Change 4x + 7y= 14 to slope intercept form
(y=mx+b)

The ages of John, Tom and Lisa are 52 years, 54 years and 68 years respectively.

According to the question,

We have the following details:

The average age of the Bear family is 58 years.

Now, let's take Tom's age to be x years, Lisa's age to be y years and  John's age to be z years.

So, we have the following expression:

(x+y+z)/3 = 58

(x+y+z) = (58*3)

(x+y+z) = 174 .... (1)

Now, John is two years younger than Tom, so we have:

z = (x-2) ....(2)

Lisa is 16 years older than John. So, we have:

y = (z+16) ....(3)

Now, putting the values of y and z in equation 1,

x+z+16+x-2 = 174

Now, again putting the value of z from equation 2,

x+x-2+16+x-2 = 174

3x+12 = 174

3x = 174-12

3x = 162

x = 162/3

x = 54 years

Now, putting the value of x in equation 2,

z = x-2

z = (54-2) years

z = 52 years

Now, putting the value of z in equation 3,

y = z+16

y = (52+16)

y = 68 years

Hence, the ages of John, Tom and Lisa are 52 years, 54 years and 68 years respectively.

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Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The limits of the range for the length of time that Act 3 could last is 33.6

The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category. In general, integrals are divided into two categories: definite integrals and indefinite integrals.

A 24-hour period was predicted for Act 3 of the 2003 Leonid meteor shower. This prediction had a 0.7-day error window. How long could Act 3 potentially last, in the range

Lower Limit: 24-0.7(24) = 0.3(24) = 7.2 hrs

Upper Limit: 24+0.7(24) = 40.8 hrs

Range = Upper Limit - Lower Limit

= 40.8 - 7.2

=33.6

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Solving a system of equations, we will see that Suvinder bought 60 of the £0.20 stamps and 40 of the £0.35 stamps.

We know that Suvinder spent £26 on 100 postage stamps, defining:

Then we can write the system of equations:

x + y = 100

x*0.20 + y*0.35 = 26

Isolating x on the first equation we get:

x = 100 - y

Replacing that in the other equation we get:

(100 - y)*0.20 + y*0.35 = 26

Solving that for y, we get:

20 - y*0.20 + y*0.35 = 26

20 + y*0.15 = 26

y*0.15 = 26 - 20 = 6

y = 6/0.15 = 40

Then:

x = 100 - y = 100 - 40 = 60

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IT HAS TO BE X=0 BECAUSE YOU ADD 8 TO X-8 THAT REMOVES THAT 8 THEN THE ADD 8 TO THE OTHERSIDE OF THE EQUAL SIGN

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: State the Angle-Arc relationship

STEP 2: Interpret the given image

STEP 3: Find the required angle

By substitution

Hence, the answer is 50°

Answer:

D

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{\frac{5\pi }{8} }{2\pi }[/tex]

   = π × 12.8² × ([tex]\frac{5}{8}[/tex] ÷ 2)

   = π × 163.84 × [tex]\frac{5}{16}[/tex]

   ≈ 160.8 cm² ( to the nearest tenth )

Answer:

3/2, 1.5

Step-by-step explanation:

When you put 36 cookies divided amongst 24 students, each student cookies one and a half cookies

Answer:

t=-132

Step-by-step explanation:

multiply -12 on both sides.

-12x11=t

t=-132

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

 where

a

=

7

and

b

=

3

x

.

(

7

+

3

x

)

(

7

−

3

x

)

Answer: -(3x - 7)(3x + 7)

Step-by-step explanation:

1. Rewrite the formula:

-[tex]9x^{2} + 49[/tex]

2. Factor -1 out of [tex]-9x^{2} + 49[/tex]

[tex]-(9x^{2} - 49)[/tex]

3. [tex]9x^{2} - 49 = (3x)^{2} - 7^{2}[/tex]

[tex]((3x)^{2} - 7^{2})[/tex]

4. Factor the difference of two squares. [tex](3x)^{2} - 7^{2} =[/tex]

[tex](3x-7)(3x+7)[/tex]

5. Add back negative:

Answer: [tex]-(3x-7)(3x+7)[/tex]

A rational number is a number that can be expressed as a ratio of two integers. Integers can be positive or negative. Rational numbers are simply fractions. For example;

-5/2, -1/5, 3/1, 4/5 etc are all rational numbers because we can write them as a ratio of two integers.

