(03.02 LC)
Look at the figure below:

Triangle ABC with a segment joining vertex A to point D on side BC.

Which information is required to prove that angle ABD is congruent to angle ACD? (6 points)


Segment AC is congruent to segment AB.

Segment AD is congruent to segment AC.

Segment BD is congruent to segment AD.

Segment AB is congruent to segment BD.

Answer:5%

Step-by-step explanation:

Given, cost of two table lamps including tax = $42

Therefore, cost of one table lamp including tax =[tex]\frac{42}{2}[/tex]=21$

Given, cost of one table lamp before tax = $20

Hence tax amount on each lamp = $21 - $20 = $1

Hence tax rate payed[tex]=\frac{\text {tax amount}}{\text {Sale Price}}\times 100[/tex]

[tex]=\frac{1}{20}\times {100}=5\%[/tex]

Answer:

Assume that the cost of the milk is x.

We are given that a sandwich costs 0.75$ more than the cost of milk. This means that:

cost of sandwich = cost of milk + 0.75

cost of sandwich = x + 0.75

Now, the customer bought 4 sandwiches and 4 containers of milk at the cost of 7$.

We will transform this into an equation as follows:

total cost = cost of 4 sandwiches + cost of 4 containers of milk

7 = 4(x+0.75) + 4(x)

Solve the above equation to get x as follows:

7 = 4x + 3 + 4x

7-3 = 8x

8x = 4

x = 0.5

Therefore:

cost of milk = x = $0.5

cost of sandwich = x+0.75 = 0.5+0.75 = $1.25

Answer:

$1.25

Step-by-step explanation:

The question is about the probability of sum of numbers obtained after rolling two dice. There are 36 possible outcomes of a roll of two dice. The probability of the event that the sum of numbers obtained is 4 or greater than 9 is 1/4.

The subject of this question is probability, focusing specifically on the sample space and likely outcomes of two number cubes, or fair six-sided dice, being rolled. Part (a) of the question asks for the sample space which includes all possible outcomes of a roll of two dice i.e., (1,1), (1,2), ..., (6,5), (6,6). There are 36 possible outcomes in total.

For part (b), we are finding the probability of the event that the sum of the numbers obtained after rolling the two dice is 4 or the sum of numbers obtained is greater than 9. There are 3 ways to get a sum of 4, i.e., (1,3), (2,2), (3,1), and 6 ways to get a sum greater than 9, i.e., (4,6), (5,5), (5,6), (6,4), (6,5), (6,6). That's 9 favorable outcomes out of the total of 36. Therefore, the probability of the event is 9/36, which simplifies to 1/4.

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The probability of getting a sum of 4 or a sum greater than 9 is determined by dividing the number of favorable outcomes by the total number of outcomes which is 13/36

The sample space of rolling two number cubes can be listed by considering all the possible outcomes when rolling two dice. Since each die has 6 sides numbered from 1 to 6, there are a total of 36 possible outcomes.

The probability of getting a sum of 4 or a sum greater than 9 can be calculated by determining the number of favorable outcomes and dividing it by the total number of outcomes.

In this case, there are 3 favorable outcomes for a sum of 4 (1+3, 2+2, 3+1) and 10 favorable outcomes for a sum greater than 9 (4+6, 5+5, 5+6, 6+4, 6+5, 6+6).

Therefore, the probability is (3+10)/36, which simplifies to 13/36.

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Answer:

The percentages are 267% and 400% respectively.

Step-by-step explanation:

To find the answers of these, you need to divide the second number by the first. This will give you the percentage.

2/3 ÷ 1/4 = 8/3 = 2.67 = 267%

You can do the same for the second one.

2/3 ÷ 1/6 = 12/3 = 4 = 400%

To determine what percentage 2/3 is of 1/4, calculate (2/3) / (1/4) * 100, resulting in 266.67%. To find the percentage 2/3 is of 1/6, calculate (2/3) / (1/6) * 100, resulting in 400%.

