interior angle of a regular polygon are same.
It is given that ABCDEF and EHG are regular polygons. It means each interior angle of regular hexagon ABCDEF is 120° and each interior angle of regular triangle EHG is 60°.
[tex]\angle EGH+\angle EGJ+\angle HGJ(exterior)=360^{\circ}[/tex]
[tex]60^{\circ}+\angle EGJ+220^{\circ}=360^{\circ}[/tex]
[tex]\angle EGJ+280^{\circ}=360^{\circ}[/tex]
[tex]\angle EGJ=360^{\circ}-280^{\circ}[/tex]
[tex]\angle EGJ=80^{\circ}[/tex]
[tex]\angle GED=\angle EGJ=80^{\circ}[/tex]
[tex]\angle CDE+\angle EDJ+\angle CDJ(exterior)=360^{\circ}[/tex]
[tex]120^{\circ}+\angle EDJ+136^{\circ}=360^{\circ}[/tex]
[tex]\angle EDJ+256^{\circ}=360^{\circ}[/tex]
[tex]\angle EDJ=360^{\circ}-256^{\circ}[/tex]
[tex]\angle EDJ=104^{\circ}[/tex]
The sum of all interior angles of a quadrilateral is 360°.
[tex]\angle GED=\angle EGJ+\angle EDJ+\angle GJD=360^{\circ}[/tex]
[tex]80^{\circ}+80^{\circ}+104^{\circ}+\angle GJD=360^{\circ}[/tex]
[tex]264^{\circ}+\angle GJD=360^{\circ}[/tex]
[tex]\angle GJD=360^{\circ}-264^{\circ}[/tex]
[tex]\angle GJD=96^{\circ}[/tex]
Therefore the measure of angle GJD is 96°.
45 POINTS FOR WHOLE PAGE!!!!!!!!!!!!!
1. simply: h+245
2. your answer is right
3. 2+1/3n (i believe)
4. 29+5m
5. I’m pretty sure the answer is 29
Arithmetic placement test
Your question doesn't look like one, but I'll give you a set of 10 questions of arithmetic. Do not forget to use PEMDAS.
6 × 7 + 87 + 19 ÷ 276 - 14 + 1291 × 2 - 4625 ÷ 5 × 74 + 6 ÷ 287 × 4 + 747 × 5 + 736 × 5 + 810 × 7 + 24
Another answer will be available in the comments just in case if this is not what you wanted.
F(x) = x^2. What is g(x)?
Answer:
The correct answer is C. g(x) = 1/4x^2
Step-by-step explanation:
In order to determine if the graph fits, take the point that is given on the parabola and see if it fits the equation. To do that we plug it in and see if it gives a true statement.
(2, 1)
g(x) = 1/4x^2
1 = 1/4(2)^2
1 = 1/4(4)
1 = 1 (TRUE)
What is the answer to the question??
Answer:
[tex]c=15[/tex]
Step-by-step explanation:
Use the Pythagorean Theorem.
[tex]a^2+b^2=c^2 \\ \\ 9^2+12^2=c^2 \\ \\ 81+144=c^2 \\ \\ c^2=225 \\ \\ c=\sqrt{225} \\ \\ c=15[/tex]
The population of mice in a vacant building is 200. The population of mice grows according to the model: M(t)=200(1.2)^t where t is the time in days. Assuming none of the mice die, how many mice will be in the building at the end of 30 days
7200. Because 1.2 *30 *200=7200
To estimate the mouse population after 30 days using the given model, M(t)=200(1.2)^t, evaluate the expression with t=30, which results in approximately 47,475 mice.
The student is asking how many mice will be in the building after 30 days according to the exponential growth model M(t) = 200(1.2)^t, where t is the time in days and M(t) is the population of mice at time t. To find the answer, we simply plug the value of 30 days into the model to get M(30) = 200(1.2)^30.
Calculating the expression:
First, calculate 1.2 raised to the power of 30, which gives us approximately 237.3769.
Then, multiply that by the initial population of 200 mice, yielding a result of approximately 47,475.38.
Therefore, after 30 days, assuming no mice die, there will be approximately 47,475 mice in the building.
If f(x)=|x| + 9 and g(x) =-6 , which describes the value of (f+g)(x)
Answer:
Step-by-step explanation:
This has a very brief answer when you know what it means.
f(x) + g(x) = abs(x) + 9 - 6
f(x) + g(x) = abs(x) + 3
Answer:
f + g)(x) = |x| + 3
Step-by-step explanation:
Add the two functions together:
f(x) = |x| + 9
+g(x) = - 6
------------------------
f(x) + g(x) = |x| + 9 - 6
= |x| + 3
The label f(x) + g(x) can be rewritten as (f + g)(x).
Thus, f + g)(x) = |x| + 3
help fast ok thx!!!!
Answer:
C
Step-by-step explanation:
Given
[tex]\sqrt{3x+8}[/tex] = [tex]\sqrt{4x+1}[/tex]
[ note that ([tex]\sqrt{x}[/tex])² = x ]
Square both sides
3x + 8 = 4x + 1 ( subtract 4x from both sides )
- x + 8 = 1 ( subtract 8 from both sides )
- x = - 7 ( multiply both sides by - 1 )
x = 7 → C
Answer:
x = 7.
Step-by-step explanation:
Squaring both sides:
3x + 8 = 4x + 1
3x - 4x = 1 - 8
-x = -7
7 = x.
What is the square root of 36. Please help
Answer:
±6
Step-by-step explanation:
Whenever you are finding the square root of something, it will ALWAYS result in a negative and positive number, or else depending on the situation of a problem.
Ex: Distance Formula → POSITIVE ANSWER ONLY
I am joyous to assist you anytime.
What is the surface area of a sphere with a diameter of 12 centimeters ?
Answer:
[tex]A=452.39\ cm^2[/tex]
Step-by-step explanation:
The formula to calculate the surface area of a sphere is the following:
[tex]A=4\pi r^2[/tex]
Where A is the area of the sphere and r is the radius of the sphere.
In this case we know that the diameter d of the sphere is:
[tex]d = 12\ cm[/tex]
The diameter is:
[tex]d = 2r[/tex].
Thus
[tex]r = \frac{d}{2}\\\\r = \frac{12}{2}\\\\r=6\ cm[/tex]
Then the surface area of the sphere is:
[tex]A=4\pi (6)^2\\\\A = 144\pi\ cm^2\\\\A=452.39\ cm^2[/tex]
Answer is provided in the image attached.
A rectangular pyramid is sliced so the cross section is perpendicular to its base and passes through its vertex. What is the shape of the cross section? trapezoid rectangle triangle square
Answer:
rectangle. trapezoid. triangle. A sphere is sliced so that the cross section does not intersect the center of the sphere
Answer:
sorry im late to this but it is a triangle
Step-by-step explanation:
because when you cut it horizontally and look at the top it is a rectangle so that is wrong trapezoid is when you look at it from the side when cut horizontally so that is wrong there is no square so that instantly becomes wrong because it is a rectangular pyramid when perpendicular it will provide you with a triangle
Which value of a would make the following expression completely factored
x^2-a
A)12
B)36
C)49
D)81
Answer:
A)
Step-by-step explanation:
We know that the expression (x^2 - a^2) can be written as (x-a)(x+a). So an expression of this type: (x^2 - a^2) wouldn't be completely factored because it could be factorized even more.
So we know that 36 = 6^2, 49= 7^2 and 81 = 9^2. So if we choose any of these options (Option B, C and D) it wouldn't be completely factored.
The correct is the option A, given that if a=12, it wouldn't be a perfect square, so it would be completely factored.
So I just did the problem and im pretty sure the answer is A
Brooke is using shiny rocks to make necklaces. Each necklace has 5 shiny rocks. Make a table that shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces
Answer:
10 necklaces = 50 rocks
15 necklaces = 75 rocks
20 necklaces = 100 rocks
25 necklaces = 125 rocks
Step-by-step explanation:
A table that shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces:
| Number of necklaces | Number of shiny rocks used |
| 10 | 50 |
| 15 | 75 |
| 20 | 100 |
| 25 | 125 |
To calculate the number of shiny rocks used, we simply multiply the number of necklaces by the number of shiny rocks per necklace. For example, to calculate the number of shiny rocks used for 10 necklaces, we multiply 10 by 5:
10 necklaces * 5 shiny rocks/necklace = 50 shiny rocks
We can do the same calculation for 15, 20, and 25 necklaces to get the following results:
15 necklaces * 5 shiny rocks/necklace = 75 shiny rocks
20 necklaces * 5 shiny rocks/necklace = 100 shiny rocks
25 necklaces * 5 shiny rocks/necklace = 125 shiny rocks
Therefore, the table above shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces.
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Answer please? Solve math
Answer:
(a)
Step-by-step explanation:
To rationalise the fraction multiply the numerator/denominator by the conjugate of the denominator.
