I constructed line AD as a perpendicular bisector of line BC. Angles BDA and CDA are both 90 degrees because of the construction of a perpendicular bisector. Angles BDA and CDA are congruent because of the transitive property of equality. Line BD is also equal to CD according to the definition of a perpendicular bisector. Triangles ABD and ACD are congruent by the angle side angle postulate. Since the parts of the congruent triangles are congruent, lines AB and AC are congruent.
The sides AB and AC opposite the congruent base angles of a triangle are congruent.
What is an isosceles triangle?An isosceles triangle is a triangle with (at least) two equal sides. A polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 180°.
For the given situation,
Triangle ABC be an isosceles triangle.
∠ABC ≅ ∠BCA.
The diagram below shows an isosceles triangle ABC with AD is the perpendicular bisector of BC.
The perpendicular bisector AD divides the line BC as BD and DC.
Then, BD = DC.
We get triangles ΔADB and ΔADC,
AD = AD [∵ common side]
⇒ [tex]\angle ADB = \angle ADC=90[/tex]
Thus by ASA theorem,
The two triangles ΔADB and ΔADC are similar.
Then by CPCT theorem,
Side AB ≅ AC.
Therefore the sides AB and AC opposite the congruent base angles of a triangle are congruent.
Hence we can conclude that the sides AB and AC opposite the congruent base angles of a triangle are congruent.
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PLEASE ANSWER
What do degrees measure?
A. the incline of an angle
B. the orientation of an angle
C. the type of angle
D. the length of an angle
Answer:
I woulda said B too...
Step-by-step explanation:
What is a more economical purchase, a 5-pound box of spaghetti priced at $6.02, or a 1.5-pound box for $1.70?
12x+7<−11 AND5x−8≥40
Answer:
12x+7<−11 x < - 1.5
5x−8≥40 x ≥ 9.6
Step-by-step explanation:
12x+7<−11 First, move the constant to the right. 12x < -11 - 7 Then, we can get the total value and then divide everything by 12. 12x < -18 -> x < - 1.5
5x−8≥40 Move the constant to the right. 5x ≥ 40+8 Then, after we add the constants, we can divide both sides by 5. 5x ≥ 48 -> x ≥ 9.6
Answer:
NO SOLUTION IS THE ANSWER FOR KHAN ACADEMY
Step-by-step explanation:
solve:4x+3y=20;4x+2y=10 by matrix method
Answer:
i don't know sorry . and study well to make your future good
The daily high temperatures in a vacation resorts in approximately normal, with a mean temperature of 75 Fahrenheit and a standard deviation of 6 degrees. What percentage of days have a high temperature between 66 and 88?
A.17.01%
B.35.62%
C.64.37%
D.72.99%
Can someone help me with this geometry question thanks will mark brainliest
For parallel lines, gradients (slope) must be the same.
The lines given in multiple choice, no line with the same gradient/slope as line y = 3x - 2.
Step-by-step explanation:
From y = 3x - 2,
The slope = 3
Let's check slopes of lines from multiple choice:
From first line
4x + 2y = 5
2y = -4x + 5 (dived 2 both sides)
y = - 2x + 5/2
The slope = -2
Continue with remaining three equations you get slopes: -1/2, -4 and 4.
Hence no equations above represent parallel equation to y = 3x - 2
Jessica had 95 dollars to spend on 6 movies. After buying them she had 17 dollars. How much did each movie cost ?
show work
Answer:
$13 per movie
Step-by-step explanation:
Each movie costed $13 because if Jessica had $95 to spend on 6 movies, and she had $17 after buying all of them, the 6 movies costed a total of $78, and 78 divided by 6=$13 per movie. Hope it helps!
Answer:
13
Step-by-step explanation:
95-17 = 78.
then divide 78 by 6 which equals 13
FIRST RIGHT GETS BRAINLIEST
Answer:
Red is sus
Step-by-step explanation:
Answer: naah i think brown is sus he faked electrical vote him out
Step-by-step explanation:
20 POINTS WILL MARK BRAINLIEST PLEASE EXPLAIN
Answer:
DCE is 54°
Step-by-step explanation:
To solve this, we must come up with an equation. Since D, C, and E are each straight lines, they are each 180°. then, each line is separating the other which splits the 180 degree line into two parts. For example, E separates D, C separates E, and so on. The exterior angles are given, but the interior aren't. So:
for angle EDC: 180 - (9x - 31)
for angle CED: 180 - (4x + 33)
for angle DCE: 180 - (7x - 2)
we know that all angles in a triangle add up to 180°. So, our equation is:
180 - (9x - 31) + 180 - (4x + 33) + 180 - (7x - 2)=180.
simplify:
180 - 9x + 31 + 180 - 4x - 33 + 180 - 7x + 2=180
540 - 20x = 180
540 - 180 = 20x
360=20x
x= 18
for angle EDC: 180 - (9•18 - 31)=49°
for angle CED: 180 - (4•18 + 33)=75°
for angle DCE: 180 - (7•18 - 2)=54°
A costume designer needs some silver and gold thread for the costumes for a school play. She needs a total of 240 yards. At a store that sells thread by the yard, silver thread costs $0.04 a yard and gold thread costs $0.07 a yard. The designer has $15 to spend on the thread.
How many of each color should she get if she is buying exactly what is needed and spending all of her budget?
Write an equation for the length constraint. Write an equation for the cost constraint. solution
Answer:
Where s represents silver and g represents gold,
Length constraint: s+g=240
Cost constraint: 0.04s+0.07g=15
s= 60
g=180
Step-by-step explanation:
The measurement of silver and gold threads in yards is given as 60 and 180 respectively.
What is a system of linear equations?A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
The given problem can be solved as follows,
Suppose the number of yards for silver threads be x and that of gold be y.
Then the equation for the total yard is given as,
x + y = 240 (1)
And, the equation for the cost is,
0.04x + 0.07y = 15 (2)
The value of x from equation (1) is x = 240 - y.
Substitute the value of x in equation (2) to obtain,
0.04(240 - y) + 0.07y = 15
=> 9.6 - 0.04y + 0.07y = 15
=> 0.03y = 15 - 9.6
=> 0.03y = 5.4
=> y = 180
Substitute the value of y in x = 240 - y to obtain,
x = 240 - 180 = 60
Hence, the costume designer should get silver and gold thread of 60 yards and 180 yards respectively.
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-3y > 9 or y - 6 > 2
Answer:
Your answer is: y < -3 or y > 8
The union consists of all of the elements that are contained in each interval.
Step-by-step explanation:
Hope this helped : )
the sum and twice the number and 18 is greater than 25
Answer:
Step-by-step explanation:
45
I need help with this question ! if someone could also explain what the answer is, that would be awesome.
Answer:
y=3/2x+3
Step-by-step explanation:
The slope is 3/2. The slope is m. We plug 3/2 into our equation.
y=mx+b
y=(3/2)x+b
Now we have to find b.
B is 3 because that's where it crosses the y axis.
So y=3/2x+3
What is the equation of the line that passes through the point -5, two and has a slope of -2/5
9514 1404 393
Answer:
y -2 = (-2/5)(x +5)
Step-by-step explanation:
You can put the given values for the point ((h, k) = (-5, 2)) and slope (m = -2/5) into the point-slope form of the equation for a line:
y -k = m(x -h)
y -2 = -2/5(x +5)
_____
This equation simplifies to ...
y = -2/5x
The ratio of boys to girls is 4:6 in Mrs. Franklin's class. If there are 36 girls, how many boys are there?
Answer:
24
Step-by-step explanation:
Lets say 4 boys to 6 girls if there are 36 girls do 4x6 to figure out the ratio of boys would be 24 boys and 36 girls if the other way around it would be 24 girls and 36 boys
Situation: The No Doze Cafe sells Pumpkin Spice Lattes for $3 and Caramel Hot Apple Cider for $2. On a cool autumn morning, the shop sold 5 more Ciders than Lattes and made $25.
Define x and y variables and write the equation/s.
The points D, E, F and G all lie on the same line segment, in that order, such that the ratio of DE:EF:FGDE:EF:FG is equal to 6:5:1.6:5:1. If DG=36,DG=36, find DF.DF.
Answer:
i
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Which expression is equivalent to 42 + 63?
Answer: 104-63 maybe?
Step-by-step explanation:
There are 1200 students in a school 51% of them are female how many are male
Answer:
Step-by-step explanation:
588 are boys
1% of 1200 is 12, 50% is 600, add 12 and 600 together, you get 612, subtract it from 1200 and it gives you 588
AYUDAAAAAAAAA PORFA NO LE ENTIENDO
1. What is the difference between Salary and Wage?
2. $15 per hour is the basic rate at a factory. After a 48-hour basic work week,
overtime is paid time and a half.
a. If no one worked overtime and the factory paid $15840 in wages one week
how many workers are in the factory?
b. During another week, a worker in the factory earns $810 in wages for
himself. How many hours did he work for?
Hi
Answer:
answer yourself
Step-by-step explanation:
2 times what equals 84
Answer:
42
Step-by-step explanation:
Let x be the missing number in the equation
Write out the equation: 2x = 84Divide each side by 2 to cancel out the 2 next to x. It should now look like this: x = 42
I hope this helps!
Using what you noticed, find the measures of the four angles at point B in this second diagram. Lines AC and DF are parallel.
Answer:
The measures of the four angles at B are
m∠EBC = 34°
m∠ABH = 34°
m∠EBA = 146°
m∠CBH = 146°
Step-by-step explanation:
∵ AC // DF
∵ HG is the transversal
∴ m∠GEF = m∠EBC ⇒ corresponding angles
∵ m∠GEF = 34°
∴ m∠EBC = 34°
∵ GH intersects AC at B
∴ m∠EBC = m∠ABH ⇒ vertically opposite angles
∵ m∠EBC = 34°
∴ m∠ABH = 34°
∵ B ∈ AC
∴ ∠EBC and ∠EBA formed a pair of linear angles
∵ The sum of the measures of the pair of linear angles is 180°
∴ m∠EBC + m∠EBA = 180°
→ Substitute m∠EBC by 34°
∴ 34 + m∠EBA = 180
→ Subtract 34 from both sides
∵ 34 - 34 + m∠EBA = 180 - 34
∴ m∠EBA = 146°
∵ ∠EBA and ∠CBH are vertically opposite angles
∴ m∠EBA = m∠CBH
∵ m∠EBA = 146°
∴ m∠CBH = 146°
please help me asap
7. option 2 : 104
8. option 4 : 54
9. option 2 : 23
10. option 2 : 6
11. option 2 : 6
Which number is greater than the absolute value of LaTeX: -\frac{3}{8}− 3 8?
Answer:
0.5
Step-by-step explanation:
We have to find a number which is greater than the absolute value of -3/8.
Absolute value of -3/8 = 3/8
3/8=0.375
Now, we have to find a number which is greater than 0.375
1/4=0.25
0.25 is smaller than 0.375
0.5 is greater than 0.375
also -5/8 and -1/8 are less than 0.375
Hence, the only number which is greater than the absolute value of -3/8 is:
0.5
Step-by-step explanation:
Round off to the highest place value of 5658
Answer:
6000
Step-by-step explanation:
You want to make the 5 a 6 and zero's for the rest. You make the five a six because if the number is 5 or higher you bump it up one number, if it is 4 or lower you don't need to bump it up or down. I hope this helps!
Place values is the value of a digit in relation to its position
5658 approximated to the highest place value is 6000
The number is given as:
[tex]\mathbf{Number = 5658}[/tex]
The number is in thousands; so, the highest place value is thousands
This means that the number must be approximated to thousands.
When 5658 is approximated to the nearest thousands, the approximated value is:
[tex]\mathbf{Approximated = 6000}[/tex]
Hence, 5658 approximated to the highest place value is 6000
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Removing which ordered pair will make the relation a function?
What numbers rounded to 200,000 when rounded to the nearest hundred thousand
Answer:
The answer would be 150,000 to 249,999
Help my 11 old daughter please I don’t know this type of math
Answer:
2nd Choice- $2.14 total
Step-by-step explanation:
The expression is just adding the factors, 1.19 and 0.95. Then the counting sets, a whole square shaded is 100 units, a bit more is shaded of the second square, which signifies the .19 cents. Then yellow shade shows the lip balm cost, which is 0.95.
Mary has 24 pounds of sugar and is going to separate it into , pound bags for the students in her class. How many bags of sugar will she have?
Answer:
24?
Step-by-step explanation: