Answer:
see explanation
Step-by-step explanation:
Given f(x) = - 20x² + 23x - 6
To find the zeros set f(x) = 0, that is
- 20x² + 23x - 6 = 0 ( multiply through by - 1 )
20x² - 23x + 6 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 20 × 6 = 120 and sum = - 23
The factors are - 15 and - 8
Use these factors to split the x- term
20x² - 15x - 8x + 6 = 0 ( factor the first/second and third/fourth terms )
5x(4x - 3) - 2(4x - 3) = 0 ← factor out (4x - 3)
(4x - 3)(5x - 2) = 0
Equate each factor to zero and solve for x
4x - 3 = 0 ⇒ 4x = 3 ⇒ x = [tex]\frac{3}{4}[/tex]
5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]
Answer:
-(4x - 3)(5x - 2) = 0
Step-by-step explanation:
Draw and compare models of 3/4 of a pizza pie and 6/8 of a same -size pie
Answer:
The two pieces of pizza are same.
6/8 is the equivalent fraction of 3/4
Step-by-step explanation:
From the figure attached with this answer shows the two pizzas. The first figure shows a pizza which is divided into 4 equal parts. Out of this 4 parts 3 parts are colored. This shows 3/4 fraction.
From the second figure we can see a pizza is divided into 8 equal parts, out this 6 are colored. This shows 6/8 fraction.
Compare two pizzas
When we compare this two colored portion we can see both shows same area of circle.
That means 6/8 is equivalent fraction of 3/4
what number times 2 equals 0.36
Answer:
X is equal to 0.18
Step-by-step explanation:
X is that number
then
2X equal to 0.36
X equal to 0.36 divided 2
X is equal to 0.18
Best regards
Choose the correct simplification of (4x3y4z5)(5x4y5z3)
is their operations that you didnt list
Answer: The answer is, 20x7y9z8.
Step-by-step explanation:
for a summer job, you work for a pool resurfacing business. you’ve finished resurfacing the pool and it is now time to fill the empty pool with water. there are 2 water hoses that you can use to refill the pool. you wonder how long it is going to take to fill the pool because you have plans with friends and you need to leave by 6:15 PM. You decide to time the water flow of hoses as it fills a 5 gallon bucket. the first hose can fill the bucket in 4 seconds while the second hose can fill the same in 36 seconds. the pool needs 20,000 gallons of water.
a. How long will it take fill the pool with the first hose? It is now 2PM, will you be able to leave by 6:15pm?
b. You get the idea both hoses to fill the pool and hopefully fill up the pool faster. Will using both hoses be enough to fill up the pool in time for you to leave at 6:15PM?
Answer:
a. 267 hrs b.
Step-by-step explanation:
a.)4 secs divided by 5 gals is .8 secs per gal, multiply by 20,000 gals, is 16,000 secs, divide that by 60 secs in an hour and you get 266.666 hrs
b.)42 hrs with both hoses
.8 secs per gal and 7.2 secs per gal = 8 secs per gal
20,000 = 8 gals per hour = 2500 secs divided by 60 secs per hour = 41.66
Three times a number plus 20, is equal to 152. Write an Equation and use it to figure out the number
Answer:
3x + 20 = 152
x= 44
Step-by-step explanation:
I need help and i need to explain how I got it
Answer:
y = (-1/8)x + 10.5
Step-by-step explanation:
The given equation is y = 8x -1. The slope is 8.
Any line perpendicular to the given equation/line has a slope which is the negative reciprocal of 8: That would be -1/8.
We'll use the point-slope formula of a straight line to come up with a formula for this specific problem: y - k = m(x - h), where (h, k) is the point in question and m is the slope.
Here we have y - 10 = (-1/8)(x - 4). This is complete in itself, But you could also present it in more compact form, as follows:
Add 10 to both sides. We get y = (-1/8)(x - 4) + 10.
Perform the indicated mult.: y = (-1/8)x + 1/2 + 10, or
y = (-1/8)x + 10.5
Taking successive discounts of 15% off and then 25% off is the same as taking a one time discount of 40%.