The conjugate of [tex]\sqrt{3}[/tex] + [tex]\sqrt{x}[/tex] is [tex]\sqrt{3}[/tex] - [tex]\sqrt{x}[/tex]
Hence
[tex]\frac{\sqrt{9}(\sqrt{3}-\sqrt{x} ) }{(\sqrt{3}+\sqrt{x} )(\sqrt{3}-\sqrt{x} ) }[/tex]
= [tex]\frac{3(\sqrt{3}-\sqrt{x} }{3-x}[/tex]
= [tex]\frac{3\sqrt{3}-3\sqrt{x} }{3-x}[/tex] → (a)
Which expression is equal to (f · g)(x)?
Answer:
A
Step-by-step explanation:
Note that
x² + 12x + 36 is a perfect square → (x + 6)², hence
[tex]\sqrt{x^2+12x+36}[/tex] = [tex]\sqrt{(x+6)^2}[/tex] = (x + 6)
Hence
f(x) × g(x)
= (x + 6)(x³ - 11)
= [tex]x^{4}[/tex] - 11x + 6x³ - 66
= [tex]x^{4}[/tex] + 6x³ - 11x - 66 → A
(f·g)(x) in mathematics denotes the product of two functions, f(x) and g(x). Its interpretation and output may vary depending on the functions f(x) and g(x), but essentially, it is a multiplication of these two functions.
Explanation:In mathematics, expressing (f·g)(x) indicates the product of two functions at a given x-coordinate. This is equivalent to f(x) multiplied by g(x). For instance, if f(x) = 2x and g(x) = 3x, then (f · g)(x) would yield (2x)(3x), resulting in 6x².
It's important to note that mathematical functions can vary, and this expression can take on various forms based on the nature of f(x) and g(x).
The provided reference information appears to be a mix of rules from differential calculus and mathematical definitions, which lack a direct relation to the original question about (f·g)(x). The primary concept here is understanding function multiplication.
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The ratio to boys to girls in Ms.chunningham's class is 2 to 3. There are 18 girls in the class.What is the total number of students in ms.chunningham's class?
A. 12
B. 30
C.45
D.27
Answer:
B.30
Step-by-step explanation:
This was picked because if u divide 18 by 3. You get 6 and if u multiply it by 2. You get 12 plus the 18 equals 30.
Evaluate the sum
A. 306
B. 240
C. 360
D. 272
Answer:
Option D. [tex]272[/tex]
Step-by-step explanation:
we know that
To evaluate the sum , use the formula
[tex]S=\frac{1}{2}(a1+an)n[/tex]
where
a1 is the first term
an is the last term
n is the number of terms
In this problem
For n=1 ------> a1=2(1)=2
For n=16 ------> an=2(16)=32
n=16 terms
substitute in the formula
[tex]S=\frac{1}{2}(2+32)16[/tex]
[tex]S=272[/tex]
You reach into a bag of coins and withdrew two coins. What is the probability you withdrew a nickel and then a dime if the bag held ten pennies, six nickels, and five dimes? A. 5/14 B. 30/441 C. 1/14 D. 15/441
Answer:
1/14
Step-by-step explanation:
The total number of coins in the bag is 10+6+5, or 21.
You reach into the bag and take ONE coin. The chances of that being a nickel is 6/21, or 2/7, since nickels compose 6 of the 21 coins in the bag.
You don't replace the nickel.
Now you have 20 coins in the bag, including 5 nickels.
The chances of your next draw being a dime is 5/20, or 1/4, since there are 5 dimes in the bag.
The joint probability of drawing a nickel and then a dime is then the product of these two probabilities:
(2/7)(1/4) = 2/28 = 1/14
Use set builder notation to represent the following set. {... -3, -2, -1, 0}
Answer:
[tex]\left\{x\in \mathbb {Z}\ : \ x \le 0 \right\}[/tex]
Step-by-step explanation:
Set-Builder Notation: A shorthand used to describe sets, often sets with an infinite number of elements.
The set {...,-3, -2, -1, 0} is the set of all negative integers and 0, so you can use such set-builder notation:
[tex]\left\{x\in \mathbb {Z}\ : \ x \le 0 \right\}[/tex]
Note: Here [tex]\mathbb{Z}[/tex] represents the set of all integers.
Final answer:
The set {... -3, -2, -1, 0} can be represented in set builder notation as {x ∈ ℤ | -3 ≤ x < 1 }, which describes all integers x that are greater than or equal to -3 and less than 1.
