The diameter of the circle is 19.8 inches.
We are given the value of side of square in the question. The diameter of the circle will be equal to the diagonal of square. The diagonal of square can be calculated using Pythagoras theorem. So, finding the diagonal of square, which will be hypotenuse.
Diagonal² = Base² + Perpendicular²
Diagonal² = side² + side²
Keep the values to find the value of diagonal
Diagonal² = 14² + 14²
Take square of values on Right Hand Side of equation
Diagonal² = 392
Diagonal = √392
Taking square root on Right Hand Side of equation
Diagonal = 19.8 inch
So, diagonal of square is diameter of circle which is 19.8 inches.
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record the letter of each graph with the given characteristics a has a vertical axis of symmetry
A parabola with a vertical axis of symmetry is graphed at the end of the answer.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), with a vertical axis of symmetry, is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
The most simple example of this is the parabola y = x², which is graphed at the end of the answer.
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The square root of 16 to the second power -14 to the second power
Answer:
is it -180?
I don't remember most of this stuff!
sorry if its wrong
Step-by-step explanation:
For Every $100 he earns, Grayson Pays Federal income tax of $19. how much federal income tax will he pay on earnings of $500?
I need help asap!!!!
Answer:
y = 2016 - 112x
Step-by-step explanation:
because he is paying 112 dollars each month for 18 months
y= 2016 -112x
for instance, he paid it for 6 months we would say
y = 2016 - 112(6)
y = 2016 - 672
y = 1334
so, y = 2016 - 112x
Please help!!! I don't need a quick answer
Answer:
780 ≥ 58.53x + 566.83
Step-by-step explanation:
He has $780 that he can spend, so the total must be less than or equal to 780.
Let x = number of biking outfits.
Costs:
Bicycle: $490.50
Reflectors: 4 × $14.98 = $59.92
Gloves $16.44
Outfits: $58.53x (The cost of x outfits is 58.53x)
The total he spends is:
490.5 + 59.92 + 16.44 + 58.53x =
= 58.53x + 566.86
This total has to be less than or equal to $780.
58.53x + 566.86 ≤ 780
This can be written as
780 ≥ 58.53x + 566.83
Write an equation to solve each problem. The first stage of a rocket burns 28 s longer than the second stage. If the total burning time for both stages is 152s , how long does each stage burn?
Answer:
From the Soldier's point of view, the American Civil War was not a continuous battle. Instead, it was long monotonous marches and long residency in camps punctuated by the terror and chaos of combat. When winter set in and the campaigning season came to a close, most Soldiers counted on a long, cold stay in a winter camp. The four log cabins at the center of the Army Heritage Trail represent the types of buildings which Soldiers in both the Union and the Confederate Armies spent the long dreary months of winter. The cabins are modeled after images from the USAHEC collection, including the Army of the Potomac's winter camp at Brandy Station and the Confederate camp at Centerville
Solve to find x and y in the diagram.
Answer choices:
x = 3, y = 15
x = 15, y = 3
x = 15, x = 8
x = 15, y = 6
Answer:
Option 2 [tex]x[/tex] = 15, [tex]y[/tex] = 3
Step-by-step explanation:
Vertical angles are equivalent. Thus [tex]4x+10y[/tex] = 90. To solve for [tex]x[/tex], we set [tex]6x[/tex] = 90, since adjacent angles equal 180. This gives us 15 as x. Plugging 15 into the first equation we get that y is equal to 3.
You and your friend are swimming against the current. You move forward 15 feet. Your friend is not a strong swimmer, so he moves back 6 feet. write each amount as the distance swam.
The amount of you swam is +15 feet and your friend swam is -6 feet.
Given that you move forward 15 feet and your friend is not a strong swimmer, so he moves back 6 feet.
The arithmetic operators means performing an addition, subtraction, multiplication, division, exponentiation, and modulus operations.
It is given that you move the forward that means you move in positive direction.
So, you move forward means you move +15 feet.
It is also given that your friend is not a strong swimmer, so he moves back that means he move in negative direction.
So, your friend moves backward means he move -6 feet.
Hence, you move forward 15 feet is +15 feet and your friend is not a strong swimmer, so he moves back 6 feet is -6 feet.
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The table represents the linear function f(x), and the equation represents the linear function g(x).
Compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
The correct option is (C) The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
Given that the following table represents the linear function f(x), and the equation represents the linear function g(x) :
x 0 2 4
f(x) 1 9 17
and g(x) = 3x + 1 .........(1)
We have to compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
From the graph, we note that (0, 1), (2, 9) and (4, 17) are three points on the line graph of function f(x).
We know that, the slope of any line having two points (a, b) and (c, d) on it is given by
m = d-b/c-a
So, the slope of the line of f(x) is
m = 9-1/2-0
m = 8/2
⇒ m = 4
Since the line of f(x) passes through the point (0, 1), so its equation will be
f(x) -1 = m(x-0)
⇒ f(x) -1 = 4(x-0)
⇒ f(x) -1 = 4x
⇒ f(x) = 4x+1 ........... (2)
The slope-intercept form of the equation of a line is y = mx + c, where m is the slope and c is the y-intercept of the line.
Comparing equation (2) and (1) with the slope-intercept form, we get
slope of f(x) = 4 and y-intercept of f(x) = 1 and
slope of g(x) = 3 and y-intercept of g(x) = 1.
Thus, the slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
Option (C) is CORRECT.
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−3/8+(−2
9/10)
Enter your answer as a simplified fraction
The simplied form of the given fraction will be -3 11/40.
What are proper and improper fractions and how to convert mixed fraction to simple fraction?There is a fraction, containing numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1 an improper fraction is ≥ 1. A mixed fraction contains a sum of whole number and a proper fraction.
WE have been given an expression as;
−3/8+(−2 9/10)
Then first we will solve the mixed fraction;
−2 9/10 = -29/10
Now solve the fraction;
−3/8+-29/10
-131/40
In mixed number form:
-3 11/40
Hence, The simplied form of the given fraction will be -3 11/40.
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"a
4. Mr. Jensen's class was tracking the average
temperature each month. Given the data below,
calculate the slope and explain what it means in
context.
Month
Avg. Temp (°F)
Jan Feb
42 56
Mar
70
Apr
84
The slope of the given problem is 14
It is a problem of linear regression Line
y = a +by
where a = ∑Y - b ∑X / N
and b = N ∑XY - (∑X×∑Y)/ ( N∑x²- (∑X)
Month(X) Temperature (y) X² XY
1 42 1 42
2 56 4 112
3 70 9 210
4 84 16 336
Total 10 252 30 700
Number of observation (n) = 4
So, b = 4(700) - (10)(252) / ( 120 - 10²)
= 2800-2520/20
= 280/20
= 14
b = 14
Now a= 252 - (14)10/ 4
=112 /4
= 28
So, The linear regression line is
y= 28 + 14x
Slope = 14
The slope here is positive which means increase in period or moving forward in month is increasing the average temperature of the month.
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Greta uses 3 cups of pasta for every 3/4 cup of sauce. How much pasta does she use per cup of sauce?
4 cups of pasta are used per cup of sauce.
Given,
Greta uses 3 cups of pasta for every 3/4 cup of sauce.
We need to find how much pasta she uses per cup of sauce.
How to compare two quantities?Example:
12 apples = 2 basket ____(1)
For 5 baskets:
We need to make 2 baskets = 5 baskets.
We can divide by 2 and multiply 5 on both sides on (1).
5/2 x 12 apples = 5/2 x 2 baskets
30 apples = 5 baskets.
We have,
3 cups of pasta = 3/4 cup of sauce
We need to make 3/4 cup of sauce as 1 cup of sauce.
Multiply 4/3 on both sides.
4/3 x 3 cups of pasta = 4/3 x 3/4 cup of sauce
4 cups of pasta = 1 cup of sauce
Thus 4 cups of pasta are used per cup of sauce.
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Solve the equation. 3/5 a = 1/4 or \frac{3}{5} a = \frac{1}{4}
A -3
B 3/20
C 5/12
D 2
Answer:
C. 5/12
Step-by-step explanation:
Let's solve your equation step-by-step.
3/5a= 1/4
Step 1: Multiply both sides by 5/3.
(5/3)*(3/5a)=(5/3)*(1/4)
a = 5/12
Hi can anybody help with (a)? I'm struggling with this question
The sum of an infinite geometric series is twice its first term.
b. Find the common ratio of the series.
The sum of an infinite geometric series is twice its first term then the common ratio(r) be 1/2.
What is an infinite geometric series?An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.
Given: S = 2a₁
a₁ be the first term
r be the common ratio
Let the equation be S = a₁/1-r
2a₁ = a₁/1-r
substitute the values in the above equation, we get
2 = 1/1-r
2 - 2r = 1
2r = 1
The value of r = 1/2
Therefore, the common ratio(r) be 1/2.
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solve for x and y
6x+5y=-10
3x+5y=20
Answer: x = -10
Step-by-step explanation:
Answer:
(- 10, 10 )
Step-by-step explanation:
6x + 5y = - 10 ( subtract 6x from both sides )
5y = - 10 - 6x → (1)
3x + 5y = 20 → (2)
substitute 5y = - 10 - 6x into (2)
3x - 10 - 6x = 20
- 3x - 10 = 20 ( add 10 to both sides )
- 3x = 30 ( divide both sides by - 3 )
x = - 10
substitute x = - 10 into (2) and solve for y
3(- 10) + 5y = 20
- 30 + 5y = 20 ( add 30 to both sides )
5y = 50 ( divide both sides by 5 )
y = 10
solution is (- 10, 10 )
PLEASEEE HELP!
6 Chasing Angles: Find the measure of all the missing interior and exterior angles in this figure using linear pairs, vertical angles, and triangle angle sum. Label the diagram
Answer:
Needs alot of steps which you can try
Step-by-step explanation:
Sum of interior angles=exterior angle
Eg, left side 60°+90° = the exterior (big angle outside triangle)
All of the lines are straight so you can find angles using (angles on a straight line) so 180°- the angle known when your solving
There is also opposites angles which are equal, you can search it up
What is the difference of the two rational expressions in simplest form? State any restrictions on the variable.
b. x-1 / x+5 - x+3 / x²+6 x+5
The simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex] is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5, x≠ -1.
As given in the question,
Given expression is [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]
Simplify the given two rational expressions by factorizing them,
[tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{x^{2} +5x +x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{(x+5)(x+1)}\\\\= \frac{x^{2} -1-(x+3)}{(x+5)(x+1)}\\\\= \frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]
Restriction on the variables is given by x≠ -5, x≠ -1.
Therefore, the simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex] is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5, x≠ -1.
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Simplify by combining like terms. 1/2 / ( x² - y²) - 5/2(x² - y²)
The simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y² .
Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .
For Example : 5y,2y are like terms .
In the given question 1/2 / ( x² - y²) - 5/2(x² - y²) the first term is a complex fraction,
[tex]=\frac{\frac{1}{2} }{(x^{2}-y^{2} ) } -\frac{5}{2(x^{2} -y^{2}) }[/tex]
Simplifying the complex fraction we get ,
= 1/2(x² -y²) -5/2(x² -y²)
= 1/(2x² - 2y²) -5/(2x² -2y²)
On further simplifying
= 1/2x² -1/2y²- 5/2x² +5/2y²
On combining the like terms of x² and y².
= 1/2x² - 5/2x² -1/2y² +5/2y²
taking LCM of like terms as 2x² and 2y².
=(1-5)/2x²+(-1+5)/2y²
= (-4)/2x² + 4/2y²
=-2/x² + 2/y²
Therefore , the simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y² .
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What’s the negative exponent ??
Answer:
[tex]10 { }^{ - 5} [/tex]
Step-by-step explanation:
that is the answer above
Last month, jennifer earned $180 for her after-school job. if she was paid $7.50 per hour, how many hours did jennifer work?
