100
let the number of football cards be x then she has 5x baseball cards
the total cards she has is 120, hence
x + 5x = 120
6x = 120 ( divide both sides by 6 )
x = 20
Allison has 20 football cards and 5 × 20 = 100 baseball cards
b=baseball cards
f=football cards
b=5f she has 5 times as many baseball cards as football cards so we multiply the football cards by 5 to make them equal
b+f=120 there are 120 football and baseball cards total
5f+f = 120 substitute 5f everywhere you see a b
6f = 120 combine like terms
f=20 divide by 6
there are 20 football cards
b=5f
b=5(20)
there are 100 baseball cards
Graph A line goes through the point (–2,3) and has a slope of –4. What is the y-intercept of the line?
slope m = –4
equation
y - 3 = -4(x + 2)
y - 3 = -4x - 8
y = -4x - 5 where slope = -4 and y intercept = b = -5
Answer
Y intercept (0, -5)
[tex]x_{1} =-2[/tex]
[tex]x_{2}=3[/tex]
Slope intercept form: y = mx + b
mx=-4
b= -5
Intercepts
x intercept=-1.25
y intercept=-5
The correct answer is y intercept =-5
Use the identity (x2+y2)2=(x2−y2)2+(2xy)2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6.
let a,b be the two numbers. we know that a2-b2=5 and a*b=6
using the formula we are given
[tex](a^2+b^2)^2 = 5^2 + 12^2 = 169[/tex] we get the solution [tex]\sqrt{169} = 13[/tex]
Answer:
13
Step-by-step explanation:
Let x and y are two numbers. The difference of the squares if the two numbers is 5 and the product of the numbers is 6 such that,
[tex](x^2-y^2)=5[/tex]......................(1)
[tex]xy=6[/tex]..........(2)
We need to find the sum of the squares of two numbers. By using following identities it can be calculated as :
[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]
Using equation (1) and (2) in above equation, we get :
[tex](x^2+y^2)^2=5^2+(2\times 6)^2[/tex]
[tex]x^2+y^2=\sqrt{5^2+12^2}[/tex]
[tex]x^2+y^2=13[/tex]
So, the sum of squares of two numbers is 13. Hence, this is the required solution.
What is the value of y = sin (θ) when θ = pi/2 ? a.−1 b.1 c.0 d. cannot be determined
The value of y = sin (θ) when θ = pi/2 is 1.
What is trigonometry?It is the branch of maths concerned with the functions of angles and their involvement in calculations.
We can calculate the value of sin(θ) as follows:
θ = π/2
π/2 is the radian form of 90°
y = sin (θ)
= sin (π/2)
= 1
The value of y = sin(θ) is 1. The correct answer is option B.
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0.2(6x+1)/3.6 = 0.5x/9
The numbers are a bit ugly, but the equation can be solved as is.
... 1.2x/3.6 + (0.2/3.6) = 0.5x/9 . . . . use the distributive property on the left
... x(1/3 -1/18) + 1/18 = 0 . . . . . subtract the right side, simplify fractions
... x(6/18 -1/18) = -1/18 . . . . . . . use 18 for common denominator
... 5x = -1 . . . . . . . . . . . . . . . . . multiply by 18
... x = -1/5 . . . . . . . . . . . . . . . . divide by 5
_____
You can eliminate decimals and fractions by multiplying the given equation by 18.
... 6x +1 = x
... 5x +1 = 0
... 5x = -1
... x = -1/5
_____
The fraction simplification can work like this:
... 0.2/3.6 = 2/36 = 1/18
... 0.5/9 = (1/2)/9 = 1/(2·9) = 1/18 . . . . or . . . . (0.5)/9 × (2/2) = (0.5·2)/(9·2) = 1/18
Answer:
x=-0.2
Step-by-step explanation:
The given equation is
[tex]\frac{0.2(6x+1)}{3.6}=\frac{0.5x}{9}[/tex]
We need to solve the given equation for x.
On cross multiplication we get
[tex]9[0.2(6x+1)]=3.6(0.5x)[/tex]
[tex]1.8(6x+1)=1.8x[/tex]
Using distribution property, we get
[tex]1.8(6x)+1.8(1)=1.8x[/tex]
[tex]10.8x+1.8=1.8x[/tex]
Subtract 1.8x and 1.8 from both sides.
