Larry, Barry, Terry are saving their money for a trampoline that costs $340.

• The amount of money Larry has saved can be represented by x.
• The amount of money Barry has saved is 1
1
2
times the amount Larry has saved.
• The amount of money Terry has saved is 1
1
3
times the amount Larry has saved.
• The total amount of money saved by Larry, Barry, and Terry is $322.

What is x, the amount of money saved by Larry?

Answer:

What is the value of the discriminant of f?

0

How many x-intercepts does the graph of f?

1

Step-by-step explanation:

I promise you i just got this question and this is the answer

The discriminant of f is 0.

The function f has one intercept.

In the given quadratic function f(x) = 25x² - 10x + 1, the coefficients are:

a = 25

b = -10

c = 1

Now, let's calculate the discriminant:

Discriminant = b² - 4ac

            = (-10)² - 4 x 25 x 1

            = 100 - 100

            = 0

The value of the discriminant of f is 0.

If the discriminant is positive (greater than 0), the quadratic equation has two distinct real roots, which means the graph intersects the x-axis at two different points.

If the discriminant is zero, the quadratic equation has one real root, and the graph touches the x-axis at one point (or has a double root).

If the discriminant is negative, the quadratic equation has no real roots, and the graph does not intersect the x-axis.

In this case, since the discriminant is 0, the graph of f has one x-intercept (or one real root).

Learn more about Discriminant here:

https://brainly.com/question/33365847

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Answer:

a) Area of the base of the pyramid = [tex]15.6\ mm^{2}[/tex]

b) Area of one lateral face = [tex]24\ mm^{2}[/tex]

c) Lateral Surface Area = [tex]72\ mm^{2}[/tex]

d) Total Surface Area = [tex]87.6\ mm^{2}[/tex]

Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. [tex]\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\[/tex]

[tex]{\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}[/tex]

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

[tex]\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}[/tex]

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

[tex]\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}[/tex]

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to Lateral Surface Area + Area of base

[tex]\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\ mm^{2}[/tex]

Hence,

a) Area of the base of the pyramid = [tex]15.6\ mm^{2}[/tex]

b) Area of one lateral face = [tex]24\ mm^{2}[/tex]

c) Lateral Surface Area = [tex]72\ mm^{2}[/tex]

d) Total Surface Area = [tex]87.6\ mm^{2}[/tex]

Answer:

Sample answer A triangular pyramid with an equilateral triangle for a base has four faces the equilateral triangular base and

three congruent isosceles triangular faces

Step-by-step explanation:

Answer:

It could be 2:5 or 6pi:15pi

Step-by-step explanation:

If you write the ratio of the surface area as a fraction, you would get [tex]\frac{20\pi *yd^{2} }{125\pi *yd^{2} }[/tex]. Simplifying it would leave [tex]\frac{4}{25}[/tex]. But this is NOT the answer because that is the ratio of the surface area. You have to square root it to find the scale factor. The square root is [tex]\frac{2}{5}[/tex]. The answers would be 2:5 and 6pi:15pi.

Answer:

6π : 15π

2 : 5

Answer:

A

Step-by-step explanation:

the area of square is 10²=100

Area of a circle is πr²=π(10/2)²=25π

100-25π=100-25*3.14=100-78.5=21.5

Step-by-step explanation:

Multiply 10 by 10, then find the area of the circle (78.54) then subtract, 100-78.54= 21.46. Then round. So its A. 21.5 meters squared

Answer:

[tex]\frac{AB}{A''B''} = \frac{1}{4}[/tex]

Step-by-step explanation:

Given the information:

<=> the two triangles are similar to each other, triangles are similar if they have the same shape, but can be different sizes, so  A″B″C″ is 4 time bigger than ABC

=> the relationship between ΔABC and ΔA″B″C″

= [tex]\frac{AB}{A''B''} = \frac{1}{4}[/tex]

We choose C.

Hope it will find you well.

Answer:

It is C because when they multiply by 3 the equations are the same

Step-by-step explanation:

Answer:

y=-3x+9 (D)

Step-by-step explanation:

Answer:

Q matches to a and P matches to b

Step-by-step explanation:

This is a volume question so we can use the volume of a cylinder to see which one corresponds to what.  Volume of a cylinder is [tex]\pi[/tex][tex]r^{2}[/tex]h.  We know that the heights of the cylinders are the same since the diagram says so.  We also know pi is the same since thats a constant.  The only thing thats different is the radius (as you can see radius of P is bigger than Q).  If the radius of P is bigger than Q and all the other things are the same (height is the same and pi is the same), then that automatically means that P has more volume than Q.  More volume means more time to fill up.  Since Q has less volume, it will take less time to fill up.  So now we look at the graph.  A shows that the height of water increases at a faster rate than that of B.  This is because there is less volume in that container (less volume=less time to fill up).  Therefore a matches to Q and therefore b matches to P

Answer:

C

Step-by-step explanation:

Let's say Abudal's score = x.

We can do,

3x + x + x + 5 = 45

5x = 45

x = 8.

That means Abdul's scored 8 points, meaning Kendall scored 24,(8*3), and that Otis scored 13, since 8 + 5 = 13.

Answer:

Step-by-step explanation:

Hank paid $2,000 upfront when he bought his car, and he pays $200 each month.

This relationship is:  

This is not proportional.

Lynn did not pay any money upfront when she bought her car, and she pays $275 each month.

This relationship is:  

This is proportional.

So the answer is:

Answer:

48 degrees

Step-by-step explanation:

A triangles degrees all add up to 180

so

180-90= 90 (90 is a square corner)

90-42= 48 (42 is the other known degree)

824 miles

Step-by-step explanation:

412×2=824 miles

or you could do 412+412=824 miles

Hope that helps! If you need any further clarification then please comment down below or message me. Good luck!

Answer:

40

Step-by-step explanation: 13 + 6 + 15 + 6 = 40 ( : - ]

Answer:

x=-4

x=-5

Step-by-step explanation:

Answer:

-4 or -5

Step-by-step explanation:

Well, you have to first understand variables a, b, and c. A in this equation is 1, b is 9, and c is 20. Then you plug those into -b ± sqrt (b^2-4ac)/2a and find that the discriminant, or what is under the square root, is one. Your two roots will be -4 and -5.

Answer:

The range of x values for which y is unique is 2·π

Step-by-step explanation:

For a function j: X → Y to be invertible, we have that for every y in Y, there is associated only one x which is an element of x

Hence, f(x) = cos(x - π/4) gives

the x intercept at two penultimate points of the graph of cos(x - π/4) are;

x = 2.36, and x = 8.64

x = 3/4·π, and x = 2.75·π = [tex]2\tfrac{3}{4}\cdot \pi[/tex]

Hence the range of x values for which y is unique is presented as follows

[tex]2\tfrac{3}{4}\cdot \pi - \frac{3}{4}\cdot \pi = 2}\cdot \pi[/tex]

The range of x values for which y is unique = 2·π.

Answer:

the first one

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The y axis or interval (0,Infinity) is forever going more lower and the x is forever going to the negatives

Answer:

A

Step-by-step explanation:

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x(x - 5) + (x -5) = 0

(x - 5)(x + 1) = 0

x - 5 = 0   ; x + 1 = 0

x = 5      ; x = -1

Answer:

Step-by-step explanation:

Subtracting a number is the same as adding its opposite. So, subtracting a positive number is like adding a negative; you move to the left on the number line. Subtracting a negative number is like adding a positive; you move to the right on the number line.

Answer:

10 sqrt(3) + 2 sqrt(5)

Step-by-step explanation:

2√75+ √20

We know sqrt(a*b) = sqrt(a) sqrt(b)

2 sqrt(25*3) + sqrt(4*5)

2 sqrt(25)sqrt(3) + sqrt(4) sqrt(5)

2 * 5sqrt(3) + 2 sqrt(5)

10 sqrt(3) + 2 sqrt(5)

Answer:

x = 12.6

Step-by-step explanation:

When you have one fraction equated to another one, the means-extremes property allows you to cross multiply, as follows:

[tex]\frac{a}{b} = \frac{c}{d} [/tex]

can be rewritten as:

a*d = c*b

For this case:

[tex]\frac{5}{7} = \frac{9}{x} [/tex]

5*x = 7*9

x = 63/5

x = 12.6

Answer:

solar prominence is the 2nd one

solar wind is the 1st one

gamma ray photon is the 3rd one

Find attached to this question, the diagram of the prism

Answer:

740m

Step-by-step explanation:

The first step determine what type of Prism we are trying to solve. Looking at the diagram, the prism is a triangular prism.

The surface area of a triangular prism is calculated as

Surface Area = bh + 2ls + lb

Where

b = base = 16m

h = height = 15m

l = length = 10m

s = side edge or length = 17m

Surface Area of the triangular prism = (16×15)m + 2(10×17)m + (10×16)m +

= 740m

Answer:

740m

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

204

Step-by-step explanation:

Plug it into a calculator

or

20 multiplied by -4.25 then subtracted by 16 times -4.25 squared.

Answer:

Step-by-step explanation:

6 1/3 plus 8 5/6 is 15 1/6

20 17/30 minus 15 1/6= 5.4 or 5 2/5

Answer:

G ≈ 1.46

Step-by-step explanation:

Given

G = [tex]\frac{R+ab}{at}[/tex] , substitute values

G = [tex]\frac{257 4.88(37.4)}{4.88(61.5)}[/tex]

   = [tex]\frac{257+182.512}{300.12}[/tex]

   = [tex]\frac{439.512}{300.12}[/tex] ≈ 1.46 ( to 2 dec. places )

Answer:

Step-by-step explanation:

l = 12 inches

w = 7 inches

h = 4.5 inches

Surface area = lw + 2wh + 2hl

                     = 12*7 + 2*7*4.5 + 2*4.5*12

                    = 84 + 63 + 108

                    = 255 square inches

If it is a closed box, surface area = 2*(lw +wh + hl)

As it is open, surface area = lw + 2wh + 2hl

Down part of the box : length *width

Upper part of the box = length*width

So, for closed box, 2lw

For open box , lw

Answer:

sorry cant :(

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

We want to find a sine function such that:

The given options are:

Notice that the first information that we have, implies that y must be equal to 2 when x = 0.

Knowing that we can discard the third option which has a y-intercept of 4.

Now the second. Remember that for a general function:

y = A*sin(k*x) + M

Where A is the amplitude and M is the midline, the maximum and minimum are given by:

A + M

-A + M

In all the remaining options we have:

A  = ± 3

M = 2

We can see that with these we get the maximum and minimum of 5 and -1.

Finally, we know that it goes through one cycle at pi.

This means that if f(x) is the function, then:

f(x) = f(x + pi)

Also remember that for a general sine function, we have:

sin(x) = sin(x + 2*pi)

Ok, now let's analyze the options (only the sine part)

1) sin(2*(x + pi)) = sin( 2*x + 2*pi) = sin(2*x)

if we evaluate this in x + pi, we will get:

sin(2*( x + pi + pi)) = sin(2*(x + 2*pi)) = sin( 2*x + 4*pi) = sin(2*x)

So yes, option 1 is a correct option (you also can see that option 4 has the exact same sine part, so that option is also correct.)

2) for the second option the sine part is:

sin(x + pi)

if we evaluate this in x + pi we get:

sin(x + pi + pi) = sin(x + 2*pi) = sin(x)

and we have:

sin(x +pi) ≠ sin(x)

Then this function does not go through one cycle at pi.

We can conclude that the two options that meet all the conditions are the first one and fourth one:

1) y = -3*sin(2*(x + pi)) + 2

4) y = 3*sin(2*(x + pi)) + 2

We can't say which one is correct if we do not look at the graph.

If the function starts increasing, then (2) is the correct one, if the graph starts decreasing, then (1) is the correct one.

Below, you can see a graph of both functions:

The green one is y = 3*sin(2*(x + pi)) + 2,  the blue one is y = -3*sin(2*(x + pi)) + 2

If you want to learn more, you can read:

https://brainly.com/question/14068845

Answer:

1176 cm3

Step-by-step explanation: