1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
raketka [301]
2 years ago
5

Only Question #5! If JKLM is a rectangle, find Measure NML

Mathematics
1 answer:
Allushta [10]2 years ago
8 0

Answer;

5. 22°

6. 74°

Step-by-step explanation:

5. Since rectangle JKLM has two equal diagonals that intersect each other, therefore JN = MN.

If JN = MN therefore:

m<NMJ = m<NJM

Thus:

3x + 38 = 7x - 2

Solve for x. Collect like terms

3x - 7x = -38 - 2

-4x = - 40

Divide both sides by -4

x = 10

✔️Find m<NMJ

m<NMJ = 7x - 2

Plug in the value of x

m<NMJ = 7(10) - 2 = 70 - 2

m<NMJ = 68°

✔️Find m<NML;

m<NML = 90 - 68° (Complimentary angles)

m<NML = 22°

6. Diagonal of a rhombus bisects teach vertex angle, this means that <U is divided into two equal parts. Therefore:

10x - 23 = 3x + 19

Solve for x. Collect like terms

10x - 3x = 23 + 19

7x = 42

Divide both sides by 7

x = 6

✔️Find m<RST:

m<SUT = m<RST (opposite angles of a rhombus are congruent)

Thus,

m<SUT = (10x - 23) + (3x + 19)

Plug in the value of x

m<SUT = (10(6) - 23) + (3(6) + 19)

= (60 - 23) + (18 + 19)

= 37 + 37

m<SUT = 74°

Also, m<RST = 74°

You might be interested in
A swimming pool is 20 feet wide and 40 feet long. If it is surrounded by a walkway of square tiles, each is 1 foot by 1 foot, ho
Lena [83]

Answer:

124 tiles

Step-by-step explanation:

2(20+40)

2(60)

120+4=124

5 0
2 years ago
Explain why it is important to solve for the variable first in order to find the measure any angle mentioned in the problem . Ye
valkas [14]
In the field of astronomy, the ability to measure angles accurately and precisely enables us to calculate the position and relative movement of the stars and galaxies in relation to each other, to determine how far distant they are from us, and even to estimate their relative size.
6 0
2 years ago
53 POINTS PLEASE HELP AND BRAINLYIST!!!
klemol [59]

Answer:

Dilations.

Step-by-step explanation:

A dilation does not preserve congruency since the post-image will be of a different size than the pre-image.

6 0
3 years ago
Read 2 more answers
PRECAL:<br> Having trouble on this review, need some help.
ra1l [238]

1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:

\displaystyle \lim_{x\to-2}f(x) = \lim_{x\to-2}(x-2) = -2-2 = \boxed{-4}

Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.

2. f(x) is continuous at x = -1, so the limit can be computed directly again:

\displaystyle \lim_{x\to-1} f(x) = \lim_{x\to-1}(x-2) = -1-2=\boxed{-3}

3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So

\displaystyle \lim_{x\to-2}f(x) = \boxed{-1}

4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.

5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case

\displaystyle \lim_{x\to2^+}f(x) = \boxed{0}

When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.

6. It should be rather clear from the plot that

\displaystyle \lim_{x\to0}f(x) = \lim_{x\to0}(\sin(x)+3) = \sin(0) + 3 = \boxed{3}

because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.

For 7-8, divide through each term by the largest power of x in the expression:

7. Divide through by x². Every remaining rational term will converge to 0.

\displaystyle \lim_{x\to\infty}\frac{x^2+x-12}{2x^2-5x-3} = \lim_{x\to\infty}\frac{1+\frac1x-\frac{12}{x^2}}{2-\frac5x-\frac3{x^2}}=\boxed{\frac12}

8. Divide through by x² again:

\displaystyle \lim_{x\to-\infty}\frac{x+3}{x^2+x-12} = \lim_{x\to-\infty}\frac{\frac1x+\frac3{x^2}}{1+\frac1x-\frac{12}{x^2}} = \frac01 = \boxed{0}

9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:

\displaystyle \lim_{x\to6}\frac{2x^2-12x}{x^2-4x-12}=\lim_{x\to6}\frac{2x(x-6)}{(x+2)(x-6)} = \lim_{x\to6}\frac{2x}{x+2} = \frac{2\times6}{6+2}=\boxed{\frac32}

10. Factorize the numerator and simplify:

\dfrac{-2x^2+2}{x+1} = -2 \times \dfrac{x^2-1}{x+1} = -2 \times \dfrac{(x+1)(x-1)}{x+1} = -2(x-1) = -2x+2

where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is

\displaystyle \lim_{x\to\infty} \frac{-2x^2+2}{x+1} = \lim_{x\to\infty} (-2x+2) = \boxed{-\infty}

6 0
2 years ago
The Johnson family pays $19.75 at the game for 3 ice cream cones and 4 funnel cakes. The Duke family pays $35.25 at the same gam
postnew [5]

Answer:

$1.75  cost of the funnel cake and $4.25 cost of the ice cream cone.

Step-by-step explanation:

x = cost of the ice cone cone

y = cost of the funnel cake

3x + 4y = 19.75      multiply (-2)       ⇔     -6x - 8y = -39.50

5x + 8y = 35.25    do not change   ⇔  +<u>  5x + 8y = 35.25</u>

                                                                     -x  =  -4.25

                                                                      x = 4.25  cost of the ice cream cone

Substitute into the second equation x = 4.25 and solve  for y

5(4.25) + 8y = 35.25

21.25 + 8y = 35.25

  8y = 14

y = 1.75    cost of the funnel cake

7 0
2 years ago
Other questions:
  • 12. Carmen multiplied a non-zero rational number by its additive inverse. Which statement about the product must be true?
    14·1 answer
  • Everyday mike is allowed to play video games for 5 minutes. How many minutes does mike play video games a week?
    12·2 answers
  • Round 438,692 to the nearest thousand
    11·1 answer
  • Dan has 4 over 5 cup of ice cream. How many 1 over 8 -cup servings are in 4 over 5 cup of ice cream?
    15·1 answer
  • Determine the distance between the following two points.
    14·1 answer
  • Select the correct answer from each drop-down menu.
    6·1 answer
  • Answer quick please.
    5·1 answer
  • What a division problem that equals 17
    10·2 answers
  • For which shape is 180 degrees the smallest angle of rotational symmetry?
    14·1 answer
  • -12 + 45<br> 25 + -77<br> Theres more in pic
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!