A rectangular box with top WXYZ and base ABCD has AB=6 cm, BC=8 cm and WA=3 cm
Calculate:
a) the length of AC
b) the angle between WC and AC

Simplest form of expression is an expression written in its simplest of terms without changing the original value of the expression. There should be no like terms or parentheses.

In the given expression, there are two like terms and no parentheses. Hence, we solve for eliminating the like terms to find the simplest form of expression.

In order to eliminate the like terms, we need solve the square root terms to its simplest form.

√32=√2x2x2x2x2=4√2  

√72=√2x2x2x3x3=6√2

Hence, the expression becomes,

2*4√2 x2+3*6√2 x2

Simplifying,

8√2 x2+18√2 x2

Adding the like terms,

(8+18)√2 x2

26√2 x2

Hence, the simplest form of expression 2 √32 x²+3 √72 x² is 26√2 x2.

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Answer:

The answer is supposedly 0.25

Answer:

The required number is 6. 6+6=12. 6×6=36.

Step-by-step explanation:

The inverse of the function y=5x+7 is y = (x-7)/5.

So,

All we have to do to find the inverse of an equation is switch the variables x and y.

Now, solve for y as follows:

Therefore,  the inverse of the function y=5x+7 is y = (x-7)/5.

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No extraneous solution.

We have to find the extraneous solution to the equation:

5 - 2[tex]\sqrt{x}[/tex] = 3

Now we have to find the value of x.

2[tex]\sqrt{x}[/tex] = 2

[tex]\sqrt{x}[/tex] = 1

x = 1

Now we have to put the value of x in the equation

5 - 2[tex]\sqrt{1}[/tex] = 3

5 - 2 = 3

3 = 3

Therefore we get no extraneous solution to the equation. x = 1 is the solution of the equation.

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1. 10 * 10 * 10 = 1000 = 10^3

2. 10 * 10 * 10 * 10 = 10,000 = 10^4

3. 10 * 10 * 10 * 10 * 10 = 100,000 = 10^5

4. 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10,000,000 = 10^7

5. Summary

Multiplication   Exp on first factor   Exp on 2nd factor    Exp on product

10^1 * 10^2                 1                                    2                             3

10^1 * 10^3                 1                                    3                              4

10^2 * 10^3               2                                   3                              5

10^4 * 10^3               4                                   3                              7

6. Multiplying two powers of ten, the product can be found by adding up the exponential values, the sum will be the exponent of the product and the base remain ten.

This refers to the exponential value of 10. Hence we can say that power as used in mathematics, is also called exponents.

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According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.

Therefore, the given expression is [tex]ln2+ln3=2[/tex]

The values get multiplied in addition. Therefore, the above expression can be written as:

Expression = [tex]ln(6)=2[/tex]

Using logarithmic definition, we can write:

[tex]6 = e^{2}\\e = \sqrt{6},-\sqrt{6}[/tex]

The solution for the given expression is [tex]e = \sqrt{6},-\sqrt{6}[/tex]

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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Answer:5

Step-by-step explanation:

4x + 5 = 5.. if its addition you take away the number if its subtraction you add the number.. take away 5 from 25.. 4 times 5 is 20

Answer:

125 small boxes

Step-by-step explanation:

[tex]n = { \tt{ \frac{volume \: of \: big \: box}{volume \: of \: small \: boxes} }} \\ \\ { \tt{n = \frac{(20 \times 10 \times 5)}{(2 \times 2 \times 2)} }} \\ \\ { \tt{n = \frac{5 \times 5 \times 5}{1} }} \\ \\ { \tt{n = 5 {}^{3} }} \\ \\ { \tt{n = 125}}[/tex]

The exponential function that would be a good model for the bouncing ball is [ 60 * [tex]0.6^{x}[/tex]] .

Given : height = 5 feet

            rebound on first bounce = 35 inches

            rebound on second bounce = 21.5 inches

To find :  exponential function that would be a good model for the                      bouncing ball

Calculation :

at x = 0

ht. = 5 feet = 60 inches

at x = 1

ht. = 35 inches

at x = 2

ht. = 21.5 inches

( 21. 5 / 35 ) * 100 = 60 % approx.

Since , the ht. rebounded is about 60% of the previous ht. rebounded , the exponential function that would be used would be of the form y = a * ( [tex]b^{x}[/tex] ) .

Therefore , the exponential function that would be a good model for the bouncing ball is [ 60 * [tex]0.6^{x}[/tex]] .

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ΔT= 313.5k-240.3k = 73.2k.

Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).

One unit increase in the Kelvin scale is the same as a one-degree increase in the Celsius scale. The only difference between these two scales is zero points of the thermometer.

ΔT= highest T° in k - lowest T° in k

40.5°c+273= 313.5k

-32.7°c+273= 240.3k

therefore the difference will be 73.2k

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We need to know about logarithm to solve this problem. The greatest integer that is less than log 0.08 is -2.

Logarithm is the exponent which is raised to a base to get a certain number. There are a few rules of logarithm, log a + log b can be written as log ab, log a- log b can be written as log a/b, when the number for which the logarithm is calculated is raised to a power, then the power can be directly multiplied to the log itself. Logarithms when written as log has a base of 10 and the logarithm of a number same as its base is always 1, log of 1 is zero.

log 0.08= log 8/100= log 8- log 100 = [tex]log 2^{3} -log 10^{2}[/tex]

=3 log2 -2log10=3x0.30-2=0.9-2=-1.1

Therefore the greatest integer that is less than the value of log 0.08 is -2.

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Solving a system of equations we can see that he repaired 15 of the fiberglass bathroom sinks and 8 of the fiberglass tub enclosures

Let's define the two variables:

x = number of fiberglass bathrooms repaired.

y = number of fiberglass tub enclosures repaired.

Then we can write the system of equations:

x + y = 23

x*$12 + y*$59 = $652

Isolating x on the first one, we get:

x = 23 - y

Replacing that in the other equation:

(23 - y)*$12 + y*$59 = $652

23*$12 + y*($59 - $12) = $652

23*$12 + y*$47 = $652

y = ($652 - 23*$12)/$47 = 8

Then:

x = 23 - y = 23 - 8 = 15

So, he repaired 15 of the fiberglass bathroom sinks and 8 of the fiberglass tub enclosures

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The  length of JK = 3√3

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

Given:

angle = 60

JL = 6√3

JK= x

Now, using trigonometry

cos [tex]\theta[/tex] = B/ H

cos 60 = x/ 6√3

1/2= x/ 6√3

x= 6√3/2

x= 3√3

Hence, the length of JK = 3√3

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The missing value of the inverse variation is 8

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.

Let say if x and y are two values and k is a constant value, then

According to inverse variation

k = xy or y = k/x

In the given question,

Take the order pair (4,6)

As it is an inverse variation, we can substitute it

y=k/x  

6=k/4

K=24

Now find the inverse variation equation

Y=k/x

Also, k=24

Solve this equation for the second pair (x,3)

As, y=24/x

    x = 24/3 = 8

Therefore, missing value is 8

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Answer:

f(10) = 905

Step-by-step explanation:

f(x) = 9x² +5; find f(10)

~Substitute x with 10

9(10)^2 + 5

~Solve exponent first

9(100) + 5

~Multiply

900 + 5

~Add

905

Best of Luck!

The answer is:

Work/explanation:

To evaluate the given function, plug in 5 for x:

[tex]\bf{f(x)=9x^2+5}[/tex]

[tex]\bf{f(10)=9(10)^2+5}[/tex]

Remember, exponents first. So we square 10 first.

[tex]\bf{f(10)=9\cdot100+5}[/tex]

Multiply, then add:

[tex]\bf{f(10)=900+5}[/tex]

[tex]\bf{f(10)=905}[/tex]

After evaluating the expression we get 12.

Given, x³ ₊ x²

Finding the value of an algebraic expression when a specified number is used to replace the variable is known as evaluating the expression. In order to evaluate an expression, we first replace the expression's variable with the given number, then we streamline the expression using the order of operations.

A procedure called evaluation involves analyzing a program critically. It entails gathering and studying data regarding a program's operations, features, and effects. Its objective is to assess a program, enhance its effectiveness, and/or provide information to help with programming decisions.

substitute the value of x =2

2³ ₊ 2²

= 8 ₊ 4

= 12

hence we get the answer as 12.

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If we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that there are two numbers which are  -√7 and 3.12345.

Let's compare the,.

We know that an irrational number is a number which can't be expressed other than using roots.

Here -√7 is an irrational number and if we represent that in decimal form then it can be written as :

-√7 = - 2.6467

Now , as this number is negative decimal number it is less than the other number given which is 3.12345 because 3.12345 is a positive decimal number. And we know that value of a positive number is always greater than a negative number.

i.e.,

3.1245 > -√7

Therefore , if we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.

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Answer:c=7

Step-by-step explanation:

The actual distance that is represented by 4 centimeters on the map is 16 kilometers

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the scale used on the map is:

1 cm = 4 km

Hence, for 4 cm represented on the map:

Actual distance = 4 cm * 4 km per 1 cm = 16 km

The actual distance that is represented by 4 centimeters on the map is 16 kilometers

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Answer: do i remember how to do this... no

Step-by-step explanation:

Answer:

A. & B.

Step-by-step explanation:

Square root of 4 is 2, and the square root of 9 is 3. These are rational, and adding fractions keeps them rational.

But the square root of 2 is irrational, and subtracting or dividing will not make them rational.

Hope this helps! :)

Answer:

it is 104

Step-by-step explanation:

you have to complete 360 degrees for shape so

89-167=256 and 256-360=104

Answer:

The record time that was achieved in 1970 was 5.78 seconds.

Step-by-step explanation:

It is given that the first one-mile speed record was made by Henry Ford in 1904 when he drove the mile in 39.40 seconds.

It is further stated that this time was 33.62 s slower than the record achieved in 1970.

Now, let us consider the first statement;

Henry Ford covered one mile in time (1904) = 39.40 sec

Now, let us consider the second statement given;

Time taken by Henry Ford (1940) was slower than the time someone else achieved in one miles by = 33.62 sec

So, to calculate the time taken in 1970;

=> 39.40 - 33.62 sec

=> 5.78 sec

Therefore, the record time that was achieved in 1970 was 5.78 seconds.

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The measure of PQT = 142.

We know what ray QS bisects angle PQT. If you draw out angle PQT and ray QS you can see that angle PQS is congruent to angle SQT. Because of the definition of angle bisector. This also means that angle SQT is half of PQT. Because of this we know that we can set the measure of PQT equal to 2 times the measure of SQT.

So we can set up and solve the following equation as such:

2(8x-25) = 9x +34

16x - 50 = 9x +34

7x -50 = 34

7x = 84

x = 12

Again I this doesn't seem to be your final answer. To find the answer the measures of each angle you're going to want to plug 12 in for x for one of the angles. So I'll do it for angle SQT.

8(12) - 25

96 -25

71

So the measure of angle SQT should be 71. Therefore since QS bisects PQR, the measure of angle PQS should also be 71. The measure of PQT should be double that which makes it 142.

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