Shawn has 2 3/4 cups of berries. He uses 5/8 cups of berries to make a smoothie. He then uses 1/2 cup for a fruit salad.
Part A: How many cups of berries did he use?

Answer:

  5 seconds

Step-by-step explanation:

Given the height function h(t) = -2x² + 2x + 40, you want the positive value of t such that h(t) = 0.

The given function can be factored as ...

  h(t) = -2(x -5)(x +4)

This will be zero when the factors are zero:

  x -5 = 0   ⇒   x = 5

  x +4 = 0   ⇒   x = -4

The positive value of t for which the height is zero is t = 5.

It took 5 seconds for the plastic boulder to hit the ground.

__

Additional comment

There are several methods available for factoring the equation. One is to factor out the leading coefficient, then factor the remaining quadratic.

  -2(x² -x -20)

To factor this, you're looking for factor pairs of -20 that have a sum of -1.

  -20 = -20(1) = -10(2) = -5(4)

The last of these, {-5, 4} has a sum of -1. These are the constants that go into the binomial factors.

Step-by-step explanation:

trapezium means especially

AD || BC

AC = BC tells us that ABC is an isoceles triangle (both legs are identically long, which makes also their angles with their baseline AB equal).

therefore, A1 = B = 80°.

and because the sum of all angles in a triangle is always 180°, we get

180 = 80 + 80 + C1

C1 = 20°

(e)(1)

because of the law of a line intersecting parallel lines with the same angles, and AC is intersecting the parallel lines AD and BC, we know that

C1 = A2 = 20°

(e)(2)

because also the sum of all angles around a single point on one side of a line is 180°, we know D1 + D2 = 180°.

we also know that D2 is an angle in an equilateral triangle (that means all 3 sides are equally long, and therefore all 3 angles are equal too = 180/3 = 60°) and therefore

D2 = 60°.

therefore, D1 = 180 - 60 = 120°.

so, for the triangle ACD we have

180 = A2 + D1 + C2 = 20 + 120 + C2

C2 = 40° = 2×20 = 2×C1

(f)(1)

a kite is a quadrilateral, and as such the sum of all angles is 360°.

again remember the symmetry of a kite, so the angles at H and at F must be equal.

H = F = x

so, we have

360 = 110 + 50 + H + F = 110 + 50 + 2x

200 = 2x

x = 100°

(f)(2)

after drawing EG we see that this line splits the kite into 2 equal (ahem, congruent) triangles due to the symmetry of a kite exactly along that line.

and that splits both angles E and G in half for each of the triangles.

again, the sum of all angles in a triangle is 180°, so

180 = 110/2 + 50/2 + x = 55 + 25 + x = 80 + x

x = 100°

Answer: Yes because it equals 87/100 which in decimal form is 0.87.

Step-by-step explanation:

Answer:

f'(5) = 1

Step-by-step explanation:

You are right. The derivative of f(x) = f'(x) = 1 a constant

If you plot y =  f'(x) = 1 it will be a vertical line passing through x = 1 (See graph)

This means f'(x) is constant and equal to 1 for all values of y

So whether it is f'(5) or f'(100) the value = 1

f'(5) = 1

Answer: 334.600

Step-by-step explanation:

I should be that, you have to look at the line

Answer:

The right answer would be 1

Step-by-step explanation:

Answer: 33

Step-by-step explanation:

3*33=99

Answer: 33

Step-by-step explanation:

9/3 = 3

90/3 = 30

99/3 = 33

The digit that when multiplied, make a cube and a square out of the number is 88.

It should be noted that this has to do with mental reasoning.

It should be noted that 8 × 8 = 64. This is the square of 8.

Also, it should be noted that 4 × 4 × 4 = 64. This gives the cube value.

Therefore, the number is 88.

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The kinetic energy of brett favre's will be 245 J.

It is given that speed is 35 meters per second and mass of football is 0.4 kg .

Using equation (1) , we get

 K.E = 1 /2 (0.4)(35)²

       = 490 / 2

       = 245 J

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Answer:

The height of the building is 24m

Step-by-step explanation:

This can be solved using the Pythagorean theorem

which states that the three sides of a right triangle are related by the equation

[tex]c^2 = a^{2} + b^{2}[/tex]  (see figure)

where c is the hypotenuse and a, b are the other two sides

Here we have c = the distance from the top of the building to the tip of the shadow = 26m

One side, the length of the shadow ie b = 10 m

So we have

[tex]26^2 = a^2 + 10^2[/tex]   where a is the height of the building

Switch sides to get

[tex]a^2 + 10^2 = 26^2[/tex]

[tex]a^2 + 100 = 676[/tex]

Subtract 100 from both sides

[tex]a^2 = 676 - 100 = 576[/tex]

[tex]a = \sqrt{576}[/tex]

a = 24

The height of the building is 24m

Answer:

12 is the coefficient.

Step-by-step explanation:

Answer:

[tex]\textsf{b)} \quad -\dfrac{\sqrt{7}}{4}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\textsf{If}\; \cos(\theta)=-\dfrac{3}{4} \implies \sf A=3 \; \textsf{and} \; H=4.[/tex]

Use Pythagoras Theorem to calculate the length of the opposite side:

[tex]\sf \implies O^2+A^2=H^2[/tex]

[tex]\implies \sf O=\sqrt{H^2-A^2}[/tex]

[tex]\implies \textsf{O}=\sqrt{4^2-3^2}[/tex]

[tex]\implies \textsf{O}=\sqrt{7}[/tex]

Therefore, substituting the values of O and H into the sine ratio:

[tex]\implies \sin\theta=\dfrac{\sqrt{7}}{4}[/tex]

As the terminal side of the angle is in Quadrant III, and sine is negative in Quadrants III and IV, the exact value of sin(θ) is:

[tex]\implies \implies \sin\theta=-\dfrac{\sqrt{7}}{4}[/tex]

According to the solving the perimeter of the tringle  = 12 cm.

Add the lengths of the triangle's sides to find its perimeter. For instance, if a triangle comprises sides a, b, as well as c, the perimeter of the that triangle is P = a + b + c.

2D objects have two dimensions, for example, width and height. A rectangle or even a circle are two-dimensional shapes. Because they have without depth, 2D forms are absolutely flat and can not be physically handled.

Points of the tringles:

A (−3,−1),

B (1,−1),

C (1,2)

we know that the:

Perimeter of the triangle = sum of all the side of the triangle

                                         = AB + BC + CA

So

Length of the AB  :

A (−3,−1),

B (1,−1),

AB =√((x2 – x1)² + (y2 – y1)²).

AB =  √((1 – (-3))² + (-1 – (-1))²).

AB = √((4) + (0))

     = √(16)

     = 4

Length of the BC :

B (1,−1),

C (1,2)

BC =√((x2 – x1)² + (y2 – y1)²).

BC =√((1 – 1)² + (2 – (-1))²).

BC =√(0)² + (3)²).

BC = √(9)

    = 3

Length of the CA:

A (−3,−1),

C (1,2)

CA =√((x2 – x1)² + (y2 – y1)²).

CA =√((1 – (-3))² + (2 – (-1))²).

CA =√((4))² + (3)²).

CA =√(16 + 9)

CA =√(25)

      = 5

The perimeter of the triangle asked  = AB + BC + CA

                                                            = 4 + 3 + 5

                                                            = 12 cm

According to the solving the perimeter of the tringle  = 12 cm.

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After riding their bikes, Larry and Jason will be 3.5 miles apart after 10 minutes of their start.

We have Larry and Jason riding their bikes at the speed of 12 miles/hr and 9 miles/hr respectively in opposite directions.

We have to determine how far apart, in miles, will Larry and Jason be after riding their bikes for 10 minutes.

The distance travelled can be calculated using the formula -

distance = speed x time

According to the question -

Average speed of Larry = 12 miles/hr

The distance covered by Larry in 10 minutes = d [1] = 12 x 10/60 =

2 miles.

Average speed of Jason = 9 miles/hr

The distance covered by Jason in 10 minutes = d [2] = 9 x 10/60 =

1.5 miles.

Distance between Jason and Larry after 10 minutes -

d[1] + d[2] = 2 + 1.5 = 3.5 miles.

Hence, Larry and Jason will be 3.5 miles apart after 10 min of riding in the opposite directions.

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Answer: 66.66%

Step-by-step explanation:

1=100%

2/3=

1*2/3=

100%*2/3=

200%/3=66.66%

Answer:-20 238

Step-by-step explanation:

Answer: The answer is not that

Step-by-step explanation:

The answer would be 1.

The 20% rate the bank borrowed Oliver the loan for 3 months gives an interest of $125.

The amount Oliver borrowed = $2,500

The interest rate applied to the loan = 20%

Required: To calculate the simple interest using the formula, I = P•R•T

Where;

I = The simple interest

P = The principal borrowed = $2,500

T = The time or loan duration = 3 months = 1/4 year

R = The rate at which the loan is applied = 20% = 0.2

Therefore;

I = $2,500 × 0.2/year × 3/12 year = $125

The correct option for the interest paid on the loan is therefore;

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Answer:

125

Step-by-step explanation:

The original price of the camera is $220.00 based on the fact that discount of 44% is $96.80

What portion of the original price is the discount?

The discount of $96.80 in dollar terms, represents 44% of the original of the camera, in other words, we can determine the 1%  of the original price of the camera by dividing the discount of $96.80 by 44

1% of the original price of the camera=$96.80/44

1% of the original price of the camera=$2.20

100% of the original price=1% of the original price of the camera*100

100% of the original price=$2.20*100

100% of the original price=$220.00

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Answer:

75-79 i87

Step-by-step explanation:

The linear function c(x) to represent the cost of tuition as a function of "the number of years since 1990" denoted by "x" is [tex][c(x) = 14x+94][/tex].

As per the question statement, the cost of tuition at a large Midwestern university was $94 per credit hour in 1994 while it had risen to $290 per credit hour in 2004.

We are required to determine a linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x".

To solve this question, we need to know the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as

[tex](y-y_{1} )=(\frac{y_{2} -y_{1} }{x_{2} -x_{1}})(x-x_{1})[/tex].

Here, if we consider (x = 0) at 1990, c(x) = 94.

And since the standard form of conversion of functions into coordinate points goes as [y = f(x)], i.e., the ordinate is a function of the abscissa, therefore in this case, [y = c(x) = 94].

Thus, we can consider (x₁, y₁) as (0, 94).

Similarly, at 2004, [x = (2004-1990) = 14], and c(x) = 290, i.e.,

We can consider as (x₂, y₂) as (14, 290).

Using the values of (x₁, y₁) and (x₂, y₂), in the above mentioned standard equation of line passing through two points, we get,

[tex](y-94)=\frac{290-94}{14-0} (x-0)\\or, (y-94)=\frac{196}{14}x\\or,(y-94)=14x\\or,y=14x+94[/tex].

Hence, the linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x" is  [tex][c(x) = 14x+94][/tex].

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The inverse of the given statement will be- Option 3, If point B is the midpoint, then point B bisects line segment AC into two congruent segments.

Here, we are given a statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.

According to the statement,

if B bisects AC ⇒ AB = BC

then, B is the midpoint.

The inverse of this will be-

if B is the midpoint of AB ⇒ AB = BC

then, B bisects AB

This can be written as-

If point B is the midpoint, then point B bisects line segment AC into two congruent segments.

Thus, option 3 is the correct answer.

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Your question was incomplete. Check below for full content-

Which statement is the contrapositive of the conditional statement:

Which statement is the inverse of the conditional statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.

1. If point B is not the midpoint, then point B does not bisect line segment AC into two congruent segments.

2. Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.

3. If point B is the midpoint, then point B bisects line segment AC into two congruent segments.

4. If point B does not bisect line segment AC into two congruent segments, then point B is not the midpoint.

Answer:

187.5 miles

Step-by-step explanation:

We can use the rationing method to solve for this problem.

2 inches on map = 75 miles actual distance

1 inch on map = (75 ÷ 2) = 37.5 miles actual distance

5.5 inches on map = (37.5 × 5) = 187.5 miles actual distance

The remainder of (2x^(3)+2x^(2)-9x+9) -:- (x+3) is 54

Expressions are mathematical statements that are represented by variables, coefficients and operators

The quotient expression is given as

(2x^(3) + 2x^(2) - 9x + 9) -:- (x+3)

Set the divisor of the expression to 0

So, we have

x + 3 = 0

Evaluate the value of x

So, we have

x = -3

Substitute 3 for x in 2x^(3) + 2x^(2) - 9x + 9

So, we have

2(3)^(3) + 2(3)^(2) - 9(3) + 9

Evaluate the expression

So, we have

54

Hence, the remainder of (2x^(3)+2x^(2)-9x+9) -:- (x+3) is 54

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Answer: to be honest looks kinda hard

Step-by-step explanation:

I think both are 4

The m∠POS would be - 65° by the angle addition postulate and substitution postulate.

Given, m∠POQ = 19° , m∠QOR = 31° and m∠ROS = 15°

Angle Addition Postulate is the measure of the larger angle is the sum of the measures of the two smaller angles.

Substitution postulate states that a quantity may be substituted for its equality in any expression.

Then substitute the angle  measurements into the resulting equation to find, m∠POS:

m∠POQ + m∠QOR = m∠POR (by angle addition)

m∠POR + m∠ROS = m∠POS (by substitution)

m∠POS = m∠POQ + m∠QOR + m∠ROS

= 19° + 31° + 15°

= 65°

Thus, the m∠POS would be - 65° by the angle addition postulate and substitution postulate.

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Answer:

4a + 2b + 5

Step-by-step explanation:

4a−1+2b+6

=4a+−1+2b+6

Combine Like Terms:

=4a+−1+2b+6

=(4a)+(2b)+(−1+6)

=4a+2b+5

The salary Mr. Keon spent 1510 on food, rent, clothes, and transport.

The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

If y is the amount of money Mr. Keon spent on food and clothes and x is Mr. Keon's salary.

Then the linear function for the relation between x and y is:

y = ( 5/8) × (x)

y = (5/8)x

The salary of Mr. Keon is 2416.

Now, Mr. Keon spent 5/8 of his salary on food, rent, clothes, and transport.

Let x be the money she spent.

Then,

x = 5/8 of Mr. Keon's salary

x = ( 5/8 ) × 2416

x = ( 2416 × 5 ) / 8

x = 12080 / 8

x = 1510

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We get that the cost of the battery is $ 8.24 per battery.

We are given that the cost of 88 batteries = $ 724.72

We need to find the cost of one battery.

We will do this by diving the cost of 88 batteries by 88.

Using division, we get that:

cost of one battery = $ 724.72 ÷ 88

Simplifying the expression, we get that:

cost of one battery = $ 8.24 per battery.

Therefore, we get that the cost of the battery is $ 8.24 per battery.

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Answer:

f(x) = -3/2 x - 2

Step-by-step explanation:

The line rises to the left so the slope is negative, also:

the slope of the line is -3/2 and the y-intercept is at (0, -2)