Answer:
a = 2 and b = - 1
Step-by-step explanation:
distribute the left side of the equation and compare the like terms with terms on the right side
7ay² + 7by - 21
compare the coefficients of like terms with 14y² - 7y - 21
7a = 14 ⇒ a = 2
7b = - 7 ⇒ b = - 1
The value of a and b from the given equation is 2 and -1 respectively;
Given the equation [tex]7(ay^2+by-3)=14y^2-7y-21[/tex]
In order to get the value of a and b that will make the equality equation true, we will have to factorize first;
[tex]7(ay^2+by-3)=14y^2-7y-21\\7ay^2+7by-21=14y^2-7y-21\\[/tex]
Next is to compare both sides to get the unknown value
[tex]7ay^2=14y^2\\7a=14\\a=\frac{14}{7}\\a =2[/tex]
Get the value of "b"
[tex]7by=-7y\\7b=-7b\\b=\frac{-7}{7}\\b=-1[/tex]
Hence the value of a and b from the given equation is 2 and -1 respectively;
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Suppose you deposit $1500 in a savings account that pays interest at an annual rate of
6%. No money is added or withdrawn from the account How many years will it take for the account to contain 2500?
Fiona and Iliana went to a going-out-of-business sale at a local video store. The store was advertizing all HD videos on sale for one price and all classic videos for a different price. Fiona bought 5 HD videos and 2 classic videos for $31. Iliana bought 5 classic videos and 3 HD videos for $30. Which system of equations can be used to find the prices of the classic and HD videos?
Answer:
5h + 2c = 31
5c + 3h = 30
Step-by-step explanation:
Let h = HD video price
Let c = classic video price
Fiona bought 5 HD videos and 2 classic videos for $31
5h + 2c = 31
Iliana bought 5 classic videos and 3 HD videos for $30
5c + 3h = 30
This is the system of equations
5h + 2c = 31
5c + 3h = 30
Answer:
Correct answer on test is D. 5 x + 2 y = 31. 3 x + 5 y = 30.
Step-by-step explanation:
Use the drop-down menus to complete each equation so the statement about its solution is true?
5 - 4 + 7x + 1 = 7x + (5 - 4 + 1) = 7x + 2
NO SOLUTIONS:
5 - 4 + 7x + 1 = 7x + a (a - any real number, except 2)
ONE SOLUTION:
5 - 4 + 7x + 1 = bx + c (b - any real number, except 7, c - any real number)
INFINITELY MANY SOLUTIONS:
5 - 4 + 7x + 1 = 7x + 2
Examples:
2x + 3 = 2x + 5 subtract 2x from both sides
3 = 5 FALSE (NO SOLUTIONS)
2x + 3 = x - 4 subtract x from both sides
x + 3 = -4 subtract 3 from both sides
x = -7 (ONE SOLUTION)
2x + 3 = 2x + 3 subtract 2x from both sides
3 = 3 TRUE (INFINITELY MANY SOLUTIONS)
1) For No Solution
5 - 4 + 7x +1 = 7x
2) For One Solution
5- 4 +7x + 1 = 3
3) For No Solution
5 - 4 + 7x + 1 = 7x + 2
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
1) For No Solution
5 - 4 + 7x +1 = 7x
2) For One Solution
5- 4 +7x + 1 = 3
3) For No Solution
5 - 4 + 7x + 1 = 7x + 2
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Eli's office recycled a total of 12 kilograms of paper over 6 weeks. After 9 weeks, how many kilograms of paper will Eli's office have recycled
Answer:
18 kg
Step-by-step explanation:
Recycling rate = 12 kg/6wk
Recycled = 9 × 12/6
Recycled = 9 × 2
Recycled = 18 kg
Which number is NOT in the solution set of the inequality x > −15?
