[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {√7}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] =\frac{7}{ \sqrt{7} }\\ [/tex]
[tex] = \frac{7}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} }\\ [/tex]
[tex] = \frac{7 \sqrt{7} }{ \sqrt{7} \times \sqrt{7} }\\ [/tex]
[tex] = \frac{7 \sqrt{7} }{7}\\ [/tex]
[tex](∵ \sqrt{a} \times \sqrt{a} = a)\\[/tex]
[tex] = √7[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
Step-by-step explanation:
Given,
7/√7
The denominator is √7.
We know that
Rationalising factor of √a is √a.
Therefore, the rationalising factor of √7 is √7.
On rationalising the denominator them
=> (7/√7) × (√7/√7)
=> 7(√7)/(√7 × 7)
=> 7√7/7.
Hence, the denominator is rationalised.
50 POINTS TO WHOEVER ANSWERS THIS NOW!!!! IM TIMED HELP.
One tool used to study refraction is a glass or acrylic prism. Two of the prisms more commonly used to study light refraction are a triangular prism with an equilateral triangle for its base and a triangular prism with a right triangle for its base. In this task, you will check whether the measurements found prove the two given prisms are right prisms and whether their bases are equilateral or right triangles.
The prism said to have an equilateral triangle base has the measurements shown.
Part A
Are the bases of the prism equilateral triangles? Why or why not? Note: The bases of a triangular prism are triangles.
Part B
For this prism to be a right prism, all the lateral faces must be rectangles. Is enough information given to prove the lateral faces are rectangles? Why or why not?
Part C
Without using a protractor, you can determine whether the angles are right angles by measuring the length of the diagonal and applying the converse of the Pythagorean Theorem.
The length of both diagonals for each lateral side is 13 centimeters. From this, can you prove that the lateral sides are rectangles? Why or why not?
Part D
Some of the measurements of the triangular prism with a right triangle base are shown.
What is the length of the hypotenuse of the base?
Part E
Which lateral face has the largest area, the bottom one, left one, or diagonal one? What is its area?
Answer:
A: The bases of a triangular prism are equilateral triangles, since they have equal sides: 5, 5, and 5 yes, since if all lateral faces are rectangles, rectangles are formed from 4 perpendicular segments, thus, if all edges of the lateral faces are perpendicular, then they are rectangles
B:they have equal length sides and equal angles. For this to be true, the bases must be squares. Because it is a right prism, the lateral faces are rectangles.
C:If we have following equation right, then the angle between shorter sides is right angle:
13² = 12² + 5²
169 = 144 + 25
169 = 169
D:4*sqrt(2)
E: LSA of a cube = 100 in²
Step-by-step explanation:
Hope this helps
UESTION 4
1
A certain number multiplied by five and then two subtracted,
the answer is seventy-seven. Find the number
Answer:
x = 15.8
Step-by-step explanation:
let the number be x
according to the question equation is
x*5 - 2 = 77
5x - 2 = 17
5x = 77 + 2
5x = 79
x = 79/5
x = 15.8
Answer:
5x - 2 = 77
x = 15.8
Step-by-step explanation:
a number - x
times 5 - 5x
minus 2 - 5x - 2
equals 77 - 5x - 2 = 77
77 + 2 = 79
79 ÷ 5 = 15.8
5(15.8) - 2 = 77
the width of a rectangle is 2 inches less than its length , and the area is 35 sqaure inches. what are thd length and width of the rectangle
Answer:
length: 7in.
width: 5in.
Step-by-step explanation:
so we know that 7*5 is 35 yes? since we already know the area, which is just l*w, and that 5 is two less that 7, we can conclude that the length is 7 and the width 5
hope this helps! lemme know if you need more
What’s the perimeter
Answer:
60 cm
Step-by-step explanation:
Perimeter = 2(12) + 2(18)
Perimeter = 2(30) = 60
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
60cm
Step-by-step explanation:
(diagram with colors below)
The two red sides can be visualized as the same length as the length, so the two red segments add up to 18cm. The same thing can be said with the blue segments and the width. We can say the perimeter can be:
18 + 18 + 12 + 12 = 60cm
you have five dollar bills and ten dollars bills for a total amount of $325. you have a total of 37 bills. A) write a system of linear equations that models the situation. B) how many of each type of bill do you have?
