The vertex of this parabola is at (3,-2). when the x-value is 4, the y-value is 3. whatis the coefficient of the squared expression in the parabolas equation

Given : AB = 44 + 3x

BC = 33 + x

CD = 64 − x

AD = 48 − 2x.

Opposite sides are AB and CD.

BC and AD.

Setting AB equals CD

We get

44 + 3x = 64 − x

Adding x on both sides, we get

44 + 3x+x = 64 − x+x

44 +4x = 64.

Subtracting 44 from both sides, we get

44-44 +4x = 64 - 44.

4x =20

Dividing both sides by 4, we get

x= 5.

Let us plug x=5 to find the length of each side, we get

AB = 44 + 3x = 44 +3(5) = 44 + 15 = 59 cm

BC = 33 + x = 33 + 5 = 38 cm

CD = 64 − x = 64 - 5 = 59 cm

AD = 48 − 2x = 48 - 2(5) = 48 - 10 = 38 cm.

[tex]11\dfrac{1}{6}\cdot4\dfrac{2}{7}=\dfrac{11\cdot6+1}{6}\cdot\dfrac{4\cdot7+2}{7}=\dfrac{67}{6}\cdot\dfrac{30}{7}=\dfrac{67}{1}\cdot\dfrac{5}{7}=\dfrac{335}{7}\\\\=47\dfrac{6}{7}[/tex]

You put x from your question its going to be multiply by the fraction.

And it gave us ⇒ [tex]11\frac{1}{6}* 4 \frac{2}{7}[/tex]

First you had to convert by the mixed numbers into improper fractions.

And it gave us ⇒ [tex]=\frac{67}{6}*4\frac{2}{7}[/tex]

Then you convert by the mixed numbers again into improper fractions.

And it gave us ⇒ [tex]\frac{67}{6}* \frac{30}{7}[/tex]

You can also cross it out by the common factor of 6.

And it gave ⇒ [tex]\frac{67}{1}*\frac{5}{7}[/tex]

Next you had to multiply by the fraction.

And it gave us ⇒ [tex]\frac{67*5}{1*7}[/tex]

And then multiply the numbers.

[tex]67*5=335[/tex]

And it gave us ⇒ [tex]\frac{335}{1*7}[/tex]

You can also multiply the numbers again.

[tex]7*1=7[/tex]

And it gave us ⇒ [tex]\frac{335}{7}[/tex]

Finally you had to convert into the improper fraction to mixed their numbers.

[tex]\frac{335}{7}=47 \frac{6}{7}[/tex]

Final answer ⇒ 47 6/7

You can also round up to the nearest tenths is 47.90= 48.00

Hope this helps! And thank you for posting your question at here on brainly, and have a great day. -Charlie

Answer: Two consecutive square numbers be 16 and 9.

Step-by-step explanation:

Let first consecutive square number be x²

Let second consecutive square number be (x+1)²

According to question,

[tex]x^2\times (x+1)^2=144[/tex]

Now we'll do this by factorisation,

[tex]144=2\times2\times2\times2\times3\times3\\\\144=16\times 9[/tex]

So, two consecutive square numbers are 16 and 9

Consecutive numbers are numbers that follow one another.

The consecutive squares are: 9 and 16

Let the bigger square be x^2

So, we have:

[tex]\mathbf{(x - 1)^2 \times x^2 = 144}[/tex]

Express 144 as 12^2

[tex]\mathbf{(x - 1)^2 \times x^2 = 12^2}[/tex]

Take square roots of both sides

[tex]\mathbf{(x - 1)\times x = 12}[/tex]

Expand

[tex]\mathbf{x^2 - x = 12}[/tex]

Rewrite as:

[tex]\mathbf{x^2 - x - 12 = 0}[/tex]

Expand

[tex]\mathbf{x^2 - 4x +3x- 12 = 0}[/tex]

Factorize

[tex]\mathbf{x(x - 4) +3(x- 4) = 0}[/tex]

Factor out x - 4

[tex]\mathbf{(x +3) (x- 4) = 0}[/tex]

Solve for x

x= -3 or x = 4

x cannot be negative.

