the area of a square is 32 cm. find the length of the diagonal
Answers
Answer:
8 cm
Step-by-step explanation:
Squares have equal side lengths so if we call each side x, then x × x gives us the area (32 cm²). This means that x² = 32 and therefore, one side is √32 cm.
Next, to work out the diagonal we can use Pythagoras' theory, since we can form a right-angled triangle. a² + b² = c² (c is the diagonal or the hypotenuse)
(√32)² + (√32)² = c²
(note: the square and the square root cancel out)
32 + 32 = 64
c² = 64 ∴ c = √64 which is 8
Hope this helps!
Answer:
The length of the diagonal is 8 cm.
Step-by-step explanation:
The side length of the square is √32 cms.
The diagonal divide the square into 2 congruent right triangles.
We use Pythagoras Theorem here:
d^2 = (√32)^2 + (√32)^2
d^2 = 32 + 32 = 64
d = √64 = 8.
Related Questions
Jerry hiked along a path. From his starting position, he hiked downhill to a valley where the elevation dropped 25 meters below his starting position. Then, he hiked up to a hill that was 40 meters higher than the valley.
The following equation describes this situation.
-25 + 40 = 15
CHOOSE 1 ANSWER
1. Jerry hiked a total of 15 meters
2. the hill was 15 meters higher than the elevation of his starting point
3. None of the above
Answers
Answer:
15 represents where Jerry is after the elevation dropped 25 meters and then rose 40 meters.
Step-by-step explanation:
It's given that Jerry hiked downhill to a valley where the elevation dropped 25 meters below his starting position. Then, he hiked up to a hill that was 40 meters higher than the valley
Hiked downhill = 25 meters
Hiked up = 40 meters
The given equation is
Here, hiked downhill represented by negative sign and hiked up resents by positive sign.
So, 15 represents that Jerry hiked up 15 meters from his starting position.
(2, the hill was 15 meters higher than the elevation of his starting point)
Answer:
2.
Step-by-step explanation:
The hill was -25 + 40 = 15 meters highe than starting point.
Juan plays little league baseball. In 36 at-bats, he had 12 hits. What is the ratio of at-bats to hits?
Answers
Answer:
The Ratio is 8:16.
Step-by-step explanation:
What is the experimental probability of rolling a number less than 4?
A: 1/2
B: 16/33
C: 1/22 D: 17/33
what is the answer?
HELP
Answers
Answer:
A. 1/2
Step-by-step explanation:
For the question, it says what is the experimental probability of rolling a number less than 4, meaning it is asking for the experimental probability of rolling a 1, 2, or 3. Assuming this is a fair 6-sided dice, the probability of rolling any number is 1/6. The probability of rolling a 1, 2, or 3 is also 1/6. Adding all those the probabilities of 1, 2, and 3 together gets 3/6, which simplifies to 1/2.
Therefore, the experimental probability of rolling a number less than 4 is 1/2.
= 0.5 which is 50% half so A:1/2 is the answer
Are the expressions 5 ( x - 3) and 5x + 15 equivalent? use the distributive property to support your answer
Answers
Answer: No
Step-by-step explanation: No, they aren't. If you look at 5 and multiply (distribute) it to negative three you will end up with -15. And 15 is not equal to negative 15.
I hope this helps!
What is the slope of the line through the points (-2, -1) and (4, 3)?
2/5
5/2
3/2
2/3
Answers
Answer:
2/3
Step-by-step explanation:
We can use the slope formula to find the slope
m = ( y2-y1)/(x2-x1)
= ( 3- -1)/ ( 4 - -2)
= ( 3+1)/ ( 4+2)
= 4/6
= 2/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{The formula for slope of a line is: }\large\boxed{\mathsf{m = \dfrac{y_2 - y_1}{x_2 - x_1} \ or\ easier \ way\ m = \dfrac{rise}{run}}}[/tex]
[tex]\large\textsf{NOW LETS ANSWER THE GIVEN EQUATION}[/tex]
[tex]\large\text{THE GIVEN EQUATION: \boxed{\rm{m = \dfrac{3 - (-1)}{4 - (-2)}}}}\\\large\boxed{m \rm{= \dfrac{3 + 1}{4 + 2}}}\\\\\\\large\boxed{m \rm{= \dfrac{4}{6}}}\\\\\\\large\boxed{m \rm{= \dfrac{4\div 2}{6\div 2}}}\\\\\\\large\boxed{m = \rm{\dfrac{2}{3}}}\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{Option\ D. \dfrac{2}{3}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
HELPPPPPPPPPPPPPP ASAP
Answers
Answer:
Use the formula of Range Large-Small Data
I think it will help you.
3
(08.01)
Line M is represented by the following equation: x - y = 8
Which equation completes the system that is satisfied by the solution (18, 10)? (4
points)
1) 2x - y = 26
2) x + y = 18
3) 2x - 2y = 36
04) x - y = -28
Answers
Answer:
1) 2x - y = 26.
Step-by-step explanation:
Solution = (18, 10)
2x - y = 26 fits the bill
as 2(18) - 10
= 36 - 10
= 26.
Two sides of a parallelogram are 170 feet and 650 feet. The measure of the angle between these sides is 113°. Find the area of the parallelogram to the nearest square foot.
Answers
The area of the parallelogram is equal to 101716 ft².
QuadrilateralsThere are different types of quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, the opposite sides of a parallelogram are equal and parallel.
Parallelogram AreaYou can find the parallelogram area from two formulas:
A=b * h , where b=base and h=height;A= a*b* sin(Θ), where a=side 1, b=side 2 and Θ=angle between the sides;The question gives: the length of both sides (170 ft and 650 ft) of the parallelogram and the angle between these sides (113°).
Thus, you can apply the formula: A= a*b* sin(Θ). Therefore:
A= 170 * 650* sin (113°)
A=101716 ft²
Read more about the area of parallelogram here:
https://brainly.com/question/21390857
2. Which exponential function matches the
values in the table below?
х
3
4
5
4,096
32,768
| f(x) 512
A f(x) = x8
B f(x) = 8*
C f(x) = 64(2)*
D f(x) = 8x
Answers
Answer:
B. f(x) = 8*
Step-by-step explanation:
putting the value given in table
=> 512 = 8³
=> 512 = 512
=> 5,096 = 8⁴
=> 5,096 = 5,096
=> 32,768 = 8⁵
=> 32,768 = 32,768
so, it's B f(x) = 8*
Answer:
The answer is B) f(x)=8^x
If apples cost $1.08 per pound, how much would 3.8 pounds cost?
Answers
Answer:
4.10
Step-by-step explanation:
1.08 * 3.8 = 4.104
but money is 2dp so...
4.10
Find m
S
12x +4
G
40°
F
E
D
4x
Answers
Answer: C
Step-by-step explanation:
Select all the expressions that are equivalent
Answers
Answer:
B, C, D
Step-by-step explanation:
One of the rules of exponents is that an exponent in the numerator is equivalent to the opposite of the same exponent in the denominator. That means ...
[tex]4^{-3}=\dfrac{1}{4^3}\qquad\text{matches C.}[/tex]
Another rule of exponents is that an exponent represents repeated multiplication. If a factor can be written using an exponent, the exponents are effectively multiplied.
[tex]4^{-3}=(2^2)^{-3}=2^{2(-3)}=2^{-6}\qquad\text{matches B.}[/tex]
Of course, that repeated multiplication can be shown explicitly:
[tex]\dfrac{1}{4^3}=\dfrac{1}{4}\cdot\dfrac{1}{4}\cdot\dfrac{1}{4}\qquad\text{matches D.}[/tex]
The equivalent expressions to 4^(-3) are B, C, D.
_____
Additional comment
The expression of G evaluates to ...
[tex]\dfrac{8^{-1}}{2^2}=(2^3)^{-1}\cdot2^{-2}=2^{3(-1)-2}=2^{-5}\qquad\text{not equivalent}[/tex]
helppppppp fasttttt!!!!!!!!!!!!!!!!!!
Answers
Answer:
7
Step-by-step explanation:
7+7=14*
14*3.14=43.96
Volume of a Cone Level 1
Answers
The volume of the cone is the amount of space in it
The volume of the cone is 264.3 cubic inches
How to determine the volume?The given parameters are:
Height, h = 9.9 inDiameter, d = 10.1 inThe volume of a cone is then calculated as:
V = 1/3π(d/2)²h
This gives:
V = 1/3 * 3/14 * (10.1/2)² * 9.9
Evaluate the product
V = 264.256905
Approximate
V = 264.3
Hence, the volume of the cone is 264.3 cubic inches
Read more about volumes at:
https://brainly.com/question/1972490
Carmen's car used 11 gallons of gas to travel 462 miles. How many miles per gallon did his car travel? Show the steps for finding the unit rate
Answers
Answer:
I'm pretty sure it's 473 if that isn't correct Then what you do Is Divide it or Mutiply it if you still don't get your answer Be sure to Ask someone
Answer:
42miles per gallon
Step-by-step explanation:
since total gallons of fuel used is 11 gallons to travel 462miles,
per gallon will be 462/11 =42miles per gallon
What is the answer, I need this for a geometry assignment.
Answers
Answer:
x= 14. (ik this not trig but side opp. 30 angle is half the hypotenuse in right triangle). pls give brainliest
Step-by-step explanation:
Write the following in order of size ,starting with the smallest. 66/100 , 0. 6 , 0. 67 , 666/1000
Answers
Answer:
0.6,66/100,666/1000,0.67
PLS HELP ME WITH THIS IM GONNA CRY ITS SO HARD....
Arsenic‐74 is used to locate brain tumors. It has a half‐life of 17.5 days. 90 mg were used in a procedure. Write an equation that can be used to determine how much of the isotope is left after x number of half-lives.
Answers
Let that be x
Use the general formula used for calculating half-life
[tex]\\ \rm\Rrightarrow A=A_o(0.5)^{\frac{t}{h}}[/tex]
H is half-life,t is timetime given xput values
The equation is
[tex]\\ \rm\Rrightarrow A=90(0.5)^{x/17.5}[/tex]
pls help T-T
i need a solution too
Answers
Answer:
I do not know it very well
Step-by-step explanation:
80
Answer:
b. 60°
Step-by-step explanation:
The exterior angles of a convex polygon total 360°. When the polygon is a regular hexagon, there are 6 congruent exterior angles.
__
Each exterior angle has a measure of ...
x° = 360°/6 = 60°
select all the expressions that are equivalent to 16^5/2
Answers
Answer:
A, C, E
Step-by-step explanation:
[tex] 16^{\frac{5}{2}} = 16^{\frac{1}{2} \times 5} = (\sqrt{16})^5 = \sqrt{16^5} = 1024 [/tex]
A. 4^5 = 1024 Yes
B. 8^5 No
C. 4^5 Yes
D. [tex] 16^{\frac{2}{5}} [/tex] No
E. [tex] 16^{2 + \frac{1}{2}} = 16^{\frac{5}{2}} [/tex] Yes
F. [tex] 16^{\frac{11}{2}} [/tex] No
Please help me out I’m really bad
Answers
x=180-120
.•.x=60
Study the image.
Make a personal connection to the photo. In three to five sentences, write a short essay that explains what type of lighting setup was used and what this image makes you think about. Use specific details in describing what the photo reminds you of personally.
Answers
Answer:
he is on high depression
he is so success ful guy
he makes an advertisement of some thing
he advertises watch
he see going to be a future doing on his life
How many lines of symmetry does the letter J have image is the J I'm talking about
Answers
Answer:
0
Step-by-step explanation:
there are no lines os symmetry in this letter there are no straight lines that don't intersect
Answer:
0
Step-by-step explanation:
If you split it in half it is not a mirror image of itself..
A study claims that the average home sale price in Kansas is less than the average home sale price in Missouri. The average sales price for 35 home sales in Kansas is $240,993 with a standard deviation of $25,875. The average home sales price for 37 homes in Missouri is $249,237 with a standard deviation of $27,110. At the (alpha) a= 0.10, is there enough evidence to reject the study’s claim?
Complete a full hypothesis test for the following. Include the hypotheses, critical
value(s), test value and graph, your decision to reject or not reject, and a summary of
the information
Answers
Since [tex]|z| = 1.301 \leq z_1 = 1.64[/tex] null hypothesis on this data is not rejected.
Null and Alternative HypothesisData;
sample mean x1 = 240993population standard deviation σ1 = 25875sample size n1 = 35sample mean x2 = 249237population standard mean σ2 = 27110sample size n2 = 35significance level α = 0.10H_o = μ1 = μ2
H_o = μ1 ≠ μ2
This is a two-tailed test and population standard deviation will be used.
Test StatisticThe z-stat is
[tex]z = \frac{x_1 - x_2}{\sqrt{\frac{\sigma_1^2}{n_1}+ \frac{\sigma_1 ^2}{n_2} } } \\z=\frac{240993-249237}{\sqrt{\frac{25875^2}{35}+ \frac{27110^2}{35} } } \\z = \frac{-8244}{6334.6388} \\z = -1.301[/tex]
The significance level is α = 0.1 and the critical value for a two-tailed test is
[tex]Z_t = Z_1 - _\alpha _/_2 = 1.64[/tex]
Since [tex]|z| = 1.301 \leq z_1 = 1.64[/tex], we can assume that the null hypothesis is not rejected.
Learn more on null hypothesis here;
https://brainly.com/question/15980493
For a football game. Adult tickets are 8 dollars and student tickets are 5 dollars. The school sells 2570 tickets and makes a total of $19,060.
how many adult ticket were sold
how many student tickets were sold
Answers
But,
$8(adults) + $5(students) = $19060
And,
Adults + Students = 2570
Let A = adults and S = students
8A + 5S = 19060
A + S = 2570
This is called a system of equations. To solve, you need to rearrange both equations to solve for one of the variables, you can pick any. This makes them cancel out so you can focus on 1 variable. After solving, you can plug the solved variable back into any of the given equations and solve for the second one.
S = 19060/5 - 8A/5
S = 3812 - (8A/5)
This is the first equation rearranged to solve for S
Second:
A + S = 2570
S = 2570 - A
Now, equal each other
3812 - (8A/5) = 2570 - A
Solve for A
3812 + A = 2570 + 8A/5
19060 + 5A = 12850 + 8A
19060 - 12850 = 3A
6210 = 3A
2070 = A
There were 2070 adults
Now, plug A back into any of the 2 equations and solve for S
A + S = 2570
2070 + S = 2570
S = 2570 - 2070
S = 500
2070 adult tickets were sold
500 student tickets were sold
What is the range of the given function?
{(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)}
{x | x = -5, -4, -2, 0, 2}
{y l y = -9, -3, 0, 5, 7}
O (x | x = -9, -5, -4, -3, -2, 0, 2, 5, 7}
O tyl y = -9, -5, -4, -3, -2, 0, 2, 5, 7}
Answers
Answer:
{-9, -3, 0, 5, 7}
Step-by-step explanation:
Well, you already have the relation of the function. The domain of a function are its x coordinates and the range are all the y coordinates:
0, -3, -9, 5, 7
We write them in ascending order:
-9, -3, 0, 5, 7
And this way we get the range
It is important to check if the coordinates you are given can form a function. In this case they do, but in other cases they might not.
If you have coordinates where for example there are two equal values of x but the y is different in both, for example (1, 2) and (1, 5), this cannot be a function because y can be on two possible destinations for the same value of x.
For the data set 1, 7, 7, 7, 8, the mean is 6
Answers
Answer:
Yes
Step-by-step explanation:
1+7+7+7+8=30
30/5= 6
The owner of a food cart sells an average of 60 frozen treats per day during the summer. Which graph best shows the relationship between the number of days and the number of frozen treats sold?
A) A
B) B
C) C
D) D
Answers
Answer:
Answer is D
Step-by-step explanation:
Day 1 = 60
Day 2 = 120
Day 3 = 180
Day 4 = 240
Day 5 = 300
Day 6 = 360
Day 7 = 420
Day 8 = 480
The graph D will show the best relationship between the number of days and the number of frozen treats sold.
What is graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
It is given that he sells 60 frozen treats per day so everyday the frozen treats are multiplied by 60.
We can see the linear relationship between frozen treats and number of days.
Day 1 - 60
Day 2 - 120
Day 3- 180
Day 4- 240
Day 5- 300
Day 6- 360
Day 7- 420
Day 8- 480
Hence the graph D will show the best relationship between the number of days and the number of frozen treats sold.
To know more about graph follow
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Solve 5(x – 4) = 2(x + 5) for x.
Question 9 options:
x = 5
x = –10
x = 10
x = –5
Answers
Answer:
Step-by-step explanation:
the answer for 5(x – 4) = 2(x + 5)
is x=10
your welcome!
Answer:
x = 10
Step-by-step explanation:
5(x – 4) = 2(x + 5) DISTRIBUTE
5x - 20 = 2x + 10 COMBINE LIKE TERMS
3x = 30 ISOLATE X
x = 10 FINAL ANSWER
I hope this helps!
A.)12
B.) 25
C.)51
D.) 77
Answers
Answer:
4x+3=2x+27
4x-2x=27-3
2x=24
x=24/2
x=12
Answer:
51
Step-by-step explanation:
2x+27=4x+3
-3 -3
__________
2x+24=4x
___________
2
x+12=2x
-x -x
___________
12=x
now plug in/check answer
2(12)+27=4(12)+3
24+27=48+3
51=51
true
