Answer:
x² - x - 12 = 0
Step-by-step explanation:
Given the x- intercepts are x = - 3 and x = 4 , then the factors are
(x + 3) and (x - 4)
Expressing as a zero product
(x + 3)(x - 4) = 0 ← expand using FOIL
x² - x - 12 = 0
Celine goes to the book fair where paperback books are $2 and hardback books are $4.50. Celine buys three
paperback and 5 hardback books. How much change will Celine receive if she has $35?
7. Equation:
8. Solve:
Answer:
7. 35-(2*3+5*4.5)
8. 6.5
9. Calculate the angle of elevation of the line of sight of a person 27.5 m away from a tree, whose
eye is 1.8 m above the ground, and is looking at the top of a 19.4 tree. (draw a diagram and
answer to the nearest degree)
Answer:
32.61° is the answer
Step-by-step explanation:
Tanx=17.6/27.5
What's the slope of (2, 1) (4,5)
Answer:
[tex]\displaystyle m = 2[/tex]
General Formulas and Concepts:
Algebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (2, 1)
Point (4, 5)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{5 - 1}{4 - 2}[/tex]Subtract: [tex]\displaystyle m = \frac{4}{2}[/tex]Simplify: [tex]\displaystyle m = 2[/tex]what is a = with a ~ thing on top?
What is 13/3.5 and could you give a step by step
Answer:
[tex]3\frac{5}{7}[/tex]
Step-by-step explanation:
13 ÷ 3.5
[tex]3.5=3\frac{5}{10}[/tex]
given the preimage and image, find the dilation scale factor
Given:
The preimage and image of a triangle in the given figure.
To find:
The dilation scale factor.
Solution:
From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).
The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).
If a figure is dilated by factor K with (0,0) as the center of dilation, then
[tex](x,y)\to (kx,ky)[/tex]
Let the scale factor be K, then the image of point A is:
[tex]A(-2,-2)\to A'(k(-2),k(-2))[/tex]
[tex]A(-2,-2)\to A'(-2k,-2k)[/tex]
From the given figure it is clear that the image of point A is A'(-4,-4).
[tex]A'(-2k,-2k)=A'(-4,-4)[/tex]
On comparing both sides, we get
[tex]-2k=-4[/tex]
[tex]k=\dfrac{-4}{-2}[/tex]
[tex]k=2[/tex]
Therefore, the dilation scale factor is 2.
Classify the triangle.
obtuse
equiangular
right
acute
Answer:
acute triangle
Step-by-step explanation:
We have 3 angles that are not equal to each other
They are all smaller than 90 degrees which means they are acute angles
Answer:
Acute
Step-by-step explanation:
Acute=less than 90 degrees
Obtuse=more than 90 degrees
Right=1 side has 90 degrees
Equiangular=every side has the same degree
Therefore, it would be Acute
need help with part b of the attached screenshot please
9514 1404 393
Answer:
(b) 82.9253
Step-by-step explanation:
The first attachment shows the rectangles. The second shows the sum of their areas.
Is it possible to relate cyclones to mathematics?
If yes, explain your thinking with the help of drawings (no need to use
downloaded images) What are the mathematical concepts, theorems and
shapes related to cyclones.
Answer:
Yes
Step-by-step explanation:
Statistics can perdict cyclones for example lets say that somewhere a cyclone happens almost every February then its statistically likely to happen this February too.
Find NM
--------------------------------
Answer:
[tex] MN= \boxed{15}[/tex]
Step-by-step explanation:
refer the attachment
therefore Let,
[tex]a = x - 3 + 16 = x + 13[/tex][tex]b = x - 3[/tex][tex]c = x + 3[/tex]according to the question
[tex] \displaystyle (x - 3 ) (x + 13) =( x + 3 {)}^{2} [/tex]
simplify square and Multiplication:
[tex] \displaystyle {x}^{2} + 10x - 39 = {x}^{2} + 6x + 9[/tex]
cancel x² from both sides:
[tex] \displaystyle 10x - 39 = 6x + 9[/tex]
cancel 6x from both sides:
[tex] \displaystyle 4x - 39 = 9[/tex]
add 39 to both sides:
[tex] \displaystyle 4x = 48[/tex]
divide both sides by 4:
[tex] \displaystyle \boxed{x = 12}[/tex]
given that,
[tex] MN= x + 3[/tex]
substitute the got value of x:
[tex] MN= 12 + 3[/tex]
simplify addition hence,
[tex] MN= \boxed{15}[/tex]
What type of slope is demonstrated by the line below? 5 (-1,3) --5 5 (0.-2)
A. Zero slope
B. Positive slope
C. Undefined slope
D. Negative slope
Answer:
D. Negative slope
Step-by-step explanation:
The slope goes down from left to right, so it is a negative slope
Up from left to right is a positive slope
A vertical line is undefined
A horizontal line is zero slope
Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?
6, 1, –4, –9, –14
Answer:
f(n) = f(n - 1) - 5
Step-by-step explanation:
The recursive formula allows a term in the sequence to be found by adding the constant difference to the previous term.
Here d = 1 - 6 = - 4 - 1 = - 9 - (- 4) = - 14 - (- 9) = - 5 , then
f(n) = f(n - 1) - 5 with n ≥ 1 and f(1) = 6
Identify the value of y.
Answer:
y = 3
Step-by-step explanation:
7. Complete the square to write
c(x)= x2 – 16x + 84 in vertex form.
Answer:
(x-8)²+20 vertex=(8,20)
Step-by-step explanation:
(x-8)² = -20
Graphing Form: y = 1(x-8)²+20
Vicky makes jewelry.she uses 42 beads for each necklace that she makes,and she has 500 beads.how many necklaces can she make explain with work?
Answer:
11
Step-by-step explanation:
Vicky used 462 beads to make 11 necklaces, she would have left 38 beads.
Answer:
He make seven necklaces
Find the missing segment
Find θ. Round to the nearest degree.
hypotenuse = 14
adjacent = 5
5.1.3: Right Triangle Trigonometry
Answer:
the answer is c
Step-by-step explanation:
when solving for theta, we are given the side length adjacent to it (5) and the length of the hypotenuse ( 14).
the trigonometric function that deals with adjacent and hypotenuse values is cosine.
you can use SOH CAH TOA
stands for :
sin = opposite/hypotenuse
cos = adjacent/ hypotenuse
tan = opposite/adjacent
we dont know theta so :
cos(theta) = 5/14
cos = about 69
check :
cos(69) = 5/14
cos(69) = 0.35836794954
5/14 = 0.35714285714
Find Point P is the incenter of DEF . point p of concurrency of the angle bisectors . find PT
PT is 8 because since P is the incenter it's equidistant from all sides.
Use a calculator to determine the unknown angle, to the nearest degree, in each of the following expressions.
tan A = 5/4
cos G = 0.88
Answer:
Using a calculator;
A is approximately 51.34°
G is approximately 28.36°
Step-by-step explanation:
Part 1
The given trigonometric ratio is presented as follows;
tan A = 5/4
Therefore, the angle, A = arctan(5/4)
Using a calculator, the value of A is found as follows;
1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)
2. Entering 5/4 into the calculator, using the keypad
3 . Selecting the arctan button to give, A ≈ 51.34°
Part 2
The given trigonometric ratio is cos G = 0.88
Therefore, G = arccos(0.88)
1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)
2. Enter 0.88 into the calculator by typing
3. Select arccos from the function menu, to give
arcos(0.88) = G ≈ 28.36°.
Instructions: Find the measure of the missing angles in the kite
Answer:
m∠1 = 103
m∠2 = 103
Step-by-step explanation:
by definition, the opposite angles of a kite are congruent.
we know that a quadrilateral's angles add up to 360.
117 º+ 37º + 2xº = 360º
2xº = 206º
xº=103º
which point is on the line that passes through point H and is perpendicular to line FG?
Answer:
The correct answer is (-6, 10).
Step-by-step explanation:
You can find the equation of the blue line and then find out which point is on the perpendicular line to that blue line but you also can figure this out visually by looking at where the points are.
Feel free to message me if you still have questions :)
Answer:
(–6, 10)
Step-by-step explanation:
Melinda walked to the mall at 4 miles per hour and then rode back home in a bus at 24 miles per hour. If her total traveling time was 14 hours, how far was it to the mall?
Given:
Melinda walked to the mall at 4 miles per hour and then rode back home in a bus at 24 miles per hour.
Total traveling time was 14 hours.
To find:
The distance between Melinda's house and mall.
Solution:
Formula used:
[tex]Time=\dfrac{Distance}{Speed}[/tex]
Let x miles be the distance between Melinda's house and mall.
Melinda walked to the mall at 4 miles per hour. So, the time taken by Melinda is [tex]\dfrac{x}{4}[/tex] hours.
Speed of bus is 24 miles per hour. So, the time taken by bus is [tex]\dfrac{x}{24}[/tex] hours.
Total traveling time was 14 hours.
[tex]\dfrac{x}{4}+\dfrac{x}{24}=14[/tex]
[tex]\dfrac{6x+x}{24}=14[/tex]
[tex]7x=14\times 24[/tex]
Divide both sides by 7.
[tex]\dfrac{7x}{7}=\dfrac{14\times 24}{7}[/tex]
[tex]x=2\times 24[/tex]
[tex]x=48[/tex]
Therefore, the mall is 48 miles far from Melinda's house.
plzz help steps if possible if not its ok j=i just need to pass this class
Answer:
[tex]\text{(B) }\cos 40^{\circ}=\frac{x}{60}[/tex]
Step-by-step explanation:
In any triangle, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse (longest side) of the triangle. (a/h)
The angle marked 40 degrees has an adjacent side of [tex]x[/tex] and the hypotenuse of the triangle is 60.
Therefore, we have the equation:
[tex]\boxed{\cos 40^{\circ}=\frac{x}{60}}[/tex]
Which of the
following shows the graph of y = 2e*?
Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if:
a) there must be exactly 3 students on the committee
b) there must be at least one teacher and at least one student on the committee
Answer:
a) 11,880
b) 7,770
Step-by-step explanation:
The number of teachers that volunteer = 6 teachers
The number of students that volunteer = 12 students
The number of people in the committee = 5 people
a) The exact number of student on the committee = 3 student
Therefore, the number of teachers in the committee of 5 = 5 - 3 = 2
The number of teachers in the committee = 2 teachers
We get;
The number of committees that can be made = ₁₂C₃ × ₆C₂ = 792×15 = 11,880
b) When there is at least one teacher and at least one student on the committee, we have;
₁₂C₄ × ₆C₁ + ₁₂C₃ × ₆C₂ + ₁₂C₂ × ₆C₃ + ₁₂C₁ × ₆C₄ = 7,770
The number of committees having at least one teacher and at least one student = 7,770
Amy needs to use a combination of the 12-cup and 36-cup baking pans to fill the order. With only eighteen 12-cup baking pans in her shop, how many of the 36-cup baking pans does she need to complete the order?
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the total orders is not given.
To solve this question, I will assume a value for the total number of order.
Let
[tex]x \to 12-cup[/tex]
[tex]n_x = 18[/tex] ---- number of 12-cup
[tex]y \to 36-cup[/tex]
[tex]n_y = ??[/tex] ---- number of 36-cup
[tex]n \to[/tex] Total order
Required
Calculate [tex]n_y[/tex]
To do this, we make use of the following equation:
[tex]n_x * x + n_y * y = n[/tex]
Substitute known values
[tex]18 * 12 + n_y * 36 = n[/tex]
[tex]216 + 36n_y= n[/tex]
Collect like terms
[tex]36n_y= n - 216[/tex]
Divide both sides by 36
[tex]n_y= \frac{n - 216}{36}[/tex]
Assume the number of orders is: 540 cups
The equation becomes
[tex]n_y= \frac{540 - 216}{36}[/tex]
[tex]n_y= \frac{324}{36}[/tex]
[tex]n_y= 9[/tex]
please help me out asap
(geometry)
Answer:
x = 30
Step-by-step explanation:
If A and B were parallel, then 2x + 50 and 5x - 80 are same- side interior angles and sum to 180° , then
2x + 50 + 5x - 80 = 180
7x - 30 = 180 ( add 30 to both sides )
7x = 210 ( divide both sides by 7 )
x = 30
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $57,077 , and the variable costs will be $11.75 per book. With the other method, the one-time fixed costs will total $22,459, and the variable costs will be $21.25 per book. For how many books produced will the costs from the two methods be the same?
Answer:
for 3644 produced books the costs will be the same.
Step-by-step explanation:
x = number of books
f(x) = production method 1 costs
g(x) = production method 2 costs
f(x) = 11.75x + 57077
g(x) = 21.25x + 22459
for what number of books (x) will that be the same ?
11.75x + 57077 = 21.25x + 22459
34618 = 9.5x
x = 34618 / 9.5 = 3644
Candice bought 6 dozen eggs and broke 9 eggs how many eggs did she have left
Answer:
63
Step-by-step explanation:
12x6=72
72-9=63
the answer is 63
Gabriela was given a 15% increase in wages. If she earned $36,000 last year, what can she expect to earn this year?
The increase in the amount of wages of Gabriela is $ 41,400
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 total amount after increase in wages be = A
Now , the initial amount of Gabriela be = $ 36,000
And , the percentage increase in the wages = 15 %
So , the equation will be
Total amount after increase in wages A = initial amount + ( percentage increase x initial amount )
Total amount after increase in wages A = 36,000 + ( 15/100 x 36,000 )
Total amount after increase in wages A = 36000 + ( 15 x 360 )
Total amount after increase in wages A = 36000 + 5400
Total amount after increase in wages A = $ 41,400
Therefore , the value of A is $ 41,400
Hence , The increase in the amount of wages of Gabriela is $ 41,400
To learn more about equations click :
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