A couple of friends decide to race each other. Liam can run 5 meters per second, and Grace
can run 8 meters per second. Because he is slower, Liam also gets a head start of 12 meters.
Shortly after they start running, Grace will catch up to Liam. How far has Grace run at that
time? How long will that take?

Answer:

[tex]\angle CFD =105^o[/tex]

Step-by-step explanation:

Given

[tex]\angle D FE = \angle DE F = 75^o[/tex]

See attachment

Required

Determine the measure of [tex]\angle CFD[/tex]

[tex]\angle CFD[/tex] and [tex]\angle DFE[/tex] are on a straight line.

So:

[tex]\angle CFD + \angle DFE = 180^o[/tex] --- angle on a straight line

Substitute known values

[tex]\angle CFD + 75^o = 180^o[/tex]

Collect like terms

[tex]\angle CFD =- 75^o + 180^o[/tex]

[tex]\angle CFD =105^o[/tex]

Answer:

y = 1/4 x +4

Step-by-step explanation:

y = -4x+9

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

the slope is -4

Lines that are perpendicular have slopes that are negative reciprocals

The slope of the perpendicular line is -1 /(-4)  = 1/4

The perpendicular line is

y = 1/4x+b

It goes through (4,5)

5 = 1/4(4) +b

5 = 1+b

b=4

y = 1/4 x +4

Answer:

D. (1, 12)

Step-by-step explanation:

Plug the number into the equation and solve it from there

f(x)=3×4^1

f(x)=3×4

f(x)=12

Answer:

Comparing quantities

profit loss

cost price selling price.....

Answer:

209/50 is the improper fraction of 4.18

mixed no. is 4 9/50

Answer:

$19.68

Step-by-step explanation:

this is not really clearly defined.

I assume it means that they are buying the item, no matter how much it costs, and that the split ratio between them also remains the same no matter the actual cost.

x = what Marcia is paying

and 132 - 18% = 132 × (100 - 18) / 100 = 132×0.82 = 108.24

so,

x + x/2 + x/3 = 108.24

6x + 3x + 2x = 649.44

11x = 649.44

x = $59.04

Mario's part is x/3 = 59.04/3 = $19.68

Answer:

A = 21

Step-by-step explanation:

Complementary angles add to 90

x-21 + 2x-15 = 90

Combine like terms

3x -36 = 90

3x-36+36 = 90+36

3x = 126

Divide by 3

3x/3 =126/3

x = 42

We want to find ZA = x-21

A = 42-21

A = 21

If the sum of the measures of two angles is 90° they are known as complementary angles.

[tex] \bf \large \longrightarrow \: \:( x \: - \: 21) \: + \: (2x \: - \: 15) \: = \: 90 \degree[/tex]

Now , Opening brackets and simplifying

[tex] \bf \large \longrightarrow \: \: x \: - \: 21 \: + \: 2x \: - \: 15\: = \: 90 \degree[/tex]

[tex]\bf \large \longrightarrow \: \:3x \: - \: 36 \: = \: 90 \degree[/tex]

[tex]\bf \large \longrightarrow \: \:3x \: = \: 90 \: + \: 36[/tex]

[tex]\bf \large \longrightarrow \: \:3x \: = \: 126[/tex]

[tex]\bf \large \longrightarrow \: \:x \: = \: \frac{126}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \:x \: = \: \cancel\frac{126}{3} \: \: \large \: ^{42} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: x \: = \: 42[/tex]

Now , we have to find ZA .

[tex]\bf \large \implies \: \:A \: = \: 42 \: - \: 21[/tex]

[tex]\bf \large \implies \: \:A \: = \: 21[/tex]

The measure of angle ZA is 21°

Answer:

0.0347 = constant of proportionality

[tex]1 * e^{0.0347t} = 15000[/tex]

Step-by-step explanation:

Given

[tex]1*e^{0.0347t}[/tex]

Solving (a): what does 0.0347 represent?

