Answer:
7
Step-by-step explanation:
2x^2 - 7x - 4 = 45
2x^2 - 7x - 49 = 0 : subtract 45 from both sides
Quadratic formula:
x = (7 ± sqrt(7^2 - 4*2*-49) ) / 4
x = (7 ± sqrt(49 - -392)) / 4
x = (7 ± sqrt(441)) / 4
x = (7 ± 21) / 4
x = (7 + 21) / 4 OR x = (7 - 21) / 4
x = 28 / 4 OR x = -14 / 4
x = 7 as it is the only positive answer
A carpenter makes wooden chairs. He has enough wood to make 30 chairs. He makes $60 profit on a dining chair and $90 profit on a rocking chair. It takes him 1 hour to make a dining chair and 2 hours to make a rocking chair. He only has 40 hours available to work on the chairs. The carpenter wants to maximize his profit given the constraints. He draws the graph below to represent this situation. Drag and drop the correct numbers to complete the statements below. Given the restraints, the carpenter can maximize profits by making Response area dining chairs and Response area rocking chairs. His total profit for all the chairs will be $Response area.
Answer:
The carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100
Step-by-step explanation:
Let x be the no. of dining chairs and y be the no. of rocking chair
Time taken by carpenter to make 1 dining chair = 1 hour
Time taken by carpenter to make x dining chairs = x hours
Time taken by carpenter to make 1 rocking chair = 2 hour
Time taken by carpenter to make y rocking chairs = 2y hours
He only has 40 hours available to work on the chairs.
[tex]\Rightarrow x+2y \leq 40[/tex]
He has enough wood to make 30 chairs.
[tex]\Rightarrow x+y\leq30[/tex]
He makes $60 profit on a dining chair and $90 profit on a rocking chair.
So, profit =60x+90y
Plot the equations on graph
Refer the attached figure
Coordinates of feasible region
(0,20),(20,10) and (30,0)
Profit =60x+90y
At(0,20)
Profit = 1800
At(20,10)
Profit = 1200+900=2100
At(30,0)
Profit=900
So,the carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100
HELLLLLLPPPPPP MEEEE PLEASEEEEE!!!!!! Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the interval . Solve algebraically, and show your work and final answer in the response box. Hint: Use the amplitude to determine what y(t) must be when the weight is halfway to its maximum negative position. Graph the equation and explain how it confirms your solution(s).
Answer:
0.20, 0.36 seconds
Step-by-step explanation:
We have already seen that the equation for y(t) can be written as ...
y(t) = √29·sin(4πt +arctan(5/2))
The sine function will have a value of -1/2 for the angles 7π/6 and 11π/6. Then the weight will be halfway from its equilibrium position to the maximum negative position when ...
4πt +arctan(5/2) = 7π/6 or 11π/6
t = (7π/6 -arctan(5/2))/(4π) ≈ 0.196946 . . . seconds
and
t = (11π/6 -arctan(5/2))/(4π) ≈ 0.363613 . . . seconds
The weight will be halfway from equilibrium to the maximum negative position at approximately 0.20 seconds and 0.36 seconds and every half-second thereafter.
The table shows the height increases in inches, of some of the girls in Gina’s class from last month to this month. What girl had a height increase that was greater than 1/2 inch?
The correct answer is Maxine
Explanation:
One of the easiest ways for knowing if a fraction is greater than another is by converting fractions to decimal numbers. This implies dividing the numerator (top number) by the denominator (bottom number). In the case of fraction, [tex]\frac{1}{2}[/tex] the decimal number is 0.5 considering 1 divided into 2 is equal to 0.5. Now to know if other fractions are greater or smaller, this process needs to be repeated.
Gina: [tex]\frac{3}{8} = 0.375[/tex]
Maxine: [tex]\frac{2}{3} = 0.666[/tex]
Shari: [tex]\frac{2}{4} = 0.5[/tex]
Vanessa: [tex]\frac{3}{12} = 0.25[/tex]
According to this, the girl with a heigh increased greater than 1/2 inch is Maxine because 0.666 (Maxine heigh increase) is greater than 0.5 (1/2 inch).
