How many triangles can be constructed with angles measuring 10,80,and 90?
Solve 2x2 − 8x = −7.
negative 2 plus or minus square root of 2
negative 2 plus or minus 2 square root of 2
quantity of 2 plus or minus square root of 2 all over 2
2 plus or minus square root of 2 end root over 2
The solutions to the quadratic equation 2x^2 - 8x + 7 = 0 are x = 2 + √2 / 2 and x = 2 - √2 / 2 using the quadratic formula.
To solve the equation 2x2 - 8x + 7 = 0, we will use the quadratic formula, where 'x' equals minus 'b', plus-or-minus the square root of 'b' squared minus four 'a' 'c', all over two 'a'. The coefficients in this case are a = 2, b = -8, and c = 7.
First, we calculate the discriminant, which is b2 - 4ac. Substituting our values we get:
(-8)2 - 4(2)(7) = 64 - 56 = 8.
The square root of 8 can be simplified to 2√2, because 8 = 4 × 2 and √4 = 2.
Finally, we substitute the values into the quadratic formula:
x = (-(-8) ± √8) / (2 × 2)
x = (8 ± 2√2) / 4
Dividing each term by 4 gives us:
x = 2 ± √2 / 2
Therefore, the solutions to the equation are:
x = 2 + √2 / 2 and x = 2 - √2 / 2
Tom makes $148.65 in 3 days how much would he make in 2 days.
Answer:
$99.10
Step-by-step explanation:
Answer:
$99.10
Step-by-step explanation:
you would divide the $148.65 by the 3 days and get $49.55. then you would multiply that by the 2 and get your awnser.
12. Describe the shape that would result from a vertical slice of the figure below
13. Explain how a cross section of the figure below can result in a trapezoid
Answer:
12. Pentagon
13. The cross-section will have one pair of parallel sides and one pair of sides that are not parallel along with two opposite triangular faces.
the hedge boundary needs to be planted around a rectangular lawn 18 m long and 12 m wide. if 3 shrubs can be planted to grow a metre hedge, how many shrubs will be needed in all?
Answer:
180Step-by-step explanation:
let P represent the perimeter of the rectangle
P = 2×(12 + 18) = 2×(30) = 60 m
then
the number of shrubs = 3×(60) = 180
The dot plots show the number of hours a group of fifth graders and seventh graders spent playing outdoors over a one-week period.
Time Spent Playing Outdoors
for Fifth Graders and Seventh Graders
2 dot plots with number lines going from 0 to 10. A dot plot titled fifth grade has 0 dots above 0, 2 above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, and 0 and 9 and 10. A dot plot titled seventh grade has 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
Which statement correctly compares the shape of the data in the plots?
Both sets of data have a peak at 5 hours and 6 hours.
The left side of the data looks similar to the right side in the seventh-grade data, but not in the fifth-grade data.
In both sets, the data cluster around 3 hours.
There is a gap in the fifth-grade data, but not in the seventh-grade data.
Answer: the answe is b
Step-by-step explanation:
The left side of the data looks similar to the right side in the seventh-grade data, but not in the fifth-grade data.
What is Dot plot?
A dot plot is a method of visually representing expectations for some data series. A dot plot visually groups the number of data points in a data set based on the value of each point.
How to determine:2 dot plots with number lines going from 0 to 10.
A dot plot titled fifth grade has 0 dots above 0, 2 above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, and 0 and 9 and 10.
A dot plot titled seventh grade has 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
statement correctly compares the shape of the data in the plots
The left side of the data looks similar to the right side in the seventh-grade data, but not in the fifth-grade data.
Learn more about dotplot:
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The sales tax in Ontario is 13%. If you paid $450 on a food bill at the restaurant, how much if it were taxes?
Solve step-by-step
Answer:
58.5%
Step-by-step explanation:
Sales tax in Ontario = 13%
If you paid $450 on food
Tax = 13%/100% x 450
= 0.13 x 450
=58.5%
The length of the base of an isosceles triangle is x. The length of a leg is 3x -4. The perimeter of the triangle is 41. Find x.
Length of base of isosceles triangle, x = 7
Step-by-step explanation:
Step 1: Given base of isosceles triangle, x = 7 and perimeter = 41Length of one leg = 3x - 4. Since two sides, other than the base of an isosceles triangle are equal, the length of the other leg = 3x - 4.
Step 2: Formula for perimeter of triangle = length of sidesStep 3: Substitute values of sides in the formula⇒ 41 = x + (3x - 4) + (3x - 4) = x + 2(3x - 4)
⇒ 41 = x + 6x - 8
⇒ 41 = 7x - 8
⇒ 49 = 7x
⇒ x = 7
Answer:
7
Step-by-step explanation:
A post it note has an area of A square inches.the width of the post it note is 4 inches.which equation represents x,the length of the post it nots in inches. A x= 4/A. B X=A+2(4) C X=A/4. D X=A-2(4)
The right answer is Option C.
Step-by-step explanation:
Given,
Area of post it note = A square inches
Width of post it note = 4 inches
Length of post it note = X
We know that;
Area = Length * Width
[tex]A=X*4\\A=4X[/tex]
As we have to find length, we will divide both sides by 4
[tex]\frac{A}{4}=\frac{4X}{4}\\\\\frac{A}{4}=X\\\\X=\frac{A}{4}[/tex]
The equation [tex]X=\frac{A}{4}[/tex] represents the length of post it notes in inches.
The right answer is Option C.
Keywords: area, multiplication
Learn more about areas at:
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Please help my little sis!
The product of two whole numbers is 14391 and their difference is 6. What are the two numbers?
Answer:
117 and 123.
Step-by-step explanation:
If the 2 numbers are x and y we have the system of equations:
x - y = 6
xy = 14391
From the first equation y = X - 6 so substituting:
x(x - 6) = 14391
x^2 - 6x= 14391
x^2 - 6x - 14391 = 0
The prime factors of -13491 are -3*3*3*13*41
Now 3*3*13 = 117 and -3 * 41 = -123,
so the factors are:
(x - 123)(x + 117) = 0.
x = 123, -117.
As x is a whole number we take the positive value 123.
So x = 123 and y = 123 - 6 = 117.
The fraction as a percent for 19/29
What is scale factor 10 cm =16 cm
Answer:
Step-by-step explanation:
20
Answer:
Scale factor = 5:8
Step-by-step explanation:
Step 1: Write out as a scale
10cm : 16cm
Step 2: Simplify
10 / 2 : 16 / 2
5:8
Answer: Scale factor = 5:8
Alex is a house painter and uses large buckets to transport his paint from room to room. He needs to measure the volume of the bucket to determine how much paint it will hold. Which measurement would be appropriate for the bucket's volume?
A) 15.4 quarts
B) 22.05 quarts
C) 20 quarts
D) 18.25 quarts
Answer:
d
Step-by-step explanation:
I need the answer key of riddle time called why did the school cook become a history teacher?
The response to the riddle " why did the school cook become a history teacher" is she was a expert in Acient grease
What is the riddle?
The riddle is based on history, and it should be noted that in term of history, ancient grease can not be underestimated because they have been existing since time past.
The city-states of ancient Greece were autonomous, however occasionally some would join alliances and hegemonies and serve a more powerful city. Greece was merely a small component of Alexander the Great's empire when it was founded—albeit for a very short time.
Which choice is NOT equal to the others? A) − 2/ 5 B) −2/ 5 C) 2/ 5 D) 2/ −5
Answer:
c) 2/5
Step-by-step explanation:
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Final answer:
The choice that is NOT equal to the others is C) 2/5, because it is the only positive fraction, while the others represent the negative fraction − 2/5.
Explanation:
The student's question asks which of the given choices is NOT equal to the others. The choices provided include A) − 2/5, B) − 2/5, C) 2/5, and D) 2/ −5. To find the answer, we must compare the values.
Options A and B are the same, which is − 2/5 or negative two-fifths. Option D, which is 2/−5, simplifies to − 2/5 because division by a negative number yields a negative result, making it equivalent to options A and B. However, option C is the only one that is different because it is 2/5, which is positive two-fifths, not negative. Therefore, the answer is C) 2/5 as it is not equal to the other options, which are all negative two-fifths.
Identify the zeros of f(x) = (x + 9)(x − 4)(6x + 1).
−9, −1 over 6,4
9, 1 over 6, 4
−9, −1 over 6,−4
−9, 1 over 6, −4
Step-by-step explanation:
We have,
f(x) = (x + 9)(x − 4)(6x + 1)
To find, all zeroes of the given equation = ?
