The fraction of the whole sandwich she ate is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The given is:
When Sierra gets home 3/4, of a sandwich is left in the refrigeratorShe cuts the remaining part into three equal partsShe eats two of themWe need to find What fraction of the whole sandwich she ate
∵ The remaining of the whole sandwich in the refrigerator is [tex]\frac{3}{4}[/tex]
∵ Sierra cuts the remaining part into 3 equal parts
- That mean divide [tex]\frac{3}{4}[/tex] by 3
∴ Each part = [tex]\frac{3}{4}[/tex] ÷ 3
- Replace ÷ by × and reciprocal 3
∴ Each part = [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{3}[/tex]
∴ Each part = [tex]\frac{1}{4}[/tex] of the whole sandwich
∵ She ate two of them
∴ She ate = 2 × [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex]
- Divide up and down by 2 to simplify it
∴ She ate = [tex]\frac{1}{2}[/tex] of the whole sandwich
The fraction of the whole sandwich she ate is [tex]\frac{1}{2}[/tex]
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Write in point-slope form an equation of the line that
passes through the given point and has the given slope.
1. (1, 5); m = 2
2. (-2, 4); m = -3
3. (4, 2); m
= 3
4. (-1, 5); m = -2
5. (2, -4); m = -3
6. (-5, 1); m = 2
Answer:
6. [tex]\displaystyle y - 1 = 2(x + 5)[/tex]
5. [tex]\displaystyle y + 4 = -3(x - 2)[/tex]
4. [tex]\displaystyle y - 5 = -2(x + 1)[/tex]
3. [tex]\displaystyle y - 2 = 3(x - 4)[/tex]
2. [tex]\displaystyle y - 4 = -3(x + 2)[/tex]
1. [tex]\displaystyle y - 5 = 2(x - 1)[/tex]
Step-by-step explanation:
In the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.
I am joyous to assist you anytime.
What equation represents this coordinate grid?
An item was listed price of $60. If the sales tax rate is 6%, how much is the sales tax (in dollars)
Susan bought 2 3/4 pounds of potato salad at $5.60 a pound. How much did she spend?
Answer:
$15.40
Step-by-step explanation:
first, let's find the 3/4. to find this, just multiply the decimal form, .75 by the price per pound because then we get the amount for 3/4 pound. that number is $4.20. next, we need to find the 2 pounds by multiplying the price per pound by the 2 pounds, which gets us $11.20. add those together and you get $15.40.
Eric wants to buy a video game that cost $24 but he only wants to spend 40% of your savings. How much must Eric saying in order to buy the game
Answer:
$14.4
Step-by-step explanation:
I don't really understand the question, but this is what I think it is
Eric needs to have $60 in savings if he wants to spend only 40% of it on a $24 video game.
Explanation:To determine how much Eric must have in savings to spend only 40% on a $24 video game, we set up a simple equation where 40% of his total savings (S) equals the price of the game ($24). The equation is 0.40 × S = $24. Solving this equation for S (total savings), we divide both sides by 0.40:
× S = $24
÷ 0.40 ÷ 0.40
S = $24 ÷ 0.40
S = $60
Therefore, Eric must have a total of $60 in savings to spend only 40% on the video game.
Please help me and explain how you got the answer
Answer:
D
Step-by-step explanation:
Straight line (straight angle) is always 180 degrees.
The angle adjacent to 115 and 115 degree angle would sum up to 180 (straight line).
So, that angle would be:
180 - 115 = 65
Now, we know the triangle's 2 angles: 85 (given) and 65 (found), thus we can find the third angle (leftmost):
85 + 65 + third angle = 180 [sum of 3 angles in a triangle is 180]
150 + third angle = 180
third angle = 180 - 150
third angle = 30
This third angle is adjacent to w and forms a straight line, so we can write:
third angle + w = 180
30 + w = 180
w = 180 - 30
w = 150
Correct answer is D
32. Which value of x will make the equation below true?
3x = 243
A). 3
B). 5
C). 8
D). 9
Find the value of x to the nearest tenth.
tan 34° = 20
Answer:
The value of x = 13.5.
Step-by-step explanation:
In this question x is missing.
So, the question would be:
tan 34° = x/20.
Now, to find the value of [tex]x[/tex]:
[tex]tan 34 = \frac{x}{20}[/tex]
[tex]\frac{x}{20} = tan 34[/tex]
Multiplying both sides by 20 we get:
[tex]x=tan 34\times 20[/tex]
On simplifying both sides we get:
[tex]x=13.49[/tex]
So, to get the value of [tex]x=13.49[/tex] to nearest tenth is 13.5. As we see in hundredth place it is 9 and 4 in tenth place, so after rounding to tenth place 4 will change to 5 so the value is 13.5.
Therefore, the value of x = 13.5.
Answer:13.5
Step-by-step explanation:
can u help me.............
Answer:
2 should be your answer
Step-by-step explanation:
There is 2 horizontal and 2 vertical in total there are 2 lines of symmetry.
How to solve 5-2x=-4x-7
Answer:
x=-6
Step-by-step explanation:
Use Substitution
so 5-2x=-4x-7
I'ma move that -4x to the other side by making it a positive
5+2x=-7
than I'ma move that 5 to the other side by making it a negative
2x=-12
to isolate the x you dived by both sides by the 2
x=-6
I doubled checked and it's -6
Answer:
Pull out like terms: 12 + 2x = 2 • (x + 6)
Solve: x+6 = 0
Then you get; X=-6
I hope this is right and hopefully it helped you
At what angle would a carpenter cut a board to create a complementary angle if the other end was cut to 35 degrees?
45 degrees
35 degrees
60 degrees
55 degrees
Answer:
55 degrees
Step-by-step explanation:
So to figure this out, you need to know what a complementary angle is. A complementary angle is a 90 degree angle.
Now you know what a complementary angle is, all you have to do is 90-35 to find the remaining angle.
90-35=55
The answer is 55 degrees
James and Lin got married and got new jobs. Lin earns $3100 more per year than James. Together they earn $81,980. How much does each of them earn per year?
Answer:
The earning to James per year is $ 39,440
The earning of Lin per year is $ 42,540 .
Step-by-step explanation:
Given as :
The total earning of James and Lin together = $ 81,980 per year
The earning of Lin is $ 3100 more per year than James
Let The earning of James = $ J
And The earning of Lin = $ J + $ 3100
So, According to question
The total earning of James and Lin together = $ 81,980 per year
Or, The earning of Lin + The earning of James = $ 81,980 per year
Or, $ J + $ 3100 + $ J = $ 81,980 per year
or, 2 $ J = $ 81,980 - $ 3100
Or, 2 $ J = $ 78880
∴ J = [tex]\frac{78880}{2}[/tex]
I.e The earning to James per year = $ 39,440
And The earning of Lin per year = $ 34,440 + $ 3100 = $ 42,540
Hence, The earning to James per year is $ 39,440
And The earning of Lin per year is $ 42,540 . answer
Decide whether the pair of lines is parallel, perpendicular, or neither.