Explanation:
To express the set that includes the numbers -3, -2, -1, and 0 using set builder notation, we start by recognizing that these numbers can be described by a pattern or rule, which is that they are all the integer numbers greater than or equal to -3 and less than 1. We can then write this using set builder notation as:
{x ∈ ℤ | -3 ≤ x < 1 }
In this notation, the variable 'x' represents the elements of the set and ∈ stands for 'element of.' ℤ is the symbol for integers. The vertical bar or colon (|) stands for 'such that.' Our notation reads as 'the set of all integers x such that -3 is less than or equal to x and x is less than 1.'
the difference between a number and 2
Answer:
n-2
Step-by-step explanation:
Difference means subtraction
n-2
Which of the following is the solution to the compound inequality 7x+3/2>13 or 5/2x-1/3>-11/2
Answer:
[tex]\large\boxed{\text{If is "or", then}\ x>-2\dfrac{1}{15}}\\\boxed{\text{If is "and", then}\ x>1\dfrac{9}{14}}[/tex]
Step-by-step explanation:
[tex]7x+\dfrac{3}{2}>13\qquad\text{multiply both sides by 2}\\\\14x+3>26\qquad\text{subtract 3 from both sides}\\\\14x>23\qquad\text{divide both sides by 14}\\\\x>\dfrac{23}{14}=1\dfrac{9}{14}\\=====================\\\\\dfrac{5}{2}x-\dfrac{1}{3}>-\dfrac{11}{2}\qquad\text{multiply both sides by 2}\\\\5x-\dfrac{2}{3}>-11\qquad\text{multiply both sides by 3}\\\\15x-2>-33\qquad\text{add 2 to both sides}\\\\15x>-31\qquad\text{divide both sides by 15}\\\\x>-\dfrac{31}{15}=-2\dfrac{1}{15}\\=====================[/tex]
Final answer:
To solve the compound inequality, each inequality is solved individually. The first inequality yields x > 1.64285714, and the second yields x > -2.06666667. As this is an 'or' compound inequality, the solution is the union of both, leading to x > 1.64285714.
Explanation:
To solve the compound inequality 7x + 3/2 > 13 or 5/2x - 1/3 > -11/2, we need to treat each inequality separately and then find the union of their solutions.
For the first inequality:
Subtract 3/2 from both sides to get 7x > 11.5.
Divide both sides by 7 to find x > 11.5/7, which simplifies to x > 1.64285714.
For the second inequality:
Multiply both sides by 6 to clear the fraction, leading to 15x - 2 > -33.
Add 2 to both sides to get 15x > -31.
Divide both sides by 15 to find x > -31/15, which simplifies to x > -2.06666667.
The solution is the set that satisfies at least one of these inequalities. Since x > 1.64285714 or x > -2.06666667, the overall solution is x > 1.64285714.
Vicki gives her children dessert 30% of the time. If her children want to know the probability that they will eat dessert 3 of the 7 days this week, which simulation design has an appropriate device and a correct trial?
A) Roll a die letting 1 represent eating dessert and 2-6 represent not eating dessert. Roll the die three times.
B) Roll a die letting 1 represent eating dessert and 2-6 represent not eating dessert. Roll the die seven times.
C) Using a table of random digits select a digit between 0 and 9. Let 0-2 represent eating dessert and 3-9 represent not eating dessert. Select three digits.
D) Using a table of random digits select a digit between 0 and 9. Let 0-2 represent eating dessert and 3-9 represent not eating dessert. Select seven digits.
The simulation design that has an appropriate device and a correct trial for this scenario is:
Using a table of random digits select a digit between 0 and 9. Let 0-2 represent eating dessert and 3-9 represent not eating dessert. Select three digits.The correct option is C.
Which simulation design has an appropriate device and a correct trial?The simulation which involves using a table of random digits to select a digit between 0 and 9, letting 0 - 2 represent eating dessert and 3 - 9 represent not eating dessert, and then selecting three digits has an appropriate device and a correct trial.
This simulation design is given below:
To simulate the probability of eating dessert in 3 of the 7 days this week, we would select three digits from the table of random digits and count the number of 0s, 1s, and 2s. The number of 0s, 1s, and 2s would correspond to the number of days the children eat dessert, and the number of 3s, 4s, 5s, 6s, 7s, 8s, and 9s would correspond to the number of days the children do not eat dessert.
We would repeat this process many times (e.g., 1000 times) to obtain an estimate of the probability of eating dessert 3 of the 7 days this week.
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simplify the expression
(2b/3)^4
Answer:
2b/3 * 2b/3 * 2b/3 * 2b/3
Good luck!!
Answer:
16b^4/81
Step-by-step explanation: