Two or more expressions with equal sign is equation, if the equation 5k^2−20k=15 then 1 and 3 are exact values of the solutions.
What is Equation?Two or more expressions with equal sign is called as Equation.
The given equation 5k^2−20k=15,
let us make it a QE by taking 15 to left.
5k^2−20k-15
a=5, b=-20, c=-15
k=-b±√b^2-4ac/2a
=20±√(-20)^2-4(5)(-15)/2(5)
=20±√400-300/10
=20±√100/10
=20±10/10
k=20+10/10 or k=20-10/10
k=3, or k=1
Therefore the solutions of equation 5k^2−20k=15 are 1 and 3.
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I need more help on other questions! Same assignment
Answer:
a. [tex]\frac{10}{3}[/tex]
b. [tex]\frac{4}{3}[/tex]
c.[tex]4\frac{2}{3}[/tex]
Step-by-step explanation:
a.
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]
[tex]3\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{7}{2}[/tex]
b.
reciprocal is technically the opposite
c.
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]
[tex]=\frac{7}{2}\div \frac{3}{4}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]=\frac{7}{2}\times \frac{4}{3}[/tex]
[tex]\mathrm{Cross-cancel\:common\:factor:}\:2[/tex]
[tex]=\frac{7}{1}\times \frac{2}{3}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]\frac{7\times \:2}{1\times \:3}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:7\times \:2=14[/tex]
[tex]=\frac{14}{1\times \:3}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:1\times \:3=3[/tex]
[tex]=\frac{14}{3}[/tex]
[tex]\mathrm{Convert\:improper\:fraction\:to\:mixed\:numbers}[/tex]
[tex]4\frac{2}{3}[/tex]
Exactly 120 years ago, students planted a tree in front of their school. Since then, the tree has grown 33 meters taller and the distance around the trunk has increased by 3 meters. Use pencil and paper. Describe how you can use this information to find at least two different unit rates. Then find these unit rates.
Answer: Rate of tree's height per year = 0.275 m per year.
Rate of tree's trunk per year = 0.025 m per year.
Step-by-step explanation:
Given data,
Exactly 120 years ago, students planted a tree in front of their school
Since then, the tree has grown 33 meters taller
The distance around the trunk has increased by 3 meters.
Define Unit rate :
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
So, we can write,
There are 2 various unit rates in this:
The increase of the tree's height per year
The increase of the tree's trunk per year
Let us assume,
The increase of the tree's height per year = x
The increase of the tree's trunk per year = y
we can solve it :
Rate of tree's height per year x = 33m / 120 years
x = 0.275 m per year.
Rate of tree's trunk per year y = 3m / 120 years
y = 0.025 m per year.
Therefore,
Rate of tree's height per year = 0.275 m per year.
Rate of tree's trunk per year = 0.025 m per year.
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WILL give branilist if correct!! Answer both questions correctly
Answer:
6. perfect squares 5 and 6
7. between integers 5 and 6
Step-by-step explanation:
[tex]\sqrt[3]{141} = 35.62\\[/tex]
Find the area of a parallelogram with a base of 9 ft a height of 4 ft.
Suppose you have entered a 42-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 5 miles per hour, and during your bicycle race, your average velocity is 27 miles per hour. You finish the race in 4 hours. What is the distance of the run? What is the distance of the bicycle race?
The distance of the running is 15 miles and the distance of the bicycling is 27 miles.
According to the statement,We have to find that the distance of the run and the bicycle race.
So, For this purpose, we know that the
The distance between two points is that the length of the trail connecting them.
From the given information:
you have entered a 42-mile biathlon that consists of a run and a race. During your run, your average velocity is 5 miles per hour, and through your race, your average velocity is 27 miles per hour. You finish the race in 4 hours.
Then
Total distance of the race = 42 miles
The average velocity of the running = 5 miles per hour
The average velocity of the bicycling = 27 miles per hour
Then
If let he covers 27 miles with the cycles then
The distance he runs = 42-27
The distance he runs = 15.
Then it means he runs for a 3 hours.
So, The distance of the running is 15 miles and the distance of the bicycling is 27 miles.
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Mr. Jordan's class is having a pizza party with the $100 they earned in a competition. A cheese pizza costs $10, and a pepperoni pizza costs $15. They must order at
least 2 pepperoni pizzas. They also must order at least twice as many cheese pizzas as pepperoni pizzas.
What is the greatest total number of pizzas Mr. Jordan's class can order?
7
please answer asap. 100 points and marked brainliest!
Answer:5 per Gallone
Step-by-step explanation:
Answer:
Gas in India is $3.88 per gallon.
This is MORE expensive than $2.36 per gallon.
Step-by-step explanation:
Use the conversion factors given to change rupees to dollars and liters to gallons. See image.
(and btw, this question has very outdated information. Gas is $5.90 per gallon today in this poster's City, State, USA)
Which equation and number line show that a number and its opposite are additive inverses?
Which equation and number line show that a number and its opposite are additive inverses?
An equation and number line which shows that a number and its opposite are additive inverses is: 2 + (-2) = 0 in graph B.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
What is an additive inverse?An additive inverse can be defined as a number (n) which when added to another number (a) makes it equal to zero (0). This ultimately implies that, an additive inverse is the opposite of another number (a).
Mathematically, an additive inverse can be represented by the following expressions:
a + n = 0
a = -n
In this context, we can reasonably infer and logically deduce that an equation and number line which shows that a number and its opposite are additive inverses is 2 + (-2) = 0 in graph B (see attachment).
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Amos says that the opposite and the absolute value of a number are always the same
Amos says that the opposite and the absolute value of a number are always the same. This is true.
How to express the information?It should be noted that from the information, Amos says that the opposite and the absolute value of a number are always the same.
For example, given the number 23, the opposite will be -23 and the absolute value is also -23. This implies that they are the same.
Therefore, Amos says that the opposite and the absolute value of a number are always the same. This is true.
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Amos says that the opposite and the absolute value of a number are always the same. True or false.
Help Please!!!!!
.
.
.
.
By using algebra and trigonometry properties, the expression (cot² t + 1) · (sin² t + 1) is equivalent to the expression cot² t + 2.
How to prove a trigonometric equivalence
In this problem we find an equivalence between two trigonometric expressions. This can be done by transforming the expression at one side by using algebra and trigonometry properties until the expression of the other side is found. The procedure is now presented and explained:
(cot² t + 1) · (sin² t + 1) Given
(cot² t + 1) · sin² t + (cot² t + 1) Distributive property
cot² t · sin² t + sin² t + cot² t + 1 Distributive property
cos² t + sin² t + cot² t + 1 cot t = cos t / sin t / Associative and commutative properties / Existence of multiplicative inverse / Modulative property
1 + cot² t + 1 cos² t + sin² t = 1
cot² t + 2 Commutative and associative properties / Definition of addition
Thus, the expression (cot² t + 1) · (sin² t + 1) is equivalent to the expression cot² t + 2.
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Will Give Brainliest!!!! Match each step with the correct justification.
Given: QM MR
a. Given
b. Subtraction Property of Equality
c. Addition Property of Equality
d. Substitution.
e. Division Property of Equality
Answer:
A D B C E
Step-by-step explanation:
That is the order of steps in the solution
Write an equation for a line perpendicular to y = 3x + 2 and passing through the point (9,1)
Step-by-step explanation:
the slope of a line is always the factor of x, and it is defined as ratio (y coordinate change / x coordinate change) when going from one point to another on the line.
in that sense it is y/x.
the perpendicular slope turns that ratio upside-down and flips the overall sign.
so, in our case, the original slope is 3 = 3/1.
the perpendicular slope is then -1/3.
so, now, we have the slope and a point, and we can start with the point-slope form of the line equation :
y - y1 = a(x - x1)
"a" being the slope, (x1, y1) being the point.
y - 1 = -1/3 × (x - 9) = -x/3 + 3
y = -x/3 + 4
and that is the usual slope-intercept form
y = ax + b
"a" is again the slope, "b" is the y-intercept (the y value when x = 0).
Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra. How old is Pamela now?
Pamela is 1 year old now.
How to solve problems on ages ?
If the present age of a person be X, thenAge after n years = X +n
Age n years ago = X - n
n times the present age = nX
If ages in the numerical are mentioned in the ratio A : B, then A : B will be AX and BX.
If the sum of ages is X and Y and the ratio of their ages is p : q respectively, then you can determine the age of Y by using the formula shown below:Age of Y = Ratio of Y / Sum of ratios x sum of ages
Age of Y = q/ (p +q) x A
In the given statement is:
Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra.
To find the how old is Pamela now.
Now, Based on the given conditions,
Formulate:
Let x be the Pamela's age
6 + 7 + x = 2(6 + x)
13 + x = 12 + 2x
x - 2x = 12 - 13
-x = -1
x = 1
Hence, Pamela is 1 year old now.
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Ms. Cody needs 2.65 yards of fabric to make one pillow. How many yards of fabric will she need to make 17 pillows?
Ms. Cody needs 45.05 yards of fabric to make 17 pillow.
What is referred as the unitary method?The unitary formula is used to measure the value of one unit given a multiple.The unitary method determines the value of a unit and then calculates the value of a necessary number of units.If we need to calculate the ratio with one quantity to another, we must employ the unitary method.The value of a unit quantity is determined by calculating first in the unitary method before calculating the value of other units. It comes in two varieties.Variation in DirectVariation in the inverseFor the given question;
Ms. Cody needs 2.65 yards of fabric to make one pillow.
For finding yards for 17 pillows, simply multiply the given yards by 17.
For 17 pillows = 17×2.65
For 17 pillows = 45.05
Thus, 45.05 yards of fabric is required to Ms.Cody to make 17 pillows.
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The larger of two numbers is 10 less than the smaller number. The sum of the two numbers is 50 . Find the two numbers.
The value of the two numbers are 30 and 20.
According to the statement
We have to find that the value of the two numbers.
So, For this purpose, we know that the
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
From the given information:
The larger of two numbers is 10 less than the smaller number. The sum of the two numbers is 50.
Then
Let the first number be x and the second number y
Then
y = x -10
And
x+y = 50
Then
Substitute the value then
x+x-10 = 50
2x = 50+10
2x = 60
x =30
Then
y = x -10
y = 30 -10
y = 20
So, The value of the two numbers are 30 and 20.
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Given f(x)=(x+3)^2 and g(x)=|x+1| , which value is a solution to the equation f(x)=g(x) ?
A. –5
B. 5
C. 4
D. -1
help asap pls
Answer:
A) [tex]x = -5[/tex]
Step-by-step explanation:
[tex](x + 3)^2 = | x + 1 |\\\to x^2 + 6x + 9 = | x + 1|[/tex]
Case 1: x + 1 is positive
[tex]x^2 + 6x + 9 = x + 1\\\to x^2 + 5x + 8 = 0\\\to \text{No solutions.}[/tex]
Case 2: x + 1 is negative
[tex]-x^2 - 6x - 9 = x + 1\\\to 0 = x^2 + 7x + 10\\\to 0 = (x + 5)( x + 2)\\\to x = -5 \text{ or } x = -2[/tex]
elise does not like sorbet
Answer: wdym
Step-by-step explanation:
Elise doesn't like sorbet.
(Assuming we fix the grammar???)
PLEASE HELP!
Solve for x: 1 < x + 3 < 4
4 > x > 7
4 < x < 7
−2 > x > 1
−2 < x < 1
Answer:
the last choice
Step-by-step explanation:
u will minus 3 from each side. that's the point
Athena's credit card has an APR of 32.99%. If her current monthly balance, before interest, is $2,719.83, what amount will she be charged for interest?
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. Athena's will be charged $74.77 for interest.
What is Interest Rate?The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.
Given,
Athena's credit card has an APR of 32.99%.
We need to convert the percentage to decimal.
32.99%=32.99/100
=0.3299
The amount will she be charged for interest is
=(2719.83*0.3299)/12
=897.27/12
=74.77
Therefore Athena's will be charged $74.77 for interest.
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Look for a pattern in the following list. Then use this pattern to predict the next number.
1
1
6,6,7,7,8,...
Type the next number in the list.
7.
"
6,
(Type an integer or a fraction.)
***
...
-3(-7b + 3) + 8b = 5b-4(1 - 6b)
Answer:
No solution
Step-by-step explanation:
Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that (28 + 45) squared = 73 squared.
3 squares are positioned to form a right triangle. The small square is labeled 28, medium square is 45, and large square is not labeled.
Which best describes Nadia’s solution?
She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate.
She is incorrect because she should have used 45 as the length of the hypotenuse.
She is incorrect because she should have squared each leg length and then found the sum.
She is correct because the hypotenuse is the longest side of the triangle.
Nadia's solution is incorrect because she should have squared each leg length and then found the sum.
What is the Pythagorean theorem?A right angled triangle is a three-sided polygon. The three sides are the length, base and the hypotenuse. The hypotenuse is the longest side of the triangle. The sum of angles in a right angled triangle is 180 degree.
The Pythagorean theorem can be used to determine the length of the hypotenuse given the lengths of the other sides of the triangle. According to this theorem, the sum of the square of the two sides is equal to the length of the hypotenuse.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse28² + 45²
= 784 + 2025 = 2809
Hypotenuse = √2809= 53
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Answer:c
Step-by-step explanation:
I did the quiz
need help with # 6 asap
The equation that is parallel and perpendicular are y + 4 = 7/5(x-35) and y+4 = -5/7(x - 35) respectively.
Equation of a lineA line is defined as the shortest distance between two points. The formula for finding the equation of a line in point slope form is:
y - y₁ = m(x-x₁) (Parallel lines)
y - y₁ = -1/m(x-x₁) (Perpendicular lines)
Given the following parameters;
Point = (35, -4)
Given the equation 7x-5y = 0
5y = 7x
y = 7/5x
Slope = 7/5
Substitute the slope and point into the equation
y + 4 = 7/5(x-35) (Parallel lines)
y +4 = -1/(7/5)(x-35) (Perpendicular lines)
y+4 = -5/7(x - 35)(Perpendicular lines)
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In an election, 313 votes are cast. How many votes are needed to have a majority of
the votes in this election?
Answer with a whole number of votes.
¿Es este polígono un paralelogramo ? Explica
Answer: No veo lo que estás mirando. Pero aquí hay un consejo para ayudarte. Un paralelogramo es una figura con cuatro lados en los que los lados opuestos son paralelos.
¡Espero que esto ayude! :)
Your teacher has 48 juice boxes and 64 candies for a Halloween party. Each student will receive the same amount of juice boxes/candies, and all juice boxes/candies must be used.
The greatest number of students that can attend the party is 16.
Given, the teacher has 48 juice boxes and
64 candies for a Halloween party.
Each student will be given an equal number of juice boxes or sweets, and each one must be consumed.
how many (greater) number of students can attend the party = ?
In order to determine the greatest students we need to calculate the greatest common divisor of the numbers.
To calculate the greatest common divisor, we need to find out the prime factors of each number.
Therefore, by the method of prime factorization.
Prime factors of 48 = 2 × 2 × 2 × 2 × 3
Prime factors of 64 = 2 × 2 × 2 × 2 × 2 × 2.
Now, HCF of (48,64) = 2 × 2 × 2 × 2 = 16
Therefore we get the gcd as 16.
Hence the greatest number of students who can attend the party is 16.
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1. Triangle ABC with coordinates A(12, -3), B(12, 3) and C(-1, -1) is reflected across
the line Y=3. What are the new coordinates?
Answer:
A'(12,9), B'(12,3), C'(-1,5)
Step-by-step explanation:
A is 6 units from the line y=3, so it will map to be 6 units away on the other side of y=3, to the point (12, 9).
Similarly, B' has coordinates (12,3) and C' has coordinates (-1, 5)
Who invented and defined zero
Answer:
Brahmagupta in 628
Step-by-step explanation:
Answer:
Zero and its operation are first defined by Brahmagupta in 628. He developed a symbol for zero: a dot underneath numbers.
Will give Brainliest!!!!!!!
Answer:
[tex]56e \geqslant 53 \geqslant [/tex]
Hi
Estimate the probability that an NBA player who makes 80% of his free throws makes 2 of his next 3 free throws.
The probability that an NBA player who makes 80% of his free throws makes 2 of his next 3 free throws is 0.384
What is probability?Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases.
Now it is given that,
The proportion of free throws the player makes, p = 80% = 0.8
The number of throws, n = 3
The throws the player makes, r = 2
Since the probability is given as,
P(r) = nCr x p^r x (1 - p)^(n-r)
So, the probability that an NBA player makes 2 of his next 3 free throws
Putting the values we get,
P(2) = ³C₂ x (0.8)^2 x (1 - 0.8)^(3-2)
Solving we get,
P(2) = 3 x 0.64 x (0.2)^(1)
Thus we get,
P(2) = 3 x 0.64 x 0.2
Multiplying we get,
P(2) = 0.384
this is the required probability that an NBA player makes 2 of his next 3 free throws.
Thus, the probability that an NBA player who makes 80% of his free throws makes 2 of his next 3 free throws is 0.384
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