∴ f(x) = (x + 9)(x − 4)(6x + 1)
⇒ (x + 9)(x − 4)(6x + 1) = 0
⇒ x + 9 = 0 or, x − 4 = 0 or, 6x + 1 = 0
⇒ x + 9 = 0 ⇒ x = - 9
⇒ x − 4 = 0 ⇒ x = 4
⇒ 6x + 1 = 0
⇒ 6x = - 1
⇒ x = [tex]\dfrac{-1}{6}[/tex]
∴ x = - 9 , [tex]\dfrac{-1}{6}[/tex], 4
Thus, the required 'option a) - 9 , [tex]\dfrac{-1}{6}[/tex], 4' is correct.
Final answer:
To find the zeros of the function f(x) = (x + 9)(x − 4)(6x + 1), we solve for x in each factor: x = -9, x = 4, and x = -1/6, which means the zeros are -9, 4, and -1/6.
Explanation:
To identify the zeros of a function, you need to find the values of x for which the whole expression equals zero. The function given is f(x) = (x + 9)(x − 4)(6x + 1). To find the zeros, we set each factor equal to zero and solve for x.
(x + 9) = 0 → x = -9
(x − 4) = 0 → x = 4
(6x + 1) = 0 → 6x = -1 → x = -1/6
Therefore, the zeros of the function are -9, 4, and -1/6.
Which ordered pair in the form(x,y) is a solution of this equation?
7x-5y=1
A] (-3,-2)
B] (-2,-3)
C] (0,4)
D] (4,0)
The ordered pair is (-2, -3)
Step-by-step explanation:
Step 1: To find whether an ordered pair is a solution, substitute values of x and y and see whether it satisfies the equation.(-3, -2) ⇒ 7 × -3 - 5 × -2 = -21 + 10 = -11 ≠ 1
(-2, -3) ⇒ 7 × -2 - 5 × -3 = -14 + 15 = 1
(0, 4) ⇒ 0 - 5 × 4 = 20 ≠ 1
(4, 0) ⇒ 7 × 4 - 0 = 28 ≠ 1
So the ordered pair is (-2, -3)
The ordered pair that is a solution to the equation 7x-5y=1 is option B, (-2,-3), as it is the only pair that satisfies the equation when the values are substituted.
Explanation:The question asks which ordered pair is a solution to the equation 7x-5y=1. To find the solution, we simply substitute the x and y values from each ordered pair into the equation and see which pair satisfies the equation.
For option A (-3,-2), let's plug it in: 7(-3) - 5(-2) = -21 + 10 = -11, which does not equal 1.For option B (-2,-3), we get: 7(-2) - 5(-3) = -14 + 15 = 1, which does equal 1. Therefore, this is the correct solution.For option C (0,4), we get: 7(0) - 5(4) = -20, which does not equal 1.Lastly, for option D (4,0), plugging it in gives us: 7(4) - 5(0) = 28, which does not equal 1.So, the ordered pair that is a solution to the equation is option B, (-2,-3).
Find the area of the shape shown below.
Answer: The Area of this shape is 32.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Area = 1/2 ×(a+b)h
a = 4, b = 12, h = 4
Area = 1/2 × (4+12)4
Area = 2(16)
Area = 32square unit
17x + 36y = 479
Y= 2x - 4
Answer:
X=7
Y=10
Step-by-step explanation:
Replace expression Y=2x-4 in 17x + 36y = 479
17x+36(2x-4)=47917x+72x-144=47989x-144=47989x=479+14489x=623x=[tex]\frac{623}{89}[/tex]x=7Now, replace X=7 in expression Y=2x-4
Y=2(7)-4Y=10Where is the vertex of the equation?y = x2 – 18x + 80
Answer:
vertex = (9, - 1 )
Step-by-step explanation:
Given a quadratic in standard form, y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² - 18x + 80 ← is in standard form
with a = 1 and b = - 18, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-18}{2}[/tex] = 9
Substitute x = 9 into the function for corresponding value of y
y = 9² - 18(9) + 80 = 81 - 162 + 80 = - 1
Vertex = (9, - 1 )
If a customer bought an item from a retailer and eventually received a $12.50
rebate check in the mail after sending in a rebate form, which of these
transactions occurred?
A. The manufacturer of the item sent the retailer a check for $12.50
who then passed it along to the customer.
B. The retailer sent the manufacturer of the item a check for $12.50,
who then passed it along to the customer.
C. The manufacturer of the item sent the customer a check for
$12.50 directly
D. The retailer sent the customer a check for $12.50 directly
Answer:
The correct option would be option D.) The retailer sent the customer a check for $12.50 directly.
Step-by-step explanation:
A customer bought an item from a retailer and eventually received a $12.50
rebate check in the mail after sending in a rebate form.
The transaction that occurred would be
D.)The retailer sent the customer a check for $12.50 directly
Answer:
the manufacturer of the item sent the customer a check for 12.50 directly.
Step-by-step explanation:
What is the value of a1 of the geometric series? Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 12 (negative one-ninth) Superscript n minus 1 Negative twelve-ninths Negative one-ninths 1 12
Answer:
12
Step-by-step explanation:
The given geometric series is
[tex] \sum_{n = 1}^{ \infty} 12( { - \frac{1}{9} })^{n - 1} [/tex]
We want to determine the first term of this geometric series.
Recall that the explicit formula is
[tex] a_{n} = 12( { - \frac{1}{9} })^{n - 1} [/tex]
To find the first term, we put n=1 to get:
[tex]a_{1} = 12( { - \frac{1}{9} })^{1 - 1} [/tex]
This gives us:
[tex]a_{1} = 12( { - \frac{1}{9} })^{0}[/tex]
[tex]a_{1} = 12(1) = 12[/tex]
Therefore the first term is 12
Answer:
12
Step-by-step explanation:
The last option, C is the answer. I just took the quiz :D
11. The completion of a chemical reaction is expressed by the equation y = 300 - 4x - XP, where y is
the number of seconds needed to complete the reaction and x is the temperature in degrees Celsius
at which the reaction occurs. If the reaction is complete in 160 sec, what is the temperature at which
the reaction occurs?
Answer:
The reaction ca occur at 10 degree Celsius or -14 degree Celsius.
Step-by-step explanation:
We are given the following in the question:
The completion of a chemical reaction is expressed by the equation
[tex]y = 300 - 4x -x^2[/tex]
where y is the number of seconds needed to complete the reaction and x is the temperature in degrees Celsius at which the reaction occurs.
We have to find the temperature at which the reaction occurs, if the completion time of reaction is 160 seconds.
Putting y = 160
[tex]160 = 300 - 4x -x^2\\x^2 + 4x - 140 = 0\\x^2 + 14x -10x -140 = 0\\x(x+14)-10(x+14)=0\\(x-10)(x+14) = 0\\(x-10) =0, (x+14) =0\\x = 10, x = -14[/tex]
Thus, the reaction ca occur at 10 degree Celsius or -14 degree Celsius.
If a^2 + b^2=c^2 then the triangle is a right triangle.
A triangle with side lengths of 12 in, 24 in and 16 inches is a right triangle.
True or False
Answer:
12² + 16² = 144 + 256 = 400 = 20²
So a triangle with side lengths of 12 in., 16 in., and 24 in. is not a right triangle.
The correct answer is False.
What is the equation in standard form for (0,3) and (7,0)
Answer:
3x + 7y = 21
Step-by-step explanation:
We have value of two points (0,3) and (7,0)
First, let's find the slope of this line. The formula for slope is:
Change in y/Change in x or (y₂ - y₁)/(x₂-x₁)
Where x₁ = 0 x₂= 7 y₁ = 3 y₂ = 0
(y₂ - y₁)/(x₂-x₁)
= (0-3)/(7-0)
=-3/7
Now we can write the equation in point-slope form:
y-y₁ = m(x-x₁)
y - 3 = -3/7(x-0)
y-3=-3x/7
y=-3x/7 + 3
Now let's convert this to standard form, by making the y-intercept by itself:
Ax + By = C
y=-3x/7 + 3
Multiply through by 7
7(y) = 7(-3x/7) + 7(3)
7y = -3x + 21
3x + 7y = 21
How can you write the expression with a rationalized denominator?
Yo sup??
This question can be solved by multiplying the numerator and denominator by 3^1/2
and the answer u will get will be
5*3^1/2-6^1/2)/3
Hope this helps
Which pair shows equivalent expressions?
