Answer: width:60.2 cm
Length: 64.2 cm
Step-by-step explanation:
Given
The area of the rectangle is [tex]3990\ cm^2[/tex]
Width of the rectangle is [tex]x\ cm[/tex]
Length of the rectangle is [tex]x+4\ cm[/tex]
Area of the rectangle is the product of length and width
[tex]\therefore 3990=(x+4)x\\\Rightarrow 3990=x^2+4x\\\Rightarrow x^2+4x-3990=0\\\Rightarrow x=60.198\ or\ -65.198\ cm\\\text{Neglecting negative term}\\\Rightarrow x=60.198\approx 60.2\ cm[/tex]
Width of the rectangle is [tex]60.2\ cm[/tex]
Length of the rectangle is [tex]60.2+4=64.2\ cm[/tex]
15) The sum of one-fourth, one-ninth and one- third of a number is 25. Find the number.
Answer:
Step-by-step explanation:
(1/4 + 1/9 + 1/3)x = 25.
x = 36
Answer:
Let the number be x
(1/4 + 1/9 + 1/3) * x = 25
25/36 * x = 25
25x = 25*36
x = 25*36/25
x = 36
Step-by-step explanation:
Determine which equations have the same solution set as 2/3 -x +1/6 = 6x by recognizing properties, rather than solving. Check all that apply.
Answer:
The answer is "0.1190".
Step-by-step explanation:
Given:
[tex]\to \frac{2}{3} -x +\frac{1}{6} = 6x\\\\\to \frac{2}{3} +\frac{1}{6} = 6x+x\\\\\to \frac{4+1}{6} = 7x\\\\\to \frac{5}{6} = 7x\\\\\to x=\frac{5}{6\times 7} \\\\\to x=\frac{5}{42}\\ \\\to x= 0.1190[/tex]
Answer:
A.) 4 - 6x + 1 = 36x
B.) 5/6 - x = 6x
F.) 5 = 42x
Step-by-step explanation:
edge.
Thank you so much thank y’all for your help
Answer:
2(4) + 2(l) >14 (second option is the answer).
arctanx=arccos(-5/13)
i know that there is no solution but i need to know how to get there
help me solve the trig equation for x!!
If φ = arccos(-5/13), then cos(φ) = -5/13. Since this is negative, you know φ is an angle that terminates either the second or third quadrant.
arctan(x) has a range of -π/2 < arctan(x) < π/2, which is to say that arctan(x) is an angle that terminates in either the first or fourth quadrant.
These quadrants don't overlap, so there is no solution to the equation.
Describe how (2 cubed) (2 superscript negative 4) can be simplified.
Answer:
1/2
Step-by-step explanation:
Given:
(2 cubed) (2 superscript negative 4)
= (2³)(2^-4)
= (2³) (1 / 2⁴)
= (2³ * 1) / 2⁴
= 2³ / 2⁴
Both numerator and denominator has the same base. Thus, pick one of the bases
Also, in indices, division sign can be translated to subtraction
Therefore,
2³ / 2⁴
= 2^3-4
= 2^-1
= 1/2¹
= 1/2
(2³)(2^-4) = 1/2
Answer:
D
Step-by-step explanation:
bc i said so
need help with this!!
Nigel's age (n) is 3 years more
than his sister's age (s).
A. N = 3N + 3
B. N =3s
C. N = 3 + s
D. S = -3s/n
Answer:
b
Step-by-step explanation:
n=3s
~~~~~~~~~~~~~~~~~
Help if you know thanks
x= - 1/2,-1
or
x= - 0.5, -1
Answer:
x = -1/2 x=-1
Step-by-step explanation:
2x( x+1.5) = -1
Distribute
2x^2 + 3x = -1
Add 1 to each side
2x^2 +3x+1 = 0
Factor
(2x+1) (x+1) =0
Using the zero product property
2x+1 = 0 x+1=0
2x = -1 x=-1
x = -1/2 x=-1
2(-3-6)+(-7+4)to the power of 2
Which best describes the relationship between the lines with equations −6x+8y=−1 and −4x−3y=2?
Answer:
it is linear
Step-by-step explanation:
Both of these both lines are perpendicular to each other.
We have the two equations of straight lines :
− 6x + 8y = −1 and −4x − 3y = 2.
We have to identify the relation between these two lines.
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to the question, we have -
−6x + 8y = −1 ...(1)
−4x − 3y = 2 ...(2)
Rearranging the terms of the equations we get -
y = [tex]\frac{3}{4} x - \frac{1}{8}[/tex] ...(3)
and
y = [tex]\frac{-4}{3}x - \frac{2}{3}[/tex] ...(4)
When compared -
The slope of line −6x + 8y = −1 is m(1) = [tex]\frac{3}{4}[/tex].
