5. A parabola has a directrix of y = -3 and a vertex
at (2,1). Which ordered pair is the focus of the
parabola?

Answer:

[tex]3^{1.5}[/tex]

Step-by-step explanation:

[tex]3 = 3^1[/tex]

[tex]\sqrt{3} = x^{0.5}[/tex]

[tex]3*\sqrt{3} = 3^{1} * 3^{0.5} = 3^{1 + 0.5} = 3^{1.5}[/tex]

Answer:

  (d)  HA

Step-by-step explanation:

You have two right triangles with the hypotenuse and one angle marked as congruent. You want to know the applicable theorem for claiming the triangles are congruent.

When two triangles are known to be right triangles, the known angle is opposite the longest side (hypotenuse), and the two legs are the sides that form that known angle. Hence, some special theorems can be invoked for right triangles:

  LA — leg, angle; equivalent to ASA

  LL — leg, leg; equivalent to SAS

  HA — hypotenuse, angle; equivalent to AAS

  HL — hypotenuse, leg; no equivalent for non-right triangles

The given triangles have the hypotenuse (H) and an acute angle (A) marked, so the HA theorem can be used to prove congruence.

__

Additional comment

The HL condition described above refers two two consecutive sides and the angle not between them (SSA). This set of descriptors will create a unique triangle if and only if the angle is opposite the longest side. In general, that will not be the case, but it is guaranteed to be the case for a right triangle.

9 students made at least 3 picture frames.

An illustration of variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data on the same graph.

Given:

The plot shows picture frames made by students last week.

Number of Frames     Number of students

              0                               6

              1                                4

              2                               1

              3                               2

              4                               7

So, the students made at least 3 picture frames

= 2+ 7

= 9

Hence, 9 students made at least 3 picture frames.

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Answer:

450 centimeters

Step-by-step explanation:

We know that,

1 meter = 100 centimeters

so 4.5 meters = 4.5*100 centimeters

                      =450 centimeters

Answer:

A

Step-by-step explanation:

The area of the given triangle is 21.33 cm²

This formula is understood for its simple calculation supporting the length of three sides of a triangle, if the length of three sides are a, b, and c, then its semi-perimeter is. s=a+b+c2. Thus, the area is given by,

A=√s(s−a)(s−b)(s−c)

Given a triangle, with lengths 8 cm, 6 cm and 12 cm

Perimeter = 8+6+12 = 26 cm

Semi perimeter = 26/2 = 13 cm

Area = √s(s−a)(s−b)(s−c)

Area = √13(13-8)(13-6)(13-12)

Area = √455

Area =  21.33 cm²

Hence, The area of the given triangle is 21.33 cm²

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Answer:

Step-by-step explanation:

[tex]\left[\begin{array}{cc}2&7\\1&3&\end{array}\right] \left[\begin{array}{cc}-3&7\\1&-2&\end{array}\right] =\left[\begin{array}{cc}2(-3)+7(1)&2(7)+7(-2)\\1(-3)+3(1)&1(7)+3(-2)&\end{array}\right] =\left[\begin{array}{cc}1&0\\0&1&\end{array}\right][/tex]

Answer:

x = 4

Step-by-step explanation:

assuming you require to find the value of x

Δ ADE and Δ ACB are similar ( by the AA postulate )

then the ratios of corresponding sides are in proportion, that is

[tex]\frac{AD}{AC}[/tex] = [tex]\frac{AE}{AB}[/tex] ( substitute values )

[tex]\frac{x}{x+x-2}[/tex] = [tex]\frac{x+2}{x+2+x -1}[/tex]

[tex]\frac{x}{2x-2}[/tex] = [tex]\frac{x+2}{2x+1}[/tex] ( cross- multiply )

(2x - 2)(x + 2) = x(2x + 1) ← expand left side using FOIL

2x² + 2x - 4 = 2x² + x ( subtract 2x² + x from both sides )

x - 4 = 0 ( add 4 to both sides )

x = 4

x < 2 and x > 12 are the answers to the inequality expressions supplied.

An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression. One-variable inequalities can have solutions that can be graphed on a number line or on a coordinate plane.

Given the inequality expressions below:

2<-2x+6 or -18>-2x+6

Solve individually;

2 < -2x + 6

2-  6 < -2x

-4 < -2x

-2x > -4

x < 4/2

x <2

For the inequality  -18>-2x+6

-18 - 6 > -2x

-24 > -2x

-2x < -24

x  > 24/2

x > 12

Hence the solution to the given inequality expressions are x < 2 and x > 12

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The distance to the top of the building changing when they are 60 feet from the base of the building is 2.19 ft/s.

In the given question we have to find how fast is the distance to the top of the building changing when they are 60 feet from the base of the building.

A family is walking toward their home, which is in an apartment building 123 feet tall.

They are walking at a rate of 5 ft/sec.

So according to the given statement diagram is

In the diagram x represent base and s represent the distance.

Using the Pythagorean theorem to find the value of s.

So the equation should be

[tex]s^2=x^2+(123)^2[/tex]........................(1)

From the question, x=60 feet

Now putting the value

[tex]s^2=(60)^2+(123)^2[/tex]

[tex]s^2[/tex] = 3600+15129

[tex]s^2[/tex] = 18729

s = 136.85

Differentiate equation 1 with respect to t using the power rule then solve the expression for ds/dt

2s ds/dt=2x dx/dt+0

2s ds/dt= 2x dx/dt

Divide by 2s on both side, we get

ds/dt= x/s dx/dt.......................(2)

They are walking at a rate of 5 ft/sec.

So dx/dt=5

Putting the value in the equation 2

ds/dt=60/136.85 ×5

ds/dt=0.438×5

ds/dt=2.19 ft/s

The distance to the top of the building changing when they are 60 feet from the base of the building is 2.19 ft/s.

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The tick marks on the two sides mean those two lengths are the same, which also means the angles opposite them are the same measure.  (AKA It's an isosceles triangle.)

Since the two missing angles are equal, we can solve:

    28 + x + x = 180

to find that x = 76.

The two angles are 76 degrees.

And since LM = LN, we know LN = 18 in.

She has to do at least 8.6 hours walking (and then 7.5 hours dog walking) for the minimum of $80 earning

Keilantra is working two summer jobs, making $12 per hour lifeguarding and $6 per hour walking dogs. Last week Keilantra worked a total of 11 hours and earned a total of $108.

x = number hours dog walking

y = number hours Lifeguarding

x + y <= 11

12x + 6y >= 80

The solution is the common area below the first line and above the second line.

The first line is above the second line (due to the y-intercept of 11 vs. 8) until the crossing point.

for the crossing point we use the regular equations :

from the first we get

x = 11 - y

using this in the second

12×(11 - y) + 6y = 80

132 - 12y + 6y = 80

6y = 52

y = 52/6 = 26/3 = 8.6

x = 11 - y = 11 - 8.6 = 2.4

So, she has to do at least 8.6 hours lifeguarding (and then 7.5 hours dog walking) for the minimum of $80 earning, all the way up to the maximum of 11 hours lifeguarding (and 0 dog walking).

Hence the answer is she has to do at least 8.6 hours lifeguarding (and then 7.5 hours dog walking) for the minimum of $80 earning.

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Answer:

Its the average of the numbers, and its the sum of all values divided by the total number of values.

Answer:

mean median and mode song rap helps me remember

The equivalent fraction for the given fraction -11/-4 is -11/(-4) and -11/-4.

Fraction.

Fraction means a number expressed as a quotient, in which a numerator is divided by a denominator.

Given,

Here we have the fraction -11/-4.

Now, we have to find the equivalent fraction of this fraction.

In order to find the equivalent fraction, we have to identify that the given term is reduceable or not.

If it is reduceable, then we have to simplify it to get the equivalent fraction.

But here the given fraction -11/-4 is not reduceable.

So, the next thing we have to do is to find the sign equivalent value for this one.

In the given fraction both the numerator and the denominator are in negative sign.

So, the equivalent fraction, must have both positive or both negative one.

Therefore, the equivalent fraction are -11/(-4) and -11/-4.

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The solution to the inequality −17 + 2x ≤ 19 − 4x is x ≤ k. The value of k is 6.

In mathematics, the relationship between two values that are not equal is defined by inequalities.

Therefore, the inequality can be solved as follows:

−17 + 2x ≤ 19 − 4x is  x ≤ k .

Let's solve for k

−17 + 2x ≤ 19 − 4x

subtract 2x from both sides of the inequalities

−17 + 2x ≤ 19 − 4x

−17 + 2x - 2x ≤ 19 − 4x - 2x

- 17 ≤ 19 - 6x

Subtract 19 from both sides of the equation

- 17 ≤ 19 - 6x

- 17 - 19 ≤ 19 - 19 - 6x

- 36 ≤ - 6x

divide both sides by -6

- 36 / -6 ≤ - 6x / -6

6 ≥ x

x ≤ 6

Therefore, k = 6

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Answer:

Step-by-step explanation:

Isolating the variable x we will get the simplified inequality (which is equivalent to the given one)

3 < x ≤ 5.2

Sadly, the options are not given, so we can get a trivial equivalent inequality which is the one where the variable x is isolated, and it gives the solution set for the inequality.

So let's isolate the variable:

-22 > -5x - 7 ≥ −33

First, we can add 7 everywhere, so we get:

-22 + 7 > -5x - 7 + 7  ≥ −33 + 7

-15 > -5x  ≥ −26

Now we can divide everywhere by -5, because it is a negative number, it changes the direction of the symbols.

-15/-5 < -5x/-5 ≤ -26/-5

3 < x ≤ 5.2

That is the equivalent inequality, and the solution set is:

(3, 5.2]

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no question;;;;;;;;;;;;;;;;;;;;;;

The constant of proportionality on this case is 3.2

What is constant of proportionality?

The ratio between any two given values that establishes what is referred to as a proportional relationship is the constant of proportionality.

Main body:

Total amount spent by Mom = $ 72

total gallon bought = 22.5

So constant of proportionality can be found by finding value of 1 gallon of gasoline, which can be found by dividing as follows,

Price of 1 gallon = total spent/ total gasoline bought

                           = 72/22.5

                           = 3.2

Hence constant of  proportionality is 3.2.

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The measure of angle 4 is 35 degrees and the measure of angle 5 is 81 degrees

The sum of angles on a straight line is equal to 180 degrees

Then the equation will be

∠3 + 81 +∠4 = 180  degrees

Substitute the value of ∠3 in the equation

64 + 81 + ∠4 = 180  

145 + ∠4 = 180

∠4 = 180 - 145

∠4 = 35 degrees

The sum of interior  angles of the triangle is 180 degrees

∠4 + ∠5 + 64 = 180

Substitute the values in the equation

35 + ∠5 + 64 = 180

∠5 + 99 = 180

∠5 = 180 - 99

∠5 = 81 degrees

Hence, the measure of angle 4 is 35 degrees and the measure of angle 5 is 81 degrees

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Hope this helps you with your question.

Answer:

Step-by-step explanation:

I did it on a graphing app

The statement best describes the depth of the fish is that from starting position of 9 meters below sea level, the fish is descending 5 meters per second

In order to know which statement best describes the depth of the fish, we have to first understand what the equation means:

Given: the equation y = -5x – 9

This can be likened to the equation of a straight line, which is of the form y =mx +c,

where m is the slope and c is the y-intercept

Comparing the given equation with the equation of a line :

y = -5x – 9

Slope(m) = -5 and  y-intercept(c) = -9

The y-intercept represents the starting while the slope is the rate of descend

Therefore, what this means is that from starting position of 9 meters below sea level, the fish is descending 5 meters per second.

