The vertex of a parabola is at -25 what is its equation

Answer:

180

Step-by-step explanation:

For each of the two right triangles, by the Pythagorean theorem, she shared side is of length 15. So, the area of each of the top two rectangles is (½)(8)(15), so their combined area is 120.

Moving onto the trapezoid, we can use the formula for the area of a trapezoid to determine its area is (½)(14+16)(4)=60.

So, the answer is 120+60=180.

The model (x+a)(x-a) will represents the factors of 4x²-9 as (2x+3)(2x-3).

The "completing the squares" method aims to construct a quadratic equation of the form where the x variable is entirely covered by a single squared term, which is the square of a linear expression in x, as the name suggests.

The quadratic equation can resemble this:

x²-a² = (x+a)(x-a)

Given equation;

⇒4x²-9

⇒(2x)²-3²

The equation can be modeled as;

(2x+3)(2x-3)

Hence the model (x+a)(x-b) will represents the factors of 4x²-9 as (2x+3)(2x-3).

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The information given illustrates that the equivalent fraction will be 2/6.

It should be noted that equivalent fraction simply means the fractions that are the same.

In this case, we are given 4/6 and 1/3. They have different numerators and denominators. The question is simply to change 1/3 to another fraction that has a denominator of 6.

This will be illustrated. The equivalent faction to 1/3 will be:

= 1/3 × 2/2

= 2/6

Therefore, the answer is 2/6.

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Answer:

Step-by-step explanation:

m represents the meters.

Answer:

Step 3 is wrong and the answer should be 576

Step-by-step explanation:

Step 1 and step 2 are correct

Step 2: 4 × 12^2

You don't multiply 12 by 4, you first complete the exponent since, in PEMDAS, Exponent is before Multiplying.

Step 3 should be: 4 × (12×12)

= 4 × 144

= 576

Answer:

The solutions of the equation |2 x-3|=17

are x=10

and x=-7

Step-by-step explanation:

Given equations is |2 x-3|=17.

It is required to find out the values of x satisfying the given equation.

To find it out, use the fact that the solution of this type of equation is 2x-3=17.

Or 2x-3=-17 and simplify the equations using simple mathematical operations.

Step 1 of 2

Solve the equation 2x-3=17,

Add 3 on both sides of the equation 2x-3=17,

2x-3+3=17+3

2x=20

Divide by 2 on both sides of the equation 2x=20,

[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{20}{2} \\&x=10\end{aligned}$$[/tex]

Step 2 of 2

Solve the equation 2x-3=-17,

Add 3 on both sides of the equation 2x-3=-17,

[tex]$2 x-3+3=-17+3$\\ $2 x=-14$[/tex]

Divide by 2 on both sides of the equation 2x=-14,

[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{-14}{2} \\&x=-7\end{aligned}$$[/tex]

For Janna to prove that △ABC∼△DEF by the SSS similarity theorem, she will use: B. DE/AB = EF/BC = DF/AC = 1/4.

According to the SSS similarity theorem, if the ratio of the corresponding sides of two triangles are equal, then both triangles are similar.

The ratio of the corresponding sides of the triangles given are:

DE/AB = 4/16 = 1/4

EF/BC = 3.25/13 = 1/4

DF/AC = 1.75/7 = 1/4

Therefore, what Janna needs is:

B. DE/AB = EF/BC = DF/AC = 1/4

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The graphs can be described as shown below.

A.) The first graph has the y-intercept at 2. Therefore, the first graph can be described by the equation, y =5x + 2.

B.) For the second graph, the graph passes through the point (-1,0). Therefore, if we substitute the value of y as 0 in the equation y=3x+3, we will get x=-1.

Hence, the equation of the second graph is y=3x+3.

C.) For the third graph, the graph passes through the point (-1.5,0). Therefore, if we substitute the value of y as 0 in the equation y=2x+3, we will get x=-1.5.

Hence, the equation of the second graph is y=2x+3.

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The original price is £75

Let the original price be x.

The reduced price is given as:

Reduced =60

So, we have:

Reduced = Original price * (1 - discount)

This gives

x * (1- 20%) = 60

Evaluate the difference

x * 0.8 = 60

Divide by 0.8

x = 75

Hence, the original price is £75

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The amount of Type A coffee that was used is 40 pounds.

From the given information;

Type A coffee costs Miguel $5.95 per pound

Type B coffee costs $4.65 per pound.

For this month, the equation can be expressed as:

A + 3A

Thus;

5.95A + 3(4.65)A = 796.00

5.95A +13.95A = 796.00

19.9A = 796.00

A = 796.00/19.9

A = 40

Therefore, we can conclude that the amount of pounds of type A coffee that was used is 40 pounds.

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Answer:

1:3 is an example and for every two boy there are 5 girls is another example

Edited: I go out Five times as much as My sister does. My sister goes out only 3 times. Which is 15:1

I see 5 blue cars for every 6 red cars. Which is 5:6

Ratio is always represented in terms of ':' like a:b

Examples

#1

The ratio of apples is 2:4 or 1:2

#2

The ratio is 10:7

The constant of proportionality in centimeters per minute is: 5.5.

To find the constant of proportionality of the table shown in the image attached below, use one pair of points, (12, 66).

Constant of proportionality, k = y/x, therefore, the proportional constant in centimeters per minute would be:

k = 66/12 = 5.5 cm per min.

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Answer:

attached

Step-by-step explanation:

Answer:

  x ≈ -8.402, 8.502

Step-by-step explanation:

The usual methods of solving quadratic equations apply to this one. Any of them can be used: graphing, factoring, completing the square, quadratic formula.

Often, when the coefficients are non-integers and have no obvious relationship to each other, the most convenient method of solution is the quadratic formula. It tells you the solution to ax²+bx+c=0 is ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Your equation has the coefficients, a = -0.07, b = 0.007, c = 5, so the solutions are ...

  [tex]x=\dfrac{-0.007\pm\sqrt{0.007^2-4(-0.07)(5)}}{2(-0.07)}=\dfrac{-0.007\pm\sqrt{1.400049}}{-0.14}\\\\x=0.05\pm\sqrt{\dfrac{200007}{2800}}=0.05\pm\sqrt{71.4310\overline{714285}}\\\\\boxed{x\approx\{-8.40169,\,8.50169\}}[/tex]

Answer:

[tex]t=8.50, -8.40\:\: \sf (2 \:d.p.)[/tex]

Step-by-step explanation:

Quadratic equations are in the form [tex]ax^2+bx+c=0[/tex],  where [tex]a\neq 0[/tex].

There are three basic methods to solve quadratic equations algebraically:

Given quadratic equation:

[tex]h(t)=-0.07t^2+0.007t+5[/tex]

Method 1 - Factoring

If the trinomial is able to be easily factored, set the equation equal to zero and factor.  Set each factor equal to zero and solve.

As the given example is not easily factored, factoring is not the best method to use on this occasion.

Method 2 - Completing the Square

If the quadratic expression is not able to be easily factored, try completing the square.

Divide all terms by [tex]a[/tex] (-0.07):

[tex]\implies t^2-\dfrac{1}{10}t-\dfrac{500}{7}=0[/tex]

Move the constant to the right side:

[tex]\implies t^2-\dfrac{1}{10}t=\dfrac{500}{7}[/tex]

Add the square of half the coefficient of t to both sides:

[tex]\implies t^2-\dfrac{1}{10}t+\left(-\dfrac{1}{20}\right)^2=\dfrac{500}{7}+\left(-\dfrac{1}{20}\right)^2[/tex]

[tex]\implies t^2-\dfrac{1}{10}t+\dfrac{1}{400}=\dfrac{200007}{2800}[/tex]

Factor the perfect trinomial:

[tex]\implies \left(t-\dfrac{1}{20}\right)^2=\dfrac{200007}{2800}[/tex]

Square root both sides:

[tex]\implies t-\dfrac{1}{20}=\pm\sqrt{\dfrac{200007}{2800}[/tex]

Add 1/20 to both sides:

[tex]\implies t=\dfrac{1}{20}\pm\sqrt{\dfrac{200007}{2800}[/tex]

As decimals to 2 decimal places:

[tex]\implies t=8.50, -8.40\:\:\sf(2 \:d.p.)[/tex]

Method 3 - Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

This can be used to find both real and imaginary or complex solutions.

Identity the variables:

[tex]a=-0.07, \quad b=0.007, \quad c=5[/tex]

Substitute the values into the quadratic formula and solve for t:

[tex]\implies t=\dfrac{-0.007 \pm \sqrt{0.007^2-4(-0.07)(5)} }{2(-0.07)}[/tex]

[tex]\implies t=\dfrac{-0.007 \pm \sqrt{1.400049}}{-0.14}[/tex]

[tex]\implies t=\dfrac{0.007 \pm \sqrt{1.400049}}{0.14}[/tex]

[tex]\implies t=8.50, -8.40\:\: \sf (2 \:d.p.)[/tex]

Finally, a non-algebraic method of solving a quadratic equation is by graphing using a graphical calculator (see attached).  The solutions are the points at which the curve intercepts the x-axis.

The congruence theorem that can be used is: B. ASA

If we have two triangles that have two pairs of corresponding congruent angles (e.g. ∠LGH ≅ ∠HKJ and ∠LHG ≅ ∠KHJ), and a pair of corresponding congruent sides (e.g. GH ≅ HK), the triangles are said to be congruent triangles by the ASA congruence theorem.

Therefore, triangles GHL and KHL in the image given are congruent triangles by the  ASA congruence theorem.

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Answer: Option 2 or B. ASA

Step-by-step explanation: Trust me!

If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful. Good luck everyone!  :)

Answer:

the answer would be no shape.

Step-by-step explanation:

imagine you have the paper in your hands, if you start from the left you would have to fold the paper 3 times, then when it comes to the last 2 squares, you wouldnt be able to close the cube. hope this helps

Answer:

an open cube

Step-by-step explanation:

your welcome

The expressions are not equivalent, even though Ella got the same result when she substituted zero for f. Then the correct option is C.

The equivalent is the expressions that are in different forms but are equal to the same value.

Ella completed the following work to test the equivalence of two expressions.

First expression,                Second expression

⇒ 2f + 2.6                           ⇒ 3f + 2.6

⇒ 2(0) + 2.6                       ⇒ 3 (0) + 2.6

⇒ 0 + 2.6                           ⇒ 0 + 2.6.

⇒ 2.6                                 ⇒ 2.6

The expressions are not equivalent, even though Ella got the same result when she substituted zero for f.

Then the correct option is C.

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I am not 100% sure but I think it is 85 degrees

DO NOT take my word for it

Step-by-step explanation:

I'm not sure but I think it is 75 degree

In rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.

The area of a rectangle is the product of its length and its width.

In the question, we are given two rectangles:-

Rectangle P:

length = 40 cm,

width = x cm,

Thus, the area = length * width = 40x.

Rectangle Q:

length = 25% more than the length of P = 40 + 25% of 40 = 40 + 0.25*40 = 40 + 10 = 50 cm.

width = y cm,

Thus, the area = length * width = 50y.

Now, we are given that, the area of rectangle Q is 10% less than the area of rectangle P.

Thus, we can write that,

Area of rectangle Q = Area of rectangle P - 10% of the area of rectangle P,

or, 50y = 40x - 10% of 40x,

or, 50y = 40x - 0.10*40x,

or, 50y = 40x - 4x,

or, 50y = 36x,

or, y = 36x/50.

We are asked to find the ratio of x:y = x/y.

Substituting y = 36x/50, we get,

x/y = x/(36x/50) = 50x/36x = 25/18.

Thus, the ratio x:y = 25:18.

Thus, in rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.

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The location of the fountain based on the information given is (-1, 0.5).

From the graph, the coordinates are (4, 2) and (-4,   -2).

The ratio is given as 5:3.

The coordinates of the fountain will be:

[(5 × -4 + 3 × 4)/(5 + 3), (5 × -3 + 3 × 2)/(5 + 3)]

= (-1, -0.5)

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The area of the garden is 33 ft².

The number of tiles required to cover the floor is 17 tiles.

The area of a dog pen is 170/9 square yards.

We need to find the area and perimeter for the given questions.

The formula to find the perimeter of a rectangle=2(Length+Breadth)

The formula to find the area of a rectangle=Length×Breadth.

Given that, a small garden has a perimeter of 24 1/4 ft and the length is 8 ft.

Now, perimeter = 2(8+Breadth)

⇒24 1/4=16+2×Breadth

⇒97/4-16=2×Breadth

⇒Breadth=97-64/4×2=33/8 ft

Now, Area=8×33/8=33 ft²

Therefore, the area of the garden is 33 ft².

Given that, the floor measures 4 1/2 ft by 3 3/4 ft.

The area of a floor=Length×Breadth=9/2×15/4=135/8 ft²

Number of tiles to cover the floor=135/8=16.875

Therefore, the number of tiles required to cover the floor is 17 tiles.

Given that, a dog pen is 3 1/3 yards wide by 5 2/3 yards long.

Now, the area of a dog pen=10/3×17/3=170/9 square yards.

Therefore, the area of a dog pen is 170/9 square yards.

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Answer:

They have none left over and they can make 43 dishes

Step-by-step explanation:

Answer:

15.

Step-by-step explanation:

Width of the strip + cut = 5/8 + 1/8 = 3/4.

11 3/8 / 3/4

=  91/8 / 3/4

= 91/8 * 4/3

= 91/6

= 15  1/6

So the answer is 15

Considering the volume of the given rectangular prism, the height is of 5.03 feet.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, we have that:

The volume is of 365 cubic feet, hence:

lwh = 365

(2h + 2)(h + 1)h = 365

(2h² + 4h + 2)h - 365 = 0

2h³ + 4h² + 2h - 365 = 0.

Using a cubic equation calculator, the height is of h = 5.03 feet.

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Answer:

x= 3

y=2

Step-by-step explanation:

Let's solve your equation step-by-step.

2=4x−10

Step 1: Flip the equation.

4x−10=2

Step 2: Add 10 to both sides.

4x−10+10=2+10

4x=12

Step 3: Divide both sides by 4.

4x/4=12/4

x=3

Answer:

since y=2 substitute y into y=4x-10

2=4x-10

2+10=4x

12=4x

Divide both sides by 4

12/4=4x/4

x=3

Therefore the answer is (2,3)

y= 4x-10

2= 4×3-10

2= 12-10

2=2

Answer:

D

Step-by-step explanation:

(ax + b)² = c

step 1 : take square root of both sides

ax + b = ± [tex]\sqrt{c}[/tex]

step 2 : subtract b from both sides

ax = - b ± [tex]\sqrt{c}[/tex]

step 3 : divide both sides by a

x = - [tex]\frac{b}{a}[/tex] ± [tex]\frac{\sqrt{c} }{a}[/tex]

Answer:

D. Take the square root of both sides

Step-by-step explanation:

Given quadratic equation:

[tex](ax+b)^2=c[/tex]

To solve, square root both sides:

[tex]\implies \sqrt{(ax+b)^2}=\sqrt{c}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{n^2}=n, \quad \textsf{assuming }n \geq 0:[/tex]

[tex]\implies ax+b=\pm\sqrt{c}[/tex]

Subtract b from both sides:

[tex]\implies ax=-b\pm\sqrt{c}[/tex]

Divide both sides by a:

[tex]\implies x=\dfrac{-b\pm\sqrt{c}}{a}, \quad a\neq 0[/tex]

The value of f(32) is 3

A function is a mathematical statement used to relate two variables .

It is given that

8f(x) = f((1/8)x)

It is also given that

f(4) = 24

now to determine the value of f(32)

8 * f(32) = f((1/8) *32)

8 *  f(32) = f(4 )

f(32) = 24 /8 = 3

Therefore the value of f(32) is 3

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Answer:

294.84 ft²

Step-by-step explanation:

A = (B + b)h/2

A = (28.5 ft + 18.3 ft)(12.6 ft)/2

A = 294.84 ft²

Answer: 294.84 ft^2

Step-by-step explanation:

Area of trapezoid=((a+b)/2)*h

here

a=28.5 ft

b=18.3 ft

h=12.7 ft

Area=((28.5+18.3)/2)*(12.7)

Area=294.84 ft^2

Answer:

12 and 8

Step-by-step explanation:

→ Set up two equations

x - y = 4

[tex]\frac{x+y}{2} =10 \\ \\x + y = 20[/tex]

→ Add the 2 equations together

2x = 24

→ Solve for x

x = 12

→ Substitute into original equation

12 - y = 4

→ Solve

y = 8