Answer:
Therefore values of a and b are
[tex]a=3\ and\ b = 2[/tex]
Step-by-step explanation:
Rewrite [tex]x^{2}-6x+7=0[/tex] in the form
[tex](x-a)^{2}=b[/tex]
where a and b are integers,
To Find:
a = ?
b = ?
Solution:
[tex]x^{2}-6x+7=0[/tex] ..............Given
Which can be written as
[tex]x^{2}-6x=-7[/tex]
[tex](\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9[/tex]
Adding half coefficient of X square on both the side we get
[tex]x^{2}-6x+9=-7+9=2[/tex] ...................( 1 )
By identity we have (A - B)² =A² - 2AB + B²
Therefore,
[tex]x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}[/tex]
Substituting in equation 1 we get
[tex](x-3)^{2}=2[/tex]
Which is in the form of
[tex](x-a)^{2}=b[/tex]
On comparing we get
a = 3 and b = 2
Therefore values of a and b are
[tex]a=3\ and\ b = 2[/tex]
Answer 2: a = 3 and b = 2
You need to buy fertilizer for a circular flower bed with a diameter
of 13 feet. If one bag will fertilize 10 square feet, how many bags
do you need to buy?
14 bags of fertilizer are needed
Solution:
Given that You need to buy fertilizer for a circular flower bed with a diameter
of 13 feet
Diameter = 13 feet
[tex]radius = \frac{diameter}{2}[/tex]
[tex]radius = \frac{13}{2} = 6.5[/tex]
Therefore radius of circular flower bed is 6.5 feet
Area of circle is given as:
[tex]\text{ area of circle } = \pi r^2[/tex]
Substitute r = 6.5
[tex]\text{ area of circle } = 3.14 \times 6.5^2 = 132.665[/tex]
Given that one bag will fertilize 10 square feet
1 bag = 10 square feet
Then number of bags needed are:
[tex]\rightarrow \frac{132.665}{10} = 13.2665[/tex]
Thus approximately 14 bags of fertilizer are needed
Arnold’s entire workout consisted of 10 minutes of warm-up exercises, 25 minutes of lifting weights, and 15 minutes on the treadmill. What was the ratio of the number of minutes he lifted weights to the total number of minutes of his entire workout?
Answer:
1:2
Step-by-step explanation:
Find the ratio of the ratio of the number of minutes he lifted weights to the total number of minutes of his entire workout and simplify it
25:10+25+15
25:50
1:2
Answer:
1 to 2
1:2
1/2
Step-by-step explanation:
Ratios can be written in three forms:
A to B
A:B
A/B
Ratios are also simplified by reducing to lowest terms like fractions are.
This problem's ratio is:
minutes lifted weights to total minutes workout
The number of minutes lifting weights is in the question: 25.
To find the total minutes of his workout, add the number of minutes he spent for all of the activities:
Total minutes = warm-up + lifting weights + treadmill
Total minutes = 10 + 25 + 15
Total minutes = 50
The ratio before simplifying is 25/50.
This ratio can be reduced to lowest terms. Both sides are divisible by 25.
25/25 = 1
50/25 = 2
The ratio in lowest terms is 1/2.
It can also be written as 1 to 2 or 1:2.
Find the value of x and y
Answer:
x = 25
y = 60
Step-by-step explanation:
Angles with meauseres 80° and 4x° are the same-side interior angles when two parallel lines are cut by transversal. This means the sum of the measures of these angles is equal to 180°.
[tex]80^{\circ}+4x^{\circ}=180^{\circ}\\ \\4x=180-80\\ \\4x=100\\ \\x=25[/tex]
Angles with measures 4x° and (2y - 20)° are vertical angles, so they are congruent:
[tex]4x^{\circ }=(2y-20)^{\circ}\\ \\4\cdot 25=2y-20\\ \\2y-20=100\\ \\2y=100+20\\ \\2y=120\\ \\y=60[/tex]
Earl Pumpernickel owns and operates The Earl of Sandwiches, a profitable catering business in Logic Town. Recently, Earl was lucky enough to land a lucrative contract that will enable him to supply food for the Big Corporation for an entire month of lunch conferences. For the upcoming week, for example, he knows that Friday’s meeting will require 12 more sandwiches than Tuesday’s meeting, which will require six fewer sandwiches than Monday’s, which will require 20 more sandwiches than Wednesday’s, which will require five fewer sandwiches than Thursday’s. If the number of sandwiches ordered for the conference that calls for the fewest is 50, how many sandwiches will Earl need to make for the Big Corporation each day next week?