So: x = 4

Square both sides

[tex]\mathbf{x^2 = 4^2}[/tex]

[tex]\mathbf{x^2 = 16}[/tex]

Calculate the smaller square

[tex]\mathbf{(x - 1)^2 = (4-1)^2}[/tex]

[tex]\mathbf{(x - 1)^2 = 9}[/tex]

Hence, the consecutive squares are: 9 and 16

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Answer:

Displacement versus time is velocity

Step-by-step explanation:

Displacement versus time is velocity

Acceleration is change in velocity over time

Speed is distance over time

Momentum is mass times velocity

The slope of a graph in physics can represent several different concepts, depending on the graph. On a distance-time graph, the slope stands for speed or velocity. Meanwhile, on a velocity-time graph, the slope signifies acceleration. Momentum is generally not represented by the slope.

In physics, the slope of a graph can indeed represent several concepts, but only when plotted correctly. These concepts include speed, velocity, acceleration, and momentum. However, when we're talking about a distance-time graph, the slope typically represents speed or velocity, depending on whether the direction of movement is accounted for or not. An increasing slope on such a graph indicates objects are moving at a faster speed or velocity over time.

On the other hand, in a velocity-time graph, the slope represents acceleration. Positive acceleration causes the velocity of an object to increase, while negative acceleration, or deceleration, slows it down. Similarly, if there is no change in the slope, it means the object is moving at a constant velocity.

Momentum, in general, is not represented by the slope of a graph but rather is the product of an object's mass and its velocity.

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it 200 each number the raito is ballones times 4

Answer:

1/4 = 3/12 and 1/6 = 2/12

Step-by-step explanation:

We are given two fractions with denominator 4 and 6.

To find the least common denominator, of 4 and 6.

Factorise 4 and 6.

4 = 2x2

6=2x3

Hence Least common denominator = 2x2x3 =12

Make the given fractions to equivalent fractions with common denominator 12.

1/4 = 1(3)/4(3) = 3/12 and

1/6 = 1(2)/6(2)= 2/12

Hence answer would be

3/12 and 2/12

To rewrite the fractions 1/4 and 5/6 with a least common denominator, find the least common multiple (LCM) of the denominators, which is 12. Multiply the numerators and denominators of each fraction by the appropriate factor to obtain the rewritten fractions.

To rewrite the fractions 1/4 and 5/6 with a least common denominator, we need to find the least common multiple (LCM) of the denominators, which in this case are 4 and 6.

To find the LCM, we can list the multiples of each denominator until we find a common multiple. For 4, the multiples are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ... And for 6, the multiples are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... The first common multiple we find is 12, so that is the least common denominator (LCD).

To rewrite 1/4 with the LCD of 12, we need to multiply both the numerator and the denominator by 3: (1 * 3) / (4 * 3) = 3/12.

To rewrite 5/6 with the LCD of 12, we need to multiply both the numerator and the denominator by 2: (5 * 2) / (6 * 2) = 10/12.

     Statements                                                                                               Reason

1. [tex]\angle A[/tex] and [tex]\angle B[/tex] are supplementary                    Given

2. [tex]m \angle A + m \angle B = 180^\circ[/tex]                Def of supplementary angles

3. [tex]m \angle A = 90^\circ[/tex]                                                                  Given

4. [tex]90^\circ + m \angle B = 180^\circ[/tex]               Substitution property of Equality

5. [tex]m \angle B = 90^\circ[/tex]                                Subtraction property of Equality

6. [tex]m \angle A = m \angle B[/tex]                           Substitution property of Equality

7. [tex]\angle A \cong \angle B[/tex]                                 Angle congruence postulate

When the measures of two angles are equal, then the angles are congruent by Angle congruence postulate.

Answer:

1.  and  are supplementary                    Given

2.                 Def of supplementary angles

3.                                                                   Given

4.                Substitution property of Equality

5.                                 Subtraction property of Equality

6.                            Substitution property of Equality

7.                                  Angle congruence postulate

When the measures of two angles are equal, then the angles are congruent by Angle congruence postulate.

Step-by-step explanation:

Answer:

  $5.99

Step-by-step explanation:

Purchase amounts are rounded to the penny.

(3/4 lb)×$7.99/lb = $5.9925 ≈ $5.99

Answer:

The correct answer is option D, the approximate population density of the bacteria in the dish is 4,246 bacteria / square inch

Step-by-step explanation:

They give us the diameter of the plate, then the first step is to calculate their area.

The area of a circle according to the diameter is:

[tex]A = \frac{\pi}{4}(d) ^ 2[/tex]

Where d is the diameter.

So:

[tex]A = \frac{\pi}{4}36\\ A = 9\pi\\ A = 28.274.inches ^ 2[/tex]

Now, to find the number of bacteria in per square inch, we divide [tex]\frac{120000}{28.274} = 4244.132.[/tex]

So, the correct answer is option D, the approximate population density of the bacteria in the dish is 4,246 bacteria / square inch

Leila's gross earnings are calculated by adding her base pay of $290 to her commission of $13.80, which is 3% of her sales over $500. For the week, her total gross earnings are $303.80.

The question involves calculating Leila's gross earnings for a week where she sold $960 worth of merchandise while working at Famous Footwear. To find her earnings, we need to calculate her base pay plus the commission on sales over $500.

Leila's base pay is $290 per week. Since she sold $960, the amount over $500 that is eligible for commission is $960 - $500 = $460. Her commission is 3% of this amount, which is 0.03 * $460 = $13.80.

Therefore, Leila's total gross earnings for the week are her base pay plus her commission: $290 + $13.80 = $303.80.

the answer is 87.96 your gonna have to trust me I don't have enough time to explain right now.

The standard form of a line:

[tex]Ax+By=C[/tex]

We have the equation of a line in the slope-point form:

[tex]y-3=\dfrac{1}{2}(x+6)[/tex]      use distributive property

[tex]y-3=\dfrac{1}{2}x+3[/tex]       add 3 to both sides

[tex]y=\dfrac{1}{2}x+6[/tex]        multiply both sides by 2

[tex]2y=x+12[/tex]       subtract x from both sides

[tex]-x+2y=12[/tex]      change the signs

[tex]x-2y=-12[/tex]

the answer to this question (-2,3)

Answer:

[tex]\text{The equation of line is }x=-4[/tex]      

Step-by-step explanation:

Given that line is passing through the point (-4, 0) and parallel to the y-axis.

we have to find the equation of the line.

[tex]\text{As the slope of y-axis is }\infty\text{ i.e }\frac{1}{0}[/tex]

Since the slope of parallel lines are equal therefore we have to find the equation of line with slope infinity and passing through the point (-4, 0).

The equation of line pass through the point (x',y') with slope m is

[tex]y-y'=m(x-x')[/tex]

The equation of line with slope infinity and passing through the point (-4, 0) is

[tex]y-0=\frac{1}{0}(x-(-4))[/tex]

[tex]x+4=0[/tex]

[tex]x=-4[/tex]

which is required equation.

Hence, option 1 is correct.

11-7=4

7*4=28

28is your answer

16/13/4=

64/13

4and12/13

From a 16 foot board, 4 full pieces each 3 1/4 feet long can be cut. Moreover, 16.0 inches, a common spacing for vertical studs, is equivalent to 40.64 centimeters.

To determine how many lengths of 3 1/4 feet can be cut from a 16 foot board, we need to divide the total length of the board by the length of each desired piece. First, we convert the mixed number 3 1/4 to an improper fraction, 13/4. Then, we perform the division: 16 feet divided by 13/4 feet.

This calculation can be set up as follows:

(16 feet) \/ (13/4 feet) = (16 feet) × (4/13) = (64/13) feet = 4 remainder 12/13

Therefore, you can cut 4 full pieces that are 3 1/4 feet long from a 16 foot board, with a remainder of 12/13 of a foot.

If we want to convert the placement of vertical studs, which are typically 16 inches apart, to centimeters, we use the conversion factor that 1 inch equals 2.54 centimeters. 16.0 inches multiplied by 2.54 equals 40.64 centimeters.

The ball hits the ground at unknown time (t) when the height (h) = 0

h(t) = -16t² + vt + h    ⇒ v = 64, h = 0, h(t) = 0, find t

 0  = -16t² + 64t

 0  = -16t(t - 4)

0 = -16t       or    0 = t - 4

  t = 0         or        t = 4

It starts at t = 0 seconds and ends at t = 4 seconds

Answer: B

Final answer:

Using the kinematic equation for vertical motion, we find that the golf ball will hit the ground after 4 seconds. We factor the kinematic equation to solve for the time given initial velocity and gravity's acceleration, ignoring the 0 time solution. TΔherefore, the correct option is b.

Explanation:

The question asks after how many seconds a golf ball hit from ground level with an initial vertical velocity of 64 ft/s will hit the ground. This problem involves kinematic equations of motion under the influence of gravity. We can use the equation for vertical motion: distance = initial velocity × time + 0.5 × acceleration × time². Since the ball returns to ground level, the distance covered is 0. Taking downward as positive, gravity's acceleration is +32 ft/s² (the usual acceleration due to gravity in units of ft/s²). We can rearrange the equation to solve for time (t): 0 = 64t + 0.5 × 32t². Factoring out t gives us t(64 + 16t) = 0, and solving for t gives us t = 0 or t = -64/16 = -4 seconds. Since time cannot be negative in this context, the positive solution reflects the time after launch, thus the answer is 4 seconds, which is option b.

3,744 inches. You would multiply 312 and 12, since there is 12 inches in a foot, to get 3,744 inches.

Hope this helped! :)

If the points P, Q and R are collinear, then a slope of line PQ and a slope of line QR are equal.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

PQ → (0, 3), (2, 0).

Substitute:

[tex]m=\dfrac{0-3}{2-0}=\dfrac{-3}{2}=-1.5[/tex]

QR → (2, 0), (4, -3).

Substitute:

[tex]m=\dfrac{-3-0}{4-2}=\dfrac{-3}{2}=-1.5[/tex]

CORRECT :)

Answer:

-3/2

Step-by-step explanation:

I just did this lesson.

The line has a slope of -3/2

Answer:

 Expression for percent of survey participants who chose fishing = [tex]\frac{29}{47} *100[/tex]

Explanation:

 Total number of boys = 60

 Number of boys who took part in survey = 18 + 29 =47

 Number of boys who chose fishing = 29.

 Percentage of an outcome = (Number of favorable outcome/ Total number of outcome) x 100

 Percentage of boys who chose fishing = (29/47)x100

 Expression for percent of survey participants who chose fishing = [tex]\frac{29}{47} *100[/tex]

To find the percent of survey participants who chose fishing, divide the number of boys who chose fishing by the total number of boys who completed the survey and multiply by 100. In this case, the percent is 48.33%.

To find the percent of survey participants who chose fishing, we need to divide the number of boys who chose fishing by the total number of boys who completed the survey and then multiply by 100. In this case, 29 boys chose fishing out of 60 boys who completed the survey. So the expression that gives the percent of survey participants who chose fishing is:

(29/60) * 100 = 48.33%

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The non real roots 1+4i and -4i will also have their complements as roots:- 1 - 4i and 4i

So the least number of roots = 5 and this will also be the least possible degree of the polynomial.

answer 5

Answer:

D

Step-by-step explanation:

the smallest integer x can be is 11 because it has to be greater than 10

The smallest integer x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle is 11

Using the triangular theorem which states that the sum of any two sides of a triangle must be less than the third side.

Given the side length of the triangle to be a, b and c

a = x

b = x+5

c = 2x - 15

According to the theorem;

b < a+c  

x+5 < x + 2x - 15

x + 5 < 3x - 15

Collect the like terms

x - 3x < -15 - 5

-2x < -20

x > -20/-2

x > 10

Since x is greater than 10, let x be 11

Hence the smallest integer x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle is 11

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Answer:

7.9 meters left. or 790 cm

Step-by-step explanation:

-58.82% is the percent increase

V=480cm³ . 10 and 12