Which equation and solution represents each situation? Solutions may be rounded to the nearest tenth. What number is 74% of 58?

Answer:

Domain is all real numbers

Range is

[tex]y\le 12.95[/tex]

Step-by-step explanation:

The given function is

[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]

This is a maximum quadratic function therefore the domain is all real numbers.

Let us complete the square to find the vertex.

[tex]f(d)=-0.6(d^2-9d)+0.8[/tex]

[tex]f(d)=-0.6(d^2+9d)+-0.6(\frac{9}{2})^2- -0.6(\frac{9}{2})^2+ 0.8[/tex]

[tex]f(d)=-0.6(d-\frac{9}{2})^2+\frac{243}{20}+ 0.8[/tex]

[tex]f(d)=-0.6(d-\frac{9}{2})^2+\frac{259}{20}[/tex]

Therefore the range is

[tex]y\le \frac{259}{20}[/tex]

[tex]y\le 12.95[/tex]

See graph

Answer:

Domain:

[tex][0,9.146][/tex]

Range:

[tex][0,12.95][/tex]

Step-by-step explanation:

we are given

a baseball follows the path graphed by the quadratic function

[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]

where

d is the horizontal distance the ball traveled in yards

ƒ(d) is the height, in yards, of the ball at d horizontal yards

Domain:

we know that domain is all possible values of x for which any function is defined

So, for finding domain , we will take smallest x-value to largest x-value

so, we can set f(d)=0 and find zeros

[tex]-0.6d^2+5.4d+0.8=0[/tex]

we can use quadratic formula

[tex]d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]d=\frac{-54\pm \sqrt{54^2-4\left(-6\right)8}}{2\left(-6\right)}[/tex]

[tex]d=-\frac{\sqrt{777}-27}{6},\:d=\frac{27+\sqrt{777}}{6}[/tex]

[tex]d=-0.14579,d=9.146[/tex]

we know that d is a horizontal distance

and distance can never be negative

so, domain will be

[tex][0,9.146][/tex]

Range:

Since, this is quadratic equation

so, it is also equation of parabola

so, firstly we will find vertex of parabola

Suppose, we have

[tex]ax^2+bx+c=0[/tex]

Vertex is

[tex]x=\frac{-b}{2a}[/tex]

so, we can compare

a=-0.6

b=5.4

c=0.8

now, we can find vertex

[tex]x=\frac{-5.4}{2\times -0.6}[/tex]

[tex]d=4.5[/tex]

now, we can find y-value

[tex]f(4.5)=-0.6(4.5)^2+5.4(4.5)+0.8[/tex]

[tex]f(4.5)=12.95[/tex]

we can see

that leading coefficient is -0.6

which is negative

so, parabola opens downward

so, range will be

[tex][0,12.95][/tex]

y - y1 = m(x - x1) Point slope form

y - y1 = 4(x - x1) Plug in the given slope m = 4

y - (-10) = 4(x - 3) Plug in the given (x1,y1) point

y + 10 = 4(x - 3) Simplify

y + 10 = 4x - 12 Distribute

y+10-10 = 4x - 12 - 10 Subtract 10 from both sides

y = 4x - 22 Combine like terms

Answer is choice A

Rounding 125.3546 to 1 decimal place involves looking at the second decimal digit (5) and rounding up, resulting in 125.4.

We look at the second decimal digit, which is a 5. Since it is 5 or more, we round the first decimal place up. Therefore, 125.3546 rounded to 1 decimal place is 125.4.

Answer:

The box has 6 sides. 2 each of 8 x 9, 8 x 12 and 9 x 12 ie 2 x (72 + 96 + 108) ie 2 x 276 which is 552 sq ins.

Step-by-step explanation:

Answer:

136

Step-by-step explanation:

The method is 2lw x 2lh x2wh

2x8x4

2x8x3

2x4x3

= 136

Answer:

no, its equal. 5/7 = 0.7142 which is 71%

Step-by-step explanation:

Answer:

8, 3 pointers =24 points 4, 2 pointers = 8points 24+8= 34 points

Step-by-step explanation:

Answer:

8 baskets worth 3 points each and 4 baskets worth 2 points each = 32 points

Answer:

f(2) = 4

Step-by-step explanation:

If you look at the graph, when x = 2, y = 4!!

Can I have brainliest?

Also I love the fact that your listening to Christmas music!!!!

Answer:

1. (2.923)   2.  i don't know what they are asking for but i believe it is the mean so add all of the data up and divide by how many data pieces there are ( there are seven

Answer:

$0.79 x 3.7 would give you 2.923 but since its money it would be $2.92 and 2) im not sure how there the same question if one is dealing with weather and the other with money, Im sorry

Answer:

no

Step-by-step explanation:

since the y=mx+b format is used here, your b is -5. for this to be correct, your y-int needs to be on -5, not -2 as you have it. Other than that, i believe you are correct

Answer:

no

Step-by-step explanation:

the point has to be on the 5

Answer:

1.75 %  

Step-by-step explanation:

The formula for the future value (FV) of an investment is

FV =PV(1 + r/n)^nt

If the interest is calculated once a year, n = 1, and the formula reduces to

     FV = PV(1 +r)^t

5550 = 5000(1 + r)⁶     Divide both sides by 5000

 1.110 = (1+r)^6              Take the sixth root of each side

 1 + r = 1.0175               Subtract 1 from each side

      r = 0.0175               Convert to percent

     r = 1.75 %

The interest rate is 1.75 %.

Answer:

see explanation

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2a + (n - 1)d ]

where d is the common difference and a is the first term

here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][(2 × 5) + 2(n - 1) ]

                        = [tex]\frac{n}{2}[/tex](10 + 2n - 2)

                        = [tex]\frac{n}{2}[/tex](2n + 8)

                        = n² + 4n

When sum = 165, then

n² + 4n = 165 ← rearrange into standard form

n² + 4n - 165 = 0 ← in standard form

(n + 15)(n - 11) = 0 ← in factored form

equate each factor to zero and solve for n

n + 15 = 0 ⇒ n = - 15

n - 11 = 0 ⇒ n = 11

but n > 0 ⇒ n = 11

The sum of n terms for the arithmetic series is:

[tex]S_n=\frac{n}{2}[8+2n ][/tex]

The value of n for which the series has sum 165 is 11

The given series is:

5 + 7 + 9 +.......

The first value, a = 5

The common difference, d = 7 - 5

d  =  2

The sum of the first n terms of an arithmetic series is given by the formula:

[tex]S_n=\frac{n}{2}[2a+(n-1)d ][/tex]

Substituting a = 5, and d = 2 into the sum of the series, we have:

[tex]S_n=\frac{n}{2}[2(5)+(n-1)(2) ]\\\\S_n=\frac{n}{2}[10+2n-2 ]\\\\S_n=\frac{n}{2}[8+2n ][/tex]

To determine the value of n for which the series has sum 165, substitute [tex]S_n=165[/tex] into the sum above

[tex]S_n=\frac{n}{2}[8+2n ]\\\\165=\frac{n}{2}[8+2n ]\\\\2(165)=n(8+2n)\\\\2n^2+8n-330=0\\\\n^2+4n-165=0\\\\n^2-11n+15n-165=0\\\\n(n-11)+15(n-11)=0\\\\(n-11)(n+15)=0\\\\n=11, n=-15[/tex]

The value of n for which the series has sum 165 is 11

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Answer:

-3

Step-by-step explanation:

2(x-6)= 6(x)

2x-12= 6x

-12=4x

x= -3

Answer: -3

Step-by-step explanation:

2(n - 6) = 6n

2n - 12 = 6n

-2n       -2n          

     -12  = 4n

      ÷4   ÷4  

       -3 = n

Answer:

(- 25, 81) does not lie on the line

Step-by-step explanation:

We can use the slope m to determine if (- 25, 81) lies on the line or not

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, 0)

m = [tex]\frac{0-4}{2-0}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

now if (- 25, 81) lies on the line then the slope between (- 25, 81) and either of the 2 points on the line should equal - 2

(x₁, y₁ ) = (- 25, 81) and (x₂, y₂ ) = (2, 0)

m = [tex]\frac{0-81}{2+25}[/tex] = [tex]\frac{-81}{27}[/tex] = - 3

The slopes are not equal hence (-25, 81) does not lie on the line

[tex]\text{Step 1:}\\\\\text{Find the equation of the line passing through the points}\\\\\text{The slope-intercept form:}\ y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b).\\\\\text{We have the points:}\\(0,\ 4)-y-intercept\to b=4\\(2,\ 0)-x-intercept\\\\\text{Therefore we have the equation:}\ y=mx+4.\\\\\text{The formula of a slope}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{put the coordinates of the points:}\\\\m=\dfrac{0-4}{2-0}=\dfrac{-4}{2}=-2\\\\\text{Therefore we have}\ \boxed{y=-2x+4}[/tex]

[tex]\text{Step 2:}\\\\\text{Put the coordinates of the point (-25, 81) to the equation of a line}\\\text{and check equality}\\\\y=-2x+4,\ x=-25,\ y=81\\\\-2x+4\to-2(-25)+4=50+4=54\neq81[/tex]

Answer:

1. BD

2. 55°

3. The shape was reflected over both axes

This what I answered

Step-by-step explanation:

Given the conditional statement ~p → q, a logo that is equivalent include the following: D. ~q → p.

In Mathematics, a conditional statement is a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement has the form "if p then q."

p → q

Where:

p and q represent sentences or statements.

Generally speaking, two expressions are considered as being logically equivalent if they have the same truth value for all possible combinations of truth values and for all variables that appear in both expressions.

This conditional statement ~p → q means if not p, then q;

where:

In this context, we can logically deduce that the negation of the consequent, q, would be sufficient to state the negation of the antecedent, not p (double negation of p). Symbolically, this can be represented as follows:

~q → ~(~p) ≡ ~q → p

Answer:

The volume of a cube whose total surface area is 150 sq. ft. is 125 cubic feet.

Step-by-step explanation:

Set up an equation that shows the relation between the side length L of the cube and its surface S:

[tex]S = 6\cdot L^2\\150 = 6\cdot L^2\implies\\|L| = \sqrt{\frac{150}{6}}= 5[/tex]

The side length of a cube with an area of 150 sq. ft is 5 ft. Now we can easily calculate the volume V:

[tex]V = L^3 = 5^3 = 125[/tex]

The volume of a cube whose total surface area is 150 sq. ft. is 125 cubic feet.

The volume of a cube with a total surface area of 150 square feet is 125 cubic feet. This is found by first dividing the total surface area by 6 to find the area of one face, then taking the square root to find the length of one side, and finally cubing this length.

To find the volume of a cube when you know the total surface area, you begin by realizing that a cube has six identical faces. Hence, the surface area of one face is the total surface area divided by 6. In this case, 150 square feet divided by 6 equals 25 square feet. This is the area of one face. Because this is a cube, the length, width, and height are equal, so the square root of 25 (which is 5) would give us the length of one side.

Now, the volume of a cube is the side length cubed. Hence, in this case, the volume would be 5 feet (the length of a side) cubed, or 5 * 5 * 5, which equals 125 cubic feet.

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Answer:

Good Morning you answer is 8/17

Step-by-step explanation:

you halve 16 and 34 getting 8 and 17

17 is a prime number so you can not divide any more

Answer:

The solution to the equation is:

Option c. b=0 and b=4

Step-by-step explanation:

5 / (3b^3-2b^2-5) = 2 / (b^3-2)

Cross multiplication:

5(b^3-2)=2(3b^3-2b^2-5)

Applying distributive property both sides of the equation to eliminate the parentheses:

5(b^3)-5(2)=2(3b^3)-2(2b^2)-2(5)

Multiplying:

5b^3-10=6b^3-4b^2-10

Passing all the terms to the right side of the equation: Subtracting 5b^3 and adding 6 both sides of the equation:

5b^3-10-5b^3+10=6b^3-4b^2-10-5b^3+10

Adding like terms:

0=b^3-4b^2

b^3-4b^2=0

Getting common factor b^2 on the left side of the equation:

b^2 (b^3/b^2-4b^2/b^2)=0

b^2 (b-4) = 0

Two solutions:

(1) b^2=0

Solving for b: Square root both sides of the equation:

sqrt(b^2)=sqrt(0)

Square root:

b=0

(2) b-4=0

Solving for b: Adding 4 both sides of the equation:

b-4+4=0+4

Adding like terms:

b=4

The solution of the equation is: b=0 and b=4 (Option c)

Final answer:

To solve the equation, we can use the quadratic formula and find the solutions for b.

Explanation:

To solve the equation 5/3b^3 - 2b^2 - 5 = 2/b^3 - 2, we need to find the values of b that satisfy the equation. To do this, we can cross-multiply and rearrange the equation to get a quadratic equation in terms of b. Using the quadratic formula, which states that b = (-b ± √(b^2 - 4ac)) / 2a, we can find the solutions for b.

Substituting the values a = 5/3, b = -2, and c = -7 into the quadratic formula, we obtain the solutions b = -4 and b = 0.

Therefore, the solution to the equation 5/3b^3 - 2b^2 - 5 = 2/b^3 - 2 is b = -4 and b = 0.

Answer:

x>-1 and x<-1

Step-by-step explanation:

Answer:

a1 = 2; an = a(n-1) + 3/2

Step-by-step explanation:

Common difference = 7/2 - 2

= 7/2 - 4/2

= 3/2  

(Also 5 - 7/2 = 3/2.)

First term a1 = 2

So the formula is  a1 = 2; an = a(n-1) + 3/2 which is the first choice.

The recursive formula for the arithmatic sequence is a₁ = 2, aⁿ = aⁿ⁻¹ + 3/2.

A recursive formula is a formula that defines any tern of a sequence in terms ofits preceding term(s).

Now the given series is-

2,7/2,5,13/2,......

Here the the first term of the series is 2

⇒a₁ = 2

Common difference (d) = (7/2) - 2 = 3/2

Now the recursive formula of an arithmatic sequence is given as,

aⁿ = aⁿ⁻¹ + d

Putting the values,

aⁿ = aⁿ⁻¹ + 3/2

Hence,the recursive formula for the arithmatic sequence is a₁ = 2, aⁿ = aⁿ⁻¹ + 3/2.

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Answer:

p<4

Step-by-step explanation:

4p+2<2(p+5)

The first step is to distribute the 2

4p + 2 < 2p + 2*5

4p +2 < 2p + 10

Subtract 2p from each side

4p +2 < 2p + 10

4p-2p +2 < 2p-2p +10

2p+2 <10

Subtract 2 from each side

2p+2-2<10-2

2p<8

Divide each side by 2

2p/2 <8/2

p<4

[tex]4p+2<2(p+5)\qquad\text{divide both sides by 2}\\\\\dfrac{4p}{2}+\dfrac{2}{2}<\dfrac{2(p+5)}{2}\\\\2p+1<p+5\qquad\text{subtract 1 from both sides}\\\\2p<p+4\qquad\text{subtract p from both sides}\\\\\boxed{p<4}[/tex]

The change in low outside temperature from Tuesday to Wednesday was -1.4°C, indicating a decrease of 1.4°C. Converting 88°F to Celsius yields approximately 31.1°C. The Celsius scale is known as 'centigrade' due to its 100-degree division between water's freezing and boiling points.

To solve for the change in low outside temperature from Tuesday to Wednesday, we subtract the low temperature for Wednesday from the low temperature for Tuesday:

Change in temperature = Temperature on Wednesday - Temperature on Tuesday

Change in temperature = (-10°C) - (-8.6°C)

Change in temperature = -10°C + 8.6°C = -1.4°C

Thus, the low outside temperature changed by -1.4°C from Tuesday to Wednesday, which means it dropped by 1.4°C.

1. To convert the temperature from Fahrenheit to Celsius:
C = (°F - 32) / 1.8. So on a warm day of 88°F:
C = (88°F - 32) / 1.8 = 56°F / 1.8 = 31.1°C approximately.

2. The Celsius scale is called "centigrade" because it is based on a scale of 100 degrees between the freezing and boiling points of water.

3. If the outside temperature is steady at 10°C and you want to maintain a shorts-and-short-sleeves comfortable inside temperature of 22°C compared to a cooler 13°C, you would need to expend more energy to maintain the higher temperature.

The difference in energy required will depend on factors like the insulation of the building, the heating system's efficiency, and the duration for which the higher temperature is maintained.

4. When a cold front causes a drop of 40.0°F:
Celsius decrease = 40.0°F / 1.8 = 22.2°C approximately.

5. Any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees:
(Change in °F) * (5/9) = Change in °C
Thus, a change in Fahrenheit degrees is 9/5 times a change in Celsius degrees.

The correct answer is -1.4⁰.

To find the change in the low outside temperature from Tuesday to Wednesday, we need to subtract the temperature on Tuesday from the temperature on Wednesday.

The temperature on Tuesday is -8.6 degrees Celsius, and the temperature on Wednesday is -10 degrees Celsius.

To subtract -8.6 from -10, we can rewrite the equation as -10 - (-8.6). When we subtract a negative number, it is the same as adding the positive number. So, -10 - (-8.6) becomes -10 + 8.6.

When we add -10 and 8.6, we get -1.4.

Therefore, the change in the low outside temperature from Tuesday to Wednesday is -1.4 degrees Celsius.

So the correct answer is -1.4⁰.

Answer:

2a+b+(-b)=2a+0

Step-by-step explanation:

Additive inverse

x+ -x =0

Answer:

a would be the answer

Step-by-step explanation: the whole point of additive inverse is to add a negative number. So putting parenthesis around the negative number and then adding it to another number, would be correct. In my opinion it also looks easier to do.

Answer:

16 1/2, or 16.5 square meters

Step-by-step explanation:

This is a simple explanation, scroll down for the details on how I got to this answer!

Step 1. Find the rate at which Rachel can paint.

(5 1/2 square meters per 1/3 hour)

Step 2. Find the area of wall space Rachel can paint in 1 hour, using this rate.

5 1/2 × 3 = 16 1/2 or 16.5 square meters

1/3 × 3 = 1 hour

Rachel can paint 16 1/2 square meters of wall space in 1 hour.

**How I solved this problem**

Step 1. To find the area of wall space Rachel can paint in 1 hour, we need to find a rate that shows her speed (square meters/hours).

In the first sentence, we are given a rate:

"5 1/2 square meters of wall space in 1/3 hour."

This can be modeled by the fraction: [tex]\frac{5\frac{1}{2} }{\frac{1}{3} }[/tex]

Step 2. To find how much she can paint in 1 hour, we can multiply this rate by 3. This is because the rate tells us that the area of wall space Rachel can paint in 1/3 hour.

Remember, to cancel out a fraction, multiply by its reciprocal, which is the fraction "flipped" (the numerator and denominator switch). We multiply 1/3 by 3/1 (3) because it is 1/3 flipped.

Since Rachel is painting at a constant rate of 5 1/2 square meters per 1/3 hour, we also need to multiply the other part of the fraction by 3, so the rate stays the same.

5 1/2 × 3 = 16 1/2 or 16.5 square meters

1/3 × 3 = 1 hour

This is our final answer: Rachel can paint 16 1/2 square meters of wall space in 1 hour.

Rachel can paint 16 1/2 square meters of wall space in one hour by multiplying her painting rate for 1/3 hour by 3.

Rachel paints 5 1/2 square meters of wall space in 1/3 hour. To determine the area she can paint in one hour, we need to use the concept of unit rate, which is the amount of work done per unit of time.

To find Rachel's painting rate in square meters per hour, we can set up a proportion. Since we want to find out how much she can paint in one full hour, we multiply the area she can paint in 1/3 of an hour by the reciprocal of 1/3 (which is 3) to calculate the full hour painting area.

So, Rachel's painting rate per hour is 5 1/2 * 3 square meters. Multiplying, we get (5 + 1/2) * 3 = (11/2) * 3 = 33/2 = 16 1/2 square meters. This is the area she can paint in one hour.

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We are required to find the fraction equivalent to 75% of 1/2

Given:

75% of 1/2

change percentage to fraction

= 75/100 × 1/2

Multiply numerator and denominator respectively

= (75 × 1) / (100 × 2)

= 75 / 200

Divide by 25

= 3 / 8

Therefore, the fraction is equal to 75% of 1/2 is 3/8

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To find the fraction that is equal to 75% of 1/2, multiply 0.75 by 1/2, resulting in 0.375.

To find the fraction that is equal to 75% of 1/2, we need to calculate 75% of 1/2.

75% can be written as a decimal by dividing 75 by 100, which gives us 0.75.

Now we can multiply 0.75 by 1/2 to get the answer.

0.75 * 1/2 = 0.375

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Answer:

Given: If triangle CFH is similar to triangle TDM with a scale factor of 4: 5.

Similar triangle states that the two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

then by definition, we have;

[tex]\frac{CF}{TD}= \frac{FH}{DM} =\frac{CH}{TM}= \frac{4}{5}[/tex]  .....[1]

From the figure, we have;

CF = x +7 , FH = x-1 , CH = x+3 , TD = 2x -13 , DM = x+6 and TM = x+ 11

Solve for x;

[1] ⇒ [tex]\frac{CF}{TD} =\frac{4}{5}[/tex]

Substitute the value of CF and TD to solve for x;

[tex]\frac{x+7}{2x-13} = \frac{4}{5}[/tex]

By cross multiply we get;

[tex]5 (x+7) = 4(2x-13)[/tex]

Using distributive property : [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]

5x + 35 = 8x - 52

Subtract 35 on both sides we get;

5x + 35 -35 = 8x - 52 -35

Simplify:

5x = 8x - 87

Subtract 8x on both sides we get;

5x -8x = 8x -87 -8x

Simplify:

-3x = -87

Divide both sides by -3 we get;

x = 29

To find the perimeter of triangle CFH;

Sides are:

CF = x + 7 = 29 + 7 = 36 units

CH = x+3 = 29 +3 = 32 units

FH = x -1 = 29 -1 = 28 cm.

Perimeter of any triangle is the sum of all the sides of the triangle.

Perimeter of triangle CFH = CF + CH + FH = 36 + 32 + 28 = 96 units

therefore, the perimeter of triangle CFH is, 96 units.

Without the perimeter of triangle TDM, we can't calculate the perimeter of triangle CFH using only the scale factor. When additional information is provided such as the length of a side in both triangles, it will be possible.

The subject of this question is mathematics, specifically regarding similar triangles and the calculation of a triangle's perimeter when the scale factor is provided. In this case, the triangles CFH and TDM are similar with a scale factor of 4:5.

When triangles are similar, corresponding sides are proportional which means one side of triangle CFH is 4/5 the length of the corresponding side of triangle TDM. If we were given the perimeter of triangle TDM, we would multiply by the ratio (4/5 or 0.8) to get the perimeter of triangle CFH. However, without this extra information, we aren't able to provide the exact perimeter of triangle CFH.

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