An isosceles trapezoid ABCD with height 2 units has all its vertices on the parabola y=a(x+1)(x−5). What is the value of a, if points A and D belong to the x−axis and m∠BAD=60°

Answer:

x=-7

Step-by-step explanation:

Subtract 33 from -30 (because subtraction is the opposite of addition.

that's leaves 9x=-63

you want to isolate the variable so divide -63 by 9 (since division is the opposite of multiplication)

x=-7

Answer:

8 kilometer per hour

Step-by-step explanation:

Given: Dani spend her summers at her grandparents cabin in canada. The cabin is [tex]42[/tex] kilometers upriver from the nearest town. The river has a downstream current of [tex]4[/tex] kilometers per hour.

To Find: If Dani can canoe from the cabin to town and back in [tex]14[/tex] hours, what is her average canoeing speed in still water.

Solution:

Let the speed of Dani in still water is  [tex]=\text{s}[/tex]

speed of downstream current is          [tex]=4\text{kmph}[/tex]

speed of Dani in downstream current [tex]=\text{s}+4[/tex]

speed of Dani in upstream current      [tex]=\text{s}-4[/tex]

Now,

Total time taken by Dani to canoe from the cabin to town and back [tex]=14\text{hours}[/tex]

[tex]\frac{42}{\text{s}-4}+\frac{42}{\text{s}+4}=14[/tex]

[tex]{\text{s}}^2-6\text{s}-16=0[/tex]

[tex](\text{s}-8)(\text{s}+2)[/tex]

[tex]\text{s}=8,-2[/tex]

as speed can't be negative the average speed of dani in still water is [tex]8\text{kmph}[/tex]

Answer:

No

Step-by-step explanation:

Direct variation: two variables, one variable is a constant multiple of another variable

y = k x  .... k constant

-x+4y=-2

4y = x - 2

y = 1/4 x -1/2  ..... y = k x + b    y is not a simple multiple of x

Answer:

I believe the answer is 55.

Step-by-step explanation:

Because if Malachy gets 44 and the ratio is 4:5 it would only make sense if Paul got 55.

Answer:

Step-by-step explanation:

25 total people

5 drank coffee and tea

tea drinkers only : 10 - 5 = 5

coffee drinkers only : 12 - 5 = 7

total people who drank anything : 7 + 5 + 5 = 17

number of people who drank neither : 25 - 17 = 8 <=====

Lo has time to run 7 errands between work and dinner.

Lo has 1 hour and 45 minutes between leaving work at 6:15 p.m. and meeting her friends at 8:00 p.m.

She needs  around 1/4 of an hour for each errand.

To find out how many errands she can run, we divide the total time available by the time required for each errand:

Convert 1 hour 45 minutes to minutes: 1 hour = 60 minutes, so 1 hour 45 minutes = 60 + 45 = 105 minutes.

Calculate how many errands she can run:  105/15 = 7.

Therefore, Lo has time to run 7 errands between work and dinner.

Answer:

11 cars

Step-by-step explanation:

There are 20 cars in my building's parking lot, 15 cars are 4-door, then

[tex]20-15=5[/tex] cars are 2-door.

5 cars are 2-door, 4 of them are 2-door and white, then

[tex]5-4=1[/tex] car is 2-door and red.

12 cars are red, 1 car is 2-door and red, then

[tex]12-1=11[/tex] cars are 4-door and red.

(1/3) are red  =  30 *1/3  = 10 are red

So...20  are white

50% are 4 door   = 15  are 4 door

So....15 are 2 door

8 are 2 door  and white.....so 12 are 4 door and white  since we have 20 white total

And since 15 are 4 door  and 12 of these are white...then 3 must be 4 door and red

Make a two-way table as follows:

                                           RED                            WHITE

2-DOOR                               7                                        8

4-DOOR                               3                                      12

TOTALS                               10                                     20

 So, it looks like you have 3 cars that are red and have 4 doors.

Answer:

The length of A'C' will also be 5 units.

Step-by-step explanation:

If a reflection takes triangle CAT to C'A'T', what is A'C'?

