The measure of the exterior angle at vertex D is: D. 54°
Recall:
The exterior angle theorem of a triangle states that the measure of an exterior angle equals the sum of the measures of two opposite interior angles of the triangle.Thus:
In ΔDEF, (8x−2)º is an exterior angle at vertex D.
m∠E = (3x−8)° (interior angle)
m∠F = (4x+13)° (interior angle)
Therefore:
(8x−2)º = (3x−8)° + (4x+13)°
Solve for x8x - 2 = 3x - 8 + 4x + 13
Combine like terms8x - 2 = 7x + 5
8x - 7x = 2 + 5
x = 7
Exterior angle at vertex D = (8x−2)º
Plug in the value of x= 8(7) - 2
= 54º (option D)
Learn more about exterior angle theorem on:
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Given f(1) = 8 and
f(n) = 3 f(n-1) - 2 then f (4) =
Answer:
190
Step-by-step explanation:
f(1)=8
f(2)=3f((2-1))-2, f(2)=22
f(3)=3f((3-1))-2, f(3)=64
f(4)=3f((4-1))-2, f(4)=190
In the rectangular trapezoid ABCD AC is driven by a CD (see figure).
Find the width of the trapezoid if AC = 3, AD = 5.
Answer:
solution given:
let's see only in a right-angled triangle Δ ACD.
AC=3 units
AD=5 units
since Δ ACD is a right-angled triangle. It satisfies Pythagoras law
[tex]AD^{2}=AC^{2}+CD^{2}[/tex]
25=9+[tex]CD^2[/tex]
[tex]CD^2[/tex]=25-9=16
[tex]CD=\sqrt{16} =4 units[/tex]
Now
Area of rectangle Δ ACD=[tex]\frac{1}{2} CD*AC=\frac{1}{2}*4*3=6\: square \:units[/tex]
similarly,
[tex]\frac{1}{2} AD*CE=6\: square \:units\\ 5*CE=6*2\\CE=\frac{12}{5}=2.4 units[/tex]
since AB=CE=2.4 units
Δ ACE is a right-angled triangle. It satisfies Pythagoras law.
[tex]AC^{2}=AE^{2}+CE^{2}\\3^2=AE^2+2.4^2\\9-5.76=AE^2\\AE and BC=\sqrt{1.24} =1.11 units[/tex]
now
area of trapezoid=area ofΔACD+Area of ΔABC
=6+[tex]\frac{1}{2}AB*BC=6+\frac{1}{2}*2.4*1.11=6+1.33 =7.33\: square \:units[/tex]
Three (3) is a common factor of 21 and 22.
O A. True
B. False
SUBMIT
Answer:
false.
Step-by-step explanation:
Factors for 21: 1, 3, 7, and 21. Factors for 22: 1, 2, 11, and 22.
Answer:
B false
hello hope this helps
Find the equation for the line bellow
1 1/2 - 1/2 pls helpppppppppp
Answer:
It would be 1 whole
Step-by-step explanation:
1/2 - 1/2 is 0 the only thing left is one whole
Calculator
6 mm
What is the area of this figure?
6 mm
Enter your answer in the box.
8 mm
8 mm
mm
Answer:
[tex] {84mm}^{2} [/tex]
Step-by-step explanation:
Area of square= l×l
Area of square= 6mm × 6mn
Area if square = 36 mm²
Area of triangle 1= ½b ×h
Area of triangle 1= ½ (6mm)(8mm)
Area of triangle 1 = 24 mm²
Area of triangle 2 is the same as area of traingle 1 because they have the same base and hight
: . area of triangles is 48mm²
Area of the figure= Area of square + Area of triangles
A of figure = 36+48
A of figure = 84 mm²
Option 2
Use trapezium formula
Area of trapezium= (a+b)/2 * h
a=6 mm (base)
b=8+6=14 mm (Base)
h= 6mm (height)
[tex]area \: of \: trapezium = ( \frac{6 + 14}{2} )(6) \\ = 60mm ^{2} [/tex]
Therefore the area of triangle= 24mm² as calculated in option 1
Area of the figure= Area of trapezium +Area of triangle
Area of figure = 60+24
= 84 mm²
Quincy feeds his dog 2.75 cups of dog food each day. Each cup of dog food costs $1.25. He multiplies the numbers together to determine how much it costs to feed his dog each day. Which expression will result in the best estimate for Quincy to use to check his multiplication?
2 times 1
2 times 2
3 times 1
3 times 2
Answer:
3 times 1
Step-by-step explanation:
2.75 - 75 or in other words 7 is closer to 10 than 0, so well round it up to the next number, 3.
1.25 - 25 or in others words 2 is closer to 0 than 10, so we'll round it down to the nearest lowest whole number, 1.
our new expression: 3 × 1. hope that helps!
if you multiply the number of cars in the parking lot by 4 there would be 32 cars how many cars are in the lot?
Answer:
8
Step-by-step explanation:
there would be 8 cars in the parking lot
What is the answer to this?
Answer:
2x+1=9
Step-by-step explanation:
[tex]\sqrt{2x+1}+5=2[/tex]
[tex]\sqrt{2x+1}=-3[/tex]
[tex]2x+1=9[/tex]
If they want you to solve, then you can go farther.
2x=8
x=4
Check for extraneous solutions:
[tex]\sqrt{2(4)+1} +5 = 2[/tex]
please help me on this one thx i really need this one.
Answer:
6 meters
Step-by-step explanation:
Every 7 floors, it goes up by 22.4 meter intervals.
Let's count down,
the 7th floor would be 50.8 - 22.4, which is 28.4.
the 0th floor would be 28.4 - 22.4, which is 6.
Answer:
6
Step-by-step explanation:
SOMEBODY PLZ HELP NO LINKS PLZ AN THANK YOU
The scatter plot shows the number of minutes people had to wait for service at a restaurant and the number of staff available at he time. A line that models the data is given by the equation y=-1.62x + 18 where y represents the wait time and x represents the number of staff available. Use the equation to make a conjecture about the wait if there are 10 staff members available
A the wait time will be about 18 minutes
B the wait time will be about 5 minutes
C the wait time will be about - 2 minutes
D the wait time will be about 2 minutes
Answer:
im not too sure but B
Step-by-step explanation:
Two trucks, A and B, start from the intersection C of two straight roads at the same time. Truck A is traveling twice as fast as truck B, and after 4 hours, the two trucks are 350 miles apart. Find the approximate speed of truck B in miles per hour.
A. 39 B. 51 C. 44 D. 78
Answer:
6
Step-by-step explanation:
PLEASE HELP!!!
Bob and Sue are 12 miles apart and moving toward each other. Bob is running at a constant speed of 5mph, and Jada walks at a constant speed of 3mph How long does it take until Bob and Sue meet?
Answer:
34 miles
Step-by-step explanation:
jn
What is an equation of the line that passes through the points (−3,8) and (-7, 8)
Answer:
y = 8
Step-by-step explanation:
Since the y- coordinates of the points are equal, both 8 , then
This indicates the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (- 3, 8 ) and (- 7, 8 ) with y- coordinates 8 , then
y = 8 ← equation of line
a.
two more than seven times x
b. the product of ten and f,
increased by one
C. r divided by eleven
Answer:
A. two more than seven times x7 × x +27x+2B. the product of ten and f increased by one10 × f + 110f+1C. r divided by elevenr ÷ 11simplify 8+2(5-×) thanks
Answer:
=8+2(5-x)
=8+10-2x
=18-2x
Answer:
hey am
I think that's be the answer
if you think it's not right
don't write
The points (8, 1) and (6, 0) fall on a particular line. What is its equation in slope-intercept form?
Answer:
y=-3/2 x + 6Step-by-step explanation:
The following stock prices reflect the closing price for the past five days. Find the 3 day SMA
(Simple Moving Average) for days 2-4.
$44.25, $44, $41.75, $40, $39.75
Answer:
solution
Step-by-step explanation: total=209.75
Solve the equation. Express radicals in simplest form.
-4k2 - 13 = -77
LAST ATTEMPT MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)
Answers:
[tex]I(-2,-1) \to I \ ' \ (-5,-2.5)\\\\J(-1,2) \to J \ ' \ (-2.5,5)\\\\K(2,-1) \to K \ ' \ (5,-2.5)\\\\[/tex]
===============================================
Explanation:
Since the center of dilation is the origin, we multiply each preimage coordinate by 2.5 (which is the scale factor).
For example, the preimage point J(-1, 2) moves to J ' (-2.5, 5)
-1*2.5 = -2.52*2.5 = 5This will cause the image triangle I'J'K' to be larger than the preimage IJK. Specifically, each side of the image is 2.5 times longer compared to the preimage.
Answer:
i' (-5, -2.5) J' (-2.5, 5) K' (5, -2.5)
Step-by-step explanation:
you just take the original coordinates and multiply them by 2.5
Luis and Erin are playing a game. They each start with 0 points. At the end of the game, Luis has 250 points, and Erin has -250
Which statement about the game is true?
A. Erin and Luis have a total of 500 points.
B. Erin has lost 250 points.
C. Luis has 250 more points than Erin.
D. Erin and Luis have an equal number of points.
Answer:
B
Step-by-step explanation:
What is the next number
3, 4, 7, 16, 11, 64, …
Answers:
A) 55
B)14
C)39
D)15
the answer is c) 39 according to the sequence
The next number 3, 4, 7, 16, 11, 64, is: 55.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
When all the terms of a geometric sequence are added, then that expression is called geometric series.
We are given the series as;
3, 4, 7, 16, 11, 64, …
If we separate the numbers that in order are in the even place of the odd ones, we would have :
3, 4, 7, 16, 11, 64,..
If we finish in 1 then they increase by 1 in 1, while in 2.- they increase in odd numbers, the following number is: 55
The correct option is A.
Learn more about a number pattern:
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plz answer fast i will mark as brainlist
Answer:
36 is the answer
Step-by-step explanation:
Hope it will help you
A birthday cake was cut into equal pieces, and 10 pieces were eaten. The
fraction below shows how much cake was left over. According to the fraction,
into how many pieces was the cake cut?
1
11
A. 1
B. 10
C. 21
O D. 11
TO
What kind of taxes are likely to pay for universities and police?
а
local taxes
b. state taxes
C federal taxes
d income taxes
Answer: I'd say the best answer is b.
Step-by-step explanation:
Express the dollowing fraction in decimal form as a terminating decimal or as a infinite repeating decimal 3/16
Answer:
3/16 as a decimal is equal to 0.1875.
Let's convert the given fraction to a decimal number.
Explanation:
To convert any fraction to decimal form, we just need to divide its numerator by denominator.
Here the fraction is 3/16 which means we need to perform 3 ÷ 16.
So, 3/16 is equal to 0.1875.
Hope that helps you in some way.
When Alex went to work the temperature
was -2°F. When he got home from work the
temperature raised 14°. What was the
actual temperature when he got home from
work?
A man buys an article for $600 and sells it for $710. what is his profit or loss
Answer:
Profit of $110
Step-by-step explanation:
$710-$600=$110
Suzie has made a conjecture that the sum of consecutive odd numbers is always a perfect square. The example she used to show this to Timmy is 1 + 3 + 5 + 7+ 16 = 42. However, Timmy was not convinced and made a Venn diagram to find a counter-example, Do you agree with Suzie's conjecture? Use evidence from the Venn diagram to support your response
Answer:
Of course you don't agree with Suzie's conjecture - if there is a counterexample (and there is) to a conjecture, that conjecture is false.
Additional note:
Any sum of consecutive odd numbers starting with 1 is a perfect square. It can be proven mathematically, but the pleasant "proof" is to look at actual geometrical squares drawn from unit squares (like in your notebook).
When you have a square of NxN (N^2 unit squares), to go to the next square you need to add N on one side, N on a neighboring side, and 1 to fill the missing unit, for a total of adding 2N+1 squares and ending up with (N+1)x(N+1).
Because you can start from a 1x1 square and then add 2*1+1 = 3 to go to 2x2, then add 2*2+1=5 to go to 3x3 and so on.
Step-by-step explanation:
Timmy is not the brightest person for making this Venn diagram. He just needed to find 1 counterexample.
A book store is hosting a special night in which familles can enjoy a story and craft time. Tickets to the event must be bought ahead of time and are $1.50 for children and $2.50 for adults. So far, 45 children's tickets have been sold, which is 60% of the total tickets sold. How many tickets have been sold so far? Show or explain how you got your answer.steps please
Answer:
45
Step-by-step explanation:
just typing this so I'll have 20