An exponential model is represented as:

[tex]f(t) = a * e^{kt}[/tex]

Where:

[tex]k \to[/tex] constant of proportionality

So, by comparison:

[tex]k = 0.0347[/tex]

Hence:

[tex]0.0347 \to[/tex] constant of proportionality

Solving (b): Formula to calculate when balance equals 15000

To do this, we simply equate the formula to 15000.

So, we have:

[tex]1 * e^{0.0347t} = 15000[/tex]

Answer:

A = 79°

Step-by-step explanation:

CosA = adjacent ÷ hypoteneous

A = Cos^-1(6÷32)

A. =. 79.19°

A= 79°

Answer:

125

Step-by-step explanation:

360-70-60-65-40

= 125

Answered by GAUTHMATH

70,000 multi purpose vehicles were sold in the year 2006

First we need to know the equivalent of 1 lakh.

1 lakh = 100,000

From the table shown, we can see that 0.7 lakh multipurpose vehicle were sold in 2016.

Converting 0.7lakh to thousands:

0.7lakh= 0.7 × 100,000

0.7lakh = 70,000

This shows that 70,000 multi purpose vehicles were sold in the year 2006

Learn more: https://brainly.in/question/2811622

Answer:

[tex] \frac{1}{9a { }^{2} } [/tex]

Step-by-step explanation:

I hope this help if it doesn't I'm sorry

Answer:

These are the intervals of the people who are at least adults and are mature enough to take the survey seriously and answer correctly

Step-by-step explanation:

oe which question are you figure it out

Answer:

218

Step-by-step explanation:  

ATQ,

22%of total books = 48

Let the total no. of books in library be x.

22/100x=48

x=4800/22

X=218(approximately)

The solution to the continuous linear relation is: (2,-7)

The data on the table can be presented as:

Relation A

[tex](x_1,y_1) = (-8,-5)[/tex]

[tex](x_2,y_2) = (-3,-6)[/tex]

Relation B

[tex](x_1,y_1) = (-8,-15)[/tex]

[tex](x_2,y_2) = (-3,-11)[/tex]

Plot the points of each relation and draw a line through the points (see attachment)

Write out the point of intersection of the two lines.

[tex](x,y) = (2,-7)[/tex]

Hence, the solution to the continuous linear relation is: (2,-7)

Read more at:

https://brainly.com/question/20291958

Answer:

B. exponential

Step-by-step explanation:

The graph is clearly decreasing exponentially, shown by the downward curve. Therefore, the answer should be B.

Answer:

0.75, 1.25

Step-by-step explanation:

first we bring the line equation into the same format as the parabola equation (y = ...)

3x - y = 1

=>

y = 3x - 1

now we can say for the intersection points both equations must have the same result.

4x² - 1 = 3x - 1

4x² - 3x = 0

x(4x - 3) = 0

there are only 2 possible cases to make this true :

x = 0

and 4x - 3 = 0

4x = 3

x = 3/4 = 0.75

for the y value let's use the easier equation (line) :

y = 3×3/4 - 1 = 9/4 - 4/4 = 5/4 = 1.25

Answer:

Hamid initially invested $1,125.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After 10 years, Hamid's account earned $900 in interest.

This means that [tex]t = 10, E = 900[/tex]

Interest rate of 0.08:

This means that [tex]I = 0.08[/tex]

How much did Hamid initially invest?

We have to find P. So

[tex]E = P*I*t[/tex]

[tex]900 = P*0.08*10[/tex]

[tex]P = \frac{900}{0.8}[/tex]

[tex]P = 1125[/tex]

Hamid initially invested $1,125.

Answer:

left is a very good approximately .9 POSITIVE correlation

right is a very good approximately -.9 NEGATIVE correlation

Step-by-step explanation:

Step-by-step explanation:

3(6+b)+2b+1

18+3b+2b+1

5b+19

Step-by-step explanation:

T0 = a³+4

T1 = a⁴x a¹ +4

T2= a³ + a³ + 4

T3= a⁴ + a⁴* a² + 4

T4= a⁴ + a⁴ x a¹ + 4

T5= a³ + a³ + a⁴+4

Answer:

hello,

Step-by-step explanation:

c(1)=5

c(2)=9

c(2)-c(1)=9-5=4

c(2)=9

c(3)=13

c(3)-c(2)=13-9=4

c(3)=13

c(4)=17

c(4)-c(3)=17-13=4

c(4)=17

c(5)=21

c(5)-c(4)=21-17=4

for n=1,2,...,k :

c(n+1)-c(n)=4 and c(n+1)=4*(n+1)+1=4n+5

c(1)=1

Answer:

24 units ²

Step-by-step explanation:

In this problem, we are given the circumference of a triangle (after finding the perimeter) and want to find the area of a circle with that circumference. Since the area of a circle is a function based on its radius, we can use the circumference to find the radius to find the area.

First, we can figure out the perimeter of the triangle, which is equal to the sum of its sides. The perimeter is 6+4+7.21 = 17.21 units.

Next, the circumference of a circle is equal to π * diameter = π * 2 * radius. Using 3.14 for π and r for radius, we get

3.14 * 2 * r = 17.21

6.28 * r = 17.21

divide both sides by 6.28 to isolate r

r ≈ 2.74

Furthermore, to find the area from the radius, we can use

area = πr². Plugging 2.74 in for r, we get

2.74² * 3.14 = area

≈23.6, rounding up to 24 units ²

The circumference is equal to the perimeter of the triangle. Then the area of the circle is 23.58 or 24 square units. Option B is correct.

It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

A triangle has sides that measure 4 units, 6 units, and 7.21 units.

Then the perimeter of the triangle will be

Perimeter = 6 + 4 + 7.21

Perimeter = 17.21

The circumference is equal to the perimeter of the triangle. Then the radius will be

[tex]2\pi r = 17.21\\\\r = 2.74[/tex]

Then the area of the circle will be given as

[tex]\rm Area = \pi r^2 \\\\Area = \pi \times 2.74^2 \\\\Area = 23.58[/tex]

Thus, the area of the circle is 23.58 square units.

More about the circle link is given below.

https://brainly.com/question/11833983

Answer:

Phương trình lượng giác cơ bản: lý thuyết, cách giải, bài tập

2. Phương trình cos x = cos α, cos x = a.

3. Phương trình tan x = tan α, tan x = a.

4. Phương trình cot x = cot α, cot x = a. ...

5. Phương trình bậc nhất đối với một hàm số lượng giác. ...

6. Một số điều cần chú ý:

Answer:

1. The graph represents the inequality y > 2x + 1

2. The y-intercept (where a line meets the y-axis) is at point (0,1). This line rises by 2 for every point it moves to the right (this is called the slope). A dotted line means that point on the line are not included in the solution set, thus you use the > symbol.

9514 1404 393

Answer:

  2. (only)

Step-by-step explanation:

The Pythagorean theorem tells you the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. To determine if these are right triangles, determine if that condition is met.

  1. 3^2 +5^2 = 9 + 25 = 34 ≠ (√35)^2 . . . . not a right triangle

  2. 5^2 +4^2 = 25 +16 = 41 = (√41)^2 . . . a right triangle

  3. 6^2 +8^2 = 36 +64 = 100 ≠ (√10)^2 . . . . not a right triangle

  4. 3^2 +3^2 = 9 +9 = 18 ≠ (3√3)^2 = 27 . . . . not a right triangle

= 57 yards.

Step-by-step explanation:

95 yards is the diagonal of the field

76 yards is the length

Find the width.

This set-up will for a right angled triangle with a length of 76 yards and Hypotenuse of 95 yards. Therefore the height will represent the width of our Rectangle.

[tex]{b}^{2} = {c}^{2} - {a}^{2} \\ {b}^{2} = {95}^{2} - {76}^{2} \\ {b}^{2} = 9025 - 5776 \\ \sqrt{ {b}^{2} } = \sqrt{3249} \\ b = 57yards[/tex]