A circle has a diameter of 11cm
A square has a side length of 7cm
Use pythagoras’ theorem to show that the square will fit inside the circle without touching the edge of the circle.
Pleas help
Answer:
The diagonal length of the square equals:
diagonal ^ 2 = 7^2 + 7^2
diagonal ^ 2 = 49 + 49
diagonal ^ 2 = 98
diagonal = 9.899 cm
The diagonal is smaller than the circle's diameter and so it will ft inside the circle.
Step-by-step explanation:
Which type of individual retirement account should you choose if you want your contributions to be tax deductible?
The case of 12 bottles of shampoo holds a total of 126 ounces. If each bottle of shampoo contains the same amount, which represents the total volume of shampoo in ounces, y, of any number of bottles, x?
Each bottle of shampoo contains 10.5 ounces. The formula for the total volume of shampoo (y) in terms of the number of bottles (x) is y = 10.5x.
Let's denote the amount of shampoo in each bottle as b (in ounces). Since there are 12 bottles of shampoo, the total volume of shampoo in ounces (y) is given by the product of the number of bottles (x) and the amount in each bottle (b). So, the equation is:
y = x * b
The problem states that the case of 12 bottles holds a total of 126 ounces. This can be expressed as:
126 = 12 * b
Now, we can solve for b by dividing both sides of the equation by 12:
b = 126 / 12
Simplifying:
b = 10.5
So, each bottle of shampoo contains 10.5 ounces.
Therefore, the formula for the total volume of shampoo (y) in terms of the number of bottles (x) is:
y = 10.5x
Answer:
Step-by-step explanation:
it is A
Amelia runs a catering business. Based on her records, her
weekly profit can be approximated by P = 2x2 - 44x – 150,
where x is the number of meals she caters and P is her profit.
When P is negative, Amelia has lost money.
1) What is the least number of meals Amelia needs to cater
in order to begin making a profit?
2) If she caters no meals one week, how much money does
she lose?
3) What is her profit for catering 50 meals?
Answer: (1) The least number of meals is 26 (2) She loses 150 if she caters no meal in one week. (3) Her profit would be 2,650 if she caters for 50 meals in one week
Step-by-step explanation: The weekly profit is given as a quadratic equation which is;
P = 2x² -44x - 150
We begin by solving for the value of x.
When 2x² -44x - 150 = 0
Divide all through by 2
x² - 22x - 150 = 0
By factorization,
(x - 25) (x + 3) = 0
(x -25) = 0 OR (x + 3) = 0
When x - 25 = 0
x = 25
When x + 3 = 0
x = -3
What this implies is that when Amelia caters for 25 meals in a week, her profit is calculated as follows
P = 2x² - 44x -150
P = 2(25)² - 44(25) - 150
P = 2(625) - 1100 - 150
P = 1250 - 1100 - 150
P = 0
(1) Therefore she must cater for at least 26 meals before she can begin to make any profit.
(2) She loses 150 if she caters no meal in one week.
This can be calculated as follows;
When x = 0,
P = 2x² - 44x - 150
P = 2(0)² - 44(0) - 150
P = 0 - 0 -150
P = -150
(3) When she caters 50 meals her profit becomes 2,650
P = 2x² - 44x - 150
P = 2(50)² - 44(50) - 150
P = 2(2500) - 2200 - 150
P = 5000 - 2200 - 150
P = 2650
1) The least number of meals Amelia needs to cater in order to begin making a profit is 25.
2) Amelia loses $150 if she caters no meals in a week.
3) For catering 50 meals, Amelia's profit is $2650.
Explanation:1) To find the least number of meals Amelia needs to cater in order to begin making a profit, we need to determine when her profit, P, becomes positive. In other words, we need to solve the quadratic equation 2x^2 - 44x - 150 = 0 for x. This equation can be factored as (2x + 6)(x - 25) = 0. Therefore, x = -3 or x = 25. Since the number of meals cannot be negative, the least number of meals Amelia needs to cater in order to begin making a profit is 25.
2) If Amelia caters no meals one week, the profit, P, is given by P = 2(0)^2 - 44(0) - 150. Simplifying this equation, we get P = -150. Therefore, Amelia loses $150 if she caters no meals in a week.
3) To find Amelia's profit for catering 50 meals, we substitute x = 50 into the profit equation P = 2x^2 - 44x - 150. Plugging in x = 50, we get P = 2(50)^2 - 44(50) - 150 = 5000 - 2200 - 150 = $2650.
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How are (3x)^2 and 3x^2 different?
Answer:
In (3x)^2, you are squaring both the 3 and the x:
9x^2
in 3x^2, you are squaring just the x:
3x^2
Answer:
(3x)^2=9x^2
(3x^2)=3x^2
Step-by-step explanation:
The difference between the two is that
(3x)^2 means the square applied to both the 3 and the x to give 9x^2
But on the other side
(3x^2) means that the square only applies to x without involving 3 which gives 3x^2
So there is difference between them
What is the domain of g(x)?
The graph of f(x) = 6(0.25) and its reflection across the y-
axis, g(x), are shown.
COND
all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers greater than or equal to 0
g(x)
A
+
1 +
f(x)
5
4 3
2
1
1 2
3
4
5 x
Answer:
y=(x+6)
2
−6
Step-by-step explanation:
What is the area in square millimeters of the triangle outlined
on the origami figure?
HELPPPPP
The area in square millimeters of the triangle outlined on the origami figure is 441 square millimeters.
In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):
Area of triangle = 1/2 × b × h
Where:
b represent the base area.h represent the height.Conversion:
7 cm to mm = 7 × 10
7 cm to mm = 70 mm.
1.26 cm to mm = 1.26 × 10
1.26 cm to mm = 12.6
By substituting the given side lengths into the formula for the area of a triangle, we have the following;
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 70 × 12.6
Area of triangle = 35 × 12.6
Area of triangle = 441 square millimeters.
If x=2 and y=4,what is the numerical value of the expression 7y minus 3x
Answer:
22
Step-by-step explanation:
If x=2 and y=4
7•4 - 3•2
28-6
So the answer is 22
This cylinder is 6 inches tall & has a volume of 60πin^3. Find the area of the cross section
Given:
Height of cylinder = 6 inches
Volume of cylinder = 60π in³
To find:
The area of the cross section.
Solution:
Volume of cylinder:
[tex]V=\pi r^2h[/tex]
[tex]\pi r^2h=60\pi[/tex]
Cancel the common factor π on both sides.
[tex]r^2h=60[/tex]
Substitute h = 6.
[tex]r^2\times 6=60[/tex]
Divide by 6 on both sides, we get
[tex]r^2=10[/tex]
Taking square root on both sides.
[tex]r=\sqrt{10}[/tex] inch
Area of cross section = [tex]\pi r^2[/tex]
[tex]=\pi (\sqrt{10} )^2[/tex]
[tex]=10 \pi[/tex] in²
The area of the cross section is 10π in².
The equation shows a number multiplied by 5. n x 5=? Which of these is true about the results?
Answer:
5n
Step-by-step explanation:
The result of n x 5 is equal to 5 times the value of n.
The equation 'n x 5' represents the product of a number n and 5. The result can be positive or negative based on the value and sign of n. Also, parenthesis placement in expressions greatly affects the outcome due to the order of operations.
Understanding the Multiplication of Numbers and Order of Operations
The equation n x 5 indicates that a number n is being multiplied by 5. The results of this product will depend on the value of n and whether n is positive, negative, or zero. For example, if n is positive, like 2, then the product is also positive: 2 x 5 = 10. If n is negative, like -3, the result is negative: (-3) x 5 = -15. It's important to remember that when two positive numbers multiply, the answer has a positive sign, and when two negative numbers multiply, the result is also positive. However, if the two numbers have opposite signs, the answer will have a negative sign.
Furthermore, the placement of parentheses can affect the result of mathematical expressions. For instance, 2 + (3 x 5) is not the same as (2 + 3) x 5 due to the order of operations. In the first expression, multiplication is performed first, resulting in 17, whereas the second expression results in 25.
Understanding the rules of multiplication, including the signs of the numbers involved and the order of operations, is essential for solving equations and expressions correctly.
What’s the correct answer for this question?
Answer:
13
Step-by-step explanation:
If they are equal to each other, than angle DF is the same as angle AC, and angle AC is 13, so DF must be 13
Val needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 58 dash m-by-58 dash m square. Val says the area is 1 comma 917.48 msquared. Find the area enclosed by the figure. Use 3.14 for pi. What error might Val have made?
