In isosceles ∆ABC the segment BD (with D ∈ AC) is the median to the baseAC. Find BD, if the perimeter of ∆ABC is 50m, and the perimeter of ∆ABD is 40m.
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Related Questions
Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lbs. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has?
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x = number of 3-lb weights
y = number of 10-lb weights
weight of 3-lb weights = 3x
weight of 10-lb weights = 10y
total weight = 3x + 10y
equation
3x + 10y = 50
in how many ways can jasmine draw a blue or yellow marble from the jar containing 28 blue marbles and 7 yellow marbles
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Factor this expression completely.
ab + 4 + a + 4b
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Rearrange.
[tex]ab+4+a+4b[/tex]
[tex]ab+a+4+4b[/tex]
Factor by grouping.
[tex]a(b+1)+4(1+b)[/tex]
[tex]a(b+1)+4(b+1)[/tex]
Find the GCF.
[tex](b+1)(a+4)[/tex]
Hope this helped.
-Benjamin
The sum of twice a first number and five times a second number is 78. If the second number is subtracted from five times the first number the result is 33. Find the numbers.
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Explanation:
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Let: "x" be the "first number" ; AND:
Let: "y" be the "second number" .
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From the question/problem, we are given:
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2x + 5y = 78 ; → "the first equation" ; AND:
5x − y = 33 ; → "the second equation" .
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From "the second equation" ; which is:
" 5x − y = 33" ;
→ Add "y" to EACH side of the equation;
5x − y + y = 33 + y ;
to get: 5x = 33 + y ;
Now, subtract: "33" from each side of the equation; to isolate "y" on one side of the equation ; and to solve for "y" (in term of "x");
5x − 33 = 33 + y − 33 ;
to get: " 5x − 33 = y " ; ↔ " y = 5x − 33 " .
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Note: We choose "the second equation"; because "the second equation"; that is; "5x − y = 33" ; already has a "y" value with no "coefficient" ; & it is easier to solve for one of our numbers (variables); that is, "x" or "y"; in terms of the other one; & then substitute that value into "the first equation".
____________________________________________________
Now, let us take "the first equation" ; which is:
" 2x + 5y = 78 " ;
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We have our obtained value; " y = 5x − 33 " .
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We shall take our obtained value for "y" ; which is: "(5x− 33") ; and plug this value into the "y" value in the "first equation"; and solve for "x" ;
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Take the "first equation":
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→ " 2x + 5y = 78 " ; and write as:
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→ " 2x + 5(5x − 33) = 78 " ;
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Note the "distributive property of multiplication" :
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a(b + c) = ab + ac ; AND:
a(b − c) = ab − ac .
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So; using the "distributive property of multiplication:
→ +5(5x − 33) = (5*5x) − (5*33) = +25x − 165 .
___________________________________________________
So we can rewrite our equation:
→ " 2x + 5(5x − 33) = 78 " ;
by substituting the: "+ 5(5x − 33) " ; with: "+25x − 165" ; as follows:
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→ " 2x + 25x − 165 = 78 " ;
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→ Now, combine the "like terms" on the "left-hand side" of the equation:
+2x + 25x = +27x ;
Note: There are no "like terms" on the "right-hand side" of the equation.
_____________________________________________________
→ Rewrite the equation as:
_____________________________________________________
→ " 27x − 165 = 78 " ;
Now, add "165" to EACH SIDE of the equation; as follows:
→ 27x − 165 + 165 = 78 + 165 ;
→ to get: 27x = 243 ;
_____________________________________________________
Now, divide EACH SIDE of the equation by "27" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
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27x / 27 = 243 / 27 ;
→ to get: x = 9 ; which is "the first number" .
_____________________________________________________
Now; Let's go back to our "first equation" and "second equation" to solve for "y" (our "second number"):
2x + 5y = 78 ; (first equation);
5x − y = 33 ; (second equation);
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Start with our "second equation"; to solve for "y"; plug in "9" for "x" ;
→ 5(9) − y = 33 ;
45 − y = 33;
Add "y" to each side of the equation:
45 − y + y = 33 + y ; to get:
45 = 33 + y ;
↔ y + 33 = 45 ; Subtract "33" from each side of the equation; to isolate "y" on one side of the equation ; & to solve for "y" ;
→ y + 33 − 33 = 45 − 33 ;
to get: y = 12 ;
So; x = 9 ; and y = 12 . The numbers are: "9" and "12" .
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To check our work:
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1) Let us plug these values into the original "second equation" ; to see if the equation holds true (with "x = 9" ; and "y = 12") ;
→ 5x − y = 33 ; → 5(9) − 12 =? 33 ?? ; → 45 − 12 =? 33 ?? ; Yes!
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2) Let us plug these values into the original "second equation" ; to see if the equation holds true (with "x = 9" ; and "y = 12") ;
→ 2x + 5y = 78 ; → 2(9) + 5(12) =? 78?? ; → 18 + 60 =? 78?? ; Yes!
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So, these answers do make sense!
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Five times the sum of a number (x) and three is equal to the sum of that number (x) and fifteen.
I just need to know how to put this from Word-Form into Number form and solve for the
x. Please help.
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its simple
5x + 15 = x + 15...subtract x from both sides, subtract 15 from both sides
5x - x = 15 - 15
4x = 0
x = 0 <=
Suppose FLX =ZAQ Which other congruency statements are correct
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XLF=QAZ
FXL=ZQA
XFL=QZA
Classify each number by indicating in which set or sets it belongs 8 and 0.25
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0.25 is a rational number
The number 8 belongs to the sets of natural numbers, integers, rational numbers, and real numbers, while the number 0.25 only belongs to the sets of rational and real numbers.
Explanation:In mathematics, numbers can belong to various sets such as the natural numbers, integers, rational numbers, real numbers, etc. In this case, the number 8 belongs to all these sets because it is a whole number without fractions or decimals. Therefore, it is a natural number, integer, rational number and real number.
On the contrary, 0.25 is a decimal which belongs to the sets of rational numbers and real numbers. It does not belong to the sets of natural numbers or integers because it is not a whole number.
Learn more about Number classification here:https://brainly.com/question/32665385
Can someone help me write an equation for this problem?
Felicity put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Her monthly payment will be $175. After 9 months how much will she have paid for the car?
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And then just solve for y.
Allen's boat used 6 gallons of gas in 5 hours. at this rate, how many gallons of gas will the boat use in 12 hours?
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50h + 0.20s + 40 part
a.identify a coefficient, a variable, and a constant in this expression. part
b.if corinne works for 25 hours and sells $300 in magazines, how much does she earn for the week? show your work to receive full credit. part
c.if corinne gets a raise and begins earning $9 per hour, would the coefficient, variable, or constant in the equation change? why?
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Coefficient: 50
Variable: h
Constant: s
b.
50(25) + 0.20(300) + 40
1250 + 60 + 40
1350
Corinne earns $1350
c.
The coefficient would change because a coefficient is the number in front of a variable, and the number changed, not the variable or constant.
which angle is included angle forJL and KL
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The leg of a right triangle is 3 units and the hypotenuse is 7 units. What is the length, in units, of the other leg of the triangle?
4
Square root of 40
Square root of 58
10
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3^2 + b^2 = 7^2
9 + b^2 = 49
b^2 = 49 - 9
b^2 = 40.....take sqrt of both sides, eliminating the ^2
b = square root of 40 <==
Answer:
square root of 40
Step-by-step explanation:
a^(2)+b^(2)=c^(2)
3^(2)+b^(2)=7^(2)
9+b^(2)=49
9-9+b^(2)=49-9
b^(2)=40
sqr b^(2)=sqr 40
b=6.32455532034
therefore,the square root of 40 is the answer
If m<3 is five times the measure of its supplement (<4), then determine the measure of each angle.
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Let y = m∠4
Because y is the supplement of x, therefore
x + y = 180° (1)
Because x is five times y, therefore
x = 5y (2)
Substitute (2) into (1).
5y + y = 180
6y = 180
y = 30°
From (2), obtain
x = 5*y = 5*30 = 150°
Answer:
m∠3 = 150°
m∠4 = 30°
Plot the inequality on the number line.
−7≤x≤−2
Choose the proper tool with the correct endpoints then click and drag the endpoints to the correct location.
Notice the trash can is available if an error is made.
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split them..
x > = -7......x < = -2
ok....u need the symbol where it shows 2 solid dots...with the line in the middle....no arrows.....one dot will be on -7 and the other dot will be on -2
Plot the inequality on the number line. the graph is attached below.
Use the tool that has solid dots at both ends
Explanation :
Plot the inequality on the number line.
−7≤x≤−2
We start plotting the point at -7. we use closed circle at -7 because we have less than or equal to sign at -7
Now we plot another point at -2. here also we use closed circle that is solid circle .
Now shaded the region between -7 and -2 because x lies between -7 and -2
The graph of number line is attached below
The tool uses here is a line with solid dot at both ends
Learn more: brainly.com/question/13350310
An item is regularly priced at $40. she bought it at a discount of 35% off the regular price. How much did she pay?
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x 35
-- = --
40 100
This will show you how much money is off of the item.
After you solve the ratio (cross multiply and divide), you should have gotten the answer $14. Then you subtract 14 from 40 to get the price of the item currently at 35% off. The answer would be $25.
As a salesperson, you are paid $100 per week plus $3 per sale. This week you want your pay to be at least $160. Write an inequality for the number of sales you need to make, and describe the solutions. A) 100 - 3s ≤ 160; s ≤ 20 B) 100 + 3s ≥ 160; s ≥ 18 C) 100 - 3s ≤ 160; s ≤ 18 D) 100 + 3s ≥ 160; s ≥ 20
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Answer:
The answer is D. Hope it helps!
Molly walked four more miles than Tim. Together, they walked ten miles. How many miles did each walk? The replacement set is {1, 2, 3, 4}.
a. Define the variable, and write expressions for the number of miles each person walked.
b. Write an equation that represents the problem.
c. Solve the equation. (Be sure to try every element in the replacement set and to show all of your work.)
d. Answer the question. (Remember, answers to word problems have units.)
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A) Variable = x ( miles Tim walked )
B) Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)
Equation: x + x+4 = 10
C) x +x+4 = 10
2x+4 = 10
2x =6
x = 3
D)
Tim walked 3 miles, Molly walked 7 miles
What is vertex on a graph
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the present age of sahil's mother is three time the present age of sahil . after 5 years their ages add up to 66 years . find theor present ages
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Sahil = x
After 5 years:
3x + 5 + x + 5 = 66
4x + 10 = 66
You finish.
What is the slope intercept form of 6x + 2y = 24?
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2y = -6x + 24...now divide both sides by 2
y = -6/2x + 24/2...now reduce
y = -3x + 12 <=== slope intercept form of y = mx + b
7x - 2 = 2y 3x = 2y - 1
Solve the system of equations by substitution.
(3/4, 13/8), (1/4, -1/8), no solution, coincident
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7x = 2y + 2
so
7x = 2y + 2
3x = 2y - 1
----------------subtract
4x = 3
x = 3/4
7x - 2 = 2y
7(3/4) - 2 = 2y
21/4 - 2 = 2y
21/4 - 8/4 = 2y
13/4 = 2y
so
y = 13/4 * 1/2
y = 13/8
answer
(3/4, 13/8)
Answer:
7x - 2 = 2y
7x = 2y + 2
so
7x = 2y + 2
3x = 2y - 1
----------------subtract
4x = 3
x = 3/4
7x - 2 = 2y
7(3/4) - 2 = 2y
21/4 - 2 = 2y
21/4 - 8/4 = 2y
13/4 = 2y
so
y = 13/4 * 1/2
y = 13/8
answer
(3/4, 13/8)
Step-by-step explanation:
What two numbers multiply to 12 and add to negative 4?
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The two numbers that multiply to 12 and add to negative 4 are -6 and 2.
To find the two numbers, we need to solve the system of equations:
1. xy = 12 (Equation 1)
2. x + y = -4 (Equation 2)
From Equation 2, we can express y in terms of x:
y = -4 - x (Equation 3)
Now, we substitute Equation 3 into Equation 1:
[tex]\( x(-4 - x) = 12 \)\\ \( -4x - x^2 = 12 \)\\ \( x^2 + 4x - 12 = 0 \)[/tex]
We can factor this quadratic equation:
[tex]\( (x + 6)(x - 2) = 0 \)[/tex]
Setting each factor equal to zero gives us two possible solutions for x:
[tex]\( x + 6 = 0 \) or \( x - 2 = 0 \)[/tex]
So, [tex]\( x = -6 \) or \( x = 2 \)[/tex].
Using Equation 3 to find the corresponding y values:
If ( x = -6 ), then ( y = -4 - (-6) = 2 ).
If ( x = 2 ), then ( y = -4 - 2 = -6 ).
Therefore, the two pairs of numbers that satisfy both conditions are (-6, 2) and (2, -6). Since the question asks for two numbers, and both pairs contain the same numbers, the answer is -6 and 2.
explain how you can solve 40 × 16 by breaking apart the numbers.
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Is it possible for a line ax+by=c to lack a y-intercept? To lack an x-intercept
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I need the steps to this, please. It says solve for x. Each figure is a parallelogram. Show your work.
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FH is one diagonal that is split into two equal pieces by the other diagonal EG.
The two parts of FH (KH and KF) are congruent to each other, so KH = KF. They combine back to FH
By the segment addition postulate
KH + KF = FH
KH + KH = FH .... KF has been replaced with KH (works because KF = KH)
2*KH = FH
Now use substitution
2*KH = FH
2*15 = FH .... replace KH with 15 (since KH = 15)
2*15 = 4x-2 ... replace FH with 4x-2 (since FH = 4x-2)
and solve for x
2*15 = 4x-2
30 = 4x-2
30+2 = 4x-2+2 ... add 2 to both sides
32 = 4x
4x = 32
4x/4 = 32/4 ... divide both sides by 4
x = 8
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Answer: x = 8
3x - 7 = 14 implies that 3x = 21
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which of the following statement are false? o vertical angles are congruent. o angles with measures between 0 and 90 are complementary. o straight angles are supplementary. o angles with measures between 90 and 180 are obtuse
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2. Angles with measures between 90 and 0 degrees are complementary. Assuming this means that two angles add to a sum of 90, this is true.
3. Straight angles are supplementary. Since a straight angle is only one angle, it is not supplementary, even though it is 180 degrees. This is false.
4. Angles with measures between 90 and 180 degrees are obtuse. This is true.
The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
The triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.
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Answer:
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Step-by-step explanation:
The rule we have is (x, y)→(2x, 2y). This means that each x-coordinate and each y-coordinate are multiplied by 2. This is a dilation by a factor of 2.
This will stretch the image by a factor of 2; this means the sides will be twice as long. This means they will not be congruent.
Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .
Step-by-step explanation:
Rigid motions form congruent figures, the common rigid motions are:
1) translation (moves figure about some distance)
2) reflection (creates mirror image)
3) rotation (rotate figure about some degrees)
Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .
Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Here the coordinates of the image are increased by using a scale factor 2.
So △D′E′F′ must be an enlargement of △DEF.
⇒△D′E′F′ is a dilation of △DEF
It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Prove or disprove: if p and q are prime numbers then pq - 2 is also a prime number.
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Counterexample:
[tex] p=2\\
q=3\\\\
pq-2=2\cdot3-2=4 [/tex]
4 is not a prime number. So, it's false.
How do you find the amount of nuetrons in an atom?