Lashonda bought a suit on sale for $603. This price was 33% less than the original price.

Step-by-step explanation:

Step 1: Given

BD bisects ∠ADC

Step 2: Given

BD ⊥ AC

Step 3: Corresponding Parts of Congruence Triangles are Congruent

∠1 ≅ ∠2

Step 4: By definition of perpendicular

∠ABD = ∠CBD = 90° (BD ⊥ AC )

∠3 and ∠4 are right angles.

Step 5: By CPCTC,

∠3 ≅ ∠4

Step 6: Reflexive postulate

Any side or angle is reflexive to itself.

DB ≅ DB

Step 7: ASA postulate

∠1 ≅ ∠2 (A),   DB ≅ DB (S)   and   ∠3 ≅ ∠4 (A),

∴ ΔABD ≅ ΔCBD (by ASA)

Step 8: By Corresponding Parts of Congruence Triangles are Congruent

DA ≅ DC

Step 9: Opposite sides of a triangle are equal.

ΔACD is isosceles.

Hence proved.

Answer:

31,

8.5

Step-by-step explanation:

1) 7.75/0.25 = (7.75×100)/(0.25×100)

= 775 ÷ 25

= 31

2) 25.5/3 = (25.5×10)/ (3×10) = 255÷30

= 8.5

I hope this was helpful, please mark as brainliest

Answer:

-1

Step-by-step explanation:

X = 2

Lets substitute the equation:

3*2 + y = 5

6 + y = 5

Using equation rules.

y = 5-6

Therefore y = -1

Answer:

y=-1

Step-by-step explanation:

3x+y=5

When x=2

Substitute the value of x in the above equation

3(2)+y=5

6+y=5

Collect like terms

y=5-6

y=-1

Answer:

C. Individual citizens have the freedom to take risks and improve their lives.

Step-by-step explanation:

Today the age of sun is 6 years.

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

Given that,

Father's present age is five times of his son's age.

Let son's age is x years,

Then father's age will be 5x.

Also, three years  ago the sum of their ages was 30.

Three years ago the age of son and father will be x - 3 and 5x - 3.

Since, the sum = 30

x - 3 + 5x - 3 = 30

6x - 6 = 30

6x = 36

x = 6

The age of son is 6 years.

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Answer:

x= -6

Step-by-step explanation:

first you want to get rid of the 4 so on both sides you subtract 4

4-x²=-32

-4      -4  that will then make the problem

-x²= -36 to get rid of the square you must do the opposite, square root ([tex]\sqrt{36}[/tex]) so it will get rid of the ²

-x= 6 then you have to get rid of the neggative on x so you will add a negative to 6

x=-6

Answer:

For 4.5 hours of work Otis's and Shireen's costs are equal

The cost for this number of hours is $277.5

Step-by-step explanation:

Let

x ----> the number of hours

y ----> the total cost

we have

Otis

[tex]y=45x+75[/tex] ----> equation A

Shireen

[tex]y=55x+30[/tex] -----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (4.5,277.5)

see the attached figure

therefore

For 4.5 hours of work Otis's and Shireen's costs are equal

The cost for this number of hours is $277.5

Answer:

C) angles are congruent and all corresponding pairs of sides are congruent a similarity transformation alt corresponding pairs

The correct statement for similarity transformations is D) In a similarity transformation, all corresponding pairs of angles are congruent and all corresponding pairs of sides are proportional.

A similarity transformation is a type of transformation that preserves the shape of a figure but can change its size and orientation. It is characterized by the property that all corresponding pairs of angles are congruent and all corresponding pairs of sides are proportional.

The statement that is NOT TRUE for similarity transformations is A) A similarity transformation is a composition of a finite number of dilations or rigid motions.

A similarity transformation is a type of transformation that preserves the shape of a figure but can change its size and orientation.

The correct statement for similarity transformations is D) In a similarity transformation, all corresponding pairs of angles are congruent and all corresponding pairs of sides are proportional.

This means that the angles in the original figure and the transformed figure are equal, and the ratio between corresponding side lengths remains the same.