Answer:
nine $5 bills and twenty-eight $10 bills
Step-by-step explanation:
f = # of five dollar bills
t = # of ten dollar bills
system of equations:
t + f = 37
10t + 5f = 325
solve the first equation for 't' to get:
t = 37-f
substitute '37-f' to 't' in second equation to get:
10(37-f) + 5f = 325
370 - 10f + 5f = 325
-5f = -45
f = 9
t + 9 = 37
t = 28
PLZ HELP! I will give brainliest!!!
Answer: x axis is time in hours, y axis is water level in centimeters
I can't see the rest of the problem since you didnt show it
Step-by-step explanation:
Line l has a slope of . The line through which of the following pair of points is perpendicular to l?
A. (-5, -6), (3,3)
B.(-9, -6), (3,3)
C. (3,-5), (-6,3)
D. (9,-2),(-6,6)
Answer:
b is the right answer
Step-by-step explanation:
Express it in slope-intercept form.
Answer:
y = 1/2x -1
The slope is increasing by 2/4, which can be reduced to 1/2. You can find this by doing rise over run.
The y intercept is -1
Help ASAP will give the Brainliest answer
The degree of the expression 4x^5y^m z is 10. What is the value of m?
A2
B 4
C5
D 10
Which of the following is most likely the next step in the series?
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The shape starts with 2 dots, then to 3 dots, and then to 4 dots. This means that the next step must have 5 dots, which option D has.
Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in josiahs account, y, after x years?
a-y=360(1.3)^x
b-y=360(0.3^x
c-y=360(0.03)^x
d-y=360(1.03)^x
Answer:
y = 360 (1.03)^x
Step-by-step explanation:
Amount in account = principle * (1+ rate) ^ time
When the interest is annual
rate is in decimal form and time is in years
y = 360 ( 1+.03) ^x
y = 360 (1.03)^x
what is the solution to the system of equations graphed below?
Answer:
C. (1, -2)
General Formulas and Concepts:
Algebra I
Reading a coordinate graphCoordinates (x, y)Solving systems of equations by graphingStep-by-step explanation:
Where the 2 lines intersect on a graph will be the solution to the systems of equations. According to the graph given. the lines intersect at (1, -2).
∴ our answer is C.
Answer:
C. (1,-2)
Step-by-step explanation:
with systems of equations, the answer is always where the lines intersect. which in this graph is at (1,-2)
hope this helps! lemme know if you need more
Which expressions are equivalent
27x/9x
Answer:
3x
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
You have [tex]\frac{27x}{9x}[/tex]
You can factor out the x in the numerator and denominator to get [tex]\frac{27}{9}[/tex]
You can further simplify this by factoring out a 9 => [tex]\frac{3(9)}{(9)}[/tex]
Thus getting 3
A sports teacher had 1025 sweets. After distributing these equally amongst all the participants in a sports meet, he had just 1 sweet left with him. Which of these could be the number of sweets given away to each participant?
Answer:
C. 8
Step-by-step explanation:
Options
A. 5
B. 6
C. 8
D. Can't say without knowing the number of participants
Number of sweet distributed = Total number of sweets - left over sweets
= 1025 sweets - 1 left over sweet
= 1024 sweets
Number of participants = Number of sweets distributed / number of sweets given to each participant
A. 5
Number of participants = Number of sweets distributed / number of sweets given to each participant
= 1024 /5 Sweets
= 204.8 participant
B. 6
Number of participants = Number of sweets distributed / number of sweets given to each participant
= 1024/6
= 170.67 participant
C. 8
Number of participants = Number of sweets distributed / number of sweets given to each participant
= 1,024/8
= 128 participant
D. Can't say without knowing the number of participants
From the options given, the number of sweets given away to each participant could be 8
Number of sweets given to each participants is 32.
Since, A sports teacher had 1025 sweets and he had one sweet left after distributing.
So, number of sweets he distributing is, [tex]1025-1=1024[/tex]
Since, distributing these equally amongst all the participants
Therefore, number of sweets given to each participants is, [tex]=\sqrt{1024}=32[/tex]
So, total number of participants is 32 and number of sweets given to each participants is 32.
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Parallel Lines
PLEASE HELP I NEED ASAP!
Answer:
B
Step-by-step explanation:
The triangles do have equal angles and proportional sides, because they are bot right triangles formed on parallel lines.
:)ur welcome
Answer: Choice B
Yes. Right triangles formed on parallel lines have proportional side lengths and congruent angles.
====================================================
Explanation:
Parallel lines always have equal slopes, but different y intercepts.
Recall that slope = rise/run.
The "rise" is the vertical portion of the triangle, while the "run" is the horizontal portion.
So let's say we had a slope of rise/run = 2/3. This means rise = 2 and run = 3.
If we had something like rise/run = 4/6, then that reduces to 2/3, showing that 4/6 = 2/3. They are the same slope.
We can use the SAS similarity theorem to prove the triangles formed in the diagram are congruent based on what is discussed above.
Because the triangles are similar, this means the corresponding angles are congruent. One such pair is the pair of right angles shown.
Mr. Alen has a tank of volume 450 cm3. Convert the volume into “m3
Answer:
0.00045 [tex]m^{3}[/tex]
Step-by-step explanation:
450 [tex]cm^{3}[/tex] ⇒ [tex]m^{3}[/tex]
1 [tex]cm^{3}[/tex] = 0.000001 [tex]m^{3}[/tex]
= 450 [tex]cm^{3}[/tex] = 450 × 0.000001 = 0.00045 [tex]m^{3}[/tex]
Answer:
450 (cm*3) = 0,00045 (m*3)
Step-by-step explanation:
What is the monthly net income?? Show work plz
angad was thinking of a number. angad halves the number and gets an answer of 78.5. form an equation with x from the information
Answer:
157
Step-by-step explanation:
Let the number Angad was thinking be 'x'
Equation:-
1/2(x) = 78.5
x = 78.5(2)
x = 157
On a coordinate plane, a curved line begins at point (1, 2) and ends at (5, 4).
What is the range of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
Step-by-step explanation:
there must be something missing here (I guess, the graph).
because just by looking at the 2 points, all 4 answer options could be wrong, or all 4 could be right.
just basing on the point coordinates I see the functional values (y) go from 2 to 4.
but we have no clue about what that curved function does in between these 2 points.
please provide the full information.
Question 27(Multiple Choice Worth 1 points)
(07.03 LC)
How many solutions does the equation 4y - 4y - 12 = 14-2 have?
One
None
Two
Infinite
Answer:
none
Step-by-step explanation:
any value on y cancel 4y and then we will have -12=12 which is not true.
What is the approximate result of converting 20 centimeters into inches? Remember that 1 inch = 2.54 centimeters.
Answer:
7.874 inches
Step-by-step explanation:
20/2.54=7.874
Answer:
7.87
Step-by-step explanation:
1/x = 2.54/20
2.54x = 20
x = 20/2.54
x = 7.87401574803
x = 7.87
What is the area of triangle ABC?
3 square units
O 7 Sguare units
11 square units
15 square units
Answer:
3
Step-by-step explanation:
base = 4-1
= 3
height = 3-1
= 2
Area = 1/2 (b)(h)
= 1/2 (3)(2)
= 3
therefore the answer is 3 square unit
Use the image to complete the equation below
Answer:
DPB
Step-by-step explanation:
Verticle angles are congruent
m∠APC = m∠DPB
Each side of a regular polygon is 2.5 cm in length .The perimeter of the polygon is 12.5 cm .How many sides does the polygon have?
with explanation please.
Answer:
There are 5 sides in the polygon.
Total perimeter of the polygon is 12.5 cm and it is a regular polygon.
Each side of the polygon is 2.5 cm.
So total number of sides is: Total perimeter of the polygon / Length of each side = 12.5 cm/ 2.5 cm = 5
Hence, the polygon has 5 sides and it is a regular pentagon.
Step-by-step explanation:
I hope this is correct, if it isn't please feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
f(x) = x2 What is g(x)?
5+
[f(x)
V
g(x)
(3, 3)
-5-
A. g(x) = 6x2
O B. 90%)-
Given:
The parent function is:
[tex]f(x)=x^2[/tex]
The graphs of f(x) and g(x) are given.
The graph of g(x) passes through the point (3,3).
To find:
The function g(x).
Solution:
From the given graph, it is clear that the graph of f(x) compressed vertically to get the graph of g(x). So,
[tex]g(x)=kf(x)[/tex]
Where, k is the stretch factor.
It can be written as:
[tex]g(x)=kx^2[/tex] ...(i)
The graph of g(x) passes through the point (3,3). Putting [tex]g(x)=3,x=3[/tex] in (i), we get
[tex]3=k(3)^2[/tex]
[tex]3=k(9)[/tex]
[tex]\dfrac{3}{9}=k[/tex]
[tex]\dfrac{1}{3}=k[/tex]
Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get
[tex]g(x)=\dfrac{1}{3}x^2[/tex]
Therefore, the correct option is D.
Estimate the measure of the following angles
Answer:
For A I'd say about 100° and for B about 150° (This is just my estimation)
Step-by-step explanation:
A is almost a right angle but a little more than 90°.
B is almost a straight/flat angle but it's less than 180°.
Answer:
a. 115(Looks kinda like 112 or 113 but it says estimate so it should work)
b. around 230
Step-by-step explanation:
What is the slope of the line containing (-2,5) and (4, -4)?
O A. -2
O B.
3
2
O c. 2
O D.
3
2
Answer: slope is -3/2
Step-by-step explanation:
(-2,5) (4,-4)
Use the slope formula y2-y1/x2-x1
5-(-4)/-2-4 = -3/2
Answer:
The slope of the line containing (-2,5) and (4,-4) is [tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
Hiiioo!! Can you please help me out with this!!! ❤️❤️:) (9)
9514 1404 393
Answer:
segment SRGivensegment PRSSS postulateStep-by-step explanation:
1. The only "Given" statement involving QR is ...
QR ≅ SR
2. You will notice that PQ ≅ PS is a Given statement.
3. The reflexive property says a segment is congruent to itself:
PR ≅ PR
4. All three sides of the triangles have been shown to be congruent. The appropriate choice for the postulate that shows congruence of the triangles is the SSS Postulate.
Which conjunction about whole numbers is true?
The sum of two non-zero even numbers is even and less than the addends.
The sum of two non-zero even numbers is even and greater than the addends.
The difference of two non-zero even numbers is odd and less than the larger number.
The difference of two non-zero even numbers is odd and greater than the larger number.
Answer:
The sum of two non-zero even numbers is even and greater than the addends
Step-by-step explanation:
The solution to the whole number equation is sum of two non-zero even numbers is even and greater than the addends
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the first number be p
Let the second number be q
Now , the values of p and q are even
So , when p = 2 and q = 4
The sum of two non-zero even numbers is even and greater than the addends
p + q > q be equation (1)
p + q > p be equation (2)
2 + 4 > 4
2 + 4 > 2
6 > 4 and 6 > 2
Hence , the equation is true and sum of two non-zero even numbers is even and greater than the addends
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A pharmaceutical company collects data on the side effects participants report for a drug it is testing. The company finds that the probability of experiencing a headache is 5 percent and the probability of experiencing both a headache and heartburn is 2 percent. If the probability of experiencing a headache or heartburn is 8 percent, what is the probability of experiencing heartburn?
1 percent
5 percent
11 percent
15 percent
Answer:
the answer is 5 percent
Step-by-step explanation:
The probability of experiencing heartburn is 5 percent. Therefore, option B is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Given that, the probability of experiencing a headache is 5 percent and the probability of experiencing both a headache and heartburn is 2 percent.
Let Event A: Headache and Event B: Heartburn.
P(A)=0.05, P(A∩B)=0.02
The probability of experiencing a headache or heartburn is 8 percent, hence:
P(A∪B)=0.08
Now, P(A∪B)=P(A)+P(B)-P(A∩B)
0.08=0.05+P(B)-0.02
P(B)=0.05 or 5%
Therefore, option B is the correct answer.
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