The perimeter of the isosceles triangle whose base is 6 cm and two equal sides are 7.5 cm is 21 centi-meters.
What is isosceles triangle?
An isosceles triangle in geometry is one with at least two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception. The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.
To calculate the perimeter of isosceles triangle, we use equation:
Perimeter = Base + 2(Two equal side)
Perimeter = 6 + 2(7.5)
Perimeter = 21 cm
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a triangle has two sides of 10 and 6 with an area of 12 units. what is the missing length.
A triangle that has two sides of 10 and 6 with an area of 12 units will have the third side length of 4.
What is the area of a triangle?The triangle can be described as the the figure that has threes sides which can be equal or varies base on the type of the triangle it is, and the area of the triangle is given, we can use the formula for the are of triangle which i s (1/2 * b * h )
Then the Area of a triangle = (1/2 * b * h)
we were given the two sides already with the area , then we can input the values as :
12 =( 1/2 * 6 * x)
where x is the third sides that is needed
x = 4
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Solve |4x - 2| + 1 > 7
The inequality is |4x-2|+1>7. By solving inequality we got x>-1 and x>2.
Given that,
The inequality is |4x-2|+1>7
We have to solve the inequality.
|4x-2|+1>7
Take +1 and right hand side we get -1
|4x-2|>7-1
Subtracting 7-1
|4x-2|>6
Now, it is modulus so we get + or -
1st we take +
4x-2>6
Take -2 and right hand side we get +2
4x>6+2
Adding 6+2
4x>8
Taking 4 to right hand side we get in the division.
x>8/4
x>2
Now, take -
-(4x-2)>6
Multiplying -1 on both sides
4x-2>-6
Take -2 and right hand side we get +2
4x>-6+2
Subtracting -6 and 2
4x>-4
Taking 4 to right hand side we get in the division.
x>-4/4
x>-1
Therefore, by solving inequality we got x>-1 and x>2.
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Simplify the quantity 8 minus one third times the square root of 9 end quantity squared plus the quantity 1 minus 5 end quantity squared.
The statement quantity 8 minus one third times the square root of 9 end quantity squared plus the quantity 1 minus 5 end quantity squared is simplified to 65
What are fractions?Fractions are defined as parts of a whole element, set or number.
There are various types of fractions, which includes;
Complex fractionsProper fractionsSimple fractionsMixed fractionsImproper fractionsBased on the information provided, we have;
8 minus one third times the square root of 9 = 8 - 1/3(√9)1 minus 5 end quantity squared = (1 - 5)²Now, substitute the values
(8 - 1/3(√9))² + (1 - 5)²
Find the square root
(8 - 1/3(3))²+ (-4)²
Find the square
(8 - 1)² + 16
7² + 16
49 + 16
Add the values
65
Hence, the value of the expression is 65
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Find all angles, osO<360, that satisfy the equation below, to thenearest 10th of a degree.cos(0) =-1/6
The cosine of the angle given is negative.
Cosine is negative in the second and third quadrant
[tex]\begin{gathered} 0\leq x\leq360 \\ \cos (\theta)=-\frac{1}{6} \\ \theta=\cos ^{-1}(\frac{1}{6}) \\ \theta=80.41^0 \\ \theta=80.4^0\text{ (to the nearest tenth)} \\ \end{gathered}[/tex]In the second quadrant,
[tex]\begin{gathered} 180-\theta \\ 180-80.4=99.6 \\ \theta=99.6^0 \end{gathered}[/tex]In the third quadrant,
[tex]\begin{gathered} 180+\theta \\ 180+80.4=260.4 \\ \theta=260.4^0 \end{gathered}[/tex]Therefore, the values that satisfy the equation are 99.6 and 260.4 degrees.
From a window 100 ft above the ground in building A, the top and bottom of building B are sighted so that the angels are 70 degrees and 30 degrees respectively. Find the height of building B?
Let's begin solving the problem by illustrating the problem using a diagram:
Let the height of building B be x
Re-drawing the triangles to show the unknown side:
Using trigonometric ratios and sine rule
Hence:
[tex]\begin{gathered} \frac{\sin110}{\frac{100}{\cos30}}\text{ = }\frac{\sin 40}{x} \\ \text{Cross}-\text{Multipy} \\ \text{x }\times\text{ sin110 }=\text{ sin40 }\times115.47 \\ \text{Divide both sides by sin110} \\ \text{x = }\frac{\sin 40\text{ }\times\text{ 115.47}}{\sin \text{ 110}} \\ x\text{ = 78.986} \\ x\text{ }\approx\text{ 79 ft} \end{gathered}[/tex]The height of the building B is 79 ft
if 2 shmoop interns can give 10 total foot massage in an hour, how many foot massages can 5 shmoop interns give in an hour?
To find the height of a very tall pine tree, you place a mirror
on the ground and stand where you can see the top of the
pine tree. How tall is the tree?
6 ft
2 ft 24 ft
ти
How tall is the tree
If to find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. The height of the tree is 72 feet.
Height of a treeGiven data;
6 ft
2 ft 24 ft
Hence,
Angle of incidence = Angle of reflection
Hence,
m ∠ ACD = m ∠ ECD
Two triangle will only be the same if their corresponding angles are congruent
So,
Sine m ∠ ACD = m ∠ ECD
m Δ ABC = Δ EDC
The corresponding of similar triangles are proportional
Hence,
BC / DC = AB / ED
= 2 / 24 = 6 / ED
2ED = 24 × 6
2ED = 144
Divide both side by 2
ED = 144 / 2
ED = 72 feet
Therefore we can conclude that the tree height is measure at 72 feet.
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what is the standard algorithm for 72 / 3
Long division gives the answer of 24 when 72 is divided by 3.
What is long division calculator?Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are typically solved using. The dividend, the quotient, the remainder, and the divisor can all be seen in the following long division.
So as we know:
Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:
3 ⟌ 7 2
Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:
2
3 ⟌ 7 2
Write the result (3 x 2 = 6) underneath the dividend after multiplying the divisor by the outcome from the previous step.
2
3 ⟌ 7 2
6
Write the solution below after subtracting the result from the previous step from the dividend's first digit (7 - 6 = 1).
Reduce the dividend's second digit (2) as follows:
2
3 ⟌ 7 2
- 6
1 2
The bottom number (12) is multiplied by the divisor (3) four times (s). Put 4 thus on top
Subtract the result of the previous step (3 x 4) from the divisor to get the solution (12), which you should write at the bottom:
2 4
3 ⟌ 7 2
- 6
1 2
1 2
Take the number above it and deduct the outcome from the preceding calculation. Write the response at the bottom after calculating (12 - 12 = 0).
The top number is the solution, and the remaining value is the bottom one.
Therefore, the result of 72 divided by 3 using long division is 24.
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A skateboard travels 55 feet in 4 seconds. Is the skateboard going faster,
slower, or the same speed as the scooter?
Answer:
Slower
Step-by-step explanation
The scooter travels 60 feet in 4 seconds, so it is going faster than the skateboard, which travels 55 feet in 4 seconds. A cargo ship traveled 150 nautical miles in 6 hours at a constant speed. How far did the cargo ship travel in one hour?
What is the distance between points A(2,9) and B(-2,6)? Round to the nearest whole number.
The distance between the point is 5.
The formula to find the distance between two points (x1, y1) and (x2, y2)
distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]
Substituting points A(2,9) and B(-2,6), we get
distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]
=[tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
= [tex]\sqrt{16 + 9}[/tex]
=[tex]\sqrt{25}[/tex]
= 5
Therefore the distance between the two points is 5.
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What is the correct answer
The measure of angle B in triangle ABC is 158°.
What is meant by the triangle?A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle would be a category of polygon.
The sum of a triangle's three interior angles is always 180.The sum of any two triangle sides is always bigger than this same length of a third side.A triangle's area is equal to half the product of it's own base and height.For the given angles of the triangle ABC.
∠BAC = 78° , ∠CAD = 46° and ∠ADB = 110°.
Now,
∠BAC = ∠BAD + ∠DAC
Put the values;
78° = ∠BAD + 46°
∠BAD = 78° - 46°
∠BAD = 32°
Now, in a triangle; the sum of all three angles is 180°.
In triangle ADB
∠ABD + ∠BAD + ∠BDA = 180°
Put the values;
∠ABD + 32° + 110° = 180°
∠ABD = 180° - 142°
∠ABD = 158°
Thus, the measure of angle B is 158°.
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what operation would be completed second in the following expression
In the PEMDAS method of solving , it goes to the five basic operations
1.Parenthesis 2. Exponents 3. Multiplication 4. Addition 5.Substraction
In this exercise there are NOT parenthesis, so then the first operation is Exponentiation and 2nd operation is Multiplication
So the answer is Multiply, the first option.
Solve for y in terms of u, v, w, and x.
vw = -yux
VW
y =
Answer:
y= vw/ux
Step-by-step explanation:
hope this help
Drag and drop the number to match the division problem to its quotient.
Answer:
The correct number is -27.
Step-by-step explanation:
-81 ÷ 3 = -27
Round to the place value of the underlined digit 698,072 the underlined digit is 6
We get 700,000 after rounding off to the place value of the underlined digit in the number 698,072.
According to the question,
We have the following number with 6 as the underlined digit:
698,072
When rounding off the number, please note that the digits to the right of the underlined digit would be zero. However, we need to be careful where we need to scale up the underlined number or it would remain the same.
For this, we need to check the number to the right of the underlined digit. If the number right next to the underlined digit is greater than 5 then the underlined digit has to be scaled up. And if it is less than 5 then the underlined digit remains the same.
So, after rounding off we will get:
700,000
Hence, the number after rounding off to 6 in 698,072 is 700,000.
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What does congruent mean? Select all that apply. PLEASE HELP!
A None of the above
B Same Shape
C Corresponding angles are the same measure
D Corresponding sides are the same length
help me please!!!!!!11!
Answer:
[tex]y=x^2-4x-2[/tex]
Step-by-step explanation:
Standard Form of Quadratic:
[tex]y=ax^2+bx+c[/tex]
Vertex Form of Quadratic:
[tex]y=a(x-h)^2+k[/tex]
h = vertex x
k = vertex y
Think of h and k as the ordered pair (h,k).
Match this ordered pair to the vertex ordered pair.
(h,k) = (2, -6)
Plug in (h,k) into vertex form:
[tex]y = a(x-2)^2-6[/tex]
Use other point to solve for a.
[tex]3 = a(5-2)^2-6[/tex]
[tex]3=a(3)^2-6[/tex]
[tex]3=9a-6[/tex]
[tex]9=9a[/tex]
[tex]a=1[/tex]
Plug a back into vertex form and expand the expression into standard form:
[tex]y=(x-2)^2-6[/tex]
[tex]y=(x-2)(x-2)-6[/tex]
Use F.O.I.L. method to expand (x-2)(x-2).
F(first): [tex]x*x=x^2[/tex]
O(outer): [tex]x*-2=-2x[/tex]
I(inner): [tex]-2*x =-2x[/tex]
L(last): [tex]-2*-2=4[/tex]
[tex]y=x^2-2x-2x+4-6[/tex]
Combine like terms:
[tex]y=x^2-4x-2[/tex]
Write the equation of the line in slope-intercept form.
The line is parallel to y + x = 3 and passes through the point (-12, 0).
Please help i will give big points
Answer:
The line is parallel to y + x =3
=> y = -x+3
the slope = -1
passes (-12, 0)
the equation would be :
y-0 = -1(x+12)
y = -x -12 Y=-x+12
Turn into mx+b form.
Y=-x+3
Plug in (-12,0)
0=-12+b
b=12
y=-x+12
It is negative X, because the slope has to be the same since it is paralle
Step-by-step explanation:
Question:The diameter of the handle on a broomstick is 3.75 centimeters. What is the length in centimeters of the diameter of 12 of the broomstick handles?
The diameter is 3.75 cm
The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -1, 0, and 4.
Which graph could be the graph of f(x)?
The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.
What is Polynomial function?
A mathematical expression of algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.
Given that;
The degree of the polynomial function f(x) is 3.
And, The roots of the equation f(x) = 0 are -1, 0, and 4.
Now, The polynomial function are calculated as;
f (x) = 0
(x + 1) (x - 0) (x - 4) = 0
x (x + 1) (x - 4) = 0
x (x² - 4x + x - 4) = 0
x (x² - 3x - 4) = 0
x³ - 3x² - 4x = 0
Thus, The polynomial function is;
x³ - 3x² - 4x = 0
Therefore, The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.
