Answer:
[tex]3x+\frac{7}{6}y[/tex]
Step-by-step explanation:
To simplify the expression, we first open the parenthesis, then we collect all the like terms. Lastly we simplify the like terms to its simplest form. Given that:
[tex]\frac{1}{2}(3x-\frac{2}{3} y)+3(\frac{x}{2}+\frac{1}{2}y )\\\\Firstly, we\ expand\ the\ parenthesis:\\\\=\frac{1}{2}(3x)-\frac{1}{2}(\frac{2}{3} y)+3\frac{x}{2}+3(\frac{1}{2} y)\\[/tex]
[tex]=\frac{3}{2}x-\frac{1}{3}y +\frac{3}{2}x+\frac{3}{2} y\\\\ Collecting\ like\ terms:\\\\=\frac{3}{2}x+\frac{3}{2}x-\frac{1}{3}y+\frac{3}{2}y\\\\Adding \ terms:\\\\=3x +\frac{7}{6}y[/tex]
help me with trig Pls !!
using given triangle, calculate length of the altitude
hope it will be helpful.......
бу2 + 13y – 8 how to factorize this?
Answer:
We have 6y² + 13y - 8. We can rewrite this as 6x² + 16x - 3x - 8. Grouping terms we get 2x(3x + 8) - (3x + 8) and since both terms have the common factor of (3x + 8) the answer is (3x + 8)(2x - 1).
Find the value of x needed to make the equation below true. 1.5(2x-4)=2(4x+2)
Answer:
x= -2
Step-by-step explanation:
1.5(2x-4)=2(4x+2)
3x-6=8x+4
-5x=10
x= -2
Solve each system by the addition method.
x + 2y = -1
5x - 4y = 16
Put your answer in ordered pair (x, y) DECIMAL form.
Answer:
(x, y) = (2, -1.5)
Step-by-step explanation:
x + 2y = -1
5x - 4y = 16
<=>
(2)x + (2)2y = (2)(-1)
5x - 4y = 16
<=>
2x + 4y = -2
5x - 4y = 16
<=>
7x = 14
<=>
x = 2
(*)x + 2y = -1
=> 2 + 2y = -1
=> 2y = -3
=> y = -1.5
=> (x, y) = (2, -1.5)
If four of the exterior angles of a convex pentagon measure
60°, find the measure of the fifth exterior angle.
Answer:
120°
Step-by-step explanation:
all exterior angles of any polygon add up to 360 therefore 4 x 60 = 240
360 - 240 = 120
The measure of the fifth exterior angle is 120 degrees if the four of the exterior angles of a convex pentagon measure 60°.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have:
If four of the exterior angles of a convex pentagon measure 60°
The sum of the total interior angles = 360
The sum of the four of exterior angles = 4(60) = 240 degrees
The measure of the fifth exterior angle = 360 - 240 = 120 degrees
Thus, the measure of the fifth exterior angle is 120 degrees if the four of the exterior angles of a convex pentagon measure 60°.
Learn more about the regular polygon here:
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Find the point-slope equation for the line that passes through the points (-8,-32) and (3,1). Use the first point in your equation.
Hey there! :)
Answer:
y + 32 = 3(x + 8)
Step-by-step explanation:
Begin by finding the slope of the line using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates of the points into the equation:
[tex]m = \frac{1 - (-32)}{3 - (-8)}[/tex]
Simplify:
[tex]m = \frac{33}{11}[/tex]
m = 3.
Point-slope form is:
y-y₁=m(x-x₁)
Plug in the coordinates of the first point, as well as the slope:
y - (-32) = 3(x - (-8)
y + 32 = 3(x + 8)
Answer: y+32=3(x+8)
Step-by-step explanation:
First you need to find the slope.The slope is the change in y divided by the change in x values.
-32 - 1 = -33
-8 - 3 = -11
-33/-11 = 3 the slope is 3
and in point-slope form is like y-b= m(x-a) where b is a y coordinate and a is the x coordinate.
it could be like y-1=3(x-3) or y+32= 3(x+8)
Jasmine knows that the area of a rectangle is the product of its base and height. Help her write an expression that represents the area of this rectangle, and then use the expression to find the area when b = 10
Answer:
Area of rectangle = H × B
Area of rectangle = 10(H)
Step-by-step explanation:
Given:
Base (B) = 10
Height = H
Find:
Area of rectangle
Computation:
Area of rectangle = Height × Base
Area of rectangle = H × B
So,
Area of rectangle = H × B [Base (B) = 10]
⇒ Area of rectangle = H × 10
⇒ Area of rectangle = 10(H)
Answer:
The expression that represents the area of this rectangle is 8b
When b = 10, the area of the rectangle is 80 square units.
Step-by-step explanation:
The rectangle’s base is b units, and its height is 8 units. The area of the rectangle is the product of its base and height, which is 8b.
To find the area of the rectangle when b = 10, substitute 10 for b in the expression:
8b= 8(10)
=80
Which statement is true about the quadratic equation 8x2 − 5x + 3 = 0? The constant term is 8.
Answer:
false
Step-by-step explanation:
the constant term is 3 not 8
hope this helps
On a coordinate plane, polygon GHIJ translates 8 units to the left to form polygon G'H'I'J'. Which of the following equations is not necessarily true? A. GH = G'H' B. G'G = 8 units C. m∠HIJ = m∠H'I'J' D. m∠HI'J = m∠H'IJ'
Answer:
The answer would be letter B. This is because the problem wants you to find the equation that is not necessarily true. In this case G'G does not equal 8 units.
dalanay enlarges a photograph tahst is 3 inches long and 2 inches wide. the length of the enlarged photograph is 15 inches. what is the width of the enlarged photograph, in inches?
Answer:
10 inches
Step-by-step explanation:
Length of photograph, L1 = 3 inches; Length of enlarged photograph, L2 = 15 inches; Width of photograph, W1 = 2 inches; Width of photograph, W2 = ?
Hence, L1/L2 = W1/W2
∴ W2 = (L2*W1)/L1 = (15 X 2)/3 = 10 inches
A salad bar offers vegetable platters in 4 sizes (small, medium, large, and super-sized) and 6 different vegetables to choose from. Different platters can be created by changing the size and/or the choice of vegetables. If Selena wants to order a platter with exactly 2 different vegetables, how many different platters could she create?
Answer:
The number of different platters Selena can create by selecting two different vegetables is 60 different platters
Step-by-step explanation:
The information given are;
The number of different sizes of salad available = 4
The number of different vegetable to choose from = 6
The number of vegetables Selena ordered = 2
The number of ways Selena can choose 2 vegetables out of 6 = ₆C₂ = 15 ways
The number of different platters (choice of vegetable and size of platter) Selena can create = The number of different sizes of salad available × The number of ways Selena can choose the vegetables
The number of different platters (choice of vegetable and size of platter) Selena can create = 4 × 15 = 60 different platters.
Area of the cone when the radius is 4cm and the height is 12cm. Rounded to the nearest tenth
What are the x-and y intercepts for the graph of 5x-2y=20?
Answer: y = (5)(2)x-10
Step-by-step explanation:
Express 160 as the product of its prime factors.
Write the prime factors in ascending order and
give your answer in index form.
Answer:
Step-by-step explanation:
160 = 2 × 2 × 2 × 2 × 2 × 5
Hope this helps
plz mark it as brainliest!!!!!!!!!!
The number 160 as a product of prime factors is 160 = 2 × 2 × 2 × 2 × 2 × 5
What are prime factors?A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.
A prime number factor is any prime number that can be multiplied by the original number to get the factor.
The prime factors of the numbers will be:-
160 = 2 × 2 × 2 × 2 × 2 × 5
Therefore, the number 160 as a product of prime factors is 160 = 2 × 2 × 2 × 2 × 2 × 5.