Answer:
Monday: 70
Tuesday: 64
Wednesday: 50
Thursday: 55
Friday: 76
Step-by-step explanation:
Equations
Let's call x to the number of sandwiches ordered for Thursday's meeting. We know that for Wednesday’s, we'll need x-5 sandwiches, for Monday's, we'll need 20 more, i.e. (x-5+20)=x+15 sandwiches. For Tuesday's it will be 6 fewer than x+15, or x+9. Finally, for Friday's, it will be 12 more than x+9 or x+21. Summarizing:
Monday: x+15
Tuesday: x+9
Wednesday: x-5
Thursday: x
Friday: x+21
The fewest of them all is x-5 and is must be equal to 50
[tex]x-5=50[/tex]
[tex]x=55[/tex]
The number of sandwiches per day is
Monday: x+15=70
Tuesday: x+9=64
Wednesday: x-5=50
Thursday: x=55
Friday: x+21=76
The histogram represents the distributions of essay scores for high school sophomores and juniors in a contest. Which statements are true about the data used to create the histogram? Select three options.
The mean is the best comparison of the measures of center.
The juniors tended to have higher essay scores than the sophomores.
The medians of both data sets are equal.
The interquartile range is the best comparison of the measure of variability.
A histogram is the best way to show that both distributions are nearly symmetric.
Answer:
B,C, and E
Step-by-step explanation:
A histogram is a graphical illustration of information in bars of diverse heights. A histogram displays the shape and spread of continuous sample data. The true statements about the data essay scores for high school sophomores and juniors in a contest are; the juniors tended to have higher essay scores than the sophomores, the medians of both data sets are equal and the histogram is the best way to show that both distributions are nearly symmetric.
Answer:
bce
Step-by-step explanation:
What is m
Enter your answer in the box.
Answer:
Angle M = 98 degrees
Step-by-step explanation:
All triangle angles add up to 180.
Set up equation like this:
(x+6)+(3x-16)+(x)=180
Combine like terms.
5x-10=180
Add on both sides.
5x=190
Divide 5 both sides.
x=38
Solve for angle M.
3(38)-16=98
What are the intercepts of the graphed function?
x-intercept = (-1,0)
y-intercept = (-3,0)
x-intercept = (0, -1)
y-intercept = (0, -3)
x-intercept = (0, -1)
y-intercept = (-3,0)
x-intercept = (-1, 0)
y-intercept = (0, -3)
Answer:
x-intercept = (-1,0)
y-intercept = (0,-3)
Explanation:
x-intercepts are points where the line crosses the x-axis.
y-intercepts are points where the line crosses the y-axis.
Answer:
D
Step-by-step explanation:
Which situation can be modeled using the equation 5x+3=27
Answer:
x=4.8
Step-by-step explanation:
5x+3=27
-3 -3
5x=24
/5 /5
x = 4.8
Answer:
Sam has 27 pencils. He has 3 loose pencils and 5 packs of pencils with x pencils in each pack.
Step-by-step explanation:
Mo’s farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
Final answer:
Using a system of equations, it's found that Mo's farm stand sold 65 pounds of peaches, with the total sales of apples and peaches being 165 pounds and revenue $337.50.
Explanation:
To determine how many pounds of peaches Mo's farm stand sold, we can set up a system of equations based on the given information about total weight and revenue from apples and peaches. The weight equation can be written as A + P = 165, where A is the weight of apples sold and P is the weight of peaches sold. The revenue equation is 1.75A + 2.50P = 337.50.
Let's solve for A using the weight equation: A = 165 - P. Substitute A in the revenue equation: 1.75(165 - P) + 2.50P = 337.50. Upon solving, we get: 288.75 - 1.75P + 2.50P = 337.50, which simplifies to 0.75P = 48.75. Therefore, P, the weight of peaches sold, is 65 pounds.
1. Jada measured the height of a plant in a science experiment and finds that, to the 1/4 nearest of an inch, it is 3/4 inches.
a. What is the largest the actual height the plant could be?
b. What is the smallest the actual height the plant could be?
c. How large could the percent error in Jada's measurement be?
The largest possible height of the plant is 1 inch, the smallest possible height is 0 inches, and the largest possible percent error in Jada's measurement is -25%.
Explanation:To find the largest possible height of the plant, we need to round up the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 1 inch. Therefore, the largest the actual height of the plant could be is 1 inch.
To find the smallest possible height of the plant, we need to round down the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 0 inches. Therefore, the smallest the actual height of the plant could be is 0 inches.
