Answer:
∠ABC = 110°
Step-by-step explanation:
Since Δ BCD is equilateral then the 3 angles are congruent with measure 60°
Thus ∠ DBC = 60°
Δ ABD is isosceles with AB = BC
Thus the base angles are congruent, that is
∠ BAD = ∠ ADB = 65°
Calculate ∠ ABD by subtracting the sum of the base angles from 180°
∠ ABD = 180° - (65 + 65)° = 180° - 130° = 50°
Hence
∠ ABC = ∠ ABD + ∠ DBC = 50° + 60° = 110°
Answer:
110°
Step-by-step explanation:
Triangle ABD is an isosceles triangle.
This means that ∠ ADB is also 65°
Use the Triangle Sum Theorem (All angles of a triangle sum up to 180°)
65 + 65 = 130
180 - 130 = 50
∠ ABD is 50°
For Triangle BCD, all of the sides are the same.
This means all of the angles will be 60° (60° * 3 = 180°)
To find ∠ ABC, you add the two angles
60° + 50° = 110°
Which of the following numbers has a prime factorization of 2 x 5 x 5?
Answer:
5×5
Step-by-step explanation:
the factorazation is 5×5
Final answer:
The number with a prime factorization of 2 x 5 x 5 is 50, which is obtained by multiplying 2 by 5 squared (2 x 25).
Explanation:
The student asked which of the following numbers has a prime factorization of 2 x 5 x 5. The prime factorization given can also be written as 2 x 52, since 5 x 5 equals 52 or 25. Therefore, we are looking for a number that is the product of 2 and 25.
By multiplying 2 by 25, we find that the correct answer is 2 x 25 = 50. Thus, the number that has a prime factorization of 2 x 5 x 5 is 50.
One counting number is 4 times great as a counting number.The product of the two number is 36.What is the sum of the two number
Answer:
The sum of the two numbers is 15
Step-by-step explanation:
Let the counting numbers be x and y.
Then we can write the following equations
x=4y.......1 (one is four times greater )
x(y)=36.....2 (the product of the two)
Putting equation 1 into equation 2, we get
4y(y)=36
[tex] {4y}^{2} = 36 [/tex]
Dividing through by 4,we get
[tex] {y}^{2} = \frac{36}{4} [/tex]
[tex] {y}^{2} = 9[/tex]
Taking square root of both side, we obtain
y=3
Putting the value of y into equation , we get
x=4(3)=12
Hence the numbers are 3 and 12
Therefore the sum of the two numbers is 3+12=15
One counting number is 4 times greater as the other counting number. The product of the two numbers is 36. The sum of the two numbers is 15.
Explanation:Let's assume the smaller counting number as X. According to the question, one counting number is 4 times greater than the other, so the larger counting number is 4X. The product of the two numbers is 36, so we can set up an equation: X * 4X = 36. Simplifying, we get 4X^2 = 36. Divide both sides by 4 to get X^2 = 9. Taking the square root of both sides, we find X = 3. Therefore, the two numbers are 3 and 4 times 3 which is 12. The sum of these two numbers is 3 + 12 = 15.
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Identify the values that create ordered pairs that are solutions to the equation 3x-5y=20
(5,y1) and (x2,2) PLZ HELP!!!!
Answer:
(5,-1)
(10,2)
Step-by-step explanation:
The given equation is 3x - 5y = 20 ........ (1)
Now, putting x = 5, in equation (1) we get,
15 - 5y = 20
⇒ 5y = - 5
⇒ y = - 1
So, the ordered pair (5,-1) is a solution of the equation (1).
Now, putting y = 2, in equation (1) we get,
3x - 10 = 20
⇒ 3x = 30
⇒ x = 10
So, the ordered pair (10,2) is a solution of the equation (1). (Answer)
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
X - 12y = - 11
X- y = -11
Answer:
x=-11, y=0. (-11, 0).
Step-by-step explanation:
x-12y=-11
x-y=-11
-------------
x=y+(-11)
x=y-11
y-11-12y=-11
-11y=-11+11
-11y=0
y=0/-11=0
x-0=-11
x=-11+0=-11
Simplify
Please help
Answer:
D
Step-by-step explanation:
Given
- 4x² - 5(x + 3) + x² ← distribute the parenthesis by - 5
= - 4x² - 5x - 15 + x² ← collect like terms
= - 3x² - 5x - 15
In the expression below, a is an integer.
12x² + ax - 20
If 3x + 4 is a factor of the expression above, what is
the value of a ?
Answer:
Step-by-step explanation:
The required simplified value of the a is given as a = 31.
What are functions?
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
for the expression
12x² + ax + 20 = 0 (because this expression has factors)
The above expression has a factor (3x + 4)
3x + 4 = 0
x = -4 / 3
above the value of x is one of the zeroes for the given expression, so when we put it in the given expression the expression terminates to zero,
so,
f(-4/3) = 0
12(-4/3)² + (-4/3)a + 20 = 0
12×16/9 - 4a/3 + 20 = 0
-4a/3 = -20 - 64 / 3
-4a/3 = [-60 - 64] / 3
-4a = -124
a = 31
Thus, the required simplified value of the a is given as a = 31.
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Add. –5 + –3 = ____
–8
–2
2
8
Answer:
A) -8
Step-by-step explanation:
-5+(-3)=-5-3=-8
Write a word problem for 3x + 15 = 42
Final answer:
The math problem 3x + 15 = 42 is represented by a word problem involving a teacher preparing for a math contest, aiming to have 42 pencils for students, leading to a solution where 9 students can participate.
Explanation:
Consider a scenario where a teacher is preparing a math contest for school and decides to include a question about buying pencils for students. The teacher figures that for every student participating, they will need 3 pencils. Along with these, the teacher wants to have an additional 15 pencils just in case. The total number of pencils the teacher aims to have is 42.
To solve, we can write the equation representing this scenario as 3x + 15 = 42. Here, x represents the number of students participating in the contest. Solving this equation will help us find how many students can participate if the teacher wants to achieve their goal of having 42 pencils ready for the math contest.
To find the number of students, we subtract 15 from both sides to get 3x = 27, and then divide both sides by 3 to get x = 9. Therefore, 9 students can participate in the math contest.
A company plans to sell purses for $20 each. The company's business manager estimates that the
cost, y, of making x purses is a quadratic function
with a y-intercept of 1,989 and a vertex of (500,4,489).
Which linear equation models the company’s income from selling x purses?
A.) y=x+20
B.)20x
C.)x/20
D.)20/x
Step-by-step explanation:
the answer is B: y = 20x on edge.
The income for selling x purses is given by the linear equation:
y = $20*x
Which linear equation models the income for selling x purses?
A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
In this case, we know that each purse is sold by $20. So, if the company sells x purses, the income will be x times $20.
So the linear equation is:
y = $20*x
Then the correct option is B
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A television that normally sells for $1,200 is on sale at a 15% discount. What is the sale price of the television?
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1200 x 0.85 = 1020
The sale price is $1020
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This rectangle has a perimeter of 120
centimeters. If the width is 20 cm, what is
measure of the length?
20 cm
x cm
The length of the rectangle, given a perimeter of 120 cm and a width of 20 cm, is 40 cm.
Explanation:This question pertains to the calculation of the dimensions of a rectangle given its perimeter and one side. In a rectangle, the perimeter is given by the formula 2(Length + Width). In this case, the perimeter is 120 cm, and the width is 20 cm. We can set up the following equation based on the given information: 120 = 2(Length + 20). After simplifying, we get 120 = 2*Length + 40, which leads to 2*Length = 120 - 40 or 2*Length = 80. Finally, solving for Length gives Length = 80 / 2 = 40 cm. Therefore, the length of the rectangle is 40 cm.
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if the price of a hamburger increased from $3.50 to $4.20 what is the percentage increase in price
Answer:
Percent increase: 20%
Step-by-step explanation:
1. 4.2-3.5 x 100=20%
3.5
2. Percent increase: 20%
The percentage increase in the price of a hamburger from $3.50 to $4.20 is a 20% increase. This is calculated by dividing the increase in price by the original price and then multiplying by 100.
Explanation:To calculate the percentage increase in the price of a hamburger that went from $3.50 to $4.20, we first find the absolute increase by subtracting the original price from the new price.
The absolute increase is $4.20 - $3.50 = $0.70.
To find the percentage increase, we then divide the absolute increase by the original price, which gives us $0.70 / $3.50 = 0.2.
Finally, to express this as a percentage, we multiply by 100, resulting in a 20% increase in the price of the hamburger.
whats the solution to 2-3x = -x-8
Answer:
x = 5
Step-by-step explanation:
Move the variable to the left side and change it's sign then move constant to the right side and change its sign you will get -3x+x = -8-2 collect like terms then calculate the difference you will get -2x = -10 Divide both sides of the equations by -2 and you will get x =5
The hypotenuse of an isosceles triangles measures 10 inches long. What is the length of one leg of the triangle?
StartFraction 10 Over StartRoot 3 EndRoot EndFraction
StartFraction 10 Over StartRoot 2 EndRoot EndFraction
10 StartRoot 2 EndRoot
10 StartRoot 3 EndRoot
Final answer:
To find the length of one leg of an isosceles right triangle with a hypotenuse of 10 inches, we use the Pythagorean theorem, which gives us a leg length of 5√2, or approximately 7.071 inches. The correct answer choice is StartFraction 10 Over StartRoot 2 EndRoot EndFraction.
Explanation:
The student is asking about the length of one leg of an isosceles right triangle where the hypotenuse measures 10 inches long. To find the length of one leg of this triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b).
Since the triangle is isosceles, the lengths of the legs are equal, so we have: a = b. The theorem can be expressed as a² + b² = c², which simplifies to 2a² = c² because a = b. We know the hypotenuse (c) is 10 inches, so the equation is 2a² = 10².
Let's find a:
2a² = 10²
2a² = 100
a² = 50
a = √50
a = √(25×2)
a = √25 × √2
a = 5√2
Therefore, the length of one leg of the triangle is 5√2, which is approximately 7.071 inches. So, the correct answer is StartFraction 10 Over StartRoot 2 EndRoot EndFraction.
A student used the following table of values and stated that the function described by the tables was a linear function
The question is missing the table. So, it is attached below.
Answer:
The function is not linear. The student didn't evaluate the rate of change for the given points on the function.
Step-by-step explanation:
Given:
From the table, the set of points of the function are:
(-1, -5), (0, 0), (2,5), (3, 10), and (4, 15)
A function is said to be linear if the rate of change of the function is always a constant.
Rate of change for any two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, the rate of change for the points (-1, -5) and (0, 0) is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-(-5)}{0-(-1)}\\\\m=\frac{5}{1}=5[/tex]
Now, the rate of change for the points (0, 0) and (2, 5) is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{5-0}{2-0}\\\\m=\frac{5}{2}=2.5[/tex]
Hence, we can observe that, the rate of change is different for the given points. Hence, it is not a linear function.
Therefore, the student didn't evaluate the rate of change for the given points on the function.
A function is linear if the difference between y-values is constant when the difference between the corresponding x-values is constant. This is known as a constant rate of change and can be identified in a table of values for an x-y relationship. However, without the actual table's values, it's impossible to confirm its linearity.
Explanation:In mathematics, a function is said to be linear if its graph forms a straight line. When analyzing a table of values, a function is linear if the difference between y-values is constant when the difference between the corresponding x-values is also constant. This is often called a constant rate of change.
For example, let's say we have an x-y table: for every 1 unit increase in x, if y increases by 2 units consistently, then the function represented by that table is linear. It directly satisfies the general definition of a linear function, y = mx + b, where 'm' is the slope (rate of change) and 'b' is the y-intercept.
However, without the actual values from the student's table, it's impossible to confirm whether the function is indeed linear. Always remember to check for a constant rate of change when reasoning about linearity.
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How many seconds are in a leep year
Answer:
3.162e+7
Step-by-step explanation:
what is the sum of a 7-term geometric series if the first term is -6, the last term is -24576, and the common ratio is 4?
Answer:
The sum of the first seven terms of this geometric series is - 32,766
Step-by-step explanation:
Let's find out the result of the sum of a 7-term geometric series, which first term is -6, the last term is -24576, and the common ratio is 4
1st term = - 6
2nd term = - 6 * 4 = - 24
3rd term = - 24 * 4 = - 96
4th term = - 96 * 4 = - 384
5th term = - 384 * 4 = - 1,536
6th term = - 1,536 * 4 = - 6,144
7th term = - 6,144 * 4 = - 24,576
Sum = - 24,576 - 6,144 - 1,536 - 384 - 96 - 24 - 6
Sum = - 32,766
We can summarize these operations of the geometric series, this way:
Sₙ= a₁ * (1 − rⁿ)/1 − r, where:
n = Number of terms of the series
a₁ = First term of the series
r = Common ratio
Replacing with the real values, we have:
S₇= -6 * (1 −4⁷)/1 - 4
S₇= -6 * (1 − 16,384)/ -3
S₇= -6 * ( − 16,383)/ -3
S₇= 98,298/ -3
S₇= - 32,766
The sum of the first seven terms of this geometric series is - 32,766
If the expression (2x^4) was written as ax^b form which of the following would be the sum of a and b?
Answer:
6
Step-by-step explanation:
2x^4
a = 2
x = x
b = 4
a + b
2 + 4
6
The sum of a and b for the expression (2x^4) in ax^b form is 6, where a is 2 and b is 4.
Explanation:The expression given is (2x^4), which is already in ax^b form. In this expression, a is the coefficient of the x term, and b is the exponent applied to the x variable. In this case, a is 2 and b is 4.
To find the sum of a and b, you simply add the two numbers together.
The sum of a and b is:
2 + 4 = 6
This result is achieved by recognizing that a represents the constant in front of the x term, and b represents the power to which x is raised.
Adding these two values gives us the sum of the coefficients and exponents in the ax^b expression.
8. How is the graph of log (x + 3) translated from the graph of log x?
Answer:
shift 3 units left.
People leaving an ice cream store were asked to name their favorite flavor of ice cream. Fifty-one people said chocolate was their favorite flavor. If 68% of the people surveyed said chocolate, how many people were surveyed?
To find the total number of people surveyed, you divide the number of people who chose chocolate (51) by the percentage that represents (0.68), resulting in 75 people surveyed.
Explanation:The question posed involves determining the total number of people surveyed based on the percentage who favored chocolate ice cream. Since 68% of the people surveyed stated that chocolate was their favorite flavor, and it is known that 51 people chose chocolate, we can set up a proportion to find the total number of people surveyed. The proportion to find the total number of respondents (let's call it x) is as follows:
0.68 x = 51
To solve for x, you would divide both sides of the equation by 0.68, which gives you:
x = 51 / 0.68
x = 75 people
Therefore, the total number of people surveyed was 75.
The mid-segments of opposite sides of a triangle are parallel to each other?
True
False
Answer:
False
Step-by-step explanation:
The mid segments are the lines between midpoints on the triangle. They aren't parallel, because they form a triangle inside the triangle.
There is 1/3 gallon of water in a 3-gallon container. What fraction of the container is filled?
Answer:
3/3 i think sorry if its wrong
Step-by-step explanation:
Answer:
1/3 of the container is filled.
Step-by-step explanation:
Which property states that order of the addends does not affect the sum?
A. commutative property of addition
B. associative property of addition
C. reflexive property of addition
D. additive identity property
Option A
Commutative property of addition states that order of the addends does not affect the sum
Solution:
The commutative property of addition tells us that it does not matter which number we add first , We will still get the same answer if we add them backwards
This property is represented as:
For two numbers a, b:
a + b = b + a
In case of three numbers a, b, c:
a + b + c = c + b + a = b + a + c
So no matter how the addends are placed, the result of the operation (sum) remains the same
For example:
When we are adding 4 and 5
4 + 5 = 9 or 5 + 4 = 9 both the ways the result remains same
Thus Commutative Property of Addition states that changing the order of addends does not change the sum
Answer:
Commutative property of addition
Step-by-step explanation:
According to the commutative property of addition, changing the order of the numbers we are adding, does not change the sum.
Good luck, your day will be awesome!
Evaluate BD fo A = 5, B = -2, C = 4, and D = -6.
-12
-8
8
12
Answer:
12
Step-by-step explanation:
B is equal to -2, and D is equal to -6. A negative times a negative is a positive, and 2 x 6 = 12 (aka 6+6)
The sum of a number and six is multiplied by negative four. The result is eight.
What is the number?
Answer:
-8
Step-by-step explanation:
(-8+6) * -4
-2 * -4= 8
Final answer:
The unknown number is -8, found by setting up the equation -4(x + 6) = 8 and solving for x.
Explanation:
To solve the problem stated, we need to set up an equation based on the provided information. The statement 'the sum of a number and six is multiplied by negative four' can be written as an algebraic expression: -4(x + 6), where 'x' is the unknown number we are trying to find.
We are told that this expression equals eight, so the equation we need to solve is -4(x + 6) = 8.