2 (two-fifths x + 2) = 2 and two-fifths x + 1
2 (two-fifths x + 2) = four-fifths x + 4
2 (two-fifths x + 4) = Four-fifths x + 2
2 (two-fifths x + 4) = 2 and two-fifths x + 8
2([tex]\frac{2}{5}[/tex]x + 4) = [tex]\frac{4}{5}[/tex]x + 4 which is the second option is the equivalent expression.
Explanation:
First, we need to calculate the value of two-fifths of x. It means 2 portions out of the five portions of x which equates to [tex]\frac{2}{5}[/tex]x.
Now we calculate the values of the two expresssions on the LHS.
1) 2 (two-fifths x + 2) = 2 ([tex]\frac{2}{5}[/tex]x + 2) = [tex]\frac{4}{5}[/tex]x + 4.
2) (two-fifths x + 4) = 2([tex]\frac{2}{5}[/tex]x + 4) = [tex]\frac{4}{5}[/tex]x + 8.
Now we determine values of the four expressions on the RHS.
1) Two and two-fifths x + 1 = 2[tex]\frac{2}{5}[/tex]x + 1
2) Four-fifths x + 4 = [tex]\frac{4}{5}[/tex]x + 4
3) Four-fifths x + 2 = [tex]\frac{4}{5}[/tex]x + 2
4) Two and two-fifths x + 8 = 2[tex]\frac{2}{5}[/tex]x + 8.
Out of the various LHS and RHS values, the [tex]1^{st}[/tex] LHS value and [tex]2^{nd}[/tex] RHS value is the same. So option 2 is the answer.
Answer:
second option
Step-by-step explanation:
The radius of a circle is 7 centimeters
What is the circumference of the circle?
What is the area of the circle?
a) So we know the formula of finding the circumference: 2*pi*R.
Assuming we make pi = 3.14: 2 * 3.14 * 7 = 43.96.
b) We also know the formula of finding the area: pi * r^2.
3.14 * 7^2. Using PEMDAS:
3.14 * 49 = 153.86
carol received 189 votes for class president. emma received twice that number of votes. how many votes did emma receive?
Answer:
Emma = 378 votes
Step-by-step explanation:
Carol = 189 votes
Emma = 2 * Carol
Substitute 189 in for Carol
Emma = 2 * 189
Emma = 378 votes
Hope this helps :)
Answer:
378
Step-by-step explanation:
you just had to multiply 189 by 2. Since twice means 2
73. Given PQRS is a parallelogram.
PR bisects Angle SPQ and Angle QRS.
SQ bisects Angle PSR and Angle RQP.
Prove PQRS is a rhombus.
Answer:
See explanation
Step-by-step explanation:
PQRS is a parallelogram, then
[tex]PQ\parallel RS\\ \\QR\parallel SP[/tex]
and
[tex]PQ\cong RS\\ \\QR\cong SP[/tex]
Also
[tex]\angle P\cong \angle R\\ \\\angle Q\cong \angle S[/tex]
1. Consider triangles PQA and RQA, where A is the diagonals intersection point. In these triangles,
[tex]QA\cong QA\ [\text{Reflexive property}][/tex]
[tex]\angle PQA\cong \angle RQA\ [\text{Because QS is angle bisector}][/tex]
[tex]\angle QPA\cong \angle QRA\ [\text{Diagonal PR divides congruent angles in congruent halves}][/tex]
Hence, by AAS postulate triangles PQA and RQA are congruent. Congruent triangles have congruent corresponding parts, so
[tex]PQ\cong RQ[/tex]
2. Consider triangles PSA and RSA. In these triangles
[tex]SA\cong SA\ [\text{Reflexive property}][/tex]
[tex]\angle PSA\cong \angle RSA\ [\text{Because QS is angle bisector}][/tex]
[tex]\angle SPA\cong \angle SRA\ [\text{Diagonal PR divides congruent angles in congruent halves}][/tex]
Hence, by AAS postulate triangles PSA and RSA are congruent. Congruent triangles have congruent corresponding parts, so
[tex]PS\cong RS[/tex]
3. Since [tex]PQ\cong RS[/tex] and [tex]PQ\cong RQ[/tex], you have [tex]RS\cong RQ[/tex]
Therefore,
[tex]PQ\cong QR\cong RS\cong SP[/tex]
Parallelogram with all congruent sides ia a rhombus.