Answer:
A. Cait treated the discount as an increase
B. (20) (1.06) (0.85)
Step-by-step explanation:
Hi, Cait treated the discount as an increase.
Cait multiplied the price (20) by the tax percentage (increase) 1.06
Since the sale tax increase is 6% and it is added to the price we have to express it in decimal form (6/100=0.06) and add it to 1.
20 (1 +0.06) = 20 (1.06)
The coupon discount is subtracted to the price. So, the correct form is:
15/100= 0.15
20 (1-0.15) = 20 (0.85)
Instead of this, Cait expressed the percent discount as a percent increase .
20 (1+0.15) = 20 (1.15)
The correct form is (20) (1.06) (0.85)
The edges of the bases of the frustum of a regular square pyramid have length 5 and 9, and the slant height of the frustum is 6. What is the Volume and SA
The volume of the frustum of a regular square pyramid with slant height 6 and square bases of edges 5 and 9 is approximately 284.99 cm³, and the surface area is 274 cm².
To calculate the volume and the surface area (SA) of the frustum of a regular square pyramid with a slant height of 6 and bases with edges of length 5 and 9, we use the following formulas:
Volume (V) of a frustum = (h/3) * (A1 + A2 + √(A1 * A2)), where h is the perpendicular height, A1 and A2 are the areas of the two bases.Surface area (SA) of a frustum = sum of the areas of the two bases + the lateral surface area. The lateral surface area = (perimeter of base 1 + perimeter of base 2) * slant height / 2.First, we need to find the perpendicular height (h) using Pythagorean theorem as the slant height is given.
For base edges of 5 (small square base) and 9 (large square base), the areas are:
A1 = 5² = 25 cm²A2 = 9² = 81 cm²The perimeters are:
P1 = 4 * 5 = 20 cmP2 = 4 * 9 = 36 cmThe lateral surface area (LSA) = (P1 + P2) * 6 / 2 = (20 + 36) * 6 / 2 = 168 cm².
Assuming that the slant height is consistent across the frustum, we find 'h' using the Pythagorean theorem:
Let's denote the difference in the side lengths of the squares as 'd'. Therefore, d = (9 - 5) / 2 = 2.
h² + d² = slant height², so h² = 6² - 2² = 36 - 4 = 32 and h = √32.
Now, we use the volume formula:
V = (√32 / 3) * (25 + 81 + √(25 * 81)) = (5.657 / 3) * (106 + 45) = 5.657 * 50.333 = 284.99 cm³, approximately.
For the surface area:
SA = A1 + A2 + LSA = 25 + 81 + 168 = 274 cm².
Connor is five years older than Charlie. If the product of their ages is 14, find Connors age and Charlie’s age
What is the area of the shaded region?
Answer:1cm?
Step-by-step explanation:
Answer:
8.86 square cm
Step-by-step explanation:
Area of shaded region = Area of rectangle - Area of circle
[tex] = 3 \times 4 - \pi {r}^{2} \\ = 12 - 3.14 \times {1}^{2} \\ = 12 - 3.14 \\ = 8.86 \: {cm}^{2} [/tex]
Which equation represents a line that has a slope of -5 and an X- intercept of 7?
Answer:
y=-5x+35
Step-by-step explanation:
Use the formula y = mx + b
m = slope, so plug in -5 as the slope
To find x-intercept we set y=0
We want the x-intercept to be 7 so we can plug that into the equation too
0=-5(7)+b
Lastly solve for b and you get your answer
The correct option is b.
The equation of the line with a slope of -5 and an x-intercept of 7 is y = -5x + 35.
Explanation:The equation that represents a line with a slope of -5 and an x-intercept of 7 is y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is -5 and the x-intercept is 7, we can substitute these values into the equation to get y = -5x + b.
To find the value of b, we can substitute the x-intercept (7) and y-intercept (0) into the equation and solve for b. Plugging these values in, we get 0 = -5(7) + b. Solving for b gives us b = 35.
Therefore, the equation of the line is y = -5x + 35.
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The complete question is given below:
Which equation represents a line that has a slope of -5 and an X- intercept of 7?
a. y = 5x + 35
b. y = -5x + 35
c. y = -5x - 35
d. y = 35x -5
What is the value of x?
Answer:
Step-by-step explanation:
since we can see that the lines are parallel
and we can see that the both are interior angles and when we sum up both angles we get 180
2x - 5 + 45 = 180
2x + 40 =180
2x = 180 - 40
2x =140
x = 140/2
x = 70
For the first 3% of Brenda's salary, her employer matches 100% of her 401(k)
contributions, and from 3% to 12%, Brenda's employer matches 50% of her
401(k) contributions. Brenda's salary is $50,000, and last year, she
contributed $6000 to her 401(k) plan. What was her employer's contribution
to the 401(k)?
A. $3000
O
O
O
B. $4500
C. $3750
O
D. $6000
Answer:$3750
Step-by-step explanation:
Answer:
3650
Step-by-step explanation:
apex
The bacteria took 1 hour and 40 minutes to fill the initial
bottle. Explain how it only took 10 minutes to fill 3
additional empty bottles.
Answer: if i can be brainliest that would be great
Bacteria growth occurs exponentially; bacteria divides into 2 every t minutes (similar to the penny doubling every day story). If one gets filled, and the contents divides once, there will be enough for 2 bottles; when these two are ready to divide, there will be enough for 4. This growth process begins very slowly - 1, 2, 4, 8, 16, 32; but it soon speeds up greatly, 64, 128, 256, 512, 1024, 2048.
Answer:
The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.
Step-by-step explanation:
admission to the fair is $5.25 for adults and $3.75 for children. A group spends $29.25 for admission. How many of each kind of ticket did they buy?
Answer:
Two adults and five children
Step-by-step explanation:
(3.75×5)+(5.25×2) = 29.25
18.75 + 10.5 = 29.25
(:
What is the product of the 2 solutions of the
equation x^2 + 4x - 21 = 0?
72 +41 – 21 = 0?
Answer:
-21.
Step-by-step explanation:
x^2 + 4x - 21 = 0
To factor this we need 2 numbers whose sum id + 4 and whose produce is -21.
These are - 3 and + 7 , so the factors are:
(x - 3)(x + & = 0
x = 3, -7.
Final answer:
The product of the solutions for the quadratic equation x² + 4x - 21 = 0 is -21, as per Vieta's formulas, which states that the product is c/a.
Explanation:
The question is asking for the product of the solutions of a quadratic equation, specifically x² + 4x - 21 = 0. In the context of the quadratic formula, a = 1, b = 4, and c = -21. The quadratic formula is given by x = [-b ± √(b² - 4ac)] / (2a). However, to find the product of the roots, we can apply Vieta's formulas, which states that the product of the roots of a quadratic ax² + bx + c = 0 is c/a.
For the equation in question, the product of the roots would be c/a = (-21)/1 = -21. This is a straightforward application of a standard property of quadratic equations. Therefore, we don't need to find the individual roots to answer the question about their product, saving time and effort.
Subtract:
–57 – 19 –16
Question 13 options:
A)
–76
B)
–35
C)
–73
D)
–92
Answer:
it's answer is D -92
As -57-19-16= -92
Answer:
D)
–92
Step-by-step explanation:
–57 – 19 – 16 =
= - (57 + 19 + 16)
= - (+ 92)
= - 92
Natalie budgets $146 for yoga training. She buys a yoga mat for $10 and pays $9 per yoga class. Which inequality represents the number of classes, c, that Natalie can take and stay within her budget?
A. 146 ≤ 9c + 10
B. 146 ≥ 9c + 10
C. 146 ≤ 10c + 9
D. 146 ≥ 10c + 9
if i can get brainliest that would be great
Answer: The answer is B. Because she can't go over 146. $10 is a one time fee and she pays $9 per classes.
Answer:
a
Step-by-step explanation:
you must subtract ten from each side to get 136 is less than or equal to 9c then divide by nine to get c=15.111111
which number does not belong? 36, 99, 9, 123
The number 123 because it is the only number that is not divisible by 9.
What are digits?In a positional numeral system, a numerical digit is a single sign that can be used singly or in combination to represent numbers.
A digit is a part of a set that, when combined, makes up a numeration system.
For example 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits.
Given the digits,
36, 99, 9, 123
If we divide by 9 then
36/9 ⇒ remainder 0
99-9⇒ remainder 0
9 ⇒ remainder 0
But
123/9 ⇒ remainder 6
Hence "The number 123 because it is the only number that is not divisible by 9".
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Factor the following polynomial: 11x^2 + 22x
Factor completely please
Answer:
Step-by-step explanation:
hello :
1-x² = (1-x)(1+x) by identity : a²-b²=(a-b)(a+b)
HELP! Is it A,B,C,or D. i really need help
Choose Yes or No to tell whether the expression represents a 20% discount off the price of an item that originally cost d dollars.
0.8d
d – 0.2
d – 0.2d
1 – 0.2d
The correct expression that represents a 20% discount off the original price d is 0.8d or d – 0.2d. The other options do not correctly represent a percentage discount from the original price.
Explanation:The expression that represents a 20% discount off the price of an item that originally cost d dollars would be calculated by first determining what 20% of the original price is, and then subtracting that value from the original price. So if the original price is d, then 20% of d is 0.2d. Subtracting that from d would give us the discounted price. Therefore, the correct expression that represents a 20% discount would be d – 0.2d, which simplifies to 0.8d.
d – 0.2 is not a percentage of d, but rather a fixed amount subtracted from d, and 1 – 0.2d is not meaningful in the context of pricing and discounts. So the expressions that represent a 20% discount off the price are:
Yes: 0.8dNo: d – 0.2Yes: d – 0.2dNo: 1 – 0.2dThe correct answers are the expressions: 0.8d and d – 0.2d.
Find the area of these composite shapes
Answer:
37.5 cm 2
Step-by-step explanation:
The area of the first figure, the rectangle is 30cm2. The base which is 5cm, times the height which is 6cm equals 30cm2. The triangle's area is 7.5cm2 because the height which is 3cm times the base which is 5cm equals 15cm. Because it's a triangle tho, we have to find half of it which 7.5cm2. 30cm2+7.5cm2 equals 37.5cm2.
can anyone help with the statements and reasons have been on this for a while :/
Answer:
statement: 2. both pairs of parallel lines are congruent
reason: 2. def. of a parallelogram
and that should be all you need
Solve the quadratic equation for x. What is one of the roots? 5x2 − 45 = 0
Answer:
x = ± 3
Step-by-step explanation:
Given
5x² - 45 = 0 ( divide through by 5 )
x² - 9 = 0 ( add 9 to both sides )
x² = 9 ( take the square root of both sides )
x = ± [tex]\sqrt{9}[/tex] = ± 3
Thus the roots are x = - 3, x = 3
Final answer:
To solve the quadratic equation 5x^2 - 45 = 0, we rearrange it to x^2 - 9 = 0 and find that the roots are x = 3 and x = -3.
Explanation:
To solve the quadratic equation 5x2 − 45 = 0, we first need to rearrange it to the standard form ax2 + bx + c = 0. In this case, the equation is already in the standard form with a=5, b=0, and c=-45. The next step is to isolate the x2 term by dividing the entire equation by 5, which gives us x2 − 9 = 0. This simplifies to (x - 3)(x + 3) = 0 due to the difference of squares. Thus, the two roots are x = 3 and x = -3.
Simplify and solve for x. 5(x+20)= 7x+30
Answer:
x = 35
Step-by-step explanation:
Solve for x:
5 (x + 20) = 7 x + 30
Expand out terms of the left hand side:
5 x + 100 = 7 x + 30
Subtract 7 x from both sides:
(5 x - 7 x) + 100 = (7 x - 7 x) + 30
5 x - 7 x = -2 x:
-2 x + 100 = (7 x - 7 x) + 30
7 x - 7 x = 0:
100 - 2 x = 30
Subtract 100 from both sides:
(100 - 100) - 2 x = 30 - 100
100 - 100 = 0:
-2 x = 30 - 100
30 - 100 = -70:
-2 x = -70
Divide both sides of -2 x = -70 by -2:
(-2 x)/(-2) = (-70)/(-2)
(-2)/(-2) = 1:
x = (-70)/(-2)
The gcd of -70 and -2 is -2, so (-70)/(-2) = (-2×35)/(-2×1) = (-2)/(-2)×35 = 35:
Answer: x = 35
Answer:
x = 35
Step-by-step explanation:
5(x+20)= 7x+30
5x + 100 = 7x + 30
-30 -30
5x + 70 = 7x
-5x -5x
70 = 2x
/2 /2
35 = x
Some help please?
What are the factors of the product represented below?
Answer:
A. (x+4) (2x+3)
Step-by-step explanation:
Plot the two decimals on the number line below 0.43, 0.39. Write an inequality comparing the two decimals. Explain your answer using the number line
Answer:
See the image below.
Step-by-step explanation:
The decimals 0.43 and 0.39 are equivalent to 43/100 and 39/100. These decimals lie between 0 and 1.
Draw a number line, mark off and label the multiples of 0.10(e.g 0.10, 0.20) in the interval 0-1.
Mark 0.43 between 0.4 and 0.5, a little closer to 0.4.
Mark 0.39 between 0.3 and 0.4, just behind 0.4.
Since 0.39 is smaller than 0.43( 0.39 lies on the left to 0.43), the inequality is:
0.39<0.43
Which is the equation for the circle with center (6, 2) and radius 8?
Answer:
[tex]\displaystyle \boxed{ (x - 6)^2 + (y - 2)^2 = 64 }[/tex]
General Formulas and Concepts:
Precalculus
Circle Equation:
[tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
Center (6, 2)
h = 6k = 2r = 8
Step 2: Find Equation
[Circle Equation] Substitute in variables:∴ we have found the equation for the circle with given properties.
---
Topic: Precalculus
Unit: Conics
The equation of a circle is [tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex].
What is circle?A circle is a shape made up of all points in a plane that are at the same distance from a central point.
Equation of the circle [tex]\[{{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}\][/tex] where (h,k) is the coordination of the center and r is the radius
Which is the equation for the circle with center (6, 2) and radius 8?put the values of h, k and r in the equation of the circle
[tex]{{\left( x-6 \right)}^{2}}+{{\left( y-2 \right)}^{2}}={{8}^{2}}[/tex]
[tex]{{x}^{2}}+{{y}^{2}}+36+4-12x-4y=64[/tex]
[tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex]
therefore, the equation of the circle is[tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex].
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2x - 3y - z = -17 6x + 5y + z = -3 2x + 2y + 2z = 8
Answer:
2x - 3y = Z
Step-by-step explanation:
5y + 2z = 2 + 12
A John is mixing paint for an art project. He combines 4 quarts of white paint with
31 gallons of blue paint. He uses 2 quarts. How much paint does he have left?
Circle the letter for all that apply. (1 gallon = 4 quarts)
A 16 quarts
B 52 gallons
C 52 quarts
D 2; gallons
E 4 gallons
Answer:
2 gallons
Step-by-step explanation:
2 gallons of paint
Explanation:
If 3/4 of a gallon covers 2/5 of a wall, this means that a half of 3/4 gallons can cover 1/5 of a wall.
By knowing this, you can just make up your own expression
(the trick is to find a way to break it down to one, so you can multiply and manipulate it to save yourself some brain cells)
15
+
15
+
15
+
15
+
15
= whole wall
if
342
=
38
= amount of paint to cover 1/5 wall
then
(38)⋅5
=
38
+
38
+
38
+
38
+
38
=
158
≈
1.875
since we're talking about real life it would be 2 gallons of paint instead of 1.875 gallons to paint the whole wall
Hope this helps!
bought a condo for $83,000. Assuming that its value will appreciate 6% per year, how much will the condo be worth in 5 years?
$60,914
$83,000
$104,786
$111,073
The condo will be worth approximately $104,786 in 5 years.
Explanation:To calculate the future value of the condo, we can use the formula: Future Value = Present Value * (1 + Interest Rate)^Number of Years. Given that the condo was bought for $83,000 and will appreciate at a rate of 6% per year, we can substitute these values into the formula to find the future value.
Future Value = $83,000 * (1 + 0.06)^5 = $104,785.81.
Therefore, the condo will be worth approximately $104,786 in 5 years.
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The value of the condo will be approximately $111,073 in 5 years.
To find out how much your condo will be worth in 5 years if it appreciates at 6% per year, you can use the compound interest formula:
Future Value (FV) = Present Value (PV) * (1 + Rate)ᵗᶦᵐ
Here:
Present Value (PV) is $83,000Rate is 6% or 0.06Time is 5 yearsPlug the values into the formula:
FV = 83,000 * (1 + 0.06)⁵
First, calculate the growth factor:
(1 + 0.06) = 1.06
Next, raise the growth factor to the power of 5:
1.06⁵ = 1.3382
Finally, multiply this result by the present value:
83,000 * 1.3382 = $111,073.
Please help I’ll give brainliest
Answer:
Ling is 27: X=2 12x + 3 = 27
Step-by-step explanation:
12 times 2= 24 -> 24+3= 27
You spin the spinner for candy land. There are 4 colors on the spinner that have equal likelihoods of occurring. These colors are red, blue, green, and yellow. What's the chance of spinning green? Record your answer as a simplified fraction using "/" as your fraction key.
Answer:
1/4
Step-by-step explanation:
If you have four colors on the spinner and you want to land on the green spot and there is 1/4 chances
1. Carlos has $1,800 in a checking account set aside for summer expenses.
He withdraws $150 per week to pay for expenses. Nicole has $1,100 in a
checking account set up for money for an end of summer vacation.
Through the summer she deposits $200 per week. After how many weeks
will both accounts have the same amount of money? *
•2 weeks
•3 weeks
•4 weeks
•5 weeks
Answer:2 weeks
Step-by-step explanation: if you subtract 1800 by 150 for the two weeks you will get 1500 and if you add 1100 by 200 every week you will get a hundred and fifty
HELP FAST!!!!!! PLEASE