Answer:
x = 7
Step-by-step explanation:
Rearrange the equation to make x the subject.
Original:
7x + 3 = 52
subtract 3 from both sides
7x = 52 -3
7x = 49
Divide both sides by 7
x = 49/7
x = 7
there are 4, 6, and 7 points on three lines. How many triangles is it possible to create with given points as vertices?
4 triangles can be created with 3 points on a line.
20 triangles can be created with 6 points on a line.
30 triangles can be created with 7 points on a line.
Combination has to do with selection.
Note that a triangle has 3 vertices. If there are 4 points on a line, the number of triangles it is possible to create is derived using the combination formula shown as:
[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]
[tex]4C_3 = \frac{4!}{(4-3)!3!}\\4C_3 =\frac{4\times3!}{3!}\\4C_3=4triangles[/tex]
This means that 4 triangles can be created with 3 points on a line.
For a line with 6 points:
[tex]6C_3 = \frac{6\times 5\times 4\times 3!}{(6-3)!3!}\\6C_3 =\frac{6\times5\times 4\times3!}{3!3!}\\4C_3=20triangles[/tex]
This shows that 20 triangles can be created with 6 points on a line.
For a line with 7 points:
[tex]7C_3 = \frac{7\times 6\times 5\times 4!}{(7-3)!3!}\\4C_3 =\frac{7\times6\times 5\times4!}{4!3!}\\4C_3=30triangles[/tex]
This shows that 30 triangles can be created with 7 points on a line.
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Use the example as a model. Simplify the expressions.
t^37 = ✔ i
t^82 = ✔ –1
Answer:
After , the sequence repeats itself
Divide 37/4 = 9 R 1. Now use the remainder and find which one of the values of i it matches.
so
Step-by-step explanation:
The expressions are simplified as;
i. t = ∛i
ii. t = 1
How to simply the expressionsFrom the information given, we have that;
Simplifying [tex]t^3^7[/tex] = √i
When [tex]t^3^7[/tex]equals i (the imaginary unit), we can solve for "t" by taking the 37th root of both sides:
[tex]t^3^7 = i[/tex]
[tex]t = \sqrt[3]{i^3^7}[/tex]
[tex]t = i^(^3^7^/^3^)[/tex]
Since i^4 = 1 (i raised to the power of 4 is 1), we can simplify the exponent:
[tex]t = i^(^1^2 ^+ ^1^/^3^)[/tex]
[tex]t = i^1^2 ^* i^(^1^/^3^)[/tex]
Now, since[tex]i^1^2[/tex] = 1 and [tex]i^(^1^/^3^)[/tex] represents the cube root of i, we have:
t = 1 * ∛i
t = ∛i
Simplifying [tex]t^8^2[/tex] = √ –1:
Take the 82nd root of -1
[tex]t^8^2 = -1[/tex]
t = [tex]\sqrt{(-1)^8^2}[/tex]
t = √1
t = 1
Learn about complex numbers at: https://brainly.com/question/10662770
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Select from the drop-down menus to correctly complete the statements about simplifying an expression with grouping symbols. When an expression has more than one set of grouping symbols, simplify within the Choose... grouping symbols first. The Choose... symbol can also be a grouping symbol. Simplify the Choose... separately. Choose... follow the order of operations within a set of grouping symbols.
Answer:
nuber 1 is sum 2 is quotient 3 is produckproduct
Step-by-step explanation:
number 1 is sum, 2 is quotient , 3 is product.
What is set?A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements.
here, we have,
an expression with grouping symbols.
When an expression has more than one set of grouping symbols,
So, the answer is,
number 1 is sum, 2 is quotient , 3 is product.
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Mike´s fitness center charges $30 per month for a membership. All-Day fitness club charges $22 per month plus an $80 initiation fee for a membership. After how many months will the total amount paid to the two fitness clubs be the same?
Answer:
10 months
Step-by-step explanation:
30x=22x+80
8x=80
x=10
The perimeter of a triangle is 65 cm. The
lengths of the sides are x cm, x+8 cm, and
X+ 12 cm.
What is the length, in cm, of the longest side of
the triangle?
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The longest side measures :
[tex]27\: \: cm[/tex][tex] \large \boxed{ \mathfrak{Explanation}}[/tex]
Perimeter of a triangle is equal to sum of measures of its all three sides, that is :
[tex]x + x + 8 + x + 12[/tex]and according to the question, the perimeter of the triangle is = 65 cm
so, let's equate both the expressions to find value of x :
[tex]x + x + 8 + x + 12 = 65[/tex][tex]3x + 20 = 65[/tex][tex]3x = 65 - 20[/tex][tex]3x = 45[/tex][tex]x = 45 \div 3[/tex][tex]x = 15[/tex]The longest side of the Triangle is :
[tex]x + 12[/tex][tex]15 + 12[/tex][tex]27 \: \: cm[/tex]27cm
Step-by-step explanation:
(xcm) + (x+8cm) + ( x+ 12cm) = 65cm
Open Bracket
xcm + x+8cm + x+12cm = 65cm
3x+ 20cm = 65cm
Collect like terms
3x = 65cm - 20cm
3x = 45cm
Divide both sides by 3
3x/3 = 45cm/3
x = 15cm
The longest side of the triangle =( x+12cm)
= (15+12)cm= 27cm
What the answer?????
Okay,
So this equation is non existent. It is not an equation nor expression.
Key Info:
x - variable
0.256 - decimal
10.3 - decimal
Hope this helps.
Add more information to your answers. ( GIVE CONTEXT )
A tablespoon is equivalent to about 4 teaspoons. A recipe calls for 2/3 cup of sugar for every 1/2 teaspoon vanilla. What is the unit rate in tablespoons
per cup?
Answer:
I understand the exercise is about unit rates, but why go out of the way to state false information? A tablespoon is exactly 3 teaspoons!
Anyway,
(1/2 tsp)/(2/3 cup) * (1tbsp)/(4tsp) = 1/2 * 3/2 * 1/4 = 3/16 tbsp/cup
Step-by-step explanation:
Ok
If y varies directly as x and inversely as z, and y=22 when x=4 and z=6, find y when x =10 and z = 25.
I give Brainliest! Please no links
Which of these is a healthy coping strategy for stress?
A
Writing your thoughts in a journal
B
Not sharing your emotions with anyone
C
Stopping your exercise routine
D
Working very hard without breaks
Answer:
A
writing your thoughts in journal
10 ft 8 ft 6 ft Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate n. A = [ ? ] ft?
Answer:
l×b×h-this is the order
10×8
=80 --area 1:maximum
10×6= 60--area2: minimum area
8×6=48--area3:middle area
if you follow the order
the answer is= 60ft
help is very much needed
Answer:
IT'S NEGATIVE 3. HOPE THIS HELPS...
Help me with math please
(-3^3+2 · -2^2)^2-4^4
(-27+2 · -4)^2-4^4
(-27+(-8))^2-4^4
-35^2-4^4
1225-256
969
Which equation in standard form has a graph that passes through the point (-2, 6) and has a slope of !.A. 3x — 2y = 12 B. 3x — 2y = 6 C. 3x — 2y = -18 D. 3x — 2y = 18
Answer:
Your answer should be C
Step-by-step explanation:
Answer:
3x - 2y = -18
Step-by-step explanation:
3x - 2y = -18 and (-2, 6)
(3)(-2) - (2)(6) = -6 - 12 = -18
Can someone PLEASE tell me the answer
Answer:
the answer is C 36
Step-by-step explanation:
Can someone please help me with this I really need help.
Answer:
The angle mPQO is 86°
Step-by-step explanation:
123°-37°
help me pleaseeeeeeeee
Answer:
Open your dictionary, Find the word you are looking for and reread the Sentence and find the right definition that BEST fits the Sentence
Thank me Later :D
Step-by-step explanation:
3 over 7 = blank over 35
Answer:
15/35
Step-by-step explanation:
7 x ? =35
7 x 5 =35
whatever you do to the bottom , you do to top so you times 3 by 5.
3 times 5 = 15, therefore, it is 15/35
Answer:
15 over 35
Step-by-step explanation:
35/7 = 5
5*3 = 15
then:
3/7 = 15/35
If 2x -3y = 3 then find 16x 64y =?
Answer:
0 is the answer on 16 x 64y
Answer:
1 x = 4 y= 2/3 = 1. 66667 see attached and join the lines to create shaded area.
Step-by-step explanation:
2x -3y = 3
16x (64y) = ?
we can multiply the 2x by 8 to find x = 16 and -3y = -24y and 3 = 24
as shown 2nd one.
16x + (64y) = c
16x -24y = 24 = 64y - 24y = c
40y = c - 24
40y/24 = y
1.66667 = y
y = 1.6667 or 1 2/3
2x -3 ( 1 2/3 ) = 3
2x - 5 = 3
2x = 8
x = 4
y = 1. 66657
The difference of twice a number and three is
Answer:
2
Step-by-step explanation:
given the difference of twice a number and one is three to find "number" let the number be x
2x - 1 =3
2x = 4
x= 2
thus the number is 2
Solve for r
K=3r-s
r=?
