The unshaded area inside the figure to the right is 648 in.² Use this fact to write an equation involving x. Then solve the equation to find the value of x.
Length of rectangle is 40 inches
Width of rectangle is 22 inches
Border inside rectangle is x
Answers
The second order polynomial that involves the variable x (border inside the rectangle) and associated to the unshaded area is x² - 62 · x + 232 = 0.
How to derive an expression for the area of an unshaded region of a rectangle
The area of a rectangle (A), in square inches, is equal to the product of its width (w), in inches, and its height (h), in inches. According to the figure, we have two proportional rectangles and we need to derive an expression that describes the value of the unshaded area.
If we know that A = 648 in², w = 22 - x and h = 40 - x, then the expression is derived below:
A = w · h
(22 - x) · (40 - x) = 648
40 · (22 - x) - x · (22 - x) = 648
880 - 40 · x - 22 · x + x² = 648
x² - 62 · x + 232 = 0
The second order polynomial that involves the variable x (border inside the rectangle) and associated to the unshaded area is x² - 62 · x + 232 = 0. [tex]\blacksquare[/tex]
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Related Questions
If a box of anything is £5. 50 for 1kg, what would 320g cost?
Answers
Answer:
Your answer is £1,760
Step-by-step explanation:
1 kg = £5.50
5.50 x 320 = 1,760
a construction crew is lengthening a road
Answers
Answer:
Step-by-step explanation:
possible answers for both domain and range can be the following:
all set of all real numbers from 0 to 90;
all set of all real numbers from 200 to 560;
all set of all real numbers from 4 to 200;
(90, 91, 92, 93, ..... 560) ;
90, 91, 92, 93, .......; or
0, 1, 2, 3, .... 200
Please help I will give
BRAINLY
5 STARS
and a THANKS
Answers
Answer:
19, 39
Step-by-step explanation:
10 colums w/ 2 rows = 20 with 1 non blue = 19 blue blocks
20 columns w/ 2 rows = 40 with 1 non blue = 39 blue blocks
log4(2-x)=log4(-5x-18)
Answers
[tex]\log_4 (2-x) = \log_4 (-5x-18)\\\\\implies 2-x = -5x -18\\\\\implies 5x -x = -18-2\\\\\implies 4x = -20\\\\\implies x = -\dfrac {20}4\\\\\implies x = -5[/tex]
You and your friend are using ribbon to make cards. Your ribbon is 78 inch wide. Your friend's ribbon is 58 inch wide. How much wider is the ribbon you are using?
Answers
Answer:
20 inches longer
Step-by-step explanation:
78-58= 20
Rebekah finds that a solution of sugar in water has a volume of 1.32 fl. oz. how should she report this amount using the metric system? (1 fl. oz. = 29.6 ml) 0.403 m 1.40 qt 37.5 g 39.1 ml
Answers
Rebekah reports the volume of sugar solution using metric system as 39.1 mL. Thus, option D is correct.
What is metric system?The metric system has been the measurement system introduced in 1790s. The system has mediated the units for the measurement of volume, mass, length.
The volume has been the space that has been occupied by matter. The volume can be denoted with SI unit L. However, the another accepted unit for volume has been mL.
Thus, the volume of sugar solution has been reported in mL.
The given sugar solution has volume of 1.32 fl. Oz
The volume in mL can be given as:
[tex]\rm 1\ fl\ oz=29.6\ ML\\\\1.32\ fl\ oz=-1.32\times 29.6\ ML\\\\1.32\ fl\ oz=39.1\ ML[/tex]
The volume of the sugar solution reported by Rebekah on the metric scale has been 39.1 mL. Thus, option D is correct.
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Answer: 39.1 mL (D)
Step-by-step explanation:
ed
Help me pls I don't understand this pls help me! :I
350in^3 x 1 gal/231in^3
Answers
Answer:
3 1/16 galones = 707 pulgadas cúbicas
Step-by-step explanation:
Fórmula: multiplica el valor en gal por 231
Luego, 3 1/16 gal × 231 = 707 in³
don't spam!! complete answe= Brainliest answer
Answers
Answer:
Step-by-step explanation:
1) [tex]\sf v_{f} =v_{i} +gt[/tex]
= 50 + (-9*8) *1
= 50 - 9.8
= 40.2 m/s
2) The acceleration of the ball at its maximum height equals to the force of gravity. -9.8 m/s²
3) The velocity at its top of the path:When the ball is thrown straight up, its velocity keeps on decreasing due the pull of gravity which pulls it towards the ground. So, the velocity at the top of its path is zero.
The freight charge on a shipment of 1200 kg is $84. 0.
Which is the rate per 100 kg?
A $0. 78
B. $4. 00
C. $5. 70
D. $7. 00
E $10. 8
Answers
te in short form: 4 hundreds + one ten + 7 ones = 7 hundreds + 2 ones = 9 hundreds + 2 tens + 6 ones =
Answers
Bec
400+10+7+700+2+900+20+6=2045
Costs of Attendance
Category Dollar Amount
Annual Tuition and Fees $9,134.00
Annual Room and Board $3,415.00
Annual Cost of Books and Supplies $1,225.00
Other One-Time Fee $750.00
Annual Scholarship and Grants $10,550.00
Using the information from the table, identify the equation in slope-intercept form that models the total cost of attendance. (1 point)
y = 13,774x + 750
y = 14,524x
y = 3,224x + 750
y = 3,974x
Answers
Answer:
y = 3,224x + 750
Step-by-step explanation:
Assuming the scholarship and grants are applied using the slope intercept form y=mx+b where m is the slope in this case the cost per year attending x the number of years attended and b the y intercept which in this case is the one time fee subtracting 13,774 by 10,550 gives us 3,224.
Since the one time fee is only in place once that would make it the y intercept therefore y=3,224x+750 is the correct answer
9)Which expression is equivalent to 3(2x + 5), no matter what value is substituted in for x?
A) 5x + 8
B) 5x + 5
06x+5
D) 6x + 15
Answers
Answer:
D) 6x+15 is the correct answer.
Step-by-step explanation:
You need to do distributive property to simplify the expression.
3(2x+5) is your expression
You need to multiply 3 by 2x and 5
6x+15 is your final.
Therefore, D is the correct answer.
while on vacation Ernesto travelled from us to Europe when he got there he converted his american dollar to euros he gave the bank teller 850$and was given back 630 euros at the end of vacation Ernesto has 150 euros to convert back to dollar how much money in us dollar did Ernesto have when he got home
Answers
Answer:
I think it would be 161.9 or 162
Michael solved this inequality as shown:
Step 1: -6(x + 3) + 10 < -2
Step 2: -6x − 18 + 10 < -2
Step 3: -6x − 8 < -2
Step 4: -6x < 6
Step 5: x > -1
What property justifies the work shown between step 3 and step 4?
A.
transitive property
B.
division property of inequality
C.
distribution property
D.
addition property of inequality
Answers
Answer:
D. addition property
Step-by-step explanation:
at step 3 you would have to add 8 to both sides of the inequality, so it would be the addition property
Answer:
D
Step-by-step explanation:
Solve for h. -18 + h = 28
h=10
Answers
Answer:
h = 46
Step-by-step explanation:
Have unknowns (h) on one side and knowns on other side.
-18 + h = 28 Add 18 on both side to move it to the right side.
h = 28 + 18
h = 46
Answer:
[tex]\boxed{\sf{h=46}}[/tex]Step-by-step explanation:
Isolate the term of h from one side of the equation.
-18+h=28First, switch sides.
⇒ h-18=28
Add by 18 from both sides.
⇒ h-18+18=28+18
Solve.
Add the numbers from left to right.
⇒ 28+18=46
⇒ h=46
Therefore, the correct answer is h=46.I hope this helps! Let me know if you have any questions.
Susan mixes red and blue paint to make purple.
Red
2 parts of red paint with 3 parts of blue paint make purple.
Susan has 50 ml of red and 100 ml of blue.
What is the maximum amount of purple she can make?
Answers
Answer:
125 mL
Step-by-step explanation:
Susan's purple paint has the proportions 2 parts red and 3 parts blue. That means the total amount of paint is (2+3)/2 = 5/2 the amount of red paint, or (2+3)/3 = 5/3 the amount of blue paint.
__
The total amount of paint Susan has is 50 mL +100 mL = 150 mL.
If Susan uses all of her red paint (with sufficient blue paint), she would have an amount of purple paint equal to ...
(5/2)(50 mL) = 125 mL . . . . purple paint
If Susan uses all of her blue paint (with sufficient red paint), she would have an amount of purple paint equal to ...
(5/3)(100 mL) = 166 2/3 mL . . . . purple paint
This is more paint than Susan has, so the amount of purple paint Susan can make is limited by the amount of red paint she has. Susan can make a maximum of 125 mL of purple paint.
_____
Additional comment
Essentially, we have rewritten the proportion to show corresponding amounts of red and blue paint:
red : blue = 2 : 3 = 50 : 75 = 66 2/3 : 100
Since Susan has only 50 mL of red, and more than 75 mL of blue, the red paint is the limiting ingredient.
Please help me it's very important that this gets done asap
Answers
Answer:
√32 or 4√2 or 5.657 (3 d.p.)
Step-by-step explanation:
Use Pythagoras’ Theoremd² + 7² = 9²Evaluate the known squaresd² + 49 = 81Subtract 49 from both sides to make d² the subjectd² = 81 - 49 = 32d = √32 = 4√2 = 5.657 (3 d.p.)
Two-step inequalities
Find the solution set of the inequality
4.2 - 1< 11.
Answers
Answer:
x < 3
Step-by-step explanation:
Your inequality: 4x - 1 < 11
4x - 1 < 11
Add 1 to both sides
4x < 11 + 1
4x < 12
**Don't switch signs because no negatives nor any specifications**
Divide 12 by 4
x < 3
Which transformation or sequence of transformations would produce an image that is not congruent to its pre‐image?
A translation of (x − 2, y + 9)
A translation followed by a rotation
A rotation of 270 degrees about the origin
A dilation followed by a translation
Answers
Answer:
A dilation followed by a translationStep-by-step explanation:
A dilation would change the size of the figureHence, on changing it, the transformation will form an image that is not congruent to its pre-imageThe transformation or sequence of transformations that would produce an image that is not congruent to its pre-image is:
A dilation followed by a translation.
If we follow a dilation with a translation, the image will be both resized and shifted. The combination of these transformations will result in an image that is not congruent to its pre-image.
On the other hand:
A translation of (x − 2, y + 9) will shift the object without changing its size or shape. The resulting image will be congruent to the pre-image.
A translation followed by a rotation can result in a congruent image if the rotation angle and translation distance are appropriately chosen. It depends on the specific values used in the transformation.
A rotation of 270 degrees about the origin will preserve the shape and size of the object. The resulting image will be congruent to the pre-image.
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PLS PLS PLS PLS HELP WITH THIS MATH
Answers
Answer:
Step-by-step explanation:
Sequence 1 Sequence 2 Ordered Pair
9 5 (9,5)
11 8 (11,8)
13 11 (13,11)
15 18 (15,18)
17 20 (17,20)
hey guys is this correct?
Answers
Answer
Yes it’s correct because are all the same
Calculate the perimeter of the shape below
Answers
Answer:
21.2
Step-by-step explanation:
4.1 + 6.5 = 10.6
10.6 x 2 = 21.2
Mrs. G bought 6 boxes of Girl Scout Cookies. 3 boxes had 16 cookies each and 2 boxes has 12 cookies each. If the total number of cookies in all 6 boxes is 102. how many cookies are in the last box? Write an equation to solve.
Answers
ignore the scribble but could somebody please help me?
Answers
Answer:
Below in bold.
Step-by-step explanation:
To get a stratified sample you work out the proportion of girls from each school.
From school A we take: (126/461) * 80 = 22 girls.
From B :- (82/461) * 80 = 14 girls.
From C :- (201/461)*80 = 35 girls
From CD :- (52/461)*80 = 9 girls.
customer pays
$
96
for
6
pillows. If each pillow costs the same amount, what is the cost per pillow, in dollars?
Answers
Answer:
96 / 6 = 32 / 2 = 16 / 1 = 16 per pillow
Step-by-step explanation:
Answer:
$16
Step-by-step explanation:
To find the cost of a single pillow, you have to divide the total cost of the pillows ($96) by the number of pillows purchased (6).
96 / 6 = 16
Therefore, the cost per pillow, in dollars, is $16. I hope this helps! Have a lovely day!! :)
PLEASEEE HELPPP 30 POINTSSS!!!
Professor Plum is putting a brick border around his irregular shaped garden. Before installing
the border, Professor Plum must cut the bricks to fit the angles of the garden. Use the given
measures to answer the question.
∡ = (6)°
∡ = (3 + 45)°
∡ = (7)°
∡ = (4 + 2)°
∡ = (2 + 15)°
∡ = ( − 9)°
What are the angle measures of each vertex of the garden? Show your work.
Answers
Answer:
174; 132; 203; 118; 73; 20°.
Step-by-step explanation:
1) the sum of the internal angles of the given figure is:
S=180*(n-2), where 'n' is number of the angles.
2) according to the rule above the sum of all the internal angles is 720°;
3) according to the item 2, m∠A+m∠B+m∠C+m∠D+m∠E+m∠F=720°. If all the angles are known, then it is possible to re-write this equation as:
6x+(3x+45)+7x+(4x+2)+(2x+15)+(x-9)=720;
23x=667; ⇔ x=29.
4) if x=29, then m∠A=174; m∠B=132; m∠C=203; m∠D=118; m∠E=73; m∠F=20°.
Please help I am confused:)
Answers
Step-by-step explanation:
#CARRY ON LEARN
PA BRAINLIEST PO
i don’t get it because my teacher
Answers
because your teacher doesn't teach you well??!
hope it helps...!!!
A circle's radius is 8 inches.
What is the circle's circumference (use 3.14 for pi and round to the
nearest tenth)?
PLS HELP!!!! No links pls and ty <3
Answers
The circumference of a circle with radius 8 inches is 50.2 inches
How to find the Circumference of a circle?The circumference of a circle can be calculated as follows;
circumference of a circle = 2πr
where
r = radiusTherefore,
circumference of a circle = 2 × 3.14 × 8
circumference of a circle = 16 × 3.14
circumference of a circle = 50.24 inches
circumference of a circle = 50.2 inches
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In circle k(O),
AC is a diameter,
AB is a chord, and
MA is tangent to the circle. Angle ∠MAB is acute. Prove that m∠MAB=m∠ACB
Answers
The circle and the lines AC & AB are illustrations of congruent angles
See below for the proof that the angles ∠ACB and ∠MAB are equal
How to prove that ∠MAB=∠ACBTo prove that ∠MAB=∠ACB, we make use of the attached diagram
From the attached diagram, we have:
∠MAB = x°
The angle at between a tangent and a radius or a diameter is a right angle.
This means that:
∠MAB + ∠BAC = 90°
Substitute ∠MAB = x°
x° + ∠BAC = 90°
Subtract x from both sides
∠BAC = 90° - x°
The angle at in a semicircle is a right angle.
This means that:
∠CBA = 90°
The angles in a triangle add up to 180°.
So, we have:
∠BAC + ∠CBA + ∠ACB = 180°
Substitute ∠CBA = 90° and ∠BAC = 90° - x°
90° - x° + 90° + ∠ACB = 180°
Evaluate the like terms
180° - x° + ∠ACB = 180°
Subtract 180° from both sides
- x° + ∠ACB = 0
Add x° to both sides
∠ACB = x°
Recall that:
∠MAB = x°
So, we have:
∠ACB = ∠MAB = x°
Hence, the angles ∠ACB and ∠MAB are equal
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