Write the word sentence as an equation. Then solve. The product of 15 and a number x is −75.

9z + 10 = 1 - 3(5 - 3z)    use distributive property

9z + 10 = 1 + (-3)(5) + (-3)(-3z)

9z + 10 = 1 - 15 + 9z

9z + 10 = -14 + 9z     subtract 9z from both sides

10 = -14   FALSE

NO SOLUTION

Answer: zero solutions.

Answer:

[tex] \sf \: z = no \: solution[/tex]

Step-by-step explanation:

Given equation,

→ 9z + 10 = 1 - 3(5 - 3z)

Now the value of z will be,

→ 9z + 10 = 1 - 3(5 - 3z)

→ 9z + 10 - 1 = -15 + 9z

→ 9z + 9 = -15 + 9z

→ 9z - 9z = -15 - 9

→ 0 = -24

→ [ z = no solution ]

Hence, there is no solution.

Answer:

4

Step-by-step explanation:

Let us consider an equilateral triangle ABC. Now, we will define midsegments:

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle (here triangle ABC). This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.

Refer the attached image:

Now, from the definition of midsegment we can see that:

[tex]PQ=\frac{1}{2}BC[/tex]

[tex]\therefore PQ=BR[/tex]

and PQ is also parallel to BR.

Now, again from the definition of midsegment we can see that:

[tex]QR=\frac{1}{2}AB[/tex]

[tex]\therefore QR=PB[/tex]

and QR is parallel to PB.

therefore, PQBR forms a parallelogram

And a diagonal of a parallelogram divides it into two congruent triangles.

Hence, triangle 2 (triangle PBR) is congruent to triangle 4(triangle PQR).

Similarly, triangle 3 (triangle QRC) and triangle 1 (triangle APQ) are congruent to triangle 4 (triangle PQR), Therefore, there are 4 congruent triangles formed when midsegments of an equilateral triangle partition the triangle.

The midsegments of an equilateral triangle partition it into four smaller congruent triangles, due to the Triangle Midsegment Theorem and the Third theorem of congruence for triangles.

When the midsegments of an equilateral triangle are drawn, they connect the midpoints of the sides of the triangle. These segments will each be parallel to one side of the triangle and half its length, according to the Triangle Midsegment Theorem. Drawing all three midsegments partitions the equilateral triangle into four congruent smaller triangles. Each smaller triangle will be similar to the original equilateral triangle.

By the Third theorem of congruence for triangles (which is often referred to as SSS or side-side-side), if three sides of one triangle are congruent respectively to the corresponding sides of another triangle, the two triangles are congruent. In this case, each smaller triangle formed by the midsegments shares a side with the original triangle and has the other two sides equal in length to the midsegments, which are congruent to each other by construction.

Therefore, all four smaller triangles are congruent to each other.

Answer:

It would be B.

Step-by-step explanation:

Dilation is the only transformation that is NOT congruent. It is similar.

Answer:

The slope is -7/2.

Step-by-step explanation:

Convert to slope-intercept form (y = mx + b  where m = the slope)

7x + 2y = 5

2y = -7x + 5

Divide both sides by 2:-

y = (-7/2)x + 5/2

so slope m = -7/2

Use the graph to determine the solution of the inequality |x + 1| + 2 > 5.

To graph this , first we make the absolute function alone

|x + 1| + 2 > 5

to make absolute function alone we subtract 2 from both sides

|x + 1|  > 3

x+1 inside the absolute function . so x=-1

From -1, move 3 units to the right and 3 units to the left.

For x>2 , shade the graph to the right

For x< -4, shade the graph to the left

The graph is attached below

The solution to the inequality is x<-4 and x>2

Answer:

Its A on E2020

Step-by-step explanation:

5x - 3 = 7

Add 3 to both sides.

5x = 10

Divide both sides by 5.

x = 2

The value of x is 2.

I’m pretty sure you are

$5.00 x 4 = $20.00.

$20.00 divided by 2 = $10.00

She will have $10.00 to save.

Hope I helped!

Good Luck!

To solve the given system of equations by substitution, 'y' from the first equation is substituted into the second, resulting in x = 4/3. Substituting this into the first equation yields y = 5/3. Therefore, the solution to the system is x = 4/3, y = 5/3.

To solve the given system of equations by substitution, we will start with the first equation y = 2x - 1 and substitute it into the second equation 6x - 3y = 7.

Substituting 'y' from the first equation into the second, we get: 6x - 3(2x - 1) = 7.

Solving this, we find 'x': 6x - 6x + 3 = 7 => x = 7/3 = 4/3.

Next, we substitute 'x' into the first equation to find 'y': y = 2(4/3) - 1 = 8/3 - 1 = 5/3.

So, the solution to the system of equations is x = 4/3, y = 5/3.

