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3 years ago

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Determine the larger of two consecutive integers whose sum add to 85

1 answer:

Vesnalui [34]3 years ago

8 0

N+(n+1) = 85. 2n+1=85, 2n=84. n=42. So the consecutive integers are 42 and 43, and the larger one is 43.

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Jerry has a miniature model of a boat. He knows that the model is 3 3/4 inches wide and 5 1/2 inches long. What is the actual le

mylen [45]

Answer:

22 feet

Step-by-step explanation:

Change 15 feet into inches using the conversion

1 foot = 12 inches, thus

15 ft = 15 × 12 = 180 inches

scale factor = 180 ÷ 3.75 = 48

Thus the actual dimensions of the boat are 48 times the model.

actual length = 48 × 5.5 = 264 inches = 264 ÷ 12 = 22 feet

6 0

3 years ago

The rectangular room shown has a length of 20 ft, width of 48 ft, and height of 10 ft. Use the Pythagorean Theorem to find lengt

Vlad [161]

For the diagonal of the floor:
20^2 + 48^2= c^2
400+2304= c^2
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Tell me if this helps!!!

4 0

3 years ago

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Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

Viefleur [7K]

QUESTION 1

Given that:

$f(x)=2x^2+3x-9$ ,

$g(x)=5x+11$ ,

and

$h(x)=-3x^2+1$

Then;

$f(x)-g(x)+h(x)=2x^2+3x-9-(5x+11)+(-3x^2+1)$

$f(x)-g(x)+h(x)=2x^2+3x-9-5x-11-3x^2+1$

Group similar terms;

$f(x)-g(x)+h(x)=2x^2-3x^2+3x-5x-11-9+1$

Simplify;

$f(x)-g(x)+h(x)=-x^2-2x-19$

QUESTION 2

Given that;

$f(x)=4x-7$ .

$g(x)=(x+1)^2$

and

$s(x)=f(x)+g(x)$

Substitute the functions;

$s(x)=4x-7+(x+1)^2$

Substitute x=3

$s(3)=4(3)-7+(3+1)^2$

$s(3)=12-7+(4)^2$

$s(3)=5+16$

$s(3)=21$

QUESTION 3

Given:

$f(x)=3x+2$

$g(x)=x^2-5x-1$

$f(g(x))=f(x^2-5x-1)$

This implies that;

$f(g(x))=3(x^2-5x-1)+2$

Expand the parenthesis;

$f(g(x))=3x^2-15x-3+2$

$f(g(x))=3x^2-15x-1$

QUESTION 4

The given function is;

$f(x)=3(x-6)^2+1$

Let

$y=3(x-6)^2+1$

$\Rightarrow y-1=3(x-6)^2$

$\Rightarrow \frac{y-1}{3}=(x-6)^2$

$\Rightarrow \sqrt{\frac{y-1}{3}}=x-6$

$\Rightarrow x=6+\sqrt{\frac{y-1}{3}}$

The range is:

$\frac{y-1}{3}\ge0$

$y-1\ge0$

$y\ge1$

The interval notation is;

$[1,+\infty)$

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3 years ago

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Yuliya22 [10]

Answer:

What do i do???

Step-by-step explanation:

4 0

3 years ago

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3^4 _______ 5^2<br><br> <<br> ><br> =

podryga [215]

Answer:

3^4 > 5^2

3^4 = 3×3×3×3 = 81

5^2 = 5×5 = 25

6 0

3 years ago

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