The percent error in Jada's measurement can be found by calculating the difference between the approximate measurement and the actual measurement, dividing it by the actual measurement, and then multiplying by 100. In this case, the approximate measurement is 3/4 inch and the actual measurement could be between 0 and 1 inch. So, the largest possible percent error would be (3/4 - 1) / 1 * 100 = -25%, and the smallest possible percent error would be (3/4 - 0) / 1 * 100 = 75%.
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The ratio of boys to girls in history class is 4 to 5. How many girls are in the class if there are 12 boys in the class.
Answer:
15 girls
Step-by-step explanation:
Answer:
15 girls
Explanation:
You first set up the ratio of boys to girls (4/5) as a fraction. Then you look. You make another fraction next to the 4/5 fraction to figure out how many girl are in the class. You know that you are trying figure out how many GIRLS are in the classroom if their are 12 boys. So on the other fraction the DENOMONATER is going to have an x on it because you don't know how many girls their are and girls (according to the fraction boys to girls (4/5) are on the bottom. So, now you cross multiply. 12x5 is 60 and 60/4 is 15. Therefore, you get 15 as your answer.
at an office supply store emilio bought 3 notebooks and 5 pens for $13.75 if a notebook costs $1.25 more than a pen how does one notebook cost?
Answer:
One notebook costs $2.50
Step-by-step explanation:
The cost of notebook is $2.50.
what is algebra?Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions.
Given:
let the number of pen be x
let the number of notebooks be y.
So, the equation can be written as
3x + 5y= 13.75....(1)
x - y = 1.25
3x- 3y = 3.75 ....(2)
Solving above 2 equation we get
8y = 10
y= 10/8
y= 5/4
y= 1.25
and, x= 1.25+1.25=2.50
Hence, the notebook costs $2.50.
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The quotient of four times a number and nine in an algebraic expression
Answer:
4x/9
Step-by-step explanation:
The quotient of four times a number and nine in an algebraic expression can be represented as (4x/9).
Explanation:The quotient of four times a number and nine in an algebraic expression can be represented as (4x/9). Here, 'x' represents the unknown number. To calculate the value of this expression, you would multiply 4 with 'x' and then divide the result by 9. For example, if the unknown number is 6, the expression would evaluate to (4 * 6)/9 = 24/9 = 2.67.
In the realm of algebraic expressions, the quotient derived from four times an unspecified number divided by nine takes on the simple yet versatile form of (4x/9), with 'x' standing in as the variable denoting the unknown quantity. The computation entails a straightforward process wherein you multiply the value of 'x' by 4 and subsequently divide the outcome by 9. For instance, if 'x' were to represent the value 6, the expression's evaluation would unfold as follows: (4 * 6)/9 = 24/9 = 2.67. This straightforward algebraic framework empowers us to efficiently compute the result based on the specific value attributed to 'x,' facilitating various calculations and problem-solving endeavors.
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Variables and Inequalities
Answer:
-5x - 6x ≤ 8 - 8x - x
-11x ≤ 8 - 9x
-2x ≤ 8
x ≥ -4
Janessa bought for 4 stamps for $1.48 at this rate how much would 10 stamps cost
Answer:
$3.70
Step-by-step explanation:
divide 1.48 by 4 = .37
multiply by 10
The sum of two consecutive numbers is 77. The difference of half of the smaller number and one-third of the larger number is 6. If x is the smaller number and y is the larger number, which two equations represent the sum and difference of the numbers? x - y = 6 and 1/2 x + 1/3 y = 77 x + y = 77 and 1/2 x - 1/3 y = 6 x - y = 77 and 1/2 x + 1/3 y = 6
The required equations that represent the sum and difference of numbers are: x + y = 77 and [tex]\frac{x}{2} - \frac{y}{3} = 6[/tex]
Solution:
Let the two consecutive numbers be "x" and "y"
Where "x" is the smaller number and "y" is the larger number
Given that sum of two consecutive numbers is 77
Therefore we frame a equation as:
x + y = 77
Also given that The difference of half of the smaller number and one-third of the larger number is 6
Therefore we frame a equation as:
half of the smaller number - one-third of the larger number = 6
half of x - one third of y = 6
[tex]\frac{1}{2}x - \frac{1}{3}y = 6\\\\\frac{x}{2} - \frac{y}{3} = 6[/tex]
Therefore the required equations that represent the sum and difference of numbers are:
x + y = 77
[tex]\frac{x}{2} - \frac{y}{3} = 6[/tex]
Plz plz plz plz plz help
Ok, so 27 is >, 30 is <, 13/5 is 2 3/5, 5 2/7 is 37/7, 9 3/4 is 39/4, and 23/3 is 7 2/3
I did not do #27 and #30, just did the table.
Which expression is equivalent to 13 - (-21)13−(−21)13, minus, left parenthesis, minus, 21, right parenthesis?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
-21-13−21−13minus, 21, minus, 13
(Choice B)
B
-21+13−21+13minus, 21, plus, 13
(Choice C)
C
-13+21−13+21minus, 13, plus, 21
(Choice D)
D
13+2113+21
The expression 13 - (-21) simplifies to 34.
Explanation:The expression 13 - (-21) can be simplified as follows:
The minus sign before the parentheses means that we need to change the sign of every term inside the parentheses.-(-21) is equivalent to +21, since the negative sign cancels out another negative sign.Therefore, 13 - (-21) simplifies to 13 + 21, which is equal to 34.So, the expression 13 - (-21) is equivalent to 34.
To find the equivalent expression for \(13 - (-21)\), you can simplify the subtraction of a negative number, which is the same as adding its positive counterpart. Therefore:
\[ 13 - (-21) \]
is equivalent to:
\[ 13 + 21 \]
Among the given choices, the expression that matches this result is:
\[ \text{(Choice D) } 13 + 21 \]
Final answer:
The expression 13 - (-21) is equivalent to 13 + 21 because we change the subtraction of a negative number to addition. The final result is 34.
Explanation:
The expression 13 - (-21) involves subtracting a negative number from a positive number. According to the rules for subtracting integers, we change the sign of the number being subtracted and then follow the rules for addition as follows:
Change the sign of the number after the minus sign. So, -(-21) becomes +21.Then, add 21 to 13, which gives us 13 + 21.The sum of 13 and 21 is 34.Therefore, the expression 13 - (-21) is equivalent to 13 + 21, which simplifies to 34.
Consider the graph of the line y = .5x- 4 and the point
(-4,2).
The slope of a line parallel to the given line is
(1/
24
A point on the line parallel to the given line, passing
through (-4, 2), is (0,4) 4.
The slope of a line perpendicular to the given line is
-2
A point on the line perpendicular to the given line,
passing through (-4,2), is
Answer:
slope of parallel line and perpendicular line are 5 and -1/5 espectively
equation of parallel and perpendicular line are y = 5x + 22 [tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex] respectively
Step-by-step explanation:
y = 5x - 4 is in the form
y = mx + c
where m is the slope of the line and c is the y intercept of thr line
therefore slope of the line = 5 and y intercept = -4
when an another line is parallel to the given line then the slope of both the lines are equal
therefore the slope the parallel line = 5
equation of a line passing through a given point [tex](x_{1} ,y_{1})[/tex] with slope m is given by [tex]y-y_{1} = m(x-x_{1} )[/tex]
given [tex](x_{1} ,y_{1})[/tex]= (-4,2)
therefore equation of line y-2 = 5(x+4)
therefore y = 2+ 5x+20
y = 5x + 22is the eqaution of required line.
when two lines are perpendiculer then
[tex]m_{1} m_{2}=-1[/tex]
where [tex]m_{1} and m_{2}[/tex] are slope of the lines therefore
m×5=-1
therefore m= [tex]\frac{-1}{5}[/tex]
therefore eqaution of line passing through (-4,2) and with slope m= [tex]\frac{-1}{5}[/tex] is given by [tex]y - 2= \frac{-1}{5} (x+4)[/tex]
[tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex]
We can see here that the line perpendicular to the given line, passing through (-4, 2), is (0, -6).
How we arrived at the solution?Let's first verify the given information and then find the point on the line perpendicular to the given line passing through (-4, 2).
Given line: y = 0.5x - 4
Slope of a line parallel to the given line:
The slope of the given line is 0.5. Parallel lines have the same slope. Therefore, the slope of a line parallel to the given line is also 0.5.
A point on the line parallel to the given line, passing through (-4, 2):
Since the slope of the parallel line is 0.5, and we know a point (-4, 2) that lies on it, we can find the equation of the parallel line using the point-slope form of a line.
Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Substitute the values: y - 2 = 0.5(x + 4)
Now, let's find a point on the line perpendicular to the given line, passing through (-4, 2):
Slope of a line perpendicular to the given line:
Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is 0.5, so the slope of the line perpendicular to it is -1/0.5 = -2.
A point on the line perpendicular to the given line, passing through (-4, 2):
Using the point-slope form again, we can find the equation of the perpendicular line passing through (-4, 2).
Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Substitute the values: y - 2 = -2(x + 4)
Now, we can find another point on the perpendicular line by setting x = 0:
y - 2 = -2(0 + 4)
y - 2 = -8
y = -6
So, another point on the line perpendicular to the given line, passing through (-4, 2), is (0, -6).
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3x + 4x = 5y + 2x
This is hard what is the answer
Answer:
x = y
Step-by-step explanation:
7x = 5y + 2x
Subtract 2x from both sides
5x = 5y
x = y
Find the total number of unit cube that fill the entire prism
Answer:
72 cubes
Step-by-step explanation:
Attached is the picture drawn (though not great one), showing 6 cube on length of prism, 3 cubes on width and 4 cubes on height of prism.
Given: Length of prism= 6
Width= 3
Height= 4
To know the number of cubes, which can fill the entire prism, we need to find volume of prism.
∴ Volume of prism= [tex]length\times width\times height[/tex]
Volume of prism= [tex]6\times 3\times 4= 72[/tex]
∴ 72 units of cube can fill the entire prism.
Anna baked 3 batches of cookies with c cookies in each batch.She than ate 8 cookies
Answer:
3c-8
Step-by-step explanation:
Write the ratio 3 to 10 in two different ways.
Answer:
3/10, 3:10
Step-by-step explanation:
3 to 10 : 3/10, 3:10
SOMEONE HELP PLEASEEE.I NEED HELP WITH 12TH GRADE TRIG.
Answer:
x = 13.7
Step-by-step explanation:
This is a right triangle so we use the trig ratios. We need an angle of reference (not the right angle) and any side (which is given, hypotenuse = 47).
We can either find the angle at the top or the right to be the angle of reference, Θ (theta).
Angle at the top:
The two angles, 17° and the unknown interior angle add to 90° because they are complementary.
∠Θ = 90° - 17° = 73°
Now use the trig ratio cosine.
cosΘ = adjacent ÷ hypotenuse
cos(73°) = x / 47
x = 47cos(73°)
x = 13.74147..... Round down the exact answer to nearest tenth
x ≈ 13.7 Answer
The value of x is the same as the side adjacent to the angle of reference I chose.
If I chose the other missing angle to be the angle of reference, I would use sine and x would be opposite.
How are the two angles related?
Answer:
They are supplementary
Step-by-step explanation:
Two Angles are Supplementary when they add up to 180 degrees.
Equation of the line that passes tjrougj the points of (0,-3) (1,-5)
Answer:
y=-2x-3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-(-3))/(1-0)
m=(-5+3)/1
m=-2/1
m=-2
y-y1=m(x-x1)
y-(-3)=-2(x-0)
y+3=-2(x)
y+3=-2x
y=-2x-3
(12345678), X=(1357), Y=(158) find (1)X' n Y
(2) (X' u Y)'
Hope it helps u............
Factor the polynomial.
x²+6x+5
Answer: (x + 1 )(x+5)
Step-by-step explanation:
Given :
[tex]x^{2}[/tex] + 6x + 5
Compare with the general quadratic equation:
a[tex]x^{2}[/tex] + bx + c
To factorize , you are to find two numbers that multiply to give ac , and add to give b.
After which you will re - write the middle number with those numbers.
From the given question , ac = 5[tex]x^{2}[/tex] , we are to find two numbers that will multiply to give 5[tex]x^{2}[/tex] and add to give 6x.
The numbers are 1x and 5x.
We will then replace the middle number by the two numbers , that is
[tex]x^{2}[/tex] + x + 5x + 5
x(x+1) +5( x +1)
(x+1)(x+5)
Which sign makes the inequality true?
60.00 ___ (56. 28 + 3.42)
The average person's speed when riding a bike along a street is 18 kilometers per hour. What conversion factor can be used to
convert this speed to meters per hour?
A 1 kilometer/
1.000 meters
B 1 meter/
1.000 kilometers
C 1,000 meters/
1 kilometer
D 1.000 kilometers/
1 meter
The conversion factor used to convert kilometer per hour to meter per hour is [tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]
Solution:
Given that average person's speed when riding a bike along a street is 18 kilometers per hour
To find: conversion factor used to convert the given speed to meters per hour
Given average speed = 18 km per hour
From the conversion parameters:
1 km = 1000 meters
or
[tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]
So, we can use the above conversion factor to convert average speed into meters per hour
18 km per hour = 18000 meter per hour
So the conversion factor used to convert kilometer per hour to meter per hour is [tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]
Thus option C is correct. 1000 meters for 1 kilometers
Answer:
its c
Step-by-step explanation: