Answer:
x = 12°
y = 1.4 cm
Step-by-step explanation:
1. Because the two triangles are similar, their corresponding angles are congruent.
so
3x + 14 = 50
Subtract 14 from both sides
3x = 36
Divide both sides by 3
x = 12
x = 12° (remember units)
Check work:
3(12) + 14 = 50
36 + 14 = 50
50 = 50
2. Because the two triangles are similar, their corresponding sides are in equal proportion.
Two sides of triangle ABE are
5.6 and 4
And two corresponding sides of triangle ACD are
5.6 + y and 5
So
5.6 / 4 = (5.6 + y) / 5
Cross multiply
5.6 * 5 = 4(5.6 + y)
Multiply 5.6 * 5 on the left
28 = 4(5.6 + y)
Distribute the 4 to each term
28 = 4*5.6 + 4*y
Simplify the right side
28 = 22.4 + 4y
Subtract 22.4 from both sides
5.6 = 4y
Divide by 4 on both sides
1.4 = y
y = 1.4 cm (remember units)
Check our work:
5.6/4 = (5.6 + 1.4)/5
1.4 = 7/5
1.4 = 1.4
A rock falls from a tower that is 416 ft high. As it is falling, its height is given by the formula h=416-16t^2. How many seconds will it take for the rock to hit the ground (h=0)?
factorise the following 1. x²-2x+15.... 2. y²-19y+90
Answer:
1. x²-2x+15
This can't be factored, I've tried multiple ways now, but it just can't be factored.
2. y²-19y+90
Let's factor y^2−19y+90
y^2−19y+90
The middle number is -19 and the last number is 90.
Factoring means we want something like
(y+_)(y+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -19
Multiply together to get 90
Can you think of the two numbers?
Try -9 and -10:
-9+-10 = -19
-9*-10 = 90
Fill in the blanks in
(y+_)(y+_)
with -9 and -10 to get...
(y-9)(y-10)
Answer:
(y−9) (y−10)
Elsa draws an angle that measures 56. Tristan draws a congruent angle.
Tristan says his angle is obtuse. Is he correct? Why or why not
Answer:
False
Step-by-step explanation:
If an angle is congruent, it means that the angle is equal to the first angle which is 56 degrees, in theory, it would be false because 56 degrees is an acute angle and not obtuse.
Find the missing value.
Hint: Use the number line to find the missing value.
-(-7)=5
{ #
-15
→
15
-10
-5
0
5
10
Answer:
= -2
Step-by-step explanation:
-2 -(-7)
= 5
I hope this Helps!2.
three vertius of sect. A B C D are A (2, 2), B (-3,2), ((
Plot those point and find the quad of D and find the area
of dood. ABCD.
40% of 1000 pls answer and ill mark you brainliest
Answer:
400
Step-by-step explanation:
THE answer is 400 FILLER FILLER FILLER :)))))))))
Answer:
400
Step-by-step explanation:
1000 times 4 =4000 and 4000 and then take off a zero
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Which of the following statements is true?
A. A data set will always have exactly one mode
B. A data set can have multiple modes
C. A data set will always have at least one mode
D. A data set will never have a mode
Answer:
B. A data set can have multiple modes.
D. A data set will never have a mode.
Step-by-step explanation:
reason for B: some data are referred to as multimodal data because they have multiple modes.
reason for D: data can lack a mode if no value appears more than two times, or frequently.
Find the area of the triangle below.
the answer is 1,102.5, to find the area of a triangle you need to multiply LxWxB/2
Find the missing part.
Step-by-step explanation:
8²+10²= x²
64+100 =x²
164=x²
√164=√x²
square and squre root do cancel each other
x=√164
hope this helps
Answer:
x = [tex]\sqrt{164[/tex]
Step-by-step explanation:
In order to find the hypotenuse of a right triangle, you have to add,
[tex]8^{2} + 10^{2}[/tex]
which simplifies to,
64 + 100 =
[tex]\sqrt164[/tex]
Hope this helps! :)
Is there a way to solve this without l'hopital's rule?
The conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved without the l'hopital's rule,
How to solve the limit expression?The limit expression is given as:
[tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex]
The limit of the expression cannot be solved without l'hopital's rule, because a direct substitution of ∞ for x would result in the following expression ∞/∞
i.e.
[tex]\lim_{x \to \infty} \frac{6 (2^{\infty}) - 1}{5(\infty)^2+ 10} = \frac{\infty}{\infty}[/tex]
So, the best way is to apply the l'hopital's rule.
This is done as follows:
[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \lim_{x \to \infty} \frac{f'(x)}{g'(x)}[/tex]
When the numerator and the denominator are differentiated, we have:
[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln(2)\cdot 2^{x + 1}}{10x}[/tex]
Further, differentiate
[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{x + 1}}{10}[/tex]
Now, we can substitute [tex]\infty[/tex] for x
[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{\infty + 1}}{10}[/tex]
Evaluate the numerator
[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{\infty}{10}[/tex]
Evaluate the quotient
[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \infty[/tex]
Hence, the conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved without the l'hopital's rule
Read more about l'hopital's rule at:
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1. The expression 5/5 + 7) is
Answer:
8
Step-by-step explanation:
1. 5/5+7=?
The fraction means divide, so you divide 5 by 5. When you divide a number by the same number, it equals one. So 5 divided by 5 equals 1.
2. 1+7=?
The next step after dividing the fraction is you add the two numbers together. so 1 plus 7 equals 8.
Which of the following is a solution of this equation?
A.
(5,0)
B.
(-1, 1)
C.
(3,-1)
D.
(-2,-3)
Answer:
D. (-2,-3)
Step-by-step explanation:
substitute the point values of [tex]x[/tex] and [tex]y[/tex] into the equation [tex]y=\frac{1}{2}x-2[/tex]
A. [tex]0=\frac{1}{2}(5)-2[/tex]
[tex]0=2.5-2[/tex]
[tex]0[/tex] ≠ [tex]0.5[/tex]
B. [tex]1=\frac{1}{2}(-1)-2[/tex]
[tex]1=-.5-2[/tex]
[tex]1[/tex] ≠ [tex]-2.5[/tex]
C. [tex]-1=\frac{1}{2}(3)-2[/tex]
[tex]-1=1.5-2[/tex]
[tex]-1[/tex] ≠ [tex]-0.5[/tex]
D. [tex]-3=\frac{1}{2}(-2)-2[/tex]
[tex]-3=-1-2[/tex]
[tex]-3=-3[/tex]
What is the next term in the sequence?
2, -4, 8, -16, ...
Answer:
32
Step-by-step explanation:
it multiplies by -2 every time
What are m/_EFG and m/_GFH
Answer:
m/_EFG= -5 and m/_GFH= 5
Step-by-step explanation:
set the linear equations equal to eachother so that it looks like
2n+23=3n+37 then you have to combine like terms by rearranging the equations. you move the numbers by canceling them out. and what you do to one side must be done to the other. after you do this the equation should look like this.
2n - 3n = -23 + 37
then finish combining the terms
-1n = 14
then divide to get -14
the final step is to plug -14 back into your original equations in the place of n. then you solve to get your answer.
2 x -14 + 23 = -5 and 3 x -14 + 37 = 5
the product of the product of 7 and 2 and the product of 8 and p
Answer:
((7*2)*(8p))
Step-by-step explanation:
The product of 7 and 2 basically means you multiply them. The product of 7 and 2 is 14 and the product of 8p cannot be known because p is undefined so keep it as 8p. the product of 14 and 8p is 112p but the answer I stated above is the unsimplified version.
Solve for x. Enter your answer using digits. 4x−14+6=12 x=
Answer:
x = 5
Step-by-step explanation:
Given
4x - 14 + 6 = 12 , that is
4x - 8 = 12 ( add 8 to both sides )
4x = 20 ( divide both sides by 4 )
x = 5
the distance of a point P(x, y) from the origin O(0, 0) is given by OP=__
Answer:-
[tex]\boxed{\sf \sqrt{x^2+y^2}}[/tex]
Explanation:-
P(x,y)O(0,0)We know distance formula
[tex]\boxed{\sf \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
[tex]\\ \sf\longmapsto OP=\sqrt{(0-x)^2+(0-y)^2}[/tex]
[tex]\\ \sf\longmapsto OP=\sqrt{(-x)^2+(-y)^2}[/tex]
[tex]\\ \sf\longmapsto OP=\sqrt{x^2+y^2}[/tex]
traders fix the price of cosmetic items 30% above the cost price when he sold an item at 25% discount there was a loss of Rs 15 find the cost price and marked price of the item
Cost price is Rs600 and marked price is Rs780.
Must click thanks and mark brainliest
Зх — 7 = 2х
Show work
There is a sequence of rigid transformations that takes A to A', B to B', and C to "
same sequence takes D to D'. Draw and label D':
Answer:
I think it's D
Step-by-step explanation:
Answer: I think its D
Step-by-step explanation:
Rigid transformation moves a shape without changing the size of the shape.
See attachment for the diagram that shows the position of D'
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
Option C, 93.6 mi³
Step-by-step explanation:
Volume of the triangular prism,
(8×3.9/2)×6
= 93.6 mi³
Find the 5th term of each geometric sequence. 32,80, 200
Answer:
12.8
Step-by-step explanation:
solve this please sir
please
the sum of 5 consecutive even numbers is 130. find the numbers.
Answer:
22, 24, 26, 28, 30
Step-by-step explanation:
If the sum of 5 numbers is 130, that means the average of these numbers is 26.
If it is the average then it is the middle, or the third number. The two numbers before it would then be 22 and 24 by subtracting twos, and the two numbers after it would be 28 and 30 by adding twos.
22, 24, 26, 28, 30
Answer:
22,24,26,28,30
Step-by-step explanation:
I call the unknown number x
I write consecutive numbers in terms of x.
x+ (x+2) + (x+4) + (x+6) + (x+8) = 130
5x + 20 = 130
5x = (130 - 20)
5x = 110
x = 22 = smallest even number
x + 2 = 24 = second even number
x +4 = 26
x + 6 = 28
x + 8 = 30
What x 1/4 = 2
? X 1/4 = 2
It’s an equation
At a breakfast buffet, 63% of people choose coffee for their beverage while 23% choose juice,
Also, 20% choose both coffee and juice. What percentage of people chose coffee only
The percentage of people who chose only coffee will be 43%.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.
At a breakfast buffet, 63% of people choose coffee as their beverage while 23% choose juice.
Also, 20% choose both coffee and juice.
Then the percentage of people who chose only coffee will be given by the difference of 63% and 20%.
⇒ 63% - 20%
⇒ 43%
Thus, the percentage of people who chose only coffee will be 43%.
More about the sets link is given below.
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Consider the following linear system.
-2x+5y=23
-10x+ky=115
The value of k that will produce a system with an infinite number of solutions is:
a. -25
b. 25
c. -5
d. 5
Answer:
b. 25
Step-by-step explanation:
To have an infinite number of solutions, both equations must be equal.
-2x + 5y = 23
-10x + ky = 115
Multiply both sides of the first equation by 5 and write it. Rewrite the second equation below the first equation.
-10x + 25y = 115
-10x + ky = 115
For the equations to be equal, you must have
25y = ky
Divide both sides by y.
k = 25
Answer: b. 25
If f(x) = x2 - 4x and f(-3), then the result is:
o -3.
O 21.
0 -21.
Answer:
answer is 6
Step-by-step explanation:
f(x) = x2 - 4x
f(-3)= -3*2-4*-3
=-6-(-12)
=6
I need help ASAP!!!Please explain your answer
Answer:
Step-by-step explanation:
V = B * h
B = pi r^2
r = 12 km
B = 12^2 * pi
B = 144 * pi
h = 7 km
Volume = 144 *7 * pi
Volume = 1008 * pi
Volume = 3165.1
Find the distance between the pair of points.
(7, 3) and (-6, -4)
A. 2.4
B. 11
C. 1.4
D. 14.8