The positive integers are 14, 15 and 16
What is an algebraic expression?
An algebraic expression can be defined as an expression that is made up of coefficients, terms, variables, factors and constants.
From the given information, we have that;
Let the consecutive integers be;
x, x+ 1, x+ 2
This can be represented as;
(x+1)(x+2) = 8(x + x+ 2)
Now, expand the bracket
x² + 2x + x + 2 = 8(2x + 2)
x² + 3x + 2 = 16x + 16
collect like terms
x² + 3x - 16x + 2 - 16 = 0
Add or subtract like terms
x² - 13x - 14 = 0
Solve the quadratic equation
x² -14x + x - 14 = 0
factor in pairs
x(x- 14) + 1(x -14) = 0
Then,
x = -1
x = 14
Take 'x' as 14
smallest integer = 14
Median = 14 + 1 = 15
Largest integer = 16
Hence, the values are 14, 15 and 16
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what is the answer of 0.08 divided by 48.86
Answer:
610.75
Step-by-step explanation:
48.86 divided by 0.08
An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b. Which statements about finding the area of the equilateral triangle are true
The options (a),(b) and (d) are true regarding the apothem of equilateral triangle.
What is an apothem of a polygon?
A line segment from a regular polygon's centre to one of its sides is known as the apothem.
The given options are the following:
a)The apothem can be found using the Pythagorean theorem.
b)The apothem can be found using the tangent ratio.
c)The perimeter of the equilateral triangle is 15 cm.
d)The length of the apothem is approximately 2. 5 cm.
e)The area of the equilateral triangle is approximately 65 cm².
Now we will see if each option is true or not
a) From below figure,
b = 8.7 / 2 = 4.35 cm
From right angled triangle ΔABD,
Using Pythagorus Theorem,
a² + b² = 5²
a² + 4.35² = 5²
a = [tex]\sqrt{5^{2} - 4.35^{2} }[/tex] = 2.5 cm
Apothem can be found using Pythagorus Theorem.
b) From the figure, the radius divide the angle 60° of equilateral triangle to two 30° angles.
So from ΔABD,
tan 30° = a / 4.35
0.577 = a / 4.35
a = 2.5 cm
The apothem can be found using tangent ratio.
c) Perimeter of given equilateral triangle = 3 × side length
= 3 × 8.7 = 26.1 cm
This option is false.
d) From options (a) and (b) we found that length of apothem a = 2.5 cm
Therefore this option is true.
e) The area of given equilateral triangle = [tex]\frac{\sqrt{3} }{4} } * side^{2}[/tex] = [tex]\frac{\sqrt{3} }{4} * 8.7^{2}[/tex]
= 32.8 cm²
Therefore this option is false.
Therefore options (a),(b) and (d) are true regarding the apothem of equilateral triangle.
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The extreme water slide forms a 20 angle with the tower it leans against 80 feet above the ground find the length of the slide x
Answer:
85.1 ft
Step-by-step explanation:
The extreme water slide forms a 20 angle with the tower it leans against 80 feet above the ground find the length of the slide x
We solve using the Trigonometric function of Cosine
cos y = adjacent/hypotenuse
y = angle = 20°
Adjacent = 80 ft
Hypotenuse = ?
cos 20 = 80/Hypotenuse
Hypotenuse = 80/cos 20
x = 85.134221798 ft
Approximately = 85.1 ft
Length of the slide = 85.1 ft
The drama club put on the play, “The wizard of Oz.” There were student tickets and adult tickets. There were 150 tickets sold to the play. Student tickets cost $3 per ticket, and adult tickets cost $5 per ticket. If the total sales were $580, how many student tickets and how many adult tickets were sold to the play? Use system of equations to solve.
On solving the provided question, we can say that - by the help of the unitary method 150* 3 = $450
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
so, we have
There were = 150 tickets sold to the play
Student tickets cost $3 per ticket
so, total will be = 150* 3 = $450
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Hey! I would appreciate some help with this
Answer:
...
Step-by-step explanation:
since they give us the side opposite of the given angle(Opposite) and we are trying to find for a (Adjacent/side), so we use TOA
tan(30)= [tex]\frac{4}{a}[/tex]
i see u dont want it solved but ill solve it anyways
since a is on the bottom then lets switch them
[tex]x=\frac{4}{tan30}[/tex]
x= 6.928
a) What type of triangle is triangle ABC? b) Give reasons for your answer. I need the correct answer for B with Reasons Not "ab and ac are the same" any word other than the same
Answer:
Δ ABC is isosceles
Step-by-step explanation:
∠ ABC and ∠ BCE are alternate angles and are congruent , that is
∠ BCE = ∠ ABC = 80°
since DE id a straight line then the angles lying on it sum to 180° , that is
∠ ACD + ∠ ACB + ∠ BCE = 180°
50° + ∠ ACB + 80° = 180°
∠ ACB + 130° = 180° ( subtract 130° from both sides )
∠ ACB = 50°
∠ BAC and ∠ ACD are alternate angles and are congruent , that is
∠ BAC = 50°
then
∠ BAC = ∠ ACB = 50°
Since the 2 base angles are congruent then Δ ABC is isosceles
Carlos bought two packages of rope, each containing 12 feet of
rope. He needs to cut pieces of rope that are each 20 inches in
length. What is the greatest number of pieces that he can cut
from these two packages of rope?
1 foot = 12 inches
Answer: 14 pieces.
Step-by-step explanation: 1 foot = 12 inches
12 feet of rope = 144 inches of rope
144 / 20 = 7.2 = 7 sections can be cut from each package.
The greatest number of pieces from 2 packages = 14 pieces
Answer
14 pieces
Step-by-step explanation:
First you need to convert the 24 feet into inches. Do this by multiplying 24 (feet) by 12 (inches) since 1 foot has 12 inches in it and you have 12 feet. This means he has 288 inches of rope. Then divide 288 by 20 since he wants to see how many 20 inch pieces he can cut. You should get 14.4 but since it asks for the greatest number of pieces you need to round it down to 14 since he wants full 20 inch pieces.
Help me out with this question (geometry)
angle 1 + angle 2 = 180
3x - 5 + 6x + 14 = 180
9x + 9 = 180
9x = 171
9x/9 = 171/9
x = 19
Can someone pls give me the answer to this?
Answer:
B
Step-by-step explanation:
Q3. a. Simplify the following ratios.
360:120:60
Answer:
6：2：1
Step-by-step explanation:
360÷60=6
120÷60=2
60÷60=1
Describe a sequence of transformation that maps DOG onto CAT
Sequence of transformation is first moving 5 unit in y axis than mirror image with y axis.
What would you say about the order of the transformations?A particular order of transformational events is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.
What kind of figure can a series of transformations map onto itself?The line of reflection must pass through the centre point for the figure to map onto itself. The sides of the figure are cut by two lines of reflection. The vertices of the figure are intersected by two lines of reflection. As a result, there are four potential lines of reflection that pass through the center.
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Multiple Choice 8th Grade Math, please help your a legend if so!
Answer:
2
Step-by-step explanation:
Answer:
It's 2 weve done the worksheet ;)
Step-by-step explanation:
At what point the graph of linear equation 2x 3y 6 cuts the Y-axis A 0 2 B 4 0 C 2 6 D 2 0?
The graph of the given linear equation 2x+3y=6 cuts the Y-axis at A(0,2).
For the graph of linear equation to cut the Y-axis its X-co-ordinate should be zero as abscissa is zero on Y-axis or the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.
From the given set of coordinates, A(0,2) B(4,0) C(2,6) D(2,0), it is clear that the graph of the equation 2x+3y=6 cuts the Y-axis at A as it’s X-co-ordinate or abscissa is zero. So, it satisfies the first condition.
To satisfy the second condition the points of a should satisfy the equation given
LHS= 2x+3y
RHS=6
A(0,2)
Substituting the values of x and y in 2x+3y,
2(0)+3(2)=6
Therefore LHS=RHS
Hence, at point A(0,2) the graph of the given equation cuts the Y axis.
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Does anybody know the equation to this?
Answer:
+3, +1
I think this is the answer because if its asking about the chart it is adding 3 on the x-axis and adding 1 on the y-axis
Hope this helps :)
Is the correct answer for S is AB and DE?
Look at the picture
Answer:
Side AB congruent to side DE
( being the side joining two congruent angles)
The area of a rectangular room is 104 square feet. The length of the room is 5 feet longer than the width. Find the dimensions of the room.
Answer:
The dimensions of the room is 8 and 13 feet.
Probability results can be _________.
a. between 0 and 1 inclusive
b. expressed as a decimal
c. greater than 1, just like fractions and decimals d. None of these statements are true.
Answer:
it's either a win or lose
i need help asap!! please help
For stuff like this you have to simplify the equation and solve for x.
But since its multiple choice you can just plug in each answer until it makes the equation true.
So here are the equations with n substituted in:
8(8+1)+3=45
7(7+1)+3=45
6(6+1)+3=45
5(5+1)+3=45
Now simplify:
8(8+1)+3=45 becomes 72+3 = 45
6(6+1)+3=45 becomes 42+3=45
5(5+1)+3=45 becomes 30+3=45
Its easiest to start with the highest option given and then go down. Because 8 is already way to high you could skip doing the math for 7 and go straight to 5 and 6.
42+3=45 becomes 45=45
30+3=45 becomes 33=45
So 6 makes this statement true.
After awhile its easy to gauge what numbers will come out to be, so you don't have to do the math for each answer.
Can someone please help me? :(
Answer:32 17/18
Step-by-step explanation:
33 + (1/9)(x)
x = -1/2
33 + (1/9)(-1/2) =
33 + -1/18
= 32 17/18
Use the distributive property to fill in the blanks below. I need help on this, it's for a grade and this is my last day of school :| please help me!
Answer:
[tex]9*(6-5) = (9*6)-(9-5)[/tex]
Step-by-step explanation:
I can't really explain, but the disturbitive property opens brackets.
You multiply the number on the outside by each of the numbers on the inside, and use the symbol in the center to do stuff between the two products.
That's probably really confusing but whatever.
Required:
a. For the balance sheet, identify how each transaction affects total assets, total liabilities, and total equity. For the income statement, identify how each transaction affects net income.
b. For the statement of cash flows, identify how each transaction affects cash flows from operating activities, cash flows from investing activities, and cash flows from financing activities.
WHAT AM I MISSING?!?!
The answers for the two questions is described below:
a. The balance sheet is a financial statement that shows a company's assets, liabilities, and equity at a specific point in time. Each transaction will affect one or more of these categories in different ways:
An increase in assets will increase total assets.
An increase in liabilities will increase total liabilities.
An increase in equity will increase total equity.
The income statement is a financial statement that shows a company's revenues, expenses, and net income over a specific period of time. Each transaction will affect net income in different ways:
An increase in revenues will increase net income.
An increase in expenses will decrease net income.
b. The statement of cash flows is a financial statement that shows the cash flows from operating activities, investing activities, and financing activities over a specific period of time. Each transaction will affect one or more of these categories in different ways:
An increase in cash from operating activities will increase cash flows from operating activities.
An increase in cash from investing activities will increase cash flows from investing activities.
An increase in cash from financing activities will increase cash flows from financing activities.
It is important to note that it can be complex to classify some transactions into one category or another, and it may require more context of the specific transaction and the company's operations.
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The base of an isosceles triangle is 7cm long. Each of the other sides is x cm long. What will be the expression for its perimeter?
Answer:
P = 2x + 7
Step-by-step explanation:
PLZ HELP I HAVE NO CLUE WHAT TO DO
Answer:
P = 10.6 sq units
A = 12.5 sq units
Step-by-step explanation:
In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between
zero and what?
In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and one.
What is scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and 1.
The image is contracted if the scale factor is less than 1 (0< k <1).
The image is enlarged if the scale factor is more than 1 (k > 1).
The image remains the same if the scale factor is 1 (k = 1).
Hence, the scale factor k should be between 0 and 1.
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If 27³+27³+27³=27x,what is the value of x?
Answer:
x = 2,187
Step-by-step explanation:
27×27×27+27×27×27+27×27×27 =27x
19,683+19,683+19,683 =27x
59,049 = 27x
divide both sides by the coefficient of x ( 27 )
59,049 / 27 = 27x / 27
x = 2,187
PLLLLZZZZ HEEELLPP MEEE!!!!!!
Consider a triangle where all three sides are known, but no angles are known. Is there enough information to find all the angles in the triangle using only the law of sines?
A) True
B) False
Answer:
maybe false
have a great day
true
Explanation:
you can use a2 +b2=c2 to find it
Suppose the dimensions of a rectangular pyramid are doubled. How does this affect its volume?
The volume is 4 times the original volume.
The volume is 2 times the original volume.
The volume is 9 times the original volume.
The volume is 8 times the original volume.
Answer:
I think its 2 times the original volume, im so sorry if im wrong!!
Step-by-step explanation:
Edit: I thought it was two but i guess it was 4, heres the real answer for people who were wondering, im so sorry!!
Solve the simultaneous equations
4x+5y=−19
6x−3y=24
At summer camp this year, Clare is leading the beadwork class. Each of the 9 craft tables has a bucket of beads. The graph shows the weight of the beads in each bucket.
If Clare distributes all of the beads equally among the 9 buckets, how much will the beads in each bucket weigh?
The beads in each bucket will weigh 1 pound
How to determine the weight of the beads in each bucket?
A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
From the graph, we have weights of 0, 1/2, 1 1/2 and 2 pounds.
In order for Clare to distributes all of the beads equally among the buckets, she need to add up weight of the beads and divide by 5.
weight in each bucket = (0 + 1/2 + 1 1/2 + 2)/5 = 5/5 = 1 pound
Thus, each bucket weighs 1 pound
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Clare made an error when solving -4x+3<23−4x+3<23.
The solution of the inequality is,
⇒ x > - 5
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ - 4x + 3 < 23
Now,
Since, The inequality is,
⇒ - 4x + 3 < 23
Solve as;
⇒ - 4x < 23 - 3
⇒ - 4x < 20
⇒ - x < 5
⇒ x > - 5
Thus, The solution is,
⇒ x > - 5
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