A) 10
B) −5
C) −10
D) −20
Answer: D).-20
Step-by-step explanation:
Answer:
-20
Step-by-step explanation:
At the depth of x metres the temperature of the water in an ocean is T degrees celsius at depths below 900 metres T is inversely proportional to x. T is given by T= 4500/x work out the difference in temperature of the water at a depth of 1200 metres and the temperature of the water at a depth of 3750 metres
Answer:
The difference in temperature between a depth of 1200 meters and 3750 meters is 2.55
Step-by-step explanation:
The temperature T of the water in an ocean at depth X below 900 meters is given by:
T= 4500/X
To calculate the difference between a depth of 1200 meters and 3750 meters, it is necessary to calculate the temperature individually.
first, 1200 meters and 3750 meters are below 900 meters, so the equation describe before is applicable.
As a result, for 1200 meters, the temperature (symbolized as T1) is given by:
T1=4500/X
T1=4500/1200
T1=3.75
For 900 meters, the temperature (simbolized as T2) is given by:
T2=4500/X
T2=4500/3750
T2=1.2
The difference between the temperature T1 and T2 is:
Difference in temperature = T1 - T2
Difference in temperature = 3.75 - 1.2
Difference in temperature = 2.55
So, the difference in temperature between a depth of 1200 meters and 3750 meters is 2.55
Abigail Eddy purchased 200 shares of stock at $11.58 per share. Her online stock-broker charged her $12.50 commission. What is the total amount that she paid for the stock? Show work.
A) 1,547.20
B) 2,328.50
C) 2,154.54
D) 2,316.00
Answer:
B) 2328.50
Step-by-step explanation:
We are given 200 shares at $11.58 per share. By multiplying the number 200 with each share value will get the cost of all shares.
Total shares = 200
Cost per share = $11.58
Cost of 200 shares: Total shares * cost per share
= 200 * 11.58 = 2316
Commission charged = $12.50
Total amount: Cost of 200 shares + Commission charged
= 2316 + 12.50
Total amount = 2328.50
which of the following options best describes the function graphed below
Answer:
Option B.
Step-by-step explanation:
The given graph is of a line which is parallel to the x axis.
Let the equation of the line is y = mx + c
where m is the slope and c is a constant representing y - intercept.
Since the graphed line is parallel to x = 0
So for the values of x = 0 equation of the line will be
y = c (constant)
Therefore, Option B. Linear constant is the answer.
PLEASE HELP! I also need an in depth explanation, not just the answer. I want to understand how to do these types of problems. How do you know which side to shade? How do you know how to graph inequalities? Thank you! Will reward the most helpful to be the brainliest!
Answer:
The correct answer option is C. y<= -4x + 25.
Step-by-step explanation:
Firstly, we will find out the equation of the line with the help of using two points (0, 25) and (-6, 49).
The slope (m) = [tex]\frac{49-25}{-6-0} =-4[/tex].
We know the standard form of the equation is [tex]y=mx+c[/tex] so the y-intercept (c) can be found by putting in the values of the slope and the coordinates of a point.
[tex]25=-4(0)+c\\\\c=25[/tex]
Therefore, the equation of the line is y = -4x + 25.
Now since the inequality is dealing with the value of y and we know that the values of y go vertically (up and down). So if we look at the graph, the shaded area includes the smaller values of y and the line is a solid one.
Therefore, the inequality will be y<= -4x + 25.
If you don't understand it this way, you can pick up a point and test the inequality.
Taking the easiest point (0, 0) to check.
0 <= -4 (0) + 25
0 <= 25 --- True
How do you write y=4x^2 -64x -265 in vertex form
Answer:
4(x-8)^2 -521
I need help, I don't understand this question.
what is f(-3) if f(x)=|2x+1|+5
Answer:
f(-3) =10
Step-by-step explanation:
When given a function f(-3), they want you to substitute x=-3 into the function f(x) and solve
f(x) =|2x+1|+5
Let x=-3
f(-3) =|2 *-3+1|+5
f(-3)=|-6+1|+5
f(-3)=|-5|+5
The absolute value of -5 is positive 5 (absolute values means always positive).
f(-3)=5+5
f(-3) =10
round .1287 to the nearest thousandth
To round 0.1287 to the nearest thousandth, we look at the next place value which here is 7. Since 7 is more than 5, we round up the thousandth place. Hence, 0.1287 becomes 0.129.
Explanation:To round the number 0.1287 to the nearest thousandth, you need to look at the ten-thousandth place (which is the fourth numeral after the decimal point). In this number, the ten-thousandth place is 7. If this digit is 5 or above, we need to round up. If it is less than 5, we stay with the number as is. Since 7 is bigger than 5, we round up. Therefore, 0.1287 rounded to the nearest thousandth is 0.129.
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What is m∠S? Enter your answer in the box. ° An isosceles triangle with vertices labeled R, S, and T. Side R T is the base. Sides R S and side S T are equal. Angle R is labeled as 3 x degrees, angle S is labeled as 2 x degrees, and angle T is labeled as 3 x degrees.
Answer:
m<S = 45°
Step-by-step explanation:
The sum of the measures of the angles of a triangle equals 180 deg.
m<R + m<S + m<T = 180
3x + 2x + 3x = 180
8x = 180
x = 22.5
m<S = 2x = 2(22.5) = 45
In an isosceles triangle, the sum of the angles must equal 180 degrees. Given the angles labeled as multiples of x, solving for x gives 22.5 degrees, and m∠S is found to be 45 degrees.
Explanation:The student is asking to find the measure of angle S in an isosceles triangle with vertices labeled R, S, and T, where sides RS and ST are equal, and the angles at R and T are labeled as 3x degrees, and angle S as 2x degrees. Since the sum of angles in any triangle is always 180 degrees, we can set up an equation by adding the angles together: 3x (angle R) + 2x (angle S) + 3x (angle T) = 180. Simplifying the equation gives 8x = 180, and solving for x gives x = 180 / 8 = 22.5 degrees. Finally, to find m∠S, we substitute x back into the expression for angle S: m∠S = 2x = 2(22.5) = 45 degrees.
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Jake is riding an escalator. After riding for 3 seconds, he was 25 inches above the ground. A. How many inches is Jake rising per second? B. At the rate Jake is rising, how many inches above the ground will he be after riding the escalator for 15 seconds? Justify your answer. C. The top of the escalator is 30 feet, or 360 inches, above the ground. Will Jake have reached the top 45 seconds after first getting on the escalator? Why or why not?
Jake reaches the top of the escalator because he exceeds the height of the escalator if he travels at the rate of 8.33 inches/second.
What is the unit rate?Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.
Given here: Jake reaches 25 inches above the ground in 3 seconds.
The unit rate of Jake's ascend is = 25/3
=8.33 inches/second
If Jake rides the escalator for 15 seconds then we would climb
=8.33×15
=124.95 inches
After 45 seconds Jake would have climbed =45×8.33
=374.85 inches
Thus after 45 seconds Jake reaches the top of the escalator.
Hence, Jake reaches the top of the escalator because he exceeds the height of the escalator if he travels at the rate of 8.33 inches/second.
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state the gradient of the line y= 5-5x
The gradient of the line y= 5-5x is -5 which is the coefficient of 'x'. This connotes a negative slope, meaning the line descends as we move along the positive x-axis.
Explanation:The equation y = 5 - 5x represents a straight line in the xy-plane. The coefficient of 'x' in the equation represents the slope of the line. Therefore, the gradient of the line is -5. This means for every unit increase in x, y will decrease by 5 units. This negative slope suggests that the line moves downwards as the x-value increases, similar to our reference figure A1 where the slope caused a rise or fall on the vertical axis for every increase of 1 on the horizontal axis.
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State weather ADB~CDB, and if so , explain how you know
Answer:
SAS
Step-by-step explanation:
AD = DC Given
<ADB = <CDB Givien
BD = BD Reflexive property.
The angle is between the 2 sides. The triangles are congruent by SAS.
An item is regularly priced at 75 $ . It is on sale for 60% off the regular price. How much (in dollars) is discounted from the regular price?
Answer: $45.00
Step-by-step explanation:
75 x 0.60 = 45
Answer:
$30
Step-by-step explanation:
First, change the percentage into decimal:
60% = 60/100 = 0.6
Multiply 75 with 0.6:
75 * 0.6 = 45
Note that this number 45 (0.6 of 75) is the amount off from the original price (75). Subtract 45 from 75
75 - 45 = 30
$30 is your answer
~
In the following diagram, find the measures of both x and y. Line I is perpendicular to line m
Answer:
x = 22.5 and y = 9
Step-by-step explanation:
Since the lines are perpendicular then the angles formed are right, hence
4x = 90 ( divide both sides by 4 )
x = 22.5
and 10y = 90 ( divide both sides by 10 )
y = 9
Please help me out with this problem
Answer:
First picture:
1)Given
2)Substitution
3) Subtraction Property of Equality
4)if altenate interior angles are equal, then the lines are parallel
Second picture:
1) Given
2)if lines are parallel, then the corresponding angles are equal
3)Substitution
4)if altenate interior angles are equal, then the lines are parallel
Please do this 24th prblm......
Answer:
6x^2 - 4y^2 + 2x^2 + 6xy
Step-by-step explanation:
Each of the adjacent sides of the rectangle has a congruent, opposite sides. The perimeter is the sum of the lengths of the 4 sides.
P = 2(3x^2 - 2y^2) + 2(x^2 + 3xy)
P = 6x^2 - 4y^2 + 2x^2 + 6xy
24.
The perimeter of a rectangle l × w is P = 2l + 2w.
We have l = 3x² - 2y² and w = x² + 3xy. Substitute:
P = 2(3x² - 2y²) + 2(x² + 3xy) use distributive property
P = (2)(3x²) + (2)(-2y²) + (2)(x²) + (2)(3xy)
P = 6x² - 4y² + 2x² + 6xy combine like terms
P = 8x² + 6xy - 4y²Which construction is illustrated above ?
Answer:
Option 2.
Step-by-step explanation:
You are bisecting angle BAC with pencil and compass.
Answer:
The angle bisector of a given angle.
Step-by-step explanation:
From the construction, < BAC is the given angle. With any radius, draw arc BC. With any radius and points B and C as the centers consecutively, draw arcs to intersect at O. Join O to A. Line /AO/ is the angle bisector of the given angle <BAC.
The construction illustrated is the angle bisector of a given angle.
Write the fact family for 1 , 5 , and 5 ?
Can you plz help me with the following questions
1. Which choice(s) best shows the value of e' (or none): 5 + 8e > 76
2. Which choice(s) best shows the value of e' (or none): e * 7 < 28
[tex]5+8e > 76\qquad\text{subtract 5 from both sides}\\\\8e > 71\qquad\text{divide both sides by 8}\\\\\boxed{e=\dfrac{71}{8}}[/tex]
[tex]e\cdot7<28\qquad\text{divide both sides by 7}\\\\\boxed{e<4}[/tex]
Drag and drop numbers into the boxes so that the paired values are in a proportional relationship.
x 2 4 [A] 7 9
y 1 2 3 3.5 [B]
Options: 3 / 3.5 / 4.5 / 5 / 6
Answer Examlpe:
A= 6 and B= 3.5
Answer:
A=6 and B=4.5
Step-by-step explanation:
You are given table
[tex]\begin{array}{cccccc}x&2&4&[A]&7&9\\y&1&2&3&3.5&[B]\end{array}[/tex]
If the paired values are in a proportional relationship, then
[tex]\dfrac{2}{1}=\dfrac{4}{2}=\dfrac{[A]}{3}=\dfrac{7}{3.5}=\dfrac{9}{[B]}.[/tex]
Note that
[tex]\dfrac{2}{1}=\dfrac{4}{2}=\dfrac{7}{3.5}=2,[/tex]
then
[tex]\dfrac{[A]}{3}=2\Rightarrow [A]=6,\\ \\\dfrac{9}{[B]}=2\Rightarrow [B]=\dfrac{9}{2}=4.5.[/tex]
Answer:
the answer is 6
Step-by-step explanation: im 100% right this guy is wrong i repeat this guy is wrong!
As I was going to St. Ives
I met a man with seven wives.
Each of his wives had seven sacks,
Each of the sacks held seven cats,
Each of the cats had seven kitts.
Kitts, cats, sacks, and wives.
How many were going to St. Ives?
Consider the poem. Use repeated reasoning to write an expressions using whole number exponents that gives a solution to "How many were going to St. Ives?
Answer:
the answer should be 2,401 were going to St. Ives
Step-by-step explanation:
7 times 7 times 7 times 7 is 2401
Answer:
The answer is B. 7^0 + 7^1 + 7^2 + 7^3
Please help!! What is the value of -(-2)^3
-(-2)^3=-(-8)=8. So the answer is 8. or the fourth answer choice.
Can sum one help me this is my last question
Answer:
Option B is correct.
the value of discriminant is, -7
Step-by-step explanation:
Given the equation: [tex]x^2 + x +2 = 0[/tex]
To find the value of discriminant [tex]b^2-4ac[/tex]
A quadratic equation is of the form [tex]ax^2+bx+c = 0[/tex] where a, b and c are coefficient of the equation.
On comparing with given equation we have;
a = 1 , b = 1 and c = 2
then;
Discriminant = [tex]b^2-4ac =(1)^2 -4(1)(2) =1 -8 = -7[/tex]
Therefore, the value of discriminant is, -7
Suppose you have a $8-off coupon at a fabric store. You buy fabric that costs $7.50 per yard. Write an equation that models the total amount of money y you pay if you buy x yards of fabric. What is the graph of the equation?
Answer:
= 7.5x-8
Step-by-step explanation:
Total cost = cost per yard * yard of fabric - coupon
total cost = 7.5 x - 8
y = 7.5x-8
Answer:
[tex]y=7.50x+8[/tex]
Step-by-step explanation:
For the equation, the amount of money is [tex]y[/tex], and the number of yards is [tex]x[/tex].
So, the problem says that the persona already have $8, which is constant, it wont' variate, that is, this is the independent term.
Then, it says the the fabric costs $7.50 per yard, and [tex]x[/tex] refer to yards, so this term would be [tex]7.50x[/tex].
Therefore, the equation to model this problem would be:
[tex]y=7.50x+8[/tex]
the point on the graph where the line crosses the y-axis is what part of a line??
The point where the line crosses the x-axis is called the [x-intercept]. The [y-intercept] is the point where the line crosses the y-axis.
Y-intercept.
What is the cartesian plane?By calculating the separations between two perpendicular lines that pass through a fixed point in Cartesian coordinates, we may find the location of a point P. Assume that O is the fixed point known as the origin and that XOX' and YOY' are the two perpendicular lines that pass through O and are referred to as the Cartesian or Rectangular co-ordinate axes.
given, the graph crosses the y-axis A point having an x-value and a y-value, is a coordinate: (x, y). The origin is the place where the two number lines converge, and it has the following coordinates: (0, 0). The x-value is zero when the graph of a function crosses the y-axis at a value b. As a result, the point is the y-intercept (0, b).
Therefore, A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.
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Collins middle school has 280 sixth grader students. if the sixth grade is 40% if the total school, how many students are in the middle school?
Answer:
700
Step-by-step explanation:
280 / 0.40 = 700
Answer:
280 *0.40 +96 STUDENTS
or
280/100 = x/40 cross multiply
9600=100x divide by 100
x=96
Step-by-step explanation: