Solve x² + 2x - 15 = 0.
The solutions to the equation are x = -5 and x = 3
How to solve the equation?The equation is given as
x^2 + 2x - 15 = 0
Expand the equation
So, we have
x^2 + 5x- 3x - 15= 0
Factorize
(x + 5)(x - 3) = 0
Solve for x
x = -5 and x = 3
Hence, the solutions to the equation are x = -5 and x = 3
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Which inequalities have no solution?
X>X
-3x < -3x
-4+X>-2+X
X-2
In mathematics, an inequality is a relation which makes a non-equal comparison between the two numbers or other mathematical expressions. Inequalities have no solution are X>X, -4+X>-2+X.
What do you mean by inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to the another value.
The a ≠ b says that a is not equal to bThe a < b says that a is less than bThe a > b says that a is greater than b (those two are known as strict inequality)The a ≤ b means that a is less than or equal to bThe a ≥ b means that a is greater than or equal to b.Inequalities are governed by following properties. All of these properties also hold if all of non-strict inequalities (≤ and ≥) are replaced by their corresponding strict inequalities (< and >) and — in case of applying a function — monotonic functions are limited to the strictly monotonic functions.
From the above equations, the inequalities having no solutions are,
X>X
-4+X>-2+X
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Question 2
Find the unit rate.
If there are 8 teaspoons for every 4 cups in a recipe. How many
teaspoons are there in one cup?
teaspoons
Find equations that enclose a region such that when rotated about the x -axis, a solid is produced with a volume of 18π cubic units.
∫45 πy2 dx is that enclose a region such that when rotated about the x -axis, a solid is produced with a volume of 18π cu units .
How do you determine a region's volume?
Depending on the axis of revolution, r=f(x) or r=f(y) and V=Adx or Ady, where A denotes the usual disc's area. The volume of the solid produced by a region under f(y) (to the left of f(y)) that is rotated around the y-axis and is bounded by the horizontal lines y=c and y=d.Volume of the solid = ∫45 πy2 dx
= π ∫45 4x dx
= 4π (x2 / 2)45
= 18π cu units
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Determine a base and a height
Answer:
base : 7 units
height : 4 units
A brick path is being installed around a circular pond. The pond has a circumference of 68 feet. The outer edge of the path is going to be 4 feet from the pond all the way around. What is the approximate circumference of the path? Round to the nearest hundredth.
The approximate circumference of the path Round to the nearest hundredth is 93.12 feet.
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
circumference of pond = 68 feet
⇒ 2πr = 68
⇒ r = 34/π
⇒ r = 10.82 feet
Now it is also given that, The outer edge of the path is going to be 4 feet from the pond all the way around
⇒ Radius of path, R = r + 4
⇒ Radius of path, R = 10.82 + 4
⇒ R = 14.828
So,circumference of the path = 2πR
⇒ circumference of the path = 2π*14.828 = 93.119 feet
⇒ circumference of the path Round to the nearest hundredth = 93.12 feet
Thus, the approximate circumference of the path Round to the nearest hundredth is 93.12 feet.
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A stop sign in the shape of a regular octagon is inscribed in a circle. Find following measure.
m< RLQ
The measure of arc NPQ is 180° while the measure of m <AOB is 69°.
What is the inscribed of a circle?An inscribed angle of a circle is an angle whose vertex is a point A on the circle and whose sides are line segments (called chords) from A to two other points on the circle.
An octagon is known to be a type of polygon that is said to have up to 8 sides. the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane. A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°.
The measure of arc NPQ is 180° while the measure of m <AOB is 69°.
The complete question is:
A stop sign in the shape of a regular octagon is inscribed in a circle.
What is the measure of arc NPQ?
A. 45°
B. 90°
C. 135°
D. 180°
2. In the figure at the right points A, B, C are on 00, and m<ACB = 690
What is the m<AOB?
A. 69°
B. 138°
C. 2780
D. 360°
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A student has some 1 bills and 5 bills in his wallet. He has a total of 15 bills that are worth 47 . How many of each type of bill does he have?
If a student has some 1 bills and 5 bills in his wallet and he has a total of 15 bills that are worth 47, then the number of 1 bills he has is equal to 7 and the number of 5 bills he has is equal to 8.
The number of bills of each type can be calculated by forming a system of equations.
Consider x to be the number of 1 bills and y to be the number of 5 bills.
The first equation can be given as,
x + y = 15
The second equation can be given as,
x + 5y = 47
The two equations can be solved by using the substitution method:
By rearranging the first equation the value of x can be calculated to be,
x + y = 15
x = 15 - y
Putting this value of x in the second equation,
x + 5y = 47
15 - y + 5y = 47
4y = 47 - 15
4y = 32
y = 32 ÷ 4
y = 8
The value of x can be determined by putting y = 8 in the first equation,
x + y = 15
x + 8 = 15
x = 15 - 8
x = 7
Hence, the number of 1 bills and 5 bills are equal to 7 and 8 respectively.
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Help marking brainlest and worth 20 points
let x^3-2x^2-6x+7=0 be a polynomicsl equation
Find all potential rational solutions using the rational route therom. Separate multiple solutions with commas if necessary.
Find all the distinct actual rational solutions. Separate multiple solutions with commas if necessary. If no solutions exist, enter none
The solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).
What is a polynomial?
A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given equation is x³ - 4x² - 7x + 10 = 0. The equation will be solved as,
x³ - 4x² - 7x + 10 = 0
x³ - 3x² - 10x - x² + 3x + 10 = 0
( x² - 3x - 10) ( x - 1 ) = 0
( x² -5x + 2x - 10 ) ( x- 1) = 0
( x - 5 )( x + 2 )( x - 1 ) = 0
Therefore, the solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).
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True or False?
4 and 1/4 are opposites
URGENTT ! PLEASE HELP :3
Question
Find the sum.
(1−5q)+2(2.5q+8)
Answer:
[tex]1 - 5q + 5q + 16 \\ = 17[/tex]
It takes Andrea 12.5 hours to drive 875 miles. What was her average Speed?
Answer:
70 miles per hour
Step-by-step explanation:
take 875mi and divide by how long it took: 12.5 hours
Solve each equation. h/5 = 215
Answer:
h= 1,075
Step-by-step explanation:
reverse the operations, 6th grade stuff man
5 x 215=h
Suppose we draw a single card from a deck of 52 fair playing cards. what is the probability of drawing an ace or a two?
The probability of getting an Ace is 1/13.
Probability of an event = number of favorable outcomes for the event/number of all possible products.
First, let's calculate the number of all possible outcomes. Randomly picking the cards could result in each of the 52 being selected. So, there are 52 possible outcomes.
But if you want an Ace in your desired event, you have four options—ace of Spades, Ace of Clubs, Ace of Hearts, and Ace of Diamonds. Therefore, the number of favorable outcomes for Aces = 4.
Therefore,
The probability of getting an Ace with a deck of 52 cards = 4/52 = 1/13.
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Write a function rule for each relation below.
1)
X:
-2
-1
0
1
2:
Y
-2
2
6
10
14
Answer:
x | y
-2. -2
-1. 2
0. 6
1. 10
2. 14
how many numbers do we have between each number on Y? 4
Step 1
this you have to use this data to make your function
f(x)=4X
Always you have to use the spaces times X
Step 2
We have to calculate what do we need to satisfy the function, in this case we have to add 6
f(x)=4x+6
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
The expression is simplified to s = -5/ 4
What are algebraic expressions?Algebraic expressions are expressions composed of terms, variables, constants, factors and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc
Given the expression;
42 = 14{ 4 + 4/ 5s}
Divide both sides by 14
42/14 = 14{ 4 + 4/ 5s}/14
3 = 4 + 4/ 5s
3 = 20 + 4s/5
cross multply
15 = 20 + 4s
collect like terms
15 - 20 = 4s
-5 = 4s
Make 's' the subject
s = -5/ 4
Thus, the expression is simplified to s = -5/ 4
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What is the Term for an answer that was obtained in a fair or controlled test
When a ball is bounced on a smooth surface, the angles formed by the path of the ball are congruent. If the path of a ball forms a 53^{\circ} angle with the floor, find \(m \angle A B C\).
The ball hits the surface at 43.5° and bounces back at 43.5°.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given that When a ball is bounced on a smooth surface, the angles formed by the path of the ball are congruent.
If the path of a ball forms a 53 angle with the floor, find the angle with the floor, x
Let the angle with the floor, x
Using, to find x, setup the equation:
x+ 53 +x=180
2x+ 53 =180
2x = 127
x= 43.5°
Therefore, the ball hits the surface at 43.5° and bounces back at 43.5°.
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WRITING IN MATH Explain why the order of the vertices is important when naming congruent triangles. Give an example to support your answer.
Because we are saying that the angles/edges in corresponding positions for each triangle are congruent.
Consider the triangle congruence statement below:
△ABC≅△DEFThis is actually a collection of six—yes, six—congruence statements.
They are as follows:
∠A≅∠D∠B≅∠E∠C≅∠FAB≅DEAC≅DFBC≅EFAs an example, consider the first congruence: ∠A≅∠D
This is implied by the fact that A and D are both listed first in their triangles (in the statement △ABC≅△DEF ). Similarly, B and E are in second place, so that's how we get ∠B≅∠E.A similar logic applies to the sides that have corresponding vertices.If the triangle congruence statement was as follows:
△ABC≅△FED
Then,
∠A would-be congruent to ∠F∠B would be congruent to ∠E∠C would be congruent to ∠DWe can see how changing the order of the triangle names changes which angles/edges are implied to be congruent.
This is why we must be cautious to name the triangles in the correct order. Otherwise, we risk claiming that two angles (or line segments) are congruent when they are not.Therefore, we are saying that the angles/edges in corresponding positions for each triangle are congruent.
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9.
(9x + 25)*
(13x - 19) /(17y + 5),
m
After simplification the solution of the given expression (9x + 25)(13x - 19)/(17y + 5) is 117x² + 154x - 475/(17y + 5).
What are expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.You must substitute a number for each variable and perform arithmetic operations to evaluate an algebraic expression. Because 6 + 6 = 12, the variable x in the preceding example is equal to 6. We can evaluate the expression after replacing the variables with their values if we know their values.So, (9x + 25)(13x - 19)/(17y + 5):
(9x + 25)(13x - 19)/(17y + 5)9x(13x - 19)+ 25(13x - 19)/(17y + 5)117x² - 171x + 25(13x - 19)/(17y + 5)117x² - 171x +325x - 475/(17y + 5)117x² + 154x - 475/(17y + 5)Therefore, after simplification, the solution of the given expression is 117x² + 154x - 475/(17y + 5).
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Select the values that make the inequality s ≤ 6 s≤6 true. (Numbers written in order from least to greatest going across.) -2 1 3 5 5.9 5.99 5.999 6 6.001 6.01 6.1 7 9 11 14
The numbers that makes the inequality s ≤ 6 true include:
-2,1, 3, 5, 5.9, 5.99, 5.999. 6How to interpret inequality graphInequality graphs are graphs made to represent inequality equations.
the equation s ≤ 6 is interpreted to be the value of s that is less than or equal to 6.
From the interpretation, any value from 6 downwards is the correct answer. Hence we have the correct numbers listed as:
-2,1, 3, 5, 5.9, 5.99, 5.999. 6Other numbers above 6 are wring and do not fit in
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Can someone pls help me I need to know if I am correct
If you have the fraction - 8/5 (the negative sign is not on either 8 or 5) it means that both numbers are negative right?
Answer:
Yes, that means the whole fraction is negative.
Also for future note, if the negative is on the top or bottom, the fraction will still be negative. Unless it says to simplify.
Hope this helps!
What is the value of x?
6
O 7
08
09
Answer:
7
Step-by-step explanation:
5x + 3 = 38
5x + 3 - 3 = 38 - 3
5x = 35
5x ÷ 5 = 35 ÷ 5
x = 7
Given point Y is between X and Z, where XY = 12 and XZ = 48, What is YZ?
Answer: 36
Step-by-step explanation:
XZ=XY+YZ
48=12+YZ
48-12=12-12+YZ
YZ=48-12
YZ=36
Find the 17 th term of each sequence. a₁₆ = 1/5, d= 1/2
7/10 is 17th term of sequence a₁₆ = 1/5, d= 1/2.
Given the 16th term and the common difference, we add the common difference from the 16th term to determine the 17th term:
a₁₇ = a₁₆ + d
= 1/5 + 1/2
= 7/10
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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What is the difference between an arithmetic sequence and an arithmetic series?
Answer:
arithmetic sequence is a sequence where the difference between a successive terms is constant
Step-by-step explanation: arithmetic series is the sum of the terms of an arithmetic sequence
i need help pls 56 points!!!!!!!
3/4, lines are parallel if they have the same gradient!!
What is the area of the figure below?
The area of the figure is 289 square unit
What is Area of a Rectangle ?The area of a rectangle can be calculated by multiplying the length and the width of the shape.
Given that
L = 20 - xB = 3x + 8A = LBBut the length and the width have two equal opposite sides. The shape is a square
20 - x = 3x + 8
20 - 8 = 3x + x
12 = 4x
x = 12/4
x = 3
L = 20 - 3 = 17
B = 3(3) + 8
B = 9 + 8
B = 17
A = 17 x 17
A = 289 square unit
Therefore, the area of the figure is 289 square unit
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Hurry please i need these done Asap?Jessica is making matching book bags for her 4 friends. 1 7/8 yards of fabric.
Moon and stars- 7 1/2
softballs- 7.4
stripes- 7 3/5
tie-dye- 7.9
Indicate which of the fabrics Jessica can and cannot use to make all of the book bags for her friend.
moons and stars can or cannot
softballs can or cannot
stripes can or cannot
tie-dye can or cannot
The fabric that she cannot use is the softballs.
Which fabric can she not use?A proper fraction is a non-integer that is made up of a numerator that is smaller in value than the denominator. A mixed fraction is a fraction that is made up of an integer and a proper fraction. An example of a mixed fraction is 1 7/8.
The first step is to determine the total amount of fabric needed for the 4 friends : 1 7/8 x 4
15/8 x 4 = 60 /8 = 7 1/2 yards
The second step is to convert the mixed fractions to decimals, by dividing the numerator by the denominator and adding the integer.
7 1/2 = 7.5
73/5 = 7.6
The fabric that cannot be used as the fabrics that are less than 7.5 yards.
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