To solve for x, first we simplify the equation:
-4x - 24 = 8
Then we add 24 to both sides:
-4x = 8 + 24
-4x = 32
Now we divide both sides by -4 to solve for x:
x = 32 ÷ -4
x = -8
Therefore, the number we are looking for is -8.
A truck can carry a maximum of 1350 ponds of weight .how many 250- pound of dirt can the truck hold
Answer:
5.4
Step-by-step explanation:
1350/250=5.4
Final answer:
A truck with a maximum capacity of 1350 pounds can carry 5 full 250-pound loads of dirt, as partial loads cannot be accommodated.
Explanation:
How many 250-pound loads of dirt can a truck carry?
To determine how many 250-pound loads of dirt a truck can carry if its maximum capacity is 1350 pounds, you need to divide the truck's maximum capacity by the weight of one load of dirt:
1350 pounds ÷ 250 pounds per load = 5.4 loads
Since the truck cannot carry a fraction of a load, it can carry a maximum of 5 full 250-pound loads of dirt before it reaches its weight limit.
How do you write 33% as a fraction
Answer:
1/3 simplified or 33/100
Step-by-step explanation:
33% is around one third of 100%. Aka, you multiply 33(.33)% by 3 to get 100% or you can leave it as 33/100.
Which of the following numbers is irrational? (1 point)
a fraction with numerator negative 15 and denominator 4, a fraction with numerator negative 7 and denominator 9, square root of 4, π
a fraction with numerator negative 15 and denominator 4
a fraction with numerator negative 7 and denominator 9
square root of 4
π
Answer:
The correct answer is D. π
Step-by-step explanation:
Let's recall that rational numbers are those that can be written as a ratio or fraction of two integers. Quite the opposite, irrational numbers can't be written as a ratio or fraction of two integers.
Upon saying that we have:
A. A fraction with numerator negative 15 and denominator 4 is a rational number because we can represent it: -15/4
B. A fraction with numerator negative 7 and denominator 9 is a rational number because we can represent it: -7/9
C. √4 is a rational number because we can represent it: 2 or 2/1
D. π is the most known irrational number because we can't represent it as a ratio or fraction: 3.14159265358979....and more can't be written as a ratio or fraction.
The correct answer is D. π
[tex]z = 3 + i \\ {z}^{5} = [/tex]??
Answer:
[tex]z^{5}[/tex] = - 12 + 316 i
Step-by-step explanation:
Given that -
z = 3 + i
[tex]z^{2}[/tex] = [tex]( 3 + i )^{2}[/tex]
[tex]z^{2}[/tex] = 9 + [tex]i^{2}[/tex] + 6 i
[tex]z^{2}[/tex] = 9 - 1 + 6 i
[tex]z^{2}[/tex] = 8 + 6 i
[tex]z^{3}[/tex] = [tex]z^{2}[/tex] × z
[tex]z^{3}[/tex] = ( 8 + 6 i ) × ( 3 + i )
[tex]z^{3}[/tex] = 24 + 8 i + 18 i + 6 i²
[tex]z^{3}[/tex] = 24 + 26 i - 6
[tex]z^{3}[/tex] = 18 + 26 i
[tex]z^{5}[/tex] = [tex]z^{2}[/tex] × [tex]z^{3}[/tex]
[tex]z^{5}[/tex] = ( 8 + 6 i ) × ( 18 + 26 i )
[tex]z^{5}[/tex] = 144 + 208 i + 108 i + 156 i²
[tex]z^{5}[/tex] = 144 + 316 i -156
[tex]z^{5}[/tex] = - 12 + 316 i
Sarah bought 3 fish. Every month the number of fish she has doubles. After m months, she will have F fish, where F = 3 x 2. If Sarah
keeps all of the fish and they all live, how many fish will Sarah have after 3 months?
A. 9
B. 18
c. 24
D. 27
E. 216
If Sarah keeps all of the fish and they all live, then there are 24 fishes will Sarah have after 3 months
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
Given,
Sarah bought 3 fish.
Every month the number of fish she has doubles.
After m months, she will have F fish, where F = 3 x 2m
If Sarah keeps all of the fish and they all live, We need to find number of fishes will Sarah have after 3 months
F = 3× 2m
M represents the number of months.
In start month 3 fishes
In first month the fishes are 6
In second month the fishes are 12.
In third month the fishes are 24.
Hence, If Sarah keeps all of the fish and they all live, then there are 24 fishes will Sarah have after 3 months
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