Answer: 22
Step-by-step explanation: 143 divided by 6.50 = 22, therefore our answer is 22
through: (-2,-3) and (5,-3)
Answer:
0, -7 or Slope is Undefined
Step-by-step explanation:
y2 - y1 / x2 - x1
(x2 - y2) (x1 - y1)
Solve the system:
5x-6y= -44
3x + 7y = 69
Answer:
Point form:
(2, 9)
Equation form:
x = 2,y = 9
Step-by-step explanation:
Solve each system by elimination.
y = 4 - x , 3x + y = 6
The solution of the given system of equations is (1, 3)
We can solve a system of equations using:
- graphical method
- elimination method
- substitution method
The given system of equations:
y = 4 - x ....... (1)
3x + y = 6 ....... (2)
To use elimination method, add x to both sides of equation (1)
x + y = 4 ....... (3)
Substract equation (3) from equation (2)
3x + y = 6
x + y = 4 –
2x = 2
x = 1
Substitute x = 1 into equation (1)
y = 4 - x
= 4 - 1 = 3
Thus the solution is (1,3)
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PR00F Write a flow proof.
Given: XY || WZ and XW || YZ
Prove: Δ X W Z ≅ ΔZ Y X
We have proved that , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX
It is given that XY ║ WZ and XW ║ YZ.
We have to prove that ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX.
What is the SSS rule of congruency of triangles ?
SSS axiom states that if two triangles have three pairs of congruent sides, then the triangles are congruent.
As per the question ;
XY ║ WZ and XW ║ YZ
So , using this data we can conclude that ;
XY = XW and WZ = YZ
The two triangles are ΔXWZ and ΔZYX
So ,
XY = XW (from given data)
and
WZ = YZ (from given data)
and
XZ = XZ (common)
∴ Both triangles are congruent to each other ;
i.e.,
ΔXWZ ≅ ΔZYX
by using the SSS axiom.
Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX
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The product of three and a number divided by six is twelve.
Answer:
24
Step-by-step explanation:
3a/6 = 12
3a = 6 * 12
3a = 72
a = 72/3
a = 24
Check:
3*24/6 = 12
72/6 = 12
9. You can buy 6 bracelets at Toy Barn for $5.40. You can buy 11 of the same
bracelets at the Dollar Deals for $10.50. (a)How much does it cost per bracelet at
each store? (b)Which store has the better buy?
Answer:
Solutions below.
Step-by-step explanation:
a) To solve this question, we can use the formula.
Average Cost per Bracelet = Total Price ÷ Number of Bracelets.
Toy Barn
Average Cost = $5.40 ÷ 6 = $0.90 per bracelet
Dollar Deals
Average Cost = $10.50 ÷ 11 = $0.95 per bracelet (rounded off to 2 decimal places)
b) The better deal comes with a lower price per bracelet, in this case, Toy Barn has a better deal.
The point N lies on the segment .
Find the coordinates of N so that is 1/3 of MP.
The coordinates of N so that MN is 1/3 of MP are:
(0,7/4)
In geometry line segment is a part of a line that is bounded by two end points, and contains every point on the that is between end points.
Given, coordinates of M(-3,-2)
and coordinates of P(9,13)
so we have,
x₁ = -3
y₁ = -2
x₂ = 9
y₂ = 13
Also we know that MN is 1/3 of MP
⇒ MN/MP = 1/3 = mn
here, m= 1 and n=3
Let the coordinates of N be (x,y)
Therefore,
(x,y) = (nx₁+mx₂)/(m+n) , (ny₁+my₂)/m+n
⇒ (x,y) = (3(-3)+1(9)/1+3) , (3(-2)+1(13)/1+3)
⇒ (x,y) = (-9+9/4) , (-6+13/4)
⇒ (x,y) = (0,7/4)
Thus the coordinates of N so that MN is 1/3 of MP is (0,7/4)
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Find the area of the polygon with the given vertices (3,7), B (5,7), C (3,-7), D (5,-7)
From the given vertices, the area of the polygon is 28.
RectanglesThe rectangle is a quadrilateral. The classification for quadrilaterals is given by the length of sides and angles. For a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).
The area of a rectangle is given by the multiplication between the base and the height.
First, you should plot the points, then see image 1.
From the figure, it is possible to see that the bases ( AB and CD) = 5-3=2
and heights (AC and BD) =-7-(-7)=7+7=14. Thus,
A= B*H= 2*14=28
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How many quarts of pure antifreeze must be added to 7 quarts of a 10% antifreeze solution to obtain a 30% antifreeze solution?
Answer: 2 quarts of pure antifreeze are needed.
Step-by-step explanation: