Given:
A rectangle has a length 5 meters more than five times the width.
The area of the rectangle is less than 100 meters squared.
To find:
The expression or inequality that represents all possible widths of the rectangle.
Solution:
Let x be the width of the rectangle.
Length of the rectangle is 5 meters more than five times the width.
[tex]length=5x+5[/tex]
Area of rectangle is
[tex]Area=length \times width[/tex]
[tex]Area=(5x+5) \times x[/tex]
[tex]Area=5x^2+5x[/tex]
The area of the rectangle is less than 100 meters squared.
[tex]5x^2+5x<100[/tex]
[tex]5x^2+5x-100<0[/tex]
Divide both sides by 5.
[tex]x^2+x-20<0[/tex]
[tex]x^2+5x-4x-20<0[/tex]
[tex]x(x+5)-4(x+5)<0[/tex]
[tex](x+5)(x-4)<0[/tex]
It is true if one factor is negative and other is positive. So,
[tex]x-4<0\Rightarrow x<4[/tex] ...(i)
[tex]x+5>0\Rightarrow x>-5[/tex] ...(ii)
Using (i) and (ii), we get
[tex]-5<x<4[/tex]
Therefore, the required expression or inequality for possible
widths of the rectangle is [tex]-5<x<4[/tex].
(-4x + 5)-( 6x +7)=0
Answer:
x = -1/5
Step-by-step explanation:
*Steps as a proof*
_________
(-4x + 5)-(6x + 7) = 0
[given]
_____________
1(-4x + 5)-1(6x + 7) = 0 [identity property of multiplication]
1(-4x + 5) + -1(6x + 7) = 0. [additive inverse property]
___________________________________
1(-4x + 5) + -1(6x) + -1(7) = 0 [distributive property]
___________________________________
(-4x + 5) + (-6x - 7) = 0 [multiplying anything by 1 is the same]
___________________________________
(-4x + -6x) + (5 + -7) = 0 [associative property of addition]
_____________________________________
-4x + -6x + (5 + -7) = 0 [subtraction property of equality] - (5 + -7). - (5 + -7)
_______________________
-4x + -6x = -(5 + -7) [simplification]
-4x + 6x = -1(5 + -7) [identity property of multiplication]
-4x + -6x = -1(5) + -1(-7) [distributive property]
-4x + -6x = -5 + 7 [simplification]
-4x + -6x = 2 [simplification]
-10x = 2 [division property of equality]
÷10 ÷10
______
-x = 2/10 [negative one property of multiplication]
×-1 ×-1
x = -2/10 [simplification]
x = -1/5 [simplification]
__________________________
I need help with number 8
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The square roots are approximately ...
√5 ≈ 2.23
√17 ≈ 4.12
√56 ≈ 7.48
√88 ≈ 9.38
√118 ≈ 10.86
These are plotted below.
The scale on a map js 1cm : 6.6 km the distance between two cities on the map is 18cm what is the actual distance between the two cities
Answer:
118.8 kmStep-by-step explanation:
Given
The scale 1 cm : 6.6 kmTo find
18 cmSolution
1 cm ⇔ 6.6 km1*18 cm ⇔ 6.6*18 km 18 cm ⇔ 118.8 kmThe larger of two numbers is one more than four times the smaller number . If the sum of the numbers is 61, find the numbers.
Step-by-step explanation:
Let the smaller number be x.
So, according to Question,
the larger number will be 1+4x.
Now, sum of the numbers is 61, like this:-
[tex]1 + 4x + x = 61[/tex]
[tex]5x = 61 - 1[/tex]
[tex]5x = 60[/tex]
[tex]\tt{x = \dfrac{60}{5}}[/tex]
[tex]\boxed{\tt{x = 12}}[/tex] is the required Answer.
Hope it helps :)
If leah has 22 boxes she gives 12 boxes to her mom how many boxes does leah have left
Subtract the amount she gives her mom from the total amount she has:
22 - 12 = 10
She has 10 boxes left.
The keyboard on a particular computer has a rectangular shape where the length is 332 mm and the width is 141 mm. Find the perimeter of the rectangle defined by this keyboard.
Answer:
946 mm
Step-by-step explanation:
(332*2)+(141*2)
What is the area of the triangle below?
Answer:The area of the triangle is given by the formula mentioned below: Area of a Triangle = A = ½ (b × h) square units where b and h are the base and height of the triangle, respectively. Now, let’s see how to calculate the area of a triangle using the given formula.
Step-by-step explanation:
Solve and graph 8(p+3)>2(4p-1)
4 + 3 (3 × 2)² - 1
how do I set up the account?
Answer:
4+(9*6)^2-1
Step-by-step explanation:
Olivia buys 4 masks that each cost the same amount
and a scarecrow, all for $176.75. If the scarecrow
costs $56.75, find out the cost of each mask cost.
Find the missing factor.
80 X
640.000
Given the function f(x) = 3x-7, which of the following represents f -1(x)?
-3x+7
Step-by-step explanation:
The entire function f is being multiplied by -1, -1 isn't being plugged in for x in this case.
f -1(x)= -1(3x-7)
f -1(x)= -3x+7
Henry wants to buy the same number of gift bags and bows. Gift bags are sold in packs of 6. Bows are sold in packs of 9. What is the least number of gift bags and bows that George can buy?
Answer:
Henry will buy 18 gift bags and 18 bows in 3 packs of gift bags and 2 packs of bows.
Step-by-step explanation:
Least Common Multiple (LCM)
Is the smallest positive number that is a multiple of two or more numbers. To find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number.
Since Henry wants to buy the same number of gift bags and bows and they are sold in packs with different quantities, we must find the LCM between those numbers.
Gift bags are sold in packs of 6. Bows are sold in packs of 9.
List the prime factors of 6: 2,3
List the prime factors of 9: 3,3
Multiply: 2*3*3=18
The LCM is 18. This means Henry will buy 18 gift bags and 18 bows in 3 packs of gift bags and 2 packs of bows.
Write an explicit rule to represent the sequence:
20, 24, 28, 32, 36,...
Answer:
add 4
Step-by-step explanation:
Percentages
Your favorite store is having a sale. You run across a shirt that originally sold for $47, but
is on a -40% Off" rack. A pair of jeans that originally
sold for $60 is advertised for "30%
Off". Your eye is attracted to a pair of designer shoes on sale for $35. You decide to
purchase the shirt, jeans, and shoes.
1) What is the sale price of the shirt?
What is the sale price of
the jeans?
2) What is the subtotal of the shirt, jeans, and the shoes?
3) You discover a coupon for 25% off the purchase price and give it to the cashier. With
the 25% off coupon what is the pre-tax cost of your purchase?
4) If the sales tax on your purchase is 5%, what is the total amount you are charged?
5) Your credit card has a monthly interest rate of 2% and a minimum payment of $10. You
make the minimum payment every month. Fill in the chart below until you pay off your
purchase.
Payment
Balance
$10.00
New Balance
Interest
Remaining
Balance
Month
1
2
3
4
5
6
7
8
9
10
Answer:
1) Shirt = $28.20 Jeans = $42
2) subtotal = $105.20
3) with the discount from the coupon, the pre-tax cost is $83.90
4) about $ 88.10 (actual answer was $88.095)
5) i have no clue bro, im sorry
Step-by-step explanation:
The sale price of the shirt is [tex]\$28.20[/tex] The sale price of the jeans [tex]\$42.00[/tex] Subtotal is [tex]\$[/tex]105.20 Pre-tax cost [tex]\$78.90[/tex] The total amount charged with 5% sales tax is [tex]\$42.00[/tex]
The sale price of the shirt:
Given -The original price of the shirt is $47, and it is on a "40% Off" sale. To find the sale price, we can calculate [tex]40\% of \$47[/tex]and subtract it from the original price:
The sale price of the shirt = [tex]\$47 - (40\% \times\$47)[/tex]
The sale price of the shirt =[tex]\$47 - (\$18.80)[/tex]
The sale price of the shirt =[tex]\$28.20[/tex]
The sale price of the jeans:
Given =The original price of the jeans is $60, and it is advertised as "30% Off." Similar to the shirt, we can calculate the sale price of the jeans:
The sale price of the jeans =[tex]\$60 - (30\% \times\$60)[/tex]
The sale price of the jeans =[tex]\$60 - (\$18.00)[/tex]
The sale price of the jeans = [tex]\$42.00[/tex]
Subtotal of the shirt, jeans, and shoes:
Subtotal = Sale price of the shirt + Sale price of the jeans + Sale price of the shoes
Subtotal = [tex]\$[/tex]28.20 + [tex]\$[/tex]42.00 +[tex]\$[/tex]35.00
Subtotal =[tex]\$[/tex]105.20
The pre-tax cost of your purchase with the[tex]25\%[/tex] off coupon:
The 25% off coupon is applied to the subtotal. We calculate 25% of the subtotal and subtract it from the subtotal to find the pre-tax cost:
Pre-tax cost = Subtotal -[tex](25\% \times Subtotal)[/tex]
Pre-tax cost = [tex]\$105.20 - (25\% \times \$105.20)\\[/tex]
Pre-tax cost =[tex]\$105.20 - (\$26.30)[/tex]
Pre-tax cost = [tex]\$78.90[/tex]
The total amount charged with 5% sales tax:
To calculate the total amount charged, we need to add the sales tax to the pre-tax cost:
Sales tax = [tex]5\% \times Pre-tax cost[/tex]
The Total amount charged = Pre-tax cost + Sales tax
The Total amount charged =[tex]\$78.90 + (5\% \times \$78.90)[/tex]
The total amount charged = [tex]\$78.90 + \$3.94[/tex]
The total amount charged =[tex]\$82.84[/tex]
The credit card payments for months are;
Payment | Balance | New Balance | Interest | Remaining Balance
Month 1 | $10.00 | $72.84 | $1.46 | $71.46
Month 2 | $10.00 | $61.46 | $1.23 | $60.69
Month 3 | $10.00 | $50.69 | $1.01 | $49.70
Month 4 | $10.00 | $39.70 | $0.79 | $38.49
Month 5 | $10.00 | $28.49 | $0.57 | $27.06
Month 6 | $10.00 | $17.06 | $0.34 | $16.40
Month 7 | $10.00 | $6.40 | $0.13 | $6.53
Month 8 | $6.53 | $0.00 | $0.00 | $0.00
The remaining balance is paid off in full by the 8th month, and the interest is calculated based on the remaining balance each month.
Learn more about sales tax here :
https://brainly.com/question/29442509
#SPJ2
The linear function that is represented by which table has the same slope as the graph?
Answer:
c
Step-by-step explanation:
Answer: Option C
(C) or Taable 3
Step-by-step explanation:
Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
Please don't use trig
Answer:
Perimeter of ΔABC =32.31 units
Area of the triangle ABC = 47.81 sq. unit
Step-by-step explanation:
In triangle ABC
[tex]\angle A = 60^{\circ}\\\angle C = 45^{\circ}[/tex]
Angle sum property of triangle : The sum of the measures of the all angles of triangle is 180°
[tex]\angle A + \angle B + \angle C = 180^{\circ}\\60 + \angle B + 45 = 180\\\angle B + 105 = 180\\\angle B = 75^{\circ}[/tex]
Now we are supposed to find the perimeter and the area of the ΔABC
We will use the sine rule to find the lengths of sides BC and AC
Sine rule : [tex]\frac{Sin A}{BC}=\frac{Sin B}{AC}=\frac{Sin C}{AB}[/tex]
[tex]\frac{Sin 60}{BC}=\frac{Sin 75}{AC}=\frac{Sin 45}{9}\\BC \times sin(45) = 9 \times sin(60)\\ BC = 11.02[/tex]
[tex]AC \times sin(45) = 9 \times sin(75)[/tex]
AC = 12.29
Perimeter of ΔABC = AB + BC + AC
Perimeter of ΔABC = 9 + 11.02 + 12.29 =32.31 units
Area by using the sine rule:
Area of the triangle ABC =[tex]\frac{1}{2} (AB)(BC) sin B[/tex]
Area of the triangle ABC =[tex]\frac{1}{2} (9)(11) sin(75)[/tex]
Area of the triangle ABC = 47.81 sq. unit
simplify
(x+4)−(x−1)
Answer:
5Step-by-step explanation:
[tex](x+4)−(x−1)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=x+4-\left(x-1\right)\\\\-\left(x-1\right):\quad -x+1\\=x+4-x+1\\\\\mathrm{Simplify}\:x+4-x+1:\\\quad 5\\\\[/tex]
HELPPP I GIVE BRAINLIEST FOR THIS ANSWER PLSSS
Answer:
Yes
Step-by-step explanation:
The lines in question have no degree angle to them. Don't let the line in the middle confuse you!
Hope this helps!
A local pizza restaurant offers a gold card for loyal customers. The gold card costs $25 for a year. With a gold card, each large pizza is a discounted cost of $12. If customers don’t have a gold card, a large pizza costs $18. How many pizzas must you purchase in a year for the gold card to be cheaper?
Answer:
5 pizzas
Step-by-step explanation:
18-12=6 each pizza with card saves 6$
$25 card cost÷$6 savings per pizza=4.16 pizza to break even. round up since cant buy fraction of pizza.
check
5 pizza with card 12 *5=60
60 + 25 = 85 spent in total
$5 *$18 = $90, no discount
4 pizza would be 73 with discount and 72 without
This Question !!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x=800
Step-by-step explanation:
2000=all sides
two sides are 200 &200 =400
the other two are 2000-400=1600
1600/2=800 each
Lines k and l are parallel. When lines k and l are cut by the transversals below, an isosceles triangle is formed. Lines k and l are parallel. Lines s and t intersect lines k and l to form a triangle. At the intersection of lines s, t, and k, clockwise from top left, the angles are blank, blank, blank, 70 degrees, 1, blank. At the intersection of lines s and l, the angles are blank, x degrees, blank, blank. At the intersection of lines l and t, the angles are x degrees, blank, blank, blank. What is Measure of angle 1? 35 degrees 40 degrees 55 degrees 70 degrees
Answer:
its 48
Step-by-step explanation:
Answer:
it's 40
Step-by-step explenation
dont need one the people have brains
Find the slope containing the two points (2,-1) and (4,-4)
Answer:
-5/2
Step-by-step explanation:
You have to take y2-y1 and divide it by x2-x1
What is the distance between 2 and 3 on the number line? Write the integer only. *
Answer:
1
Step-by-step explanation:
The distance between any two numbers on the number line is their difference:
3 - 2 = 1
_____
Any two consecutive integers have a distance between them of 1 on the number line.
If you can walk 5.3 miles in 3.2 hours, how many minutes does it take to walk 1.74 miles?
Answer:
Let x be the number of hours for 1.74 miles
5.3 miles 3.2 hours
1.74 miles x
When you cross multiply the above numbers you get the equation:
5.3x = 5.568
x = 5.568/5.3
x = 1.05
Therefore it takes 1.05 hours to walk 1.74 miles.
What percent of all children like the Simpsons? Round your answer to the nearest tenth of a percent. Type a numerical answer.
Answer:
0.3
Step-by-step explanation:
You know the total amount of children like simpsons are 90, and the total can be calculated by adding the 100+110+90 to get the total amount of children in all groups. You then can divide 90 by 300 to get the percent.
Hope this helps!
I think that chart is a bit overdue or inaccurate xd
A rotation maps point A(5, 4) to A’(–4, 5).
Which describes the rotation?
180° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
90° clockwise rotation
Answer:
90° counterclockwise rotation
Step-by-step explanation:
I just took the quiz and got it correct,
Hope this helps.
Answer:
answer above is correct
Step-by-step explanation:
Which expression is equivalent to 2(3x-8)?
Answer:
6x-16
Step-by-step explanation:
2(3x-8)
distribute the 2
2 x 3x = 6x
2 x -8 = -16
Seven friends bought pizza. Each friend pitched in the same amount. If the pizza came to a total of $14.49, how much did each friend pay?
Answer: 7p = $14.49
Step-by-step explanation: BRAINLIEST MEEE
SOLVE FOR D
S=D/T
THANK YOU