Since some of this fractions can lead to both negativa and positive integers, hence rational number is a positive or negative whole number including 0.

Hence all the options are correct since rational numbers are are also repeating decimals

The equation for a line parallel to y = 3x + 2 that passes through the point (2, 1) is y = 3x - 5.

The point slope form is used to calculate the equation of a straight line that is inclined to the x-axis at a given angle and passes through a given point.

Depending on the information available, the equation of a line can be found using a variety of methods. Among the methods are:

The given equation of line is y = 3x + 2.

We need to find the equation of line parallel to the given line and it passes through the point (2, 1).

Slope of line y = 3x + 2 is given as:

By comparing the given equation with y = mx + c, we can say that the slope(m) = 3

Let, a point with coordinates (x, y) be on the line parallel to given line.

Finding slope again we get,

[tex]\frac{y-1}{x-2}[/tex] = 3

y-1 = 3x - 6

∴ y = 3x - 5

As a result, a line parallel to y = 3x + 2 that passes through the point (2, 1) has the equation  y = 3x - 5.

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⇒g(f(x)) means that in the place of x in the function g you will plug in the function f.

⇒This means that [tex]2x^{2} -5[/tex] will be plugged in the place of x in 5x+7 and the simplify.

⇒[tex]=5(2x^{2} -5)+7\\\\=10x^{2} -25+7\\=10x^{2} -18[/tex]

⇒Now you have the unknowns The coefficient of the variable [tex]x^{2}[/tex] is 10 and the constant number is -18.

FOR THE FURST QUESTION.

[tex] {27}^{ \frac{1}{2} } \\ = (3^{3} )^{ \frac{1}{2} } \\ = {3}^{3 \times \frac{1}{2} } \\ = 3^{ \frac{3}{2} } [/tex]

FOR THE SECOND QUESTION

[tex] \sqrt{2} \\ = ( \sqrt[3]{8} )^{ \frac{1}{2} } \\ = ( {8}^{ \frac{1}{3} } )^{ \frac{1}{2} } \\ = 8^{ \frac{1}{3} \times \frac{1}{2} } ) \\ = 8^{ \frac{1}{6} } [/tex]

FOR THE THIRD ONE

[tex] \frac{ \sqrt{2} }{16} \\ = \frac{ \sqrt{2} }{16} \\ = \frac{ {2}^{ \frac{1}{2} } }{ {2}^{4} } \\ = 2^{ \frac{1}{2} - 4 } \\ = 2^{ - \frac{7}{2} } [/tex]

ATTACHED IS THE SOLUTION

we have the function

f(x)=1/2Ix+4I-3

the vertex of the given function is the point

(-4,-3) ---------> III quadrant

therefore

(a) 291/2020

Divide the total for the 10-14 year column by the total.

(b) 77/465

There are 465 people from the east, 77 of which were loyal for 10 to 14 years

(c) 437/1010

There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.

(d) 145/376

376 people are from the West, (45+100)=145 of which are at least 10.

(e) 32/157

157 people were loyal for less than a year, 32 of which were from the East.

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

The simplified form of the given expression is 25 x² y ²⁶.

What is the simplified form of the expression?

Simplifying expressions mean rewriting the same algebraic expression in a compact form such that there are no like terms.

What are the exponent rules?

The different Laws of exponents used to solve the above mentioned question are:

[tex]x^{m}.x^{n} = x^{m+n} \\\frac{x^{m} }{x^{n} } = x^{m-n} \\(x^{m})^{n} } = x^{mn }[/tex]

According to the given question.

We have an expression (5xy⁷)²(y⁴)³

To simplify the above expression we use the exponent rules.

Therefore,

(5xy⁷)²(y⁴)³

(5² x² y²×⁷) (y ⁴׳)

(25 x² y¹⁴ ) (y¹²)

25 x² y¹⁴⁺¹²

25 x² y ²⁶

Therefore, the simplified form of the given expression is  25 x² y ²⁶

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1.

2.

3.

In the figure of the second exercise there is one block which is not visible.

4.

We can see that the figure is made with 8 blocks

5.

The maximum length of the figure would be 6. You need 3 blocks to get a heigth of 3 units. Then you can add the other 5 blocks to the one which is in the base to make the figure with a length of 6 units.

Step-by-step explanation:

the initial distance is 2 2 /5mile or 2.4 mikes and the final is 8 1/10 or 8.1 mile . Therefore total distance to hike is

Distance=8.1 - 2.4 = 5.7miles

since they will trek at 3 miles per hour the time needed is : 5.7 MILE/ 3MILES PER hour

time: 1.9HOURS

since they started at 10am and there is 2 HOURs ALLOWANCE from noon ,THEREFORE they will reach the marker by noon 0.10 hour left

THAT'S ALL MISS

Answer:

y=1.4x+5.8

You have to do y2-y1 over x2-x1.

Answer:

Step-by-step explanation:

Equation: 7x - 9 = 5 (x+2) 7x - 9 = 5x + 10 2x = 19 x = 9.5

Answer:

The equation is y = 50 + 25x. The slope is the additional cost per hour, and the y-intercept is the cost of the service call to appear at the house.

raina runs 6 miles in 55 minutes

so it speed is 6/55 miles per minute

that means in one minute he runs 6/55 miles

so in 44 minutes

in 44 minutes he will run 24/5 miles or 4.8 miles

Answer:

[tex]x=\dfrac{1}{5}, \quad y=6[/tex]

Step-by-step explanation:

Given equations:

[tex]\begin{cases}y=10x+4\\2y+5x=13\end{cases}[/tex]

To solve the given equations by substitution, substitute the first equation into the second equation and solve for x:

[tex]\begin{aligned}\textsf{Equation 2}: \quad 2y+5x&=13\\\\y=10x+4 \implies 2(10x+4)+5x&=13\\20x+8+5x&=13\\25x+8&=13\\25x+8-8&=13-8\\25x&=5\\\dfrac{25x}{25}&=\dfrac{5}{25}\\x&=\dfrac{1}{5}\end{aligned}[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\begin{aligned}\textsf{Equation 1}: \quad y &=10x+4\\\\x=\dfrac{1}{5} \implies y&=10\left(\dfrac{1}{5}\right)+4\\y&=\dfrac{10}{5}+4\\y&=2+4\\y&=6\end{aligned}[/tex]

Therefore, the solution to the equations is:

[tex]x=\dfrac{1}{5}, \quad y=6[/tex]

Using given function, we conclude that it will take 3 seconds the ball to reach a height of 45 meters.

In this question, we have been given a function h = 30t - 5t²

This function is used to find the height (h) of the ball in meters after 6 seconds.

We need to find the amount of time required to reach ball to a height of 45 meters.

here, height h = 45 meters

to find : time t

h = 30t - 5t²                          ........................(Given function)

45 = 30t - 5t²

30t - 5t² - 45 = 0

5t² - 30t + 45 = 0

t² - 6t + 9 = 0

(t - 3)² = 0

t - 3 = 0

t = 3 seconds

Therefore, it will take 3 seconds  the ball to reach a height of 45 meters.

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For the given options, we will find the function that has the greatest rate of change as x approaches infinity

The first function is a linear

The second function is quadratic

The third function is exponential

By reviewing the graph of the three functions, we can know that the exponential function has the greatest rate of change as x approaches infinity

So, the answer will be option C) h(x)