When finding the percent of a fraction, you are essentially calculating what part of 100 the fraction represents. To find what percent 2/3 is of 1/4, you need to set up a proportion such that 2/3 is to 1/4 as x is to 100.

To solve this, you divide 2/3 by 1/4 and then multiply by 100:

Percent = (2/3) / (1/4) * 100

Percent = (2/3) * (4/1) * 100

Percent = 8/3 * 100

Percent = 800/3

Percent = 266.67%

Similarly, to find what percent 2/3 is of 1/6, you can use the same approach by dividing 2/3 by 1/6 and then multiplying by 100.

Percent = (2/3) / (1/6) * 100

Percent = (2/3) * (6/1) * 100

Percent = 12/3 * 100

Percent = 400%

Therefore, 2/3 is 266.67% of 1/4, and 400% of 1/6.

Answer:

y = 1/3 x +1

Step-by-step explanation:

y-5=1/3(x-12)

Distribute the 1/3

y-5 = 1/3x -1/3 *12

y-5 = 1/3 x -4

Add 5 to each side

y-5+5 = 1/3 x-4+5

y = 1/3 x +1

Answer:

x≠-12; x≠0

Step-by-step explanation:

A fraction denominator cannot be 0.

3x(x+12)≠0

if you multiply a number by zero, the product is also zero

3x≠0

x≠0

x+12≠0

x≠-12

Answer:

f(2) =5

Step-by-step explanation:

We have a function f(x) = 3x-1

When we find f(2) ,let x=2

f(2) = 3*2-1

      = 6-1

    =5

Convert mixed number to improper fraction:

[tex]1\dfrac{3}{4}=\dfrac{1\cdot4+3}{4}=\dfrac{4+3}{4}=\dfrac{7}{4}\\\\4\dfrac{1}{6}=\dfrac{4\cdot6+1}{6}=\dfrac{24+1}{6}=\dfrac{25}{6}\\\\1\dfrac{3}{4}\times4\dfrac{1}{6}=\dfrac{7}{4}\times\dfrac{25}{6}=\dfrac{7\times25}{4\times6}=\dfrac{175}{24}=\dfrac{168+7}{24}=7\dfrac{7}{24}[/tex]

Final answer:

To solve 1 3/4 x 4 1/6, we convert the mixed numbers to improper fractions and multiply them, resulting in an incorrect statement that the answer is 1/4; the calculated multiplication is 175/24, which can be further simplified.

Explanation:

To solve the multiplication problem 1 3/4 x 4 1/6, we'll first need to convert the mixed numbers into improper fractions.

For 1 3/4, which is 1 + 3/4, we convert it to an improper fraction by multiplying the whole number by the denominator and adding the numerator, which gives us (1*4) + 3 = 7/4.

For 4 1/6, which is 4 + 1/6, we convert it to an improper fraction by doing the same process: (4*6) + 1 = 25/6.

Now, we multiply the two improper fractions: (7/4) x (25/6).

To multiply fractions, we multiply the numerators together and the denominators together:

7 x 25 = 175
4 x 6 = 24

So, (7/4) x (25/6) = 175/24.

Finally, we simplify the improper fraction by dividing 175 by 24, which results in a mixed number or a decimal.

For this case we have the following variable:

We have then that Matthew spent 15% fewer hours at the beach than landen did.

Therefore, the number of hours Mateo spent at the beach is:

[tex]L - 0.15L = 0.85 L[/tex]

Answer:

The number of hours Mateo spent at the beach is:

[tex]L - 0.15L = 0.85 L[/tex]

Answer: No

Step-by-step explanation:

A function has exactly one y output for each x input, and since the input -1 has two outputs, -1 and 2, it is not a function.

Hi there,

The Answer is no

To solve This we need to Remember That a relation can only be a Function if one number from X goes to Y.

In This instance, -1 goes to 2 and -1, While 6 goes to 3 and 4 to 3

Keep In mind that All the number given are points

Hope this Has Helped

|~Adan |

Answer:

$6.15 an hour

Step-by-step explanation:

To find how much money our raise is, we can multiply the percent times our salary

6 * .025 = .15

Our raise is 15 cents an hour

Take what we were making plus our raise

6+.15

$6.15

This is what we will be making per hour.

[tex]VY=wxz\qquad\text{divide both sides by }\ V\\\\\boxed{Y=\dfrac{wxz}{V}}[/tex]

Answer:↓

98+36864

Step-by-step explanation:

Answer:

Rectangles and squares have 90° corner angles.

Answer:

Step-by-step explanation: Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

Final answer:

The formula for finding the median depends on whether the total number of data values is odd or even. If it is odd, the median is the middle value when the data is ordered from least to greatest. If it is even, the median is the average of the two middle values when the data is ordered.

Explanation:

The formula for finding the median depends on whether the total number of data values is odd or even. If it is odd, the median is the middle value when the data is ordered from least to greatest. If it is even, the median is the average of the two middle values when the data is ordered. For example, if you have the data set 2, 4, 6, 8, 10, the median would be 6 because it is the middle value. But if you have the data set 2, 4, 6, 8, the median would be (4+6)/2 = 5 because it is the average of the two middle values.

Answer:

yes

Step-by-step explanation:

one way to help is to just do 1x5=5 and add on the two zeros  to get 500

Answer:

True

Step-by-step explanation:

10 * 5 = 50

If we ad a zero to one of the numbers, we add a zero to the answer

100 * 5 = 500

10 * 50 = 500

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=\stackrel{doubled}{2r}\\ h=\stackrel{\textit{divided by 3}}{\frac{h}{3}} \end{cases}\implies V=\cfrac{\pi (2r)^2\left( \frac{h}{3} \right)}{3} \\\\\\ V=\cfrac{\pi (2^2r^2)\left( \frac{h}{3} \right)}{3}\implies V=\cfrac{~~\frac{4\pi r^2 h}{3}~~}{3}\implies V=\cfrac{4\pi r^2 h}{3\cdot 3}\implies \stackrel{\frac{4}{3}\textit{ of the original}}{V=\cfrac{4}{3}\cdot \cfrac{\pi r^2 h}{3}}[/tex]

Final answer:

When the radius is doubled and the height is divided by 3 in the volume formula for a cone, the new volume is 4/3 of the original volume.

Explanation:

The student has provided the formula 1/3 π r^2 • h, which represents the volume of a cone.

To find the ratio of the new volume to the original volume after the radius (r) is doubled and the height (h) is divided by 3, we must substitute these changes into the formula and simplify.

Original volume formula is V = 1/3 π r^2 • h.

If the radius is doubled (2r) and the height is divided by 3 (h/3), the new volume formula becomes

V' = 1/3 π (2r)^2 • (h/3).

After simplification, the new volume becomes V' = 1/3 π 4r^2 • h/3, which further simplifies to V' = 4/9 π r^2 • h.

Therefore, the ratio of the new volume V' to the original volume V is 4/3.

Answer: the equation is slope-intercept form y = -2/3x

Answer:

x=0.996

Step-by-step explanation:

[tex]3e^{2x} +5=27[/tex]

To take natural log ln , we need to get e^2x alone

Subtract 5 on both sides

[tex]3e^{2x}=22[/tex]

Now we divide both sides by 3

[tex]e^{2x}=\frac{22}{3}[/tex]

Now we take 'ln' on both sides

[tex]ln(e^{2x})=ln(\frac{22}{3})[/tex]

As per log property we can move exponent 2x before ln

[tex](2x)ln(e)=ln(\frac{22}{3})[/tex]

The value of ln(e) = 1

[tex]2x=ln(\frac{22}{3})[/tex]

Divide both sides by 2

[tex]x=\frac{ln(\frac{22}{3})}{2}[/tex]

x= 0.996215082

Round to nearest thousandth

x=0.996

Answer:

The coordinates of orthocenter of the triangle are (1,5).

Step-by-step explanation:

The given vertices are A(0,6), B(4,6) and C(1,3).

Orthocenter of a triangle is the intersection point of all altitudes.

The product of slopes of two perpendicular lines is -1.

The slope of AB is

[tex]m_{AB}=\frac{y_2-y_1}{x_2-x_1}=\frac{6-6}{4-0}=0[/tex]

The slope of AB is 0, therefore slope of line which is perpendicular to AB is [tex]\frac{-1}{0}[/tex].

Point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is the slope.

The equation of altitude on AB form C is

[tex]y-3=\frac{1}{0}(x-1)[/tex]

[tex]0=x-1[/tex]

[tex]x=1[/tex]                              ..... (1)

Slope of BC is

[tex]m_{BC}=\frac{y_2-y_1}{x_2-x_1}=\frac{6-3}{1-4}=1[/tex]

The slope of BC is 1 therefore the slope of altitude on BC from A is -1.

The equation of altitude on BC from A is

[tex]y-6=-1(x-0)[/tex]

[tex]y=-x+6[/tex]                         ..... (2)

Using (1) and (2) we get

[tex]x=1, y=5[/tex]

The  intersection point of two altitudes is (1,5). Therefore coordinates of orthocenter of the triangle are (1,5).

Answer:

11/16

Step-by-step explanation:

Answer:

Decimal: 0.6875 Fraction: 2.75/4

Step-by-step explanation:

To convert percent into a decimal you move the decimal point two places to the left. So 68.75% is equal to 0.6875.

To find the fraction form we know that 68.75% is 68.75/100 because percent is of one hundred. We can simply 68.75/100 by dividing the numerator and denominator by 25 and we get 2.75/4.  So 68.75% as a fraction is 2.75/4.

Answer:

Step-by-step explanation:

We are given value of sine trigonometric ratio = 0.9123.

We need to find the angle in degrees whose measure has a sine of 0.9123.

So, we need to find the value of [tex]sin^{-1}(0.9123)[/tex].

On plugging [tex]sin^{-1}(0.9123)[/tex] in calculator, we get

65.82°.

Now, we need to round it to the nearest whole degree.

Therefore, 65.82°≈ 66°.

Answer:

$887,761.38

Step-by-step explanation:

The principal amount the home is valued is $375,000 and it increases at a rate of 9% a year which is 0.09 and the amount of time it grew is 10 years. Therefore:

[tex]A_{final}=375000(1+0.09)^{10}=375000(1.09)^{10}=887761.38[/tex]

After 10 years the house is worth $887,761.38 if this trend continues

Answer:

$887,761.38

i know this i s the answer because i had a quiz.

PLz mark brainlest

Answer:

The sequence is: Refection across y-axis, Horizontal Shrink, Horizontal Translation and Reflection across x-axis.

Step-by-step explanation:

Since, we are given f(x) = square root x.

The sequence of transformations which transform f(x) into g(x) is given by:

1. Reflection across y-axis i.e. f( x ) to f( -x )

2. Horizontal Shrinking i.e. f( -x ) to f( -x/2 )

3. Horizontal Translation i.e. f( -x/2 ) to f( -x/2 + 3 )

4. Reflection across x-axis i.e. f( -x/2 + 3 ) to -f( -x/2 + 3).

The step by step graphical representation can also be viewed below.

Answer:

31. Yes (Y)

WXYZ ~ DABC

S.F.=4

32. Yes (Y)

GHIJ ~ KLMN

S.F.=2/3

33. Missing length: 16

34. Missing length: 30

35. x=7

36. x=10

Step-by-step explanation:

31. The polygons are similar if:

WX/DA=XY/AB

Then:

WX/DA=24/6→WX/DA=4

XY/AB=16/4→XY/AB=4

Like WX/DA=4=XY/AB, the polygons WXYZ and DABC are similar

Scale Factor: S.F.=XY/DA=XY/AB→S.F.=4

32. The polygons are similar if:

GH/KL=HI/LM=IJ/MN=GJ/KN

Then:

GH/KL=6/9=(6/3)/(9/3)→GH/KL=2/3

HI/LM=4/6=(4/2)/(6/2)→HI/LM=2/3

IJ/MN=4/6=(4/2)/(6/2)→IJ/MN=2/3

GJ/KN=4/6=(4/2)/(6/2)→GJ/KN=2/3

Like GH/KL=HI/LM=IJ/MN=GJ/KN=4, the polygons GHIJ and KLMN are similar

Scale Factor: S.F.=GH/KL=HI/LM=IJ/MN=GJ/KN→S.F.=2/3

33. If the polygons are similar, their sides must be proportional, then:

x/24=10/15

Simplifying the fraction on the right sides of the equation, dividing the numerator ans denominator by 5:

x/24=(10/5)/(15/5)

Dividing:

x/24=2/3

Solving for x: Multiplying both sides of the equation by 24:

24(x/24)=24(2/3)

Multiplying:

x=8(2)

x=16

34. If the polygons are similar, their sides must be proportional, then:

54/63=(54/9)/(63/9)→54/63=6/7

48/56=(48/8)/(56/8)→48/56=6/7

x/35=6/7

Solving for x: Multiplying both sides of the equation by 35:

35(x/35)=35(6/7)

Multiplying:

x=5(6)

x=30

36. (8x-2)/63=42/49

Simplifying the fraction on the right sides of the equation, dividing the numerator ans denominator by 7:

(8x-2)/63=(42/7)/(49/7)

Dividing:

(8x-2)/63=6/7

Solving for x: Multiplying both sides of the equation by 63:

63(8x-2)63=63(6/7)

Multiplying:

8x-2=9(6)

8x-2=54

Adding 2 both sides of the equation:

8x-2+2=54+2

Adding:

8x=56

Dividing both sides of the equation by 8:

8x/8=56/8

Dividing:

x=7

37. (6x-6)/63=42/49=30/35

Simplifying the fractions

(6x-6)/63=(42/7)/(49/7)=(30/5)/(35/5)

Dividing:

(6x-6)/63=6/7

Solving for x: Multiplying both sides of the equation by 63:

63(6x-6)63=63(6/7)

Multiplying:

6x-6=9(6)

6x-6=54

Adding 6 both sides of the equation:

6x-6+6=54+6

Adding:

6x=60

Dividing both sides of the equation by 6:

6x/6=60/6

Dividing:

x=10

Answer: Barlow has more by 178

Step-by-step explanation:

Solve for Barlow first: 4/9 of 873 is 388 boys.

Solve for Willow: since 2/3 of the students are girls, that means that 1/3 of them are boys: 1/3 of 630 = 210

Barlow has more, now find out by how many: 388 - 210 = 178.

Barlow School has a greater number of boys than Willow School, with 178 more boys.

To determine which school has a greater number of boys, we can calculate the number of boys in each school by using the given ratios. At Barlow School, 4/9 of the 873 students are boys. At Willow School, 2/3 of the students are girls, which means that 1/3 of the students are boys since there are only boys and girls at the school.

First, we calculate the number of boys at Barlow School:

Then, we calculate the number of boys at Willow School. Since 2/3 of the 630 students are girls, we need to find 1/3 to find the number of boys:

To find out which school has the greater number of boys, we compare the numbers:

Thus, Barlow School has a greater number of boys. To find out by how many, we subtract the number of boys at Willow School from the number of boys at Barlow School:

The formula of a slope:

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

We have the points (-4, 2) and (-2, 2). Substitute:

[tex]m=\dfrac{2-2}{-2-(-4)}=\dfrac{0}{-2+4}=0[/tex]

90% Would be your answer.

Answer:

90%

Step-by-step explanation:

If 9/10 alien races believes that invading Earth is a bad idea, than 90% of the alien races believes that it is a bad idea. This answer was found by converting the fraction into a percentage. There are many ways to do this, but here are two ways. If you put 9/10 into a decimal, you get 0.9, which is 90%. Or, you could multiply 9/10 by 10/10, which will get you 90/100, or 90%. I hope that my answer helped you!

4:7

40/10=4

70/10=7

:)

Hope this helped

Answer:

4:7

Step-by-step explanation:

40 divided by 10 = 4

70 divided by 10 = 7