Answer:
Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.
Step-by-step explanation:
According to the statement, we have the following information about the lengths of the right triangle:
Hypotenuse
[tex]3\cdot x + 14[/tex]
Long leg
[tex]3\cdot x + 13[/tex]
Short leg
[tex]x[/tex]
By the Pythagoric Theorem, we have the following expression:
[tex](3\cdot x + 14)^{2} = x^{2} + (3\cdot x + 13)^{2}[/tex] (1)
[tex]9\cdot x^{2}+84\cdot x + 196 = x^{2} + 9\cdot x^{2} + 78\cdot x + 169[/tex]
[tex]9\cdot x^{2} + 84\cdot x + 196 = 10\cdot x^{2} + 78\cdot x +169[/tex]
[tex]x^{2} -6\cdot x -27 = 0[/tex]
[tex](x-9)\cdot (x+3) = 0[/tex]
As length is a positive variable by nature, then the only possible solution is [tex]x = 9[/tex]. Lastly, the side lengths of the right triangle are:
Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.
PLEASE HELP ME
Arnold deposits $6,000 into a certificate of deposit that pays 8% interest compounded quarterly . How much interest does his account earn in the first 3 years?
Answer:
8
Step-by-step explanation:
please help, seventh grade math problem
Answer:
12
Step-by-step explanation:
divide into two shapes. the first one being 2 x 4 units and the second being 2 x 2.
2 x 4 = 8
2 x 2 = 4
8 + 4 = 12
The answer is 12 square units.
Please mark brainliest if it was correct and helped!
Answer:
12
Step-by-step explanation:
just count the blocks
brainliest please???
Which procedure justifies whether Negative 3 x (5 minus 4) + 3 (x minus 6) is equivalent to Negative 12 x minus 6?
Answer: The expressions are not equivalent because -3(2)(5-4)+3(2-6)=-18 and -12x-6=-30
Step-by-step explanation: Honestly I just did the math but wasn’t sure what it was. Educated guess, I got it right on the test
Select all the statements about rotations that are true
A- The shapes of the figure does not change.
B- The positions of the figure does not change.
C- The size of the figure does not change.
D- The orientation of the figure does not change.
E- The coordinates of the figure do not change.
Please help I will give 100 points
Answer:
a. true
b. false
c. false
d. true
e. false
Step-by-step explanation:
A. true, a shape is not warped by a rotation
b. false, the points on the figure will change
c. false, the size is not affected by a rotation
d. true, the orientation changes in a rotation
e. false, the coordinate points on the figure are altered
Answer:
A- The shapes of the figure does not change.
C- The size of the figure does not change.
D- The orientation of the figure does not change
Write 11 k-6 (2k+5)in expanded form and find the sum
Answer:
Option B
Step-by-step explanation:
Expression representing the series is,
[tex]\sum_{k=6}^{11}(2k+5)[/tex]
Here, k = Number of terms
By placing k = 6, 7, 8, 9, 10, 11 in the expression we can get the terms of the series.
For k = 6,
(2k + 5) = 2(6) + 5
= 17
For k = 7,
(2k + 5) = 2(7) + 5
= 19
For k = 8,
(2k + 5) = 2(8) + 5
= 21
For k = 9,
(2k + 5) = 2(9) + 5
= 23
For k = 10,
0(2k + 5) = 2(10) + 5
= 25
For k = 11,
(2k + 5) = 2(11) + 5
= 27
Therefore, expanded form will be,
17, 19, 21, 23, 25, 27
There, is a common difference in each successive to previous term,
d = 19 - 17
d = 2
Number of terms 'n' = 6
First term = 17
Sum of an arithmetic sequence is given by,
[tex]S=\frac{n}{2}[2a+(n-1)d][/tex]
Therefore, sum of the given sequence will be,
[tex]S=\frac{6}{2}[2(17)+(6-1)2][/tex]
= 3(34 + 10)
S = 132
Option B will be the correct option.
5 and 1/4 - 4 and 1/2
Step-by-step explanation:
answer: 3/4 or 0.75
=5 1/4 - 4 1/2
=21/4 - 9/2
= (21-9) / 4
=3/4 or 0.75
If the square of a positive integer is added to four times to integer the result is 117 find the integer.
Answer:
x = -2 ± 452i
Step-by-step explanation:
x² + 4x = 117
x² + 4x - 117 = 0
if you solve this quadratic by using the quadratic formula you get:
x = -2 ± 452i
452i is an imaginary number that equals [tex]\sqrt{-452}[/tex]
explain why a3*a2 dosnt equal a6... Plz I need help!
Answer: a^3 · a^2 ≠ a^6 as the laws of exponents states that the multiplication rule for two exponents with the same bases equates to addition, so that a^3 · a^2 = a^3+2 = a^5.
Based on Milton Friedman's observations, it is likely that he would agree that socialism provides the best government for which a free market can exist.
