Which congruence statement correctly compares the two triangles shown? answers: A) ΔBCD ≅ ΔMKL B) ΔCBD ≅ ΔKLM C) ΔDCB ≅ ΔMLK D) ΔBCD ≅ ΔMLK

Answer:

65°

Step-by-step explanation:

180°-50°:130°

130°÷2:65°

130° divide by 2 because the shape was isosceles triangle

Answer:

The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.

Step-by-step explanation:

In order to calculate the daily intake of sodium we first need to calculate the mass of sodium present in both snacks, this is given by their sum.

[tex]\text{total sodium} = 1310 + 350 = 1660 \text{ mg}[/tex]

We can now apply a rule of three for which the total sodium from the snacks is related to 66.4% in the same proportion as "x" mg, which is the value we want to know, is related to 100%. So we have:

[tex]\frac{1660}{x} \frac{mg}{mg} = \frac{66.4\%}{100\%}[/tex]

[tex]66.4*x = 1660*100\\x = \frac{166000}{66.4} = 2500 \text{ mg}[/tex]

The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.

Answer:

2,500 mg

1,310 + 350 = 1,660

1,660 is 66.4% of 2,500

Answer:

See Explanation Below

Step-by-step explanation:

Given

[tex](sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.[/tex]

Required

Prove

To start with; we open the bracket on the left hand side

[tex](sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)[/tex]

[tex](sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)[/tex]

[tex](sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x[/tex]

[tex](sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x[/tex]

Reorder

[tex](sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x[/tex]

From trigonometry;

[tex]sin^2x + cos^2x = 1[/tex]

So;

[tex](sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x[/tex]

becomes

[tex](sin x - cos x)^2 = 1 - 2sinx cos x[/tex]

Also from trigonometry;

[tex]sec^2x - tan^2x = 1[/tex]

So,  

[tex](sin x - cos x)^2 = 1 - 2sinx cos x[/tex]

becomes

[tex](sin x - cos x)^2 = sec^2x - tan^2x - 2sinx cos x[/tex]

Proved

Answer:

42

Step-by-step explanation:

j(5+k) + 15

Let j = 3 and k = 4

3(5+4) + 15

Parentheses first

3 (9) +15

Multiply

27 + 15

Add

42

Answer:

42

Step-by-step explanation:

j(5+k)+15

=3(5+4)+15

=3(9)+15

=27+15

=42

Answer:

The average rate of change for the amount of money is A) $25 per month

Step-by-step explanation:

From the graph we can see Sarah earn $50 every two months, 50/2 = 25/1 so we can determine Sarah's average rate of change from month 0 to month 12 is $25 dollars per month. Hope this helped, let me know if you have any questions! :)

Answer:

50 = 6 notes

20 = 10 notes

10 = 9 notes

Step-by-step explanation:

to check whether it is correct :

50×6 + 20×10 + 10×9 = 590 (total money of Shruti)

Answer:

What does this mean

Step-by-step explanation:

Answer:

Answer:

(x , y)=(-31/306 , 775/51)

Step-by-step explanation:

6x-2y=-144x-3y=-31

Write as a system of equations.

6x-2y=-31

-144x-3y=-31

Multiply both sides of the equation by 24.

144x-48y=-744

-144x-3y=-31

Sum the equations vertically to eliminate at least one variable.

-51y=-775

Divide both sides of the equation by -51.

y=775/51

Substitute the given value of y into the equation 6x-2y=-31.

6x-2x775/51=-31

Solve the equation for x.

x=-31/306

The possible solution of the system is the ordered pair (x , y).

(x , y)=(-31/306 , 775/51)

Step-by-step explanation:

Answer:

(6, 2)

Step-by-step explanation:

Step 1: Use substitution

x - 4 = 1/3x

Step 2: Isolate x

2/3x = 4

x = 6

Step 3: Plug back into original equation(s)

y = 6 - 4

y = 2

Answer:

(6,2)

Step-by-step explanation:

Let's use the substitution method.

x-4=1/3x

3x-12=x

3x=x+12

2x=12

x=6

y=6-4

y=2

Answer:

The median is usually preferred in these situations because the value of the mean can be distorted by the outliers. However, it will depend on how influential the outliers are. If they do not significantly distort the mean, using the mean as the measure of central tendency will usually be preferred.

Answer:

C. When the sample size is large and includes outliers.

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Circumference C=2πr  r=radius [tex]\pi =3.14[/tex]

C=2(3.14)9.7

C=60.9

Answer:

180 degrees

Step-by-step explanation:

Answer:

4.

Step-by-step explanation:

Answer:

the answer is NOT b, i got that wrong on the quiz

Step-by-step explanation:

Answer:

The correct answer is C.

Step-by-step explanation:

(1,-2) (4,-4) (9,-6)

Answer:

C

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (3, 9) ← 2 points on the line

m = [tex]\frac{9-3}{3-1}[/tex] = [tex]\frac{6}{2}[/tex] = 3 → C

Answer:

the answer is C

Step-by-step explanation:

you take 3,9 over 1,3... 3,9 so 9+ 3 over 3+ 1 it will look like a fraction 12/4 then  

                                      1, 3       you simply to get positive 3  

Answer:

x<12

Step-by-step explanation:

Divide both sides by 5

5(x+5) < 85

   5         5      

then simply

Answer:

x < 12

Step-by-step explanation:

[tex]5(x+5)<85\\\\5 * x = 5x\\\\5 * 5 = 25\\\\5x+25<85\\\\5x+25-25<85-25\\\\5x<60\\\\\frac{5x}{5}<\frac{60}{5}\\ \boxed{x<12}[/tex]

Answer:

The real part is -1

Step-by-step explanation:

The real axis is the horizontal axis

The value on the horizontal axis is -1

Answer:

Her weight is approximately 122.8lb

Step-by-step explanation:

Given

Inverse proportion;

Weight = 123lb when distance = 3960 miles from center of earth

Required

Calculate the weight when distance is 3.2 miles above sea level

Let weight be represented by W and distance by D

From the question, we understand that;

Weight is inversely proportional to square of distance;

Mathematically; this is

[tex]W \alpha \ \frac{1}{D^2}[/tex]

Convert proportion to equation

[tex]W = \frac{k}{D^2}[/tex]

Where k is the constant of  proportionality

When W = 123; D = 3960.

This implies that

[tex]123 = \frac{k}{3960^2}[/tex]

Make k the subject of formula

[tex]k = 123 * 3960^2[/tex]

[tex]k = 1928836800[/tex]

Calculating her weight when she's at the top of mountain, 3.2 miles above sea level

First, her distance from center of earth has to be calculated

Distance = Previous distance + 3.2

Distance = 3960 + 3.2

Distance = 3963.2

Now, her weight can be calculated using [tex]W = \frac{k}{D^2}[/tex]

Substitute for k and D

[tex]W = \frac{1928836800}{3963.2^2}[/tex]

[tex]W = \frac{1928836800}{15706954.24}[/tex]

[tex]W = 122.801452817[/tex]

[tex]W = 122.8\ (Approximated)[/tex]

Answer:

336.00 km distance of train

Step-by-step explanation:

Alex = 20mins =12km We distribute to 1hr to find 60mins = 36km p/h.

Roy = 2hrs 20 mins and is 4x the speed of the car.

So 36km x 4 p/h =  144km p/h

2hrs and 20 = 144 x 2.3333 = 335.9952 = 336km

Answer:

336 km

Step-by-step explanation:

"Alex takes 20 minutes to travel 12 km in her car."

Alex's speed = (12 km)/(20 min) = 0.6 km/min

"Alex drives at an average speed that is 1/4 of the average speed that Roy's train travels."

Therefore, Roy's speed is 4 times Alex's speed.

Roy's speed = 4 * 0.6 km/min = 2.4 km/min

Roy travels for 2 hours and 20 minutes = 2 * 60 min + 20 min = 140 min

speed = distance/time

distance = speed * time = 2.4 km/min * 140 min = 336 km

Answer:

[tex]\mathrm {7.1 \: inches}[/tex]

Step-by-step explanation:

Circumference of a circle is [tex]\pi d[/tex]

The diameter is [tex]2.25[/tex] inches as shown in the readings of the scale.

[tex]2.25\pi[/tex]

[tex]\approx 7.06858347058[/tex]

Answer:

Please mark be brainliest and I hoped this helped!

x = 80°

Step-by-step explanation:

These are both isosceles triangles, so the top 2 angles are both 65°. The last angle of that triangle is 180° - (65° + 65°) which is 50°. Then, the opposite of that angle is in the next traingle. It is also 50°. So the 2 base angles are both 50°, so x is 180° - (50° + 50°) which is 80°.

The measure of angle 'x' is 65 degrees and this can be determined by using the properties of the isosceles triangle.

Given :

Angles  ---  [tex]65^\circ[/tex] and x

The following steps can be used in order to determine the measure of angle 'x':

Step 1 - Both the triangles are isosceles triangles because in both the triangles two sides are similar.

Step 2 - Let the upper triangle be ABC and the lower triangle be DBE.

Step 3 - The angle B of the triangles can be calculated as:

[tex]\angle A + \angle B + \angle C = 180[/tex]

[tex]65+65+\angle B = 180[/tex]

[tex]\angle B = 50^\circ[/tex]

Step 4 - Now, angle 'x' can be calculated as:

[tex]\begin{aligned}\\\angle D + \angle B + \angle E &= 180\\x+x + 50 &= 180\\2x &= 130\\x &= 65^\circ\\\end{aligned}[/tex]

The measure of angle 'x' is 65 degrees. Therefore, the correct option is B).

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Answer:

x =72

Step-by-step explanation:

120 = x+48  alternate interior angles are equal

Subtract 48 from each side

120-48 = x

72 =x

Answer: 65 grams

Step-by-step explanation:

If 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold, you should first calculate the amount of gold that makes up this percentage.

That is, 85% of 130 grams.

85/100 × 130 = 110.5

Then, let X be what will be added to the above value to make 90%. So,

(110.5 + X) / ( 130 + X ) × 100 = 90

Divide both sides by 100

(110.5 + X) / ( 130 + X ) = 90/100

(110.5 + X) / ( 130 + X ) = 0.9

Cross multiply and open the bracket

110.5 + X = 117 + 0.9X

Collect the like terms

X - 0.9X = 117 - 110.5

0.1X = 6.5

Divide both sides by 0.1

X = 6.5/0.1

X = 65 grams

Therefore, the amount of pure gold that should be added is 65 grams

Answer: The answer is the second one/b.

Answer:

D. 22/1=x/3

Step-by-step explanation:

Well what you multiply by the top you must do the bottom and opposite way also goes, sometimes so to get three as shown in (x/3) you must use the 1 from (22/1) times something to equal 3. In this it would be 1*3=3 so I multiplied three to the bottom and what I do the the bottom I haft to do to the top so 22*3=x and x is equal to 66 witch makes (D. 22/1=x/3) the correct option. If you want or need to check a good way to is to use a calculator to multiply 22*3 just as a small check up.

Answer:

x = 9.7

Step-by-step explanation:

The area of a triangle is A = b * h / 2 where A, b, and h are the area, base and height respectively. We know that A, b, and h equal 47, x, and x respectively so we can write:

47 = x * x / 2

47 = x² / 2

94 = x²

x = ±√94

In context, x can't be negative so the answer is x = √94 = 9.7.

Answer:

9.70 inches

Step-by-step explanation:

Area of a triangle is equal to base times height divided by 2.

[tex]bh/2[/tex]

Base and height is x.

[tex]xx/2=47[/tex]

Solve for x.

[tex]x^2=47 \times 2[/tex]

[tex]x^2=94[/tex]

[tex]x=\sqrt{94}[/tex]

[tex]x=9.69536[/tex]

Answer: If you want to make more cookies then what is called for in this situation then you would need 6 cups of milk.

Step-by-step explanation: You have 2 cups of milk and 3 cups of flour of course. In order to make a complete batch you need 2 cups of milk and 3 cups of flour. In order to make a second batch you need the same things as you did for the first batch. Therefore two batches of cookies requires 4 cups of milk and 6 cups of flour. In this situation you want to make 3 batches of cookies. The required items are 6 cups of milk and 9 cups of flour.

Answer:

To find < E we use tan

tan E = opposite / adjacent

DF is the opposite

EF is the adjacent

DF = 11

EF = 11

tan E = 11/11

tan E = 1

E = 45

Hope this helps

Answer:

45 degrees

Step-by-step explanation:

Since this triangle is isosceles, we know that the other angles, D and E, are both 45 degrees because of the sum of interior angles of a triangle always equaling 180 degrees.

The answer is E) 22

This is the answer because the triangles are similar, so a proportion can be made. So it would be 28/42=x/33. Then you solve for x, which equals 22.

Answer:

n(m%)

Step-by-step explanation:

By Translate the following into an expression: m% of n. Thus, the expression is 0.01mn.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

We have to Translate the following into an expression:

m% of n

m x 1/100 x n = 0.01mn

Thus, the expression is 0.01mn.

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Answer:

D) [tex]x=4 \textdegree[/tex]

Step-by-step explanation:

Before answering this question, we must first understand what an angle bisector is. An angle bisector is any ray, line, or line segment that splits an angle into two congruent, smaller angles.

That being said, since [tex]DF[/tex] bisects [tex]\angle ADE[/tex], we can say that [tex]\angle ADF \cong \angle FDE[/tex]. If you'll remember, congruent angles have equal measures, so [tex]m\angle ADF = m\angle FDE[/tex].

Substituting the given values of the angle measures into the equation and solving, we get:

[tex]9x-1=8x+3[/tex]

[tex]9x=8x+4[/tex] (Add 1 to both sides)

[tex]\bf x = 4 \textdegree[/tex] (Subtract 8x from both sides)

Hope this helps!

Answer:

[tex]x = 4[/tex]

Answer D is correct.

Step-by-step explanation:

( ADF angle = FDE angle)

[Because DF is the angle bisector]

[tex]9x - 1 = 8x + 3[/tex]

[tex]9x - 8x = 1 + 3 \\ x = 4[/tex]

hope this helps you.