In the diagram, P is a point on ST such that P is between S and T. If SP = x + 3, PT =2x-1 and ST = 17, find the length of PT

Answer:

x=8

Step-by-step explanation:

-x-6=-14

-x=6-14

x=14-6

x=8

The slope of the road as reduced fraction  [tex]\frac{1}{20}[/tex] for grade which is 5%.

The slope of a road is defined as the ratio of the vertical height that a road rises to the horizontal distance covered to rise to that height.

While slope is expressed as a fraction grade is the percentage form of that fraction. The slope can also be defined as [tex]tan[/tex] [tex]\theta[/tex] where [tex]\theta[/tex] is the angle of elevation of the road. For example a slope of [tex]\frac{1}{4}[/tex] has a grade of 25%.

Here the given grade is 5%.

Per-cent refers to per one-hundred. So a 5% grade is 5 per one -hundred.

That means if the road is climbing then for every 100 units of horizontal distance covered, the altitude increases by 5 units.

Now slope of the road=vertical distance ÷ horizontal distance

[tex]=\frac{5}{100}\\=\frac{1}{20}[/tex]

Therefore we can say that the slope of the road is [tex]\frac{1}{20}[/tex]

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m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°;

Bisector BD bisects ∠ABC.

∠ABD= (8x+35)°, ∠CBD= (11x+23)°.

As given, bisector BD bisects the angle ABC so this means, the angle ABC is divided into two halves.

So,

angle ABD= angle CBD.

and ∠ABD= (8x + 35)° (i)

∠CBD= (11x + 23)° (ii)

So,

(8x + 35)° = (11x + 23)°

On solving the above equation, we have

3x= 12

x= 4.

Putting x=4 in (i) we have,

∠ABD= 8(4) + 35

∠ABD= 67°

As ∠ABD = ∠CBD, we have

∠CBD= 67°

Now,

∠ABC= ∠ABD + ∠CBD

∠ABC= 67° + 67°

∠ABC= 134°.

Hence, m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.

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Answer:

38

Step-by-step explanation:

5 x 10 -7= 43

8.5 x 10 -4= 81

81-43= 38

Answer:

[tex] 1.7 \times 10^3 = 1700 [/tex]

Step-by-step explanation:

To find how many times x is smaller than y, divide y by x.

Here we want to find how many times 5 × 10^-7 is smaller than 8.5 × 10^-4, so we divide 8.5 × 10^-4 by 5 × 10^-7.

[tex] \dfrac{8.5 \times 10^{-4}}{5 \times 10^{-7}} = [/tex]

[tex] = \dfrac{8.5}{5} \times \dfrac{10^{-4}}{10^{-7}} [/tex]

[tex] = 1.7 \times 10^{-4 - (-7)} [/tex]

[tex] = 1.7 \times 10^{-4 + 7} [/tex]

[tex] = 1.7 \times 10^3 = 1700 [/tex]

The missing coordinate can either be - 16 or 8.

Let the missing coordinate be x.

Now, we know that the distance between (-3, -4) and (6, x) is 15.

Using the distance formula, we get that:

Distance² = (x₂ - x₁)² + (y₂ - y₁)²

Substituting the values in the formula, we get that:

15² = (6 + 3)² + ( x + 4)²

225 = 9² + x² + 16 + 8 x

225 = 81 +x² + 16 + 8 x

225 = x² + 8 x + 97

x² + 8 x - 128 = 0

x² + 16 x - 8 x -128 = 0

x ( x + 16) - 8 ( x + 16) = 0

(x + 16)(x - 8) = 0

x = -16 or x = 8.

Therefore, the missing coordinate can either be - 16 or 8.

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The pair of equations show you how to find 16 – 9 is 9+1=10, 10+6=16. Therefore, option B is the correct answer.

The given numerical expression is 16-9.

A numerical expression in mathematics can be a combination of numbers, and integers combined using mathematical operators such as addition, subtraction, multiplication, or division.

Now, the pair of equations show you how to find 16 – 9 is 9+1=10,

10+6=16

Therefore, option B is the correct answer.

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we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.

We are given the frequency distribution table as:

X                 f    

5                 2

4                 5

3                 6

2                 4

1                  3

We need to find cumulative frequency (c f) and percentiles(c %)

c % = 100 × ( c f / n )

c f means the frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

n = 20

X                 f             c f             c %

5                 2              2            10 %

4                 5              7            35 %

3                 6             13            65 %

2                 4             17            85 %

1                  3            20           100 %

Therefore, we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.

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Answer:

23000

Step-by-step explanation:

(2 x 10⁴) + (3 x 10³)

= (2 x 10000) + (3 x 1000)

= 20000 + 3000

= 23000

Answer:

It is 0.2678 percent .....

Step-by-step explanation:

First, find the vector.

= (4,2) - (-3,5)

= (4-(-3),2-5)

= (7,-3)

And then, find the distance.

= √(7² + (-3)²)

= √(49 + 9)

= √58 ✓

The plane will be at an altitude of 21,000 feet, 6 minutes after lift off.

For any equation, x = y + a, if we are given the value of any one of the variables, that is either x or y, we can find the value of the other.

Here, we are given an equation

a = 3400t + 600

where a = altitude of the plane in feet

and t = time (in minutes) passed after the plane's lift off

If the altitude of the plane is 21,000 feet

⇒ a = 21,000

Substituting this in the equation, we get

21,000 = 3400t + 600

21,000 - 600 = 3400t

20,400 = 3400t

3400t = 20,400

t = 20,400/ 3,400

t = 204/ 34

t = 6

Thus, the plane will be at an altitude of 21,000 feet, 6 minutes after lift off.

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Answer:

9 26/30 or 9 13/15

Step-by-step explanation:

20/30 6/30

Answer:

9 13/15

Step-by-step explanation:

Answer: D

Step-by-step explanation:

16/30 x100= 53.3%

Answer:

D

Step-by-step explanation:

A relation is a function is each input maps onto no more than one output.

Answer:

Step-by-step explanation:

2 + (-5)

just like subtracting

2-5

=-3

Answer:

-3

Step-by-step explanation:

I have had this question before, and -3 is the answer.

The value of 9 - √7 is between 6 and 7:

4 < 7 < 9

⇒   √4 < √7 < √9

⇒   2 < √7 < 3

⇒   -3 < -√7 < -2

⇒   9 - 3 < 9 - √7 < 9 - 2

⇒   6 < 9 - √7 < 7

The range the number of clients, y, the company will have after x years of the function will be -∞ ≤ y ≤ ∞

The range of a function is the complete set of possible dependent variable values. While domain is the set of all possible independent values. We can substitute domain to get range.

From the given graph, the line of the equation of the graph is a linear. We can then say that y = - ∞, y = 1 and y = ∞

Y = 1 when x = 0

Therefore, the range of the function will be -∞ to +∞ That is,

-∞ ≤ y ≤ ∞

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Answer:

1,∞ is the answer

Step-by-step explanation:

Answer: wait what is the question asking i can’t really see

Step-by-step explanation:

Answer: 2 7/9

Step-by-step explanation:

6 1/9 - 3 1/3

first change so denominators are the same (times the second fraction by 3)

6 1/9 - 3 3/9

now borrow form first fraction

5 10/9 - 3 3/9

subtract whole numbers and numerators with each other

2 7/9

pls give brainiest

The roster form of the given sets will be S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}, S = { blue, red, green } and S = { Math, Science, English, Hindi, SST, Computer }.

We are given some sets in descriptive form.

We have to write it in the roster form.

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

1 ) The set of all counting numbers less than 10.

Roster form will be:

S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}

2) The set of primary colors.

Roster form will be:

S = { blue, red, green }

3 ) The set of all subjects in grade 7 level:

Roster form will be:

S = { Math, Science, English, Hindi, SST, Computer }

Therefore, the roster form of the given sets will be S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}, S = { blue, red, green } and S = { Math, Science, English, Hindi, SST, Computer }.

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Answer:

x = 14

Step-by-step explanation:

These are corresponding angles, so the angles are equal to each other.

6x - 35 = 3x + 7

3x - 35 = 7

3x = 42

x = 14

Answer:

1, 0.75, 1.25, 3, 0

Step-by-step explanation:

To find the value of the function, we find the y coordinate of the point with the given x value.

Work Shown:

g(x) = x^2 - 4

g(f(x)) = ( f(x) )^2 - 4

g(f(x)) = ( 2x-1 )^2 - 4

g(f(x)) = (2x-1)(2x-1) - 4

g(f(x)) = 4x^2-2x-2x+1 - 4

g(f(x)) = 4x^2 - 4x - 3

Answer:

3.3972 repeating dbbdeebebbbebe

Step-by-step explanation:

wvehhww3g33gg3g33vv3hh333h33hhh3

Answer:

C. not covered by workers' compensation and could recover damages from the employer.

Step-by-step explanation:

Answer:

15x = 15x

or

0 = 0

Step-by-step explanation:

21(x + 1) - 6x = 15x + 21

21x + 21 -6x = 15x + 21

21x - 6x = 15x

15x = 15x

or

0 = 0

this equation is always true

The area of the shape will be 1326 cm².

It should be noted that the area is calculated by multiplying the dimensions that are given.

Therefore the area will be:

= Length × Width

= 34 × 39.

= 1326 cm²

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in the figure, the first number line goes with x [tex]\leq[/tex]5

the second number line goes with x [tex]\geq[/tex] 5

the third number line goes with x > 5

the fourth number line goes with x < 5

Two less than 3/2 of a number x is  no more than 5/2 is shown as:

3/2 x- 2 [tex]\leq[/tex] 5 1/2

3/2 x [tex]\leq[/tex] 11/2 + 2

3/2 x [tex]\leq[/tex] 15/2

3x [tex]\leq[/tex] 15

x [tex]\leq[/tex] 5

The sum of two times a number (x) and -2 is at least 8 is shown as :

2x+(-2) [tex]\geq[/tex] 8

2x - 2 [tex]\geq[/tex] 8

2x [tex]\geq[/tex] 8+2

2x [tex]\geq[/tex] 10

x [tex]\geq[/tex] 5

Seven subtracted from 4 times a number (x) is more than 13 is shown as

4x -7 > 13

4x > 13+7

4x > 20

x > 20 ÷ 4

x > 5

Four added to 3 times a number (x) is less than 19 is shown as

3x + 4 < 19

3x < 19-4

3x < 15

x < 15 ÷ 3

x< 5

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The value for which the ball's height is 28 feet are 0.817sec and 1.683sec using quadratic equations.

What is a quadratic equation?

ax^2 + bx + c = 0

where x represents an unknown, and a, b, and c represent known figures, where a ≠ 0. is still, not quadratic, as there's no ax^2 term,( If a = 0( and b ≠ 0) also the equation is direct.)

Given,

h(0)=6 ft (six)

v(0)=40 ft/sec (fourty)

h(t)=6+40t-16t2 (equation)

for h=28 ft(twenty eight)

28=6+40t-16t2 (equation)

or 16t2 - 40t + 22 = 0 (equation)

or 8t2 - 20t + 11= 0(equation)

on solving the quadratic equation

t=0.817sec and 1.683sec (answer)

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