Answer:
Step-by-step explanation:
To prove that a quadrilateral ABCD is a trapezium when the diagonals intersect at a point O such that AO/BO=CO/DO, we can use the fact that opposite sides of a trapezium are parallel.
First, let's draw a diagram to represent the given information:
[asy]
pair A, B, C, D, O;
A = (0,0);
B = (2,0);
C = (3,2);
D = (1,2);
O = intersection point(A-C, B--D);
draw(A--B--C--D--cycle);
draw(A-C);
draw(B--D);
label("A", A, W);
label("B", B, E);
label("C", C, E);
label("D", D, W);
label("O", O, N);
label("$\theta_1$", (B+O)/2, NE);
label("$\theta_2$", (O+D)/2, NE);
label("$\theta_3$", (O+C)/2, NW);
label("$\theta_4$", (A+O)/2, NW);
[/asy]
Since the diagonals intersect at point O, the angles formed by the diagonals at O are supplementary (that is, they add up to 180 degrees). In other words, we have:
θ1 + θ2 = 180 degrees
θ3 + θ4 = 180 degrees
Since AO/BO=CO/DO, the triangles AOB and COD are similar. This means that the ratios of their sides are equal. We can write this as:
AO/BO = CO/DO
We can also write this as:
AO/DO = CO/BO
Then, since the angles formed by the diagonals at O are supplementary, we have:
θ1 + θ2 = 180 degrees
θ1 + θ4 = 180 degrees
Subtracting these two equations gives us:
θ2 - θ4 = 0
Since the angles are equal, they are also opposite angles of the quadrilateral ABCD. Therefore, the opposite sides of AB and CD are parallel, which means that ABCD is a trapezium.
in the past year, a veterinarian finds a 35% of animals she treats are cats. Assuming the pets are brought to the vet randomly, what is the probability that exactly 2 of the next 5 animals brought in will be cats?
ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.
What is an equation?There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.
X now has 300 mg of sodium in it.
[tex]x = 300[/tex]
Y also has 450 mg of sodium in it.
[tex]y = 450[/tex]
Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.
Let the number of frozen dinners be "b," and the number of soup cans be "a."
ax + by = 6000
a(300) + b(450) = 6000 .
Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation
[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]
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Square root of 54 in simplified form
Answer:
3√6
Step-by-step explanation:
[tex]\sqrt{54} =\sqrt{9*6}=\sqrt{9} *\sqrt{6}=3*\sqrt{6} =3\sqrt{6}[/tex]
Answer:
3/6 i cant use the weird symbol bc my keyboard
Step-by-step explanation:
Given: 15x < -45
Choose the solution set
a) {x l x<-3}
b) {x l x>-3}
c) {x l x< 3}
d) {x l x> 3}
Angela has 24 golf balls and 18 golf clubs. She wants to sell packages of balls and clubs bundles together. What is the greatest number of packages she can sell with no leftover balls or clubs? Do not include units.
Answer:
GCF of 18 and 24 is 6. So she can sell 6 packages with 4golf balls and 3 golf clubs
Step-by-step explanation:
Give brainliest please
Is this a polynomial? 3x^-2-5
On solving the provided question, we can say that - the value of the following polynomial will be 3x^2 = 5 => x^2 = 5/3
what are polynomials?A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.
here,
[tex]3x^{-2}-5[/tex]
3x^2 = 5
x^2 = 5/3
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what is the value of the expression 3.5 + (1 + 4) x (6.5 + 1.5)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3.5 + (1 + 4)\times (6.5 + 1.5)}\\\mathsf{1 + 4 = \bf 5}\\\mathsf{6.5+1.5=\bf 8}\\\mathsf{3.5+5\times8}\\\mathsf{5\times8=\bf 40}\\\mathsf{3.5+40}\\\large\text{= \bf 43.5}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf 43.5}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A monomial with a degree of 3
The polynomial 4 · x³ is a monomial of degree 3.
What is a monomial?
In algebra there are two types of numbers: constants and variables. Constants are constant real numbers, while variables are real numbers that may represent more than a real number.
Polynomials are the result of combination of constants, variables and fundamental operators (addition, multiplication) and can be classified according to the number of terms:
Monomial - Polynomial with one term.
Binomial - Polynomial with two terms.
Trinomial - Polynomial with three terms.
Polynomial - Polynomial with four or more terms.
The grade of the polynomial is the maximum power that accompany a term in a polynomial in standard form. Then, we can bring an example of polynomial with a degree 3 below:
p(x) = 4 · x³
This is a monomial (polynomial with one term) with degree 3.
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What is the value of 7/8+ (-2/3) - (-4)?
