Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.

ANSWER:
CORRECT (SELECTED)
Josiah's distance from the starting line at a time when he is behind Chana
Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance.

The number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.

Formula for permutation with repetition

[tex]^nPr = n^r[/tex]

Formula for permutation without repetition

[tex]^nPr = \frac{n!}{n-r!}[/tex]

We have = 5

r = 3

a. If repetition is allowed,

Permutation = [tex]5^3[/tex] = 125 ways

b. If repetition is not allowed,

Permutation = [tex]\frac{5!}{5-3!}[/tex]

Permutation = [tex]\frac{5*4*3*2*1}{2*1}[/tex]

Permutation = [tex]\frac{120}{2}[/tex]

Permutation = 60 ways

Thus, the number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.

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Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110

Geometric sequence are sequence that increase in an exponential manner.

Given the recursive sequence 0, 2, 14, 36, 68

From the sequence

0 + 2 = 2

2 + 12 = 14

14 + 22 = 36

36 + 32 = 68

68 + 42 = 110

Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110

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Answer:

option A: West Europe, East Europe, and Asia

Explanation: Europe and Asia as a whole are called Eurasia.

hope that helps...

Answer: x = 6

Step-by-step explanation:

B(7,3) maps onto B'(5,3).

The perpendicular bisector of [tex]\overline{BB'}[/tex] is x=6, so that is also the line of reflection.

Answer:

x = 6

Step-by-step explanation:

Taking test as we speak

The bisection method will converge to the solution after three iterations.

It should be noted that after one iteration, x1 will be:

= (1 + 9)/2

= 10/2

= 5

Since f(x¹) > 0, x² will then replace x1. Now x0 = 1 and x1 = 5.

After the second iteration, x2 will be:

= (1 + 5)/2

= 3

Also, this is greater than 0. The third iteration will be:

m= (1 + 3)/2

= 2.

Now, f(2) = 2⁴ -2³ - 2² - 4

= 0

Therefore, the method converges exactly to the root in 3 iterations.

Complete question:

The bisection method is applied to compute the zero to a function f(x) = x⁴ - x³ - x² - 4 in the interval (1, 9). The method converges y a solution after .............. iterations.

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Answer:

•3✓7

✓3.✓21

=✓3×✓3✓7

=3✓7

Answer:

3rd answer is correct

Step-by-step explanation:

√3 × √21

√3 × √(7 × 3)

√( 3 × 3 × 7 )

√ ( 3 × 3 ) × √7

3√7

Answer:

[tex]y = -2x + 5[/tex]

m = -1

b = 5

Step-by-step explanation:

Hello!

Slope - Intercept Form: [tex]y = mx+b[/tex]

The slope of the line is the rate of change, or how the graph changes in y as it changes in x.

Slope can be calculated by the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).

Calculate Slope

The slope is -2.

The y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.

The intersection happens at point (0,5), so the y-intercept is 5.

We found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.

Equation: [tex]y = -2x + 5[/tex]

Answer:

Option (2)

Step-by-step explanation:

cos 50° = y/z

z = y/cos 50°

Answer:

[tex]200 cm^2[/tex]

Step-by-step explanation:

A = (1/2)bh

A = (1/2)(18)(30)

A = 270 square cm

A = (1/2)(16)(25)

A = 200 square cm

Answer:

200 square centimeters

Step-by-step explanation:

The area of a triangle can be calculated using the formula: [tex]A = \frac{1}{2}bh[/tex] where b is the base and h is the height. So if the base is 16 cm and the height if 25 cm you simply plug the values into the equation to find the area

Plug Values In:

[tex]A = \frac{1}{2}(16 cm)(25 cm)[/tex]

Multiply 16 cm and 25 cm:

[tex]A = \frac{1}{2}(400 cm^2)[/tex]

Multiply by 0.5 (or technically divide by 2)

[tex]A = 200 cm^2[/tex]

[tex]{ \red{ \bold{option \: (d)}}} \: { \green{ \tt{ {2}^{8p} = {2}^{5p + 3}}}} [/tex]

Step-by-step explanation:

I said option (d) is correct. Because, the answer of 2^8 is 256 i.e.,

[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}}}[/tex]

[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{256}}}[/tex]

The value of 16^2 = 256.

Also, the answer of 2^5 is 32. i.e.,

[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2}}}[/tex]

[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{32}}}[/tex]

The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.

A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.

When a line divides letter T vertically, it means that two mirror images will be created.

Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.

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Answer:

-8

Step-by-step explanation:

Slope = (y1-y2) / ( x1-x2)

            = ( f-4) / (-8 - -6)      =  6

                  (f-4) / -2    = 6

                    f-4 = -12

                     f = - 8

Answer:

f = -8

Explanation:

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given:

Inserting into slope formula:

[tex]\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6[/tex]

[tex]\sf \rightarrow \dfrac{4-f}{2 } = 6[/tex]

[tex]\sf \rightarrow 4-f = 12[/tex]

[tex]\sf \rightarrow -f = 12-4[/tex]

[tex]\sf \rightarrow -f =8[/tex]

[tex]\sf \rightarrow f =-8[/tex]

Step-by-step explanation:

(3x+6)= 48(Alternate angles)

3x=48-6

3x=42

x=14

2y+48=5y-9 (Sum of two opposite interior angles= exterior angle)

48+9=5y-2y

57=3y

y=19

Answer:

Step-by-step explanation:

Answer: according to my work i got

LCM - Lowest Common Factor

HCF - Highest common factor

Step-by-step explanation:

please mark brainlest!!

yw! =^.^=

Answer:

  f(x) = -5x +48

Step-by-step explanation:

A fairly easy way to write the equation of the perpendicular line is to swap the x- and y-coefficients, negating one of them. Then choose the constant in the equation to make it true at the given point.

In this instance, we find it convenient to leave the coefficient of y as positive.

  5y = x -10 . . . . . . original equation

  y = -5x +c . . . . . . with coefficients swapped, x-coefficient negated

At the given point, the equation becomes ...

  8 = -5(8) +c

  48 = c . . . . . . . add 40

The equation of the line is then ...

  y = -5x +48

  f(x) = -5x +48 . . . . . . in functional notation

There are 5 nickels, 3 dimes, and 9 pennies.

Let d = The number of dimes

Let n = number of nickels

Let p = The number of pennies

As given, there are two more nickels than dimes and three times as many pennies as dimes:

d+2=n

3d=p

0.10d+0.05n+0.01p=0.64

Plug in the value to find d

[tex]0.10d+0.05(d+2)+0.01(3d)=0.64[/tex]

[tex]0.10d+0.05d+0.1+0.03d=0.64[/tex]

[tex]0.18d=0.64[/tex]

[tex]d=3[/tex]

The value of p is equal to 3d

p=3(3)=9

n=d+2

n=3+2

n=5

Hence, there are 5 nickels, 3 dimes, and 9 pennies.

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Answer: 3

Step-by-step explanation:

Median is a statistical measure that determines the middle value of a dataset listed in ascending order.

arranged data  is   0,1,2,3,3,5,9,12

number of data terms=8

if data is  even then

median=(3+3)/2=3

The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months

Each month, there is an increase by a factor of 0.06 of the previous months model.

From geometric sequence formula of aₙ = ar^(n - 1),

where;

a is first term

r is common ratio

aₙ is nth term

we have;

1,008.9 = 671 * 1.06^(n - 1)

1008.9/671 = 1.06^(n - 1)

In 1.504 = (n - 1) In 1.06

0.408 = (n - 1) * 0.058

n - 1 = 0.408/0.058

n = 7.03 + 1

n ≈ 8 months

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The slope is m=6 and length of line is 3.5√37.

The slope of a line is a measure of its steepness.

Given:

endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5

slope= 8-2/3-2= 6

Now, using distance formula,

d= √(3-2)² + (8-2)²

d= √1+ 36

d= √37

As, Line AB is dilated by a scale factor of 3.5.    

So, new d= √37*3.5

new d= 3.5√37

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Answer: The base graph has been shifted down 90 units.

Step-by-step explanation:

See attached image.

The number of miles the bird can fly for 60 minutes is 20 miles.

A bird can fly 5 miles in 15 minutes.

Let's find the rate before we can find the number of miles the bird can fly in 60 minutes.

Therefore,

rate = distance / time

rate = 5 / 15  = 1 / 3 miles per minutes

Therefore,

1 / 3  = d / 60

cross multiply

60 = 3d

d = 60 / 3

d = 20 miles

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Answer:

70

Step-by-step explanation:

【Answer】The least common multiple of 35 and 70 is 70.

                          [tex]\orange{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}[/tex]                        

To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{35 \ \ \ 70}\\ 35 \ \ \ 35\\ 7 \ \ \ \ 7\\ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 5\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]

                                        [tex]\sf{L.c.m.(35,70)=2\times5\times7}[/tex]

                                          [tex]\boxed{\boxed{\sf{L.c.m.(35,70)=70}}}[/tex]

Answer:

(x+2)²+(y-4)²=36

Step-by-step explanation:

1) to determine the coordinates of the centre of the given circle. It is point A (-2;4);

2) to determine the length of the radius: to calculate the distance between the point A(-2;4) and any point on the circle, it is 6 [units];

3) to make up the required equation according to the scheme:

(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the coordinates of the centre, r - the length of the radius.

4) finally, (x+2)²+(y-4)²=6².

PS. for more details see the attachment.

In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.

Trigonometric Functions: SOH-CAH-TOA

Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.

tan(23) = x / 2

x = tan(23) * 2

x = 0.8489

x = 0.8

Hope this helps!

Step-by-step explanation:

Given: f(x) = 3x² -5x + 4

To find f(-2), simply substitute x = -2 in function f(x).

f(-2) = 3(-2)² -5(-2) + 4

f(-2) = 12 + 10 + 4

f(-2) = 26

Answer: 26

For an ordered pair (x, y) in a relation, the y element represents the range.

Answer: range

Answer:

Step-by-step explanation:

the objects which have less density than water will float

and the objects which have more density than the density of liquid will sink in liquid or will not float.

Answer:

182 inches

Step-by-step explanation:

1 book is 13 inches thick.

So when 14 of those books are stacked together (lets take the book cover has non-existent thickness since the question did not mention),

Height of stack of 14 books = 14 x Thickness of 1 book = 14 x 13inches

= 182 inches