Please select the best answer from the choices provided
T
F
Answer:
correct option is F
Step-by-step explanation:
Suppose there is a book the cost of which is $100
You got successive discounts of 15% off and then 25% off
So after getting 15% discount cost of book=$85
again on $85 there is a discount of 25%
it means
25% discount on $85=[tex]\frac{25\times 85}{100} \\[/tex]
=$21.25
It means after successive discounts of 15% off and then 25% off cost of book=[tex]85-21.25[/tex]
after successive discounts of 15% off and then 25% off cost of book=$63.75
On the other hand if you got 40% discount on the same book which costs $100
then after discount of 40% its cost will be=$60
It means,Taking successive discounts of 15% off and then 25% off is not same as taking a one time discount of 40%.
Therefore correct option is F
Answer:
false
Step-by-step explanation:
got it right on edg
The attic shown is a triangular prism. Insulation will be placed inside the walls, not including the floor. Find the surface area that will be covered with insulation
Answer:
[tex]1,125\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the triangular prism that will be covered with insulation is equal to the area of the two triangular faces plus the two lateral rectangular faces
so
[tex]SA=2[\frac{1}{2}(15)(15)]+2[(30)(15)]= 1,125\ ft^{2}[/tex]
Is it a function why or why not ??
it is a function because each input (x) has a unique output (y) that is not repeated
In order for a relationship between numbers x and y to be considered a function from x to y, you need to have one unique y for every x. This doesn’t mean that each y needs exactly one x; for instance, the function y = x² is a function from x to y and has two y values associated with most x values (x = 2 and x = -2, for instance, both give you y = 4).
Essentially, if we give a function some x value, we want to know exactly what y value we’re getting out of it.
The pictured table gives you two possible values for x = 2; given a 2 as input, we have no idea whether to go to 1 or 7 for our output, so it would not be a function from x to y.
(Interestingly, a function from y to x would satisfy that “one output per input” requirement, so if you wanted to impress your teacher, you could answer “yes, but only from y to x, NOT x to y”)
A line passes through the point (4,–2) and is perpendicular to the line with the equation y = 2⁄3x + 4. What's the equation of the line?
Answer:
y= -3/2x + 1
Step-by-step explanation:
The slope of this line is 2/3. The slope of the line perpendicular to this line will be the negative reciprocal or -3/2.
Write the equation using the slope m=-3/2 and the point slope form.
[tex]y-y_1=m(x-x_1)\\y--2=-\frac{3}{2}(x-4)\\y+2=-\frac{3}{2}(x-4)[/tex]
This is the equation of the line. You can convert it to slope intercept form:
[tex]y+2=-\frac{3}{2}(x-4)\\y+2 = -\frac{3}{2}x + 3\\y=-\frac{3}{2}x +1[/tex]
What is the area in square millimeters ?
The correct option is c.
The area of the figure is [tex]\( 320 \)[/tex] square millimeters.
To find the area of the given figure, which is composed of a triangle and a rectangle, follow these steps:
1. Calculate the area of the rectangle: The area of a rectangle is found by multiplying the length by the width. From the figure, we see that the length is 20 mm and the width is 15 mm. So, the area [tex]\( A_{\text{rectangle}} \)[/tex] is:
[tex]\[ A_{\text{rectangle}} = \text{length} \times \text{width} = 20 \, \text{mm} \times 15 \, \text{mm} \][/tex]
2. Calculate the area of the triangle: The area of a triangle is found by using the formula [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \)[/tex]. The base of the triangle is 20 mm (same as the length of the rectangle) and the height, which is the perpendicular distance from the base to the opposite vertex, is 2 mm. So, the area [tex]\( A_{\text{triangle}} \)[/tex] is:
[tex]\[ A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \, \text{mm} \times 2 \, \text{mm} \][/tex]
3. Add the areas of the rectangle and triangle to find the total area: The total area [tex]\( A_{\text{total}} \)[/tex] is the sum of [tex]\( A_{\text{rectangle}} \)[/tex] and [tex]\( A_{\text{triangle}} \)[/tex].
[tex]\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} \][/tex]
Now let's calculate the areas with the given dimensions.
