3 Sarah left home at 10:00 and cycled north in
a straight line. The diagram shows a
displacement-time graph for her journey.
a Work out Sarah's velocity between 10:00 and 11:00.
On her return journey, Sarah continued past her
home for 3 km before returning.
b Estimate the time that Sarah passed her home.
c Work out Sarah's velocity for each of the last two
stages of her journey.
d Calculate Sarah’s average speed for her entire journey.​

Answer:

f = -5/3

Step-by-step explanation:

-3/4f = 5/4

Multiply each side by -4/3 to isolate f

-4/3*-3/4f = 5/4*-4/3

f = -5/3

Answer:

Hey there!

We have -3/4f=5/4

Multiply both sides by -4/3, to cancel out the -3/4.

f=-5/3

Hope this helps :)

Answer:

x = 27

Step-by-step explanation:

Step 1: Write out equation

54 + 6x = 216

Step 2: Solve for x

6x = 162

x = 27

Answer:

x=27

Step-by-step explanation:

54+6x=216

Collect like terms:

6x=216-54

6x=162

Divide both sides by the coefficient of x

6x\6=162\6

x=27

Answer:

x = 19.

Step-by-step explanation:

By the tangent - secant theorem:

BD^2 = AB * EB

so:

8^2 = (x - 7 + 4) * 4

4(x - 3) = 64

4x - 12 = 64

4x = 64 + 12 = 76

x = 76/4

= 19.

Answer:

Step-by-step explanation:

[tex](g\circ f)(x) = g\big(f(x)\big)[/tex]

so:

[tex]I.\quad (g\circ f)(a)=\sqrt{f(a)}=\sqrt{a^2-4}=\sqrt{(a+2)(a-2)}\\\\II.\quad (g\circ f)(a)=2f(a)-2=2(\frac12a-1)-2=a-2-2=a-4\\\\ \bold{III.\quad (g\circ f)(a)=\sqrt{f(a)-5}-2=\sqrt{5+a^2-5}-2=\sqrt{a^2}-2=|a|-2}\\\\ IV.\quad (g\circ f)(a)=4f(a)-5=4(3-3a)-5 = 12-12a-5=-12a+7[/tex]

Answer:

5/9

Step-by-step explanation:

There are 9 total combinations and 3 of them include a burger, 2 of them that have salad but not a burger. If you add them together it equals 5/9

The probability of selecting a combination that includes a burger or a salad is 5/9

Since the total of 6 outcomes include fries or fruit as the side dish.

There is a total of 9 possible meal combinations. A person must choose an Entree and a side dish.

The Entrees consist of burgers, tacos, and pizzas.

The side dishes consist of salad, fries, and fruit.

To find the number of combinations consisting of fries or fruit, we calculate the individual combinations.

With fries as side dish, which can choose a burger, a pizza or a taco as your Entree.

There are 3 combinations each, there are a total of 6 combinations with fruit or fries as the side dish.

There are 9 total combinations and 3 include a burger, rest 2 that have salad but not a burger.

then probability = 5/9

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ2

Answer:

11

Step-by-step explanation:

3 times 11 gives you 33 which would be the product

3 x 11 = 33

subtract the 12(twelve) from the 33(product)

33 - 12 = 21

Answer:

Step-by-step explanation:

Area of a trapezoid = 1/2(a + b) × h

where

h is the height

a and b are the other sides

From the question

h = 3 feet

a = 5 feet

b = 7 feet

Area = 1/2(5+7) × 3

= 1/2 ( 12) × 3

= 6 × 3

The answer is

= 18

Hope this helps you.

Answer:

D. 127.5 square units

Step-by-step explanation:

AC=17

BD=15

AB=11.5

Diagonal (1&2) are given, base of the rhombus is also given.

