[tex]y= x^2 -5~~~~~~...(i)\\\\y = -2x +3~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~~~~x^2 -5 = -2x+3\\\\\implies x^2 -5 +2x -3 = 0\\\\\implies x^2 +2x -8 = 0 \\\\\implies x^2 +4x -2x -8 = 0\\\\\implies x(x+4) -2(x+4) = 0\\\\\implies ( x+4)(x-2) = 0\\ \\\implies x = -4,~ x = 2\\\\\text{Substitute x = 2 in eq (ii)}:\\\\y = -2(2) +3 = -4 +3 = -1\\\\\text{Substitute}~ x = -4 ~\text{in eq (ii)}:\\\\y = -2(-4) +3 = 8 +3 = 11\\\\\text{So,} ~(x, y)=\{(2,-1), (-4,11) \}\\\\\text{Hence the answer is option B.}[/tex]
2.2 Determine the general solution of 2.2.1 3 sin x = cos x
2.2.2 2 cos²x + 5 sin x = 4
Step-by-step explanation:
try this solution, note, the answers are underlined with green colour.
P is the point (2, 7) and Q is the point (6, -3).
What is the gradient of PQ?
The Gradient of the line PQ is -5/2.
What is Gradient?Gradient the basically the ratio between the change in vertical coordinate to change in horizontal coordinates.
Here, P (2, 7) and Q (6, -3)
Now, Gradient = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{-3 -7}{6 - 2}[/tex]
m = -10/4
m = -5/2
Thus, the Gradient of the line PQ is -5/2.
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A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is 4.9 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 5859 MB. How many downloads of the standard version were there?
The number of the standard versions downloaded will be 2790 standard versions.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
A Web music store offers two versions of a popular song.
The size of the standard version is 2.1 megabytes (MB).
The size of the high-quality version is 4.9 MB.
Yesterday, the high-quality version was downloaded four times as often as the standard version.
The total size downloaded for the two versions was 5859 MB.
Then the number of the standard versions were downloaded will be
→ 5859 / 2.1
→ 2790 standard versions
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Solve for x, please show work!
Answer:
x = 3°
Step-by-step explanation:
The external angle where secants/tangents meet is half the difference of the intercepted arcs.
__
Here, that means ...
18x = (1/2)(194° -86°)
18x = 1/2(108°) = 54° . . . . . simplify
x = 3° . . . . . . divide by 18
467532 rounded by 100 000
Answer:
Round off value = 500000
Step-by-step explanation:
467532 > 500
- Round up
⇒ 500,000
Find AC.
brainly is forcing me to make this longer but its just that
Answer:
24.49 units
Step-by-step explanation:
It si NOT a right triangle, so you'll have to use law of sines
angle C = 180 - 45-75 = 60 degrees
30 / sin60 = AC / sin 45
AC = 30 * sin 45 / sin 60 = 24.49 units
Find the product of
[tex]8(4\sqrt 7-\sqrt18)[/tex]
Answer:
[tex]32\sqrt{7}-24\sqrt{2}[/tex]
Step-by-step explanation:
[tex]8(4\sqrt{7}-\sqrt{18})\\\\8(4\sqrt{7}-3\sqrt{2})\\\\32\sqrt{7}-24\sqrt{2}[/tex]
A store employee conducted a survey of 325 randomly selected customers. According to the survey, 212 of the customers often use the app to shop. Get app | Meijer How many people would you expect to use the app if all 2,000 people in the community visited the store?
The number of people out of 2000 expected to use the app will be 1300.
What is a survey?A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics.
It is given that:-
A store employee conducted a survey of 325 randomly selected customers. According to survey 212, customers often use the app to shop.
We need to find the data for 2000 people who visited the store.
So the percentage of the people who are using the app will be calculated as:-
[tex]= \dfrac{212}{3254}=65\%[/tex]
So the number of the people out of 2000 will be:-
[tex]N\ = 2000\times \dfrac{65}{100}=1300\ \[/tex]
Hence the number of people out of 2000 expected to use the app will be 1300.
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What is the greater common factor of 24 and 32
Answer:
8
Step-by-step explanation:
To calculate the greatest common factor of 24 and 32, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the greatest factor that exactly divides both 24 and 32, i.e., 8.
Answer:
8
(factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 32 = 1, 2, 4, 8, 16, 32)
https://www.flocabulary.com/unit/gcf-lcm/
What is the sum?
