What real-world knowledge did you use to understand the STEM Task?

Answer: NO SOLUTION

Step-by-step explanation:

6x + 4x - 1 = 2(5x + 4)

10x - 1 = 2(5x+4)

10x - 1 = 10x + 8

-1 = 8

NO SOLUTION

The unknown side length of the right triangle is 58 units.

What is pythagoras theorem for a right triangle?
In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Mathematically, Hypotenuse² = Base² + Perpendicular²

Given, the length of the perpendicular of the right triangle = 42 units
Also, the length of the base of the right triangle = 40 units
Let the length of the hypotenuse of the right triangle = 'x' units
Following the statement of the pythagoras theorem as established in literature, we have: Hypotenuse² = Base² + Perpendicular²
Substituting the values from the question given, we get:
x² = 42² + 40² = 3364 ⇒ x = √3364 ⇒ x = √58² ⇒ x = 58
Therefore, the unknown side length of the right triangle is 58 units.

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[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{7 - 6}{3 - 1} \\ m = \frac{1}{2} [/tex]

I ALSO PROVIDED YOU WITH THE FORMULA OF FINDING THE GRADIENT/SLOPE FOR FUTURE USE

HOPE THIS HELPS.

Answer: Y= 1/2x + 5.5

Answer:

Step-by-step explanation:

To solve for x, isolate this equation from left to right.

4x+10=-26

First, subtract by 10 from both sides.

4x+10-10=-26-10

Solve.

-26-10=-36

4x=-36

Then, you divide by 4 from both sides.

4x/4=-36/4

Solve.

-36/4=-9

[tex]\Rightarrow \boxed{\sf{x=-9}}[/tex]

As a result, the solution is x=-9, which is the correct answer.

I hope this helps, let me know if you have any questions.

Answer:

-9

Step-by-step explanation:

First you subtract 10 from each side

4x + 10 = -26

-10 -10

then you divide by your x

4x = -36

4 4

the 4s cancel out leaving you with x only

x = -36/4

x = -9

Answer:

Step-by-step explanation:

1) Find DGE

Bisecting an angle makes it half. A straight line is 180

180/2 = DGE

90 = DGE

2) Find FGE

Bisecting an angle makes it half. A straight line is 180

180/2 = FGE

90 =  FGE

Answer:

2/3 = y

Step-by-step explanation:

to solve you got to cancel out the 7
so 7y/7.
whatever you do to one side, you do to the other.
14/3 ÷ 7 = 7y/7
14/3 ÷ 7 = 0.6666... = 2/3 = y

The exponential equation [tex]14=5^x[/tex] is equivalent to the  given logarithmic equation.

The exponential function that is represented as y=[tex]m^x[/tex], where:

m=base, m>0

x= exponent

Knowing some of the main logarithm rules.

example: [tex]log(a*b)= log a + log b[/tex]

example: [tex]log\frac{a}{b} = log a - log b[/tex]

example: [tex]log\frac{a^b} = b*log a[/tex]

For solving this question, you should apply the logarithm rules and  rewrite the function as an exponential equation.

[tex]log_5(x)}-{log_5(25)=7[/tex]

[tex]\frac{log_5(x)}{log_5(25)} =7[/tex]

[tex]{log_5(x)}=7{log_5(25)}[/tex]

[tex]{log_5(x)}=7{log_5(5^2)}[/tex]

[tex]{log_5(x)}=7*2[/tex]

[tex]{log_5(x)}=14[/tex]

[tex]x=5^{14^}[/tex]

Therefore, the  exponential function is [tex]14=5^x[/tex]

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Step-by-step explanation:

in general, a linear function is always of the structure

y = ax + b

"a" is the slope of the line and is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

"b" is the y-intercept (the y-value when x = 0).

so, if we don't see the solution right away with experience, we have to use the data points (usually starting with the first 2) to solve them 2 equations with 2 variables a, b :

2 = a×1 + b = a + b

1 = a×2 + b = 2a + b

now we can simply subtract the first equation from the second and get

1 = 2a + b

- 2 = a + b

------------------

-1 = a + 0

a = -1

1 = 2×-1 + b = -2 + b

b = 3

and the equation is

y = -x + 3

therefore, when the input is n (that means f(n))

y = output = -n + 3

Answer: (*^▽^*)        []~(￣▽￣)~*

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Tanya yearly salary is

$35000 + 8% of her sales

Let her sales be x

Since, her sales is x

35000 + 0.08x > salary

To determine her necessary sales to earn over $50, 000

Let $50, 000 be her benchmark salary

35,000 + 0.08 * x > 50000

35000 + 0.08x > 50000

0.08x > 50000 - 350000

0.08x > 15000

Divide both sides by 0.08

0.08x/0.08 > 15000/0.08

x > 15000 / 0.08

x > 187,500

Therefore, she will need a sales of 188,000 and above to earn above $50,000

Answer:

(x+3)(x–8)

Step-by-step explanation:

Normally you will always write factors in this form: (variable + smallest number)(variable – largest number)

Correct form: (x+2)(x–8)

Incorrect form: (x–2)(x+8)

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If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Definition of the proportionality constant?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

K = y/x is the equation for the proportionality constant. The equation for the slope of a line through the origin, m = y/x, is the same as this. One can determine the value by using the equation for the line's slope.

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The amount as a percentage is 15% which represents the number 1 to 20 containing the digit 2.

The percentage is defined as a ratio expressed as a fraction of 100.

We know that the numbers 1 to 20 that contain the digit 2 are 2,12, and 20.

So, the quantity of the numbers is 3

It’s out of 20 numbers, this means 3/20

Calculating percentages indicated above can be readily computed using the formula below:

Percentage = (Value/Total Value) × 100

The amount as a percent = (Value/Total Value) × 100

The amount as a percent = (3/20) × 100

The amount as a percent = 15%

Thus, the amount as a percentage is 15% which represents the number 1 to 20 containing the digit 2.

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The functions that are equivalent are

What are roots of a number?

The root of a number is the inverse of the exponents. for instance

a squared has an inverse of square root of a.  

mathematically:

a^2 = (a)^1/2  has an inverse of √a

The data given:

[tex]\sqrt[4]{162^{x} }[/tex]

Solving the given data for the equivalence

[tex]\sqrt[4]{162^{x} }=162^{x/4}[/tex]

The above proves option A correct

[tex]\sqrt[4]{(3*3*3*3*2)^{x} }[/tex]

[tex]\sqrt[4]{(3^{4} *2)^{x} }[/tex]

[tex](3\sqrt[4]{(2) })^{x}[/tex]

The above solution makes option B correct

[tex](3\sqrt[4]{(2) })^{x}=(3{(2)^{1/4} })^{x}[/tex]

The above proves Option D correct

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complete question

Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.

f (x) = 162 Superscript StartFraction x Over 4

f (x) = (3 RootIndex 4 StartRoot 2 EndRoot) Superscript x

f (x) = 9 RootIndex 4 StartRoot 2 EndRoot Superscript x

f (x) = 126 Superscript StartFraction 4 Over x

f (x) = left-bracket 3 (2 Superscript one-fourth Baseline) right-bracket Superscript x

The two cars are 5 kilometers far apart from each other.

What is Pythagoras theorem?

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

Two cars leave the same parking lot, with one heading north and the other heading east.

After several minutes, the northbound car has traveled 3 kilometers, and the eastbound car has traveled 4 kilometers.

Now,

The straight path is find by using the Pythagoras theorem as;

Straight path = √3² + 4²

                    = √9 + 16

                    = √25

                    = 5 km

Therefore,

The two cars are 5 kilometers far apart from each other.

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Rotate R and reflect 90

Step-by-step explanation:

The distance between the person and the shuttle is changing at a rate of 640 feet/sec when the shuttle is 4000 ft high and is rising at a rate of 800 ft/sec.

Considering x to be the height of the triangle and y to be the hypotenuse of the triangle, a right-angled triangle will be formed according to the given information having a base of 3000 feet which is the distance of the person from the launch pad.

In this right-angle triangle x will be the height of the shuttle and y will be the distance between the person and the shuttle.

Now we apply the Pythagorean theorem to the triangle;

y² = x²+(3000)²

Now differentiating this equation with respect to time,t :

2y (dy/dt) = 2x(dx/dt) + 0

dy/dt = x(dx/dt)/y

As the shuttle is rising at a speed of 800 ft/sec, (dx/dt)=800

Substitute 4000 for x into the equation, y²=x²+(3000)², to find y;

y² = (4000)²+(3000)²

y = 5000

Now we substitute 4000 for x, 5000 for y, and 800 for dx/dt in the equation, dy/dt = x(dx/dt)/y

dy/dt = 4000(800) / 5000

dy/dt = 640

Therefore, the distance between the person and the shuttle is increasing at a rate of 640 feet/sec.

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Answer:95

Step-by-step explanation:

This can simply be answered by adding the first digit of both numbers which would be 9 then add the secound number of both  numbers and that would be 5

The answer is 95

Answer:

if its 6^2 + 3^3 then its 63

Step-by-step explanation:

6^2 simplified is 36 and 3^3

6 x 6 = 36 + 27 = 63

                                        3 x 3 x 3 =27

                                        3 x 3= 9

                                        9 x 3= 27

The function is

The limit when x->+/- infinite are (analitically)

And, from the figure,

Therefore,

Therefore, the answer is option C, a>1.

The dinner bill of Sally before the tip is $53.

Given that, Sally left an 18% tip. The tip was 9.50.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the dinner bill of Sally be x.

Now, 18% of x = 9.50

⇒ 18/100 × x = 9.50

⇒ 0.18x = 9.50

⇒ x = 9.50/0.18

⇒ x = 52.77

≈ 53

Therefore, the dinner bill of Sally before the tip is $53.

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Answer:

D

Step-by-step explanation:

-3 ft means that it is three feet below zero. That means 0 means the sea level.

Answer:

x = 3

or

x = -3

(explanation in the picture above)

Answer: x = 3 or x = -3

Step-by-step explanation:

Absolute values make the answer always positive, as they cancel out the negative sign. So to solve an absolute value equation, we must solve for both the positive and negative of the answer.

3x = 9

3x = -9

x = 3 or x = -3

The answers are given below.

First of all, we will know about GCF and expressions.

GCF (GREATEST COMMON FACTOR) - The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both.

Expression are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

1). 5/6(-2y+3) (simply multiply 5/6 with both terms using expansion)

=-2(5/6)+3(5/6)

=-5/3+5/2

2). 6(3s-2.5-5s)= 18s-15-30s = -12s-15

3). 3/10(4m-8)+9m = 12/10m-24/10+9m

= 6/5m-12/5+9m

=6/5m+9m-12/5

=51/m-12/5

4). 2.25-2(7.5-4h)= 2.25-15+8h

= 8h-12.75

5). 3(a-7)= 3a-21

6). -6(2+x)= -12-6x

7). -5(3m-4)= -15m+20

8).  -9(-5-4c)= 45+36c

9).  4.5(3s+6)= 13.5s+27

10).  -1.4(-5+7g)= 7-9.8g

11). 2/5(6-5p)= 12/5-2p

12).  -4/3(3q-10)= -4q+40/3

13). 2(3+4y+5)= 6+8y+10 = 8y+10

14. The expression 8x + 2 factored using the GCF is= 2(4x+1)

15. The expression 3y-24 factored using the GCF is = 3(y-8)

16. The expression 14p-28 factored using the GCF is= 14(p-2)

17. The expression 6+16k factored using the GCF is= 2(3+8k)

The coefficient of the variable terms of following are given below

18. The expression 1/7a + 1/7 factored is= 1/7

19. The expression 1/3b - 1/3 factored is= 1/3

20. The expression 3/8d + 3/4 factored is= 3/8

21. The expression 2.2x+ 4.4factored is= 2.2

22. The expression 0.15c - 0.072 factored is= 0.15

23. The expression 3/8z + 1 factored is=3/8

24. The expression 6s - 3/4 factored is=6

25. The expression 5/2k - 2 factored is=5/2

26. Factor -4 out of 8d + 20 The factored expression is= -4(-2d-5)

27. Factor -6 out of 18z - 15 The factored expression is=-6(-3z+5/2)

28. Factor -0.25 out of 7g + 3.5 The factored expression is=-0.25(-28g-14)

29. Factor -1/2 out of -1/2x+ 6 The factored expression is=-1/2(x-12)

30. Factor -1.75 out of -14m - 5.25n The factored expression is=-1.75(8m+3n)

31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=-1/4(2x+5y)

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Answer:

Step-by-step explanation:

The repeated part is 194805, six digits. Let the fraction be x.

Convert as follows:

Find prime factors of both numerator and denominator and simplify by cancelling common factors:

The common factors are:

When they cancel we are left with:

Answer:

3.75 represents how much the flower grows every week.

Step-by-step explanation:

The correct answer is option B that is No, because two points with the same x-value have different y values.

A relation in mathematics may be defined as the term which describes the relationship between the input and output variables. A function may be defined as the expression in which for one value of input variable x there is only one output variable y. The input variable is called independent variable and output variable is called dependent variable. From the graph given in question it can be seen that at point x = 2 there are two points on the y axis that are y = 2 and y = 11. So, this violates the basic definition of function as for input x there are two outputs y and hence it cannot be regarded as function.

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Answer:

[tex]\begin{aligned}&\phantom{=.} \dfrac{1}{8}x \cdot \dfrac{-4}{5}x\\\\&=\dfrac{1}{2} \cdot \dfrac{\boxed{-1}}{5} \cdot x \cdot \boxed{x}\\\\& = \dfrac{\boxed{-1}}{\boxed{10}} \;x\;^\boxed{2}\end{aligned}[/tex]

Step-by-step explanation:

According to the Commutative Property Law of Multiplication, changing the order or position of the numbers does not change the end result.

Therefore, collect like terms by moving the fractions to the left and the variables to the right.

As the denominator of the first fraction has been divided by 4, the numerator of the second fraction should also be divided by 4.

Therefore:

[tex]=\dfrac{1}{2} \cdot \dfrac{\boxed{-1}}{5} \cdot x \cdot \boxed{x}\\[/tex]

[tex]\textsf{Apply\;the\;fraction\;rule} \quad \dfrac{a}{c}\cdot \dfrac{b}{d}=\dfrac{ab}{cd}.[/tex]

[tex]\textsf{Apply\;the\;exponent\;rule}\quad \:aa=a^2.[/tex]

Therefore:

[tex]=\dfrac{\boxed{-1}}{\boxed{10}} \;x\;\boxed{^2}[/tex]

We will improve the argument by stating that two intersecting lines have vertically opposite angles equal in magnitude.

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