Height is not given

Area of a rhombus given the diagonals

=1/2×d1×d2

Where,

d1=AC=17

d2=BD=15

Area of a rhombus=1/2×d1×d2

=1/2×17*15

=1/2×255

=127.5

D. 127.5 square units

Answer:

D for sure

Step-by-step explanation:

Answer:

a= 5    and   b=1

Step-by-step explanation:

To solve, we will follow the steps below:

2x + 3y = 7

(a-b)x + (a+b)y = 3a + b - 2​

We should note that since it has infinitely many solutions then,

[tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]

Hence

2/a-b  =  3/a+b   =     7/3a +b-2

2/a-b  =  3/a+b

cross-multiply

3(a-b) = 2( a+b)

open the bracket

3a - 3b = 2a + 2b

collect like term

3a - 2a = 2b + 3b

a = 5b  -------------------------------------------(1)

Similarly

3/a+b   =     7/3a +b-2

cross-multiply

7(a+b)  = 3(3a+b -2)

7a + 7b = 9a + 3b -6

take all the variables to the left-hand side of the equation

7a - 9a+ 7b-3b =   -6

-2a + 4b = -6 ---------------------------------(2)

but a = 5b

substitute a= 5b in equation (2)   and solve for b

-2(5) + 4b = -6

-10  +  4b  = -6

add 10 to both-side of the equation

-10  + 10+ 4b  = -6+10

4b = 4

divide both-side of the equation by 4

b = 1

substitute b= 1 in equation (1)

a = 5b

a =5(1)

a=5

Therefore,   a= 5    and   b=1

Answer:

(8.5+x)×2=24

8.5+x=12

x=3.5

Answer:

Breadth = 3.5cm

Step-by-step explanation:

Perimeter = 2L + 2B

24cm = 2(8.5) + 2B

2B = 24 - 17

B = 7÷2

B = 3.5

Answer:

$ 84.50

Step-by-step explanation:

Regular price = $130

Discount = 35% of 130

               = [tex]\frac{35}{100}*130[/tex]

              = 0.35 * 130

             = $ 45.50

Price of the sunglasses after discount = Regular price - discount

                                                               = 130 - 45.50

                                                              = $ 84.50

Answer:

Step-by-step explanation:

4. A) [tex]\frac{13}{100}[/tex]×79.50 = 10.335

tax=10.335

total cost=79.50+10.335=89.835

B) [tex]\frac{13}{100}[/tex]×189.99=24.6987 = tax

189.99+24.6987=214.6887

5) [tex]\frac{20}{100}[/tex]×544.99=108.998

yes Brittany will have enough money

Answer:

Option B

Step-by-step explanation:

Area of kite = product of 2 diagonals, p and q / 2

here, p = 10 + 10 = 30 feet

q = 3 + 3 = 6 feet

∴ Area = 30 × 6 / 2

90 ft^2

Hope it helps

plz mark as brainliest!!!

Answer:

[tex]\boxed{Area = 90 ft^2}[/tex]

Step-by-step explanation:

Diagonal 1 = p = 3+3 = 6 ft

Diagonal 2 = q = 10+20 = 30 ft

Area = [tex]\frac{pq}{2}[/tex]

Area = [tex]\frac{(6)(30)}{2}[/tex]

Area = 3*30

Area = 90 ft^2

Answer:

B 120 cubic centimetres

Answer:

16/5

Step-by-step explanation:

xy/-5

(2)(-8)/-5

-16/-5

=16/5

Answer:

Step-by-step explanation:

Let the number be x

5/9 of the number is 90

Which is

5/9 of x = 90

5/9 × x = 90

5/9x = 90

Multiply through by 9

That's

5x = 810

Divide both sides by 5

5x/5 = 810/5

x = 162

Therefore the number is 162

Hope this helps you

Answer:

Hey there!

20^2+54/9

400+54/9

400+6

406

Hope this helps :)

Answer:

406

Step-by-step explanation:

20²+6

=400+6

=406

Answer:

They made 36 three-point field goals

Step-by-step explanation:

For free throws , we have one point each.

So here, the total points they made from free throws is 22 * 1 = 22 points

So the number of points made from field goals would be 184-22 = 162 points

So the issue we have now is knowing the number of 3-point field goals that was made.

How can we get this?