[tex]10.8x+1.8-1.8x-1.8=1.8x-1.8x-1.8[/tex]
[tex]10.8x-1.8x=-1.8[/tex]
[tex]9x=-1.8[/tex]
Divide both sides by 9.
[tex]x=-\frac{1.8}{9}[/tex]
[tex]x=-0.2[/tex]
Therefore, the value of x is -0.2.
Can someone graph x < 2?
To graph x < 2, draw a number line with an open circle at 2, and shade to the left of the circle. This indicates all numbers less than 2 are included, while 2 itself is not.
Explanation:To graph the inequality x < 2, you first need to draw a number line. Let's represent x by a point on the number line. The inequality x < 2 means that x can be any value less than 2, but not 2 itself.
To represent this on the number line, you would place an open circle (which represents exclusion) at 2, and then shade or draw an arrow pointing to the left (representing all numbers less than 2). This visually shows that the solution contains all numbers less than 2, but not 2 itself.
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Q #5 please I need your help
"Standard form" is the form ...
... ax +by = c
where a, b, c are mutually prime integers and the leading coefficient is positive. (If a ≠ 0, then it is "leading". If a = 0, then b is the leading coefficient.)
Of the choices offered, the only one that is equivalent to the given equation is ...
... -x + 6y = 5
_____
However, "standard form" requires the leading coefficient be positive, so an appropriate answer would be ...
... x -6y = -5
or
... 6y -x = 5
____
This is another one for my "broken question" file.
Pedro has been given two segments and the measure of an angle between them. He is trying to construct a congruent triangle. This is what he has done so far. What step has he just completed? A) Copy the angle. B) Copy the first line segment. C) Construct the segment between the endpoints of the two copied line segments. D) Copy the second line segment with one endpoint at the same endpoint of the first line segment.
Answer:
Copy the second line segment with one endpoint at the same endpoint of the first line segment.
c is correct a is wrong
Answer:
Option A : copy the angle
Step-by-step explanation:
We can see that to make congruent triangles he first copied the segments
He copied the segment and drew segment FG
Then he copied the length of BH and then keeping compass on point F cut the line segment FG at I
Then he measured the angle ABC and then intersect the previous arc at J
So, we can see that he just copied the angle
So, his recent completed step was copy the angle .
So, Option A is correct
Hence Option A copy the angle is true .
what is the y-intercept of (2, 18) and (6, 6)?
Assuming you want the y-intercept of the line through those two points, you can find it a couple of different ways.
The slope of the line is ...
... slope = (change in y)/(change in x) = (6-18)/(6-2) = -12/4 = -3
We are given the y-value for x=2. When x decreases by 2 to x=0, then the y-value changes by (-2)·(-3) = +6, from 18 to 24.
___
You can also write the equation of the line in point-slope form as ...
... y = -3(x -2) +18
Again, when x=0, the y-intercept is ...
... y = -3(0 -2) +18 = 6 +18 = 24
The y-intercept of the line through (2, 18) and (6, 6) is 24.
Pls help need ans ASAP
MP = MP, so triangle MPN ≅ triangle MPK by SSS. That means ∠NMP ≅ ∠KMP by CPCTC, so
... ∠NMP + ∠PMK = ∠NMK
... 2×∠PMK = 50° . . . substitute ∠PMK for ∠NMP, with which it is congruent
... ∠PMK = 25° . . . . . divide by 2
What does the intersection of two coplanar lines form?
a. a point
b. a line
c. a plane
d. an angle
The intersection of two coplanar lines forms a point.
Option A is the correct answer.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The intersection of two coplanar lines forms:
a.
a point
This is true.
Because two lines that intersect and form a point are called coplanar.
b.
a line
This is not true.
c.
a plane
This is not true.
Two axis makes a plane.
d.
an angle
This is not true.
An angle is formed when two straight lines or rays meet at a common endpoint.
Thus,
A point is formed by the intersection of two coplanar lines.
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Plz plz plz help
At the local convenience store, bubble gum outsells non-bubble gum by a five-to-one ratio. If the store sold 276 pieces of gum today, how many of them were pieces of non-bubble gum?
46 non bubblegum
230 bubble gum
46
sum the parts of the ratio 5 + 1 = 6
divide 276 by 6 to find 1 part of the ratio
[tex]\frac{276}{6}[/tex] = 46 ← 1 part
the store sold 46 non-bubble gum
and 230 bubble gum
what is the square root √−100=__+___i
the answer is:
√100 = 0 + 10 i
hope this helps! :o)
ASAP PLZ HELP GEOMETRY BELOW
Answer:
i think is d
Step-by-step explanation:
PLZ HELP ASAP GEOMETRY
Josh is building an enclosure with recycled cardboard for his collection of model cars. His design is as shown below:
What is the length of side BC in inches?
a. 14
b. 42
c. 49
d. 63
the correct answer is 63 because they are multiplying the length of each side by 7.
Answer: Option 'd' is correct.
Step-by-step explanation:
Since we have given two figures:
John's design is similar to Josh's project.
ML = 8 inches
CD = 56 inches
KL = 9 inches
We need to find value of 'BC'.
So, there ratio would be :
[tex]\dfrac{ML}{CD}=\dfrac{KL}{BC}\\\\\dfrac{8}{56}=\dfrac{9}{BC}\\\\\dfrac{1}{7}=\dfrac{9}{BC}\\\\BC=9\times 7\\\\BC=63\ inches[/tex]
Hence, Option 'd' is correct.
The equation of a line is 6x-2y=12. Find the x-intercept and the y-intercept.
a.x = -2 , y= 6
b.x = 2 , y= -6
c.x = -2 , y= -6
a.x = 2 , y= 6
Which shows the line 3x -2y = -18 in slope-intercept form?
y=3/2x+9
y=2/3x+9
y=-3/2x-9
y=2/3x-9
A line passes through the point (-1,3) and has a slope of -2. What is the equation of the line in slope-intercept form?
y=2x+5
y=-2x+5
y=2x+1
y=-2x+1
A line passes through the points (1,7) and (-4,-3). What is the equation of the line in standard form?
4x-2y=10
4x+2y=10
4x-2y=-10
4x+2y=-10
Which points are a solution to the inequality <−3+4? (Choose all that apply)
(Select all that apply.)
(0,4)
(-2,7)
(3,-4)
(-1,-5)
First four is BBBC，The last one doesnt make sense to me，you probably didnt write it right
Answer:s
Step-by-step explanation:
Write an expression for the calculation divide 10 in half and subtract from 50 divide into fifths
There are several issues with this English description, as there often are.
We assume you mean you want to divide 10 into two equal parts, then subtract one of those parts from 50.
... (10/2) is half of 10
When that is subtracted from 50, the result is
... 50 - (10/2)
We assume you want one fifth of this result. Other interpretations are that you are subtracting 10/2 from (50/5), or that you are using the difference as the denominator with 1/5 or some other number of fifths as the numerator (dividing <the difference> into 1/5).
Then your expression might be ...
... (1/5)(50 -10/2)
_____
There are ways to write math expressions in English so they are unambiguous. This isn't one of them. It must be done very carefully, as English is often intentionally vague and subject to a variety of interpretations (as most human languages are). Good punctuation helps.
what is 1 and 1/4% of 200?
Find the equation of the line in slope-intercept form.Slope is 2/3 through (3, 4)
Remark
You have been told that the slope of the line is 2/3. That means that if the general equation is y = mx + b is the equation for the slope intercept formula and since m = the slope, then m also equals 2/3
y = (2/3)x + b
Use the point to find b
when x = 3
y = 4 This comes from the point
4 = (2/3) * 3 + b multiply 2/3 and 3 together
4 = 6/3 + b Simplify 6/3
4 = 2 + b Subtract 2 from both sides
4 - 2 = b Combine
2 = b
Equation
y = (2/3)x + 2
Hey there!!
What is slope-intercept form ?
Ans :- y = mx + b
Where 'm' is the slope and 'b' is the y-intercept.
Given :
Slope = 2/3
Coordinate : ( 3 , 4 )
Now, plugging in all these values, we get :
... 4 = ( 2/3 )×3 + b
... 4 = 2 + b
b = 2
Hence, the y -intercept is 2.
Getting this into slope-intercept form :
y = ( 2x/3 ) + 2
Hope my answer helps!!
Use the Counting Principle to find the probability of choosing the 8 winning lottery numbers when the numbers are chosen at random from 0 to 9.
A. 1 in 100,000,000
B. 1 in 43,046,721
C. 1 in 1,000,000,000
D. 1 in 10,000,000
Answer: A. 1 in 100,000,000
Step-by-step explanation:
The given digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
The total number of digits = 10
Now by using the counting principle, the probability of choosing one number is given by :-
[tex]\text{P(one number)}=\dfrac{1}{10}[/tex]
Therefore, the probability of choosing 8 numbers (with replacement ) will be :
[tex]\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}=(\dfrac{1}{10})^8=\dfrac{1}{100,000,000}[/tex]
HELP WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 98 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Use the definition of a ratio to verify that 4/5 is equivalent to 16/20.
multiply numerator/ denominator by the same value 4 to create an equivalent ratio
[tex]\frac{4}{5}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{16}{20}[/tex]
\frac{4}{5} × \frac{4}{4} = \frac{16}{20}
The curve of best fit to model the data is given below.
y=18,582(0.90)^x
Use the exponential model to complete the following statements. Round to the nearest whole number, if necessary.
There were ______ visitors on the opening weekend.
There were approximately _____ visitors on the 9th weekend.
The number of visitors was about 15,051 after ______ weekends.
Answer:
1) There were 18582 visitors on the opening weekend.
2) There were approximately 7199 visitors on the 9th weekend.
3) The number of visitors was about 15,051 after 2 weekends.
Step-by-step explanation:
Given : The curve of best fit to model the data is given below.
[tex]y=18582(0.90)^x[/tex]
To find : Complete the statements,
1) There were _____ visitors on the opening weekend.
2) There were approximately _____ visitors on the 9th weekend.
3) The number of visitors was about 15,051 after ______ weekends.
Solution :
[tex]y=18582(0.90)^x[/tex] is the exponential equation:
where, y is the number of visitors and x are the weekends since opening
1. Since the opening weekend is the day of the the park's opening.
So, replace x=0 in our exponential equation to get the number of visitors on the opening weekend:
[tex]y=18582(0.90)^x\\y=18582(0.90)^0\\y=18582(1)\\y=18582[/tex]
Therefore, There were 18582 visitors on the opening weekend.
2. To find the approximate number of visitors on the ninth weekend.
We replace x=9 in our exponential equation:
[tex]y=18582(0.90)^x\\y=18582(0.90)^9\\y=7199.0475[/tex]
Rounded to the nearest integer : y=7199
Therefore, There were approximately 7199 visitors on the 9th weekend.
3. Here, we know that the number of visitors is 15051
Since y represents the number of visitors.
So, replace y=15051 in our exponential equation and solve for x:
[tex]y=18582(0.90)^x\\\\15051=18582(0.90)^x\\\\ \frac{15051}{18582} =0.90^x\\\\0.90^x= \frac{5017}{6194} \\\\ln(0.90^x)=ln(\frac{5017}{6194})\\\\xln(0.90)=ln(\frac{5017}{6194})\\\\x= \frac{ln(\frac{5017}{6194})}{ln(0.90)} \\\\x=2.0002[/tex]
Rounded to the nearest whole number : x=2
Therefore, The number of visitors was about 15,051 after 2 weekends.
Point B is in the interior of ∠AOC, m∠AOC = 108°. Find m∠AOB, if m∠AOC = 3m∠AOB.
To find the measure of angle AOB when given that angle AOC is 108 degrees and m∠AOC = 3m∠AOB, use the relationship between the angles to calculate m∠AOB as 36 degrees.
Given: ∠AOC = 108°, m∠AOC = 3m∠AOB
To find: m∠AOB
Steps to solve:
Since ∠AOC = 108° and m∠AOC = 3m∠AOB, we can set up an equation: 108 = 3x, where x is m∠AOB.
Solving the equation, x = 36°. Therefore, m∠AOB = 36°.
At a bargain store.Tanya bought 5 items that each cost the same amount. Tony bought 6 items that each cost the same amount, but each was $1.75 less than the items that tanya bought. both tanya and Tony paid the same amount of money. what was the individual cost of each person's items?
(A) write an equation. let x represent the cost of one of tanya's items.
(B) solve the equation. show your work
(C) check your solution. show your work
(D) state the solution in complete sentences.
(A) For x representing the cost of one of Tanya's items, her total purchase cost 5x. The cost of one of Tony's items is then (x-1.75) and the total of Tony's purchase is 6(x-1.75). The problem statement tells us these are equal values. Your equation is ...
... 5x = 6(x -1.75)
(B) Subtract 5x, simplify and add the opposite of the constant.
... 5x -5x = 6x -6·1.75 -5x
... 0 = x -10.50
... 10.50 = x
(C) 5x = 5·10.50 = 52.50
... 6(x -1.75) = 6·8.75 = 52.50 . . . . . the two purchases are the same value
(D) The individual cost of Tanya's iterms was $10.50. The individual cost of Tony's items was $8.75.
What value of x makes the vertical parts of the letter N parallel? (4x + 12)°7x° When x = , the alternate interior angles are congruent and the vertical parts of the letter N are parallel.
what is x?
Answer:
x = 4
Step-by-step explanation:
We assume that the given expessions represent the measures of the alternate interior angles, so are equal.
... (4x + 12)° = 7x°
... 12 = 3x . . . . . . . divide by degrees, subtract 4x
... 4 = x . . . . . . . . . divide by 3
_____
Then the angles are 7x° = 28° = (4x+12)°.
Nathan wants you to solve this puzzle: " I am thinking of a number. If you divide my number my 3 and add -3 you will get 4. What is my number. Show all your work
number is 21
let the number be n then dividing by 3 gives [tex]\frac{n}{3}[/tex] and adding - 3 gives
[tex]\frac{n}{3}[/tex] - 3 = 4 ( add 3 to both sides )
[tex]\frac{n}{3}[/tex] = 7 ( multiply both sides by 3 )
n = 3 × 7 = 21
(6x^2-2x+4)+(3x^2-4x-3) show work
Since the sign between parentheses is +, we can simply drop the parentheses and combine like terms.
... = x²(6 +3) +x(-2 -4) +(4 -3)
... = 9x² -6x +1
A cake recipe asked for 4⁄6 of a cup of oil, but Brad accidentally poured 5⁄6 of a cup of oil into the batter. How much extra oil did Brad pour into the batter?
The drama club is washing cars for a fundraiser if the rate continues how many cars will they wash in 4 hours
In order to calculate the number of cars the drama club could wash in 4 hours, one needs to know their washing rate per hour. Supposing it to be 2 cars/hour, the multiplication of the rate by the number of hours (2 * 4), shows that they could wash 8 cars.
Explanation:The subject of this question is mathematics, specifically rate problems in the context of a real-world situation. In order to solve a problem like this, we need to know the rate at which the drama club is washing cars. This information is missing from the question, so let's suppose that they wash 2 cars per hour. In that case, their rate of washing cars is 2 cars/hour. Then, if you want to find out how many cars they could wash in 4 hours if they continue at this pace, you'll need to multiply their rate by the number of hours.
Let's calculate: Rate (2 cars/hour) * Time (4 hours) = 8 cars.
This means that if they keep washing cars at a rate of 2 cars per hour, they will have washed 8 cars in 4 hours.
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2x2 + 9x + 8 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
The solutions for the equation 2x^2 + 9x + 8 = 0 are x = (-9 + √17)/(4) and x = (-9 - √17)/(4), which are approximately 0.44 and -4.94, respectively.
Explanation:To solve the equation 2x^2 + 9x + 8 = 0, we can use the quadratic formula. The quadratic formula states that the solutions for any quadratic equation of the form ax^2 + bx + c = 0 can be calculated using the formula:
x = (-b ± √(b^2 - 4ac))/(2a)
For the given equation, a = 2, b = 9, and c = 8.
Plugging these values into the formula, we get:
x = (-9 ± √(9^2 - 4*2*8))/(2*2)
Simplifying, we have:
x = (-9 ± √(81 - 64))/(4)
x = (-9 ± √17)/(4)
So, the solutions for the equation 2x^2 + 9x + 8 = 0 are x = (-9 + √17)/(4) and x = (-9 - √17)/(4), which are approximately 0.44 and -4.94, respectively.
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What percent increase is this?
225 to 255
Answer:
The percent increase is [tex]13.33[/tex]%
Step-by-step explanation:
First we need to calculate the increase:
Increase in value = [tex]255-225[/tex]
=[tex]30[/tex]
Percent increase = [Increase in value / Initial value]*100
=[tex]\frac{30}{225} *100[/tex]
=[tex]13.33[/tex]%
Therefore,
the percent increase is [tex]13.33[/tex]%