3x - 6y = -13 and
18x + 9y = 5
A) Parallel
B) Perpendicular
C) Neither
The lines are: B) Perpendicular
Step-by-step explanation:
we have to convert both lines in slope-intercept form to find slopes
So,
[tex]3x - 6y = -13\\-6y = -3x-13\\\frac{-6y}{-6} = \frac{-3x-13}{-6}\\\frac{-6y}{-6} = \frac{-3x}{-6}+\frac{-13}{-6}\\y = \frac{1}{2} +\frac{13}{6}[/tex]
Let m1 be the slope of first line
[tex]m_1 = \frac{1}{2}[/tex]
For the second line:
[tex]18x + 9y = 5\\9y = -18x+5\\\frac{9y}{9} = \frac{-18x+5}{9}\\\frac{9y}{9} = \frac{-18}{9}x+\frac{5}{9}\\y = -2x+\frac{5}{9}[/tex]
Let m2 be the slope of line 2
So,
If the lines are parallel, their slopes are equal
If the lines are perpendicular, product of their slopes is -1
We can see that
[tex]\frac{1}{2} * -2 = -1[/tex]
Hence,
The lines are: B) Perpendicular
Keywords: Slopes, Parallel lines
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The lines given by the equations 3x - 6y = -13 and 18x + 9y = 5 are neither parallel nor perpendicular because their slopes, 1/2 and -2 respectively, are neither equal nor negative reciprocals of each other.
Explanation:To decide whether the pair of lines given by the equations 3x - 6y = -13 and 18x + 9y = 5 is parallel, perpendicular, or neither, we need to find the slope of each line. First, we convert the equations into the slope-intercept form, which is y = mx + b where m is the slope.
For the first equation, 3x - 6y = -13, we solve for y:
-6y = -3x - 13y = (1/2)x + 13/6The slope of this line is 1/2.
For the second equation, 18x + 9y = 5, we also solve for y:
9y = -18x + 5 y = -2x + 5/9The slope of this line is -2.
Since the slopes of the two lines are neither equal (which would make them parallel) nor negative reciprocals of each other (which would make them perpendicular), the lines are neither parallel nor perpendicular.
(Score for Question 3:_ of 16 points)
3. Mr. Sanchez's class sold fruit pies for $1.55 each and Mr. Kelly's class sold bottles of fruit juice for $1.40
each. Together, the classes sold 60 items and earned $88.20 for their school.
(a) Write and solve a system of equations that model the problem. Show all your work
(b) Which class earned more money?
(c) How much more money did that class earn?
Answer:
Answer:
a) Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.
b) Mr. Kelly's class
c) Mr. Kelly's classs earned $1.40 more than Mr. Sanchez's class.
Step-by-step explanation:
Let x be the number of fruit pies sold and y be the number of bottles of fruit juice sold.
Together, the classes sold 60 items, so
x + y = 60
Mr. Sanchez’s class sold fruit pies for $1.55 each, so x fruit pies cost $1.55x.
Mr. Kelly’s class sold bottles of fruit juice for $1.40 each, so y bottles of fruit juice cost $1.40y.
Together, the classes earned $88.20 for their school, so
1.55x + 1.40y = 88.20.
a) You get the system of two equations:
[tex]\left\{\begin{array}{l}x+y=60\\ \\1.55x+1.40y=88.20\end{array}\right.[/tex]
From the first equation:
[tex]x=60-y[/tex]
Substitute it into the second equation:
[tex]1.55(60-y)+1.4y=88.2\\ \\155(60-y)+140y=8,820\\ \\9,300-155y+140y=8,820\\ \\-15y=8,820-9,300\\ \\-15y=-480\\ \\15y=480\\ \\y=32\\ \\x=60-32=28[/tex]
Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.
b) Mr. Sanchez's calss earned:
[tex]\$1.55\cdot 28=\$43.40[/tex]
Mr. Kellyz's calss earned:
[tex]\$1.40\cdot 32=\$44.80[/tex]
Since [tex]\$44.80>\$43.40,[/tex] Mr. Kelly's class earned more.
c) Mr. Kelly's classs earned [tex]\$44.80-\$43.40=\$1.40[/tex] more than Mr. Sanchez's class.
if 2 is the square root of four what is the squre root of 81
5)
→ A down payment of $400 is what percent of the cost of $2500?
This needs to be shown full work on elementary math class ASAP!
Answer:
The percent of down payment of the cost $2500 is 16% .
Step-by-step explanation:
Given:
Down payment = $400.
Cost = $2500.
Now, to find the percent of down payment of the cost.
According to question:
$400 / $2500 × 100.
⇒[tex]\frac{400}{2500} \times 100[/tex]
⇒[tex]0.16\times 100[/tex]
⇒[tex]16[/tex].
Therefore, the percent of down payment of the cost $2500 is 16%.
16% is the answer to your question.
Is the discriminant of f positive, zero, or negative?
Answer:
Negative
Step-by-step explanation:
whats the unit rate of 122 and 4?
Answer: 30.5
Step-by-step explanation:
30.5 times 4 equals 122
Select the equation of the line that passes through the point (3,5) and is
perpendicular to the line x = 4, (2 points)
O 1) y = 5
O2) x = 5
O3) y = 4
O 4) x=3
The equation of the line that passes through the point (3 , 5) and is
perpendicular to the line x = 4 is y = 5 ⇒ answer 1
Step-by-step explanation:
Let us revise some notes about the horizontal and vertical lines
The horizontal line is a line parallel to x-axisThe equation of a horizontal line passes through point (a , b) is y = b, because the y-coordinates of all points on the line are equalThe vertical line is a line parallel to y-axisThe equation of a vertical line passes through point (a , b) is x = a, because the x-coordinates of all points on the line are equalThe horizontal line and the vertical line are perpendicular∵ The equation of the given line is x = 4
- From the 4th note above the given line is a vertical line
∴ The given line is a vertical line
- The perpendicular line to a vertical line is a horizontal line
∴ The perpendicular line to the given line is horizontal
∵ The perpendicular line passes through the point (3 , 5)
∵ The equation of the horizontal line is y = b, where b the
y-coordinate of any point lies on the line
∵ The point (3 , 5) lies on the line
- The y-coordinate of the point is 5
∴ b = 5
∴ The equation of the perpendicular line is y = 5
The equation of the line that passes through the point (3 , 5) and is
perpendicular to the line x = 4 is y = 5
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The quadratic function g(x) = a.ca + bx+c has the complex roots (-7+ 4i) and (-7 – 4i). You may assume that a=1. What is the value of b? What is the value of c?
The value of b is 14
The value of c is 65
Step-by-step explanation:
The quadratic equation ax² - bx + c = 0, where a = 1 has two roots
Their sum = bTheir product = c∵ The quadratic function is g(x) = ax² + bx + c
∵ a = 1
∴ g(x) = x² + bx + c
∵ g(x) has two complex roots (-7 + 4i) and (-7 - 4i)
∴ g(x) = 0
∴ x² + bx + c = 0
∵ The general form of the quadratic equation is x² - bx + c = 0,
with sum of roots b and product of roots c
- Compare them
∴ x² - (-b) + c = 0
∵ -b = the sum of the two roots
∴ -b = (-7 + 4i) + (-7 - 4i)
- Add like terms
∴ -b = (-7 + -7) + (4i + -4i)
∴ -b = -14 + 0
∴ -b = -14
- Multiply both sides by -1
∴ b = 14
The value of b is 14
∵ c is the product of the two roots
∴ c = (-7 + 4i)(-7 - 4i)
- Remember (a + b)(a - b) = a² - b²
∵ (-7 + 4i)(-7 - 4i) = (-7)² - (4i)²
∵ (-7)² = 49
∵ (4i)² = 16i²
∵ i² = -1
∴ (4i)² = -16
∴ (-7)² - (4i)² = 49 - (-16) = 49 + 16 = 65
∴ (-7 + 4i)(-7 - 4i) = 65
∴ c = 65
The value of c is 65
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11. Find the values of x and y.
(1 pc
(14y+30)°
(3x)0
156°
x=8, y = 9
x = 10, y = 9
x = 8, y = 10
Answer:
Reasoning and Proof Unit Test
Step-by-step explanation:
1. 67
2. counterexample
3. If you join the gym, then it is free for the first three months.
Hypothesis: you join the gym
Conclusion: it is free for the first three months
4. Yes; two lines intersect at right angles if (and only if) they are perpendicular
5. An angle is obtuse if and only if its measure is greater than 180
6. Symmetric Property
7. 12
8. RT-ST
9. x=8, y=9
10. 7
11. Symmetric Property
12. invalid
13. A. is Substitution Property of Equality, B. is Supplementary Angles, C. is Subtraction Property of Equality
14. (A) 180, (B) 180, (C) transitive property, (D) 3, (E) 3
15. The value of x is 3.
a) Addition of line segments
b) Substitution rule
c) Simplification by addition of like terms
d) Collecting lie terms
e) Dividing both sides by 8
AB = 2x
BC = 6x + 8
AC = 32
AB + BC = AC (Addition rule)
Addition of the component segments of a line
2x + 6x + 8 = 32 (Substitution rule)
Substituting for AB, BC, and AC in the equation AB + BC = AC
8x + 8 = 32 (Simplification)
Simplifying 2x + 6x + 8 = 32 by adding like terms
8x = 24 (Collecting like terms)
8x = 32 - 8
8x = 24
x = 3 (Divide both sides by 8)
8x / 8 = 24/8
x = 3
16. If it is square it is a Quadrilateral.
17. 7y = 8x - 14
7(6) = 8x - 14
Collect like terms.
42 = 8x - 14.
8x = 42 + 14
8x = 56
x = 56/8
x = 7
These are all the correct answers as of 2022
To complete her holiday wrapping, Bella needs identical strips of ribbon measuring 3.5 feet each. She has 85 feet of ribbon in total. About how many pieces of ribbon can she cut from this long strip? PLS ANSWER ASAP
Bella can cut 24 pieces of ribbon from this long strip
Solution:
Given that Bella has 85 feet of ribbons in total
She needs identical strips of ribbon measuring 3.5 feet each
To find: Number of peices of ribbon can she cut from long strip
Number of peices of ribbon can she cut from long strip can be calculated by dividing the total feet of ribbon she has by length of identical strips she needs
Mathematically written as:
[tex]\text { Number of Strip that can be cut }=\frac{\text { Total length of ribbon }}{\text { Length of each piece }}[/tex]
[tex]\begin{array}{l}{\text { Number of Strip that can be cut }=\frac{85}{3.5}} \\\\ {\text { Number of Strip that can be cut }=24.28 \approx 24}\end{array}[/tex]
Hence , the number of strip can be 24 each of size 3.5 feet
Rewriting the expression 15x+9 as 9+ 15x is an example of the ———— property of ———-?
Rewriting the expression 15x+9 as 9+ 15x is an example of the commutative property of addition
Solution:The commutative property of addition states that when two numbers are being added, their order can be changed without affecting the sum.
To “commute” means to move around or travel.
According to the commutative property of addition, changing the order of the numbers we are adding, does not change the sum
When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4
For addition, the rule is a + b = b + a
Here in the problem 15x + 9 is equivalent to 9 + 15x
Hence, rewriting the expression 15x+9 as 9+ 15x is an example of the commutative property of addition
The process of rewriting 15x + 9 as 9 + 15x uses the Commutative property of addition. This asserts that changing the order of addition doesn't affect the sum.
Explanation:Rewriting the expression 15x+9 as 9+15x is an example of the Commutative property of addition. The Commutative property states that the order in which you add or multiply numbers does not affect the sum or product. So in your case, 15x + 9 = 9 + 15x because of the Commutative property of addition. This is true for addition of ordinary numbers as well, for instance 2 + 3 will yield the same result as 3 + 2.
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Represent the model shown below using a
multiplication equation.
ロロロロロ
ロロロロロ
ロロロロロ
ロロロロロ
Answer:
5×4=20
Step-by-step explanation:
5 blocks across multiplied by the 4 blocks down equals 20 blocks all together
What value of x will make the equation 5x-2/11 = -7 a true statement
Answer:
X=-15
Step-by-step explanation:
Multiply both sides by 11
5x-2=-77
add 2 to both sides
5x=-75
Divide both sides by 5
x=-15
The value of x equal to -15 will make the given equation a true statement.
What is an equation?It is a mathematical statement that shows that two mathematical expressions are equal.
The given equation is
(5x-2) / 11 = -7
Multiply both sides by 11
i.e. 5x-2 = -77
Then add 2 to both sides
i.e. 5x = -75
Divide both sides by 5
i.e x = -15
Hence, the value of x that will make the equation 5x-2/11 = -7 a true statement is -15.
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Translate this sentence into a equation
The sum of 21 and Vanessa's savings is 68
Find the x- and y-intercepts of the line
(-6.-6), (2, -4)
The x-intercept is
Answer:
x-int = 18
y-int = -9/2
Step-by-step explanation:
Use slope-intercept form y=mx + b
To find the slope, substitute the two points into the slope formula and solve.
[tex]m = \frac{y2 - y1}{x1 - x1} \\m = \frac{-4 - (-6)}{2 - (-6)} \\m = \frac{2}{8}\\m= \frac{1}{4}[/tex]
Substitute a random point (2,-4) and m=1/4 into slope-intercept form
y = mx+b
-4 = 1/4 (2) + b
-4 = 2/4 + b
-4 = 1/2 + b
Isolate b to solve
b = -4 - 1/2
b = -8/2 - 1/2
b = -9/2 <= this is the y-intercept
b is the y-intercept in slope-intercept form
Substitute b= -9/2 and m=1/4 to get the equation of the line.
y = 1/4 x - 9/2
Substitute y for 0 to find the x intercept
y = 1/4 x - 9/2
0 = 1/4 x - 9/2
9/2 = 1/4 x
x = (9/2) / (1/4)
x = (9/2) X (4/1)
x = 36/2
x = 18
Ashley solved the equation for m using the following steps.
-4.5 + m = 17
-4.5 -4.5
m = 12.5
What was Ashley’s error?
Ashley should have subtracted 17 to both sides.
Ashley should have added 4.5 to both sides.
Ashley should have added 17 to both sides.
Ashley’s work does not have an error.
Answer:
Ashley should have added 4.5 to both sides.
Step-by-step explanation:
Given expression:
[tex]-4.5+m=17[/tex]
Ashley's solution:
Subtracted 4.5 to both sides and got,
[tex]m=12.5[/tex]
Correct solution:
Adding 4.5 to both sides.
[tex]-4.5+m=17[/tex]
[tex]+4.5[/tex] [tex]+4.5[/tex]
∴ [tex]m=21.5[/tex]
Error made by Ashley was subtracting 4.5 both sides. Instead he should have added 4.5 both sides.
Nathan hit 19 homeruns. He scored 3 fewer homeruns than twice the number of homeruns hit by jason. Write and solve an equation to show how many homeruns Jason hit
Jason hit 11 homeruns.
Step-by-step explanation:
Homeruns hit by Nathan = 19
Let,
Homeruns hit by Nathan = x
Homerun hit by Jason = y
According to given statement;
x = 2y - 3 Eqn 1
We know that Nathan hit 19 homeruns, therefore, putting x=19 in Eqn 1
[tex]19=2y-3\\19+3=2y\\22=2y\\2y=22[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{22}{2}\\y=11[/tex]
Jason hit 11 homeruns.
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Solve for x -1/2(x+5)=-10
Answer:
-15
Step-by-step explanation:
x-1/2(x+5)=-10
x-1/2x-5/2=-10
2/2x-1/2x-5/2=-10
1/2x-5/2=-10
1/2x=-10+5/2
1/2x=-20/2+5/2
1/2x=-15/2
x=(-15/2)/(1/2)
x=(-15/2)(2/1)
x=-15/1
x=-15