All categories

8 days ago

Complete the statement if m gdf = 54 then m edf =

Mathematics

2 answers:

lawyer [12K]8 days ago

7 0

edf = 54 as well since both angles correspond to each other

lawyer [12K]8 days ago

5 0

Response:

If m∠GDF = 54° then m∠EDF =54°.

Step-by-step reasoning:

Using the information provided: m∠GDF = 54°, $\angle GDF\cong \angle EDF$ , $\angle DGF\cong \angle DE F$ , $\angle DFG\cong \angle DFE$ .

We need to determine the measure of angle EDF.

In triangles DFG and DFE,

$\angle GDF\cong \angle EDF$ (Provided)

If two angles are congruent, their measures will be equal.

$m\angle GDF=m\angle EDF$

We have that m∠GDF = 54°.

Substituting the value of ∠GDF into the previous statement.

$54^{\circ}=\angle EDF$

Thus, the measure of angle EDF is confirmed to be 54°.

You might be interested in

At the warm-up event for Oscar’s All Star Hot Dog Eating Contest, Al ate one hot dog. Bob then showed him up by eating three hot

Inessa [12133]

Answer: Zeno consumed 51 hot dogs.

The total number of hot dogs consumed was 676.

Step-by-step explanation:

Al started by eating one hot dog. Bob then outperformed him by devouring three hot dogs. Carl, not wanting to fall behind, ate five hot dogs. This pattern continued, with each participant consuming two hot dogs more than the previous one. This indicates that the quantity of hot dogs eaten by each contestant followed an arithmetic sequence.

The formula for finding the nth term in an arithmetic series is given by

Tn = a + (n - 1)d

Where

a denotes the first term in the sequence.

d signifies the common difference.

n stands for the total terms in the sequence.

<pBased on the details provided,

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We aim to find how many hot dogs the 26th contestant, T26, consumed. Thus,

T26 = 1 + (26 - 1)2 = 1 + 50

T26 = 51 hot dogs

The formula to calculate the sum of n terms in an arithmetic sequence is

Sn = n/2[2a + (n - 1)d]

Hence, to find the total number of hot dogs consumed by 26 contestants, S26 is calculated as

S26 = 26/2[2 × 1 + (26 - 1)2]

S26 = 13[2 + 50]

S26 = 13 × 52 = 676 hot dogs

5 0

1 month ago

Ranger was given this expression to simplify. 4(2x – 5) What advice to simplify the expression would you give Ranger? Check all

Zina [11976]

This situation exemplifies the distributive property, where the number outside the parentheses impacts all the terms within through multiplication. Therefore, the resulting action here is:

<span>The 4 should be multiplied by each term found inside the parentheses.

</span>

5 0

1 month ago

Read 2 more answers

1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v

Svet_ta [12268]

Answer:

(1) The necessary proportion of spirit to varnish stands at 1:3.

(2) A total of 80 ml of mineral spirit is required.

(3) The ratio of the heights to the widths of the tapestries is 3:2.

Step-by-step explanation:

(1) To achieve a mixture containing 25% mineral spirit, the blend consists of 25% spirit and 75% varnish.

Therefore, $\frac{spirit}{varnish}=\frac{25}{75}$

$=\frac{1}{3}$

Consequently, the proportion of spirit to varnish is 1:3.

(2) Using 240ml of varnish indicates this is 75% of the entire solution, which means the ratio of varnish to the total solution is 3:4.

Let the total solution quantity be $x$ .

Thus, $240:x=3:4$ .

⇒ $\frac{240}{x}=\frac{3}{4}$

⇒ $3x=240*4$

⇒ $x=\frac{240*4}{3}$

⇒ $x=320$

This means the total solution amounts to 320 ml.

Now, calculating Spirit = Total solution - Varnish

⇒Spirit = 320ml-240ml

⇒Spirit = 80ml

Therefore, when using 240 ml of varnish, you will require 80 ml of mineral spirit.

(3) The dimensions of Robison's tapestries are uniform at 1.5m in length and 1m in width. Initially, to obtain whole numbers, we multiply these dimensions by 10.

Thus, the dimensions become 15m long and 10m wide.

Now, the proportion of Height to Width is 15:10

⇒ $\frac{Height}{Width} =\frac{15}{10}$

⇒ $\frac{Height}{Width} =\frac{3}{2}$

Thus, the proportion of the heights of the tapestries to their widths is 3:2.

8 0

14 days ago

What algebraic expression represents GK, if GK =37, what are GH and JK. GJ=4x+2 and HK=6x-1

Inessa [12133]

The outcome is "GK=37, GH=14, and JK=19".

The problem references a missing attachment file, thus please find it attached.

The provided values are:

GJ=4x+2

HK=6x-1

Given GK =37

Need to calculate:

HJ=?

From GK: GK = GJ+JK yields GJ+(HK-HJ)

= 4x+2+((6x-1)-x) yields

9x+1...(a)Substituting (a) into the equation gives: 9(4)+1 yields 37 solves to x=4... for answer (b) and (c). Substituting x=4 yields:

GH=14 and JK=19.

8 0

17 days ago

Ax+16=b−3x what is a= and what does b= ?

PIT_PIT [11881]

Response:

Slope=4

x−intercept=−

=−4

b−intercept=

=16.0000

Detailed breakdown:

7 0

1 month ago