The slope of line −4x − 3y = 2 is m(2) = [tex]\frac{-4}{3}[/tex].
We can see that -
m(1) x m(2) = - 1
The product of the slopes of two perpendicular lines is -1.
Hence, these both lines are perpendicular to each other.
To solve more questions on relation between straight lines, visit the link below -
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In Exercises 1-4, determine whether the dilated figure or the original figure is closer to the center of dilation. Use the given location of the center of dilation and scale factor k.
1. Center of dilation inside the figure; k = 3
Center of ditation inside the figure, k = 1/2
3. Center of dilation outside the figure: = 120%
4. Center of dilation outside the figure; k = 0.1
When the Center of dilation is inside the figure
The original figure is closer to the center of dilationThe dilated figure is closer to the the center of dilationWhen the Center of dilation is outside the figure
3. The original figure is closer to the the center of dilation
4. The dilated figure is closer to the center of dilation
The center of dilation is the fixed point from which the distances in a dilation are measured
The scale factor is ratio of the side lengths of an original figure or preimage to the side lengths of the newly formed image
Center of dilation is inside the figure
Where the center of dilation is inside the figure, and the scale factor is larger than 1, k = 3 > 1, we have;The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation
Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure
2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;
The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation
Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure
Center of dilation outside the figure
3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;
The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure
4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1
The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation
Learn more about scale factors and center of dilation here;
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help please...what is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6. be exact with your answer.
Answer:
the answer is a
Step-by-step explanation:
sory lawl
i mean e
answer e!
good luck w summer geometoery
can y’all help me out
Answer:
B: y = {-13, -5, 3, 15}
Step-by-step explanation:
Let's plug each x-value into this equation: f(x) = 4x + 3
Domain: {-4, -2, 0, 3}
First, let's start with -4:
f(x) = 4x + 3
y = 4x + 3
y = 4(-4) + 3
y = -16 + 3
y = -13
Next, let's do -2:
f(x) = 4x + 3
y = 4x + 3
y = 4(-2) + 3
y = -8 + 3
y = -5
After that, let's do 0:
f(x) = 4x + 3
y = 4x + 3
y = 4(0) + 3
y = 0 + 3
y = 3
Finally, let's do 3:
f(x) = 4x + 3
y = 4x + 3
y = 4(3) + 3
y = 12 + 3
y = 15
Now that we have all our y-values, let's set up the range:
Range (y-values): {-13, -5, 3, 15}
As you can see, the only answer choice that includes this range is B;
{-13, -5, 3, 15}.
Which graph represents the function f(x)=|x−1|−3 ?
please help asap, see attached photo. This is due in 1 hour!!! please answer both questions. Both 5 and 6
Answer:
A and C
Step-by-step explanation:
5) logx+log(x+9)=2
log(x(x+9))=2, log(x^2+9x)=2
6) log(x^2+9x)=2
(x^2+9x)=36 or 6^2
I’ll mark u as a brainliest!! pls help me
Answer:
Shorter leg is 7
Bigger leg is 7√3 = 12.1 (rounded to the nearest tenth)
PLEASE HELP!
Find the value of x.
Answer Options:
A. 12
B. 11
C. 10
D. 16
Explanation:
We use the intersecting chords theorem here.
This is the idea where multiplying the pieces of each chord lead to the same product
6*x = 5*12
6x = 60
x = 60/6
x = 10
Answer:
C.) 10
Step-by-step explanation:
I got it correct on founders edtell
pls help. pls show work as well thank you:)
Answer:
Step-by-step explanation done
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AABC= ALMN?
Check all that apply
O A. LL
O B. ASA
I C. LA
D. HL
E AAS
3 Answers:
Choice A. LLChoice D. HLChoice F. SAS==========================================================
Explanation:
Let's go through the answer choices one by one.
A) This can be used because LL = leg leg, and this means we have two pairs of congruent legs. Those pairs are AC = LN and CB = NM. The LL theorem only applies to right triangles.B) This cannot be used. We don't have info about two pairs of angles. We only know that one pair of angles are the same (those 90 degree angles). So we can't form the second "A" in "ASA". This idea will come up again in choice C and choice E.C) This cannot be used. Why not? Because the "A" of "LA" refers to "acute angle". But unfortunately we don't know anything about the acute angles (whether they are congruent or not). The LA theorem can only be applied to right triangles.D) This can be used. We can use the HL (hypotenuse leg) theorem because we see that AB = LM are the pair of congruent hypotenuses, and you can use any of the congruent leg pairs to form the L of HL. Similar to LL and LA, the HL theorem only works for right triangles.E) This cannot be used. Like with choice B, we can't form the second "A" of "AAS".F) This can be used because we have two pairs of congruent sides, with a pair of congruent angles between those sides. Those angles being the marked 90 degree angles. It turns out that LL theorem is a special case of the SAS theorem.In short, we can use choice A, choice D, choice F. We can't use the other three choices because we lack the info about any other pairs of angles.
The congruence theorem or postulate that we can use to show that triangle ABC is congruent to triangle LMN is LL (Side-Side-Side), the correct option is A.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
We are given that;
Sides are equal
Now,
Based only on the information given in the diagram, we can use the following congruence theorems or postulates to show that triangle ABC is congruent to triangle LMN:
A. LL (Side-Side-Side): This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In this case, we know that AB = LM, AC = LN, and BC = MN, so we can use LL to show that triangle ABC is congruent to triangle LMN.
B. ASA (Angle-Side-Angle): This theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, we do not know any angle measures, so we cannot use ASA to show that the triangles are congruent.
Therefore, by the congruent triangles the answer will be LL (Side-Side-Side).
Learn more about congruent triangles here:
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a.) x ≥ 2
b.) x > 2
c.) x < 2
d.) x ≤ 2
Answer:
x < 2
Step-by-step explanation:
There is an open circle at 2 so that means it is not equal to
The line goes to the left so x is less than 2
x < 2
Answer:
c.) x < 2
Step-by-step explanation:
open circle means > or <
the line is going to the left, meaning < or ≤
from this, we know the inequality is x < 2
please find the answer
there are options given below
plz give answer asap
Answer
33.3
Step-by-step explanation:
if u multiply the 2, and then find the ratio of them in comparison to the number under, you will find the rate decreases by 10 percent every time, the first situation it is 4/8 = 5/10, second situation is it 32/80= 4/10, and htis situation is most like 3/10, right ? so the answer would be 33.3 :)
if 2x + 3x.find the value of x
if 2x + 3x = ? the question is incomplete or is it about traingle
If (3+√5)(4-√5)=a+b√5, where a and b are integers, then what is the value of a + b?
calcula el valor de A - B, si se sabe que: A=
Answer:
[tex]P=\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]P=\frac{(x+3)^2-(x-3)^2}{(x+6)^2-(x-6)^2}[/tex]
[tex]=\frac{[(x+3)-(x-3)][(x+3)+(x-3)]}{[(x+6)-(x-6)][(x+6)+(x-6)]}[/tex]
[tex]=\frac{6(2x)}{12(2x)}[/tex]
[tex]=\frac{1}{2}[/tex]
Por tanto, el valor de P será [tex]\frac{1}{2}[/tex]
AYUDAAAAA
Un litro de leche de búfala equivale a 1.7 litros de leche de vaca. ¿si tengo
27 litros de leche de búfalo, a cuantos litros de leche de vaca equivaldría?
Answer:
27 litros de leche de búfalo equivalen a 45.9 litros de leche de vaca.
Step-by-step explanation:
Sabiendo que un litro de leche de búfala equivale a 1.7 litros de leche de vaca, podemos calcular el equivalente de capacidad de la vaca para 27 litros de leche de búfala mediante Regla de Tres Simple:
[tex]x = 27\,L\times \frac{1.7\,L}{1\,L}[/tex]
[tex]x = 45.9\,L[/tex]
27 litros de leche de búfalo equivalen a 45.9 litros de leche de vaca.
pleeaseeee help me !!!
Answer 3. -7.5 is located to the left of 6.5 on a number line oriented from left to right.
show the work please and thank you
Answer:
Option a, 13
if you solve it, you get 13 as the answer
³√(5x-1)=4
or, 5x-1=64
or, 5x=65
or, x=13
which expression is equivalent to 10 a+ 3b -2a+b
Answer:
Step-by-step explanation:
Simplify like terms.
10a-2a+3b+b = 8a+4b
Answer:
8a +4b
4(2a+b)
Step-by-step explanation:
10 a+ 3b -2a+b
Combine like terms
10a-2a +3b+b
8a +4b
We can factor out 4
4(2a+b)
Can someone help with these 2?
Answer:
a. 25 ft squared
b. 0.3
Step-by-step explanation:
a. if the perimeter is 20 that means that each side would be 5 because its a square and 5 x 5 is 25.
b. 0.3 to the third power is 0.027
write the equation of the line that passes through the point (-2,4) and (5,8). Put your answer in fully reduced point slope form, unless it is a vertical or horizontal line.
Answer:
y-4=4(x+2)/7
Step-by-step explanation:
slope(m) = (8-4)/(5-(-2)) =4/7
b = 4-(4/7)×(-2) = 36/7
y = mx+b
y = 4x/7+36/7
in point-slope form,
y-4=4(x+2)/7