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Answer: (3,2)

Step-by-step explanation:

[tex]7x-7y=7\\\-4x-7y=-26[/tex]

subtract second equation from the first

[tex]11x=33\\x= 3[/tex]

plug x = 3 back into first equation

[tex]7(3) - 7y = 721 - 7y = 7-7y = -14\\y = -2[/tex]

Answer:

x=3 y=2

Step-by-step explanation:

The weighted average of the weighted points on the number line is -0.2.

A weighted average refers to the average of a data set that considers certain numbers as more important. Weighted averages are commonly used in statistical analysis, stock portfolios and teacher grading averages. In order to determine the weighted average of the weight points on the number line:

Hence, the average weight is -0.2.

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75% of the eruptions lasted between 1.77 and 4.93 minutes.

Chebyshev's Theorem calculates the proportion of observations that are within a given number of standard deviations of the mean. This theorem is applicable to many different probability distributions. Chebyshev's inequality is another name for Chebyshev's theorem.

According to Chebyshev’s theorem, the proportion of the data lying within k standard deviations of the mean is always at least 1 – 1/k^2, where k>1.

Given

Mean = 3.35

SD = 0.79

Mean – 1*SD = 3.35 – 1*0.79

= 3.35 – 0.79

= 2.56

Mean + 1*SD =3.35 + 1*0.79

= 3.35 + 0.79

= 4.14

Mean – 2*SD =3.35 – 2*0.79

= 3.35 – 1.58

= 1.77

Mean + 2*SD =3.35 + 2*0.79

= 3.35 + 1.58

= 4.93

Here, we have k = 2

For k = 2,

= 1- (1/k2)

= 1- (1/(2)2

= 1- ¼

= ¾

at least ¾ or 75% of all values lie within 2 standard deviations of the mean.

Therefore 75% of the eruptions lasted between 1.77 and 4.93 minutes.

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Answer: Write an equation in standard form that has a y-intercept at (0,-3) and also contains the point (4,5)

Step-by-step explanation:

Answer:

h

Step-by-step explanation:

i did the quize good luck

Answer:

i dont see image..

Step-by-step explanation:

Answer: D. Y-2 = -7/4(X+9)

The rigid transformation of the pre-image ΔABC, that produces the image ΔDEF is option E as follows;

E. [tex]R_{(90^{\circ},\,(0,\, 0))}[/tex]

A rigid transformation is one in which the distances between each pair of points on the pre-image is preserved on the image, such that the pre-image and the image have the same size.

The coordinates of the vertices of ΔABC are;

A(-3, -3), B(-1, -4), C(-3, -4)

The coordinates of the vertices of ΔDEF are; D(-3, 3), E(-4, 1), F(-4, 3)

The formula for the rotation of a point (x, y) 90° clockwise about the origin is presented as follows;

Pre-image point [tex]{}[/tex] (Rotation 90° clockwise)  Image point after rotation

(x, y)            [tex]{}[/tex]                        ⇒               [tex]{}[/tex]           (-y, x)

The points in the image ΔDEF of pre-image triangle ΔABC which corresponds to points on ΔABC are;

Vertex A in triangle ΔABC corresponds to vertex D on triangle ΔDEF

Vertex B in triangle ΔABC corresponds to vertex E on triangle ΔDEF

Vertex C in triangle ΔABC corresponds to vertex F on triangle ΔDEF

The transformation of (x, y) ⇒ (-y, x), (which is the transformation of a 90° clockwise rotation about the origin), on the vertices of ΔABC are;

A(-3, -3)    [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex]  D(-3, 3)

B(-1, -4)    [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex]  D(-4, 1)

C(-3, -4)    [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex]  F(-4, 3)

Therefore, the triangle ΔDEF can be obtained from the triangle ΔABC by a rotation of 90° clockwise about the origin.

The correct option is; E [tex]R_{(90^{\circ}, (0, \,0))}[/tex]

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