Starting with ΔCAT triangle as shown in figure (a).

Reflections are said to be Isometries as it does preserve the distances.

If the shape or triangle ΔCAT reflected it will remain the same size. As a result, the reflected image would be 'congruent' to the original object.

Lets suppose, ΔCAT is reflected across  y axis.  

The rule for reflection of the point (x,y) across the y-axis is actually the point (-x,y).

Reflect a point across the y-axis, the y-coordinate will remain the same, but the x-coordinate will be transformed into its opposite (the sign of x-coordinate will be changed).

C(0, 0)   →  C'(0, 0)

A(-2, 1)  →  A'(2, 1)

T(-1, 4)  →  T(1, 4)

length of Side AT = 3 units

length of Side TC = 4 units

length of Side AC = 5 units

As reflections are said to be Isometries as it does preserve the distances.

So, if ΔCAT reflected is reflected across  y axis. ΔC'A'T' preserves the distances. The length of each segment of the preimage would be equal to its corresponding side in the image as shown in figure (a).

So, the length of A'C' will also be 5 units.

Keywords: reflection, transformation, triangle

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Answer:

The length of A'C' will also be 5 units.

Step-by-step explanation:

Answer: y = 8x

Step-by-step explanation: please see attachment for explanation

Answer:

y=8x

Step-by-step explanation:

Answer:

0.044117

Step-by-step explanation:

We have the equation:

3 ÷ 68 = 0.044117

Calculated to 6 decimal places.

How far do you want to calculate the decimal places for the answer? Here are some examples:

   31 divided by 16 = 1.937500 calculating to 6 decimal places

   31 divided by 16 = 1.937 calculating to 3 decimal places

   22 divided by 15 = 1.466666666 calculating 9 decimal places

   22 divided by 15 = 1.466666 calculating 6 decimal places

   22 divided by 15 = 1.466 calculating to 3 decimal places

Note that this is not the same as rounding to a specific number of decimal places. For example, 22 divided by 15 = 1.466 when calculated to 3 decimal places because you stop once you reach the third decimal place. On the other hand, 22 divided by 15 = 1.467 when rounded to 3 decimal places. In order to round to the third decimal place you must calculate to at least the fourth decimal place so that you know how to round the third decimal place

Hope This Will Help!!!!! :) :)

Answer: 22  R (Remainder) 2

Step-by-step explanation:

First, see how many times 3 goes into 6.

3x2=6

So, subtract 6 from 6, which equals 0. Bring down the 8. See how many times 3 goes into 8.

3x2=6

3 goes into 8 two times. Subtract 6 from 8, which equals 6. 8 minus 6 equals 2, which becomes the remainder.

Answer:

0.4714

Step-by-step explanation:

The diagram shows:

Then the total number of registered voters is

[tex]3,371,556+3,006,202=6,377,758[/tex]

Thus, the probability that a registered voter voted in the election is

[tex]\dfrac{3,006,202}{6,377,758}\approx 0.4714[/tex]

The probability that a registered voter participated in the election can vary significantly. In the U.S. 2020 Presidential Election, 77 percent of registered voters voted. However, it's vital to consider the full context, including the total and voting-age populations, and understand that turnout rates can vary by factors like age.

The probability that a registered voter voted in the election depends on various factors such as the year, voters' ages and other socioeconomic factors. In the U.S., for instance, in the 2020 Presidential Election, 77 percent of registered voters cast their vote. However, it's vital to keep in mind that while this data is significant, it doesn't give full context without considering factors such as the eligible voting-age population or the total population.

Furthermore, it's useful to understand the concept of a 90 percent confidence level when interpreting statistics related to voter turnout. In this context, the statement 'We estimate with 90 percent confidence that between 56.4 percent and 63.6 percent of all students are registered voters.' suggests that there's a 90 percent probability that the actual percentage of registered voters among all students falls between the specified range.

On a related note, the age group also influences voter turnout. For instance, in 2016, 51 percent of eligible voters between the ages of eighteen and twenty-four registered, but only 39 percent of them voted. Conversely, 75 percent of eligible voters aged from sixty-five to seventy-four registered, and of these, 68 percent voted. Hence, the probability of a registered voter voting in the election can vary quite a bit based on age, among other factors.

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Answer:

what decimals?

Step-by-step explanation:

Answer:The answer can be calculated by doing the following steps;

Step-by-step explanation:

Answer:

the Answer should be 2 2/9

Step-by-step explanation:

I can assure you i i worked this problem out and i'm 100% sure :) Hope i helped some of ya'll! :>

Answer:

1680

Step-by-step explanation:

12+7+6=25

12+20*12=252

20+20+7=47

7*20*12=1680

Answer: -4x+2

Step-by-step explanation: Simplify the expression.

Hope this helps you out! ☺

[tex](h-p))(y) = -y^3-3y^2+7y+5[/tex]

Step-by-step explanation:

Given

[tex]h(y) = -3y^2+5\\p(y) = y^3-7y[/tex]

We have to find the difference of two functions given

So,

[tex](h-p)(y) = h(y) - p(y)\\= (-3y^2+5)-(y^3-7y)\\=-3y^2+5-y^3+7y\\=-y^3-3y^2+7y+5[/tex]

Hence,

[tex](h-p))(y) = -y^3-3y^2+7y+5[/tex]

Keywords: Functions, variables

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Answer:

Y equals three x minus two

Final answer:

The equation y = 3x - 2 represents a line with a slope of 3 and a y-intercept of -2.

Explanation:

The equation y = 3x - 2 represents a line in the Cartesian coordinate system. This equation follows the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope (m) is 3, meaning that for every one unit increase in x, y increases by 3 units.

The y-intercept (b) is -2, indicating that the line crosses the y-axis at the point (0, -2). To find an equation for a line given a point and a slope, you can use the point-slope form, y - y1 = m(x - x1). With the point (-7, 1) and slope 3, the equation is y - 1 = 3(x + 7).

The formula to calculate the height (h) of a cone, given its volume (V) and radius (r), is [tex]\(h = \frac{3V}{\pi r^2}\)[/tex]. This formula isolates the height by multiplying both sides of the volume formula by [tex]\(3/\pi r^2\).[/tex]

To isolate the height (h) in the volume formula of a cone ([tex]\(V = \frac{1}{3}\pi r^2 h\)[/tex]), we can rearrange the formula to solve for h.

Starting with the given formula:

[tex]\[ V = \frac{1}{3}\pi r^2 h \][/tex]

To find h, we can multiply both sides of the equation by [tex]\(3/\pi r^2\)[/tex] to isolate h:

[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]

Therefore, the formula to calculate the height (h) of a cone, given its volume (V), radius (r), is:

[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]

This formula allows you to determine the height of a cone when you know its volume and radius.

Final answer:

To calculate the force required, we use the formula F = k * (W / sqrt(V)) * (1 / d), where F is the force, W is the weight, V is the velocity, and d is the distance. We can find the constant of variation k by substituting the given values of F, W, V, and d into the formula. After finding k, we can plug in the new values of W, V, and d to calculate the force required.

Explanation:

To solve this problem, we can use the formula F = k * (W / sqrt(V)) * (1 / d), where F is the force, W is the weight, V is the velocity, and d is the distance.

First, we can calculate the constant of variation k by substituting the given values of F, W, V, and d into the formula. This gives us: 36 = k * (120 / sqrt(100)) * (1 / 50).

Solving for k, we get k = 36 * 100 * 50 / 120 = 1500.

Next, we can plug in the new values of W, V, and d into the formula and solve for F. Substituting W = 200, V = 256, and d = 800, we have: F = 1500 * (200 / sqrt(256)) * (1 / 800).

Simplifying further, we get F = 1500 * 200 / (16 * 800) = 18.75 Newtons.

Answer:

The total price of the meal after tax and tip is $31.62.

Step-by-step explanation:

Given:

Their bill is = $25.40.

Sales tax = 5.5%.

Tip to waitress = 18%.

Now, to find the total price of the meal after tax and tip.

So, to get the price of the meal after sales tax :

$25.40 + 5.5% of $25.40.

[tex]=25.40+\frac{5.5}{100} \times 25.40.[/tex]

[tex]=25.40+\frac{139.70}{100}[/tex]

[tex]=25.40+1.397=\$26.797[/tex]

Now, to get the total price after tax and tip:

$26.797 + 18% of $26.797.

[tex]=26.797+\frac{18}{100} \times 26.797[/tex]

[tex]=26.797+0.18\times 26.797[/tex]

[tex]=26.797+4.823[/tex]

[tex]=\$31.62.[/tex]

Therefore, the total price of the meal after tax and tip is $31.62.

Answer:

12.8oz.

Step-by-step explanation: 128 oz in a gallon/5/2

Answer:

3003 number of 5-member chess teams can be chosen from 15 interested players.

Step-by-step explanation:

Given:

Number of the interested players =  15

To Find:

Number of 5-member chess teams that can be chosen = ?

Solution:

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula[tex]nCr = \frac{n!}{r!(n - r)!}[/tex]

where

n represents the total number of items,

r represents the number of items being chosen at a time.

Now  we have n = 15 and r = 5

Substituting the values,

[tex]15C_5 = \frac{15!}{5!(15- 5)!}[/tex]

[tex]15C_5 = \frac{15!}{5!(10)!}[/tex]

[tex]15C_5 = \frac{15!}{5!(10)!}[/tex]

[tex]15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{5 \times 4 \times 3 \times 2 \times 1(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)}[/tex]

[tex]15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11}{(5 \times 4 \times 3 \times 2 \times 1)}[/tex]

[tex]15C_5 = \frac{360360}{120}[/tex]

[tex]15C_5 = 3003 [/tex]

Final answer:

The expression 12.70 - n + 9 + n/4 is simplified by combining like terms, resulting in 21.70 + 1.25n.

Explanation:

The student's question involves simplifying the expression 12.70 - n + 9 + n/4. To simplify this expression, we first combine like terms. As 'n' and 'n/4' are like terms, we simplify by combining them which can be done by adding 1n (which is the same as n) with 1/4n. Here are the steps:

This completes the simplification process for the given expression. It is important to ensure terms are like terms before combining them and to perform accurate arithmetic operations when combining numerical values.

Answer:

[tex]A'(-0.25,0.75)\\\\B'(1.75,-0.25)\\\\C'(-1,-0.25)[/tex]

Step-by-step explanation:

A Dilation is defined as  a transformation in which the image and the pre-image have the same shape, but their sizes are different.

When the scale factor is greater than 1, the image obtained after the  dilation is greater than the pre-image and it is an "Enlargement".

When the scale factor is is between 0 and 1,  the image obtained after the  dilation is smaller than the pre-image and it is an "Reduction".

In this case you know that the triangle ABC was dilated by this scale factor:

[tex]scale\ factor=\frac{1}{4}[/tex]

With the origin as the center of dilation.

Since:

[tex]0<\frac{1}{4}<1[/tex]

It is a Reduction.

You can identify that the vertices of the triangle ABC are:

[tex]A(-1,3)\\\\B(7,-1)\\\\C(-4,-1)[/tex]

So you need to multiply the coordinates of each vertex  of the triangle ABC by [tex]\frac{1}{4}[/tex], in order to get the coordinates of the triangle A'B'C. Then, you get:

[tex]A'=(\frac{1}{4}(-1),\frac{1}{4}(3))=(-0.25,0.75)\\\\B'(\frac{1}{4}(7),\frac{1}{4}(-1))=(1.75,-0.25)\\\\C'(\frac{1}{4}(-4),\frac{1}{4}(-1))=(-1,-0.25)[/tex]

The coordinates of the vertices of triangle A'B'C' include the following;

A' (-1/4, 3/4).

B' (7/4, -1/4).

C' (-1, -1/4).

In Mathematics and Euclidean Geometry, dilation is a type of transformation that is used for altering the dimensions of a geometric figure, but not its shape.

In this scenario and exercise, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:

Ordered pair A (-1, 3) → (-1 × 1/4, 3 × 1/4) = Ordered pair A' (-1/4, 3/4).

Ordered pair B (7, -1) →  (7 × 1/4, -1 × 1/4) = Ordered pair B' (7/4, -1/4).

Ordered pair C (-4, -1) →  (-4 × 1/4, -1 × 1/4) = Ordered pair C' (-1, -1/4).

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Missing information;

Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. The triangle was dilated using a scale factor of 1/4.

The coordinates of the vertices of triangle ABC are given. You can use the scale factor to find the coordinates of the dilated image.

Enter the coordinates of the vertices of triangle A'B'C' below.

(Decimal values may be used)

Answer:

(x, y ) → (- y, - x )

Step-by-step explanation:

Consider the coordinates of corresponding vertices of the 2 triangles, that is

A(1, 7 ) → D(- 7, - 1 )

Note the coordinates of D are the negative reversals of A

Thus (x, y ) → (- y, - x )

Answer:

16 hours acts of television we must watch in eighth weeks to meet your goal.

Step-by-step explanation:

This problem requires us to determine the total hours we spend on watching television in eight week if we spend two hours watching television each week. This problem can easily be solved by multiplying 2 hours with number of week that is 8 week.

= 8 * 2 = 16

The width of rectangle is 6.

Step-by-step explanation:

Given,

Area of rectangle; w²+4w=60

As w is the width, we will solve the equation to find w.

[tex]w^2+4w=60[/tex]

Subtracting 60 from both sides

[tex]w^2+4w-60=0[/tex]

Factorizing the equation;

[tex]w^2+10w-6w-60=0\\w(w+10)-6(w+10)=0\\(w+10)(w-6)=0[/tex]

Either,

w+10=0         => w=-10

Or,

w-6=0           =>w=6

As width cannot be negative, therefore

Width = 6

The width of rectangle is 6.

Keywords: area, rectangle

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Answer:

Karen has 6 quarters and 2 dimes

Step-by-step explanation:

Let

x ----> the number of quarter coins Karen has

y ----> the number of dimes coins Karen has

Remember that

[tex]1\ quarter=\$0.25\\1\ dime=\$0.10[/tex]

we know that

Equation that represent the amount of coins Karen has

[tex]x+y=8[/tex]

isolate the variable y

[tex]y=8-x[/tex] ----> equation A

Equation that represent the value of coins Karen has

[tex]0.25x+0.10y=1.70[/tex] ----> equation B

Solve the system of equations by substitution

substitute equation A in equation B

[tex]0.25x+0.10(8-x)=1.70[/tex]

solve for x

[tex]0.25x+0.80-0.10x=1.70[/tex]

[tex]0.25x-0.10x=1.70-0.80[/tex]

[tex]0.15x=0.90[/tex]

[tex]x=6[/tex]

Find the value of y

[tex]y=8-x[/tex] ----> [tex]y=8-6=2[/tex]

therefore

Karen has 6 quarters and 2 dimes

   Statement                            Reason

-------------------------------------------------------------------------------------

1. CD=DC                        Reflexive Property

2. D-midpoint of AB                Given

3. AD=BD                         Definition of Midpoint

4. CD⊥AB                                  Given

5. m<CDA=m<CDB         Definition of Perpendicular Lines

6. ΔACD≅ΔBCD                           SAS

$ 82.03  in 25 yrs

$ 74.30 in 20 yrs

Step-by-step explanation:

Every year, the cost of the jeans increases by 2% which is equivalent to 0.02 in decimal points. The get the cost of the jean for every year we are multiplying the principle cost by;

100 % + 2% = 102% OR 1.02 in decimal

This increase occurs 25 time for 25 years. Therefore;

1.02 ^ 25 * 50

= 1.641 * 50

= $ 82.03

To get the price in 20 years;

1.02 ^ 20 * 50

= 1.486 * 50

= $ 74.30

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