7. A triangle has sides with lengths of 10 metres,
16 metres and 20 metres. Is it a right angled
triangle? Explain your reasoning.
​

The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46

Step-by-step explanation:

The equation of a line is y = m x + b, where

∵ The line contains the points (4.6 , -8) and (6.6 , 2.2)

∴ [tex]x_{1}[/tex] = 4.6 and [tex]x_{2}[/tex] = 6.6

∴ [tex]y_{1}[/tex] = -8 and [tex]y_{2}[/tex] = 2.2

∵ [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- Substitute the values above in the rule of m

∴ [tex]m=\frac{2.2-(-8)}{6.6-4.6}=\frac{2.2+8}{2}=\frac{10.2}{2}=5.1[/tex]

∴ The slope of the line is 5.1

∵ The equation of a line is y = m x + b

Substitute m by 5.1

∴ y = 5.1 x + b

To find b substitute x and y by the coordinates of point (4.6 , -8) OR point (6.6 , 2.2)

∵ x = 6.6 and y = 2.2

∴ 2.2 = 5.1(6.6) + b

∴ 2.2 = 33.66 + b

- Subtract 33.66 from both sides

∴ -31.46 = b

∴ y = 5.1 x + (-31.46)

∴ y = 5.1 x - 31.46

The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46

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Answer:

The number of dimes = 32

The number of quarters  = 14

Step-by-step explanation:

Here, the total number of coins combined = 46

Let us assume the number of dimes = m

So, the Number of quarter = Total Coins - Number of dimes  = 46 - m

Now,as we know:

1 dime = $0.1

So, m dimes  = m x ($0.1) = $(0.1 m)

1 Quarter  = $0.25

So, ( 46 - m ) Quarters  = (46 - m ) x ( $ 0.25)   = 11.5 - 0.25 m

Also, given the total amount of coins = $ 6.70

⇒ Value of (Dimes + Quarters) = $ 6.70

or, (0.1 m) +  11.5 - 0.25 m  = 6.70

-0.15 m = - 4.8

or, m = 4.8/0.15  =  32

⇒ m = 32

Hence, the number of dimes = m = 32

And the number of quarters  = 46 - m= 46 -32 = 14

Answer:

P=0.39

Step-by-step explanation:

We use the Hypergeometric distribution to find the probability

The normal deck of cards has 52 cards, 26 red and 26 black

Taking 4 cards out of the whole deck can be done (without replacement) in

[tex]\begin{pmatrix}52\\4\end{pmatrix}[/tex]

different ways .

Taking 2 red cards can be done in

[tex]\begin{pmatrix}26\\2\end{pmatrix}[/tex]

different ways. Same applies to the black cards

So, the required probability can be computed as

[tex]P=\frac{\begin{pmatrix}26\\2\end{pmatrix}\begin{pmatrix}26\\2\end{pmatrix}}{\begin{pmatrix}52\\4\end{pmatrix}}[/tex]

[tex]{\begin{pmatrix}52\\4\end{pmatrix}}=\frac{52!}{4!48!}=270725[/tex]

[tex]{\begin{pmatrix}26\\2\end{pmatrix}}=\frac{26!}{2!24!}=325[/tex]

[tex]P=\frac{325x325}{270725}=0.39[/tex]

h(x) = 4x - 10

Step-by-step explanation:

The given is:

We need to find h(x) = f(x) + g(x)

∵ f(x) = -2

∵ g(x) = 4x - 8

∵ h(x) = f(x) + g(x)

- Substitute f(x) and g(x) in h(x), and then add the like terms

∴ h(x) = (-2) + (4x - 8)

- Simplify the right hand side

∴ h(x) = -2 + 4x - 8

- Add like terms in the right hand side

∴ h(x) = 4x + (-2 - 8)

∵ -2 - 8 = -10

∴ h(x) = 4x + (-10)

∴ h(x) = 4x - 10

h(x) = 4x - 10

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Answer:

The restaurant sold 175 hotdogs and 525 hamburgers.

Step-by-step explanation:

Let the restaurant sold x hotdogs and y hamburgers.

Given the restaurant sold 350 more hamburgers than hotdogs.

So, we can write x + 350 = y ....... (1)

Again given that the number of total hotdogs and hamburgers sold in the restaurant is 700.

So, x + y = 700 ........ (2)

Solving equations (1) and (2) we get  

2x + 350 =700

⇒ 2x = 350

⇒ x = 175

Then from equation (1) we get,

y = 350 + 175 = 525

Therefore, the restaurant sold 175 hotdogs and 525 hamburgers. (Answer)

Answer:

57

Step-by-step explanation:

Write and solve a proportion.

47 / 289 = x / 350

x ≈ 57

Answer:

7<24

Step-by-step explanation:

I'm bad at explaining but I hope this helps if I'm actually right

7<4×6

7<24

The required inequality for  7 less than the product of 4 and 6 is 7 < 24.

Equality is determined for statement 7 less than the product of 4 and 6.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
The statement states that 7 is less than the product of 6 and 4
Now,

the product of 6 and 4 = 6 * 4 = 24, Implies
7 < 24

Thus, the required inequality for  7 less than the product of 4 and 6 is 7 < 24.

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Answer:

2900

Step-by-step explanation:

Very easy. Evaluate P(0).

P(0) = 2900e^0.039(0) = 2900e^0 = 2900(1) = 2900

Answer:

4 5/12

Step-by-step explanation:

4 3/4 = 19/4

19/4 = 57/12

1/3 = 4/12

57/12 - 4/12 = 53/12 = 4 5/12

Answer:

The definition of a control experiment is a test where the person conducting the test only changes one variable at a time in order to isolate the results. An experiment where all subjects involved in the experiment are treated exactly the same except for one deviation is an example of a control experiment.

Step-by-step explanation:

Answer/Explanation:

You need a control to show how 1 changed variable will change to result.

Answer: $37.45(to the nearest hundredths)

Step-by-step explanation:

% increase in last year living cost =5%

% increase in last year income =5%

This year income = $39.420

To calculate last year income implies

5% decrease of this year income; thus:

5/100 * $39.420 = $1.971

Last year income = $39.420 - $1.971 = $37.449 = $37.45 (to the nearest hundredths)

Answer:

37.4490 (rounded to the nearest hundredth) = 37.45

Step-by-step explanation:

ok so her bills or wateva went up 5% right and she gets a lil 5% raise or sumn from her job which made her money got up to $39.42. so if you think about it all you do is multiply 39.42 and (5%) which = 0.05 in decimal form and then after you multiply you should get 1.9710 and once you get that you gone take her money she getting now which is 39.42 - her 5% raise she got and once you subtract you gone get 37.4490 or 37.45 rounded

For the function f(x) = x^2 range will be { 4 , 16 , 68 , 81 }

Given that:

[tex]\text {Function is } f(x)=x^{2}[/tex]

Domain of the function is {-2, 4, 8, 9}

Need to determine range of the function.

Domain of the function is possible input of the function that is x and range of the function is possible output of the function that is f(x)  

As there are only four input values for x that are -2,4,8,9 we can determine the range by calculating value of f(x) for each of the x

[tex]\begin{array}{l}{\text {At } x=-2:} \\\\ {f(x)=f(-2)=-2^{2}=4}\end{array}[/tex]

[tex]\begin{array}{l}{\text {At } x=4:} \\\\ {f(x)=f(4)=4^{2}=16}\end{array}[/tex]

[tex]\begin{array}{l}{\text {At } x=8:} \\\\ {f(x)=f(8)=8^{2}=64} \\\\ {\text {At } x=9:} \\\\ {f(x)=f(9)=9^{2}=81}\end{array}[/tex]

Thus the range of given function is { 4 , 16 , 68 , 81 }

Answer:

1 right angle

Step-by-step explanation:

The sides are not in common

Answer:

1 right angle

Step-by-step explanation:

They dont have the same number of sides

Final answer:

To find the intercepts of the given line, the equation is rearranged into the slope-intercept form, revealing the y-intercept directly and allowing for easy calculation of the x-intercept by setting y=0. Thus, the x-intercept is 4/3.

Explanation:

To determine the intercepts of the line given by the equation -3x - 4 = -5y - 8, we should find both the x-intercept and y-intercept. The general form of a line is given by y = mx + b, where m is the slope, and b is the y-intercept.

Steps to find the intercepts:

Rearrange the equation to the slope-intercept form y = mx + b by adding 3x to both sides and then adding 8, resulting in -5y = 3x - 4. By further dividing both sides by -5, we get  y = -3/5x + 4/5.

To find the y-intercept (b), set x=0 in the rearranged equation, which gives y = 4/5. Thus, the y-intercept is 4/5.

To find the x-intercept, set y=0 in the rearranged equation, resulting in 0 = -3/5x + 4/5. Multiplying both sides by 5 and then dividing by -3, we find x = 4/3. Thus, the x-intercept is 4/3.

Since the multiplicative inverse of a fraction p/q is the fraction that swaps its numerator and denominator, i.e. q/p, we have that the inverse of 2/3 is 3/2.

