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17 days ago

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mrs sogiba is catering for her sons birthday party. she has invited some of her sons friends to the party. the number of friends

is a composite multiple of her sons age on his birthday. she has baked 48 cupcakes and each child will recieve exactly the same number of cupcakes. use your knowledge of multiples and factors to find ouy how old her son will be on his birthday. (this is not his first bithday party)

2 answers:

tester [12.3K]17 days ago

7 0

Only numbers that are composite factors and that, when increased by 1, divide evenly into 48 will work. Thus 15 is suitable. Fifteen is composite, and adding 1 to it gives a number that divides 48. Therefore the son is 15.

Zina [12.3K]17 days ago

3 0

Answer: 16

please award the brainliest and enjoy your day!

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Response:

Move 2 units to the left

Reflect the graph across the y-axis

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Detailed explanation:

Provided:

Basic function: $f(x)=\log x$

Transformed function: $f(x)=\log(-2x-4)+2$

Extract -2 from the transformation function f(x)

$f(x)=\log[-2(x+2)]+2$

Now, we can observe the step-by-step transformations

$f(x)=\log x$

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$f(x)=\log(x+2)$

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$f(x)=\log(-2x-4)+2$

Thus, applying four transformation steps results in the new function $f(x)=\log(-2x-4)+2$

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1 month ago

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If George is 33 1/3% richer than Pete, than Pete is what percent poorer than George?

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Answer:

25%

Step-by-step explanation:

George has a wealth that is 33 $\frac{1}{3}$ % ( $\frac{100}{3}$ %) greater than Pete's. Let’s assume Pete's wealth percentage is 100%.

Thus, George's wealth percentage = 100% + $\frac{100}{3}$ %

= $\frac{400}{3}$ %

= 133 $\frac{1}{3}$ %

To find out how much poorer Pete is compared to George, we can calculate;

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= $(\frac{100}{3})$ × $\frac{3}{400}$ × 100

= 0.25 × 100

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1 month ago

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The calculated 95% confidence interval for the percentage of coffee drinkers expressing addiction ranges from 21% to 31%. By defining the sample proportion and acknowledging a sample size of 675, while also factoring in a maximum margin of sampling error set at ±5%, the final confidence interval for addiction rates among all surveyed coffee drinkers is established.

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1 month ago

What is 0.002 1/10 of

PIT_PIT [12445]

<span>0.002 1/10 of what
=> (1/10)a = 0.002
=> Multiply both sides by 10 to solve for the unknown number, since we need the value whose one-tenth is 0.002.
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1 month ago

Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o

Svet_ta [12734]

For $\fbox{\begin \\\math{x}=6\\\end{minispace}}$ the function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ both yield the same result.

Detailed breakdown:

The functions involved are

$f(x)=-x^{2}+4x+12$

$g(x)=-x+6$

Step 1:

Insert $x=1$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(1)$ .

$f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15$

Insert $x=1$ in $g(x)=-x+6$ to find the value of $g(1)$ .

$g(1)=-1+6\\g(1)=5$

Step 2:

Insert $x=2$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(2)$ .

$f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16$

Substitute $x=2$ into $g(x)=-x+6$ to find the value of $g(2)$ .

$g(2)=-2+6\\g(2)=4$

Step 3:

Replace $x=3$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(3)$ .

$f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15$

Also, replace $x=3$ in $g(x)=-x+6$ to find the value of $g(3)$ .

$g(3)=-3+6\\g(3)=3$

Step 4:

Insert $x=4$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(4)$ .

$f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12$

Also, replace $x=4$ in $g(x)=-x+6$ to obtain the value of $g(4)$ .

$g(4)=-4+6\\g(4)=2$

Step 5:

Insert $x=5$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(5)$ .

$f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7$

Replace $x=5$ in $g(x)=-x+6$ to find the value of $g(5)$ .

$g(5)=-5+6\\g(5)=1$

Step 6:

Insert $x=6$ into $f(x)=-x^{2} +4x+12$ to find the value of $f(6)$ .

$f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0$

Also, substitute $x=6$ in $g(x)=-x+6$ to obtain the value of $g(6)$ .

$g(6)=-6+6\\g(6)=0$

Step 7:

According to the provided condition $f(x)=g(x)$ .

(a). Insert $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ into the previously mentioned equation.

$-x^{2} +4x+12=-x+6$

(b). Multiply through by $-1$ on both sides.

$x^{2} -4x-12=x-6$

(c). Move the term $x-6$ to the left side of the equation.

$x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0$

(d). Divide the middle term so that its sum equals 5 and the product equals 6.

$x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1,6$

From the analysis above, it is noted that for $x=6$ both functions $f(x)$ and $g(x)$ yield the same outcome.

Using a direct approach:

$f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1$

The table representing function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ is included below.

For more information:

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. Which is the graph of f(x) = (x – 1)(x + 4)?

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16 days ago