work out the equation of the line which has a gradient of -2 and passes through the point (1,7)

Answer:

Step-by-step explanation:

Slope m = -6

Point (-9, -3)

y1 = -3 and x1 = -9

The equation is y - y1 = m(x - x1)

y - (-3) = -6[x - (-9)]

y + 3 = -6(x + 9)

y + 3 = -6x - 54

y = -6x - 54 - 3

y = -6x - 57

Slope-intercept form:  y = mx + b  

[m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]

Since you know:

m = -6             Substitute/plug it into the equation

y = mx + b

y = -6x + b         To find b, plug in the point (-9, -3) into the equation

-3 = -6(-9) + b [two negative signs cancel each other out and become positive]

-3 = 54 + b       Subtract 54 on both sides

-57 = b

y = -6x - 57

Answer:

The effect of doubling all the dimensions of a triangular pyramid will have on the volume of the pyramid is to increase it by 8 times.

Step-by-step explanation:

i) volume of triangular pyramid  = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] Area [tex]\times[/tex] height

     = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] (Base of triangle [tex]\times[/tex] perpendicular height of triangle) [tex]\times[/tex] height

ii) if we double all the dimensions then the three variables((Base of triangle, perpendicular height of triangle, height of pyramid) will be doubled

  and the volume of the new pyramid will be 8 times that of the original one.

Answer:

False

Step-by-step explanation:

The answer is 34.

Because you do 90-56=34

x=34

Answer:

x= 34

Step-by-step explanation:

Answer:

15 students ride the bus home.

Step-by-step explanation:

Divide 25 by 5.  Next multiply the product by 3 and you have your answer.

Answer: incomplete question

Complete question:A group sold 150 flowers and trees. They sold the flowers for $3.00 each and the trees for $2.00 each. They made $300.00 from this sale.

Which equation will help to determine the number of flowers and the number of trees sold?

A. 2F + 3T = 150

B. F + T = 300

C. 3F + 2T = 300

D. F + T = 150 + 300

Answer: C. 3F + 2T = 300

Step-by-step explanation:

Let F stand for flower and T for trees

Flowers sold for $3 and trees sold for $2

Therefore, F + T = 150. . .1

3F + 2T = $300. . .2

Equation 2 would help determine the cost of selling tree.

3F+2T=$300

Answer:

I think that the answer is c

To solve the system of equations, subtract one equation from another to eliminate a variable, then substitute back to find the values of x, y, and z. The correct solution is (x = 0, y = 1, z = 0).

To solve this system of equations, we can use various methods such as substitution, elimination, or matrices. Let's solve it using elimination:

Given the system of equations:

1. ( 4x + 3y + 6z = 3 )

2. ( 5x + 5y + 6z = 5 )

3. ( 6x + 3y + 6z = 3 )

We'll eliminate one variable at a time. Let's start by eliminating ( z ):

From equations 1 and 3, we see that (4x + 3y + 6z) and (6x + 3y + 6z) have the same coefficients for ( z ) but different constants. Subtracting equation 3 from equation 1, we get:

[ (4x + 3y + 6z) - (6x + 3y + 6z) = 3 - 3 ]

[ 4x - 6x = 3 - 3 ]

[ -2x = 0 ]

[ x = 0 ]

Now, substitute ( x = 0 ) into one of the original equations. Let's use equation 1:

[ 4(0) + 3y + 6z = 3 ]

[ 3y + 6z = 3 ]

[ 3y = 3 - 6z ]

[ y = 1 - 2z ]

Now, we have expressions for ( x ) and ( y ). Let's substitute ( x = 0 ) and ( y = 1 - 2z ) into equation 2:

[ 5(0) + 5(1 - 2z) + 6z = 5 ]

[ 5 - 10z + 6z = 5 ]

[ -4z = 0 ]

[ z = 0 ]

So, we found ( x = 0 ), ( y = 1 - 2z = 1 - 2(0) = 1 ), and ( z = 0 ).

Therefore, the solution to the system of equations is ( (x = 0, y = 1, z = 0) ), which corresponds to option c.

System 1: The solution is (x, y) = (-4, 5)

System 2:  The solution is [tex](x, y) = (\frac{11}{3}, -3)[/tex]

Solution:

Given system of equations are:

2x + 3y = 7 ------ eqn 1

-3x - 5y = -13 --------- eqn 2

We can solve by elimination method

Multiply eqn 1 by 3

6x + 9y = 21 ------ eqn 3

Multiply eqn 2 by 2

-6x - 10y = -26 ------- eqn 4

Add eqn 3 and eqn 4

6x + 9y -6x - 10y = 21 - 26

-y = -5

y = 5

Substitute y = 5 in eqn 1

2x + 3(5) = 7

2x + 15 = 7

2x = -8

x = -4

Thus the solution is (x, y) = (-4, 5)