The value of fraction will be;
⇒ 101/24
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The expression is,
⇒ 7/8+ (-2/3) - (-4)
Now,
Since, The expression is,
⇒ 7/8+ (-2/3) - (-4)
Simplify as;
⇒ 7/8 - 2/3 + 4
⇒ (21 - 16)/24 + 4
⇒ 5/24 + 4
⇒ (5 + 96) / 24
⇒ 101/24
Thus, The solution is,
⇒ 101/24
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The length of the shorter leg of a 30-60-90 Special Right Triangle is 6 cm long. How
long is the hypotenuse of the triangle?
Pls help
the answer is 12
I just took the test and the hypotenuse is always 2 times the smaller leg
HELP ME PLEASE
I RLLY NEED IT
Answer:
2. (8, 5) and (2,9)
3. I don’t know how to show this to you.
One root of the equation 4x² + 12x + k = 0, k = Z and x = R, is five times the other root.
Find the value of k.
We found the value of K is 5 and the root of equation is x = -1/2 and x = -5/2
What is quadratic equation?An equation of second order polynomial having one variable is called quadratic equation. Second order means the highest power used with variable is 2.
How to determine the value of k in the question?We are given, 4x²+ 12x +k =0, k =Z and x = R
the quadratic equation is 4x²+12x+k =0
we know the roots of a quadratic equation is x = - b ± √ (b² - 4ac) / 2a
when the quadratic equation is ax²+bx+ c= 0
Hence, roots of the equation given in question will be,
x = - 12 ±√ (12² - 4×4×k) / 2×4
x = - 12 ± √(144-16k) / 8
as per the condition given in question, one root of this equation is 5 times the other root.
hence, - 12 -12 √(144-16k) / 8 = [- 12 + √(144-16k) / 8] × 5
multiplying both sides by 8
- 12 - √(144-16k) = [-12 + √(144-16k)] ×5
- 12 - √(144-16k) = - 60 + 5√(144-16k)
- 12 + 60 = 6√(144-16k)
48 = 6√(144-16k)
8 = √(144-16k)
64 = 144 -16k
16k = 80
k = 5
the value of k =5
by putting the value of k =5
x = -12 ± √ (144 - 80) / 8 = (-12 ± 8) /8
x = -1/2 and x = -5/2
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Solve: 2x - 5 = 4x + 3
Important: No spaces in your answer
(any spaces within the answer can get the whole answer wrong)
How many 2/3 Tablespoons are in a half Tablespoon
Therefore , the solution of the given question of equation come out to be
x = 1/3 tablespoon .
Define equation.Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.
Here,
Given : 2/3 cup Tablespoons
We have to find the half Tablespoons
So,
In order to find the half Tablespoons
Thus,
=> 1 Tablespoon = 2/3Tablespoons + x
where x is the half Tablespoons
=> x = 1/3 tablespoon
Therefore , the solution of the given question of equation come out to be
x = 1/3 tablespoon .
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What is the probability that the student selected at random preferred bananas or grapes? 26 58 42 34
Answer:
I do not know.
Step-by-step explanation:
Find a formula for the nth term
of the arithmetic sequence.
First term -12
Common difference 4
an = 4n + [? ]
I just need the second part please help!
Answer:
4n - 16.
Step-by-step explanation:
nth term = a1 + d(n-1)
= -12 + 4(n - 1)
= -12 + 4x + 4*-1
= -12 + 4x - 4
= 4n - 16,
If Nayesha pumps 9.4 gallons of gas in her gas tank and each gallon costs $2.98, how much money will she spend? QUCIKLY
Answer:
28.012
Step-by-step explanation:
9.4*2.98 = 28.012
Based on information from a large insurance company, 67% of all damage liability claims are made by single people under the age of 25. A random sample of 52 claims showed that 43 were made by single people under the age of 25. Does this indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company
Answer:
Yes. This indicates that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company.
Step-by-step explanation:
Damage liability claims by single people under the age of 25 = 67%
Sample size = 52 claims
Claims made by single people under the age of 25 from the sample = 43 out of 52 claims
In percentage terms, the claims made by single people under the age of 25 from the sample = 43/52 = 83%
Since 83% > 67% (with a difference of 16%)
The height h (in feet) of a fireworks shell shot vertically upward as a function of time t (in s) is h(t)=-16t^2+144t+4 . How long should the fuse last so that the shell explodes at the top of its trajectory?
Answer:
Step-by-step explanation:
h(t)=16t²+144t +4
=16(t²+9t+(9/2)²)-16(9/2)²+4
check your problem statement.
Please help me with this information please
Answer: try 5 it is most likly right
Step-by-step explanation:
N/A
WILL GIVE BRAINLIEST!! 100 POINTS!
NO OUTSIDE WEBSITE LINKS, AND ANSWER WITH DIAGRAM AND EXPLANATION/PROOF
a line and a line segment are given. Construct a line parallel to the given line on a distance equal to the given segment.
I WILL report if your answers are inappropriate or contain external links :)
Need photo of the segment.
There are approximately 3.6 million deaths per year in Nigeria. Express this quantity as deaths per minute
Answer:
6.84931507 = 6-7 deaths
Step-by-step explanation:
3,600,000 / 525600 (minutes in a year) = 6.84931507
Joe decided to track the temperature in his town for five consecutive days. On Monday, the temperature was 23°C. On Tuesday, it decreased by 9°C and then increased by 7°C on Wednesday. On Thursday, the temperature rose 4°C and then decreased by 5°C on Friday. What was the overall temperature change over those five days?
Using a subtraction operation, the overall temperature change over those five days that Joe tracked the temperature in his town was a decrease of 3°C.
How is the temperature change computed?The temperature change can be computed by determining the differences in temperature from one day to the next and summing the differences.
The temperature change can also be computed by finding the difference between the ending period's temperature and the beginning period's temperature.
Days Temperature Change
Monday 23°C 0
Tuesday 14°C (23 - 9) -9
Wednesday 21°C (14 + 7) +7
Thursday 25°C (21 + 4) +4
Friday 20°C (25 - 5) -5
Overall change = -3°C
= 20°C - 23°C = -3°C
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1 Look at the coordinate plane shown.
Fill in the blanks to complete the sentences.
To locate a point on the coordinate grid, start at the
Then move
along the
and then move
along the
--axis,
L-axis.
The ordered pair for point A is (
The ordered pair for point B is (
What is the major theme and minor theme in “Arachne and the weaving contest”
The central theme of Arachne is human limitation and hubris.The center of the ellipse is located midway between the foci .
What is major axis ?The center of the ellipse is located midway between the foci. The minor axis is the line segment going through the center and perpendicular to the major axis, with both endpoints on the ellipse. The length of the ellipse's major axis is equal to the bigger of 2a or 2b, while the length of its minor axis is equal to the smaller. The major axis, which is the largest distance between any two points on the ellipse, is the line that connects both foci and runs from one end to the other. The minor axis, which is the shortest path between two points on the ellipse, is the line that passes through the center of the major axis in a perpendicular direction.
given
The central theme of Arachne is human limitation and hubris. Arachne, a young girl who is a remarkably gifted weaver, thrives on the adulation of her customers.
As a result of her youth and inexperience as well as her awareness of her exceptional talents, Arachne eventually boasts that her weaving is even greater than Athena's.
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What is the surface area of the retagular prism based on the net
A . 34cm
B . 70 cm2
C . 310 cm2
D . 350 cm3
Answer:
90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say I love uStep-by-step explanation:
You have 54 pictures to put in a photograph album.
Each page of the album holds 4 pictures.
How many pages can you fill?
1 page of an album with 4 photos on the page.
13 pages
14 pages
12 pages
15 pages
350 is what percent of 400?
Answer:
87.5%
Step-by-step explanation:
350 ÷ 400 = 0.875 = 87.5%
Answer:
350 is 87.5% or 7/8 of 400.
(Hope this helps! Btw, I answered first. Brainliest please!! :D)
Write 49D2
in the base-ten system.
Each position in base 10 is worth ten times the place to its right, and there are ten numbers (0–9). 49D2 in the base-ten system is equal to 204064.
What does base-10 value 2 have?When you come to "two," you discover that there isn't a single digit in base-two math that stands for "two." Instead, you enter a "1" for "1 two" and a "0" for "0 ones" in the twos and units columns, respectively.
[tex]49D2 in the base-ten system is 4916^3 + 1316^2 + 216^1 \\\\= (494096) + (13256) + (216) \\\\= 200704 + 3328 + 32\\ \\= 204064[/tex]
Binary has a basis of 2 or 10.A binary counting system simply employs the numerals 0 and 1 in each place. Base 2 is another name for binary. In binary, a second place is required to represent a number greater than 1.
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PLEASE HELP I WILL GIVE BRIANLI EST
The number of students at the open house is B. 468.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
We know if a and b are two quantities in a total quantity (ax + bx) the amount of a single quantity can be obtained by [a/(a+b)]× (ax + bx).
Given, The ratio of students to adults at the open house is 9 : 7 and the total number of students and adults at that place is 832.
Therefore,
The number of students is,
= (9/9+7)×832.
= (9/16)×832.
= 9×52.
= 468.
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1/4(10-3+5)2 pls help
Answer:
6
Step-by-step explanation: