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alukav5142 [94]

2 years ago

14

The bottom of a ladder must be placed 5 feet from a wall. The ladder is 18 feet long. How far above the ground does the ladder t

ouch the wall?

2 answers:

Setler79 [48]2 years ago

6 0

Answer:

The ladder meets the wall at 17.29 feet from the ground.

Step-by-step explanation:

Pythagorean Theorem ⇒ a^2 + b^2 = c^2

5^2 + b^2 = 18^2

25 + b^2 = 324

b^2 = 299

b = 17.291616

anygoal [31]2 years ago

6 0

13 feet pal now go get ‘em

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How to find x please help

o-na [289]

You know the adjacent and you need to find the opposite, so you would use tangent. Your equation would look like this; tan 26°= x/28. You would need to multiply both sides by 28 to simplify it to this; 28*tan 26°= x
Solving this, you would get an answer of 13.7

6 0

3 years ago

Amy received a $80 gift card for a coffee store. She used it in buying some coffee that cost $8.24 per pound. After buying the c

SVEN [57.7K]

Answer:

5 pounds

Step-by-step explanation:

Given that:

Amount of gift card = $80

Cost of coffee per pound = $8.24

Amount left in the card = $38.80

To find:

Number of pounds of coffee bought = ?

Solution:

Let the number of pounds of the coffee bought = $x$ pounds

Cost of 1 pound = $8.24

Cost of $x$ pounds = $8.24 $\times x$

Writing the equation as per question statement:

$80 - 8.24x = 38.80\\\Rightarrow 80 - 38.80 = 8.24x\\\Rightarrow 8.24x = 41.2\\\Rightarrow x = \dfrac{41.2}{8.24}\\\Rightarrow \bold{x = 5\ pounds}$

Therefore, 5 pounds of coffee was bought.

3 0

3 years ago

The sum of 5x and 2x is a least 70

diamong [38]

Answer:

7x ≥ 70

Step-by-step explanation:

5x + 2x ≥ 70

7x ≥ 70

x ≥ 10

Hope this helps!

-sruthi123

5 0

3 years ago

Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is $x=6$ for $h(x)=0$ .

Thus Kendra dives out of the water surface at 6 feet from the board.

3 0

2 years ago

Help please with numbers 1-5

Marysya12 [62]

1 one is the answer

2 is the answer either

all the equations are in it's simeplest form

4 0

3 years ago