Answer:
(x+11)(x-11)
Step-by-step explanation:
A ^2 - B ^2 =(A+B) (A-B).. (*)
x^2 - 121=
x^2 - 11^2=(*)
(x+11)(x-11)
16. CRITICAL THINKING
Two figures are congruent. Are the areas of the two figures
the same? the perimeters? Explain your reasoning.
Both area and perimeter are the same. They have the same shape and dimensions.
This is because congruency means that the two figures are identical, one is the clone of the other.
Two congruent figures have identical shape and size, meaning their perimeters and areas are both equal.
If two figures are congruent, this means that they are identical in shape and size. Congruent figures are essentially the same figure superimposed from one location to another. According to the definition of congruent figures, corresponding angles and sides are equal. Therefore, since the dimensions of congruent figures are the same, the perimeters of the figures must also be the same. This is because perimeter is a linear measure, which is the sum of the lengths of the sides of a figure.
Similarly, since congruent figures are identical in size, their areas must also be the same. Area is a measure of the extent of a 2-dimensional surface enclosed by a figure. Since the figures are congruent, they cover the same amount of 2-dimensional space, thus their areas are equal. Theorems 9 and 12 mentioned in the reference material confirm these properties.
Given: - 4x>4.
Choose the solution set.
Answer:
x < - 1
Step-by-step explanation:
Given
- 4x > 4
Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity.
x < - 1
Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 60 quarts of 4% butterfat milk.
Answer:
20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk is used to make 60 quarts of 4% butterfat milk.
Step-by-step explanation:
We are given the following in the question:
Let x quarts of 6% butterfat milk be used and y quarts of 3% butterfat milk be used to make 60 quarts of 4% butterfat milk.
Thus, we can write the equation:
[tex]6\%\times x + 3\%\times y = 4\%\times 60\\6x + 3y = 240[/tex]
Total amount of 3% butterfat milk = 60
Thus, we can write the equation:
[tex]x+y = 60[/tex]
Solving the two equation, we get,
[tex]6x + 3y-(3x+3y) = 240 - 3(60)\\3x = 240-180\\3x = 60\\x = 20\\y = 60-20 = 40[/tex]
Thus, 20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk is used to make 60 quarts of 4% butterfat milk.
To get 60 quarts of 4% butterfat milk, mix 20 quarts of 6% butterfat milk with 40 quarts of 3% butterfat milk by setting up and solving a system of linear equations.
Explanation:To solve this problem, we can set up a system of equations based on the quantities and percentages of butterfat in the milk types. Let's call the amount of 6% butterfat milk x quarts and the amount of 3% butterfat milk y quarts. According to the question, we want to end up with 60 quarts of 4% butterfat milk. Therefore, we have:
First, we multiply the second equation by 100 to simplify the percentages:
6x + 3y = 4 × 60
Simplify the right side:
6x + 3y = 240
Now, divide by 3 to get:
2x + y = 80
We can subtract the first total volume equation from this new equation:
(2x + y) - (x + y) = 80 - 60
Omit the similar terms to solve for x:
x = 20
We substitute x back into the initial total volume equation:
20 + y = 60
And solve for y:
y = 60 - 20
y = 40
Therefore, to get 60 quarts of 4% butterfat milk, 20 quarts of 6% butterfat milk and 40 quarts of 3% butterfat milk must be mixed together.
What are the values of x in the equation 4x2 + 4x - 3 = 0?
Answer:
x= 0.5
or x= -1.5
Step-by-step explanation:
Let's solve your equation step-by-step.
4x2+4x−3=0
Step 1: Factor left side of equation.
(2x−1)(2x+3)=0
Step 2: Set factors equal to 0.
2x−1=0 or 2x+3=0
x= 1/2 or x= −3/2
Answer:
A. x = –1.5, 0.5
Which of the following is the graph of y = negative 4 StartRoot x EndRoot? On a coordinate plane, an absolute value curve opens down and to the right in quadrant 1 and starts at (0, 0). On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at (0, 0). On a coordinate plane, an absolute value curve opens up and to the right in quadrant 4 and starts at (0, 0). It goes through (5, negative 2). On a coordinate plane, an absolute value curve opens up and to the right in quadrant 4 and starts at (0, 0). It goes through (5, negative 9).
Answer:
see the procedure
Step-by-step explanation:
we have
[tex]y=-4\sqrt{x}[/tex]
we know that
The domain of a function is the set of all possible values of x
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
In this problem
The domain for x is the interval [0,∞)
All real numbers greater than or equal to zero
The range for y is the interval (-∞,0]
All real numbers less than or equal to zero
The graph in the attached figure
therefore
On a coordinate plane, an absolute value curve opens down and to the right in quadrant 4 and starts at (0, 0)
Answer:
Option C on Edge
Step-by-step explanation:
you're welcome
15 is 60% of what number?
Answer:
25
I don't know how to explain because I put random numbers and multiplied it by .6 and I found it once it equaled 15. Sorry I couldn't explain it more.
Rectangle ABCD is drawn on a coordinated plane. A=(-6,9) and B=(5,9) What could be the locations of points C and D
Answer:
It would be C=(6, -9); D= (-5,-9)
Step-by-step explanation:
If you plot -6,9 and 5,9 on a four quadrant graph you can see the answer. (sorry I'm not good at explaining, I'm on the same question as you currently and this is the answer I got, I'm pretty sure the one above isn't correct.)
The locations of points C and D are (16, 9) and (5, 9) or (-17, 9) and (-6, 9), respectively depending on the orientation of the rectangle.
To calculate the locations of points C and D in the rectangle ABCD, consider that opposite sides of a rectangle are parallel and have equal lengths.
Given points A=(-6,9) and B=(5,9), know that points A and B lie on a horizontal line at y=9. Since opposite sides of a rectangle are parallel, points C and D should also lie on a horizontal line parallel to AB.
So, the y-coordinate of points C and D should be 9 as well.
The x-coordinate for points C and D, consider that opposite sides of a rectangle are of equal length. The length of AB represents the width of the rectangle.
The length of AB = x-coordinate of B - x-coordinate of A
AB = 5 - (-6)
AB = 11 units.
Since, opposite sides are parallel, points C and D should also have the same y-coordinate as A and B. Their x-coordinates must differ by 11 units to maintain equal side lengths.
Possible coordinates for C and D:
C = (5+11, 9) = (16, 9)
D = (-6+11, 9) = (5, 9)
Alternatively:
C = (-6-11, 9) = (-17, 9)
D = (5-11, 9) = (-6, 9)
Therefore, the possible locations for points C and D are (16, 9) and (5, 9) or (-17, 9) and (-6, 9) .
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Is 8 feet 6 inches greater than 100
8 feet and 6 inches is equal to 102 inches, so yes
Answer: No. if your talking about 100 inches then 8 feet is 96 inches +6 = 102 inches so therefore 8 feet 6 inches is grater than 100 inches.
Find the perimeter of this shape
Answer:
4+7+3+5=19
Step-by-step explanation:
what is 45 times 35 divided by 344
Answer:
45 times 35 = 1575 and 1575 divided by 344 = 4.578488372
Answer: 4.58
Step-by-step explanation:
45 times 35 = 1, 575
1,575/344 = 4.58 to 2 decimal place
The tables show the books read by two different students. Explain how to determine which student read faster.
The first student read faster than the second student.
Step-by-step explanation:
Step 1:
To determine how long each student takes to read a book, we divide the time taken to read by the number of books read in that period.
Time taken to read a book = [tex]\frac{time taken to read}{number of books read in that period}[/tex].
In the given table, the second column values are times taken to read and the first column represents the number of books read in that period.
Step 2:
For the first student, the time taken is calculated.
The first student's time taken to read a book = [tex]\frac{30}{3}[/tex] = [tex]\frac{50}{5}=\frac{70}{7}[/tex] = 10 minutes to read a book.
Step 3:
Similarly, the time taken to read a book is calculated for the second student.
The first student's time taken to read a book = [tex]\frac{24}{2}=\frac{48}{4}=\frac{72}{6}[/tex] = 12 minutes to read a book.
Step 4:
Now we compare the times taken. The first student read a book in 10 minutes while the second student took 12 minutes for a book. So the first student read faster.
A line passes through the points (15,c) and (21,25) and has a slope of - 5/3
Find the value of c.
Answer: c=35
Step-by-step explanation:
to find the slope, you do y2-y1/x2-x1. So you will set up your equation like this:
25-c/21-15 = -5/3
this slope has been simplified by dividing by 2, because 21-15=6 and they simplified it to 3. So the original answer for 25-c was -10. So this means that c=35.
The diagram below shows scalene triangle JKL.
Which is true about the diagram? Select two options.
Measure of angle J K H + measure of angle J K L = 180 degrees
Measure of angle J K L + measure of angle J L K + measure of angle K J L = 180 degrees
Measure of angle J K H = measure of angle J L K
Measure of angle J K L + measure of angle J L K = 90 degrees
Measure of angle K J L = measure of angle K L J
The correct statement about the diagram is,
⇒ Measure of angle JKH + measure of angle JKL = 180 degrees
⇒ Measure of angle JKL + measure of angle JLK + measure of angle KJL = 180 degrees
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
The diagram is shown.
Now, By definition of linear pair of angles, we get;
⇒ m ∠JKH + m ∠JKL = 180°
And, The sum of angles in triangle is 180°
Hence, We get;
⇒ m ∠ JKL + m ∠ JLK + m ∠ KJL = 180 degrees
Thus, The correct statement about the diagram is,
⇒ Measure of angle JKH + measure of angle JKL = 180 degrees
⇒ Measure of angle JKL + measure of angle JLK + measure of angle KJL = 180 degrees
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Carrie started at the southeast corner of Franklin Park, walked north 240 yards, turned and walked west 80 yards, and then turned and walked diagonally back to where she started. What is the area of the triangle enclosed by path she walked?
The area is 9,600 square yards.
Carrie's walk forms a right-angled triangle, with the two legs being her north and west paths, and the hypotenuse being the diagonal path back to the start. To find the area of the triangle, we can apply the formula for the area of a right-angled triangle, which is (1/2) * base * height. In this case, the base is her westward walk (80 yards), and the height is her northward walk (240 yards).
Using the formula, the area equals: (1/2) * 80 yards * 240 yards, yielding an area of 9,600 square yards.
2. The length of a rectangle is 12 cm and the area is 96 cm2. What is the width?
2.
3. I need to buy a carpet for a room that measures 3 m by 2 m. How many
square meters do I need?
4. The diameter of a circle is 3 cm. What is the circumference?
5. A painting measures 40 cm by 35cm. How many squared cm does its
surface cover?
6. The circumference of a circle is 15.7 cm. What is the diameter?
7. One side of a square measures 15cm. What is its area?
8. If the area of a rectangle is 60 cm and its width is 6 cm. What is its length?
9. The area of a square is 81 cm? What is the length of one of its sides?
10. The area of a circle is 201 cm? What is the diameter?
Answer:
Step-by-step explanation:
2. To find area, you use this equation: A = l*w
Let's input the values we do know to find the width.
96 = 12 * w
Divide both sides by 12 to isolate the w.
8 = w
The width is 8 cm.
3. We need the find the area of the floor to figure out how many square meters they need. to find area, we multiply the length by the width.
3 * 2 = 6
You need 6 sq. m.
4. To find the circumference, use the equation: C = 2 * pi *r
To find the radius, divide the diameter by 2.
3/2 = 1.5
C = 2pi(1.5)
C = 3pi
The circumference is 3pi. This can also be simplified to 9.42 or 9.4
5. To find the amount of square cm. it covers, multiply the length and width.
40 * 35 = 1,400
The surface covers 1,400 sq. cm.
6. To find circumference, use this equation: C = d * pi
Input the values you do know to find the diameter
15.7 = d * pi
divide both sides by pi to isolate d
4.77 = d
The diameter is approximately 4.8 cm.
7. To find area, multiply length by width. Since we know all sides of a square are the same, you can multiply 15 by 15 to get the answer.
15 * 15 = 225
The area is 225 sq. cm.
8. To find area, use this equation: A = l * w
put the values you know into the equation to find the length.
60 = l * 6
divide both sides by 6 to isolate the l
10 = l
The length is 10 cm.
9. To find the area of a square, the equation is: A = s^2
Input the values you know to find the length of a side.
81 = s^2
Find the square root of both sides to isolate the s.
9 = s
The length of one side is 9 cm.
10. To find the area of a circle, use this equation: A = pi * r^2
Input the values you know and solve for r.
201 = pi * r^2
Find the square root of both sides and divide both sides by pi to isolate the r.
7.998 = r
The radius is approximately 8 cm. Multiply this value by 2 to find the length of the diameter.
8 * 2 = 16
The diameter is approximately 16 cm.
To find the product of 42.12 and 10³, move the decimal point in 42.12 __ places to the right because 10³ has __ zeros.
Answer:
Both answers are 3.
Step-by-step explanation:
10^3 = 10 * 10 * 10 = 1000
When you multiply 42.12 by 10^3, you are multiplying 42.12 by 1000.
When you multiply a number by a power of 10, such as 10, 100, 1000, etc., move the decimal point of the number to the right the same number of places as the number of zeros in the power of 10.
42.12 * 1000 = 42,120
Final answer:
To find the product of 42.12 and 10³, move the decimal point in 42.12 three places to the right because 10³ has three zeros. Thus, the product is 42120.
Explanation:
To find the product of 42.12 and 10³, you need to move the decimal point in 42.12 three places to the right because 10³ has three zeros. Multiplying by powers of ten is simplified by moving the decimal point to the right for each zero in the power of ten. For instance, multiplying 2.4 by 100 involves moving the decimal two places to the right to get 240, since 100 has two zeros.
When you multiply 42.12 by 10³, which is the same as multiplying by 1000 (10 x 10 x 10), you're effectively shifting the decimal point three places to the right. If there aren't enough digits, you can use zeros as placeholders. However, in this case, there are sufficient digits to move the decimal without adding additional zeros.
Therefore, 42.12 multiplied by 10³ would be 42120. This is because you move the decimal point three places to the right to account for the three zeros in 10³, changing 42.12 into 42120.
as a salesperson, jonathan is paid $50 per week of the total amount he sells. this week, he wants to earn at least $100. write an inequality with integer coefficients for the total sales needed to earn at least $100 and describe with a solution represents
Answer: 1/5
Step-by-step explanation:50%50=1
100%50=0.5
What is 34.02 estimated?
Answer: 34
Step-by-step explanation:
Final answer:
To estimate 34.02, we would round it to the nearest whole number which is 34.
Explanation:
When asked to estimate 34.02, we look for a number that is close in value but simpler or more convenient to use.
Estimation often involves rounding to a certain place value depending on the level of precision required.
In this case, we can round to the nearest whole number. 34.02 is very close to 34, so the estimated value is 34.
This is based on traditional rounding rules where if the digit right after the place you are rounding to is less than 5, you keep the digit the same. If it is 5 or more, you round up. Since the decimal part .02 is less than .05, we do not round up.
a cone is twice as tall as a cylinder of the same radius. what is the ratio of there volumes?
The ratio of the volume of the cone to the cylinder is 2/3.
We have,
The volume of a cone is given by the formula:
= (1/3)πr²h
The volume of a cylinder is given by the formula:
= πr²h
The radius of both shapes as r, and since the cone is twice as tall as the cylinder,
h(cone) = 2 h(cylinder)
Ratio = V(cone) / V(cylinder)
= [(1/3) π r² (2h(cylinder)] / (πr²h(cylinder))
= (2/3) h(cylinder) / h(cylinder)
= 2/3
Therefore,
The ratio of the volume of the cone to the cylinder is 2/3.
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A retail store offers all television sets at 80% or 80/100 of their original price if the customer buys a store membership for 100.00. If the p is the price of a television set. How much will a 1500.00 television cost
Answer: $1875
Step-by-step explanation:
If 80% of original price= $1500
Let the remaining 20% be x
Write as:
80/100 = $1500
20/100 = x
Cross multiply
0.8x = 1500 x 0.2
0.8x= 300
Divide both sides by 0.8
x = 300/0.8
x = 375
Therefore, 80% = 1500; 20% = 375
Price of $1500 TV without membership = $1,500 + $375
=$1,875
Answer:
It should be C. The expression is (p x 80/100) +10p and the cost is 1,300
Step-by-step explanation:
sorry if it’s wrong
What is the coefficient of y when the expression 1/3(9y-3)-2y is simplified?
Answer:
Coefficient of y is 1 since the answer is y-1
Step-by-step explanation:
In the attached file
What is the radius and diameter of the following circle?
Answer:
The radius is 9 and the diameter is 18.
Step-by-step explanation:
Because the radius is half the diameter which is 18.
Answer:
the diameter is 18 cm and the radius is 9
identify the numerical coefficient of the term 5xy?
Answer:
5
Step-by-step explanation:
Answer: its 5
Step-by-step explanation:
the coefficient is the leading number
what is the answer to this
-2(4x-3)=10
Answer:
x= -1/2
Step-by-step explanation:
-2(4x-3)=10
Divide each side by -2
-2/-2 *(4x-3)=10/-2
4x-3 = -5
Add 3 to each side
4x-3+3 = -5+3
4x = -2
Divide each side by 4
4x/4 = -2/4
x = -1/2
Answer:
x=-0.5 or x=-1/2
Step-by-step explanation:
Divide both sides by the numeric factor on the left side, then solve.
Are 4(x-3) and 6x-2(x-3) equivalent?
Answer:
No, 4x - 12 ≠ 4x + 6
Step-by-step explanation:
Step 1: Distribute both expressions
4(x - 3)
(4 * x) + (4 * -3)
(4x) + (-12)
4x - 12
6x - 2(x - 3)
6x - (2 * x) - (2 * -3)
6x - (2x) - (-6)
6x - 2x + 6
4x + 6
Answer: No, 4x - 12 ≠ 4x + 6
Answer:
No its not because when solved you get 4x-12I need help for #9 please help I got math class in 30 minutes :))!! Thank u
In questions it's given that ∠B = 85°, which is an error and correct answer is ∠B = 95°.
Step-by-step explanation:
We know that sum of alternate angles in a parallelogram is 180°. Using this property, we will solve the question! We have a parallelogram inscribed in a circle with measure of angles as ∠A=100° and ∠D=85°. Now, according to property : ∠A + ∠C = 180° and ∠D + ∠B = 180°.
Let's consider for ∠D + ∠B = 180°:
⇒ 85° + ∠B = 180°
⇒∠B = 180° - 85°
⇒∠B = 95°
Also, for ∠A + ∠C = 180°:
⇒ 100° + ∠C = 180°
⇒∠C = 180° - 100°
⇒∠C = 80°
In questions it's given that ∠B = 85°, which is an error and correct answer is ∠B = 95°.
Expand and simplify 4(2x+4)+5(4x+3)
Answer:
see below
Step-by-step explanation:
4(2x+4)+5(4x+3)
Distribute
4*2x+4*4 +5*4x+ 5*3
8x+16 +20x +15
Combine like terms
28x +31
What is the answer to 5x-11=34
Answer:
x = 9Step-by-step explanation:
[tex]5x-11=34\qquad\text{add 11 to both isdes}\\\\5x-11+11=34+11\\\\5x=45\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{45}{5}\\\\x=9[/tex]
Answer:
x = 9
Add all numbers up get 45
5x = 45
divide both sides and get 9
what is the expression equivalent to 64 - x^2
Answer: -(x+8)(x-8)
Step-by-step explanation:
-(x^2-64)
x^2-8^2x^2
x^2-8^2=(x+8)(x-8)
-(x+8)(x-8)
A rational number between 13/15 and 14/15
Hey there!
You can find a number halfway between two numbers by simply adding them together and then dividing by two!
13/15+14/15=1 4/5
1 4/5÷2=9/10
Your number is 9/10.
I hope this helps!
Sure, let's find the rational number between 13/15 and 14/15.
A straightforward way to get a rational number between any two given rational numbers is to calculate their average, or arithmetic mean. This is because the mean of any two numbers always falls between those two numbers.
So, let's calculate the mean of 13/15 and 14/15:
1. Begin by adding these two fractions: 13/15 + 14/15
2. In order to add fractions, we need a common denominator, which we already have in this case: 15.
Just add the numerators: 13 + 14 = 27
So, the sum of 13/15 and 14/15 is 27/15.
3. Now, calculate the mean of the two numbers by dividing their sum by 2 since mean = (a+b) / 2
So, we have: (27/15) / 2 = 27/30
Here you have it - the rational number between 13/15 and 14/15 is 27/30 or 0.9 in decimal form.