The two statements below are different ways to say that the sides of these similar triangles are proportional.

Complete the equations that go with the statements.
Drop down options
1: e,f
2: q,r
3: p,q,r
4: d,e,f

Answer: g + r = 17

2.5g + 3.5r = 52.5

Step-by-step explanation: Let g be the number of games Nolan played and r be the number of rides Nolan went on. We can write the following system of equations to represent the problem:

g + r = 17

2.5g + 3.5r = 52.5

We can solve this system of equations using elimination, substitution, or graphing.

Answer:

1679 songs

Step-by-step explanation:

         23

       x73

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

            69

    +   1610

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

         1679

The line's equation that is parallel to the given line is=  3x - 8

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

The line's equation in the form of the slope intercept is,

y = mx + c

m is the line's slope, and c is its y-intercept.

line equation provided that,

Therefore, the line's slope is

Finding the equation of the line that crosses (4,4) and runs parallel to the provided lines is necessary.

Because all parallel lines have the same slope.

Equation for the necessary line is,

Replace point (4,4) in the line above.

In order for the line equation to become,

3x - 8

Hence, The line's equation that is parallel to the given line is=  3x - 8

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The two-column method can be used to prove that the triangles ΔACD and ΔBCD are congruent is presented as follows;

Statements [tex]{}[/tex]                                         Reasons

1. AC ≅ BC   [tex]{}[/tex]                                        1 Given

2 D is the midpoint of AB [tex]{}[/tex]                  2 Given

3. CD ≅ CD [tex]{}[/tex]                                         3 Reflexive property → CD = CD

4 ∠ACD ≅ ∠BCD [tex]{}[/tex]                               4 Median line of an isosceles triangle bisects the vertex angle

5 ΔACD ≅ ΔBCD  [tex]{}[/tex]                              5. SAS congruency postulate

The two-column method consists of two columns, including a statement column and a reasons column, in which each statement made is provided with an accompanying reason.

The reasons in the prove for the congruency of the triangles, ΔACD and ΔBCD are as follows;

Reflexive property

The reflexive property of equality indicates that the value of a number or measure is equal to itself, therefore, the length of the segment CD is the same as the length of the segment CD.

Median of an isosceles triangle

In an isosceles triangle, two sides are congruent. The median segment drawn from the altitude of an isosceles triangle forms two congruent segment at the base, such that the two triangles formed by the median line are congruent, by Side-Side-Side, SSS congruency postulate, therefore, the angles formed at the vertex of the triangle by the median segment are also congruent

SAS congruency postulate

The Side-Angle-Side congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

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Answer:

d = 9°

Step-by-step explanation:

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

soln

27° + (8d – 9)° = 90°

27° + 8d – 9° = 90°

27°–9° + 8d = 90°

18° + 8d = 90°

8d = 90° – 18°

8d = 72°

divide both sides by (8)

d = 9°

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The given statements are:

We can then use the ASA congruence theorem to prove the triangles are congruent, aka they are mirror copies of one another.

Each "A" refers to facts (1) and (3) shown above. Fact (2) is the "S" of ASA.

ASA = angle side angle

Answer:

Step-by-step explanation:

Given f(x) = √(3+x) and g(x) = √(3-x), you want the domains of various combinations of f and g.

The domain of each of these functions is the interval on which it is defined. The domain of the square root function is all argument values greater than or equal to zero.

The argument of the square root will be non-negative when ...

  3 +x ≥ 0

  x ≥ -3 . . . . . . subtract 3

  -3 ≤ x . . . . . . written using left-pointing arrow

The argument of the square root will be non-negative when ...

  3 -x ≥ 0

  3 ≥ x . . . . . add x

  x ≤ 3 . . . . . written using left-pointing arrow

Any combination of functions f and g will only be defined on the domain where both f and g are defined. That is, the domain will be the intersection of the domains of f and g:

  (-3 ≤ x) ∩ (x ≤ 3) = -3 ≤ x ≤ 3

The domain of f+g is the intersection of the domains of f and g.

  [-3, 3]

The domain of f-g is the intersection of the domains of f and g.

  [-3, 3]

The domain of f ·g is the intersection of the domains of f and g.

  [-3, 3]

The domain of f/g is the intersection of the domains of f and g, excluding the value of x that makes g(x) = 0. That value is x=3.

  [-3, 3)

__

Additional comment

The graphs of the combinations of functions are attached. You notice the graph of f/g tends to infinity as x → 3. It is undefined at x=3.

Answer: 21 meters cost $28.5

Step-by-step explanation:

divide 19 by 14 and multiply by 21

21 meters cost $28.5

Answer:

The amount of goo remaining after 32 minutes is approximately 54.7 grams.

Step-by-step explanation:

The half-life of a substance is the amount of time it takes for half of the substance to decay. To find the half-life of the goo in the experiment, we need to solve the equation G ( t ) = G ( 0 ) / 2 for t , where G ( 0 ) is the initial amount of goo and G ( t ) is the amount of goo remaining after time t .In this case, G ( 0 ) = 176 grams and G ( 135 minutes ) = 11 grams, so we can write the equation as follows:11 grams = 176 grams / 2Solving for t , we get:t = 135 minutes * ( 1 / 2 ) = 67.5 minutesThis is the half-life of the goo in the experiment.To find the amount of goo remaining after time t , we can use the equation G ( t ) = G ( 0 ) * ( 1 / 2 ) ^ ( t / t1/2 ) , where G ( 0 ) is the initial amount of goo, t is the time at which we want to find the amount of goo remaining, and t1/2 is the half-life of the goo.In this case, G ( 0 ) = 176 grams, t = 32 minutes, and t1/2 = 67.5 minutes, so we can plug these values into the equation to find the amount of goo remaining after 32 minutes:G ( 32 minutes ) = 176 grams * ( 1 / 2 ) ^ ( 32 minutes / 67.5 minutes )This equation tells us that the amount of goo remaining after 32 minutes is approximately 54.7 grams.

Answer:

77.04

Step-by-step explanation:

A=3.14r^2

a=3.14(6)^2

A=3.14(36)

A=77.04

Answer: 113 ft^2

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

in the first one, 6 16 8, (6×8)/3=16

in the third one, 9 21 7, (9×7)/3=21

using the same comcept, 5 ? 6, (5×6)/3=10

so, ?=10

Answer:

C/25 + H/40 = 15

Step-by-step explanation:

Let's call C the number of city miles, and H the number of highway miles.

The total gas used is therefore:

C/25 + H/40

The fuel tank holds 15 gallons, so:

C/25 + H/40 = 15

There are 22 different ways to organize the word mathematics because no two consecutive letters are the same.

Total number of ways to organize the word "mathematics".

The same letter does not appear twice.

The following word has the letters 2M, 2A, 2T, H, E, I, C, and S.

We will first organize H,E,I,C,S in five different ways;

−H−E−I−C−S−

No, we could arrange 2M, 2T, and 2A as we have 6 gaps;

= 6!/(2!.2!.2!)

So there are a total of;

= 5 x 6!/(2!.2!.2!)

= 22.5

= 22 ways

Thus, there are 22 different ways to organize the word mathematics because no two consecutive letters are the same.

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The equation of the​ line, in​ slope-intercept form, containing the point ( 5,2. 2) and (9,2. 6) is  y=0.025x+2.375 where 0.025 is the value of slope and 2.375 is the y-intercept.

Take into account the slope-intercept form of the equation y = 6 x + 9 y=6x+9. The x and y intercepts are known. When x = 0, the y-intercept also happens, and when y equals 0, the x-intercept also happens. By setting the value of y to 0, we may find the x-intercept.

The values of the slope and y-intercept reveal details of the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

To calculate the equation of line containing points (5,2.5) and (9,2.6) we will use the formula y=mx+b

Here, m = (y2-y1)/(x2-x1)

So, m = (2.6-2.5)/(9-5)

m= 1/40

m=0.025

Now finding b by using formula y=mx+b using x= 5 and y= 2.5

2.5=(0.025)(5)+b

2.5=(0.125)+b

b=2.375

so equation of line is y=0.025x+2.375 in slope-intercept form.

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Answer:

180-125 = x

x= 55 ( allied angle)

[tex]4^x=3 \\\\[-0.35em] ~\dotfill\\\\ 4^{2x-2}\implies 4^{2x}\cdot 4^{-2}\implies (4^x)^2\cdot \cfrac{1}{4^2}\implies \cfrac{(4^x)^2}{16}\implies \cfrac{(3)^2}{16}\implies \cfrac{9}{16}[/tex]

Answer:

24

Step-by-step explanation:

6*4=24

Answer:

X-intercept : (-2,0)

Y-intercept : (0,6)

Answer:y-intercept (0,6),x-intercept (-2,0)

Step-by-step explanation:

To find the y-intercept set x=0

-3(0)+y=6

y=6

y-intercept (0,6)

To find the X-intercept set y=0

-3x+0=6

-3x=6

x=-2

x-intercept (-2,0)

it doesn't have solution

Answer: 50 + 0.25 is less than 90

Step-by-step explanation:

well, let's just divide them anyway and check it out.

hmmm 6.1 ÷ 0.1, well, when dividing decimals, we can first check the decimals on each hmmm 6.1 has one decimal and 0.1 has one decimal, so for the one decimal on 6.1 0.1 gets one "0" and for each decimal on 0.1, 6.1 gets  one "0".

That means we can change the values with no dots to say 610 and 10, so we end up with a division of 610 ÷ 10 = 61.  We can write that as 61.0 hmmm woopsie, the dot moved to the right by one slot.

The 16 miles out of 40 miles. Then the percentage will be 40%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The 16 miles out of 40 miles. Then the percentage is calculated as,

P = (16 / 40) x 100

P = 0.40 x 100

P = 40%

The 16 miles out of 40 miles. Then the percentage will be 40%.

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The missing part of the question is given below.

Determine the percentage.

Answer:

f(2) = 9

Step-by-step explanation:

to evaluate f(2) substitute x = 2 into f(x) , that is

f(2) = 4(2) + 1 = 8 + 1 = 9

Answer:

Step-by-step explanation:

An equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.

Given that, the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Here, slope of a line y=-1/5x-9 is m=-1/5.

The slope of a line perpendicular to given line is m1=-1/m2

So, slope =5

Substitute m=5 and (x, y)=(7, 10) in y=mx+c, we get

10=5(7)+c

⇒c=-25

Substitute m=5 and c=-25 in y=mx+c, we get

y=5x-25

Hence, an equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.

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It will take 40 minutes for her to plant all 70 flowers that she has. By using proportions, we can find this value.

To calculate a word problem using proportions is as follows:

Consider the details of the word problem in proportions as

a : b = c : d

Here, a: b is the ratio of an event, and c : d is the ratio of another event.

Then, to find the value of c we need to reframe the above proportion into

c = ad/b

This is also said to be a cross formula in terms of word problems.

It is given that, Caroline is planting flowers in her garden.

She plants her first 7 flowers in 4 minutes.

After 12 minutes, she planted 21 different flowers.

Then, she takes x minutes for planting 70 flowers.

(Since the rate of planting is the same)

So, we can write

70 : 21 = x : 12

⇒ x = (70× 12)/21 = 40 minutes

Therefore, Caroline takes 40 minutes for planting all 70 flowers.

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Answer:

She needs to get at least 96 on the 4th test to earn an average of at least 90 in the class.

Step-by-step explanation:

(97+78+89+?) divided by 4 at\geq 90

It is divided by 4 because it is the average of 4 test scores.

To Solve: (97+78+89+?) divided by 4 at\geq 90

Multiply by 4 on both sides 97+78+89+? at\geq 360

Isolate variable: ? at\geq 96