Answer:
width=4in.
length=13in
Step-by-step explanation:
let the width of the rectangle be x
then the length will be x+9
Area= length×width
52= (x+9)x
52= x²+9x
x²+9x-52=0
x²+13x-4x-52=0
x(x+13) - 4(x+13)= 0
(x-4)(x+13)=0
x=4 or -13
dimension cannot be negative
hence x=4in
the width is 4in. and the length is 4+9=13in.
The solution is, width=4in.
length=13in
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
The area of a rectangle is 52 in^2.
If the length is 9 inches more than the width.
let the width of the rectangle be x
then the length will be x+9
Area= length×width
so, we have,
52= (x+9)x
52= x²+9x
x²+9x-52=0
x²+13x-4x-52=0
x(x+13) - 4(x+13)= 0
(x-4)(x+13)=0
x=4 or -13
dimension cannot be negative
hence x=4in
so, we get,
the width is 4in. and the length is 4+9=13in.
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how do I dilate triangles using scale factors? step by step
Answer:
so first you
Step-by-step explanation:
find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image.
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost
The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
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Which one cuz they are in different order.!!!
Answer:
wot
Step-by-step explanation:
A rug in the classroom is 3/4 yard wide and 8/6 yards long. What is the area of the rug in square yards?
PLEASE BE ANSWERED IN 30 MINS TOPS
Answer:
i think area of the rug is 1 square yards
Step-by-step explanation:
area = 3/4×8/6
area = 2/2
area = 1 square yards
Segment AB and CD intersect at point E, measure of angle ABC =6x+20 and measure of angle DEB=10x. What is the value of x?
Answer:
x = 5
Step-by-step explanation:
6x + 20 = 10x
I hope this helps!
HELPP PLS I NEED THIS WUICK ILL GIVE BRAINLEST
Answer:
x = 20
Step-by-step explanation:
(2x+10) = 180 - 130
2x + 10 = 50
2x= 40
x = 20
hope this helps! :)
On Monday Tiffany spent 5 2/8 hours studying. On Tuesday she spent another 2 1/8 hours studying. What is the combined length of time she spent studying
Answer:
7 3/8 hours
Step-by-step explanation:
5 + 2 = 7
2/8 + 1/8 = 3/8
Therefore, 7 + 3/8 =
7 3/8 hours
the sum of kyras and calebs age is 37. calebs age is equal to twice the quantity of kyras age decreased by 4. let k represent kyras age.
Please help ASAP. Trigonometry
Write TWO different equations that you could use to solve for x. You don't need to solve.
Answer:
cos(52°) = 18/x
x = 18·sec(52°)
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Cos = Adjacent/Hypotenuse
In this geometry, that means ...
cos(52°) = 18/x
You can use the relation sec(x) = 1/cos(x) to rewrite this as ...
x = 18·sec(52°)
_____
You can also use the complementary angle and the complementary trig function.
sin(90° -52°) = 18/x
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the sum of 32 2/9+ 23 4/9
Answer:
The answer is 55 6/9, but when simplified, it is 55 1/3
Which table correctly lists the reasons to prove angle 1 approximately equal to angle 3 comma given that stack A B with left right arrow on top intersects stack C D with left right arrow on top ?
Based on the right application of the reflexive property and subtraction property of equality, the table that correctly lists the reasons to prove that m∠1 ≅ m∠3 is: the table in option B (See attachment below).
The reflexive property of equality states that:
a + b = a + b.
Since m∠1 + m∠2 = 180°, and m∠2 + m∠3 = 180°, therefore, based on the reflexive property, we would have:
m∠1 + m∠2 = m∠2 + m∠3.
Thus, subtracting m∠2 from both sides of the equation will leave us with: m∠1 = m∠3 (subtraction property of equality).
Therefore, based on the right application of the reflexive property and subtraction property of equality, the table that correctly lists the reasons to prove that m∠1 ≅ m∠3 is: the table in option B (See attachment below).Learn more about the reflexive property on:
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For a basic subscription, a cable television provider charges an activation fee of $60, plus $125 per month. What linear function represents the total cost of a basic cable subscription for t months? What is the total cost for two years of service?
Answer:
t=23
Step-by-step explanation:
A town has two shopping malls. A survey conducted on the shopping preferences of the town's residents showed that 62% of the residents visit Comet Mall, 73% of the residents visit Star Mall, and 48% of the residents visit both malls. The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is
Using Venn probabilities, it is found that:
The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is 0.87 = 87%.In this problem, the events are:
Event A: Visits Comet Mall.Evenet B: Visits Star Mall.In this problem:
62% of the residents visit Comet Mall, hence [tex]P(A) = 0.62[/tex].73% of the residents visit Star Mall, hence [tex]P(B) = 0.73[/tex].48% of the residents visit both malls, hence [tex]P(A \cap B) = 0.48[/tex]The probability of either is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Hence:
[tex]P(A \cup B) = 0.62 + 0.73 - 0.48 = 0.87[/tex]
The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is 0.87 = 87%.You can learn more about Venn probabilities at https://brainly.com/question/25698611
Answer:
87%.
Step-by-step explanation:
The probability that a resident chosen at random shops at either Comet Mall or at Star Mall is 87%.
A palm tree is 30 feet tall and casts a 48 foot shadow. The woman standing next to the palm tree casts a shadow similar to that of the palm tree. How tall is the woman if she casts an 8 foot shadow?
Answer:
48 feet foot I took the testttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt oh yeah yeah yeah
Step-by-step explanation:
Can someone answer this no bots please I will give you brainliest… please
Answer: Alice
Step-by-step explanation: Alice won because she started furthest From the starting line.
Does anyone get this??
Answer:
the answer is 12m
Step-by-step explanation:
u know the side c and side B.
C=15m but u have to square it which is 225
B=9m but u have to square it which is 81. then subtract 82 from 225.which will give u 144 which is a perfect square route of 12
Samir bought 6 equally priced pencils for $2.10.
How much will 10 of these pencils cost?
$1.26
$2.63
$2.86
$3.50
Price of 6pencils=2.10
Price of one pencil
[tex]\\ \sf\longmapsto 2.10/6=0.35[/tex]
Price of 10pencils
[tex]\\ \sf\longmapsto 0.35(10)=\$3.5[/tex]
The cost of ten pencils is $3.50.
Given
Samir bought 6 equally priced pencils for $2.10.
Unit rate;A rate is a ratio that is used for comparing two different kinds of quantities which have different units.
The cost of 1 pencil is;
[tex]\rm =\dfrac{2.10}{6}\\\\=0.35[/tex]
Therefore,
The cost of 10 pencils is;
[tex]= 10 \times 0.35\\\\=3.50[/tex]
Hence, the cost of ten pencils is $3.50.
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12.5(20 + 35) - 38(16)
Answer:
79.5
Step-by-step explanation:
20+35=55
38*16=608
12.5*55=687.5
687.5-608=79.5
Hope this helps! Plz give brainliest! Also, pls sub to kgirl633 on yt.
Answer: 79.5
Step-by-step explanation:
HURRRRRYYYYYYYY. I HAVE 5 MINUTES
Answer:
x = - 9/10
workings
2/3 x = - 3/5
multiply by 3/2 on both sides
x = - 9/10
Answer:
2/3x=-3/5
x=-3/5*3/2
x=-8/10
The base of a triangle is v245 cm and its height is V20 cm. Find its area.
The given information of the base length and the height of the
rectangle are sufficient to find the area of the triangle.
Correct response:
The area of the triangle is 35 cm.²Methods used for finding the areaGiven that the parameters are;
The base of the triangle = [tex]\sqrt{245}[/tex] cm
The height of the triangle = [tex]\mathbf{\sqrt{20}}[/tex] cm
Required:
To find the area of the triangle
Solution:
[tex]Area \ of \ a \ triangle = \mathbf{ \dfrac{1}{2} \times base \times height}[/tex]Therefore, the area, A, of the given triangle is given as follows;
[tex]A = \dfrac{1}{2} \times \sqrt{245} \ cm \times \sqrt{20} \ cm= \dfrac{1}{2} \times \sqrt{4,900} \ cm^2= \dfrac{1}{2} \times 70 \ cm^2 = 35 \ cm^2[/tex]
The area of the triangle, A = 35 cm²Learn more about the area of plane shapes here:
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Find sin 90° + cos 360° + tan 0°
Answer:
2
Step-by-step explanation:
sin 90 is 1;
cos 360 is cos 0, or 1; and
tan 0 is 0.
Thus, sin 90° + cos 360° + tan 0° = 1 + 1 + 0 = 2
Over six months, a family's electric bills averaged $55 per month. The bills for
the first five months were $57.60, $60, $53.25, $50.75, and $54.05. What was
the electric bill in the sixth month? Find the median, mode, and range of the
six electric bills.
3y=6
Find the slope of the line described by each equation
The sum of two numbers is 25. One number is twice the seond number plus seven.
What are the two numbers?
Determine the unit rate. Use mental math when you can. 6 golf balls for $15
Answer:
1 golf ball : $2.50
Step-by-step explanation:
You can first divide 6 and 15 by 3, and get 2 and 5.Then, you divide 5 by 2, which is 2.5Therefore, the unit rate is 1 golf ball : $2.50A half circle is joined to an equilateral triangle with side lengths of 12 units.
What is the perimeter of the resulting shape? Type your answer in the box below.
Answer:
P = 12 pi units + 24 units.
Step-by-step explanation:
All sides of an equilateral triangle are of the same length. Here that length is 12 units. We take a circle of diameter 12 units and cut it in half through its center. Finally, we join the triangle (remembering that all of the side lengths are 12 units) to the half circle of diameter 12 units.
The half circle portion of the resulting shape has circumference 2(pi)(12 units) divided by 2, or 12 pi units. This is half the formula C = 2(pi)(r). The two non-attached sides of the triangle have a total length of 24 units.
Thus, the perimeter of the resulting figure is P = 12 pi units + 24 units.
Calculate the area of the triangular region determined by the points D(-4,3) E(-7,-8) F(-2, -3)
Answer:
The area is 27
Step-by-step explanation:
Area =1/2 [x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]
Area =1/2 [2(-6 - 8) + 3(8 - 4) + 7(4 + 6)]
=1/2 [2(-14) + 3(4) + 7(10)]
=1/2 (-28 + 12 + 70)
=1/2 (54)
Area = 27
what is the equation of the line with slope -7 which goes through the point (2,5)
Answer:
y=-7x+19
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-7(x-2)
y=-7x+14+5
y=-7x+19
The equation of the line with slope - 7 which goes through the point (2, 5) is
y = - 7x - 19.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A line passes through points (2, 5) with a slope of - 7.
∴ 5 = -7(2) + b in slope-intercept form.
5 = - 14 + b.
b = - 19.
y = - 7x - 19.
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Help me out please!!!!!!
Step-by-step explanation:
y = 2x + 9
y = -x - 3
there are multiple ways to solve this.
let's follow the approach that both x-expressions must be equal :
2x +9 = -x - 3
3x = -12
x = -4
y = -x - 3 = 4 - 3 = 1
Simplify.
(–28xy) ÷ (–4)
−7xy
17ab
−17ab
7xy
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