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What is the answer to the question
From the right triangle, and using the definitions of the tangent and the cosine functions, we have:
[tex]\begin{gathered} \tan B=\frac{AC}{BC}=\frac{b}{a}\Rightarrow b=a\cdot\tan B...(1) \\ \\ \cos B=\frac{BC}{AB}=\frac{a}{c}\Rightarrow c=\frac{a}{\cos B}...(2) \end{gathered}[/tex]From the problem, we identify:
[tex]\begin{gathered} B=55.7\degree \\ a=266\text{ km} \end{gathered}[/tex]Finally, using these values, we can find b and c.
Using (1):
[tex]\begin{gathered} b=266\cdot\tan55.7\degree \\ \\ \therefore b=389.941\text{ km} \end{gathered}[/tex]Using (2):
[tex]\begin{gathered} c=\frac{266}{\cos55.7\degree} \\ \\ \therefore c=472.028\text{ km} \end{gathered}[/tex]29-(11-2³)+6²÷4 simplify each Expression
The simplified form of the expression 29 - ( 11 - 2³ ) + 6² ÷ 4 is 35
What is the simplified form of the given expression?Given the expression in the question;
29 - ( 11 - 2³ ) + 6² ÷ 4
To simply, replace 2 raised to the power of 3 with 8 and 6 raised to the power of 2 by 36
29 - ( 11 - 2³ ) + 6² ÷ 4
29 - ( 11 - 8 ) + 36 ÷ 4
Now, remove the parenthesis by performing the operation inside the parenthesis.
29 - ( 11 - 8 ) + 36 ÷ 4
29 - 3 + 36 ÷ 4
Now, divide 36 by 4
29 - 3 + 36 ÷ 4
29 - 3 + 9
Next, add -3 and 9
29 + 6
Add 29 and 6
35
Therefore, 35 is the simplified form of the expression.
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The volleyball team bought 12 new volleyballs. The price for each volleyball was $26. How much did the team spend? Select the choice that shows all of the partial products of 12 × 26.
A.
12, 70, 4, 400
B.
12, 90, 14, 200
C.
12, 62, 4, 260
D.
12, 60, 40, 200
========================================================
Explanation:
Imagine a rectangle that is 12 by 26. Multiplying the length and width will get us the area.
We can break the 12 into 10+2
Also, break the 26 into 20+6
Check out the diagram below. We have 4 smaller rectangles. Finding the product of those sub-areas will then get us the partial products needed.
In the bottom right corner we have a 2 by 6 rectangle, so it has area 2*6 = 12 square units. This is one of the four partial products. The other partial products are found the same way.
Once you determine the four partial products, we then add them up
12+60+40+200 = 12+100+200 = 12+300 = 312
Therefore, 12*26 = 312 which we can use a calculator to confirm.
A person on a moving walkway travels 80 ft in 40 sec. What equation represents this relationship? How many feet will the person travel in 10 sec?A. y = 1/2x; 5 ftB. y = 4x; 40 ftC. y = 2x; 20 ftD. y = 2x; 2 ft
We need to find which expression represents the situation given, in this case we have two values a distance (80 ft) and the elapsed time (40 s). The time is the input of the equation, it will be placed on the "x" variable and the distance is the output of the equation, it will be placed on the "y" variable. We need to find the expression that outputs "80" when we input 40. Let's check them one by one:
A.
[tex]y=\frac{1}{2}\cdot40=20[/tex]This outputs 20 ft when we input 40 s, therefore it is not this one.
B.
[tex]y=4\cdot40=160[/tex]This one outputs 160 ft when we input 40 s, therefore it is not this one.
C.
[tex]y=2x=2\cdot40=80\text{ }[/tex]This one outputs 80 ft when we input 40 s, therefore this is the correct expression.
We now need to use this expression to calculate the distance the person will travel in 10 seconds, so we will make x equal to 10 s.
[tex]y=2\cdot10=20\text{ }[/tex]The person will walk 20 ft.
The correct option is "C".
Which number line shows the solution to the inequality 5 ≤ 8-3x ≤ 14?
The number line 5 ≤ 8-3x shows the solution to the inequality as x cannot be more than 1.
What is inequality?A inequality compares two values and indicates whether one is smaller, larger, or simply not equal to the other.
a ≠ b is the information that a and b are not equal.
If a > b, a is greater than b. (these two are defined as strict inequality)
a ≤ b proves that a is less than or equal to b
a ≥ b proves that a is greater than or equal to b
The number line 5 ≤ 8-3x shows the solution to the inequality as x cannot be more than 1.
If x is more than 1, lets say 2
Then the inequality as follows
5 ≤ 8-3(2) ≤ 14
5 ≤ 8-6 ≤ 14
5 ≤ 2 ≤ 14 this statement becomes false
Therefore x, must be lower than 1
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Algebra 2, 50 points, include steps please
(6-4i)(1+5i)-(3-i)
The simplified representation of the complex number expression is
23 + 37i
a + bi, where a and b are real numbers, can be used to represent any complex number.
A complex number is a component of a number system that includes an element with the symbol I, sometimes known as the imaginary unit, and that extends the real numbers by satisfying the equation i² = -1. i was described as an imaginary number by René Descartes since no real number can fulfil the aforementioned equation. The complex number a + bi is known as having real and imaginary parts, respectively, A and b. The group of complex numbers is denoted by the letter C.The complex number expression is (6-4i)(1+5i)-(3-i)
now let us simplify,
or, (6-4i)(1+5i)-(3-i)
or, 6 + 30i - 4i -20i² -3 + i
or, 6 + 36i + 20 - 3 + i (we know that i² = -1)
or, 23 + 37i
Therefore the simplified complex expression is 23 + 37i
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How many solutions over the complex number system does this polynomial
have?
3x6x³-4x²+3x+52 = 0
Enter your answer as an integer.
Polynomials are algebraic expressions that consist of the variables and coefficients. Six complex number system, polynomial 3x6x³-4x²+3x+52 = 0 have.
What do you mean by polynomial?Polynomials are algebraic expressions that consist of the variables and coefficients. Variables are also sometimes called the indeterminates. We can perform the arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.
We have following polynomial for this situation.
We observe that polynomial graph only intersects the vertical axis once.
There are no additional x-axis cutoff points in graph.
As a result, polynomial:
6 difficult solutions
No actual solution
So, we can 6 difficult solutions.
We have following polynomial for this situation.
We observe that polynomial graph only intersects the vertical axis once.
There are no additional x-axis cutoff points in graph.
As a result, polynomial:
6 difficult solutions
No actual solution
So, 6 complex solutions can be said to exist.
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Convert 32.5% to a decimal number. If needed round to the nearest thousandth.
In order to convert a percent to a decimal number we need to move the decimal point two units to the left
[tex]32.5\text{\%}=0.325[/tex]Please help will give crown! Here is the question 2(-2)-4=12 solve it and tell me where it goes on a graph if you want, I'll give 400 points, if i can!
The solution to the given equation (2(-2) - 4 = 12) is -20 and its graphical solution is shown in the image attached below.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
Next, we would solve the given equation as follows:
2(-2) - 4 = 12
Let us introduce a variable x into the equation as follows:
x = 2(-2) - 4 - 12
x = -4 - 4 - 12
x = -20
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Triangle A has a height of 8 inches and a base of 2 inches. Triangle B has a height of 16 inches, what is the base?
The base of Triangle B is 1 inches.
Given,
Triangle A has a height of 8 inches
and base of Triangle is 2 inches
Let's Find the Area of Triangle A
We know that the formula of Area of Triangle
Area of Triangle = [tex]\frac{1}{2}[/tex] × b × h
where, b is the base and h is the height of triangle.
Plug the values of base and height in above formula.
Area of Triangle A = [tex]\frac{1}{2}[/tex] × 2 × 8
Hence, Area of Triangle A is 8 sq. inches
In this question, Some part is missing that is:
Triangle A is similar to Triangle B
Now, For Triangle B is given:
Triangle B has a height of 16 inches
and, to find the base of the triangle.
We know, Area of Triangle A is 8 sq. inches.
Area of Triangle B = [tex]\frac{1}{2}[/tex] × b × h
8 = [tex]\frac{1}{2}[/tex] × b × 16
8 = 8b
b = 1 inches
Hence, The base of Triangle B is 1 inches.
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