Answer:
1). AC=8.25cm
2). DB=7cm & EC=14cm
3). See Explanation
Step-by-step explanation:
According To the Question,
Given That, In ∆ABC, D and E are points on the sides AB and AC respectively such that DE is parallel to BC.
1). If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC.
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD / BD = AE / EC
⇒ 2.5 / 3 = 3.75 / EC
On Solving we get,
⇒ EC * 2.5 = 3.75 * 3
⇒ EC * 2.5 = 11.25
⇒ EC = 11.25 / 2.5
⇒ EC = 4.5 cm
Thus,
AC = AE + EC
⇒ AC = 3.75 + 4.50
⇒ AC = 8.25 cm
Hence the measure of AC is 8.5 cm.
2). If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD / BD = AE / EC
⇒ 4 / (x-4) = 8 / (3x-19)
on solving we get,
⇒ 3x-19 = 2(x-4)
⇒ 3x-19 = 2x-8
⇒x=11
Thus, DB =x–4 ⇒ 11-4 ⇒ DB=7cm
And, EC =3x-19 ⇒ 3×11-19 ⇒ EC=14cm
3). If AD=2cm , BD= 4cm , show that BC = 3 DE
Thus, AB = AD + DB = 2+4 = 6cm
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD/AB = DE / BC
⇒ 2 / 6 = DE / BC
on solving we get
⇒ BC = 3 DE Hence, Proved
if A={1,2,3} and B={a,b,c} find A×B and B×A. Also show both of them in arrow diagram. I need for exam
Answer:
the above answer help you guy.
What is the simplest form of this expression?
Answer:
a is correct option......
What is the solution
Answer:
x = -72
Step-by-step explanation:
-72 + 8 = -64
The third square root of -64 is -4
Solve for x. Round to the nearest tenth of a degree, if necessary
Step-by-step explanation:
here's the answer to your question
HELP ASAP PLEASE!!!!!!!
Answer:
the answer is 2
Step-by-step explanation:
it doesn't match the other but is 2
The equation below has one solution. 9 x minus 10 = 3 x + 2 What is the solution to the equation? –2 –1 1 2
Answer:
x=2
Step-by-step explanation:
To the nearest square metre, calculate the curved surface area of the half pipe if it is 9m long? (With a radius of 2.5m)
Answer:
70.686 [tex]m^{2}[/tex]
Step-by-step explanation:
A=2πrh (area of cylinder without top or bottom)
A = 2[tex]\pi[/tex](2.5)(9)
A = 141.372
divide by two for half of pipe.
A = 70.686
Change 18° into sexagesimal seconds.
Answer:
She's, "HOT"!
Step-by-step explanation:
A baker's bread recipe calls for 3
cups of flour. She plans to make 2 loaves of
bread
If the baker's measuring scoop holds cup, how many scoops of
flour will she need in all?
A recipe for a soup calls for 2/4 cup of chopped onion and 1/5 cup of chopped
celery. What is the total amount of celery and onion needed for the soup?
Answer:
The total amount of celery and onion needed for the soup is 7/10 cup.
Step-by-step explanation:
2/4 + 1/5 = 7/10 cup.
hope it helped :)
mark me brainliest!
In how many ways can the 6 students with an identical twins on a round table?
Answer:
120
Step-by-step explanation:
5*4*3*2*1
Write an equation for a quadratic function in factored form with
zeros at x = -4 and x = 0 that passes through the point (-3,6).
Answer:
[tex]f(x)=-2x(x+4)[/tex]
Step-by-step explanation:
We want to find the equation of a quadratic function in factored form with zeros at x = -4 and x = 0 that passes through the point (-3, 6).
The factored form of a quadratic is given by:
[tex]f(x)=a(x-p)(x-q)[/tex]
Where p and q are the zeros and a is the leading coefficient.
Since we have zeros at x = -4 and x = 0, let p = -4 and q = 0. Substitute:
[tex]f(x)=a(x-(-4))(x-0)[/tex]
Simplify:
[tex]f(x)=ax(x+4)[/tex]
And since we know that the function passes through the point (-3, 6), f(x) = 6 when x = -3. Thus:
[tex](6)=a(-3)(-3+4)[/tex]
Simplify:
[tex]6=a(-3)(1)[/tex]
Thus:
[tex]-3a=6\Rightarrow a=-2[/tex]
So, our quadratic function is:
[tex]f(x)=-2x(x+4)[/tex]
URGENT HELP NOW PLEASE QUICKK!!!!
Answer:
(2,-2)
Step-by-step explanation:
Its just (-7+9 , 1-3)
Answer:
P' = (2,-2)
Step-by-step explanation:
P = (-7,1)
T(x,y) = (x + 9, y - 3)
(-7 + 9,1 - 3) = (2,-2)
Find the length of x
Answer:
x = 3
Step-by-step explanation:
Hi there!
1) Prove similarity
The two triangles are similar due to angle-angle similarity. They both have an angle measured 90 degrees and the angles of the two corners that touch are equal, because opposite angles are equal.
2) Solve for x
Now, we can set up a proportion to solve for x:
[tex]\frac{x}{4} =\frac{4.5}{6} \\x=\frac{4.5}{6} *4\\x=3[/tex]
Therefore, x is 3 units long.
I hope this helps!
which equation is represented by the table
Answer:
B. b = 3a + 2
Step-by-step explanation:
We can write the equation in slope-intercept form as b = ma + c, where,
m = slope/rate of change
c = y-intercept/initial value
✔️Find m using any two given pair of values, say (2, 8) and (4, 14):
Rate of change (m) = change in b/change in a
m = (14 - 8)/(4 - 2)
m = 6/2
m = 3
✔️Find c by substituting (a, b) = (2, 8) and m = 3 into b = ma + c. Thus:
8 = 3(2) + c
8 = 6 + c
8 - 6 = c
2 = c
c = 2
✔️Write the equation by substituting m = 3 and c = 2 into b = ma + c. Thus:
b = 3a + 2
PLEASE I NEED HELP. summer school
Answer:
1. Y+2/5y
2. y-0.32y
3. Y-2/5y
4. y+0.32y
Step-by-step explanation:
simplify 2a+5b/4+3a+2b/8
Answer:
Step-by-step explanation:
Combine like terms
[tex]2a + \frac{5b}{4}+3a + \frac{2b}{8}=2a + 3a +\frac{5b}{4}+\frac{2b}{8}\\\\ = 2a + 3a + \frac{5b}{4}+\frac{b}{4}\\\\= 5a + \frac{5b+b}{4}\\\\= 5a +\frac{6b}{4}\\\\= 5a + \frac{3b}{2}[/tex]
Answer:
[tex]2a+5\frac{b}{4}+3a+2\frac{b}{8}[/tex]
First multiply by 8
[tex]2\cdot8a+5\cdot8\cdot\frac{b}{4}+3\cdot8\cdot a+2\frac{b}{8}\cdot8[/tex]
We multiple and divide where we can
[tex]16a+10b+24a+2b[/tex]
And now it's simple
30a+12b
If 1 pint is equal to 2 cups, then 5 pints would equal how many cups
If 1 pint is equal to 2 cups then 5 pints equals 10 cups
5 times 2 equals 10.
What is the value of the expression below
(-64)^2/3
Answer:
16
Step-by-step explanation:
[tex](-64)^2/3[/tex]
64 = [tex]2^{6}[/tex]
[tex]2^{6} ^{\frac{1}{3} } ^{2}[/tex]
[tex]2^{ 2^{2} }[/tex]
[tex]2^{4}[/tex]
16
If the radius of circle is 50cm then find its area?
Answer:
Area=7850 cm
Step-by-step explanation:
Since the formula for area is A=c(radius squared), we need to plug in the radius first. 50x50=2500. We can identify 'pi' as 3.14 and use that decimal instead of a longer one. The product of 2500 and 3.14 is 7850. Therefore, your answer is 7850 cm
Please help me I need this doing for my maths hwk and I really don’t know
1. make r the subject of the relation. 2. Find the value of r when s=117, m = 2 and n=-3. m=r-s ÷2nr
Answer:
Hence, the required answers are (i) r= -s/(2nm-1) and r=g.
Step-by-step explanation:
solution: m= r-s/2nr
i) m= r-s/2nr 2) m(2nr) = r-s (i) s=117 ,m=2, n=-3
2) 2xnxmxr= r-s 2) r= -s/(2nm-1)
3) move the "r" on the right to the 2) r= -117/(2x(-3)x2)-16
-2nrm-r= -s
- r(r-2nm-1)= -s 2) r= (-117/-13)=)r=g
- r= -s/(2nm-1)
Hence, the required answers are (i) r= -s/(2nm-1) and r=g.
The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly 12 centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum volume
Answer:
Vmax = 192.33 cm³
Step-by-step explanation: An error in the problem statement. The sides of the box could not be 12 cm. We assume 1.5 cm
Inside dimensions of the box:
Outer dimensions : 12 10 8
2 * 1.5 = 3 3 3 3
Inside dimensions: 9 7 5
The volume of a right circular cylinder is:
V(c) = π*r²*h r is the radius of the base and h the height
By simple inspection is obvious that volume maximum will occur when r is maximum, and r is maximum, only when the base of the cylinder is in the rectangle 12*10. ( Inside dim 9*7 ) In that case r = 7/2 r = 3.5 cm
Then the height is 5 cm.
And the maximum volume of the cylinder is:
Vmax = 3.14* ( 3.5)²*5
Vmax = 192.33 cm³
In triangle XYZ. the measurements of angle X and angle Y are 45° Which is the longest side of the triangle
Answer:
the side XY
Step-by-step explanation:
we know 2 angles in a triangle. but are 45 degrees.
that means the third angle Z is 180-45-45 = 90 degrees.
the side opposite of the largest angle is the longest side.
opposite of Z is the side XY.
A group of 80 frogs was observed. The mean distance of their hops is 69 inches with a standard deviation of 3.5 inches. How many frogs would you expect to jump more than 72.5 inches?
Hello,
[tex]z=\dfrac{X-69}{3.5} \\\\For\ X=72.5, \\\\z=\dfrac{72.5-69}{3.5} =1\\[/tex]
Using table of a normal reduced law:
p(z≤1)=0.8413
Thus p(z≥1)=1-0.8413=0.1587
There are 80*0.1587=12.696 ≈13 (frogs)
Answer:
12 frogs
Step-by-step explanation:
Hello,
Using table of a normal reduced law:
p(z≤1)=0.8413
Thus p(z≥1)=1-0.8413=0.1587
There are 80*0.1587=12.696 ≈12 (frogs) you don't round up because you cant have .7 percent of a frog.
ps. I copy and pasted caylus's response but corrected their answer because it was correct except the rounding up part.
area of trapezoid? i keep getting it wrong lol the shape is confusing to me please help
Answer:
Area= [tex]154m^{2}[/tex]
Step-by-step explanation:
A= [tex]\frac{a+b}{2} h=\frac{12+16}{2} (11)=154[/tex]
can you please help me with number 4 please?
1. What measure of variability is the simplest?
A. Mean Deviation
B. Range
C. Standard Deviation
D. Variance
Answer:
range
Step-by-step explanation:
Write an equation of the line in slope-intercept form
The slope intercept form of the line is ,
> y = mx + c
where ,
m is slope of the linec is y interceptExample :-
> y = 2x + 5
The line passes through (0,5) with a slope of 2 .Find the size of each of the unknown angles. Help me plz
Answer:
2a+15 = 125(being alternate angle)
or,2a = 125-15
or,2a = 110
or,a = 110÷2
,a = 55
again,2a+15+b+30=180(Being co-interior angle)
or,2×55+15+b+30=180
or,110+15+30+b=180
or,155+b=180
or,b=180-155
Therfore,b=25