Write the equation of the directrix of the parabola shown below.
y2 + 16y+ 4x + 4 = 0

Answer:

Step-by-step explanation:

If A is parallel to B, then angles 2 and 4 are same side interior and they are supplementary. Thus,

2x + 10 + 4x + 80 = 180 and

6x = 90 so

x = 15

Answer:

725$ give brainliest ;)

Step-by-step explanation:

We want to find the total number of integers that are larger than 40 and smaller than 99 that also are multiples of 3.

The answer is 18.

We can solve this just by counting.

The first multiple of 3 larger than 40 is:

3*14 = 42

Now we know that 99 is also a multiple of 3 and that the multiples of 3 are separated by a distance of 3 units, then the total number of multiples of 3 between 42 and 99 is given by:

(99 - 42)/3 = 19

But we need to remove 1, because we used 99 and we have the restriction that our numbers must be "smaller" than 99.

Then we have a total of 18 multiples of 3 between 40 and 99.

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Answer:                69 cm

To find the perimeter of the triangle, add together the length of all sides.

A right triangle has three sides and we know that:

When we know two sides in a right triangle, we can find the third side using the Pythagorean theorem:

a² + b² = c²

The variables 'a' and 'b' represent the base and height. The variable 'c' represents the hypotenuse, the longest side.

Since we know the base and height, substitute them into the formula and solve for the hypotenuse.

a² + b² = c²                Start with the Pythagorean theorem.

24² + 16² = c²            Substitute the base and height.

576 + 16² = c²            Solve 24².

576 + 256 = c²          Solve 16².

832 = c²                     Add.

Now, let's start to isolate 'c', which means making it alone on one side of the equal sign.

√832 = √c²               Square root both sides.

√832 = c                   Square root is the opposite of ², so it cancels out.

c ≈ 28.8...                  Keep the variable on the left side.

The question says to find the approximate perimeter, so let's round 28.8 to the nearest whole number.

The hypotenuse, 'c', is about 29 cm.

Now, we know the three sides:

Add together all three sides.

Perimeter = base + height + hypotenuse

Perimeter = 24 cm + 16 cm + 29 cm

Perimeter = 69 cm

∴ The perimeter of the right triangle is approximately 69 cm.

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To find the point on the line 3x + y = 4 that is closest to the point (-3, 1), we can use the concept of perpendicular distance.

First, let's express the equation of the given line in slope-intercept form (y = mx + b):

y = -3x + 4

Now, we can consider a perpendicular line passing through the point (-3, 1). The slope of the perpendicular line will be the negative reciprocal of the slope of the given line, which is 1/3.

Using the point-slope form of a line (y - y1 = m(x - x1)), we can write the equation of the perpendicular line:

y - 1 = (1/3)(x + 3)

y - 1 = (1/3)x + 1

y = (1/3)x + 2

To find the intersection point of the two lines, we can solve the system of equations:

y = -3x + 4

y = (1/3)x + 2

By equating the two equations, we get:

-3x + 4 = (1/3)x + 2

Simplifying the equation:

-3x - (1/3)x = 2 - 4

-10/3 x = -2

x = 6/5

Substituting the value of x back into either equation, we find:

y = -3(6/5) + 4

y = -18/5 + 20/5

y = 2/5

Therefore, the point on the line 3x + y = 4 closest to the point (-3, 1) is (6/5, 2/5).

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Answer:

walang value si ex..hahahah

73 is the answer

use pythagorean

Yes, there is always such a function.

What is function?

In arithmetic, a function from a collection X to a collection Y assigns to every part of X precisely one part of Y.

Main body:

Take a sequence of continuous functions gn which converges pointwise, but not uniformly, to 0. Then fn=f+gn converges pointwise, but not uniformly to f.

For an example of such gn, you can take the following:

gn(x)=    \(\left \{ {{if x < 1/n} \atop {2 if 1/n < = x < 2/n}} \right.\)  

and 0 otherwise.

The graph of gn will be a triangle starting at (0,0), going up to (1,1n), then down to (2/n,0), and then flat horizontal from there. This does converge pointwise to 0 (as at any non-zero point a∈[0,1], eventually 2/n<a, and gn(a)=0), but not uniformly, as it always has a maximum value of 1.

Hence the given function is the required function,

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An example of a function f: R^2 -> R that is continuous at 0, has directional derivatives at 0 for all u in R^2, but is not differentiable at 0 can be provided.

Consider the function f(x, y) = |x| + |y|. To prove that f is continuous at 0, we need to show that the limit of f(x, y) as (x, y) approaches (0, 0) exists and is equal to f(0, 0).

Let's evaluate the limit:

lim_(x,y)->(0,0) (|x| + |y|) = 0 + 0 = 0

Since the limit is equal to 0 and f(0, 0) = |0| + |0| = 0, the function is continuous at 0.

Next, we need to show that the directional derivatives of f at 0 exist for all u in R^2. The directional derivative D_u f(0) can be calculated using the definition:

D_u f(0) = lim_(h->0) (f(0 + hu) - f(0))/h

For any u in R^2, the limit exists and is equal to 1 since f(0 + hu) - f(0) = |hu| = |h||u| and |u| is constant. Thus, the directional derivatives exist for all u in R^2.

However, f is not differentiable at 0 because the partial derivatives ∂f/∂x and ∂f/∂y do not exist at 0. Taking the partial derivative with respect to x at (0, 0) yields:

∂f/∂x = lim_(h->0) (f(h, 0) - f(0, 0))/h = lim_(h->0) (|h| - 0)/h

This limit does not exist since the value of the limit depends on the direction of approach (from the positive or negative side). Similarly, the partial derivative with respect to y does not exist.

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Answer:

Hola! :)

* 100cm <> 1 m

De acuerdo a la escala

1cm => 100cm = 1m

Entonces

1cm => 1m

x => 70m

x = 7cm

Cada lado en la maqueta mide 7 cm

Visto la maqueta en planta solo se verá un cuadrado su superficie sera lado al cuadrado

El volumen de la maqueta sera lado al cubo

dame corazon y 5 estrellas x fas

Step-by-step explanation:

Answer:

19.63

Step-by-step explanation:

Find the radius

5 / 2 = 2.5

2.5² = 6.25

6.25 × π = 19.63

The answer which are true about the two rectangular pyramids are;

It follows from the task content that the dimensions of the rectangular prisms are the same and are as given.

On this note, it follows that the volume of the composite figure is; 1.5(9)(5) + 1.5(9)(5) = 135units³.

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4℉.

What we know about Degrees is that there is a Positive type and a negative type.

(i.e: 30℉ is positive and -30℉ is negative.)

If the temperature was -4℉ at 7AM, then it is negative. If it goes up by an amount that is more than 4 then that negative will go up to a positive temperature. In this case: At 9AM it was 8° warmer.

Warmer is a keyword. If it is warmer by an amount, Negative temperatures will go up to a positive and positive temperature will just go up. If it gets cooler, negative temperatures will go down further and positive temperatures will go down to a negative.

So lets work out this problem with our newfound knowledge.

-4° F at 7AM

8°  warmer at 9AM

-4 + 8 = 4.

The temperature was 4°  at 9AM.

-Snooky

since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.

\(\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}\)

The required length of the side BM is 29.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

In the given question,

Point M is the midpoint of line AB.

AM = 4x + 13,

and BM = 3x + 17

To find the length of MB, use midpoint property.

Since, Point M is the midpoint of AB,

Therefore, AM = MB

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.

The length of MB, where M is midpoint of AB, is 29.

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Deon's Coffee Shop used 26 pounds of type A coffee.

Let's consider Deon's Coffee Shop, which used "a" pounds of type A coffee and "4a" pounds of type B coffee. The total cost of the blend is $578.50, so we can equate the total cost of the type A and type B coffee to that amount. This leads us to the following equation: 5.45a + 4.20(4a) = 578.50.

To solve the equation, we simplify it: 5.45a + 16.80a = 578.50. Combining like terms, we get 22.25a = 578.50.

To find the value of "a," we divide both sides of the equation by 22.25. Therefore, a = 26. Hence, Deon's Coffee Shop used 26 pounds of type A coffee.

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Using Pythagoras theorem to evaluate the given data we will get the result as 5√3.

We know that 5 is half of ten,

on squaring them we get ,

a+25=100

a=75

=5

The answer is A, 5.

In a line, a line segment has two distinct endpoints. The line segment's length is fixed, as is the distance between two fixed points. The length can be measured in metric measures like centimetres (cm), millimetres (mm), or traditional units like feet or inches.

A closed line segment includes both endpoints, whereas an open line section excludes both endpoints. A half-open line segment is a line segment with exactly one endpoint.

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Answer:

fourth one = 780

Step-by-step explanation:

-4-30-3 =-37

8/10-2 = -6/5

3(-92)+28 = 248

-26* -30 = 780

The equation of the normal line at the point (2, 1, -3) is: r = (2, 1, -3) + λ(4, 2, -6)

Given information: The equation of the surface is: 2x² + y² + 2z = 3Point (2, 1, -3). The equation of the tangent plane and normal line to the surface at point (2, 1, -3).

Formula used: Equation of a plane is given by the form: ax + by + cz = d where (a, b, c) is the normal to the plane at the point (x0, y0, z0).

The normal vector is given by the gradient of the surface, r, at point (2, 1, -3). The normal vector is given by: r = (2x, 2y, 2z). Therefore, the normal vector at the point (2, 1, -3) is: r = (2(2), 2(1), 2(-3))r = (4, 2, -6). Hence, the equation of the tangent plane at the point (2, 1, -3) is:4x + 2y - 6z = d. To find d, we substitute the point (2, 1, -3) into the equation of the plane.4(2) + 2(1) - 6(-3) = dd = 22.

Hence, the equation of the tangent plane at the point (2, 1, -3) is:4x + 2y - 6z = 22. The normal line passes through the point (2, 1, -3) and has a direction vector given by the normal vector of the plane. Hence, the equation of the normal line is: r = (x, y, z) + λ(4, 2, -6)where (x, y, z) is the given point (2, 1, -3).

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(1.25 x 12)/ 0.6=

25

Hope this helps :)

Answer:

a. 240pieces

b. 4800+ 10x

Step-by-step explanation:

a. 40÷4=10, 120÷5=24, 10×24=240

b. (240×20)+ (x×10)= 4800+ 10x ===> x is the number of cars

Answer:

C. g(x) = 4x²

Step-by-step explanation:

we have one specific point on g(x) : (1,4)

so, for x=1 the functional value (y) has to be 4.

A. (4×1)² = 4² = 16 and not 4. => wrong

B. 1/4 × 1² = 1/4 and not 4. => wrong

C. 4×1² = 4 and that IS 4 => correct

D. 16×1² = 16 and not 4 => wrong

Answer:

i)

Your answer is correct

ii)

Given m∠BAX = 42° and ∠DAB is complementary with BAX ⇒

DC = BC ⇒ intercepted arcs are same ⇒

mDC = mCB ⇒ mDCB = ∠DAB = 48° ⇒

iii)

∠CBA

∠CBA is supplementary with ∠ADC as opposite angles of cyclic quadrilateral (∠ADB = ∠BAX = 42°)

∠BAE

EA║CB and AB is transversal ⇒ CBA and BAE are supplementary angles:

∠DCE

let x be the number of ballpoint boxes and y the number of felt tip boxes

so we get

so we get that the number of felt tip boxes is 6, and therefore the number of ballpoint boxes is 6*3=18

The triangle similarity can be proven by three methods, and the AA similarity postulate states that two triangles are similar if and only if their corresponding angles are congruent.

If they have the same shape but different sizes. This is what is known as similarity. In mathematics, there are three ways to prove that two triangles are similar: AA, SAS, and SSS.

In the case of AA similarity postulate, two triangles are similar if and only if two corresponding angles are congruent, meaning they have the same degree measure.

Similarly, if triangle ABC is similar to triangle JKL by AA similarity postulate, it means that the corresponding angles of both triangles are congruent.

Therefore, it is possible that triangle ABC is similar to one or more of the triangles given, but it is not possible to say without further information such as the angles and lengths of the sides.

Complete Question:

Define triangle is ​△ABC​ similar to Similarity property and why?

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Answer:

Ij and 8

Step-by-step explanation:

Answer:

When dividing two fractions, the process is very easy.  You simply multiply the numerator fraction by the reciprocal of the denominator fraction.  In other words:

\(\frac{a}{b} \div \frac{c}{d} \\= \frac{a}{b} \times \frac{d}{c} \\= \frac{a \times d}{b \times c}\)

Step-by-step explanation:

\(\begin {array}{c|cc} 2 & 1842 & 90 \\ \cline{2-3}3 & 921 & 45 \\ \cline {2-3} & 307 & 15 \end{array}\)

Answer:

x = -4

Step-by-step explanation:

1/2x - 20 - x = 6x -3 -2x +1

-1/2x -20 = 4x -2

-1/2x -4x = -2 +20

-9/2x = 18

9/2x = -18

9x = -36

x = -4

Give brainliest please!

hope this helps :)