The inverse of the statement "If a number is divisible by 2, then it is even" is "If a number is not divisible by 2, then it is not even." According to logical operations in mathematics, an inverse involves both swapping and negating the components of the original statement.
Explanation:In the field of mathematics, the inverse of a statement swaps both the hypothesis and the conclusion, and applies a negation to them. The original statement given is, "If a number is divisible by 2, then it is even". The inverse of this statement switches and negates the components, resulting in: "If a number is not divisible by 2, then it is not even". Therefore, the second provided option is the correct one.
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What is decomposing fractions
Explanation:
"Decomposing fractions" means breaking them into a sum of fractions, often unit fractions (fractions with a numerator of 1). Here are a few examples:
3/8 = 1/8 + 1/8 + 1/8
5/6 = 1/2 + 1/3
3/4 = 1/2 + 1/4
Two mechanics can assemble 10 bicycles in 8 hours. How many bicycles could one mechanic assemble in 8 hours?
Answer:
5 bicycles
Step-by-step explanation:
In the same time period (8 hours), half as many mechanics can assemble half as many bicyles: 10/2 = 5.
roberto has 12 tiles. each tile is 1 square inch. he will arrange them into a rectangle and glue 1-inch stones around the edge. how can roberto arrange the tiles so that he uses the least number of stones?
Answer:
the answer is 4 and 2
Step-by-step explanation:
What is the equation for the vertical asymptote of f(x)= (x+2)/(4x+4)
if y = 6x - 3 which of the following see represents possible inputs and outputs of the function represented as ordered pairs
PLEASEEEEE HEEEEEELPPPPPPPPPPPPPPP
Suppose ABCD is a rhombus such that the angle bisector of ∠ABD meets AD at point K. Prove that m∠AKB = 3m∠ABK.
1. Let m∠ABK=x°. Since line BK bisects ∠ABD, then
m∠ABK=m∠KBD=x°.
Also m∠ABD=m∠ABK+m∠KBD=2x°.
2. The diagonal BD of rhombus ABCD bisects ∠ABC, then
m∠ABD=m∠DBC=2x°.
This gives you that
m∠ABC=4x°.
3. Angles A and B are supplementary, so
m∠A+m∠B=180°,
m∠A=180°-4x°.
4. Consider triangle ABK. The sum of the measures of interior angles in triangle is always 180°, thus
m∠A+m∠ABK+m∠AKB=180°,
m∠AKB=180°-x°-(180°-4x°),
m∠AKB=3x°=3m∠ABK.
Answer:
Given information: ABCD is a rhombus, angle bisector of ∠ABD meets AD at point K.
[tex]\angle ABK\cong \angle DBK[/tex] (Definition of angle bisector)
[tex]m\angle ABK=m\angle DBK[/tex] (Definition of concurrency)
Let as assume the measure of angle ABK is x.
[tex]m\angle ABK=x[/tex]
[tex]m\angle ABD=m\angle ABK+m\angle DBK[/tex]
[tex]m\angle ABD=x+x[/tex]
[tex]m\angle ABD=2x[/tex]
All sides of a rhombus are same.
Since AB=AD, therefore ABD is an isosceles triangle and two angles of an isosceles triangle are congruent.
[tex]m\angle ADB=m\angle ABD[/tex]
[tex]m\angle ADB=2x[/tex]
According to exterior angle theorem, sum of two interior angles of a triangle is equal to third exterior angle.
Using exterior angle theorem, we get
[tex]m\angle AKB=m\angle ADB+m\angle DBK[/tex]
[tex]m\angle AKB=2x+x[/tex]
[tex]m\angle AKB=3x[/tex]
[tex]m\angle AKB=3(m\angle ABK)[/tex]
Hence proved.
f(x)=x^2-2x-1 and g(x)=5x-1/7x-3
find f(x+7) and g(x/2)
A total of
276
tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
Final answer:
The number of adult tickets sold for the school play was 92, found by setting up an equation where the number of adult tickets plus twice the number of adult tickets equals the total of 276 tickets sold.
Explanation:
Calculating the Number of Adult Tickets Sold
The student is asked to find out how many adult tickets were sold for the school play, given that a total of 276 tickets were sold and the number of student tickets was two times the number of adult tickets sold. Let's denote the number of adult tickets as x and the number of student tickets as 2x. The total number of tickets is the sum of adult and student tickets which can be represented as:
x + 2x = 276
Combining like terms, we get:
3x = 276
To find the value of x, we divide both sides by 3:
x = 276 / 3
x = 92
Therefore, the number of adult tickets sold was 92.
3(10+2j) please help me
NAME_____________________________________DATE_________________PER._______
TRAPEZOIDS
RSTV is an isosceles trapezoid. Decide whether each statement is TRUE or FALSE.
Justify your answer.
1. TRUE or FALSE
Why?
TR ⊥ SV
2. TRUE or FALSE
Why?
∠RVT ≅ ∠STV
3. TRUE or FALSE
Why?
∠SRV & ∠TVR are
supplementary.
WXYZ is an isosceles trapezoid with bases WZ and XY and median MN. Use the given
information to solve each problem.
4. MN = ____________ Find MN if WZ = 11 and XY = 3.
5. m∠XMN = ____________ Find m∠XMN if m∠WZN = 78°.
6. XY = ____________ If MN = 10 and WZ = 14, find XY.
7. x = ____________ What is the value of ‘x’ if m∠MWZ = (15x –5)° and m∠WZN = (90 – 4x)°?
8. x = ____________ If m∠XWZ = (2x – 7)° and m∠XYZ = 117°, find
the value of ‘x’.
9. x = ____________ If MN = 60, XY = 4x – 1, and WZ = 6x + 11, find
the value of ‘x’.
10. x = ____________ If MN = 10x + 3, WZ = 11, and XY = 8x + 19,
find the value of ‘x’.
11. x = ____________ If MN = 2x + 1, XY = 8, and WZ = 3x – 3, find
the value of ‘x’.
Can someone do this for me? im having a hard time and I have a 42 in math rn and I just need these done cause they are late.. if anyone likes geometry then here you go
Answer:NAME: Nzube Erobu DATE: 02/ 06 / 2020
Step-by-step explanation: With reference to the attached document, below:
1) False, the lines linking between TR and SV are diagonals
2) True, ∠RVT = ∠ STV because they have the same right angled triangles.
3) True, because they separate triangles that have all angles in each triangle summing up to 180°
4) (11 + 3)/2 = 14/2= 7
7) (15x - 5)° + (90 - 4x)° = 180°
(15x - 4x + 90 - 5)° = 180°
( x + 85)° = 180°
∴ x = 180° - 85° = 95°
8) (2x - 7)° + 117° = 180°
2x° +117° - 7° = 180°
2x° + 110° = 180°
2x = 180° - 110°
∴ x = 70°/2 = 35°
9) 4x - 1 + 6x + 11 = 60
4x + 6x + 11 -1 = 60
10x + 10 = 60
10x = 60 - 10 = 50
∴ x = 50/10 = 5
10) 18x + 19 - (10x + 3) = 11
18x - 10x + 19 - 3 = 11
8x + 16 = 11
8x = 11 - 16 = - 5
∴ x = - 5/8
11) 2x + 1 + 3x - 3 = 8
2x + 3x - 3 + 1 = 8
5x - 2 = 8
5x = 8 + 2= 10
∴ x = 10/5 = 2
For which set of lines is it reasonable to state that The two lines are ALMOST perpendicular to each other? A) y = 2.1x + 3, y = 2.1x + 5 B) y = 0.9x + 5, y = -1.26x + 8 C) y = 5x + 1.25, y = -5x + 1.25 D) y = 3 4 x + 0.28, y = 4 3 x + 0.29
×
[tex] \frac{x}{4} = \frac{6}{12} [/tex] solve the proportions
state the degree of the polynomial xy+3x2-7+x
simplify 28-(8+4). (4-2).
The value of 28-(8+4). (4-2) is 4
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
28-(8+4). (4-2)
=28-(32-16+16-8)
=28-24
=4
Therefore, the value of the algebra will be 4
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To simplify 28-(8+4)·(4-2), calculate the operations within the parentheses first, resulting in 28-12·2. Multiplying 12 by 2 gives 24, and subtracting this from 28 yields the simplified answer, which is 4.
Explanation:The question requires us to simplify the expression 28-(8+4)·(4-2). We start by simplifying the operations inside the parentheses:
Next, we multiply the results from the parentheses:
Lastly, we subtract this value from 28:
Therefore, the simplified expression is 4.
Can I have help with this please?
Try this:
2. 2.5/5=16/32; 2/4=16/34.
3. one - 6;6;6; two - 6;8;10; three - 5;10;12.
Does 3pi/5 have a supplementary angle?
What does x equal (x/4)+12=38
your banking cupcakes for the school dance and your recipe makes 24 cupcakes and needs 2 cups of milk . you need to make 288 cupcakes how many quarts of milk will you need
A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed,32 plant to buy a school newspaper. If 360 students bought papers,predict the number of students enrolled at the school.
The number of students enrolled at the school is 540.
A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed, 32 plan to buy a school newspaper. If 360 students bought papers, predict the number of students enrolled at the school. To solve this, we use a proportion based on the survey results to predict the total enrollment. The proportion of students who plan to buy the newspaper based on the survey is 32 out of 48, which simplifies to 2 out of 3 when reduced. If 360 students actually bought the paper, and assuming the proportion holds for the entire school, we can set up the equation:
2/3 = 360 / total students
To find the total number of students, solve for 'total students':
total students = 360 × 3 / 2
total students = 540
Therefore, based on the survey results and the actual number of newspapers bought, we can predict there are 540 students enrolled at the school.
If an object is projected upward with an initial velocity of 125 125 ft per sec, its height h after t seconds is h equals negative 16 t squared plus 125 t h=−16t2+125t. Find the height of the object after 5 5 seconds.
The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers. Find the two integers.
Your cousin has a goat in his backyard, tied with a 4 foot rope. The goat can move in a circular motion the length of the rope. What is the area of the backyard where his goat can eat the grass? Hint: The 4 foot rope represents the radius of the circle.
1. What equation can be used to calculate the area of the yard that his goat can eat the grass?
2. What is the area of this circle in your cousin’s backyard?
3. What would the new area be if he decides to use a 5 foot rope?
What is the value of the leading coefficient a if the polynomial function P(x) = a(x + b)2(x − c) has multiplicity of 2 at the point (−3, 0) and also passes through the points (2, 0) and (0, 36)?
answers:
−2−3336
Twenty, which is 4 more than half, of the students in Bryan’s homeroom have tickets to attend the school’s musical. Choose Yes or No to tell whether each of the following equations can be used to find the number of students in Bryan’s homeroom.
The equations that can be used to find students with tickets is given as m/2 + 4 = 20. The correct options are (B) and (D).
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
Suppose the number of students in homeroom be m.
Then, as per the question the equation can be written as,
m/2 + 4 = 20
It can also be written as,
4 = 20 - m/2
Hence, the required equation for the given case is m/2 + 4 = 20.
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The complete question with all the options is attached here.
Find the value of x. Then find the measures of B and C
How to find the x intercepts of f(x)=-2x^2+x+5
what fraction would you add to 29/6 to make 4
Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other 52 mi. before they each drop their anchors. What is the distance between the ships to the nearest mile?
Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Explanation :
Since we have shown in the figure below :
a=70 mi.
b=52 mi.
c=x mi.
[tex]\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}[/tex]
So, we use the cosine rule , which states that
[tex]c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03[/tex]
So, c = x= 106.03 mi.
Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Solve for x: x^4 = 3^x
What value is equivalent to ∣ −14 ∣?