Answer:
K=3r-s
K+s=3r
K/3+s/3=r
Step-by-step explanation:
k=3r-s
k+s=3r
k+s/3 = r
r = k+s/3
Pls help. Thank you!
Answer:
x = 15
Step-by-step explanation:
Here's an easy way to solve this:
OAP appears to be a right isosceles triangle. Angle O is a right angle, so the other angles are congruent (the same).
180-90 = 90
90÷2 = 45
3x = 45
x = 15
[tex]\sf 300+200+200[/tex]
Step-by-step explanation:
300+200+200 = 700.
so simple
hope this helps you.
Write the equation of the graph below in slope intercept form.
(2,0) and (0,-3)
Step by step
Answer:
y2- y1 over
x2 -x2
[tex] - 3 - 0 = - 3[/tex]
[tex]0 - 2 = - 2[/tex]
Step-by-step explanation:
slope is m =
[tex]m = - \frac{3}{2} [/tex]
use the -3 for b and you get
[tex]y = - \frac{3}{2} x - 3[/tex]
slope intercept form
which company offers the best deal?why?
Answer:
where question？
Step-by-step explanation:
i dont know the question it cant be solve
Answer:
I don't see the question. it cannot be solved
Solve using order of operations: 72/8+6/3-4(10)
Answer:
the answer is -29
Step-by-step explanation:
A 5-pound bag of dog food costs $11.25. What is the unit price of the dog food in dollars per pound?
Answer:
$2.25
Step-by-step explanation:
5 lbs = $11.25
The unit price in this context means the price of a 1-pound bag of dog food so you would divide $11.25 by 5:
$11.25 ÷ 5 = $2.25
Hope this helps!
Answer:
2.25 ($) per pound
Step-by-step explanation: 11.25 / 5 = 2.25 per pound Alternative workings we simply divide by 10 to find 11.25 / 10 = 1.125 then multiply by 2 1.125 * 2 = 2.25 ($) per pound
Explain how you can use mental math to
calculate 2^8.
Answer:
think about what 2 times 8 equals
Step-by-step explanation:
Rationalisie the denominator of: 4√3/2-√2
Answer:
[tex] \longmapsto4 \sqrt{3} + 2 \sqrt{6} .[/tex]
Step-by-step explanation:
[tex]\sf{\dfrac{4\sqrt{3}}{2 - \sqrt{2}}}[/tex]
By Rationalizing the denominator:-
[tex] = \sf{\dfrac{4\sqrt{3}}{2 - \sqrt{2}} \times \dfrac{2 + \sqrt{2}}{2 + \sqrt{2}}}[/tex]
[tex] = \sf{\dfrac{4\sqrt{3}(2 + \sqrt{2})}{(2)^2 - (\sqrt{2})^2}}[/tex]
[tex] = \sf{\dfrac{4\sqrt{3}(2 + \sqrt{2})}{4 - 2}}[/tex]
[tex] = \sf{\dfrac{4\sqrt{3}(2 + \sqrt{2})}{2}}[/tex]
[tex] = \sf{\dfrac{\not{4}\sqrt{3}(2 + \sqrt{2})}{\not{2}}}[/tex]
[tex] = \sf{2\sqrt{3}(2 + \sqrt{2})}[/tex]
[tex] = \sf{4\sqrt{3} + 2\sqrt{6}}[/tex]
[tex] \therefore \sf{\dfrac{4\sqrt{3}}{2 - \sqrt{2}} = 4\sqrt{3} + 2\sqrt{6}}[/tex]
if a/b= (3/7)2 ÷ (9/7)0, then find the value of (b/a)2?
pls answer fast
[tex]\\ \sf\longmapsto (3/7)2\div (9/7)0[/tex]
Anything multiplied with 0 gives 0[tex]\\ \sf\longmapsto (3/7)2\div 0[/tex]
[tex]\\ \sf\longmapsto \infty[/tex]
Now
[tex]\\ \sf\longmapsto \dfrac{b}{a}=\dfrac{1}{\infty}=0[/tex]
[tex]\\ \sf\longmapsto (\dfrac{b}{a})^2=0^2=0[/tex]
Find the slope of the line that contains the points (2,5) and (4,8).
Answer: Slope = 3/2 or 1.5
Answer: y= 1.5 x+2 or y=3/2x+2
Step-by-step explanation:Slope (m) =
ΔY
ΔX
=
3
2
= 1.5
θ =
arctan( ΔY )
ΔX
= 56.30993247402°
ΔX = 4 – 2 = 2
ΔY = 8 – 5 = 3
Distance (d) = √ΔX2 + ΔY2 = √13 = 3.605551275464
y = 1.5x + 2
or
y =
3 x
2
+ 2
When x=0, y = 2
When y=0, x = -1.3333333333333