So, if we multiply both sides of the equation by 3/2, we have

[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=16\cdot\dfrac{3}{2}[/tex]

3/2 and 2/3 are multiplicative inverse of each other, and by definition this means that they give 1 when multiplied:

[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=1\cdot a=a=16\cdot\dfrac{3}{2}[/tex]

On the right hand side, we have

[tex]16\cdot\dfrac{3}{2}=8\cdot 3=24[/tex]

And so the solution is [tex]a=24[/tex]

To find the three consecutive odd integers, we can solve an equation representing the given information.

Let the smallest odd integer be x. The next consecutive odd integer will be x + 2, and the largest odd integer will be x + 4.

The problem states that when the larger two integers are added, the result is nine less than three times the smallest integer:

(x + 2) + (x + 4) = 3x - 9

Simplifying the equation, we have:

2x + 6 = 3x - 9

Adding 9 to both sides:

2x + 15 = 3x

Subtracting 2x from both sides:

15 = x

So the smallest odd integer is 15. The consecutive odd integers are 15, 17, and 19.

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Answer:

1. false

2. true

Step-by-step explanation:

1. false because fractions are rational

2. true because it can be turned into a fraction

Answer:

16990.616 $ you can expect to have in your account after five years.

Step-by-step explanation:

Given that,

Amount invested is principal amount (p) = $ 15000

Annual rate of interest (r) = 2.5% = 0.025

Compounded quarterly (n) = 4

Sum of the amount after 5 years (t)

We know that from compound interest formula,

[tex]\text { Final amount }(\mathrm{A})=P\left(1+\frac{r}{n}\right)^{n t}[/tex]

To find the final amount substitute the given values in the above formula,

[tex]\text { Final amount }(\mathrm{A})=15000\left(1+\frac{0.025}{4}\right)^{4 \times 5}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000\left(1+6.25 \times 10^{-3}\right)^{20}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000(1.00625)^{20}[/tex]

[tex]\text { Final amount }(\mathrm{A})=15000 \times 1.132707738[/tex]

Final amount (A) = 16990.62

The final amount that he can expect is $ 16990.62.

The 0.46 percentage of the number 80 is 0.368 .

Given data:

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %.

The percentage value is represented as p.

The value of p = 0.46%

So, p = 0.0046

The number is represented as q.

The value of q = 80

Now, A = p * q

On simplifying the equation:

A = 0.0046 * 80

A = 0.368

Hence, the percentage value is 0.368

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Answer:

B

Step-by-step explanation:

Given

3(2x - 8) - 11x ← distribute parenthesis

= 6x - 24 - 11x ← collect like terms

= - 5x - 24 → B

Answer:

x=1, -2

Step-by-step explanation:

x^2-6x+7x-2

x^2+x-2

factor out the trinomial,

(x-1)(x+2)

zero property

x-1=0, x+2=0,

x=0+1=1

x=0-2=-2

Answer:

[tex]\large\boxed{5\dfrac{3}{10}\ hectometers=530\ meters}[/tex]

Step-by-step explanation:

[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]

[tex]5\dfrac{3}{10}=5.3\\\\1\ hectometers=100\ meters\qquad(1\ hm=100m)\\\\5\dfrac{3}{10}\ hm=5.3\ hm=5.3\cdot100\ m=530\ m[/tex]

Answer:

(5x+10) + (x+14) =180

6x+24=180

x=26

Angles are 140 and 40

Step-by-step explanation:

Answer:

About 300 calories

The drawing will help

top left i guessed and got it correct

Answer:

A is correct so technically the top left hope this helps

Step-by-step explanation:

Answer:

14 bags of snacks.

Step-by-step explanation:

x = the first number

y = the second number

x minus y = 3

x plus y = 13

x - y = 3

x + y = 13

3 x = 8 x + y = 13 8 + y = 13 y = 5 x - y = 3 x +y = 13 2x = 16  

The first number = 8

The second number = 5

2x = 16

Difference of the numbers is 3

x = 8



8 – 5 = 3

Sum of the numbers is 13

x + y = 13



8 + 5 = 13

8 + y = 13

y = 5

4 snacks plus beverages = 371 beverages = snacks plus 19

The 8th grade class supplied bags of snacks and beverages for the school dance. They supplied 19 more beverages than bags of snacks. The dance was supplied with a total of 371 items.

x = the number of snacks

y = the number of beverages

snacks plus beverages = 371

beverages = snacks plus 19

x + y = 371

y = x + 19

5 x + y = 371

y = x + 19

Number of snacks = 176

Number of beverages = 195

x + x + 19 = 371

2x = 371

total number of snacks = 371

2x = 352

= 371?



