Answer:
The length of the rectangle is 15 cm.
Step-by-step explanation:
breadth(b)=?
length(l)= 3+2b
perimeter(P)= 42 cm
Now,
P = 2 ( l+b )
or, 42= 2 ( 3+2b+b)
or, 42 = 2 ( 3+3b)
or, [tex]\frac{42}{2}[/tex] = 3+3b
or, 21 = 3+3b
or, 21-3 =3b
or, 18 = 3b
or, [tex]\frac{18}{3}[/tex] = b
or, 6 = b
Here, Breadth(b)= 6 cm
Length (l) = 3 + 2*6
= 3 + 12
=15 cm
14. Simplify 4+ (-3) - 2 x (-6)
O A. 13
O B. 12
C.-11
O D. -10
Answer:
13
Step-by-step explanation:
1-2×(-6)=
1-(-12)=
1+12=13
please someone help me to prove this.
Step-by-step explanation:
8 cos 80° cos 140° cos 160°
4 (2 cos 80° cos 140°) cos 160°
4 cos 160° (2 cos 80° cos 140°)
Use product to sum formula.
4 cos 160° (cos 60° + cos 220°)
4 cos 160° (½ + cos 220°)
2 cos 160° + 4 cos 220° cos 160°
2 cos 160° + 2 (2 cos 220° cos 160°)
Use product to sum formula again.
2 cos 160° + 2 (cos 60° + cos 380°)
2 cos 160° + 2 (½ + cos 380°)
2 cos 160° + 1 + 2 cos 380°
2 cos 160° + 1 + 2 cos 20°
Use shift identity cos(180 − θ) = -cos θ.
-2 cos 20° + 1 + 2 cos 20°
1
Our question that we have at hand here is 8(cos 80°)(cos 140°)(cos 160°). We need to convert that into 'decimal form' to prove that it equals 1. However decimal form doesn't generally give us a decimal, in this case.
Let's start by using the identity cos(s)cos(t) = cos(s + t) + cos(s - t) / 2. In this case we are looking particularly at the expression (cos 80°)(cos 140°), where s = 80, and t = 140.
[tex]\cos \left(80^{\circ \:}\right)\cos \left(140^{\circ \:}\right)=\frac{\cos \left(80^{\circ \:}+140^{\circ \:}\right)+\cos \left(80^{\circ \:}-140^{\circ \:}\right)}{2}[/tex]
[tex]=8\cdot \frac{\cos \left(80^{\circ \:}+140^{\circ \:}\right)+\cos \left(80^{\circ \:}-140^{\circ \:}\right)}{2}\cos \left(160^{\circ \:}\right)[/tex]
[tex]= 4\cos \left(160^{\circ \:}\right)\left(\cos \left(220^{\circ \:}\right)+\cos \left(-60^{\circ \:}\right)\right)[/tex]
To further simplify this expression, we know that cos(- 60°) = cos(60°). This may not seem like a very effective step, but we can apply a few trivial identities here. Remember that cos(60°) = 1 / 2,
[tex]4\cos \left(160^{\circ \:}\right)\left(\cos \left(220^{\circ \:}\right)+\frac{1}{2}\right)[/tex]
[tex]= 4(0.25)\\= 1[/tex]
And hence we proved that 8(cos 80°)(cos 140°)(cos 160°) in decimal form, = 1.
If a classroom has 7 students with black hair and there are 24 students in the
class, what percentage of the students have black hair? (Round your answer to
the nearest tenth of a percent)
Answer:
29.2%
Step-by-step explanation:
The fraction of students with black hair is 7/24. To convert that to a percentage, multiply by 100%.
7/24×100% = 29.1666(repeating)% ≈ 29.2%
The development of a city over the past twenty
years cost $962,234,534,288,644. What is the value
of the digit 3 in this number
Answer:
The 3 in that longest number I have seen in the world is 30 Billion.
Step-by-step explanation:
Million: 6 places before
Billion: 9 places before
Hope this helps!
the area of a square is 36 units what is the perimeter?
Area of square = 36 unit²
To Find :Perimeter of square[tex].[/tex]
SoluTion :◈ Side of square :
[tex]:\implies\sf\:Area=(side)^2[/tex]
[tex]:\implies\sf\:36=(side)^2[/tex]
[tex]:\implies\sf\:side=\sqrt{36}[/tex]
[tex]:\implies\bf\:side=6\:unit[/tex]
◈ Perimeter of square :
[tex]:\implies\sf\:perimeter=4\times (side)[/tex]
[tex]:\implies\sf\:perimeter=4\times 6[/tex]
[tex]:\implies\underline{\boxed{\bf{\purple{perimeter=24\:unit}}}}[/tex]
Something that represent today’s culture ( sum that isn’t tech or social media)
It depends on which culture you're looking at to be honest. But in the current environment, one item that is fairly prevalent is the coronavirus facemask. You could say it symbolically represents the idea of trying to stay safe and it represents a new norm (that many may consider strange since people are used to seeing each other's faces).
The sum of only negative numbers.
Is it positive or negative
Answer: negative
Step-by-step explanation: Whenever you are adding negative
numbers together, you will always get a negative number.
For example, (-1) + (-1) will give you -2.
In the same way, (-5) + (-4) gives you -9.
Answer: negaitive
When you add a negative plus a negative you always get another negative
Write the phrase as an algebraic expression. A number plus six and three tenths. PLEASE HEEELP
Answer:
n + 6(3/10)
Step-by-step explanation:
6(3/10) is written as a mixed number
Answer:
x+6.3
Step-by-step explanation:
x+6.3
Simplify -2x+7=15, i need help understanding why it is -4
Answer:
-4
Step-by-step explanation:
Step 1: Subtract 7 from both sides.
−2x+7−7=15−7
−2x=8
Step 2: Divide both sides by -2.
−2x
−2
=
8
−2
x=−4
A=1/2(a+b)h, solve for h?
Answer:
[tex]\huge \boxed{h=\frac{2A}{a+b} }[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle A=\frac{1}{2} \cdot (a+b) \cdot h[/tex]
Multiplying both sides by 2:
[tex]2A=(a+b) \cdot h[/tex]
Dividing both sides by (a + b):
[tex]\displaystyle \frac{2A}{a+b} =h[/tex]
[tex]\rule[225]{225}{2}[/tex]
Six less than 4 times a number
Answer:
4x-6
Step-by-step explanation:
Six less than four times a number is four times x because times is multiplying and then subtracting six because less means minus (subtraction)
Which equation represents a line that is parallel to Y equals negative 4X +3 and passes through the point (-3,2)
The picture is the answers.
Please help
Answer:
Hey there!
A line parallel to y=-4x+3 would have a slope of -4.
Point slope form: y-2=-4(x+3)
Simplify: y=-4x-10
Let me know if this helps :)
Answer:
A
Step-by-step explanation:
So we want an equation that is parallel to:
[tex]y=-4x+3[/tex]
And passes through:
[tex](-3,2)[/tex]
First, since we want the equation to be parallel to the first, the slope must be -4. This is because parallel lines have the same slope.
Now that we know the slope of our equation is -4, we can use the point-slope form to figure out the rest.
The point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
m is -4. Let (-3,2) be x₁ and y₁. Thus:
[tex]y-2=-4(x--3)[/tex]
Simplify:
[tex]y-2=-4(x+3)[/tex]
Distribute:
[tex]y-2=-4x-12[/tex]
Add 2 to both sides:
[tex]y=-4x-10[/tex]
So our answer is A :)
Jaylon has a wrench labeled 0.1875 inch and bolts
labeled in fractions of an inch. Which size bolt will
best fit the wrench? Explain.
Answer: 3/16
Step-by-step explanation:
- you divide 3/16 which gets you to the answer of 0.1875
A fraction is a way to describe a part of a whole. The size of the bolt that will best fit in the wrench is 3/16 inches.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Jaylon has a wrench labeled 0.1875 inch and bolts labeled in fractions of an inch.
Now, the size of the bolt that will best fit in the wrench will be the bolt of size same as the wrench. Therefore, if we rewrite the size of the wrench it will be,
Size of the bolt = Size of the wrench
= 0.1875 inches
= 1875/10000 inches
Divide both the numerator and the denominator by 625
= 3/16 inches
Hence, the size of the bolt that will best fit in the wrench is 3/16 inches.
Learn more about Fraction here:
https://brainly.com/question/1301963
#SPJ2
Mr Tom shared $300 between his two sons aged 15 years and 10 years in
the ratio of their ages. Calculate the amount of money each boy received.
Answer:
Son of 15 years $180
Son of 10 years $120
Step-by-step explanation:
15 + 10 = 25
25 300
15 x = 300*15/25
x = 180
25 300
10 x = 300*10/25
x = 120
Son of 15 years $180
Son of 10 years $120
[tex]\sqrt{24n^3}[/tex] (simplify radical) please show work
Answer:
The answer is
[tex]2n \sqrt{6n} [/tex]Step-by-step explanation:
[tex] \sqrt{24 {n}^{3} } [/tex]First of all factor out the perfect square out.
In this question the perfect squares are 4 and x²
So we have
[tex] \sqrt{4 \times {n}^{2} \times 6n} [/tex]Separate the radicals
That's
[tex] \sqrt{4} \times \sqrt{ {n}^{2} } \times \sqrt{6n} [/tex]Simplify
[tex] \sqrt{4} = 2 \\ \sqrt{ {n}^{2} } = n[/tex]So we have
[tex]2 \times n \times \sqrt{6n} [/tex]We have the final answer as
[tex]2n \sqrt{6n} [/tex]Hope this helps
Answer:
[tex]2n \sqrt{6n} [/tex]
Step-by-step explanation:
[tex] \sqrt{24n {}^{3} } [/tex]
Factor out the perfect square ⬜[tex] \sqrt{2 {}^{2} } \times 6 {n}^{3} [/tex]
[tex] \sqrt{ {2}^{2} } \times 6n {}^{2} \times n[/tex]
Please the square root is for the entire formula ⬆️⬆️⬆️the root of the product is equals to the root of each Factor[tex] \sqrt{2 {}^{2} } \sqrt{n {}^{2} } \sqrt{6n} [/tex]
reduce the index of the radical and exponent with 2[tex]2 \sqrt{n {}^{2} } \sqrt{6n} [/tex]
[tex]2n \sqrt{6n} [/tex]
Solution2n square root 6n
[tex]2n \sqrt{6n} [/tex]
Hope this helps.....
Which statements are true? Check all that apply
Select the correct answer from the drop-dov
Consider this population data set: 4, 6, 7, 11, 12, 18, 26, 23, 14,, 31, 22, and 12. The values 11, 31, 22, and 12 constitute a random sample drawn from the data set. The sample mean is more than the population mean by
Answer: The sample mean is more than the population mean by 3.5
=======================================================
Explanation:
To get the population mean, first add up all the population values
4+6+7+11+12+18+26+23+14+31+22+12 = 186
Then divide that over 12 as there are 12 values in the population
186/12 = 15.5
The population mean is 15.5
----------
The sample mean is computed the same way
add the values = 11+31+22+12 = 76
Divide the sum by 4 = 76/4 = 19
The sample mean is 19
The sample mean is larger by 19 - 15.5 = 3.5
What is the value of the expression below when z = 2? 4z2 – 3z – 4
Answer:
6Step-by-step explanation:
[tex]4z^2 - 3z - 4\\z =2[/tex]
Substitute 2 for z in the given equation
[tex]4(2)^2 - 3(2) -4\\[/tex]
Follow the PEMDAS order of operations
[tex]\mathrm{Calculate\:exponents}\:\left(2\right)^2\::\quad 4\\=4\cdot \:4-3\left(2\right)-4\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:4\times\:4\::\quad 16\\=16-3\left(2\right)-4\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:3\left(2\right)\::\quad 6\\=16-6-4\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:16-6-4\::\quad 6[/tex]
Answer:
Step-by-step explanation:
Plug in z = 2 in the expression
4z² - 3z - 4 = 4*2² - 3*2 -4
= 4*4 - 6 - 4
= 16 - 6 - 4
= 10 - 4
= 6
Factorise a2 -10a-24
Answer:
(a+2)(a-12)
Step-by-step explanation:
[tex]a^2-10a-24\\\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(a^2+2a\right)+\left(-12a-24\right)\\\\\mathrm{Factor\:out\:}a\mathrm{\:from\:}a^2+2a\mathrm{:\quad }a\left(a+2\right)\\\\\mathrm{Factor\:out\:}-12\mathrm{\:from\:}-12a-24\mathrm{\\:\quad }-12\left(a+2\right)\\=a\left(a+2\right)-12\left(a+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}a+2\\=\left(a+2\right)\left(a-12\right)[/tex]
Answer:
(a + 2)(a - 12)
Step-by-step explanation:
a^2 - 10a - 24
using splitting method
a^2 - 12a + 2a - 24
taking separate common from both pairs
a(a - 12) + 2(a - 12)
(a + 2)(a - 12)
Describe the set of all points of the form (2 y) where y is a real number
Answer:
Following are the answer to this question:
Step-by-step explanation:
In the given-question, the information is missing. first, we declare the missing information, after that we define its solution:
Missing information:
plotting the Points (2, 0), (2, 4), (2, 1), and (2, -1).
solution:
please find the attachment.
In the given attachment file, all the points lie within the same line, which indicates its points, and the set may be interpreted throughout the form of (2,y), or even the points may also be placed on the line x=2.
.9 times what equals 1.5
Answer:
5/3
Step-by-step explanation:
x*0.9=1.5
x=15/9
x=5/3
Lets solve your question step by step:-
Given,
0.9*x = 1.5
0.9x = 1.5
=} 0.9x/0.9 = 1.5/0.9
x = 1.666667
So,
9 times 1.666667 (x) is 1.5
Hope it helps :)
you and 2 decide to each order a pizza for lunch would you rather
Answer:
My answer to the question is option B
Answer:
hmmmm Option A for me
Step-by-step explanation:
The sum of the angle measures of a triangle is 180°. Two angles of a triangle measure 40°and 60°, so Juan concludes that the third angle measures 80°. What do you notice about the how the conclusions were made from the statement above?
Answer:
Step-by-step explanation:
Third angle = 180 - (40 + 60)
= 180 - 100
= 80°
When you subtract the sum of 40 and 60 from 180, you will get the third angle.
find the distance between the 2 points on the graph.
HELPPPP
Answer:
6^2 + 3^2 = sqrt 45
the answer is the sqrt of 45
Step-by-step explanation:
Answer:
[tex] 3\sqrt{5} [/tex]
Step-by-step explanation:
Use the distance formula and the coordinates of the points.
The upper left point is (-5, 3).
The lower right point is (-2, -3)
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] d = \sqrt{(-2 - (-5))^2 + (-3 -3)^2} [/tex]
[tex] d = \sqrt{3^2 + (-6)^2} [/tex]
[tex] d = \sqrt{9 + 36} [/tex]
[tex] d = \sqrt{45} [/tex]
[tex] d = \sqrt{9 \times 5} [/tex]
[tex] d = 3\sqrt{5} [/tex]
Line, Line Segment, Ray...
A) are two - dimensional
B) have no dimension
C) are three-dimensional
D) are one dimensional
Answer:
A
Step-by-step explanation:
They are all straight paths with end points but a line is never ending but it is still two dimensional
Answer:
D - Are One dimensional
Step-by-step explanation:
Line , Line segments and Ray's are all one dimensional objects
I'm confused about what the expression is.
Answer:
4(x+y)
Step-by-step explanation:
x+y is one side length and there are 4 side lengths.
Solve for x.
45+ Go +1) =
2x
Answer:
x= [tex]\frac{1}{2}[/tex]go+23
Step-by-step explanation:
Use the discriminant to describe the roots of each equation. Then select the best description.
X^2-4x+4=0
x^2-4x+4=0
now;
x^2-4x=0-4
x^2-4x=-4
x(x-4)=-4
x^2-4x+4
X² + 9x + 4 = FACTORISE
Answer:
[tex]$-\frac{1}{4} (-2x-9+\sqrt{65})(2x+9+\sqrt{65})$[/tex]
Step-by-step explanation:
We have a second-degree polynomial:
I will find the roots (y = 0) completing the square:
[tex]$x^2+9x+\frac{81}{4}-\frac{81}{4}+4=0$[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 -\frac{81}{4} +4 =0$[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 -\frac{81}{4} +\frac{16}{4} =0$[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 -\frac{65}{4} =0$[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 =\frac{65}{4} $[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 =\pm \sqrt{\frac{65}{4} } $[/tex]
[tex]$x =-\frac{9}{2} \pm \frac{\sqrt{65} }{2} $[/tex]
[tex]$x =\frac{-9 \pm \sqrt{65} }{2} $[/tex]
[tex]$\boxed{x_1 =\frac{-9 + \sqrt{65} }{2}} $[/tex]
[tex]$\boxed{x_2 =\frac{-9 - \sqrt{65} }{2}} $[/tex]
Luis deposited $300 into his bank account. He now has $4,511. Enter and solve an equation to find how much was in his account before the deposit. Let a represent the variable.