Please select the best answer from the choices provided
T
F
Answer:
False
Step-by-step explanation:
I did the E2020 assignment
please help will mark brainlist!!
Answer:
x=28
y=28
Step-by-step explanation:
Equation 1:
Dived both sides by 0.75 to remove 3/4 from x.
(x-12)=16
Now, add 12 to both sides.
x=28
Equation 2:
Same here, divide both sides by 0.75.
y-12=16
Add 12 to both sides.
y=28
Get brainly if right !!
John and Jack divided their math homework. John solved twice
as many problems as Jack, plus one more problem. How many
problems did each boy solve if there are 28 assigned problems?
Answer:
Jack=9, John= 19
Step-by-step explanation:
28/3=9 1/3, counting as nine, as thats what got the right answer in my homework.
9 *2) +1= 19, no idea why the plus one, thats just what showed up
J1=19
J2=9
Hi I'm bad at math the questions is -r - 20r = please help
Answer:
−21r
Step-by-step explanation:
Combine Like Terms:=−r+−20r
=(−r+−20r)
=−21r
Answer:=−21r
please click the crown button (brainliest) thanks!!hope this helps!! <3
What is the area of the triangle?
Answer:
Area of triangle 12 ft^2 Area of shaded region 84 ft^2
Step-by-step explanation:
area of triangle 6 x 4 / 2 =12
Shaded region 96-12= 84 ft^2
In ∆PQR, ∠P = 90degrees , PQ= 12 cm, PR=16cm. Find ∠Q
Answer:
∠Q = 53.13 degrees
Step-by-step explanation:
Given that ∆PQR, ∠P = 90degrees , this means that the triangle is a right angled triangle
Hence using the notation
SOH CAH TOA
where S is sine, C is cosine, T is tangent and O, A and H represents the size of the opposite, adjacent and hypotenuse sides
Considering ∠Q and the given sides
PR=16cm is the opposite side,
PQ= 12 cm is the adjacent side hence we use TOA
Tan Q = 16/12 =
Q = Arc tan 16/12
= 53.13 degrees
How much would you need to deposit into an account that pays 6.5% interest compounded semiannually to have $10,000 after 7 years?
Answer:
6390.56
Step-by-step explanation:
[tex]AV=PV(1+\frac{i}{n})^{nt}\\10000=x(1+\frac{.065}{2})^{7*2}\\10000=1.564807232*x\\6390.53=x[/tex]
9514 1404 393
Answer:
$6490.57
Step-by-step explanation:
The future value is given by the compound interest formula ...
A = P(1 +r/n)^(nt)
Principal P earns annual rate r compounded n times per year for t years.
Filling in the given values, we have ...
10000 = P(1 +0.065/2)^(2·7) = P(1.0325^14)
P = 10000/1.0325^14 ≈ 6390.5635
You would need to deposit $6390.57 into the account to have $10,000 in 7 years.
_____
Additional comment
Using the rounded-down result of the computation will result in a value after 7 years of $9,999.99, not quite $10,000. Rounding the computed value up to $6390.57 ensures the account balance will actually be $10,000.00 after 7 years.
If the balance is rounded to the nearest penny each time interest is added, then the balance after 7 years will be exactly $10,000.00. If there is no intermediate rounding, the resulting balance will be $10,000.01.
Most of the time, the answer key doesn't pay attention to details like this. Your expected answer may be $6390.56, or $6391 if rounded to dollars.
write in algebraic expression the difference between a number m and the product of m and n. If you can help it would mean a lot
Answer:
m - mn
Step-by-step explanation:
The two numbers are denoted by m and n respectively.
From the question, we can deduce the following points;
- the difference between m and another variable (mn).
- product or multiplication of m and n.
Translating the word problem into an algebraic expression, we have;
m - (m*n)
m - mn
What was the concentration of the drug 4 hour(s) after injection?
Answer:
it's 47÷4=11 3/4 will be your final answer
9 - x < - 11
Show steps please
Answer: x > 20
Step-by-step explanation:
9 - x < - 11
In this scenario, we've to collect like terms in order to.wolve for x. This will be:
9 - x < - 11
- x < - 11 - 9
- x < - 20
Divide both side by -1
-x/-1 < -20/-1
When we divide by a coefficient with minus sign, the sign changes too from less than to greater than
-x/-1 < -20/-1
x > 20
what is the volume of a sphere if the radius is 9?
ANSWER IN TERMS OF PI !!!
What is the shape of the cross-section formed when a cylinder intersects a
plane as shown in the drawing?
O A. circle
B. oval
C. rectangle
OD. square
Answer: circle
Step-by-step explanation:
The shape of the cross-section is formed when a cylinder intersects the plane is a circle option (A) is correct.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we know, the circle is a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
As we can see in the picture the cylinder is cut by a plane that is parallel to the base of the cylinder.
The base of the cylinder is a circle.
the shape of the cross-section is formed when a cylinder intersects a
the plane is a circle.
Thus, the shape of the cross-section is formed when a cylinder intersects the plane is a circle option (A) is correct.
Learn more about the cylinder here:
brainly.com/question/3216899
#SPJ2
A map scale reads: 2 inches = 25 miles. Which distance does 6 inches represent
Answer:
the other side
Step-by-step explanation:
Answer:
75 miles
Step-by-step explanation:
2 * 3= 6
25 * 3= 75
What is the area of this quadrilateral?
2 ft
4 ft
6 ft
6 ft
4 ft
2 ft
A. 28 square feet
0
B. 48 square feet
a o
C. 18 square feet
D. 36 square feet
Answer:
the answer would be a
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
just got it correct
Find the measure of an angle in standard position for each reference angle.
Step-by-step explanation:
1. 90+65= 155°
2. π+ π/6 = 7π/6 or 210°
3. 24+180=204°
4. 3π/2 + 2π/9 = (27π+4π)/18 = 31π/18
or 310°
Find the value of (6^0 − 7^0) × (6^0 + 7^0)
Answer:
-13
Step-by-step explanation:
6-7 x 6+7
-1 x 13
-13
How to solve 4x - 5 = 2x + 19?
Answer:
x = 12
Step-by-step explanation:
4x - 5 = 2x + 19
First subtract the 2x from 4x.
2x - 5 = + 19
Then add the 5 to the 19.
2x = 24
Divide 24 by 2 in order to get x by itself.
x = 12
Can the surface area of a sphere and the volume of a sphere be the same numerical value if the units are measured relative to the same unit of length?
A. Yes; the radius would need to be the unit radius, 1.
B. Yes; the radius would need to be 3.
C. No, the surface area would always be greater than the volume.
D. No, the volume would always be greater than the surface area.
Answer:
Volume = surface area
[tex]\frac{4}{3}\pi r^3 = 4\pi r^2\\\\\frac{r}{3} = 1\\r = 3[/tex]
option B
. if 3, 2, y, 10 are in proportion, find the value of y
Answer:
y = 15
Step-by-step explanation:
Given :
3, 2, y, 10
If the numbers are in proportion :
We can thus say :
3/2 = y/10
Cross multiply
3 * 10 = 2 * y
30 = 2y
Divide both sides by 2
30 / 2 = 2y / 2
15 = y
19 POINTS the answer is not the first or second option I’m maybe think the last one
Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units:
Rooms 1 2 3 4 5
Owned 0.003 0.002 0.023 0.105 0.218
Rented 0.008 0.027 0.287 0.362 0.165
Rooms 6 7 8 9 10
Owned 0.225 0.198 0.149 0.053 0.024
Rented 0.095 0.033 0.013 0.003 0.004
Required:
a. Express "the unit has 7 or more rooms" in terms of X. x≥7. What is the probability of this event?
b. Express the event {X > 7} in words.
c. What important fact about discrete random variables does comparing your answers to (a) and (b) illustrate?
Answer:
Part a:
"The unit has 7 or more rooms" in terms of X is given by the unit which has 7, 8, 9 or 10 rooms.
P{ X≥7}= 0.424
Part b:
The event {X > 7} in words is that the unit has more than 7 rooms. .
Part C:
A continuous random variable is given by intervals of numbers
A discrete random variable is the variable that is obtained by counting.
Step-by-step explanation:
Part a:
"The unit has 7 or more rooms" in terms of X is given by
{ X≥7} = {x=7} + {x=8} + {x=9} + {x=10}
the unit which has 7, 8, 9 or 10 rooms.
The probability of this event is given by
P{ X≥7} =P {x=7} + P {x=8} + P {x=9} + P {x=10}
P{ X≥7} = 0.198 + 0.149+ 0.053 + 0.024
P{ X≥7}= 0.424
Part b:
The event {X > 7} in words is that the unit has more than 7 rooms. This does not include the unit having 7 rooms.
Part C:
A continuous random variable takes all the values in the given interval as in part a.The random variable X takes the values between 7 and 10 inclusive of 7.
A discrete random variable is the variable that is obtained by counting as in part b. The variable X takes the values of the units with 8 , 9 or 10 rooms.
The estimated difference of 3209 and 1893, when rounded off to the nearest ten is
o(a) 1300
(b) 1310
(c) 1320
0 (d) 1000
Answer:
[tex] = (3209) - (1893) \\ = 1.32 \times {10}^{3} \\ = 1320[/tex]
[tex] \small{ \star{ \underline{ \blue{becker}}}}[/tex]
Answer:
1320
Step-by-step explanation:
round off
3209 ≈ 3210
1893 ≈ 1890
estimated difference = 3210 - 1890 = 1320