371 = 371

x = 176

19 more beverages than snacks

y = x + 19

= 195

y =



195 = 195

y = 195

6 The seventh and eighth grade bands held a joint concert

The seventh and eighth grade bands held a joint concert. Together there were 188 band members. If the eighth grade band is 3 times as big as the seventh grade band, how big is the eighth grade band?

x = size of the 7th grade band

y = size of 8th grade band

7th grade and 8th grade together = 188 8th grade is 3 x 7th grade

x + y = 188

y = 3x

7 x + 3x = 188 x = 47 y = 3(47) y = 141 x + y = 188 y = 3x 4x = 188 

7th grade band = 47 students

8th grade band = 141 students

x + 3x = 188

4x = 188

7th and 8th grade together = 188

= 188?

x = 47



188 = 188

y = 3x

8th grade is 3 times as big as 7th grade

y = 3(47)

141 = 3(47)



141 = 141

y = 141

8 x + y = 81 x = 2y earrings plus necklaces = 81

Amy has 81 pieces of jewelry. She has twice as many earrings as she has necklaces

x = number of earrings

y = number of necklaces

earrings plus necklaces = 81

earrings = 2 x necklaces

x + y = 81

x = 2y

9 2y + y = 81 y = 27 x = 2(27) x = 54 x + y = 81 x = 2y 3y = 81  x = 2y

Number of earrings = 54

Number of necklaces = 27

2y + y = 81

3y = 81

81 pieces of jewelry total

= 81?

y = 27



81 = 81

x = 2y

Twice as many earrings as necklaces

x = 2(27)

2(27) = 54



54 = 54

x = 54

10 9x + 6y = 48 6x + 12y = 72 9 rose plus 6 lily = 48

Julia is making candles. In the morning, she made 9 rose candle plates and 6 lily candle plates. They had a total of 48 candles. In evening, she made 6 rose candle plates and 12 lily candle plates. They had a total of 72 candles. How many candles did each plate have?

x = candles on rose plates

y = candles on lily plates

9 rose plus 6 lily = 48

6 rose plus 12 lilly = 72

9x + 6y = 48

6x + 12y = 72

11 x = 2 6(2) + 12y = 72 12y = 60 y = 5 [9x + 6y = 48] (-2) 6x + 12y = 72

Candles on the rose plates = 2

Candles on the lilly plates = 5

-18x - 12y = -96

6x +12y = 72

9 rose and 6 lilly is 48 plates

9(2) + 6(5) = 48

-12x = -24



= 48

x = 2

6 rose and 12 lilly is 72 plates

6(2) + 12y = 72

6(2) + 12(5) = 72?

y = 72



= 72

12y = 60

y = 5

12 3 adults plus 12 children = 162 3 adults plus 8 children = 122

The cost of admission to a popular music concert was $162 for 12 children and 3 adults. Admission for another group was $122 for 8 children and 3 adults. How much was the admission for each child and adult?

x = the cost of one adult ticket

y = the cost of one child ticket

3 adults plus 12 children = 162

3 adults plus 8 children = 122

3x + 12y = 162

3x + 8y = 122

13 3x + 12y = 162

[3x + 8y = 122] (-1)

The cost of one adult ticket = $14

The cost of one child ticket = $10

3x + 12y = 162

-3x + -8y = -122

12 children and 3 adults spent $162

12 at $10 and 3 at $14 = $162?

4y = 40



$120 + $42 = $162

y = 10

8 children and 3 adults spent $122

3x + 12(10) = 162

8 at $10 and 3 at $14 = $122?

3x = 162



$80 + $42 = $122

3x = 42

x = 14

Answer:

14

Step-by-step explanation:

To solve the expression, rewrite each term with the same denominator and then add them together. The final answer is 2.345.

To solve the expression 1 15/100 +1/50 +1.175, we need to rewrite all the terms with the same denominator. The least common denominator (LCD) of 100 and 50 is 100. Therefore, we can rewrite the expression as follows:

1 15/100 is equivalent to 1.15

1/50 is equivalent to 0.02

Now, we can add the three terms together:
1.15 + 0.02 + 1.175 = 2.345

Therefore, the final answer is "2.345."

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When [tex]\(a = -0.5\) and \(b = 5\), the value of \(4a + b\) is \(3\).[/tex]

To find the value of [tex]\(4a + b\) when \(a = -0.5\) and \(b = 5\)[/tex], we simply substitute the values of a and b into the expression 4a+b and then perform the arithmetic.

Given that [tex]\(a = -0.5\) and \(b = 5\)[/tex], we have:

[tex]\[4a + b = 4(-0.5) + 5\][/tex]

Now, let's calculate:

[tex]\[4a + b = -2 + 5\]\[4a + b = 3\][/tex]

Answer:

5(2x-7)

Step-by-step explanation: