Translate the following phrase into an algebraic expression or equation.
the square of the difference of two numbers
What Is The Perimeter Of The triangle ? A(1,2) B(4,6) C(4,2)
A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?
The correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]. Therefore the correct option is 2.
The volume [tex]\( V \)[/tex] of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
For a square pyramid, the base area is given by [tex]\( \text{Base Area} = \text{side length}^2 \)[/tex].
In this case, the side length is [tex]\( x \)[/tex] and the height is [tex]\( y \)[/tex]. Therefore, the expression for the volume [tex]\( V \)[/tex] is:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
Now, let's compare this with the given options:
1. [tex]\( \frac{1}{3}xy \)[/tex] cm³
2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³
3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³
4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³
Now, we can see that the correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3}x^2y \, \text{cm}^3 \][/tex]
So, the correct option is option 2: [tex]\( \frac{1}{3}x^2y \)[/tex] cm³.
The correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]
Complete question:
A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?
1. [tex]\( \frac{1}{3}xy \)[/tex] cm³
2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³
3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³
4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³
Twice a number decreased by seven
Jose is painting a backdrop for the school play. The rectangular backdrop is 60 inches by 45 inches. If his container of paint can cover 25 square feet, does he have enough paint to paint the backdrop?
The area of a rectangular backdrop is 18.75 square feet and container has enough paint.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Given that, the rectangular backdrop is 60 inches by 45 inches.
We know that, 1 feet =12 inches
So, 60 inches = 60/12 = 5 inches
45 inches = 45/12 = 3.75 inches
Here, Area = 5×3.75
= 18.75 square feet
If his container of paint can cover 25 square feet.
So, Jose has enough paint.
Therefore, the area of a rectangular backdrop is 18.75 square feet and container has enough paint.
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What is the value of y?
Enter your answer in the box.
y =
Answer-
[tex]\boxed{\boxed{y^{\circ}=26^{\circ}\ 45'}}[/tex]
Solution-
As the triangle ABC is an isosceles triangle, with AC = BC.
So the angles A and B will be same, i.e
[tex]\Rightarrow \angle A=\angle B[/tex]
[tex]\Rightarrow 34^{\circ}=(x-5)^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}=34^{\circ}+5^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}=39^{\circ}[/tex]
As sum of all angles in a triangle is 180°, so
[tex]\Rightarrow \angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]\Rightarrow 34^{\circ}+39^{\circ}+4y^{\circ}=180^{\circ}[/tex]
[tex]\Rightarrow 4y^{\circ}=180^{\circ}-34^{\circ}-39^{\circ}[/tex]
[tex]\Rightarrow 4y^{\circ}=107^{\circ}[/tex]
[tex]\Rightarrow y^{\circ}=\dfrac{107^{\circ}}{4}[/tex]
[tex]\Rightarrow y^{\circ}=26.75^{\circ}[/tex]
[tex]\Rightarrow y^{\circ}=26^{\circ}\ 45'[/tex]
A water tank can hold 234 cubic meters of water. How many gallons can the water tank hold?
A. 6,176 gallons
B. 61,776 gallons
C. .886 gallons
D. 23,400 gallons
Focus tests suggest that costumers love the new gPhone X1, but they think the 5.82-inch long screen is too long. The engineers come back with a design they called the gPhone X2 with a screen that is 5/8 inch shorter than the X1. Will the new X2 be shorter that its main competitor, the 5 1/5-inch rover 6?
Suppose a triangle has sides a, b, and c, and let theta be the angle opposite the side of length a. If cos theta > 0 what must be true?
A. a2 + b2 > c2
B. a2 + b2 = c2
C. b2 + c2 < a2
D. b2 + c2 > a2
When cosθ >0 then , b² + c² > a².
What is triangle?
" Triangle is a 2 dimensional shape which is having three sides and three vertices. Sum of all the interior angles of a triangle is 180°."
Formula used
As per Cosine Rule
For a given ΔABC,
cosθ = [tex]\frac{b^{2} + c^{2} - a^{2} }{2bc}[/tex]
According to the question,
cosθ >0
⇒ [tex]\frac{b^{2} + c^{2}-a^{2} }{2bc}[/tex] >0
⇒ b² + c² >a²
Hence, we conclude that Option D is correct.
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Which element is located at B42?
Evaluate (4/9)^1/2
help would be great
To evaluate (4/9)^1/2, you find the square root of 4, which is 2, and the square root of 9, which is 3, hence the result is 2/3.
The student has asked to evaluate the expression (4/9)^1/2. To do this, you take the square root of both the numerator and the denominator separately. The square root of 4 is 2 and the square root of 9 is 3, therefore, the evaluation of the expression (4/9)^1/2 is equivalent to 2/3.
5k+(−2k)−(−1) what is the answer please give it to me
Decide which of the two points lies on the graph of the line
X= -3
A. 2,-3
B. -3,2
Jolinda scores 21 points during her basketball game. Her team scores a total of 28 points. What fraction of the team’s points does Jolinda score? Choose the answer in simplest form.
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
If Jolinda scored 21 points of 28 total, the fraction is:
[tex]\frac{21}{28}=\frac{3}{4}= 0.75(or75\%)[/tex]
Remember that a fraction is the representation of a portion among the total.
In addition, this fraction also would represent the effectiveness of Jolinda, we could say that she is able to score a 75% of team's points.
Please help with math question!
PLEASE HELP ME BOTH MY TUTORS LEFT AT THE SAME TIME I NEED MAJOR HELP!!! PPPPLLLLEEEEAAAASSSSEEE
What is the length of an arc with a central angle of 5/4π radians and a radius of 34 centimeters?
Use 3.14 for pi.
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What is the value of y?(picture)
Enter your answer in the box.
Round your final answer to the nearest whole number.
What is tanB ? (picture)
Enter your answer, as a simplified fraction, in the box.
Based on the diagram, what is tanA ?(picture)
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What is the value of x?
sin(x+34)°=cos(2x+20)°
Enter your answer in the box.
What is the value of x?
cos63°=sinx
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Kyle is converting 13°F to °C. His work is shown. Is Kyle's answer correct? If not, find his mistake and determine the correct answer to the nearest degree. Given: 5 9 (°F − 32) Step 1: 5 9 (13°F − 32) Step 2: 5 9 (45) Step 3: 25° C
Given:
The temperature is given in Fahrenheit (13 degree F).
To Find:
The correct temperature in Celsius.
Answer:
The temperature in Celsius is approximately -11 degree C.
Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.
Step-by-step explanation:
Any temperature can be changed from F to C by using the formula
[tex]C=(\frac{5}{9})(F-32)\\\\C=\frac{5(F-32)}{9}[/tex]
So, we will convert the given temperature in F to C by performing three simple steps.
Step 1 - We will subtract 32 from the Fahrenheit temperature.
Step 2 - Multiply this number by 5.
Step 3 - Divide the resulting number by 9.
So,
Step 1: 13-32 = -19
Step 2: -19*5 = -95
Step 3: -95/9 = -10.55 approx
Thus, the temperature in Celsius is approximately -11 degree C.
Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.
Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.
Given:
Kyle is converting 13°F to °C.
The formula used to convert F to C is
C= 5/9 (F- 32)
Now, Substitute F= 13 into the formulas as
C= 5/9 (13 - 32)
C = 5/9 (-19)
C= -95/ 9
C= -10.55
Thus, the temperature in Celsius is -11 degree C.
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Walter's savings account has a balance of $273. After 5 years, what will the amount of interest be at 5% compounded quarterly? a. $6.83 c. $77.00 b. $68.00 d. $82.00
Answer:
c
Step-by-step explanation:
sam and bethan share £54 pounds in the ratio 5:4 workout how much each person gets
ratio is 5:4
5+4 =9
54 pounds divided by 9 = 6
6*5 = 30
6*4 = 24
Sam gets 30 pounds Bethan gets 24 pounds
solve the system by substitution
2x-y+z=-4
z=5
-2x+3y-z=10
To solve the system by substitution, substitute the value of z in the equations and solve them simultaneously.
Explanation:To solve the system by substitution, we need to substitute the value of z in the other equations. Given that z=5, we can substitute this value in the first and third equations:
2x - y + 5 = -4
-2x + 3y - 5 = 10
Now, we can solve these two equations simultaneously to find the values of x and y.
To solve a system of equations by substitution, express one variable in terms of the other and substitute it into the other equations to eliminate that variable before solving for the remaining variables.
Explanation:To solve this system of equations by substitution:
Start by expressing one variable in terms of the other variable from one of the equations. In this case, we can express z as 5 since it is given.Substitute the value of z into the other two equations to eliminate the variable z.Solve the resulting system of equations for the remaining two variables.By following these steps, you can find the values of x, y, and z that satisfy the system of equations.
In ΔABC shown below, ∠BAC is congruent to ∠BCA:
Given: Base ∠BAC and ∠ACB are congruent.
Prove: ΔABC is an isosceles triangle.
When completed (fill in the blanks), the following paragraph proves that Line segment AB is congruent to Line segment BC making ΔABC an isosceles triangle.
Construct a perpendicular bisector from point B to Line segment AC.
Label the point of intersection between this perpendicular bisector and Line segment AC as point D:
m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector.
∠BDA is congruent to ∠BDC by the definition of congruent angles.
Line segment AD is congruent to Line segment DC by _______1________.
ΔBAD is congruent to ΔBCD by the _______2________.
Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ΔABC is isosceles by definition of an isosceles triangle.
Fill in the blanks 1 & 2.
A. 1. Angle-Side-Angle (ASA) Postulate
2. corresponding parts of congruent triangles are congruent (CPCTC)
B. 1. corresponding parts of congruent triangles are congruent (CPCTC)
2.Angle-Side-Angle (ASA) Postulate
C. 1. the definition of a perpendicular bisector
2. Angle-Side-Angle (ASA) Postulate
D. 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. the definition of a perpendicular bisector
The measurement of the complement of an angle exceeds the measure of the angle by 25%. Find the measurement of the angle and its complement.
The angle measures 40 degrees, and its complement, which is 25% larger than the angle, measures 50 degrees. This is solved using elementary algebra by setting up an equation with the angle as 'x' and its complement as '90-x', and then simplifying the equation to solve for 'x'.
Explanation:The question involves finding the measure of an angle and its complement when given that the complement exceeds the measurement of the angle by 25%. To solve this, let's use algebra. Let the measure of the angle be x degrees.
Since the complement of an angle adds up to 90 degrees with the angle itself, the complement can be represented as 90 - x degrees. According to the problem, the complement is 25% more than the angle, so we can write the equation:
90 - x = x + 0.25x
Simplifying, we get:
90 - x = 1.25x
90 = 2.25x
Dividing both sides by 2.25 gives us the measure of the angle x:
x = 40 degrees
Since the complement is 90 - x, we find:
Complement = 90 - 40 = 50 degrees
Therefore, the angle measures 40 degrees, and its complement measures 50 degrees.
A train travels from city a to city b and then to city
c. the distance from a to b is 200 miles and the distance from b to c is 70 miles. the average speed from a to b was 50 miles per hour, and the average speed from b to c was 35 mph. what was the average speed from a to c (that is for the entire trip) in miles per hour?
there are 18 rows of seats in the auditorium there are 24 seats in each row how many seats are in the auditorium in all
How to find the slope of a line perpendicular to each given line?
Find the volume of the triangular prism.
A. 120 yd3
B. 130 yd3
C. 240 yd3
D. 260 yd3
The equation of line AB is (y-3)=5(x-4) what is the slope of a line perpendicular to line AB
Introduction to addition or subraction of fractions with different denominator 2/3+1/4
Write 4.7 as a mixed number with a fraction in simplest form.
A) 4/7
B) 7/10
C) 4 1/7
D) 4 7/10
Answer:
D) 4 7/10
Step-by-step explanation:
Any fraction may be written as a mixed number. This type of number is formed by one or more whole parts plus a fractional part.
4.7 = 4 + 0.7
4 + 7/10
4 7/10
Following this same reasoning we can turn a mixed number into improper fraction and improper fraction into mixed number.
Consider the following equation, bh+hr=25 when solving for h
Answer:
[tex]h=\frac{25}{b+r}[/tex]
Step-by-step explanation:
Given equation,
[tex]bh+hr=25[/tex]
For solving this equation for h,
We need to isolate h in the left side of the equation,
We can write,
[tex]h(b+r) = 25[/tex] ( by the converse of distributive property ),
Divide both sides by b + r,
[tex]h=\frac{25}{b+r}[/tex]
Which is the required equation.