To know more about prime factors follow
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simplify radical sign 16a^8b^-2
Answer:
[tex] \frac{ {4a}^{4} }{b} [/tex]solution,
[tex] \sqrt{16 {a}^{8} {b}^{ - 2} } \\ [/tex]
Use negative power rule:
[tex] {x}^{ - a} = \frac{1}{ {x}^{a} } [/tex]
[tex] \sqrt{ {16}^{8} \times \frac{1}{ {b}^{2} } } \\ [/tex]
Simplify:
[tex] \sqrt{ \frac{ {16a}^{8} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {16a}^{8} } }{ \sqrt{ {b}^{2} } } \\ [/tex]
Use this rule:
[tex] \sqrt{ab} = \sqrt{a} . \sqrt{b} [/tex]
[tex] \frac{ \sqrt{16. \sqrt{ {a}^{8} } } }{ \sqrt{ {b}^{2} } } [/tex]
Since, 4*4=16 ,the square root of 16 is 4
[tex] \frac{ \sqrt{ {4}^{2} } \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } [/tex]
Simplify:
[tex] \frac{4 \: \sqrt{ {(a}^{4) ^{2} } } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 {a}^{4} }{b} [/tex]
Hope this helps...
Good luck on your assignment...
Classify the following triangle. Check all that apply.
Answer:
NO
Step-by-step explanation:
IMAGE
What is the smallest positive integer n for which [tex]n^{2}[/tex] is divisible by 18 and [tex]n^{3}[/tex] is divisible by 640?
Answer:
120
Step-by-step explanation:
n^2 has a factor of 18, so factors of 3^2·2. Since n^2 is a perfect square, we know n must have a factor of 3·2 = 6.
n^3 has a factor of 640, so factors of 2^7·5. Since n^3 is a perfect cube, we know n must have a factor of 2^3·5 = 40.
The least common multiple of 6 and 40 is 120.
The smallest positive integer n is 120.
_____
Check
120^2/18 = 800
120^3/640 = 2700
Pls help me with trig!!!
for 32 but if you understand 33 pls i need the help
I’m guessing number 32 is true, since it asks you to round to the nearest integer.
To solve this problem, use the Pythagorean Theorem, which is a^2 + b^2 = c^2, where c is the hypotenuse. The hypotenuse of the triangle is always the longest side, meaning the hypotenuse would be 15.23.
To ensure these measurements can be used in order to make a right triangle, substitute the numbers into the Pythagorean Theorem.
6^2 + 14^2 = 15.23^2.
36 + 196 = 231.9529
232 = 231.9529
Because we were asked to round, that makes the equation 232 = 232, meaning the answer is true.
There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. d How many sets can be formed (including empty set)
Answer:
1,024Step-by-step explanation:
The number of sets that can be generated from the given set is determined by calculating the power of the set. Power of a set is expressed as 2ⁿ where:
n represents the number of elements in the set.
Given the set S = {0,1,2,3,4,5,6,7,8,9}.
n(S) = 10
The Power of the set = 2^n(S)
Power of the set = 2^10 = 1,024
This means that 1,024 different sets can be formed from the given set including the empty set.
In an arithmetic series, what is the sum of the first 22 terms if the first term is 12 and the common difference is 3?
Answer:
561
Step-by-step explanation:
an = dn - (a-d)
The difference is 3.
The first term is 12.
an = 3n - (12-3)
an = 3n - 9
Put n as 1, 2, 3, 4, 5 ....22.
3(1) - 9 = -6
3(2) - 9 = -3
3(3) - 9 = 0
3(4) - 9 = 3
3(5) - 9 = 6
...
3(22) - 9 = 57
Add the first 22 terms.
-6+-3+0+3+6+9+12+15+18+21+24+27+30+33+36+39+42+45+48+51+54+57
= 561
Jo paints some tennis balls and puts them in a bag. She picks a ball at random from the bag and replaces it. She repeats this 60 times, and gets a ball not painted 50 times. Find the experimental probability of getting a painted ball from Jo's bag.
Answer:
1/6
Step-by-step explanation:
An experimental probability is the number of times an event occurred when actually attempted.
So, if Jo does the experiment 60 times and receives 50 unpainted balls, then calculate how many painted balls she got:
60-50 = 10.
So, the probability of picking a painted ball = 10/60 = 1/6
Hope this helps
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)
Answer:
4 (20) + 6(6) = 120
4(20) + 4 (6) = 100
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations with the information given:
Build time (hours) = 4c + 6a = 120
Test time (hours) = 4c + 4 a = 100
Where c represents the number of child bikes and a represents adult bikes.
So, for 20 child bikes and 6 adult bikes:
4 (20) + 6(6) = 120
4(20) + 4 (6) = 100
Feel free to ask for more if needed or if you did not understand something.
if a 10-pound turkey costs $20.42.how much does a 21-pound turkey cost
Answer:
$42.88
Step-by-step explanation:
Let's create a proportion using the following setup:
cost/pounds=cost/pounds
We know that it costs $20.42 for a 10 pound turkey.
$20.42/10 pounds= cost/pounds
We don't know how much a 21 pound turkey costs, so we can say that it costs $x for a 21 pound turkey.
$20.42/ 10 pounds= $x/ 21 pounds
20.42/10=x/21
We want to find x, by getting x by itself.
x is being divided by 21. The inverse of division is multiplication. Multiply both sides by 21.
21*(20.42/10)=(x/21)*21
21* 20.42/10=x
21*2.042=x
42.882=x
Round to the nearest cent, or hundredth.
42.88=x
x= $42.88
A 21 pound turkey costs $42.88
⚠️⚠️⚠️GIVING AWAY HUGE POINTS FOR ANYONE WHO COMPLETES THIS AND GETS THEM RIGHT!!!!!!!⚠️⚠️⚠️
Answer:
The average speed for his journey from York to Blackpool is 61.4 KM/H
Step-by-step explanation:
Select the correct answer from each drop-down menu. Polygon ABCDE rotates 45° clockwise about point F to form polygon FGHIJ, shown in the figure. Find the measure of each angle of polygon ABCDE. m∠ABC = ° m∠BCD = ° m∠DEA = ° m∠CDE = °
Answer and Step-by-step explanation:
As it is mentoned in the question
Polygon ABCDE rotates around point F in clockwise direction to create polygon FGHIJ
And as we can see in the figure that
So we conclude that
A = F ⇒ 117°
B = G ⇒ 90°
C = H ⇒ 127°
D = I ⇒ 90°
E = J ⇒ 117°
Therefore this is the answer and the same is to be considered
Answer:
m∠ABC = 90117127°m∠BCD = 90117127°m∠DEA = 90117127°m∠CDE = 90117127°
Step-by-step explanation:
Help please!!!! Thanksss
Answer:
Correct option: E
Step-by-step explanation:
The group must have 1 man and 1 woman.
So, for the woman slot, we have 4 possible choices, because we have 4 women and 1 slot to occupy.
For the man slot, we have 2 possible choices, because we have 2 men and 1 slot to occupy.
So the number of different groups we can make is the product of the number of possibilities for each slot:
Number of groups = 4 * 2 = 8
Correct option: E
Terri rode her bike very slowly to the top of a big hill. Then she coasted back down the hill at a much faster speed. The distance from the bottom to the top of the hill is 3 kilometers. It took Terri ¼ hour to make the round trip. What was her average speed for the entire trip?
Answer:
Terri’s speed can be calculated like this:
her speed- [tex]\frac{6km}{0.25h}[/tex]=24km/h
Step-by-step explanation:
An irregular parallelogram rotates 360° about the midpoint of its diagonal. How many times does the image of the parallelogram coincide with its preimage during the rotation?
Answer:
2
Step-by-step explanation:
The question, is basically asking for the order of rotational symmetry for the parallelogram. This is 2, which means while spinning the parallelogram around its centre point 360 degrees, it looks exactly the same, or matches with its original at 2 points
Guys I need help what is 8+[4+(-9)] please.
Answer:
-9 + 4 = 4 - 9 = -5
-5 + 8 = 8 - 5 = 3
3 is the answer
Step-by-step explanation:
8+[4+(-9)]
-9 + 4 = 4 - 9 = -5
-5 + 8 = 8 - 5 = 3
3 is the final answer.
Find the sum of the arithmetic series for which a_1 = 7, n = 31, and a_n = 127.
Answer: 2077
There are 31 terms.
S₃₁ = 31(a₁+a₃₁)/2 = 31(7+127)/2 = 2077