An 18ft ladder leans against a house, reaching a point 14ft above the ground. How far is the foot of the ladder from the bottom of the house

Answer:

B) [tex]f(x)=2(x-7)^2-3[/tex].

Step-by-step explanation:

The vertex form of the equation is given by [tex]f(x)=a(x-h)^2+k[/tex].

We plug in the vertex to obtain:

[tex]f(x)=a(x-7)^2-3[/tex].

Since the graph passes through (5,5) and (9,5), they must satisfy its equation.

[tex]5=a(9-7)^2-3[/tex].

[tex]5+3=4a[/tex].

[tex]8=4a[/tex]

Divide both sides by 4.

[tex]a=2[/tex]

Therefore the equation is:

[tex]f(x)=2(x-7)^2-3[/tex].

Answer:

1527 feet

Step-by-step explanation:

I believe the correct answer is D. (if it’s not D then A)

Answer:

The measure of angles of △SPT are

∠PTS=35°, ∠PST=19°, ∠SPT=126°

Step-by-step explanation:

Given the figure in which

m∠EPT=54° and arc TP=70°

we have to find angles of △SPT

By tangent chord angle theorem, which states that the angle make by a tangent to a circle and a chord is equals to half of the angle measure of the intercepted arc i.e

[tex]\angle PTS=\frac{1}{2}\angle POT[/tex]

[tex]\angle PTS=\frac{1}{2}\times 70^{\circ}=35^{\circ}[/tex]

As ∠EPT and ∠SPT form linear pair therefore their sum equals to 180°

⇒ ∠EPT+∠SPT=180°

54°+∠SPT=180°

∠SPT=126°

In △SPT, by angle sum property of triangle

∠PST+∠SPT+∠PTS=180°

∠PST+126°+35°=180°

∠PST=19°

Answer:  1st, 3rd  and 5th answers are correct

Step-by-step explanation:

Answer:

A) The theoretical probability of spinning any one of the five colors is 20%.

C) The theoretical probability of spinning green is equal to the experimental probability of spinning green.

E) If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

Step-by-step explanation:

Let's find the probability of each events.

Probability of a event = The number of favorable outcomes / The total number of possible outcomes.

Here the total number of possible outcomes = 10.

Probability of getting blue = 1/10 = 0.10

Probability of getting green = 2/10 = 1/5= 0.20 = 20%

Probability of getting red = 0/10 = 0

Probability of getting orange = 4/10 = 0.40

Probability of getting yellow = 3/10 = 0.30

The above are the experimental probability.

The theoretical probability of getting green = 1/5 = 0.20 = 20%

By looking at the results, the following statements are true.

A) The theoretical probability of spinning any one of the five colors is 20%.

C) The theoretical probability of spinning green is equal to the experimental probability of spinning green.

E) If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

i^2 = -1

Replace i^2 with -1 and simplify:

(5(-1) - 3) * (6i*2^6) =

(-5 - 3) * (6i * 64) =

-8 * 384i =

-3072i

Answer:

Step-by-step explanation:

The graph is done using Desmos. Just by substitution x = 1 will force the graph to go to y = 0, but graphs are not always that good. This one gets 1.111

to get y = 0. I'd use 1 if you had to answer it and a computer will mark it.

Answer: [tex]A=100ft^2[/tex]

Step-by-step explanation:

You can use the following formula calculate the area of a rectangle:

[tex]A=w*h[/tex]

Where "w" is the width of the rectangle and "h" is the height of the rectangle.

In this case you know that this rectangle is 12.5 feet wide and  8 feet tall.  Therefore, you can substitute values into the formula to find its  area.

Then, you get that the area of this rectangle is the following:

[tex]A=(12.5ft)(8ft)\\\\A=100ft^2[/tex]

Using the Pythagorean theorem find  the length of Mountain Highway.

25^2 + x^2 = 65^2

625 + x^2 = 4225

x^2 = 4225 - 625

x^2 = 3600

x = √3600

x = 60 miles.

The total distance for Mountain highway and Oak road = 60 + 25 = 85 miles.

Airport road is shorter by 85 - 65 = 20 miles

The answer is A.

Answer:60

Step-by-step explanation:

9339,8,&,,&3:9,&:.&

Answer:

Step-by-step explanation:

Use tangent.

[tex]tangent=\dfrac{oppositive}{adjacent}[/tex]

We have

[tex]oppositive=10\\adjacent=8[/tex]

Substitute:

[tex]\tan(z)=\dfrac{10}{8}\\\\\tan(z)=1.25[/tex]

look at the picture

[tex]z\approx51^o[/tex]

Answer: 12 bricks

Step-by-step explanation:

To find how many 6" bricks are needed to fit the 72" gap, just divide.

72/6=12

12 bricks are needed.

Answer:

113.0 inches squared

Step-by-step explanation:

The area of a circle with radius r is given as;

[tex]Area=pi*r*r[/tex]

We plug in the radius given and solve for the area;

[tex]Area=3.14*6*6\\Area=113.04[/tex]

Answer:

c = 14

Step-by-step explanation:

For this triangle we have to

[tex]a=18.2\\B=62\°\\C=48\°[/tex]

We want to find the length of b

We know that the sum of the internal angles of a triangle is 180 °

then

[tex]A + 62 +48=180\\\\A=180-62-48\\\\A=70\°[/tex]

Now we use the sine theorem to find the length of c:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Therefore:

[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}\\\\c=\frac{sin(C)}{\frac{sin(A)}{a}}\\\\c=a*\frac{sin(C)}{sin(A)}\\\\c=(18.2)\frac{sin(48)}{sin(70)}\\\\c=14[/tex]

Answer:

c= 14

Step-by-step explanation:

First, let's find the angle A, because it's easy and because we'll need it.

We know that the sum of the interior angles of a triangle is 180, and we have 2 angles... so we can easily find A:

A = 180 - 62 - 48 = 70 degrees

Now, we can use the law of Sines to find c:

[tex]\frac{c}{sin(C)} = \frac{a}{sin(A)}[/tex]

so...

[tex]c = \frac{a * sin(C)}{sin(A)} = \frac{18.2 * sin(48)}{sin(70)} = 14.39[/tex]

The precise answer is 14.39, but you are asked to round up to the closest whole number... so 14.

Answer:

A:5

Step-by-step explanation:

Both W and A have to equal each other. 5*4=20-7=13.

5*2=10+3=13

Answer:

Step-by-step explanation:

In this problem we have independent events, that is, the event "picking a girl" doesn't affect an "picking a boy", also, picking picking a girl doesn't affect the probability of the other subjects.

So, the probability when the first girl is being picked is:

[tex]P_{1}=\frac{7 \ girls}{9 \ students}[/tex]

Because among the total 9 students, there are 7 girls.

Now, after picking one girl, there remains 6 girls and 8 students to be picked. So, the probability of the second girl would be:

[tex]P_{2}=\frac{6 \ girls}{8 \ students}[/tex]

Then, the probability of the third girl:

[tex]P_{3}=\frac{5 \ girls}{7 \ students}[/tex]

The fourth girl probability:

[tex]P_{3}=\frac{4 \ girls}{6 \ students}[/tex]

Therefore, the probability of picking all 4 girls would be the product of each probability, because events are independent (we use product when they are independent):

[tex]P=\frac{7 \ girls}{9 \ students} \times \frac{6 \ girls}{8 \ students} \times \frac{5 \ girls}{7 \ students} \times \frac{4 \ girls}{6 \ students}\\P=\frac{5}{18}=0.28 \ (or \  28\%)[/tex]

Therefore, there's 28% probability that every student in the group is a girl.

The probability that everyone in the group is a girl is 0.2778

The distribution of the students is given as:

Boys = 2

Girls = 7

Total = 9

The selection of the 4 girls at random is:

So, the probability that all students are girls is:

P = 7/9 * 6/8 * 5/7 * 4/6

Evaluate

P = 0.2778

Hence, the probability that everyone in the group is a girl is 0.2778

Read more about probability at:

https://brainly.com/question/251701

Answer:

1.) b/19

Step-by-step explanation:

a/b=12/19

you can always swap the b and the 12 (quick SAT trick)

To find the ratio that completes the equivalent proportion for a/12 using the given proportion a/b = 12/19, you will need to use cross multiplication.
Let's denote x as the unknown value that we are trying to find such that a/12 = b/x. To solve for x, we set up the proportion like this:
a/12 = b/x
Now let's cross multiply:
a * x = 12 * b
Since we know from the initial proportion that a/b = 12/19, we can substitute 12/19 for a/b in the equation:
(12/19) * b * x = 12 * b
Now we have b on both sides of the equation, and assuming b is not equal to zero, we can divide both sides of the equation by b to solve for x:
(12/19) * b * x / b = 12 * b / b
12/19 * x = 12
Now we need to isolate x:
x = 12 / (12/19)
To simplify this, you can multiply 12 by the reciprocal of 12/19, which is 19/12:
x = 12 * (19/12)
The 12s cancel each other out:
x = 19
Therefore, the ratio that completes the equivalent proportion is b/19.
The correct answer is:
1.) b/19

Answer:

12-6u

Step-by-step explanation:

To remove the parenthesis, we must multiply the number on the outside to each value within the parenthesis

This means that

[tex]6(2-u)\\\\6*2-6*u\\\\12-6u[/tex]

The distributive property is used to remove parentheses by multiplying each term within the parentheses by the number outside. Thus, the expression 6(2 - u) becomes 12 - 6u.

The distributive property is a mathematical principle that shows how to expand an expression involving brackets (or parentheses). To use the distributive property to remove the parentheses in the expression, you multiply the number outside the parentheses by each term inside the parentheses individually. Let's apply this to the expression you provided, 6(2 - u).

First, multiply 6 by 2. This results in 12. Next, multiply 6 by -u. This gives -6u. Therefore, the expression 6(2 - u) without parentheses, using the distributive property, is 12 - 6u.

https://brainly.com/question/37341329

#SPJ11

Answer:

D. 21/2

Step-by-step explanation:

We simply have to evaluate the first three terms based on the progression's formula:

t= 1,  the first term is 8, as we see:

[tex]8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{1-1} = 8 * 1 = 8[/tex]

t=2, the second term is 2, as we see:

[tex]8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{2-1} = 8 * \frac{1}{4} = 2[/tex]

t=3, the third term is 1/2, as we see:

[tex]8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{3-1} = 8 * \frac{1}{16} = \frac{1}{2}[/tex]

The sum of the first 3 terms is then: 8 + 2 + 1/2 = 10 1/2

Among the answer choices, D. 21/2, which is 10 1/2.

Answer:

20 units³

Step-by-step explanation:

Since all dimensions are being reduced by 1/3, that means that the total volume will decrease by 1/3 * 1/3 * 1/3 = 1/27 the size of its original.

That means that the new volume is 1/27 * 540 = 20 units³

Answer

B

Step-by-step explanation:

5-2x<7

subtract 5 on both sides

-2x<2

divide by -2

x>-1

so its B

Answer:

±1,±5,±1/2,±5/2,±1/4,±5/4

Step-by-step explanation:

Given polynomial

4x^3+8x^2-x+5

as a(n)= 4

divisors of 4 = ±1,±2,±4

as a(0)= 5

divisors of 5= ±1,±5

finding possible roots

Factors of constant term(1,5)/Factors of leading coefficient(1,2,4)

±1,±5

±1/2,±5/2

±1/4,±5/4 !

5.6 miles, I think. 3.25 divided by 0.58 is 5.6, rounded to tenths.

Answer: 1.885 miles

Step-by-step explanation:

Given: One lap around a park = 0.58 mile

The number of laps walked by Jessica= 3.25

Then, in miles , the distance walked around the park by Jessica will be (Multiply the number of laps to the value of one lap in miles) :

[tex]3.25\times0.58=1.885\text{ miles}[/tex]

Hence,  Jessica walked 1.885 miles around the park.

Answer:

Step-by-step explanation:

So all you need to do is multiply the Base by the Height so 16 multipled by 8 is simply 64. Thus the are of the triangle with a base of 16 inches and a height of 8 inches is 64 Inches.

Final answer:

To find the area of a triangle with a given base and height, use the formula Area = (1/2) × base × height. In this case, with a base of 16 inches and a height of 8 inches, the area would be 64 in².

Explanation:

The area of a triangle is calculated using the formula (1/2) × base × height. To find the area of a triangle with a base of 16 inches and a height of 8 inches, you plug the values into the formula:

Area = (1/2) × base × height

Area = (1/2) × 16 inches × 8 inches

Area = 64 in²

The other factor of the quadratic expression 6x^2 – 7x + 2, once factored, is either (3x - 2) or (2x - 1), depending on which one you view as the 'other' in context.

The student's question asks for the other factor of the quadratic expression 6x2 – 7x + 2.

To find this, one must factor the quadratic expression into the form of (ax + b)(cx + d).

Here are the steps to do so:

So, the expression factors into (2x - 1)(3x - 2). If one of the factors of the original expression is (x - a), where 'a' is a root of the equation 6x2 – 7x + 2=0, the other factor would be either (2x - 1) or (3x - 2).

Answer:

slope = -1.5

Step-by-step explanation:

A set of three or more points are said to be collinear if they all lie on the same straight line.

We have been given the following collinear set of points;

P(0, 3), Q(2, 0), R(4, -3)

This implies that P, Q, and R lie on the same line.

The slope of a line is defined as; (change in y)/(change in x)

Using the points P and Q, the slope of the line is calculated as;

(0-3)/(2-0) = -3/2 = -1.5

Answer:

-3/2

Step-by-step explanation:

Answer:482.7972

Step-by-step explanation:

Answer:

x= 21/2 = 10.500  

Step-by-step explanation:

2.2      Solve  :    2x-21 = 0  

Add  21  to both sides of the equation :  

                     2x = 21

Divide both sides of the equation by 2:

                    x = 21/2 = 10.500

x = 21/2 = 10.500

The solution of the equation for the unknown value x is decimal number 10.5. Option C is correct.

The solution of an equation is the value of the variable of the equation, for which the equation is satisfied.

To solve an equation for its variable, isolate the variable on one side of the equation using the mathematical operations.

The equation of unknown value x is given as,

4x = 42

This equation has to be solved for x. For this isolate the x divide the equation with 4 both side.

(4x/4)=(42/4)

x=10.5

Hence, the solution of the equation for the unknown value x is decimal number 10.5. Option C is correct.

Learn more about the solution of the equation here;

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Where you see an x in the expression replace it with -5

3(-5) - 9

Using the rules of PEMDAS simplify

-15 - 9

-24

Hope this helped!

~Just a girl in love with Shawn Mendes

[tex]

x^2+20=2x \\

x^2-2x+20=0 \\

x=\frac{2+\vee-\sqrt{-76}}{2}\Longrightarrow\boxed{x\notin\mathbb{R}}

[/tex]