Driving on the highway, you can safely drive 60 miles per hour. "How far can you drive in ‘h' hours?" What is the range of the function which defines this situation? A. 60 B.The number of hours you drive C.The amount of gas you use D.The distance you drive
Answer:
D.The distance you drive
Step-by-step explanation:
If you describe this situation as function, then it will look as:
f(h)= 60hFor h=1 you have f(1)= 60 milesFor h=2 you have f(2)= 120 miles etc.The range of the function is the set of output values
In this case the range is the distance you drive
Correct option is D.
Answer:
The distance you drive
Step-by-step explanation:
i just took the test
the question is in the attachment...
Answer:
11 minutes. 1/4 of 44 is 11
I need help ASAP THANK YOU!!
Answer:
A. Volume: 819, Surface Area: 598
B. Surface area
C. Volume
Step-by-step explanation:
Sorry I'm late, but here I go.
The volume of a rectangular prism is [tex]lwh[/tex] or [tex]bh[/tex]. (l being length, w being width, and h being height.)
So if we multiply the 3 values of 13, 9, and 7, we get 819. This is the volume.
To find the surface area, we can take note that 4 sides are the exact same, and the remaining two are the same. Let's find the area of the top/bottom of the prism.
[tex]13\cdot9=117[/tex]
Since there are two, bottom and top:
[tex]117\cdot2 = 234[/tex].
Now, there are the remaining 4 sides. Let's find the area of one then multiply it by 4.
[tex]13\cdot7=91\\91\cdot4=364[/tex]
Adding 364 and 234 gets up 598, so this is the surface area.
If we are painting something, the surface area is being painted, as we can't paint inside the box. However if we fill up the box with something (concrete in this case), it will be the volume.
Hope this helped!
Answer:
a.
v= 819 cm3
sa= 542 cm2
b. surface area
c. volume
Step-by-step explanation:
Volume of a rectangular prism: Length x width x height
Replacing with the values given:
V = 13 x 9 x 7 = 819 cm3
Surface area = S = 2 × (W × L + L × H + H × W)
S = 2 ( [9x13]+ [13 x7] +[7x9]) = 2 ( 117+91+63)= 542 cm2
b . Surface area, because we only have to paint the exterior of the brick.
c. Volume, because is the amount of concrete that the brick has.
△ABC and △JKL are two triangles such that ∠A≅∠J and ∠B≅∠K. Which of the following would be sufficient to prove that the triangles are congruent? A ACJL=BCKL B ∠C≅∠L C AB≅JK D BC≅Jk
We need to know the rules of congruence of triangles to solve the given problem. The required condition that is sufficient to prove that the triangles are congruent is option (C) AB≅JK.
There are three rules of congruence of triangles, if two triangles satisfy any one of these rules then we can say that the triangles are congruent. The three rules are, SSS which means three sides are equal, ASA which means two angles and their corresponding sides are equal and SAS which means that two sides and the angle between them is equal. When two angles are said to be congruent it means they have the same measure that is they are equal. In this question we know that ∠A≅∠J and ∠B≅∠K , we can see that two angles are equal, if we can have the corresponding side of these two angles to be equal then we can say that the two triangles are congruent. The corresponding side of these angles are AB and JK.
Therefore we can see that the required condition to prove that the triangles are congruent is option (C) AB≅JK.
Learn more about congruency of triangles here:
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Question 30 The Royal Fruit Company produces two types of fruit drinks. The first type is pure fruit juice, and the second type is pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Answer:
The answer is below
Step-by-step explanation:
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?
Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).
Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:
x + y = 80 . . . 1)
Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:
0.65x + 0.9y = 68 . . . 2)
We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:
0.65x + 0.65y = 52 . . . 3)
Subtract equation 3 from 2 and solve for y:
0.25y = 16
y = 16/0.25 = 64
y = 64 pints
Put y = 64 in equation 1:
x + 64 = 80
x = 80 - 64 = 16
x = 16 pints
Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.
Which is the best estimate for the percent equivalent of 7 Over 15
Approximate what the value of [tex]7/15[/tex] is by using calculator.
[tex]7/15\approx0.47[/tex].
And now just multiply by 100 to get percentage.
[tex]100\cdot0.47=\boxed{47\%}[/tex].
Hope this helps.
Answer:
24%
Step-by-step explanation:
7\15 x 100
simplify and get=140\3
dived140\3=48\2
simplify 48\2=24%
What is the area of this polygon?
Enter your answer in the box.
units2
Answer:
39 units²
Step-by-step explanation:
The figure is composed of a rectangle VEDR and Δ RMV
Area of rectangle = VE × ED = 5 × 6 = 30 units²
Area of Δ = 0.5 × RV × perpendicular from M to RV
= 0.5 × 6 × 3 = 9 units²
Thus
Area of polygon = 30 + 9 = 39 units²
What is the vertex of the graph of the function f(x) = x2 + 3x - 2?
Answer:
see below
Step-by-step explanation:
We need to write it on vertex form (f(x) = a(x - c)² + d where (c, d) is the vertex) and to do that we will complete the square.
f(x) = x² + 3x - 2
= (x² + 3x + 9/4) - 9/4 - 2
= (x + 1.5)² - 4.25
The vertex is (-1.5, -4.25).
Please can someone help
Answer:
a) 0
b) 1
c) 0
Step-by-step explanation:
These are common values from the unit circle but you could also just check with your calculator. Just be sure to set it to degree mode and not radian mode.
Which glide reflection describes the mapping ABC DEF. This is practice for me plz, give answer with explanation. Non-sense answer will get reported
Answer:
c. translation (x,y) -> (x-4, y-1) followed by reflection about y=0
Step-by-step explanation:
The strategy is to translate B to E then reflect about the x-axis (y=0)
From B to E, the process is
(x,y) -> (x-4, y-1)
Therefore it is a translation (x,y) -> (x-4, y-1) followed by reflection about y=0
Which is the correct algebraic expression after combining like terms? 6 + 8 x minus 7 minus x 7 x minus 1 7 x + 13 9 x minus 1 9 x + 13
Answer:
7x-1
Step-by-step explanation:
i did the test
Answer:
7x-1
Step-by-step explanation:
correct answer on edge
These tables of values represent continuous functions. For which function will the y-values be the greatest for very large values of x?
Answer:
The table D represents the function that will have the greatest y-values for very large values of x.
Step-by-step explanation:
The table A represents a linear function, for which each one unit increment in the "x" variable produces a three unit increment in the "y" variable. This means that the growth rate of this function is 3.
The table B also represents a linear function, for which each one unit increment in the x variable produces a 100 unit increment in the y variable. This means that the growth rate of this function is 100.
The table C also represents a linear function, for which each one unit increment in the x variable produces a 10 unit increment in the y variable. This means that the growth rate of this function is 10.
The table D on the other hand does not represent a linear function, since the growth rate is variable and increases for greater values of x. This means that as x grows larger, the growth rate of the function also grows larger, resulting in a much greater y value for very large x values if we compare it to a linear function, like the other options.
Answer:
D
Step-by-step explanation:
BIGBRAIN
27 - (2 + 3) - 10 ÷ 2
Answer:
27_5_10/2
27_5_5
22_5
17
5x+4y=25 - (5x+2y=3)
Answer:
T1he values for x and y of the equations is y = 11, and x = -19/5.
Step-by-step explanation:
To solve this question, we need to rearrange the expression:
5x+4y=25 - (5x+2y=3)
Look, if we subtract one equation to the other, then:
5x+4y=25 [1]
-(5x+2y=3) [2]
Which is the same as:
5x+4y=25
-5x-2y=-3
Subtract them:
5x+4y=25
-5x-2y=-3
---------------
2y =22
y = 22/2 = 11
Then, y = 11.
To find x, we can substitute y in either equation [1] or [2].
Let us use [1]
5x+4y=25
5x+4(11)=25
5x+44=25
5x=25-44
5x=-19
x = -19/5
Then, the values for x and y of the equations is y = 11, and x = -19/5.
ASAP!!! PLEASE help me solve this question! No nonsense answers, and attach solutions please.
Answer:
2<F(x)<5
Step-by-step explanation:
We can guess that it come between 2 and 5 given the pattern that we see in the table, but there’s no reason we can’t solve it to be sure.
F(x)=3 (Times the square root of 1.5-1)+2
3(square root of .5)+2
3(0.7)+2
2.12+2
4.12
So, yes, it is between 2 and 5
2<F(x)<5
The equation of line l is -3y+4x=9 Write the equation of a line that is parallel to line l and passes through the point (-12,6). a) -3y+4x-69=0 b)-3y+4x-69=0 c)-3y+4x-39=0 d) 3x-3y+66=0
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
- 3y + 4x = 9
3y = 4x - 9
Divide both sides by 3
y = 4/3x - 3
Comparing with the above formula
Slope / m = 4/3
Since the lines are parallel their slope are also the same
So slope of the parallel line l is also 4/3
Equation of the line using point (-12 , 6) is
y - 6 = 4/3(x + 12)
Multiply through by 3
That's
3y - 18 = 4(x + 12)
3y - 18 = 4x + 48
We have the final answer as
4x - 3y + 66 = 0Hope this helps you
which of the graphs best represents f(x)= -2 cos 4x-1?
Answer:
see file attached
Step-by-step explanation:
2) The senior classes at High School A and High School B planned separate trips to the local
amusement park. The senior class at High School A rented and filled 2 vans and 14 buses with
294 students. High School B rented and filled 3 vans and 7 buses with 161 students. Each van
and each bus carried the same number of students. Find the number of students in each van and
in each bus.
A) Van: 9, Bus: 28 B) Van: 11, Bus: 27
C) Van: 20, Bus: 7 D) Van: 7, Bus: 20
Answer:
D) Van: 7, Bus: 20
Step-by-step explanation:
Add the amount of students together (455 students in total)
Then I added the amount of buses and vans together (5 Vans and 21 Buses)
Then I plugged in each answer
5 x 7 = 35
455 - 35 = 420
420 / 21 = 20
10500 people visited an art gallery in 2002.This was an increase of 25% on 2001.How many visitors were there in 2001?
Answer:
The amount in 2001 is 8400
Step-by-step explanation:
Let x be the amount in 2001
There is an increase of 25% to get to the amount in 2002
x+ .25x = 1.25 x
1.25x = 10500
Divide each side by 1.25
1.25x / 1.25 = 10500/1.25
x =8400
The amount in 2001 is 8400
What the answer now answer only if now answer corry
Answer:
Approximately 11.5 units.
Step-by-step explanation:
We need to find the side opposite to ∠W. We are given the two angles ∠W and ∠X. We are also given that Side X is equal to 7. Therefore, we can use the Law of Sines.
Now, like last time, use the Law of Sines:
[tex]\frac{\sin(V)}{v}=\frac{\sin(W)}{w}=\frac{\sin(X)}{x}[/tex]
We can ignore the first term. Plug in 144 for ∠W, 21 for ∠X, and 7 for x.
[tex]\frac{\sin(144)}{w}=\frac{\sin(21)}{7}[/tex]
Cross multiply:
[tex]7\sin(144)=w\sin(21)\\w=\frac{7\sin(144)}{\sin(21)} \\v\approx11.4812\approx11.5[/tex]
3. Consider the sequence,-8, -5, -2, 1, ...
a) Determine the explicit formula for the general term, 1,, of this sequence in simplified
form. (2 marks)
b) Use this formula to determine the value of t20. (1 mark)
c) Algebraically determine which term has a value of 40. (1 mark)
Answer:
a) [tex]a_n=3\,n-11[/tex]
b) [tex]a_{20}=49[/tex]
c) term number 17 is the one that gives a value of 40
Step-by-step explanation:
a)
The sequence seems to be arithmetic, and with common difference d = 3.
Notice that when you add 3 units to the first term (-80, you get :
-8 + 3 = -5
and then -5 + 3 = -2 which is the third term.
Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:
[tex]a_n=a_1+(n-1)\,d[/tex]
That in our case would give:
[tex]a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11[/tex]
b)
Therefore, the term number 20 can be calculated from it:
[tex]a_{20}=3\,(20)-11=60-11=49[/tex]
c) in order to find which term renders 20, we use the general form we found in step a):
[tex]a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17[/tex]
so term number 17 is the one that renders a value of 40
Use the quadratic formula to find the exact solutions of x2 − 5x − 2 = 0. x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a x equals 5 plus or minus the square root of 33, all over 2 x equals negative 5 plus or minus the square root of 33, all over 2 x equals 5 plus or minus the square root of 17, all over 2 x equals negative 5 plus or minus the square root of 17, all over 2
Answer:
x = [ -b +- sqr root (b^2 - 4ac)] / 2a
a = 1
b = -5
c = -2
x = [- - 5 +- sqr root (-5^2 -4 * 1 * -2)] / 2 * 1
x = [5 +- sqr root (25 + 8)] / 2
x1 = 5.3723
x2 =-0.37228
Step-by-step explanation:
Exact solution for the give quadratic equation are
[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]
Quadratic EquationQuadratic equation of the form [tex]ax^2+bx+c=0[/tex]
For any quadratic equation we get two values for x. we can find the values for x by applying quadratic formula .
Quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Given equation is [tex]x^2-5x-2=0[/tex]
The value of a=1, b= -5 and c=-2
Substitute all the values in the formula.
To find out exact solutions , we need to simplify the final answer.
Exact solutions are without any decimals.
[tex]x=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\pm \sqrt{33}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\p+ \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5+\sqrt{33}}{2}\\\\x=\frac{-\left(-5\right)- \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5-\sqrt{33}}{2}\\[/tex]
Exact solutions are
[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]
Learn more information about 'Quadratic formula ' here
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at the rate of 15 per 6 oz. bar of chocolate, how much would a pound
Answer:
40
Step-by-step explanation:
We know there are 16 oz in a pound
We can use ratios
15 x
----- = ----------
6 oz 16 oz
Using cross products
15 * 16 = 6x
240 = 6x
divide by 6
240/6 = 6x/6
40 =x
Taylor had \$147$147dollar sign, 147. Then she spent \$42$42dollar sign, 42 on sneakers. Then, Taylor earned \$53$53dollar sign, 53 by winning a race in her new sneakers! Estimate how much money Taylor has left
Answer:
She has 158 dollars.
Step-by-step explanation:
This problem tells us that originally Taylor had 147 dollars, but she spent 42 dollars on sneakers, thus she now has [tex]147-42 = 105[/tex] dollars. However, she later won a race wearing those sneakers and earned 53 dollars, therefore she now has [tex]105 + 53 = 158[/tex] dollars.
Thus, Taylor has 158 dollars left now.
Divide 3x^4 - 4x^3 -3x -1 by x-1 Verify using division algorithm Steps please thanks
Answer:
3x³ − x² − x − 4 + (-5/(x−1))
Step-by-step explanation:
Use long division (see attached picture).
Which describes how to graph g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function?
Answer:
[tex]f(x) =\sqrt[3]{x}[/tex]
Step-by-step explanation:
Hello!
Considering the parent function, as the most simple function that preserves the definition. Let's take the function given:
[tex]g(x) = \sqrt[3]{x-5}+7[/tex]
To have the the parent function, we must find the parent one, let's call it by f(x).
[tex]f(x) =\sqrt[3]{x}[/tex]
This function satisfies the Domain of the given one, because the Domain is still [tex](-\infty, \infty)[/tex] and the range as well.
Check below a graphical approach of those. The upper one is g(x) and the lower f(x), its parent one.
Answer:
5 units to the right and 7 units up (B on edge)
Step-by-step explanation:
“a railroad bridge spans a gorge 40 feet wide and connects two cliffs at heights of 98 and 158 feet above the bottom of the gorge. a train is crossing this gorge from the higher cliff to the lower. when the front of the train has traveled three-fourths of the bridge's length, how many feet is it above the bottom of the bottom of the gorge?”
Answer:
Height above the bottom gorge is 113 feet
Step-by-step explanation:
The width of the gorge = 40 feet
The height of the higher cliff = 158 feet
The height of the lower cliff = 98 feet
The length of the bridge = √((158-98)² + 40²) = 72.11 feet
The slope of the bridge = (158-98)/40 = 1.5
The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet
The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°
The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet
Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;
Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.