Answer:
We need to find the area of the semicircles + the area of the square.
The area of a square is equal to the square of the lenght of one side.
As = L^2 = 58m^2 = 3,364 m^2
Now, each of the semicircles has a diameter of 58m, and we have that the area of a circle is equal to:
Ac = pi*(d/2)^2 = 3.14*(58m/2)^2 = 3.14(27m)^2 = 2,289.06m^2
And the area of a semicircle is half of that, so the area of each semicircle is:
a = (2,289.06m^2)/2 = 1,144.53m^2
And we have 4 of those, so the total area of the semicircles is:
4*a = 4* 1,144.53m^2 = 4578.12m^2
Now, we need to add the area of the square 3,364 m^2 + 4578.12m^2 = 7942.12m^2
This is nothing like the provided anwer of Val, so the numbers of val may be wrong.
Answer:
The answer is 4,112.00 m
Step-by-step explanation:
Val subtracted the square's area from area of the semicircles when it should be added to it.
The area of each triangular base is:
A = 1/2(b)(h) A = 1/2(4)(3)
A =
in.2
There are two bases, so total base area is
in..
he lateral area is:
A = 8(4) + 8(3) + 8(5)
A =
in.2
The total surface area is
in.
Answer:
A=6
Total base area is 12
A=96
Total surface area is 108
Answer:
Step-by-step explanation:
A=6
There are two bases, so total base area is 12
A= 96
The total surface area is 108
Use the properties of exponents to solve for each
variable
4^8 •4² = 4^a
(2^4)^5 = 2^b
5^6
Step-by-step explanation:
[tex] \because \: {a}^{m} . {a}^{n} = {a}^{m + n} \\ \therefore \: {4}^{8} . {4}^{2} = {4}^{8 + 2} = {4}^{10} \\ \\ \because \: ({a}^{m})^{n} = {a}^{m \times n} \\ \therefore \:({2}^{4})^{5} = {2}^{4 \times 5} = {2}^{20} \\ \\ {5}^{6} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15625[/tex]
The solution are:
a = 10b = 205^6 = 15625To solve for each variable using the properties of exponents, we can use the following steps:
Identify the base and exponent in each expression.
Use the properties of exponents to simplify the expressions.
Solve for the variable.
4^8 •4² = 4^a
Identify the base and exponent in each expression:
Base: 4
Exponent: 8 in the first expression, 2 in the second expression, and a in the third expression
Use the properties of exponents to simplify the expressions:
4^8 •4² = 4^(8+2) = 4^10
Solve for the variable:
4^a = 4^10
a = 10
(2^4)^5 = 2^b
Identify the base and exponent in each expression:
Base: 2
Exponent: 4 in the first expression, 5 in the second expression, and b in the third expression
Use the properties of exponents to simplify the expressions:
(2^4)^5 = 2^(4*5) = 2^20
Solve for the variable:
2^b = 2^20
b = 20
5^6
Identify the base and exponent:
Base: 5
Exponent: 6
Simplify the expression:
5^6 = 5*5*5*5*5*5 = 15625
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Line segment BA is tangent to the circle.
A circle is shown. Secant D B and tangent B A intersect at point B outside of the circle. Secant D B intersects the circle at point C. The length of A B is x, the length of B C is 55, and the length of C D is 120.
What is the length of line segment BA? Round to the nearest unit.
Answer:
Hence the length of line segment BA as 98 units
Step-by-step explanation:
Given:
BA as tangent to circle ,DB as secant which intersect at point C at circle
Length BC= 55 and CD=120
To Find:
Length of line segment AB.
Solution:
This follows the relationship between tangent and secant in circle terms as:
Consider as figure such that ,
AB as tangent , DB as secant C be point at circle
So secant total distance = DB=BC+CD =55+120=175
Using formula as ,
[tex]AB^2=BC(BC+CD)[/tex]
We have to find AB
Here BC=55 and CD=120
[tex]AB^2=55(120+55)[/tex]
[tex]AB^2=55(175)[/tex]
[tex]AB^2=9625[/tex]
[tex]AB=98.10[/tex]
So nearest unit for length will be 98
Hence the length of line segment BA as 98 units
Answer:
98 units
Step-by-step explanation:
edge
Hurry. A catapult launches a pumpkin with an upward velocity of 150 ft./s.
The height of the pumpkin, h, in feet after t seconds is given by the
function h = -16t2 + 150t + 20. How long does it take the
pumpkin to reach its maximum height? What is the pumpkin's
maximum height? Round to the nearest hundredth, if necessary.
Answer:
Time taken to reach maximum height=4.69 seconds
Maximum Height=371.56feet
Step-by-step explanation:
Given the height function of the pumpkin:
[Tex]h = -16t^2 + 150t + 20[/tex]
The pumpkin reaches it's maximum height at its axis of symmetry.
Therefore, we determine its equation of symmetry.
The equation of symmetry:
[Tex]t=-\frac{b}{2a}[/tex]
a=-16, b=150.
Therefore:
[Tex]t=-\frac{150}{2*-16}=4.6875[/tex]
The pumpkin reaches maximum height after 4.6875 seconds.
At t=4.6875
[Tex]h = -16(4.6875)^2 + 150(4.6875)+ 20\\=371.5625\approx 371.56 \:feet[/tex]
The pumpkin's maximum height is 371.56 feet.
Solve for p.
9(p - 4) = -18
Answer:
p=2
Step-by-step explanation:
9(p - 4) = -18
Divide each side by 9
9/9(p - 4) = -18/9
p-4 = -2
Add 4 to each side
p-4+4 = -2+4
p = 2
A recipe requires 5/6 of a cup of sugar. If Mrs. Marina is going to make on half of the recipe, then how much sugar does she need?
Answer:
5/12
Step-by-step explanation:
Let the unknown number of sugar requires by 1/2 recipe be x
1 recipe requires 5/6 cup of sugar
1/2 recipe requires x cup of sugar
Cross multiply
x=1/2×5/6
x=5/12
So the amount of sugar requires to make 1/2 recipe is 5/12
Does the quadratic function y=-2x+3x^2+5 open upward or downward? Explain
Answer:
It would open upward.
Step-by-step explanation:
If you see on the equation, there is a positive (+) sign on the [tex]3x^2[/tex]. If you see the positive sign on anything that is squared, and it is asking for a quadratic function, then it will always open upward. If you see a negative sign on anything that is squared, and is asking for a quadratic function, then it will open downward.
Answer:
Upwards
Step-by-step explanation:
The reason is this quadratic function has a positive coefficient which is 3. The reason 3 is the coefficient is that 3 is the one with the X with a square in it. if 3 would have been negative, well the answer would be the opposite.
Hope That Helped
Compare the perimeter and area of the original figure to the perimeter and area of the reduced figure using the scale factor. A smaller rectangle has a length of 3 and width of 1. A larger rectangle has a length of 6 and width of 2. Which statements are true about the comparison between the two figures? Check all that apply. The scale factor is 2. The scale factor is One-half The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle. The area of the reduced figure is half the area of the original figure. The area of the reduced figure is (One-half) squared, one-fourth times the area of the original figure.
Answer:
- The scale factor is one-half
- The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle
-The area of the reduced figure is (1/2)^2 = 1/4 times the area of the original figure
Step-by-step explanation:
The ratio of the length of the original rectangle to that of the reduced rectangle is 6 to 3, or a factor of 1/2. The ratio of the width of the original rectangle to that of the reduced rectangle is 2 to 1, or, again, a factor of 1/2. So, because this ratio of 1/2 is constant, we know the total scale factor is 1/2, making B correct.
The perimeter of a rectangle is: [tex]P=2l+2w[/tex], where l is the length and w is the width. The perimeter of the reduced figure is: P = 2 * 3 + 2 * 1 = 6 + 2 = 8 units. The perimeter of the original figure is: P = 2 * 6 + 2 * 2 = 12 + 4 = 16 units.
Notice that 16 * (1/2) = 8, which means that the perimeter of the scale-factored, reduced rectangle is "the product of the scale factor (which is 1/2) and the perimeter of the original rectangle (which is 16)". So, C is correct.
The area of a rectangle is: [tex]A=lw[/tex], where l is the length and w is the width. The area of the reduced figure is: A = 3 * 1 = 3 units squared. The area of the original figure is: A = 6 * 2 = 12 units squared.
Notice that 12 * (1/4) = 3, which means that E is correct, but D is wrong.
Hope this helps!
Answer:
Statement 2: The scale factor is One-half
Statement 3: The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle.
Statement 5: The area of the reduced figure is (One-half) squared, one-fourth times the area of the original figure.
Step-by-step explanation:
A smaller rectangle has a length of 3 and width of 1
Perimeter: 2(3+1) = 8
Area: 3×1 = 3
A larger rectangle has a length of 6 and width of 2
Perimeter = 2(6+2) = 16
Area = 6×2 = 12
Comparing areas:
Smaller : larger
3 : 12
1 : 4
Comparing perimeters:
Smaller : larger
8 : 16
1 : 2
What is the area of the triangle?
8 cm
14 cm
Answer:
The answer is 56 cm2
Step-by-step explanation:
You have to multiply the height times the base then divide that answer by two.
8x14= 112
112/2= 56
Answer:
Step-by-step explanation: Area = 1/2 b.h
= 1/2 8cm.14cm
= 1/2 112 Square cm
= 112/2
= 56 Square cm.
A box shaped like a right rectangular prism
measures 5 centimeters by 3 centimeters by
2 centimeters. What is the length of the interior
diagonal of the prism to the nearest hundredth?
Answer:
[tex]\sqrt{38}[/tex]
Step-by-step explanation:
Given that:
The 3 demensions of the right rectangular prism measures 5 centimeters by 3 centimeters by 2 centimeters.
Because we do not know which one is the height, the length and the width of the box, so we assume them (it does not affect the length of the interior
diagonal )
the height : 5 centimetersthe length : 3 centimeters the width : 2 centimetersTo find the length of the interior diagonal of the prism, we use the following formula:
d = [tex]\sqrt{l^{2} +w^{2} +h^{2} }[/tex] = [tex]\sqrt{5^{2} +3^{2} + 2^{2} } = \sqrt{38}[/tex]
Hope it will find you well.
Answer
38 or about 6.16
There are two nets that contain circles. What statement is true about both nets?
Answer:
They both contain circles or its either they both are nets.
Step-by-step explanation:
A student claimed 7 and -7 are the two cube roots of 343.
Do you disagree or agree
Answer:
i think disagree ._.
The price of a car has been reduced from $23,500 to $17,155. What is the percentage decrease of the price of the car?
I think I would be 30% maybe... I could be wrong
Answer:
27%
Step-by-step explanation:
First get the decrease
Decrease = $23500 - $17155
= $6345
Percentage decrease = decrease/initial price x 100%
That’s
$6345/$23500 x 100%
0.27 x 100%
27%
The percentage decrease in the price of the car is 27%
Please help!
I don't understand..
Answer:
58 should be the answer
Step-by-step explanation:
<CBD is 90 and <BDC is 32 as well since its the same as angle <BDA and 180 in every triangle so 180-90-32=58.
Find the indicated values, where [tex]g(t)= t^2 -t and f(t)=1+x[/tex].
f(2g(1)).
I need help with this I've been trying to solve it for over half an hour.
Answer:
659.4 cm^2
Step-by-step explanation:
The area of the curved surface of the cone = πrL
= π*7*16
= 3.14 * 112
= 351.68 cm^2,
Surface area of the hemisphere = 2 π r^2
= 2*3.14*7^2
= 307.72 cm^2.
Total area = 351.68 + 307.72
= 659.4 cm^2.
What is the radius of the circle given by the
equation (x + 4)2 + (y − 3)2 = 4?
A. 16
B. 4
C. √4
D. 12
Answer:
C sqrt (4) or 2
Step-by-step explanation:
(x + 4)^2 + (y − 3)^2 = 4
We know that the equation for a circle can be written in the form
(x -h)^2 + (y − k)^2 = r^2 where (h,k) is the center and r is the radius
Rewriting the above equation
(x - -4)^2 + (y − 3)^2 = 2^2
The center is (-4,3) and the radius is 2
I need help on this Question.!
Answer:
see below
Step-by-step explanation:
m/n = 1/7
Using cross products
7m = n
This is a direct proportion