3y/ y^2+7y+10 + 2/y+2
Answer:
5
___
y+5
Step-by-step explanation:
first
----> 3y 2(y+5)
---------------------- + ----------
(y+2)(y+5) (y+2)(y+5)
then
----> 3y+2(y+5)
------------
(y+2)(y+5)
then
----> 3y+2y+10
----------
(y+2)(y+5)
then
-----> 5(y+2)
---------
(y+2)(y+5)
then
-----> 5
-------
y+5
What is the quotient of 9-x2/
3x
and
x2 +6x+9/
3x?
44 rem
Im sorry if its wrong
x + 14 = 28
Solve for ‘x’.
[tex] \Large{\boxed{\sf x = 14}} [/tex]
[tex] \\ [/tex]
Explanation :Given equation:
[tex] \sf x + 14 = 28 [/tex]
[tex] \\ [/tex]
Subtract 14 from both sides :
[tex] \sf x + 14 - 14 = 28 - 14 \\ \\ \\ \boxed{\boxed{\sf x = 14}} [/tex]
[tex] \\ \\ [/tex]
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(Brainliest will be given :D) (Please help, with hints!) The floor plan of an office was drawn using a scale of 1 inch = 4 feet.
The reception area on the floor plan is 3 inches by 5 inches.
What are the dimensions of the reception area?
HINT: Write and solve a proportion comparing the scale of 1 inch = 4 feet to each of the dimensions of the reception area of the floor plan (one for 3 inches and one for 5 inches).
Using proportions, it is found that the dimensions of the reception area of of 12 feet by 20 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the scale factor is of 1 inch = 4 feet, meaning that each inch on the drawing represents a dimension of 4 feet.
The drawing is of 3 inches by 5 inches, hence the real dimensions are given by;
3 x 4 = 12 feet.5 x 4 = 20 feet.More can be learned about proportions at https://brainly.com/question/24372153
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8 = 3y - 12 - 8y What is the value of y?
Answer:
y = -4
Step-by-step explanation:
8 = 3y - 12 - 8y
Combine like terms
8 = -5y -12
Add 12 to each side
8+12 - 5y-12+12
20 = -5y
Divide each side by -5
20/-5 = -5y/-5
-4 =y
13. A statistics student had excluded three outlier values when
constructing a histogram of a frequency distribution. His teacher
directed him to remake the histogram and include the outliers.
Which of the following must be true?
O The class boundaries would change.
O The interpretation of the histogram remains the same.
O The shape of the histogram changes.
O The shape of the histogram remains the same.
The statement first “the class boundaries would change" is the correct.
What is statistics?Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analysing it even further.
We have:
A statistics student had excluded three outlier values when constructing a histogram of a frequency distribution.
As we know, the statistics described as the procedure of collecting data, classifying.
And from the given data we can conclude the class boundaries would change.
Thus, the statement first "the class boundaries would change" is the correct.
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Answer:
O The shape of the histogram changes
Step-by-step explanation:
There is no guarantee that the outliers are larger or less than the pre-existing class boundaries. Therefore the only thing we can be sure will happen is that the shape of the histogram will change given that any addition or subtraction of variables contributes to the shape regardless.
In a triangle, an exterior angle formed by producing a side is half of a right angle. One of the two opposite interior angles is twice the Other; find the sizes of each interior angle of triangle.
Step-by-step explanation:
let's explain this a bit.
when the exterior angle is a certain size, then the interior angle is 180 - that exterior angle.
in our case the exterior angle is half of a right angle, so it is 90/2 = 45°.
the corresponding interior angle is 180-45 = 135°.
the sum of all angles inside a triangle is always 180°.
so,
x + 2x + 135 = 180
3x = 45
x = 15°
2x = 30°
so, the 3 interior angles are
135°, 15°, 30°
USING Pythagoras theorem find the formula of equilateral triangle.
Answer:
Answer with explanation is below~
Step-by-step explanation:
We could easily obtain the formulae/formula of an equilateral triangle not only through Pythagoras Theorem, but also through Heron's formula.
INTRODUCTION:
What's equilateral triangle?
It's an triangle, whose all sides're of equal measurement.What's Heron Formula?
It's just a formula actually,take an example:Let,a,b and c denotes the lengths of 3 sides of any triangle,then the area will be given as:[tex] \boxed{\rm \: Area= \sqrt{s(s - a)(s - b)(s - c)} \: units ^{2}} [/tex]
Where,
s = (a+b+c)/2 {Half of the perimeter, basically}What's Pythagoras' Theorem?
It's actually like a formula but a theorem introduced by Pythagoras.SOLVING:
Let,ABC an equilateral triangle of sides a.
Now:Draw a perpendicular straight line AM to the side BC(Name each part of triangle)
So it's clear that ∆AMB is a right angled triangle at M, BM = (1/2)BC = a/2.
Please note AM here represents the height of ∆ ABC.
Let's use Pythagoras' theorem now.[tex] \boxed{\rm \: AM = \sqrt{AB^2-BM^2}}[/tex]
AB = aBM = a/2[tex] \rm \: AM = \sqrt{a {}^{2} - { \bigg( \cfrac{a}{2} \bigg) }^{2} } [/tex]
[tex] \rm \: AM = 3 \: \cfrac{a {}^{2} }{4} [/tex]
[tex] \rm \: AM = \cfrac{ \sqrt{3} }{2} \: a[/tex]
Now find the area of ∆ABC:
[tex] \rm \triangle \: ABC = \cfrac{1}{2} \times \: BC \times A [/tex]
[tex] \rm \: \triangle \: ABC = \cfrac{1}{2} \times a \times \cfrac{ \sqrt{3}}{4}a [/tex]
[tex] \boxed{\rm\triangle \: ABC = \cfrac{ \sqrt{3 } }{4} a {}^{2} \: units {}^{2}} [/tex]
Hence,the formulae of equilateral triangle using Pythagoras' theorem is {√(3)/4} a^2
[tex] \rule{225pt}{2pt}[/tex]
Extras:
Now let's find the area using Heron's Formula.
Solving:
Let each side of an equilateral triangle be a.
SO, then:
s = (3a/2)
We know that, (Heron's formula)
[tex] \rm \: A = \sqrt{s(s - a)(s - b)(s - c)} [/tex]
Now the area A :
[tex]\rm AR(A)= \sqrt{ \cfrac{ 3a } 2 \bigg(\cfrac{ 3a }{2} - a \bigg)\bigg(\cfrac{ 3a }{2} - a \bigg)\bigg(\cfrac{ 3a }{2} - a \bigg)} [/tex]
[tex]\rm AR(A)= \sqrt{ \cfrac{3a}{2} \bigg( \cfrac{a}{2} \bigg)\bigg( \cfrac{a}{2} \bigg)\bigg( \cfrac{a}{2} \bigg)}[/tex]
[tex]\rm \boxed{ \rm AR(A)= \cfrac{ \sqrt{ 3a}}{4} \: a {}^{2} \: \: units {}^{2}} [/tex]
And voila! we're done!
I hope this helps! :)
[Figure of Equilateral triangle is attached, it denotes the triangle we need to draw while finding the formulae through Pythagoras' theorem. ]
Find the slope.
y= X/3 + 4
M= ?/?
Answer:
m=1/7
Step-by-step explanation:
The slope of y=x/3 + 4 is 1/7.
x/3+4 = x/7 so m = 1/7.
Answer:
m = 1/3
Step-by-step explanation:
The equation given is in slope-intercept form, which has the basic structure:
y = mx + b
In this equation, "m" is the slope and "b" is the y-intercept.
The value of "b" is 4.
The value of "m" is 1/3. This is because (x/3) is the same as (1/3 times x).
In circle K with m/JKL = 30 and JK = 15 units, find the length of arc JL.
Round to the nearest hundredth.
Answer:
7.85
Step-by-step explanation:
Arc Length Formula
[tex]\text{arc length} = 2 \pi r (\frac{\text{angle in degrees}}{360^\circ})[/tex],
where r is radius.
Given information:
m<JKL = 30°
JK = r = 15 units
Substitute in equation and solve.
[tex]\text{arc length} = 2 \pi r (\frac{\text{angle in degrees}}{360^\circ})\\\text{arc length} = 2 \pi (15) (\frac{30^\circ}{360^\circ})\\\text{arc length} = \frac{5}{2} \pi \approx 7.85398\\\text{arc length} = 7.85 \text{ units}[/tex]
What do u know about Trigonometry in grade 11
Answer:
A lot
Step-by-step explanation:
So basically you learn a lot
Y= x^2-4x+2 what is the vertex
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+2} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -4}{2(1)}~~~~ ,~~~~ 2-\cfrac{ (-4)^2}{4(1)}\right)\implies (2~~,~~2-4)\implies (2~~,~~-2)[/tex]
Julian’s friend James also has a tank in the shape of a triangular prism. The dimensions of James’ tank are each exactly 2 3/4 times the dimensions of Julian’s tank. If the area of the triangular base of Julian’s tank is approximately 400 square inches, what is the approximate area of the triangular base of James’ tank?
3,025 square inches
2,035 square inches
3,045 square inches
4,025 square inches
The approximate area of the triangular base of James’ tank is 3025 in²
To find the approximate area of the triangular base of James' tank, we need to know what scale is.
What is scale?A scale is the ratio of two dimension. It is given by scale = New dimension/old dimension
Given that the dimensions of James’ tank are each exactly 2 3/4 times the dimensions of Julian’s tank.
The scale of the area of James' tank to the area of triangular base of Julian's tank is S = (2³/₄)²
= (11/4)²
= 121/16
Let
A = area of triangular base of James' tank, A' = area of triangular base of Julian's tank = 400 in²So, scale, S = A/A'
The approximate area of the triangular base of James’ tankSo, making A subject of the formula, we have
A = SA'
A = 121/16 × 400 in²
A = 121 × 25 in²
A = 3025 in²
So, the approximate area of the triangular base of James’ tank is 3025 in²
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what fraction of one day is 36 mins
Answer:
1 day = 1440min
so 36min of a day = 36/1440 = 1/40
Solve for x: 12x= 36
Please show all the steps that were given above that you must take to solve for x.
Step-by-step explanation:
x=36/12
x=2
I hope it's helpful for you12x = 36
x = 36÷12
x = 3
Hope it helps......
The edge of the square is 33 cm.
Calculate the square diagonally!
Take out the multiplier before the root sign!
Answer:
46.6
Step-by-step explanation:
[tex] {x}^{2} = {33}^{2} + {33}^{2} \\ x = \sqrt{2178} \\ x = 46.6 \: cm[/tex]
can someone help me with this q?
Answer:
rounded = 170 in^3 and 2nd question =2.772 in^3
Step-by-step explanation:
h: 12 1/8 = 12.125
w: 1 3/4 = 1.75
l: 8
----------------------------------
h*w*l = 169.75 in^3
rounded = 170 in^3
oh there's another.. wait
same with this question
.----------------------------------
h*w*l
10.5 * 12 * 22 = 2.772 in^3
Chords AB and CB intersect at E in circle O, as shown in the diagram below. Secant
PFA and tangent PD are drawn to circle O from external point and chord AC is drawn. The ratio of BF:FC:CA:AB = 3:3:4:8. Find the measures of FC,∠P,∠CEA, and ∠ABC.
Answer:
Step-by-step explanation:
A quadratic function has 2 distinct roots. Always never sometimes
Answer:
Always
Step-by-step explanation:
[tex]ax^{2} + bx + c = 0[/tex]
Mr. Benito just purchased 24 paint sets and a few sketch books for his art class. The total bill wūs $241. The paint sets cost a total of $105 and the sketch books $8 each. How many sketch books did he buy?
Answer:
He bought 32 sketchbooks
Step-by-step explanation:
E equals 32
Answer:
17
Step-by-step explanation:
We know:
The total bill was $241
The paint sets cost $105
Each sketchbook is $8
First, subtract the cost of the paint sets from the total bill. That leaves the entire cost of all of the sketch books.
241-105=136
Next, divide the cost of the sketch books by 8 to find the cost of one sketchbook.
136/8=17
Therefore, Mr. Benito bought 17 sketchbooks.
i need help with 7th grade math 30 points and brainleist ASAP
Answer:
The scale factor is 8. The model is scaled by 8 to get the sculpture.
If they want it in reverse, the answer is 1/8. The model is 1/8th of the sculpture's size.
Sculpture = scale factor * model
[we get this equation because the model must be turned into a sculpture so we want to find how much bigger the model is compared to sculpture]
Let's take the length of the sculpture and model to put in.
x
56 = scale factor * 7
56/7 = scale factor
8 = scale factor
Answer:
1/8
Step-by-step explanation:
Take the scale factor as a ratio between the model and the sculpture.
Take any of the listed dimensions (length, for example) and divide.
7/561/8