2a + 3b = 7
-> 3(2a + 3b) = 21
6x + 10y = 40
-> (6x+10y)/2 = 20
Therefore, 6a + 9b = 21 ; 3x + 5y = 20.
The value of 6a + 9b is 21 and the value of 3x + 5y is 20
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equations are,
2a + 3b = 7 (1)
and 6x + 10y = 40 (2)
To find the value of 6a + 9b,
Multiply equation (1) with 3,
3(2a + 3b) = 7 x 3
6a + 9b = 21
To find the vale of 3x + 5y,
Divide equation (2) by 2,
1/2(6x + 10y) = 40/2
3x + 5y = 20
The required values are 21 and 20.
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what is 3 +7x(2+9x) simplify as a expression
Find x ifwrewrijqeowehj
3x+x+(x+12)=152
<AOD =<COB(VERTICAL OPPOSITE ANGLES)
[tex]5x+12=152\\5x=152-12\\5x=140\\\frac{5x}{5} =\frac{140}{5} \\x=28[/tex]
x=28°
be reminded that <COB IS MADE OF ALOT OF BRANCH ANGLES THAT WE HAD TO ADD TO GET IT
i.e <COE,<EOF AND <FOB
How many was the phone before the discounted price?
Answer: depends how many you have with you
Step-by-step explanation:
does not matter how many you have
Q= (R-M) over 2
R-M/2
R= 21
M= 15
The image best explains, I cannot math and math cannot me, please I need help.
Answer:
3
Step-by-step explanation:
(21-15)/2
6/2
= 3
......
Answer:
3
Step-by-step explanation:
substitute the numbers into the equation Q= (21-15)/2
you then start with the numbers within the parathesis: 21 - 15 = 6
then divide it by 2: 6/2 = 3
answer: Q = 3
56x raise to power minos 4 divided by 14x raise to power minos 8
56x raise to power minus 4 divided by 14x raise to power minus 8 has its answer calculated as 4[tex]x^2[/tex] by solving through formulas of exponents and powers.
What are exponents?A mark placed exactly or right above a mathematical equation or a numeral that helps to denote the action of raising to a power of something.
Exponent is also defined as one of the methods of expressing many large numbers in terms of powers. This means that exponent refers to how many times a single number or an equation is multiplied by itself.
The statement 56x raise to power minus 4 divided by 14x raise to power minus 8 can be simplified in equational terms as
[tex]\frac{56x^-{4}}{14x^{-8}}[/tex]
which can be further simplified as [tex]4x^{4}[/tex]
What does the term Exponentiation stand for?Exponentiation is a type of mathematical operation that can be written as bⁿ, involving two numbers. The base b and then the exponent or power n is included in it and pronounced as "b to the power n".
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is the algebraic expression t^2/t^4 equivalent to t^2?
Answer: no
Step-by-step explanation:
t^2/t^4 is 1/t^2 which is not t^2
Complete the sentence below.
35 280 is ten times bigger than
Answer:
3528
Step-by-step explanation:
35280 divided by 10 is 3528. To check your work, multiply 3528 by 10. The answer is 35280.
Hope this helps! :)
are 5x^2 and -9x^2 like terms
true or false
Answer:
true
Step-by-step explanation:
when unlike terms are added, they cannot be "combined".
examples of unlike terms: [tex]2x +3[/tex] and [tex]5y - 2[/tex] and [tex]6y^2 - 4x^2[/tex]
[tex]5x^2 and -9x^2[/tex] are like terms because they both contain the variable x and have an exponent of 2.
Consider the function f(x) = x3 − 6x2 + 11x − 6.
PART A: One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). Use that factor to divide and further factor the polynomial and find the x-intercepts without using technology.
PART B: Describe key characteristics of the graph of the function such as the number of x-intercepts, the y-intercept, and the end behavior without using technology. Explain with complete sentences using components of the function to support your answer.
For the function x³ - 6x² + 11x - 6, we have that:
a) The x-intercepts are: x = 1, x = 2, x = 3.
b) The y-intercept is of y = -6, while the end behavior is that it decreases to the left and increases to the right.
What are the x-intercepts of the function?The function is given as follows:
f(x) = x³ - 6x² + 11x - 6
x - 3 is a factor of the function, meaning that x = 3 is a x-intercept and the function can be written as follows:
x³ - 6x² + 11x - 6 = (x - 3)(ax² + bx + c)
Then we have to build a system of equations to find the coefficients as follows:
x³ - 6x² + 11x - 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c.
Then the coefficients are given as follows:
a = 1.b - 3a = -6 -> b = -3.-c = -6 -> c = 2.Then the factor is given by:
x² - 3x + 2.
Hence the other intercepts of the polynomial are found when:
x² - 3x + 2 = 0
(x - 2)(x - 1) = 0.
x - 2 = 0 -> x = 2.
x - 1 = 0 -> x = 1.
What is the y-intercept and the end behavior?The y-intercept is the value of f(x) when x = 0, that is, f(0), hence:
f(0) = 0³ - 6(0)² + 11(0) - 6 = -6.
For the end behavior, we need to find the limits as x goes to infinity, hence:
Positive infinity = (∞)³ = ∞. -> increases to right.Negative infinity = (-∞)³ = -∞. -> decreases to left.When the limit goes to infinity, we consider only the term with the highest exponent of the polynomial.
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A leaky faucet drips 1/4 fluid ounce of water every 20 minutes. How many Gallons of water will leak from this faucet in 1 year? (Round to the nearest gal.)
Answer:
51
Step-by-step explanation:
I may have made a mistake somewhere along the way but if not then it is 51 gallons.
The way i did this was to multiply 20 minutes by 3 to equal an hour, then multiply that by 24 to equal a day, then multiply that by 365 to equal a year.
That gives you the numbers you need to multiply the ounce by. So first multiply 1/4 by 3 to get 3/4. Next you multiply 3/4 by 24 to get 72/4 or 18. Then you multiply 18 by 365 to get 6570 ounces in a year. Finally you translate that to gallons and you get 51.328125, which rounds down to 51.
Alsooo, i wouldnt mind a good old brainliest if im correct :)
Find the zeros of the functions:
f(x)=3x+7
f(x)=1/5x-7
Answer: x= -5
Step-by-step explanation: Zero is x
f(-5)= -15 +7= -8
f(-5)= -1 - 7 = -8
Answer is -8
reciprocal of b-1/b
FOR A RECIPROCAL OF FRACTION WE SWAP POSITIONS. WHATEVER WAS IN THE NUMERATOR BECOMES THE DENOMINATOR AND WHAT WAS IN THE DENOMINATOR BECOMES THE NUMERATOR.
THIS MEANS THAT AS A RESULTS WE HAVE
[tex] \frac{b}{b - 1} [/tex]
ATTACHED IS THE SOLUTION.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
d
Step-by-step explanation:
Pythagorean theorem : a2 + b2 = c2
Here, ‘a’ is the vertical side i.e. wall
‘b’ is the base side i.e. bottom = 5 m
‘c’ is the hypotenuse i.e. the ladder = 10 m
If b = 5 m, c = 10 m
Then, a2 = c2 - b2 = (10 x 10) - (5 x 5) = 75
a = √75 = 8.66 m
The the top of the ladder is at 8.66 m.
Sandeep is making fruit dip for a party. His recipe calls for 1/2 of a teaspoon of cinnamon and 3/4 of a cup
of yogurt. Using this ratio, how much cinnamon does Sandeep need if he uses 3 cups of yogurt?
2 teaspoon of cinnamon need if he uses 3 cups of yogurt
What is ratio ?By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part to part ratio, whereas the second is a part to whole ratio. The relationship between two separate entities or organizations is shown by the part-to-part ratio. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio describes how one group compares to another. For instance, five people enjoy reading books out of every ten persons. Since the ratio of the component to the total is 5:10, 5 out of every 10 persons enjoy reading.
Given that :Sandeep is making fruit dip for a party. His recipe calls for 1/2 of a teaspoon of cinnamon and 3/4 of a cup
of yogurt.
[tex]0.5 : 0.75 = x : 3[/tex]
x = 2
2 teaspoon of cinnamon need if he uses 3 cups of yogurt
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What’s the relationship between the number of
$4 lunches
you buy with a $100 school
lunch card and the money remaining on
the card
The relationship will be a solid line .
How to find the relationship between the given amounts?
Given:
The amount of one lunch =$4
The amount of the school lunch card=$100
Let, the amount remaining on the card= b
Let the number of lunches to buy = a
The equation is given by,
b = 100 - 4a
When 1 lunch is bought ,a= 1 ;
b= 100 - 4(1) = 96
When 2 lunches are bought ,a= 2;
b= 100 - 4 (2)= 92
When 3 lunches are bought ,a= 3;
b= 100 - 4 (3)= 88
When 4 lunches are bought ,a= 4;
b= 100 - 4 (4)= 84
Since ,the decrease is gradual and same, the relationship will be a solid line.
The complete question is:
What is the relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card. Is the relationship a solid line or a set on unconnected points?
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Write a quadratic function in standard form containing the point (-7, 5) and
vertex (1, 9)
The quadratic function in the standard form containing the point (-7, 5) and vertex (1, 9) is y = (-1/16)(x - 1)² + 9.
How is a quadratic function formed with a vertex and a point?The vertex form of a quadratic function with vertex (h, k) is written as
y = a(x - h)² + k, where (x, y) denotes a point on the parabola. Real integers a, h, and k are also included.
Given:
Point (x, y) = (-7, 5)
Vertex (h,k) = (1, 9)
The general equation of quadratic function in vertex form is:
y = a(x - h)² + k
To solve for a, substitute the given point (x,y) = (-7,5) into the equation.
5 = a(-7 - 1)² + 9
a(-8)² = -4
a = -4 /64
a = -1/16
Therefore, the required quadratic function is,
y = (-1/16)(x - 1)² + 9
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Ruby has $0.86 worth of pennies and nickels. She has 4 more nickels than pennies. Determine the number of pennies and the number of nickels that Ruby has.
86 = 1p + 5n
n = p + 4
86 = 1p + 5(p + 4)
86 = 1p + 5p + 20
66 = 6p; p = 11
86 = 1(11) + 5n
86 = 11 + 5n
75 = 5n; 15 = n
11 pennies, 15 nickels
11(1) + 15(15) = 11 + 75 = 86
subtract the quotiet of 70 divided by 2 from 60
The algebraic representation of the expression "subtract the quotiet of 70 divided by 2 from 60" is 60 - 70/2" which gives the result 25
Algebraic representation of expressionQuotient means the result obtained from the division of an expressionThe divisor is the expression or term used to divide the expressionThe dividend is the expression being divided by another expression.the quotiet of 70 divided by 2
= 70/2
subtract the quotiet of 70 divided by 2 from 60
= 60 - 70/2
= 60 - 35
= 25
In conclusion, the result of the expression "subtract the quotiet of 70 divided by 2 from 60" is 25
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Find an equation in point-slope form for the line having the slope m = -4 and containing the point (7,2)
Answer: y=-4x+30
Step-by-step explanation: put into point slope form y-y1=m(x-x1). M is out slope with the given point (7,2) 7 is out x and 2 is our y. Give us y-2=-4(x-7) once done distribute yo get y-2=-4x+28. Add the 2 from the left to the right. to get y=-4x+30
Which scale is equivalent to 1 cm to 1 km?
1 to 1,000
10,000 to 1
1 to 100,000
100,000 to 1
1 to 1,000,000
Answer:
1 to 100,000
Step-by-step explanation:
There are 100,000 cm in a km
katie is studying the polynomial and determines the polynomial has three real roots. do you agree or disagree with katie's statement? explain your reasoning.
Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. you disagree with Katies statement because the function has four real roots
Katie is studying the polynomial and determines the polynomial has three real roots. Do you agree or disagree with Katie's statement? Explain your reasoning.
the complete question is
Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. Do you agree or disagree with Katies statement? Explain your reasoning.
Write properties of function:
x intercept/zero: [tex]x_{1}[/tex] = 3/2 ; [tex]x_{2}[/tex] = 4 ; [tex]x_{3}[/tex] = -[tex]\sqrt{3}[/tex] ; [tex]x_{4}[/tex] = [tex]\sqrt{3}[/tex]
Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. you disagree with Katies statement because the function has four real roots
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Evaluate the exponential expression: (y 3/xy 2)²=_______, if x = 2 and y = 6.
1. 9
2. 36/144
3. 6/144
4. 15
The value of the exponential expressions is 9. Option 1
What is an algebraic expressions?
An algebraic expression can be defined as an expression that is composed of coefficients, variables, terms, constants, and also factors.
These expressions may also consist of arithmetic or mathematical operations such as;
ParenthesesMultiplicationDivisionSubtractionBracketAddition, etcGiven the exponential expression as;
(y³/xy²)²
For when x = 2 and y = 6
We have to substitute the value into the expression, we have;
{(6³/(2)(6)²)}
Find the cube and square of the values, we have;
{ 216/2(36) }²
expand the bracket
{ 216/72}²
Find the quotient
{3}²
Find the square
9
Hence, the value is 9
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At a health camp the number of children was three times the number of men.the number of men was 240 less than the number of women. if the number of children x give an equation that can be used to get the number of men if the total number of people who attended was 2400
The equation that can be used to get the number of men if the total number of people who attended was 2400 is x + 3x + x + 240 = 2400.
How to illustrate the information?It should be noted that from the information given, in the health camp the number of children was three times the number of men and the number of men was 240 less than the number of women.
Number of men = x
Number of children = 3x
Number of women = x + 240
Total number of people = 2400
The appropriate equation will be:
x + 3x + x + 240 = 2400
5x + 240 = 2400
Collect like terms
5x = 2400 - 240
5x = 2160
Divide
x = 2160 / 5
x =432
Therefore, the total number of men is 432 men.
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pls help ASAP
./././././././././././././././././././././././././././././././././././././././././././././././././././././././
Answer: the second one
Step-by-step explanation:
commutative is like
A+b=b+A
So 4+(-6)=-6+4
Which is like 4-6=-6+4
7-(-4) is__units from 7 in the ____ direction
7-(-4) is 4 units from 7 in the negative direction. See the explanation and the linear scale attached.
What direction is being referred to in the above Question?The direction being referred to is the direction of the number on a numerical scale or Linear Scale.
In the attached linear scale, we can see that the arrow stops at 11. This is arrived at by expanding the bracket:
7 - (-4)
the subtraction signs cancel out each other creating a positive sign. Hence we have:
7 + 4
= 11.
Hence, 11 is 4 units away from 7 in the negative direction. That is going toward zero is negative or a reduction hence, to get to 7 you need to go toward the negative section of the scale.
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convert -20°C to degrees Fahrenheit using the formula F = 9/5C + 32. (F=9/5(-20)+32)
Answer:
- 4° F
Step-by-step explanation:
substitute C = - 20 into the formula
F = ([tex]\frac{9}{5}[/tex] × - 20 ) + 32 = (9 × - 4) + 32 = - 36 + 32 = - 4° F
Hey need help with this problem! Will give brainliest if right
Answer: 9,800
Step-by-step explanation:
She should save 9,800 yearly.
2/10 = 20/100 ; 20%
20% = 0.2
0.2 x 49,000
(which is 20% of 49,000)
= $9,800
Please! Help me find the range of this graph as an inequality :((
Answer: [tex]\text{y} \ge 2[/tex]
Reason:
The lowest point on the graph occurs when y = 2. This is a closed endpoint so it's included with the graph. So either y = 2 or y > 2, both of which combine to get the answer shown above.
Activity 2: Which are not quadratic equations? How do you describe quadratic equation?
Answer:
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.
The weather forecast for the weekend is a 35% chance of rain on Saturday and a 65% chance of rain on Sunday. Your friend says that means there is a 100% chance of rain this weekend. What error did your friend make?
Answer:
Because these probabilities are independent, the friend was supposed to multiply them, not add them. So the probability of rain this weekend is
.35 × .65, or .2275, meaning that the probability of rain this weekend is 22.75%