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Answer:

8x - 5y - 13

Step-by-step explanation:

(6x - 3y - 12) - (2x +2y - 10)

(6x - 3y - 12) - 2x - 2y + 10

6x - 3y - 23 - 2x - 2y + 10

8x - 5y - 13

Answer:

4x+y=22

Step-by-step explanation:

6x+3y-12-(2x+2y)=10

Based on BODMAS we will have to deal with the bracket first

6x+3y-12-2x-2y=10

To continue with the solution we will have to collect like terms

That is,

6x-2x+3y-2y=10+12

4x+y=22

This can't be solved further because we don't really know the value of x and y...it can only be solved further by knowing the value of either x or y but we are not given...so we will have to leave our final answer to be

4x+y=22

Answer:

x=-7

Step-by-step explanation:

9x + 16 = 4x - 19

Subtract 4x from each side

9x-4x + 16 = 4x-4x - 19

5x+16 = -19

Subtract 16 from each side

5x+16 -16 = -19-16

5x = -35

Divide each side by 5

5x/5 = -35/5

x = -7

Answer:

x = -7

Step-by-step explanation:

in order to solve this , make x the subject of formula:

9x + 16 = 4x - 19

9x + 16 - 4x = -16

5x = -19 - 16

5x =-35

x = -35 / 5

Answer: the square root of 17 is irrational.

Step-by-step explanation:

17 can not be divided evenly therefor it is irrational

Answer: 66cm^3

Step-by-step explanation:AB=a2

V=a2h

3

Solving forV

V=ABh

3=11·18

3=66cm³

Answer:

x=4

Step-by-step explanation:

-8-x=x-4x

Combine like terms

-8 -x =-3x

Add x to each side

-8 -x+x = -3x+x

-8 = -2x

Divide each side by -2

-8/-2 = -2x/-2

4 = x

Answer:

Equation 1: x + y = 10

Equation 2: y = 4x

Step-by-step explanation:

its right kekkek

Therefore, the equation is of the form

[tex]x+y=10[/tex]

[tex]y=4x[/tex]

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

The sum of two numbers is [tex]10[/tex]. The larger number is [tex]4[/tex] times the smaller number.

Let the smaller number is [tex]x[/tex]

Let the larger number is [tex]y[/tex]

The first equation is [tex]x+y=10[/tex] nad the second equation is [tex]y=4x[/tex].

Hence, the equation is of the form

[tex]x+y=10[/tex]

[tex]y=4x[/tex]

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Answer:

they are always positive

Step-by-step explanation:

they are always positive because two negatives equal a positive.

If both the integers are negative, then their sum is always negative.

We need to find if both the integers are negative, then what is their sum.

Adding integers is the process of finding the sum of two or more integers. It may result in an increase or a decrease in value, depending on whether the integers are positive or negative or a mixture. The addition of integers is an arithmetic operation performed on integers with the same sign or with different signs to find the sum.

Therefore, if both the integers are negative, then their sum is always negative.

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The cross-section will be a 10-sided polygon only when the plane makes a narrow angle with the base, i.e. it will cut one base and 8 edges of the prism, resulting in there being 10 points of intersection, leaving a 10-sided polygon as the cross-section.

Answer:

D

Step-by-step explanation:

I took it rate this one

Answer:

the answer is 5 1/4

Step-by-step explanation:

because u flip it then multiply then u get ur answer

To divide 1/6 and 7/8, we first find the reciprocal of 7/8 which is 8/7, then multiply 1/6 by 8/7 to get 8/42. We simplify this fraction to lowest terms by dividing both the numerator and denominator by their GCD, which is 2, to get the final result, 4/21.

This mathematics question is asking you to divide two fractions, which is 1/6 and 7/8. To do this, you would multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is achieved by switching the numerator and the denominator.

In this case, the reciprocal of 7/8 is 8/7. So, the equation becomes 1/6 * 8/7, which simplifies to 8/42. But this is not in lowest terms. To find the fraction in lowest terms, you would find the Greatest Common Divisor (GCD) of the numerator and the denominator. In this case, the GCD of 8 and 42 is 2.

Dividing both the numerator and denominator by 2, we get 4/21, which is the fraction in lowest terms.

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Answer:

yes

Step-by-step explanation:

Answer:

984 cm^2

Step-by-step explanation:

Base: 10 × 24 = 240

Rectangular faces: 13 × 24 = 312 (×2 = 624)

Triangular faces: 12 × 10 = 120

Add: 240 + 624 + 120 = 984

Answer:

That is a cylinder and cylinder volume = PI * radius^2 * height

radius = x + 5

height = x

volume = PI * (x + 5)^2 * x

volume = PI * (x^2 + 10x + 25) * x

volume = PI * x^3 + 10x^2 + 25x

Step-by-step explanation:

Answer:B

Step-by-step explanation:On  usa test prep

The identification of the population and the sample for the given situation is option B. The population is all classrooms in the high school; the sample is the 10 classrooms selected.

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Solution:

Given that,

[tex]\text{ product of } 42.12 \text{ and } 10^3[/tex]

Which means,

[tex]42.12 \times 10^3[/tex]

Here, the exponent of 10 is positive ( which is 3)

When the exponent is positive, we have to move the decimal point to right

When you multiply a number by a power of 10, ( 10!, 10^2, and so on ) move the decimal point of the number to the right the same number of places as the number of zeros in the power of 10

Here, exponent is 3 , therefore move the decimal point right 3 places in 42.12

Therefore,

[tex]42.12 \times 10^3 = 42120[/tex]

Final answer:

The probability of drawing a yellow or green marble from a bag with various colored marbles is calculated by adding the individual probabilities of drawing a yellow marble and a green marble. Since there are 8 yellow and 2 green marbles out of a total of 20, the combined probability is 0.5 or 50%.

Explanation:

The question relates to the probability of drawing a yellow or green marble from a bag containing marbles of various colors. To find this probability, we must consider the total number of marbles and the number of yellow and green marbles specifically. If a bag contains 3 blue, 2 green, 8 yellow, 4 red, and 3 orange marbles, the total count of marbles is 20.

The probability of drawing a yellow marble (P(Yellow)) is the number of yellow marbles divided by the total number of marbles, which is 8/20 or 0.4. The probability of drawing a green marble (P(Green)) is the number of green marbles divided by the total number of marbles, which is 2/20 or 0.1.

The combined probability of drawing either a yellow or a green marble is found by adding the individual probabilities because these two events are mutually exclusive (they cannot both happen at the same time). So, the probability of drawing a yellow or green marble (P(Yellow or Green)) is P(Yellow) + P(Green) = 0.4 + 0.1 = 0.5.

Therefore, the probability of drawing a yellow or green marble is 0.5 or 50%.

Answer:

Step-by-step explanation:

[tex]\frac{x^{4}+6x^{3}+5x^{2} -15x-2} {x+3}[/tex]

Answer:

Option 4

Step-by-step explanation:

x + 3 x = -3

(-3)⁴ + 6(-3)³ + 5(-3)² - 15(-3) - 2

= 7

Remainder is 7, so not a factor

Answer: 26

Step-by-step explanation: you divide 468 and 18 and you get 26.

Answer:

30

Step-by-step explanation:

4.5(32÷8)+12

32/4 = 4

4.5 x 4 = 18

18 + 12 = 30

Answer:

30

Step-by-step explanation:

PEMDAS

32/8 =4

4.5*4=18

18+12=30

Answer:

36 bottles for 4 is a slightly better deal per bottle.

Step-by-step explanation:

The cost per bottle is 0.1111111$ per bottle in the 36 pack.

Answer:

36 bottles for $4

Step-by-step explanation:

First you need to calculate the price for one bottle, the lower the cost, the better buy. Do this by dividing the price by the amount of bottles:

= $3 ÷ 24

= 0.125 cents

= $4 ÷ 36

= 0.111 cents

The cheaper option and the better buy is the 36 bottles for $4.

Answer:

The equation in slope-intercept form of a line with slope [tex]m\:=-\:\frac{4}{3}[/tex]  and y - intercept = -2  will be:

                                                [tex]y=-\:\frac{4}{3}x-2[/tex]

Step-by-step explanation:

As the slope intercept form is given by

[tex]y=mx+b[/tex]

here

As the given slope is

[tex]m\:=-\:\frac{4}{3}[/tex]

y - intercept = b = -2

so substituting the values in the slope intercept form

[tex]y=mx+b[/tex]

[tex]y=\left(-\:\frac{4}{3}\right)x+\left(-2\right)[/tex]

[tex]y=-\:\frac{4}{3}x-2[/tex]

Therefore, the equation in slope-intercept form of a line with slope [tex]m\:=-\:\frac{4}{3}[/tex]  and y - intercept = -2  will be:

                                                [tex]y=-\:\frac{4}{3}x-2[/tex]

Answer:

Hi there!

The correct answer is: Counterclockwise rotation about the origin by 90 degrees then followed by reflection about the x axis

Answer:

Option 1

Counterclockwise rotation about the origin by 90° followed by a reflection about the x-axis