8 - y = 3x ------ eqn 1

2y + 3x = 5 ----- eqn 2

We can solve by susbtitution method

From given,

y = 8 - 3x ----- eqn 3

Substitute eqn 3 in eqn 2

2(8 - 3x) + 3x = 5

16 - 6x + 3x = 5

3x = 16 - 5

3x = 11

[tex]x = \frac{11}{3}[/tex]

Substitute the above value of x in eqn 3

y = 8 - 3x

[tex]y = 8 - 3 \times \frac{11}{3}\\\\y = 8 - 11\\\\y = -3[/tex]

Thus the solution is [tex](x, y) = (\frac{11}{3}, -3)[/tex]

Answer:

Step-by-step explanation:

let x represent the number

9x + 60 = 10x - 2

60 + 2 = 10x - 9x

62 = x <===

Answer:

-2x+4=-16

-2x = -16-4

-2x = -20

x = -20/-2

x = 10

The factored form of the expression representing the area of the flower border surrounding a rectangular sitting area with dimensions 3x by 5 feet is 18x + 66 square feet.

The flower border surrounds a rectangular sitting area with dimensions 3x by 5 feet. To find the area of the flower border, we need to consider the difference in the areas of the outer rectangle (which includes the border) and the inner rectangle (the sitting area). The outer rectangle has dimensions (3x + 6) by (5 + 6), accounting for the 3-foot wide flower border on each side.

The expression for the area of the flower border can be written as follows:

Area of Flower Border = (Length of Outer Rectangle) * (Width of Outer Rectangle) - (Length of Inner Rectangle) * (Width of Inner Rectangle)

= (3x + 6) * (5 + 6) - (3x) * (5)

Now, let's factor the expression:

= (3(x + 2)) * (11) - (3x) * (5)

= 33x + 66 - 15x

Combining like terms, we get:

= 18x + 66

So, the factored expression representing the area of the flower border is 18x + 66 square feet.

The surface area of the box if it is scaled up by a factor of 10 is 10425 square inches

Solution:

Given that, surface area of a box is 104.25 square inches

The area of a scaled object will be equal to the scale factor squared multiplied by area of original box

If the scale factor is three, the area of the new object will be nine times, or three squared, the area of the original object.

Therefore, by above definition,

Let "z" be the scale factor

x =  the surface area of the scaled box

y = the surface area of the original box

Here,

z = 10

y = 104.25

Then we get,

[tex]x = z^2 \times y\\\\x = 10^2 \times 104.25\\\\x = 100 \times 104.25\\\\x = 10425[/tex]

Thus the surface area of the box if it is scaled up by a factor of 10 is 10425 square inches

Answer:

The friend was driving at the speed of 75 miles per hour.

Step-by-step explanation:

Given:

Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles.

If the trip took 10 hours.

Now, to find the speed the friend was driving.

As, given:

Distance = 750 miles.

Time = 10 hours.

Now, to get the speed we put formula:

[tex]Speed=\frac{Distance}{Time}[/tex]

[tex]Speed=\frac{750}{10}[/tex]

[tex]Speed=75\ miles\ per\ hour.[/tex]

Therefore, the friend was driving at the speed of 75 miles per hour.

Measures of angles are X = 102° and Y = 78°

Step-by-step explanation:

⇒ 24 + Y + Y = 180

⇒ 2Y = 180 - 24 = 156

⇒ Y = 156/2 = 78°

⇒ X = 24 + Y = 24 + 78 = 102°

Answer:

x = 9 5/11

Step-by-step explanation:

22x + 7 = 215

22x = 215-7

22x = 208

x = 208/22

x = 9 5/11

[tex]\text{Hey there!}[/tex]

[tex]\text{For what value of x is the equation 22x + 7 = 215?}[/tex]

[tex]\mathsf{22x+7=215}\\\mathsf{Subtract\ by\ 7\ on\ your\ sides}\\\mathsf{22x+7-7=215-7}\\\mathsf{7-7=0\leftarrow cancel\ that\ because\ we\ DO\ NOT\ need it}\\\mathsf{215-7= 208\leftarrow keep\ that\ because\ helps\ us\ solve\ for\ x}\\\mathsf{Equation:22x=208}\\\mathsf{Divide\ by\ 22\ on\ your\ sides}\\\mathsf{\dfrac{22x}{22}=\dfrac{208}{22}}\\\\\mathsf{\dfrac{22x}{22}\leftarrow cancel\ out\ this\ because\ it\ gives\ you\ the\ value\ of\ 1}[/tex]

[tex]\mathsf{\dfrac{208}{22}\leftarrow keep\ this\ because\ it\ helps\ us\ solve\ for\ x}\\\\\mathsf{x=208\div22}\\\\\mathsf{\uparrow Solve\ that\ and\ you\ have\ the\ value\ of\ x}\\\\\boxed{\boxed{{\mathsf{Answer:x=\dfrac{104}{11}}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

I'm assuming you're learning how to simplify and solve algebraic expressions. This is a word problem? In any case, in 6+t=20 you're trying to isolate the variable, t. It makes more sense to subtract 6 from both sides of the equation. On the left side, subtracting 6-6 = 0, leaving us with t, and if we subtract 6 from 20 (remember you have to do the same thing on both sides), you get 14. Therefore, t = 14.

I'm trying to make of it what the word problem is trying to say. You could subtract 20 from both sides, but it's not going to leave you with an isolated variable, and then you'll get negative numbers involved unnecessarily. Colins reasoning (if it means that he came up with that equation simply based on Marge's "subtracting 20 from both sides of the equation to solve it), doesn't make sense to me at all. I would say his reasoning does not make sense, because of all I explained above. I hope that helps even just a little. I feel like something else is missing from the question.

Step-by-step explanation:

Final answer:

Colin's reasoning about subtracting 20 from both sides of the equation 6+t=20 is incorrect because it does not logically solve for 't'. The correct method is to subtract 6 from both sides to isolate 't', leading to the solution t=14.

Explanation:

Colin's reasoning does not make sense because if Marge subtracted 20 from both sides of the equation 6+t=20, she would have been solving the equation improperly. When solving for 't', you would want to isolate the variable on one side, which means subtracting or adding the opposite of whatever value is with 't'. If we start with Colin's proposed equation:

And we subtract 6 from both sides to isolate 't', we get:

Which simplifies to:

Therefore, subtracting 20 from both sides wouldn't make sense in this context since that operation would not help to solve for 't' in the equation 6+t=20.

Answer:

55% or 55/100 or 11/20

Step-by-step explanation:

1/4 is equal to 25%

Add: 30+25=55

So the percent will be 55%

Percents are always out of 100, so to convert 55% into a fraction, you simply have to put 55 over 100: 55/100

Find the greatest common factor, which is 5.

Divide:

55÷5=11

100÷5=20

So the simplified fraction will be 11/20.

Answer:

[tex]y-2=3(x-3)[/tex]

Step-by-step explanation:

We want to write the equation of a line in point-slope form.

This is given by:

[tex]y-y_1=m(x-x_1)[/tex]

We have that line passes through (3,2).

Assuming the line has a slope of m=3, then the equation in point slope form is:

[tex]y-2=3(x-3).[/tex]

Final answer:

The point-slope form of the line that passes through the point (3, 2) with a slope of ½ is represented by the equation y - 2 = ½(x - 3).

Explanation:

The equation that shows the point-slope form of the line that passes through the point (3, 2) with a slope of ½ is derived from the point-slope equation format: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Plugging the given point and slope into this formula, we get the equation y - 2 = ½(x - 3).

When solving for y to get the slope-intercept form, it's important to distribute the slope ½ across the (x - 3) term resulting in the equivalent equation: y = ½x + ¼.

The polynomial 4x5 – 16x2 + 13x8, when rearranged in standard form by ordering the terms in descending degree, becomes 13x8 + 4x5 – 16x2.

The question asks to express the given polynomial 4x5 – 16x2 + 13x8 in standard form. In mathematics, a polynomial is generally expressed in standard form when its terms are written in decreasing order by degree.

Here, the degrees from highest to lowest of the terms in our polynomial are 8, 5, and 2. So the polynomial in standard form would be: 13x8 + 4x5 – 16x2

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Answer:

6.71

Step-by-step explanation:

From Pythagoras theorem, we know that;

x^2 = 6^2 + 3^2

x^2 = 36 + 9

x^2 = 45

x = sqrt(45)

x = 6.71

well, we know the tree is growing at a rate of 36 feet every 3 years, how many feet is that in 1 year alone?   well, simply 36/3 = 12.

so the tree is growing 12 feet per year.

when it was first planted, it was 5 feet tall, and then after every year, we have to add 12 feet subsequently, let's do that

year 1 .......... 5 + 12(1)

year 2 .......... 5 + 12(2)

year 3 .......... 5 + 12(3)

year 4 .......... 5 + 12(4)

year 5 .......... 5 + 12(5)

year 6 .......... 5 + 12(6)

year 7 .......... 5 + 12(7)

year y .......... 5 + 12(y)

[tex]\bf \stackrel{\textit{height}}{h}~~=~~\stackrel{\textit{initial height}}{5}~~+~~\stackrel{\textit{yearly rate}}{12y} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{tree is now}}{77} = 5 + 12y\implies 72=12y\implies \cfrac{72}{12}=y\implies \boxed{6=y}[/tex]

The angle above 111 degrees must be 69 degrees because of supplementary angles (111+69=180)

And since the triangles are congruent, angle 2 must be 69 degrees as well.

Hope this helped.

Answer:

12.56 units

Step-by-step explanation:

C=pid

C = 3.14(4)

C = 12.56

For a 7 to have a value that is 1/10 of the 7 in 3,762, it needs to be in the tens place of a number. Only choice B, 738, meets this requirement.

To solve this question, we need to first understand the place value of numbers. In the number 3,762, the 7 is in the hundreds place, which signifies that it represents 700. A 7 that has 1/10 of this value would, therefore, represent 70. So, we're looking for a number where 7 appears in the tens place.

By reviewing choices A through D, we can determine that the correct answer is B. 738. In this number, the 7 is in the tens place, which means it is worth 70, or 1/10 of the value of the 7 in 3,762.

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The solution is x = 11

Step-by-step explanation:

The original equation is

[tex]7(x+2)=91[/tex]

Lin uses the distributive property, which states that

[tex]a(x+y)=ax+ay[/tex]

By applying the property to this case,

[tex]7(x+2)=91\\7x+14=91[/tex]

Then we subtract 14 on both sides:

[tex]7x+14-14=91-14\\7x=77[/tex]

Finally, we divide by 7 on both sides:

[tex]\frac{7x}{7}=\frac{77}{7}\\x=11[/tex]

Noah starts by dividing each side by 7, so he gets

[tex]\frac{7(x+2)}{7}=\frac{91}{7}\\x+2=13[/tex]

Then he can subtract +2 from both sides:

[tex]x+2-2=13-2\\x=11[/tex]

So, they get the same result. The similarity between the two methods is that they both divide by 7, while the difference is that Lin has to subtract 14, while Noah has to subtract 2.

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Lin's solution method: 7x+14=91, 7x=77, x=11

Noah's solution method: x+2=13, x=11

Both methods involve dividing by 7, but Noah does the division first, while Lin does the division last. Also, Lin's method involves subtracting 14, while Noah's method involves subtracting 2. Both solutions are correct and valid. Noah's solution could be considered more efficient for this example, because it takes fewer steps and has equally complicated arithmetic work.

Final answer:

To find the total number of seats in the stadium section, we determine there are 14 rows and 10 seats per row, resulting in a total of 140 seats.

Explanation:

To determine the total number of seats in this section of the basketball stadium, we'll first find out how many rows and columns are present, based on the provided information. Kyleigh is seated in the 7th row from the back and the 8th row from the front of the section. This implies that there are a total of 14 rows (7+8-1 because the row Kyleigh is seated in counts for both the front and the back).

Similarly, Kyleigh's seat is the 4th row from the right and 7th from the left. This means there are a total of 10 seats in each row (4+7-1, as Kyleigh's seat counts for both the right and the left).

To find the total number of seats in this section, we multiply the number of rows by the number of seats per row: 14 rows × 10 seats per row = 140 seats.

Answer:

A. 112 feet

B. 3 seconds

C. 256 feet

Step-by-step explanation:

The function [tex]d(t)=-16t^2+96t+112[/tex] describes the height of the quarter above the water.

When [tex]t=0,[/tex] then

[tex]d(0)=-16\cdot 0^2+96\cdot 0+112\\ \\d(0)=112\ feet[/tex]

Part A. The quarter was tossed from 112 feet.

Find the vertex of parabola represented by quadratic function d(t):

[tex]t_v=\dfrac{-b}{2a}=\dfrac{-96}{2\cdot (-16)}=3\\ \\d(t_v)=d(3)=-16\cdot 3^2+96\cdot 3+112\\ \\d(3)=-144+288+112\\ \\d(3)=256\ feet[/tex]

Hence,

Part B. It will take 3 seconds to reach the maximum height.

Part C. The maximum height is 256 feet

Answer:

0.35

Step-by-step explanation:

a randomly chosen person's chance of being an athlete is 100%, or 1.00

Therefore: if the probability of a randomly chosen athlete is a swimmer is 0.65 or 65%, The probability of a randomly chosen athlete to NOT be a swimmer is:

1.00 - 0.65 = 0.35 or 35%

Final answer:

The probability that a randomly chosen athlete is not a swimmer is 0.35, calculated by subtracting the probability of being a swimmer (0.65) from 1.

Explanation:

If the probability that a randomly chosen athlete is a swimmer is 0.65, this means that there is a 65% chance of selecting a swimmer from a group of athletes. Since the total probability for any event is always equal to 1 (or 100%), we subtract the swimmer probability from 1 to find the probability that an athlete is not a swimmer.

To calculate: 1 - 0.65 = 0.35. Therefore, the probability that a randomly chosen athlete is not a swimmer is 0.35, or 35%.