The altitude of an equilateral triangle is 4.2 meters long. Find the perimeter of the triangle. It is a 30,60,90 triangle and please dont use SIN, TAN, COS.

Answer:

=4r⁷

Step-by-step explanation:

(2r⁹) (8r⁴)

=_____

4r⁶

16r¹³

=______

4r⁶

=16r¹³ ÷ 4r⁶

=4r⁷.

Answer: 4r⁷

Step-by-step explanation: (2r⁹) (8r⁴) = _____ 4r⁶ 16r¹³ = ______ 4r⁶ 16r¹³ ÷ 4r⁶ 4r⁷

The required equations are y = 3x + 2, y = 3x + 5 which have no solution.

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

For no solution of equation,

equation of line must be parallel and for parallel line, Slope should be same.

Or we can say There won't be a solution if (a1/a2) = (b1/b2) (c1/c2). An inconsistent pair of linear equations is the name given to this kind of equation.

y = 3x + 2

y = 3x + 5

Thus, required two equation are y = 3x + 2, y = 3x + 5 which have no solution.

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Lola is correct because each expression has a value of 1. Option A is correct.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.

here,
Given expression
A = [tex][[a /b]^{-4}]^0[/tex]
B = [tex][[a /b]^{0}]^{-4}[/tex]

Since we know that,
a⁰ = 1

So,
A = [1]
B = 1⁻⁴ = 1

Thus, Lola is correct because each expression has a value of 1. Option A is correct.

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Answer: x = 32 & y = 51

Step-by-step explanation:

Since

ΔMNP ≅ ΔTUS

Therefore

NP ≅ US

2x - y = 13

y = 2x - 13 __eq_1

Since

ΔMNP ≅ ΔTUS

therefore

∠N ≅ ∠U

so, if we find ∠N we'll be able to find ∠U as well



since the sum of angles of a triangle is 180, therefore

∠N = 180 - (∠M + ∠P )

∠N = 180 - (142 + 24)

∠N = 14°

we know ∠N ≅ ∠U

therefore

14 = 2x - 50

2x = 64

x = 64÷2

x = 32 __eq_2

putting eq_2 in eq_1

y = 

2x - 13

y = 2 (32) - 13

y = 51 __eq_3

x = 32 & y = 51 ...Answer

hope that helps...

Answer:

0.115

Step-by-step explanation:

For each quadratic equation, the value of a, b and c are mentioned below. Also maximum or minimum points are mentioned here.

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

a. y = 3x²-3x + 5, comparing this with general quadratic equation ax² + bx + c and get a = 3 and b = -3 and c = 5

thus x = - (b/2a)

x = - (-3/6)

x = -1/2

as a > 0 thus the equation has the minimum value and that is:

y = 3(-1/2)² -3(-1/2) + 5

y = 3/4 + 3/2 + 5

y = 13/2

b. y = -2x² + x  comparing this with general quadratic equation ax² + bx + c and get a = -2 and b = 1 and c = 0

thus x = - (b/2a)

x = - (1/-4)

x = 1/4

as a < 0 thus the equation has the maximum value and that is:

y = -2(1/4)² + (1/2)

y = -1/8 + 1/2

y = 3/8

c. y = 1/2x² + 6 comparing this with general quadratic equation ax² + bx + c and get a = 1/2, b = 0 and c = 6

thus x = - (b/2a)

x = - (1/2×0)

x = 0

as a > 0 thus the equation has the minimum value and that is:

y = 1/2(0)² + 6

y = 6

d. y=-3x² + 1/2x - 2 comparing this with general quadratic equation ax² + bx + c and get a = -3, b = 1/2 and c = -2

thus x = - (b/2a)

x = - [(1/2)/-6]

x = 1/12

as a < 0 thus the equation has the maximum value and that is:

y=-3(1/12)² + 1/2 (1/12) - 2

y = - 1/48 + 1/24 - 2

y = -45/48

e. y=x²-2x+6 comparing this with general quadratic equation ax² + bx + c and get a = 1, b = -2 and c = 6

thus x = - (b/2a)

x = - (-2/2)

x = 1

as a > 0 thus the equation has the minimum value and that is:

y=(1)²-2(1)+6

y = 5

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Examining the right triangle figure attached the value of sin  A is

The trigonometry sin A is worked using the pneumonic SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

Information from the question, viewing from angle A

opposite = 20

adjacent = 15

hypotenuse = 25

The value of sin A is calculated using sin, SOH

et the angle be x

sin x = Opposite / hypotenuse

sin x = 20 / 25

sin x = 4 / 5

sin x is 4/5

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Using BODMAS, the answer of the given question is  13232 / 15.

The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to BODMAS rule. Any expression can only be solved correctly if the BODMAS rule or the PEDMAS rule are applied.

The other operations must be solved in the same order. Brackets (B) are followed by the order of powers or roots, which is then followed by multiplication, addition, subtraction, and finally division.

According to the question,

[tex]27 \frac{2}{3} \times 32 - \frac{2}{5} \div 64^{\frac{5}{6} }[/tex]

Using BODMAS,

⇒ 83/3 × 32 - [tex]\frac{2}{5}[/tex] ÷ [tex]64^{\frac{5}{6} }[/tex]

⇒ 83/3 × 32 - 2/5 ÷ [tex](2^{6})^{\frac{5}{6} }[/tex]

⇒ 83/3 × 32 - 2/5 ÷ 2⁵

⇒  83/3 × 32 - 2/5 × 1/2⁵

⇒  83/3 × 32 - 2⁴/5

⇒ 2656 / 3 - 2⁴/5

⇒ 2656 / 3 - 16/5

⇒ 13280 -  48 / 15

⇒ 13232 / 15

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The Booster Club sold 45 tickets to the adults and 110 tickets to the students.

In the given question, the Booster Club selling tickets wants to keep track of how many adult and student tickets they sold.

At a recent cross country meet, spectators had to pay to get in.

It cost $7 for adults and $3 for students.

However, they did know they sold 155 total tickets and made $645.

Let total x tickets sold to adults.

Let total y tickets sold to students.

They sold total 155 tickets. So the required equation is:

x + y = 155...(1)

The cost of one adult ticket is $7. So the cost of x tickets are 7x.

The cost of one student ticket is $3. So the cost of y tickets are 3y.

They earned total $645. So the required equation is:

7x + 3y = 645...(2)

Now solving the both equation using the elimination method

Multiply the equation 1 by 3 and then subtract by equation 2, we get

7x + 3y - (3x + 3y) = 645 - 465

After solving, we get

4x = 180

Divide by 4 on both side, we get

x = 45

Now putting the value of x in equation 1, we get

45 + y = 155

Subtract 45 on both side, we get

y = 110

Hence, the Booster Club sold 45 tickets to the adults and 110 tickets to the students.

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Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value(s) for the variable are entered, two algebraic expressions that are equivalent will have the same value (s).

An algebraic expression is a mathematical expression made up of variables, coefficients, constants, and operations including addition, subtraction, multiplication, and division. In most cases, something is said to be equivalent if two of them are the same.

Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning.

The two expressions, however, produce the identical outcome when the values are inserted into them.

Example

If the provided expression has an equivalent, write it down: 3x+9

Solution:

expressed in this way: 3x+9

The analogous equation is equal to the expression when 3 is removed from it, which is = 3(x+3).

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Answer:

4.2 has a greater value

since 4.2 is greater than 3.6

Step-by-step explanation:

Since neither numbers are negative, the absolute value around the numbers do not change the values. So nothing changes and we know 4.2 is greater than 3.6

To evaluate an algebraic expression is to determine its value when a certain number is used in place of the variable. Therefore the correct option is 25/49

To evaluate the expression of 5/7 to the power of 2 we will-

[tex]5/7² = 5/7 X 5/7 = 25/49[/tex]

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A system of linear equations can be classified into 3 different ways based on their nature of roots and their graphical representation.