Remember they made 85 baskets? so if we subtract the number of free throws, then we can have the number of field throws and that is 85-22 = 63

Now, let the number of 2 points throws be x and the number of 3 points throws be y

From our earlier analysis;

x + y = 63 ••••••••• (i)

Now the total number of three pointers would be 3 * y = 3y and the total number of two pointers would be 2 * x = 2x

Adding both gives a total of 162

Thus;

2x + 3y = 162 •••••••• (ii)

So we have two equations to solve simultaneously.

From equation 1, we can say that;

x = 63-y

Let’s substitute this into equation 2

2(63-y) + 3y = 162

126 -2y + 3y = 162

126+y = 162

y = 162-126

y = 36

This means that they made 36 three-point field goals

Answer:

OD.0

Step-by-step explanation:

because 2(X+4)-1 = 2x+7

or, 2x+8-1 = 2x+7

or, 2x+7= 2x+7

and it cancels out eachother so it will be 0

The equation 2(x + 4) - 1 = 2x + 7 has infinite solutions

The equation is given as:

2(x + 4) - 1 = 2x + 7

Open the bracket

2x + 8 - 1 = 2x + 7

Evaluate the difference

2x + 7 = 2x + 7

Both sides of the equation are the same.

Hence, the equation has infinite solutions

Read more about equation solutions at:

https://brainly.com/question/18760518

Answer:

a) 60 degrees

Step-by-step explanation:

b) The triangle shown is an equilateral triangle as all the sides are the same. This means that all the angles are the same as well.

Angles in a triangle add up to 180 degrees. There are 3 angles. Each angle is 60 degrees.

Angle x is an exterior corresponding angle and hence, that is why x = 60 degrees.

Answer:

All of the measures of the interior angles of an equilateral triangle are 60°. Because x and 60° are alternate interior angles of parallel lines, this means that they are equal, therefore x = 60°.

Answer:

A)21

B) 70

C)89

Step-by-step explanation:

Answer:

Step-by-step explanation:

b=180° - 110° =70°

a = 21°

C= 180° - b - a= 180 - 70 - 21= 89°

[tex]good \: luck[/tex]

Answer:

72

Step-by-step explanation:

Angle XYZ is an inscribed angle. An inscribed angle is equal to half of its arc.

144/2 is 72.

The value of XYZ is 72.

Answer:

x = -12

Step-by-step explanation:

-10x+1+7x=37

Combine like terms

-3x+1 = 37

Subtract 1 from each side

-3x+1-1 = 37-1

-3x = 36

Divide by -3

-3x/-3 = 36/-3

x = -12

Answer:

Please find attached the graph of the following function;

[tex]\left\{\begin{matrix}x - 1 & if & -2 \leq x < 0\\ 1 & if & x = 0 \\ 3 & if & 0 < x \leq 2\end{matrix}\right.[/tex]

Step-by-step explanation:

We note that the function is linear from x = 2 to just before x = 0

The linear relationship of the function f(x) with x changes just before x = 0

At x = 0, the value of f(x) is indicated as 1

From just after x = 0, the function is a straight horizontal line y = 3

The function also changes value immediately after x = 0 to the line y = 3

The areas where the function is defined are shown in continuous lines

Answer:

1

Step-by-step explanation:

Because the pre image and dilated image are congruent, the scale factor is 1.

Answer:

x = 10

Step-by-step explanation:

One of the smaller angles that is created by the angle bisector measures 5x+4.

An angle bisector cuts an angle into two equal parts. So, 5x+4 = 1/2 (108) or

2(5x+4)=108 (divide both sides by 1/2)

10x+8=108 (distribute)

10x=100 (subtract 8 from both sides)

x=10 (divide by 10)

x=10

Answer:

Mean = 0.38082 checks per day

Variance = 0.38082

Standard deviation = 0.61711

Step-by-step explanation:

In a Poisson distribution, the variance (V) is equal to the mean value (μ), and the standard deviation (σ) is the square root of the variance.

A year has 365 days,, if 139 checks were written during a year, the mean number of checks written per day is:

[tex]E(x)=\mu=\frac{139}{365}\\ \mu=0.38082\ checks/day[/tex]

Therefore, the variance and standard deviation are, respectively:

[tex]V=\mu=0.38082\\\sigma=\sqrt{V}=\sqrt{0.38082}\\ \sigma =0.61711[/tex]