The area of the rectangle is [tex]\( 300 \)[/tex] square millimeters, and the area of the triangle is [tex]\( 20 \)[/tex] square millimeters. Adding these together gives us the total area of the figure:
[tex]\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 300 \, \text{mm}^2 + 20 \, \text{mm}^2 = 320 \, \text{mm}^2 \][/tex]
Therefore, the answer is [tex]\( 320 \)[/tex] square millimeters.
The options are give here:
A. 175 square millimeters.
B. 200 square millimeters.
C. 320 square millimeters.
D. 350 square millimeters.
Rose purchased 2 packs of red pens, 4 packs of black pens, and 3 packs of blue pens. The cost of each pack of pens was $2.50. The expression $2.50 • 2 + $2.50 • 4 + $2.50 • 3 represents the total cost of the pens. Which expression also represents the total cost of the pens? A. $2.50 • 2 • 4 • 3 B. $2.50 • (2 + 4 + 3) C. $2.50 + (2 • 4 • 3) D. $2.50 + 2 + 4 + 3
Answer: B
Step-by-step explanation:
If she bought 9 packs of pens at 2.50$ each then she spent 22.50$ on pens. If you add up the packs and multiply by the price you get your answer. 2.50 * (2+3+4) = 22.50$
Cooper’s Storage and Shipping Company is working with a local business to package some office supplies. The supplies are packed inside a cube – shaped box with side lengths 4 ½ in. These boxes are then packed into a shipping box with dimensions of 18 in x 9 in x 4 ½ in. What is the volume of the cube – shaped box? Show your work. What is the volume of the shipping box? Show your work. How many boxes of office supplies can be packed into the larger box for shipping? Show your work.
Answer:
1. Volume of cube-shaped box = 91.125 cubic inches
2. Volume of shipping box = 729 cubic inches
3. 8 boxes of office supplies can be packed into the larger box for shipping.
Step-by-step explanation:
1.
The first question asks for the volume of a cube. The formula is V = s^3, where, s is the side length and V is the volume. Thus plugging in, we get:
[tex]V=s^3\\V=(4\frac{1}{2})^3\\V=(4.5)^3\\V=91.125[/tex]
Volume of cube-shaped box = 91.125 cubic inches
2.
The second question asks for the volume of the shipping box. Since 3 measurements are given, the shipping box is a rectangular prism. The volume of a rectangular prism is V = l * w * h, where
V is the volume
l is the length
w is the width, and
h is the height
Plugging in all the info we know (multiplying the 3 numbers - dimensions), we can get the volume of the shipping box. So:
[tex]V=lwh\\V=(18)(9)(4\frac{1}{2})\\V=(18)(9)(4.5)\\V=729[/tex]
Volume of shipping box = 729 cubic inches
3.
Since the volume of a single box of office supplies (cub-shape) is 91.125 cu. in., and the volume of larger shipping box is 729, we can divide 729 by 91.125 to find how many of them would fit the large box.
[tex]\frac{729}{91.125}=8[/tex]
Hence, 8 boxes of office supplies can be packed into the larger box for shipping.
Answer:
8
Step-by-step explanation:
4 1/2=9/2*9/2=81/4*9/2=729/8
9/1*9/2*18/1=1,458/2
1,458/2*8/729=11,664/1,458
=8
So eight boxs of office supplies can be packed.
The volume of a cone is 50 pi cubic feet. Its height is 6 feet. In feet, what is the radius of the cone? Round the answer to the nearest tenth.
Answer:
The radius of the cone is [tex]5\ ft[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
In this problem we have
[tex]V=50\pi\ ft^{3}[/tex]
[tex]h=6\ ft[/tex]
substitute in the formula and solve for r
[tex]50\pi=\frac{1}{3}\pi r^{2}(6)[/tex]
Simplify
[tex]25=r^{2}[/tex]
square root both sides
[tex]r=5\ ft[/tex]
Answer:
5ft
Step-by-step explanation:
I did the test
What is 28% of 80? please answer as a decimal
Answer:
22.4
Step-by-step explanation:
Is means equals and of means multiply
W = 28% * 80
Change to decimal form
W = .28 * 80
W = 22.4
28 percent of 80 is 22.4
Answer:
22.4
Step-by-step explanation:
80/x = 100/28
80/x = 3.57142857143
times both sides by x
x cancels out on the left and leaves on the right 3.57142857143 x
80/3.57142857143 = x
22.4 = x
what is 2 times 1/8?
Please help
Answer:
The answer is 1/4
The decimal form is:0.25
Step-by-step explanation:
2/1 x 1/8 + 2x 1/1 x 8+ 2/8= 2 (divide by) 2/ 8 (divide by) 2=1/4
(I added a 1 to 2 because you can't divide a fraction withour two numbers)
I AM NOT A PRO AT MATH ,SO IF I'M WRONG PLEASE LET ME KNOW :)
What is 5 to the 6th power aka 5x5x5x5x5x5
Answer:
15625
Step-by-step explanation:
5x5=25
25 x 25 x 25=15625
PLEASE HELP! BRAINLIEST!
Answer:
x=4
Step-by-step explanation:
We can find the length of RT by using the Pythagorean theorem
sin theta = opposite side/ hypotenuse
sin 60 = 2 sqrt(3)/ RT
Multiply each side by RT
RT sin 60 = 2 sqrt(3)
Divide by sin 60
RT = 2 sqrt(3)/ sin 60
RT = 4
Then
tan theta = opposite side/ adjacent side
tan 45 = x/RT
tan 45 = x/4
4 tan 45 = x
4 = x
the table shows the amount of apple sause made from one apple of each size. Patrice has 17 medium apples and 23 large apples. What is thetotal amount of apple sause that she can make with these apples?
Final answer:
Explaining how to calculate the total amount of apple sauce using medium and large apples.
Explanation:
The total amount of apple sauce Patrice can make with 17 medium apples and 23 large apples is:
17 medium apples x amount of apple sauce from one medium apple
23 large apples x amount of apple sauce from one large apple
Add the results from the above two calculations to find the total amount of apple sauce.
what is the distance between the points (-3,-1) and (5,1)
The formula for distance is [tex]\sqrt{(x_{2} -x_{1}) } + (y_{2} -y_{1}) }}[/tex]
if we plug our points into the equation we get √68
(5y-12)+(-5y-1) Find the sum or difference.
Answer: -13
Step-by-step explanation:
5y -5y cancel out and the -12-1=-13 and that’s how you get -13.
The sum or difference of the given expression (5y-12)+(-5y-1) simplifies to -13.
Explanation:The original problem presented is to evaluate the expression (5y-12)+(-5y-1). The operation between the two parenthesis is a sum (as indicated by the '+').
To solve, execute the operation in each parenthesis then execute the operation between. The operation inside the first parenthesis is a subtraction, yielding 5y-12. Similarly, the operation inside the second parenthesis is also a subtraction, yielding -5y-1. However, it is a good practice to treat subtraction of whole numbers as adding a negative. Finally, the operation between the two results is a sum (5y-12+(-5y-1)).
The desired result is achieved by applying the appropriate algebraic rules. So, we can rewrite this as: (5y-12) + (-5y -1) = 5y -12 -5y -1 = 0y -13 = -13.
Learn more about Algebra here:https://brainly.com/question/32436021
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The system of equations y=-2x+3 and y= x is graphed. What is the solution to the system of equations?
Answer:
1,1
Step-by-step explanation:
I did this earlier today
The solution of the system of equations in terms of (x,y) is (1,1)
The system of equations can either be solved using the simultaneous equation method or the elimination method. Here, we will be using the simultaneous equation method.
Given that:
y = -2x + 3 --- (1)
y = x ---- (2)
Let replace the value of y in equation (2) back to equation (1)
∴
y = -2x + 3 becomes:
x = -2x + 3
x + 2x = 3
3x = 3
x = 3/3
x = 1
Since (x) is = 1
From equation (2), we know that y = x
∴
y = 1
Therefore, we can conclude that the solution of the system of equations in terms of (x,y) is (1,1)
Learn more about the system of equations here:
https://brainly.com/question/12895249?referrer=searchResults
How much do you need to subtract from 53/6 to make 8
To make 8 from 53/6, you need to subtract 5/6. This solution involves converting 8 to the same denominational fraction as 53/6 (which is 48/6) and then subtracting this from 53/6.
Explanation:The question asks how much you need to subtract from 53/6 to make 8. To find out, we start by expressing the desired final number and the given fraction:
Convert 8 to a fraction with a common denominator with 53/6, which is 6, so 8 equals 48/6.To find out how much to subtract from 53/6 to get 48/6, we subtract the two fractions: 53/6 - 48/6.The subtraction gives us 5/6. Therefore, you need to subtract 5/6 from 53/6 to make 8.This demonstrates a basic understanding of fraction subtraction and the concept of working backwards to solve a problem, both of which are key skills in mathematics.
A DVD box set in the shape of a rectangular prism measures 10 inches by 8 inches by 6 inches. What is the surface area of the DVD box set?
Answer:
A=376
the formula is (wl+hl+hw)
Step-by-step explanation:
PLEASE HELP UWU
describe the graph:
f(x)= (3/4)^x +4
Answer:
See attached picture.
y-intercept at (0,5) and asymptote at y = 4.
Step-by-step explanation:
This graph has a base 3/4 that is less than 1. This means it will start high and end low.
It has also been shifted up 4 units by adding 4. This means the asymptote moves to from y = 0 to y =4. The y-intercept of the parent function will also move from (0,1) to (0,5).
What is the area in terms of pi
Answer:
C = 70π cmA = 2,450 cm²Step-by-step explanation:
The perimeter of the given figure is equal to the circumference of whole circle.
The formula of a circumference of a circle:
[tex]C=\pi d[/tex]
d - diameter
We have d = 70 cm. Substitute:
[tex]C=70\pi\ cm[/tex]
The area of given figure is equal to the area of rectangle 70cm × 35cm.
(look at the picture).
The area of a rectangle:
[tex]A=(70)(35)=2,450\ cm^2[/tex]
Find the missing height in the diagram
Answer:
4 ft
Step-by-step explanation:
12 ft - 8 ft = 4ft
Best regards
Need Help ASAP Please
(2b^3 -7b^2) + (3b^2 + 3b^3) =
2b^3 + 3b^3 -7b^2 + 3b^2=
5b^3 -4b^2
I WILL AWARD BRAINLIEST!!! PLEASE HELP!!! SOLVE FOR EACH!!!!
Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation
1) y−2x=3; A(...; 6), B(15; ...)
2) 4.5x+3y=2; A(...; 1/3 ), B( 2/3 ; ...)
Answer:
1. A(3/2,6)
B(15,33)
2.A(2/9,1/3)
B(2/3,-1/3)
Step-by-step explanation:
1) y−2x=3; A(...; 6), B(15; ...)
We know y =6
Substitute this into the equation
6 -2x =3
Subtract 6 from each side
6-6 -2x=3-6
-2x = -3
Divide by -2
x = -3/-2
x = 3/2
A(3/2,6)
We know x = 15
y - 2(15) =3
y - 30 = 3
Add 30 to each side
y-30+30 = 3+30
y = 33
B(15,33)
2) 4.5x+3y=2; A(...; 1/3 ), B( 2/3 ; ...)
We know y = 1/3
4.5x + 3(1/3) = 2
4.5x +1 =2
Subtract 1 from each side
4.5x +1-1=2-1
4.5x = 1
Divide each side by 4.5
x = 1/4.5
x = 10/45
x =2/9
A(2/9,1/3)
Let x =2/3
4.5(2/3) +3y =2
3 +3y =2
Subtract 3 from each side
3-3+3y = 2-3
3y = -1
Divide by 3
y = -1/3
B(2/3,-1/3)
Answer:
1. A(3/2;6) B(15;33)
slope=2
2. A(2/9;1/3) B(2/3;-1/3)
slope=-1.5
Step-by-step explanation:
Hope this helps,
Have a great day
Solve:
2^x=32
X=_________a0
Answer:
x = 5
Step-by-step explanation:
As you know 32 = 2^5
so
2^x = 32
2^x = 2^5
Since both have same base 2
x = 5
32=2^x
Prime factors of 32
32 = 2 * 16
16 = 2 * 8
8 = 2 * 4
4 = 2 * 2
32 = 2*2*2*2*2
32 = 2^5
x=5
Hope this helps :)