Step 1: Examine the given graph.

Step 2: Determine if the lines cross exactly once, are exactly the same, or are parallel to each other.

Step 3: Classify the system of linear equations as consistent dependent, consistent independent, or inconsistent based on your findings in step 2.

A system of linear equations is consistent dependent if it has an infinite number of solutions i.e the graphs of the lines in the system are the same, it is consistent independent when it has exactly one solution i.e the graphs of the lines in the system cross exactly once and a system is inconsistent if it has no solutions i.e the graphs of the lines do not intersect and they are parallel.

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plot the frequency distribution with frequency 11, 8, 7, 5, 2, 2,2 and box numbers on X axis

It will show a graph which is Positively skewed.

Answer: x=3-4y

                 _____

                   5

Step-by-step explanation:

Answer:  k = 5/2 = 2.500

Step-by-step explanation: k=25​=221​=2.5

Total Surface area of the inner cube = 6 * 2 = 12 m²

Take a vertical cross-section through the center of the arrangement as shown in the following figure —

The surface area of the outer cube is 24 m²

Therefore, each face of this cube equals  4 m²

=> Each edge of the larger cube is two meters

The inner sphere's diameter is 2 meters since it meets the surface of the outer cube.

Thus, the sphere's radius (Viz OR) is equal to 1 m.

Taking into account Right Triangle OQR, QR  = √ [ 1² + 1² ] = √2 m

=> The smaller cube's face area is equal to 2 m².

The inner cube's total surface area is equal to 6 * 2 = 12 m²

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The full question:

A sphere is inscribed in a cube that has a surface area of 24 m2. A second cube is then inscribed within the sphere. What is the surface area of the inner cube?

The measure of angle ABE is 40 degrees.

When two lines intersect each other, the vertically opposite angles are equal.

Therefore, angle ABE = angle CBD

angle ABE = 40 degrees.

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After 8years the investment will have worth 2800

Simple interest is the interest amount for a particular principal amount of money at some rate of interest. In contrast, compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Simple interest is given as:

I = (P×R×T)/100

where P = principal

R = rate of the interest

T = time for the loan / savings

therefore I = 2000× 5× 8/100

I = 800

Therefore that amount realized after 8years

= 2000+800 = 2800

therefore the investment will worth 2800 after 8 years.

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If the rank of matrix A is equal to the number of columns of A, and the rank of matrix A is equal to the rank of the augmented matrix [A|b], then the system Ax = b will have a unique solution for all choices of b. Otherwise, the system Ax = b will not have a unique solution for all choices of b.

To determine if the system ax = b has a solution for all choices of b, we need to look at the rank of the matrix A and the rank of the matrix formed by appending the vector b to the matrix A.

The rank of a matrix is the number of linearly independent rows or columns in the matrix. If the rank of matrix A is equal to the number of columns in A, then matrix A is full rank and the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the number of columns in A, then matrix A is not full rank, and the system Ax = b will not have a unique solution for all choices of b.

If the rank of matrix A is equal to the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will not have a unique solution for all choices of b.

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To find the pay/hour that makes traveling on the plane and bus travel equally attractive, we can use the concept of "opportunity cost" by comparing the cost of the plane ticket with the cost of the bus ticket plus the pay/hour.

One way to do this is to use the concept of "opportunity cost," which is the cost of foregone opportunities. In this case, the opportunity cost of traveling by plane is the cost of the plane ticket, while the opportunity cost of traveling by bus is the cost of the bus ticket.

To find the pay/hour that would make traveling by plane and bus equally attractive, we can set up an equation where the opportunity cost of the plane ticket equals the opportunity cost of the bus ticket plus the pay/hour. This equation can be written as:

Plane ticket cost = Bus ticket cost + Pay/hour

To find the pay/hour, we will have to know the costs of the plane and bus tickets and solve the equation for Pay/hour.

Pay/hour = Plane ticket cost - Bus ticket cost

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The percentage of students are boys = 51.5% and The percentage of students always wear glasses = 21.3%

What is percentage ?

percentage can be defined as the product of ratio of given value , total value and hundred.

Given ,

A principal of a school with 484 students collected information about how many of the students wear glasses complete the two way frequency table

So, the number of boys always wears glasses are 40

the number of boys sometimes wears glasses are 48

the number of boys never wear glasses are 161 .

Total number of boys = 249

the number of girls always wears glasses are 36

the number of girls sometimes wears glasses are 55

the number of girls never wear glasses are 144.

Total number of girls = 235

Total number of students always wears glasses = 76

Total number of students sometimes wears glasses = 103

Total number of students never wear glasses = 305 .

Total number of students = 484 .

The percentage of students are boys = 51.5%

The percentage of students always wear glasses = 21.3%

Hence, The percentage of students are boys = 51.5% and The percentage of students always wear glasses = 21.3%

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Answer:

21 dollars is the change.

Step-by-step explanation:

If u do division 25/4 its equals to 5.25 which could be the answer too.

Place your protractor on a straight line to measure the acute angle. Line up the horizontal line on the baseline of your protractor, placing the centre of your protractor over the vertex. Examine where the diagonal line crosses the protractor to specify the number of degrees in the acute angle.

Measuring angles is a significant topic in geometry. An angle can be measured by operating a protractor, precisely. An angle is measured in degrees, hence it's called ‘degree measure’.

One complete revolution is equivalent to 360 degrees, hence it is divided into 360 parts. Each part of the one complete revolution is a degree. If we know how to measure angles, then it will be very easy to construct an angle using a protractor.

Any angle whether it is an obtuse, acute, right or reflex angle, can be calculated using a protractor. Although we are able to differentiate between acute, obtuse or reflex angles, based on the right angle.

If we have two acute angles to calculate, then we cannot calculate the greater angle among the two. Thus, we have to use a protractor to measure the angles accurately.

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Answer:the frist one

Step-by-step explanation:

There will be approximately around 5000× 2¹⁸ = 262,144,000 bacteria.

Similar to the function of protonophores, bacterial populations have natural defences against antibiotics. These mechanisms interfere with the membrane electrochemical gradients that allow bacterial populations to develop persister subpopulations that are drug-tolerant.

Every four hours, the population will double, making a total of 18 times in a 72-hour period.

In the beginning there are 5000 bacteria and There are 24 hours in a day, hence there will be 72 hours in 3 days (3× 24).

There will be around 5000 × 2¹⁸ = 262,144,000 bacteria.

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Answer:

8.3 miles

Step-by-step explanation:

1 2/3 times 5= 8.3. He rode 8.3 miles

The store manager can use f∘g function to find the final price of a bicycle.

Let the buying price be Y,

Store is offering sale on the item given by function,

f(x) = x - 30

And offering an additional discount given by function,

g(x) = x - 0.1x = 0.9x

So final price be written as;

0.9x - 30    [ 10% off and 30$ discount ]

Then 0.9x - 30 = f∘g ( operations of functions of functions ).

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

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If in a survey of women in a certain country (ages 20 - 29), the mean height was 63.2 inches with a standard deviation of 2.67 inches.

a. The height that represents the 95th percentile is 67.61.

b. The height that represents the first quartile is  61.4.

Mean (μ) = 63.2

Standard deviation  (σ) =  2.67

a. The value of the 95th percentile

Value of the 95th percentile = 63.2 + 1.65(2.67)

Value of the 95th percentile = 63.2 + 4.4055

Value of the 95th percentile = 67.61

b.  value of the first quartile (25th percentile)

Value of the  first quartile = 63.2 + (-0.67) (2.67)

Value of the  first quartile = 63.2 + (-1.7889)

Value of the  first quartile = 61.4

Therefore the height that represents the 95th percentile is 67.61 and the height that represents the first quartile is  61.4.

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