Answer:
correct me if im wrong but im assuming four just cause if you count what you have all ready not couting the 15 pies. You have at leat 12 and not couting the lemon pies. And from there you basically have to just thing and do the math and I got at least 3 to 5 pies that should be blueberry. srry for my spekling it ducks
We can expect that out of the next 15 pies sold, approximately 5 of them will be blueberry pies.
What is a relative frequency?Relative frequency is a statistical measure that expresses the proportion or percentage of times an event occurs in relation to the total number of events.
We have,
To estimate how many of the next 15 pies sold should be blueberry pies, we can use the relative frequency of blueberry pies in the given data.
The relative frequency of a pie flavor is the ratio of the number of pies of that flavor to the total number of pies.
The total number of pies sold in this data is:
= 2 + 3 + 2 + 4 + 1
= 12
The number of blueberry pies sold is 4.
The relative frequency of blueberry pies.
= 4/12
= 1/3
This means that 1/3 of the pies sold were blueberry pies.
To estimate the number of blueberry pies out of the next 15 pies sold, we can multiply 15 by the relative frequency of blueberry pies.
= 15 x (1/3)
= 5
Therefore,
We can expect that out of the next 15 pies sold, approximately 5 of them will be blueberry pies.
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Help with number 16 please
Answer:
the answer is c. 300
Step-by-step explanation:
18+32×12÷2
base 1 + base 2 × height ÷ 2
On a coordinate plane, a parabola opens up. It goes through (negative 3.25, 5), has a vertex of (1.75, negative 2.75), and goes through (6.25, 5). Solid circles appear on the parabola at (negative 3, 4), (0, negative 2), (1.75, negative 2.75), (3, negative 2), (6, 4).
Which is f(6) for the quadratic function graphed?
–2
–0.5
1.5
4
Answer:
-2
Step-by-step explanation:
/jwkkskjdkdiifididirit
Answer:
4
Step-by-step explanation:
I need help with this question. I have a few correct and need help with the ones that are not.
Step-by-step explanation:
For the first one, you have the -2 step right, but now we're at
f(x) -2 = x³
We have to take the cube root of each side to solve for x, which looks like
∛(f(x)-2) = x or (f(x)-2)^(1/3) = x. This makes our inverse function ∛(x-2) Putting a 3 to the side multiplies the value by 3, and doesn't cube root it.
For your next incorrect answer, you simply need to plug the inverse function that I just gave in.
For the one after that, the question is asking to plug in f(x). We know that our inverse is ∛(x-2) , and the question is asking to plug f(x) in for x here. Thus, in the box, simply put down x³+2
For the last incorrect answer, we need to find the cube root of something, and by plugging in f(x) into the previous one, we are left with ∛(x³+2-2). Therefore, in the box, simply put down x³ as that is what's left
Contains the point (-5, 1) and is perpendicular to the line 2x − y = 4
Answer:
Step-by-step explanation:
2x − y = 4
2x − 4 = y
y = 2x - 4
negative inverse of slope is perpendicular
y = -1/2 x - 4
~~~~~~~~~~~~~~~~~~~~~~~
point slope form of a line
(-5, 1) & m = -1/2
1 = -1/2 (-5) + b
1 = 5/2 + b
b = -3/2
Final answer: y = -1/2 x - 3/2
or if you prefer: 2y + x = -3
HELP PLEASE IM STUCK!
1. Which of these describes the relation for this set of coordinate pairs?
{(-1, 5), (12, 18), (0, 6), (-3, 3), (4, ?), (?, 11)}
a. x - y = 6 b. f(x) = x +6 c. f(x) = 6 d. y = 6x e. None of these
Answer:
b) f(x) = x + 6
Step-by-step explanation:
The coordinate (0, 6) makes the y-intercept = 6. Only one of these functions has that intercept: f(x) = x + 6. If you plug in each coordinate the outputted y-value matches up, making this the right answer.
There is a study on exercise and health: a group of women who have been exercising regularly for 5 years are grouped and given a wellness exam and compared to a group of women who have not exercised in the past five years. What kind of data collection is this?
Experiment
Survey
Simulation
Observational Study
Answer:
Survey Data Collection.
Step-by-step explanation:
This is a survey because there are survey questionnaires (wellness exam).
Answer:
Observational Study Is the Answer
Solve for k:
6=7k+1
K=
Answer:
5/7
Step-by-step explanation:
6=7k+1
-1 -1
--------------
5= 7k
Divide both sides by 7k
k= 5/7
[tex]\huge\color{purple}\boxed{\colorbox{black}{k=0.714}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]➺ \: 6 = 7k + 1[/tex]
[tex]➺ \: 7k = 6 - 1[/tex]
[tex]➺ \: 7k = 5[/tex]
[tex]➺ \: k = \frac{5}{7}\\ [/tex]
[tex]➺ \: k = 0.714[/tex]
Therefore, the value of [tex]k[/tex] is [tex]0.714[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex]➺ \: 6 = 7k + 1[/tex]
[tex]➺ \: 6 = 7 \times 0.714 + 1[/tex]
[tex]➺ \: 6 = 5 + 1[/tex]
[tex]➺ \: 6 = 6[/tex]
➺ L. H S. = R. H. S.
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
I NEEED HELPPPPP PLEASEEEE UM BEGGING SOMEONE PLEASEEEEEEEEEEEE
Answer:
p = 28.56
Step-by-step explanation:
Circumference of circle
c = 2πr
Since this is a semicircle the perimeter is half the circumference
p = πr
p = 3.14 * 4
p = 12.56
---------------------------
Triangle
the outer perineter is just the two outer sides
p = 6 + 10
p = 16
-------------------------
total outer perimeter
p = 12.56 + 16
p = 28.56
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Use the following for problems 22-25
Problem 22
a)
The face cards are Jack, Queen, King. We have four copies of each.
There are 3*4 = 12 face cards total.
12/52 represents the probability of picking a face card.
4/52 represents the probability of picking an ace, since we have 4 aces out of 52 cards. We don't drop to 51 since we put the first card back.
Multiplying the fractions gives (12/52)*(4/52) = 48/2704 = 3/169
Answer: 3/169----------------------
b)
We do the same steps as before, but the 4/52 will be changed to 4/51. This is because the first card is not put back.
(12/52)*(4/51) = 48/2652 = 4/221
Answer: 4/221========================================================
Problem 23
a)
4/52 represents the probability of picking a '2', and it also represents the probability of picking a '10' if we put the first card back
(4/52)*(4/52) = 16/2704 = 1/169
Answer: 1/169----------------------
b)
We'll change the second instance of 4/52 into 4/51 because that first card isn't put back
(4/52)*(4/51) = 16/2652 = 4/663
Answer: 4/663========================================================
Problem 24
a)
4/52 = probability of picking an ace
12/52 = probability of picking a face card
4/52 = probability of picking '7'
Each denominator is 52 because we are putting the cards back
(4/52)*(12/52)*(4/52) = 192/140608 = 3/2197
Answer: 3/2197----------------------
b)
We do the same thing as before, but we decrease the denominator by 1 each time we pull out another card
(4/52)*(12/51)*(4/50) = 192/132600 = 8/5525
Answer: 8/5525========================================================
Problem 25
a)
The probability of picking a king is 4/52. This is the same whether we're on the first king, second or third. This is because we're putting the card back.
(4/52)*(4/52)*(4/52) = 64/140608 = 1/2197
Answer: 1/2197----------------------
b)
Now that the cards aren't put back, we'll have the denominators drop by 1 each time (52,51,50)
So the probability is
(4/52)*(4/51)*(4/50) = 64/132600 = 8/16575
Answer: 8/16575A ball is thrown from an initial height of 3 feet with an initial upward velocity of 21 ft/s. The ball height h (in feet) after t seconds is given by the following. h=3+21t-16t^2 find all values of t for which the balls height is 9 feet.
Answer:
Step-by-step explanation:
The position equation is given as
[tex]s(t)=-16t^2+21t+3[/tex] and we are looking for the times when the position of the ball is 9 feet. That means that we simply plug in a 9 for s(t) and factor to solve for t:
[tex]9=-16t^2+2t+3[/tex] and
[tex]0=-16t^2+21t-6[/tex] and this is what we factor to find t:
t = .42 sec and then again on its way back down at t = .89 sec
if a loaf of bread coast £1.52 how much change will you get from £10 if you buy 4loaves
Answer:
Balance will be £3.92
Step-by-step explanation:
Cost of 1 loaf = £1.52
Therefore, cost of 4 loaves = 4 x 1 . 52 = £6.08
So if you pay with £10 your balance will be = 10.00 - 6.08 = £3.92
The solution is £ 3.92
The amount of money after the purchase of 4 loaves of bread is given by the equation A = £ 3.92
What is an 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.
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 data ,
Let the equation be represented as A
Now , the value of A is
The total amount of money = £ 10
The cost of one loaf of bread = £ 1.52
Now , the number of loaves of bread = 4 loaves
So , the cost of 4 loaves of bread = 4 x cost of one loaf of bread
Substituting the values in the equation , we get
The cost of 4 loaves of bread = 4 x 1.52
The cost of 4 loaves of bread = £ 6.08
The amount of money after the purchase A = total amount of money - cost of 4 loaves of bread
Substituting the values in the equation , we get
The amount of money after the purchase A = £ 10 - £ 6.08
The amount of money after the purchase A = £ 3.92
Therefore , the value of A is £ 3.92
Hence , the amount is £ 3.92
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A study attempts to examine whether watching a lot of television or playing a lot of video games will have a detrimental effect on a child's academic success at school and/or their success at sports. he experiment is conducted on the basis that the age of the child will be important in determining this effect but the gender of the child will not. Select all the elements that are FACTORS of this experiment:
a. age of the child
b. gender of the child
c. time spend reading books over a year
d. time spent playing video games over a year
e. success at sports
f. academic success at school
g. time spent watching television over a year
Answer : A,D,G
Step-by-step explanation:
A factor of experiment is the controlled independent variable.
The factor of experiments are,
d) Time spent playing video games over a yeare) Success at sportsf) Academic success at schoolg) Time spent watching television over a yearHence option d,e,f and g is the factor of experiment.
What is the factor of experiment means?A factor of experiment is the controlled independent variable.
Given information
The experiment is conducted on the basis of age.
The experiment is not conducted on the basis of gender.
In the experiment the relation between watching TV a lot or playing video game and child's academic success at school and/or their success at sports tried to obtained.
Factors of this experiment-
a) Age of the child- As in the statement it is cleared, that the age of the child is a base of the experiment but the age can not be a controlled independent variable. Thus the age of the child is the not a factor of this experiment.b) Gender of the child-As for the study for the given problem, the gender is not important. Thus the gender of the child in not a factor of this experiment.c) Time spend reading books over a year-The study is to determine the relation between watching TV a lot or playing video game and child's academic success and not about reading books. Thus the time spend reading books over a year is not a factor of this experiment.d) Time spent playing video games over a year- The study is to determine the relation between playing video game and child's academic success or success in sports. Thus, time spent playing video games over a year is a factor of this experiment.e) Success at sports-As the success at the sports is the part of the study. Thus, success at sports is a factor of this experiment.f) Academic success at school- As the academic success at the school is the part of the study. Thus, academic success at school is a factor of this experiment.g)Time spent watching television over a year-The study is to determine the relation between a lot of television watching and child's academic success or success in sports. Thus, time spent watching television over a years a factor of this experiment.Thus the factor of experiments are,
d) Time spent playing video games over a yeare) Success at sportsf) Academic success at schoolg) Time spent watching television over a yearHence option d,e,f and g is the factor of experiment.
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If -9x(x + A) + 2 = (Bx + 2)(3x - 1) + 4, find the constants A and B.I am stuck at the step of solving B,can you help me?write down you steps and answer please
Answer:
A = -1
B = -3
Step-by-step explanation:
you need to do all the multiplication on both sides and then simply compare the factors of the various powers of x.
so,
-9x² - 9×A×x + 2 = 3×B×x² + 6x -Bx - 2 + 4
-9x² - 9×A×x + 2 = 3×B×x² + (6-B)x + 2
the x-less constants 2 = 2 are correct. now we need to compare the factors for the other parts of x.
we have left and right only one expression of x²
-9x² on the left
3×B×x² on the right
therefore,
-9 = 3×B
=> B = -3
otherwise the equation would not be correct for all values of x.
the only other parts remaining are
-9×A×x = (6-B)x = (6 - -3)x = (6+3)x = 9x
=>
-9×A = 9
-A = 1
A = -1
remember, all parts of the left and of the right side must be equal for the equation to be true in all cases.
find the value of c to the nearest tenth
9514 1404 393
Answer:
x ≈ 9.3
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(50°) = 6/x
Solving for x gives ...
x = 6/cos(50°) ≈ 9.3343
x ≈ 9.3
__
There is no 'c' to find the value of.
Answer:
x ≈ 9.3
Step-by-step explanation:
Since , this is right triangle, we can use trigonometry functions;
cos θ = Adjacent side / Hypotenuse
Where, θ = 50°
Hypotenuse = xAdjacent side = 6Solve for x
cos 50° = 6 / x
Multiply both side by x
cos 50° × x = 6 / x × x
cos 50° × x = 6
divide cos50° by both sides
cos 50° / cos 50° × x = 6 / cos 50°
x = 6 / cos 50°
x ≈ 9.33434296
Nearest tenth :- x ≈ 9.3
Give an example of reciprocals?
Answer:
1/6 = 6
1/7 = 7
1/8 = 8
24/5 = -1/5 or 5
Step-by-step explanation:
Find sin θ, cot θ, and csc θ, where θ is the angle shown in the figure.
Give exact values, not decimal approximations.
Step-by-step explanation:
everything can be found in the picture
As per the given angle values, the value of sin θ = √19 / 10, cot θ = 9 / √19 and csc θ = 10 / √19.
Let's begin by labeling the sides of the right-angled triangle. The hypotenuse is the side opposite the right angle and has a length of 10 units. The adjacent side, which is the side adjacent to the angle θ, has a length of 9 units.
Using these side lengths, we can apply the trigonometric definitions to find the required values:
Sine (sin θ):
The sine of an angle θ in a right-angled triangle is defined as the ratio of the length of the side opposite the angle (opposite side) to the length of the hypotenuse. The formula for sine is: sin θ = opposite / hypotenuse.
In our case, the opposite side is the side we want to find, and the hypotenuse is 10 units. Therefore, sin θ = opposite / 10.
Using the Pythagorean theorem:
opposite² + 9² = 10²
opposite² + 81 = 100
opposite² = 100 - 81
opposite² = 19
opposite = √19 (taking the positive square root as the length cannot be negative)
Now, we can calculate sin θ:
sin θ = √19 / 10
Cotangent (cot θ):
The cotangent of an angle θ in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the opposite side. The formula for cotangent is: cot θ = adjacent / opposite.
In our case, the adjacent side is 9 units, and we have already found the length of the opposite side, which is √19. Therefore, cot θ = 9 / √19.
Cosecant (csc θ):
The cosecant of an angle θ in a right-angled triangle is defined as the ratio of the length of the hypotenuse to the length of the opposite side. The formula for cosecant is: csc θ = hypotenuse / opposite.
Again, the hypotenuse is 10 units, and the opposite side is √19. Thus, csc θ = 10 / √19.
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The slope f '(x) at each point (x, y) on a curve. y = f (x) is given along with a particular point (a, b) on the curve. Use this information to find f (x).
[CLO-3] f '(x) = 9 x 2 + 4 x - 4; (0, -7)
By the fundamental theorem of calculus,
f(x) = f (0) + ∫₀ˣ f '(t) dt
We're given that the plot of f(x) passes through the point (0, -7), so f (0) = -7, and
f(x) = -7 + ∫₀ˣ (9t ² + 4t - 4) dt
f(x) = -7 + (3t ³ + 2t ² - 4t )|₀ˣ
f(x) = -7 + (3x ³ + 2x ² - 4x)
f(x) = 3x ³ + 2x ² - 4x - 7
what is the median of 66 69 68 69 70 70.
create an equation to solve for x then solve for x.
Answer:
Step-by-step explanation:
In parallelogram adjacent angles are supplementary
∠U +∠V = 180
9x + 15 + 6x + 15 = 180
Combine like terms
9x + 6x + 15 + 15 = 180
15x + 30 = 180
Subtract 30 from both sides
15x = 180 - 30
15x = 150
Divide both sides by 15
x = 150/15
x = 10
∠U = 9x + 15
= 9*10 + 15
= 90 + 15
∠U = 105
∠V = 6x + 15
= 6*10 + 15
= 60 + 15
∠V = 75
Answer:
Equation: [tex]2(9x + 15 + 6x + 15) = 360[/tex]
x = 10°
∠U = 105°
∠V = 75°
Step-by-step explanation:
Hello!
The sum of angles in a parallelogram is 360°. The opposite angles of a parallelogram are congruent.
Part AEquation: [tex]2(9x + 15 + 6x + 15) = 360[/tex]Solve[tex]2(9x + 15 + 6x + 15) = 360[/tex][tex]9x + 15 + 6x + 15 = 180[/tex][tex]15x + 30 = 180[/tex][tex]15x = 150[/tex][tex]x = 10[/tex]The value of x is 10°.
Part BTo find the measures of each angle, simply plug in 10° for x in each equation.
∠U[tex]9x + 15[/tex][tex]9(10) + 15[/tex][tex]90 + 15[/tex][tex]105[/tex]Angle U is 105°.
∠V[tex]6x + 15[/tex][tex]6(10) + 15[/tex][tex]60+15[/tex][tex]75[/tex]Angle V is 75°.
Amy has 2437 stamps and Maria had 1347 stamps. Amy gave some stamps to Maria. In the end, Maria had 3 times as many stamps as Amy. How many stamps did Amy have in the end?
Answer:
946
Step-by-step explanation:
Let :
Amy's stamp = 2437
Maria's stamps = 1347
Let Number of stamps Amy gave to Maria = x
After Giving stamps to Maria ; we have the equation :
Amy's stamps = 2437 - x
Maria's stamps = 1347 + x
(1347 + x) = 3(2437 - x)
1347 + x = 7311 - 3x
x + 3x = 7311 - 1347
4x = 5964
x = 5964 / 4
x = 1491
Number of stamps Amy has in the end :
2437 - 1491 = 946
10x-3(x-6)=x+30 please help me
Step-by-step explanation:
10x-3(x-6)=x+30
10x-3x+18=x+30
7x+18=x+30
6x=12
x=2
Answer:
x=2
Step-by-step explanation:
10x-3(x-6)=x+30
Distribute
10x -3x+18 = x+30
Combine like terms
7x +18 = x+30
Subtract x from each side
7x-x +18 = x+30-x
6x +18 = 30
Subtract 18
6x+18-18 = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x=2
show that the slope of the line joining the points A(1,1) and B(1,1+h)^2 is 2+h.
Answer:
??????????????
Step-by-step explanation:
sorry di ko po alam godbless po
The average daily volume of a computer stock in 2011 was μ=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2018 is different from the 2011 level. Based on a random sample of 40 trading days in 2018, he finds the sample mean to be 31.8 million shares, with a standard deviation of s=14.6 million shares. Test the hypotheses by constructing a 95% confidence interval.
(a) State the hypotheses for the test.
(b) Determine if the researcher will reject the null hypothesis.
Answer:
The 95% confidence interval is ( 27.126 , 34.674)
Step-by-step explanation:
Given
The t critical value at 0.05 level = 2.023 for the df = 39
Confidence interval = 95%
Mean
[tex]\bar{x} - t * \frac{s}{\sqrt{n} } < \mu < \bar{x} + t * \frac{s}{\sqrt{n} }[/tex]
Substituting the given values we get -
[tex]\30.9 - 2.023 * \frac{11.8}{\sqrt{40} } < \mu < \30.9 + 2.023 * \frac{11.8}{\sqrt{40} }\\27.126 < \mu < 34.674[/tex]
Hence, the 95% confidence interval is
( 27.126 , 34.674)
The length of a rectangle should be 9 meters longer than 7 times the width. If the length must be
between 93 and 163 meters long, what are the restrictions for the width, p?
Write the solution set as an algebraic inequality solved for the variable.
Answer:
If we define W as the width:
12m ≤ W ≤ 22m
Step-by-step explanation:
We have a rectangle with length L and width W.
We know that:
"The length of a rectangle should be 9 meters longer than 7 times the width"
Then:
L = 9m + 7*W
We also know that the length must be between 93 and 163 meters long, so:
93m ≤ L ≤ 163m
Now we want to find the restrictions for the width W.
We start with:
93m ≤ L ≤ 163m
Now we know that L = 9m + 7*W, then we can replace that in the above inequality:
93m ≤ 9m + 7*W ≤ 163m
Now we need to isolate W.
First, we can subtract 9m in the 3 sides of the inequality
93m - 9m ≤ 9m + 7*W -9m ≤ 163m -9m
84m ≤ 7*W ≤ 154m
Now we can divide by 7 in the 3 sides, so we get:
84m/7 ≤ 7*W/7 ≤ 154m/7
12m ≤ W ≤ 22m
Then we can conclude that the width is between 12 and 22 meters long.
The transformations to the parent function of a quadratic equation are given below. Write an equation of the new function in vertex form.
translated 3 units down ___
reflected over the x-axis, then translated 5 units left ___
Answer:
What does it mean?
explain properly i will answer your question.
Answer:
11.f(x)=^2-3Step-by-step explanation:12.And slide everything five units down. So a over here that's negative three negative one. So if we slide at five you just down we go one two three four five and get here.HELP ME PLEASE IF YOU DO YOU WILL GET BRAINLESS AND PLEASE EXPLAIN THE BEST YOU CAN
Answer:
<3=75°
Step-by-step explanation:
Angle 3 and angle 2x+95 are supplementary( supplementary angles add up to 180°)
So <3+2x+95=180
<3+2x=180-95
<3+2x=85( let's call this equation 1)
Next, angle 5 and angle 8x+71 are opposite angles (opposite angles are equal) therefore <5=8x+71
Now, <3 and <5 are co-interior angles(co-interior angles are supplementary)
So <3+8x+71=180
<3+8x=180-71=109
Thus, <3+8x=109(let's call this equation 2)
Now solving equation 1 and 2 simultaneously:
Make <3 the subject of equation 1
<3=85-2x
Put <3=85-2x into equation 2
85-2x+8x=109
6x=24
x=24/6=4
Now, remember that angle 2x+95 becomes
2(4)+95
8+95=103°
Therefore<3=180-105=75°
Denver is about 5,200 feet above sea level. Which number line best represents this interger?
Answer: First Number Line
Step-by-step explanation:
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between and minutes. Find the probability that a randomly selected passenger has a waiting time minutes.Find the probability that a randomly selected passenger has a waiting time minutes.
Answer:
Incomplete question, but the concepts of the uniform distribution needed to solve this question are given here.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between a and b minutes.
From here, we get the values of a(smallest value) and b(highest value).
Question of the probabilities:
In the two probability questions, you will get the value of x, and will apply one of the three formulas given above, depending on the question, to find the desired probability.
Factor each trinomial completely.
A. 2x^2 + 17x + 21
B. 3x^2 - 17x + 10
Answer:
A) (2x+3)(x+7) B) (3x-2)(x-5)
Step-by-step explanation:
A) 2x^2+17x+21=(2x+3)(x+7)
B) 3x^2-17x+10=(3x-2)(x-5)
You have some marbles. When you make a shape of an equilateral triangle, you either have 4 extra, or you need 28 more to complete the shape. How many marbles do you have? How long is a side of the biggest equalateral triangle that you can make make with your marbles?
Answer:
You have 500 marbles.
The longest side of the biggest equalateral triangle that you can make with your marbles is 31
Step-by-step explanation:
28 + 4 = 32
So our equation is:
TR(32) - 28
Now find Triangular Number 32: (32 *33)/2=528
528 - 28 = 500
So, we have 500 marbles
Now we need to find the longest side of the biggest equalateral triangle that you can make make with your marbles
Let's go back to 28 + 4 = 32
One row above 32 is 31
So the longest side of the biggest equalateral triangle that you can make with your marbles is 31
Hope this helps!