what is the sum of the interior angles of an equilateral triangle?

Answer:

Step-by-step explanation:

1.

3,4,5 will make a triangle.

2.

sum of any sides > third side

difference of any two sides < third side

3+4=7>5

4+5=9>3

5+3=8>4

again

4-3=1<5

5-3=2<4

5-4=1<3

so it makes one triangle.

3.

3,4,8

4.

3+4=7 not >7

again

8-4 =4 not <3

so they do not make a triangle.

Answer:

y = -2/3x + 6

Step-by-step explanation:

replace the coordinates in the equation

y= mx + c

y= 8

x= -3

8= -2/3 (-3) + c

c + 2 = 8

c = 8 - 2

c = 6

y= -2/3x + 6

Answer:

32

Step-by-step explanation:

The interior angles of a triangle add up to 180.

Subtract 98 and 50 from 180.

180-(98+50)=32

Step-by-step explanation:

you add all the values and equate them to 180

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that,

In triangle ABC

[tex] \purple{\rm :\longmapsto\:\angle A + \angle B = 125 \degree \: - - - (1) }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle B + \angle C = 150 \degree \: - - - (2)}[/tex]

We know,

Sum of all interior angles of a triangle is supplementary.

[tex] \purple{\rm :\longmapsto\:\angle A + \angle B + \angle C = 180\degree }[/tex]

On adding equation (1) and (2), we get

[tex] \purple{\rm :\longmapsto\:\angle A + \angle B + \angle B + \angle C = 125\degree + 150 \degree \:}[/tex]

[tex] \purple{\rm :\longmapsto\:\angle A + \angle B + \angle C + \angle B = 275\degree \:}[/tex]

[tex] \purple{\rm :\longmapsto\:180\degree + \angle B = 275\degree \:}[/tex]

[tex] \purple{\rm :\longmapsto\:\angle B = 275\degree - 180\degree \:}[/tex]

[tex] \purple{\rm :\longmapsto\:\angle B = 95\degree \:}[/tex]

On substituting the value in equation (1) and (2), we get

[tex] \purple{\rm :\longmapsto\:\angle A + 95\degree = 125\degree }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle A = 125\degree - 95\degree }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle A = 30\degree }[/tex]

Also, from equation (2), we get

[tex] \purple{\rm :\longmapsto\:95\degree + \angle C = 150\degree }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle C = 150\degree - 95\degree }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle C = 55\degree }[/tex]

Hence,

[tex]\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{\angle A = 30\degree } \\ \\ &\sf{\angle B = 95\degree } \\ \\ &\sf{\angle C = 55\degree } \end{cases}\end{gathered}\end{gathered}[/tex]

Answer:

angle A=30°

angle B=95°

angle C=55°

Answer:

[tex]slope \: or \: gradient = y2 - y1 \div x2 - x1 \\ 3 - 2 \div 4 - 1 \\ 1 \div 3 \\ y = mx + c \\ 2 = 1 \div 3 \times 1 + c \\ 2 = 1 \div 3 + c \\ 2 - 1 \div 3 = c \\ c = 5 \div 3 \\ y = 1 \div 3x + 5 \div 3[/tex]

Answer:

207 cm

Step-by-step explanation:

Because ΔPQR ≅ΔSTU and the longest side in the ΔPQR is RP then the longest side in ΔSTU must be SU = 92 cm

Perimeter of triangle PQR is

P(ΔPQR) = 36+48+24 = 108 cm

Because the triangles are are similar their sides are in proportion.

But how much bigger did the second triangle get?...is (92/48) times bigger

P(ΔSTU) = 180*(92/48) = 207 cm

...you can also use proportions to find each side and then find the perimeter

TU = 24*92 /48 = 46

TS = 36*92/48 = 69

SU = 92

P(ΔSTU) = 92+69+46 =207 cm

*the triangles are not drawn to scale

The equation with only one unique solution is 9 − |2x − 1| = 9, with the solution x = 1/2. D.

To determine which equation has only one unique solution, let's analyze each equation:

|3 − x| = 3

In this equation, the absolute value term represents a distance.

By setting up two cases, where the absolute value is positive and negative, we can find the solutions.

Case 1:

3 - x = 3

Solving for x, we have x = 0.

Case 2:

x - 3 = 3

Solving for x, we have x = 6.

Thus, this equation has two solutions.

|x − 2| − 7 = 7

Similar to equation A, the absolute value term represents a distance.

By adding 7 to both sides, we have |x - 2| = 14.

This equation implies that the distance between x and 2 is 14.

There are two possible values for x: x = 2 + 14 = 16 and x = 2 - 14 = -12.

This equation has two solutions.

-4|x| + 1 = -3

To solve this equation, we isolate the absolute value term:

-4|x| = -4

Dividing both sides by -4:

|x| = 1

The absolute value of any number is always positive or zero.

The equation |x| = 1 has two solutions: x = 1 and x = -1.

9 − |2x − 1| = 9

The absolute value term represents a distance.

Subtracting 9 from both sides, we have |2x - 1| = 0.

The only way the absolute value of a real number can be equal to zero is if the number inside the absolute value is zero.

Thus, we set 2x - 1 = 0 and solve for x:

2x - 1 = 0

2x = 1

x = 1/2

Equation D has only one unique solution: x = 1/2.

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Answer:

-12 gal / min

Step-by-step explanation:

[tex] \frac{ - 60 \: gallon}{5 \: minutes} = - \frac{60}{5} = - 12[/tex]

Answer:

13 and 6

Step-by-step explanation:

Answer:

I think it`s the second one

Step-by-step explanation:

Answer: The answer is the second choice. Hope this helps!

Answer:

The answer to A is: "Angle 2 is congruent to angle 3"

The answer to B is: "Angle 3 is congruent to angle 7"

I hope you find this useful, Mark as Brainliest please, it's very much appreciated.

Explanation:

In one minute, Diego can type 35 words;140÷4

At this rate, it will take him 11 minutes to type 385 words;385÷35

Therefore, he can type 525 words in 15 minutes; 35×15

Answer:

Hope this helps.

Step-by-step explanation:

1. 385 x 4 = 1540/140

    =11

2. 15/4 = 3.74 x 140

    =525

Answer:  1 1/14

Step-by-step explanation: sorry if im wrong

Step-by-step explanation:

there u have it, since y is 0, we make a straight line that passes through 2 and shade the numbers that are <2

Step-by-step explanation:

8

a. total cost ($)

→ 25 = 25×2.5 = $62.5

→ 50 = 50 × 2.5 = $125

→ 75 = 75 × 2.5 = $187.5

b. 2.5n

c. $400/2.5 = 160

therefore, she can make 160 crafts by $400.

9. 7x + 12 = 18

→ 7x = 18 - 12 = 6

→ x = 6/7

therefore value of x is 6/7.

hope this answer helps you dear...take care

Answer:

p < 14/3

Step-by-step explanation:

Answer:

a.divide both sides with 3

Step-by-step explanation:

Answer:

y = 2/3x - 5  or   in standard form 3y = 2x - 5

Step-by-step explanation:

Remember this fact: Parallel lines have the same slope

Step 1   Solve for y  so that the equation is in the slope- intersect form

         2x - 3y = 6

          -3y = -2x + 6  

           -3y/-3  = -2x/-3 + 6/-3

             y = 2/3 x -2        

  now we know the slope is 2/3  or

   when the equation is in Standard form Ax + By = C   you can use this fact:  slope = - A/B    so  the slope = -2/-3 = 2/3

    Remember the   Parallel lines have the same slope

     Find the y-intersect "b"     use the slope = 2/3 and point (6, -1)

      y = mx + b

       -1 = 2/3(6) + b

       -1 = 4 + b

       -5 = b    

Now write the equation of line that is parallel to the given line and passes through  point (6, -1)

y = 2/3x - 5  or  in standard form 3y = 2x - 5

QPR is 68 degrees

triangle=180 degrees

180-44=136

136/2=68 (R=68 and S=68)

R has two angles so both are 68 degrees

QPR=68 degrees

Answer:

26.6

Step-by-step explanation:

simplify -26.6 divided by -1 to 26.6

Answer:

26.6

Step-by-step explanation:

- 26.6 / - 1

- 26.6 = - 1 x 26.6

- 1 = - 1 x 1

- 26.6 / - 1

= ( - 1 x 26.6 ) / ( - 1 x 1 )

= ( - 1 / - 1 ) x ( 26.6 / 1 )

= 1 x 26.6

= 26.6

Answer:

see explanation

Step-by-step explanation:

The vertex is the coordinates of the turning point of the parabola

The axis of symmetry is a vertical line passing through the vertex with equation

x = c ( where c is the x- coordinate of the vertex )

vertex = (0, 0 ) , axis of symmetry is x = 0 ( the y- axis )

(1)

vertex = (- 2, 4 ) , axis of symmetry is x = - 2

(2)

vertex = (7, 1 ) , axis of symmetry is x = 7

(4)

vertex = (- 3, - 2 ) , axis of symmetry is x = - 3

Answer:

42.3

Step-by-step explanation:

add both angles then subtract by 180 and the negative number is your answer

Answer:

10. put a dot on the number 10

Step-by-step explanation:

3-(-5)-(-2)

when subtracting negatives, you actually end up adding

so

3+5+2=10

3 - (5) - (-2) = 10.

The solution will be positive 10 on the line.

Answer:

1) answer is 2x^2 - x + 6

2) answer is 2x^2 + 2x + 2

Step-by-step explanation:

i dont know if this is what you wanted, but i tried to follow the directions as best i could

Answer:

2x2 - 2x + 6 - (-3x)  = 2x2(tiny) + x + 6

or

-(3 - 2x2) + 5 +2x = 2x2(tiny) + 2x +2

Step-by-step explanation:

I don't remember exactly how you find the smallest, sorry...

So a line that is perpendicular is a line that intercepts other line at a 90 degree angle.

Slope of perpendicular lines is the opposite sign and the reciprocal of the other.

So if your slope was 2 the perpendicular line would have a slope of -1/2.

So the equation, 2x + y = 3

Can be rewritten as

y= -2x+3

Perpendicular slope: 1/2

Since it intercepts/ passes the coordinates (5,4) it means that those values are included in the function input x and output y.

y=mx+b

4=1/2(5)+b

Solve for b (y intercept)

4-2.5=b

1.5=b

So the equation of the perpendicular is

y=1/2x+3/2 or y=.5x+1.5

Answer:A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements. Curly braces are used to indicate that the objects written between them belong to a set

Answer: A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements.

Curly braces are used to indicate that the objects written between them belong to a set.

A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements.

here, we have,

N={1,2,3,4,.......}

Determine the sets of natural number

Represent this set with letter N

From definition of natural numbers, they are integer numbers starting from 1;

In other words: 1,2,3,4,5, and so on.

To represent this as a set of N, we have

N={1,2,3,4,.......}

The ..... means that the counting still continues.

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Inequalities are used to represent unequal expressions

The inequality that represents the number  of  seeds her apple could  have is [tex]\mathbf{A < 6}[/tex]

Represent the fruits with the first letter.

So, we have:

[tex]\mathbf{W =3A - 1}[/tex] --- watermelon is one less than three times apple

[tex]\mathbf{O =5A - 13}[/tex] --- orange is thirteen less than five times apple

[tex]\mathbf{W > O}[/tex] --- the seeds in watermelon exceeds orange

Substitute expressions for W and O in [tex]\mathbf{W > O}[/tex]

[tex]\mathbf{3A - 1 > 5A - 13}[/tex]

Collect like terms

[tex]\mathbf{13- 1 > 5A - 3A}[/tex]

[tex]\mathbf{12 > 2A}[/tex]

Divide both sides by 2

[tex]\mathbf{6 > A}[/tex]

Rewrite as:

[tex]\mathbf{A < 6}[/tex]

The inequality that represents the number  of  seeds her apple could  have is [tex]\mathbf{A < 6}[/tex]

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Answer:

j=10-3k

Step-by-step explanation:

here you go...i hope it's correct

If the equation is (3j+k)/2=15-4k then j=10-3k

Two or more expressions with an Equal sign is called as Equation.

The given equation is (3j+k)/2=15-4k

We need to prove j=10-3k

(3j+k)/2=15-4k

Apply cross multiplication and solve for k

3j+k=2(15-4k)

3j+k=30-8k

Subtract k from both sides

3j=30-9k

Divide both sides by 3

j=10-3k

Hence, if the equation is (3j+k)/2=15-4k then j=10-3k

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