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           Today          2 years ago

Chris:   x + 3            (x + 3) - 2   = x + 1

Nathan: 18               (18) - 2       = 16

Jacob:   x                (x) - 2          = x - 2

Chris + Nathan + Jacob = sum

x + 1  +     16     +   x - 2   = 59

                            2x - 15 = 59   added like terms (x and x) and (1, 16, and -2)

                                   2x = 74   added 15 to both sides

                                     x = 37    divided both sides by 2

Answer: Jacob is 37 yrs old

Answer:

4 umbrellas

Step-by-step explanation:

Number of Umbrellas              Total Money

                1                                            $12                

                2                                           $24

                3                                           $36

                4                                           $48

She can't go over $48 because $48 + $12 is $60, which is more than she has ($54). So the max amount of umbrellas she can buy is 4.

Here is your equation:

[tex]12x-5=127[/tex]

You're trying to find x, and to do that, the variable must be alone. That means you need to cancel out everything with it. The only thing with the variable 12x is -5. To cancel that out, you have to do the opposite of it, which is +5. Add 5 to both sides.

[tex]12x-5+5=127+5 \\12x=132[/tex]

12x(12 times x) is equal to 132. You need to find x. You have to do the opposite of times 12, which is divide by 12. Divide both sides by 12.

[tex]\frac{12x}{12} = \frac{132}{12} \\ \\x=11[/tex]

Your answer is x is equal to 11 ; x = 11

If you have any questions, feel free to ask in the comments! :)

we can see that

For x is 0, 1, 2, 3 ,4

f(x) is  0 , 1 ,  4, 9 , 16

g(x) is -2 , -1 , 1 , 5 , 13

so, g(x) is greater than f(x) for x is 0, 1, 2, 3 ,4

It means that f(x) exceeds g(x) on [0,4]

But for x=5

f(x) is 25

g(x) is 29

Here, we can see that g(x) exceeds f(x) at x=5

so, there must be intersection point between x=4 and x=5

so, option-C.........Answer

Each option describes different behaviors and relationships between the two functions over the interval [0, 5]. Without further details, we can only conceptualize the scenarios provided.

To compare the graphs of f(x) and g(x) over the interval [0, 5], we can evaluate the options provided:

Without the exact equations or a graph to analyze, we cannot definitively determine which option is correct. However, we can conceptualize the scenarios described:

Option A suggests f(x) is consistently greater than g(x) throughout the interval. Option B suggests the opposite. Option C introduces an intersection point, where f(x) transitions from being greater to less than g(x). Option D indicates g(x) is initially greater, with a reversal after an intersection between 4 and 5.

If we had the graphs or more specific information, we could more precisely identify the correct statement.

Answer:

The answer is 15 months.

Step-by-step explanation:

p = $500

r = 6.5% or 0.065

A = $543

t = ?

The formula to be used here is :

[tex]A=pe^rt[/tex]

[tex]t=(log(A/p)/log(e))/r[/tex]

Putting the values in formula we get:

[tex]t=(log(543/500)/log(e))/0.065[/tex]

[tex]t=(log(1.086)/log(e))/0.065[/tex]

This gives t = 1.3 years

In months it will be 1 year(12 months) + 3 months = 15 months.

Hence, the answer is 15 months.

Answer:

15 months

Step-by-step explanation:

Final answer:

To solve the equation 3/8 + b/3 = 5/12 for b, we find a common denominator, combine the fractions, and then isolate and solve for b. The solution for b is 1/8.

Explanation:

The equation presented by the student is 3/8 + b/3 = 5/12. To solve for b, we must first get a common denominator for the fractions to combine them. In this case, the common denominator is 24, since it is the least common multiple of 8 and 3. Multiplying each term by 24 yields:

(3/8)*24 + (b/3)*24 = (5/12)*24

9 + 8b = 10

Next, we isolate the variable b by subtracting 9 from both sides of the equation:

8b = 10 - 9

8b = 1

Finally, divide both sides by 8 to solve for b:

b = 1/8

Thus, the value of b that satisfies the given equation is 1/8.

The slope is -22/9. Use the formula (y2-y1)/(x2-x1)

(-1/3 +4)/(-1/3-7/6)

This line is already in slope-intercept form.

The slope of the line is 9, and the y-intercept is 0.

Because of this, we can find every y value for any x value simply by replacing x with the value of the x coordinate.

By replacing x with 2, we can see what the y coordinate would be when x is 2.

9(2) = 18

The y value would be 18, which is not 10, meaning (2, 10) is not a solution to the equation.

The point (2,10) is not a solution to the equation y = 9x because when x is substituted into the equation, it results in y = 18, not y = 10 as in the point.

To determine if the point (2,10) is a solution to the equation y = 9x, we need to substitute the x-value from the point into the equation and see if the corresponding y-value matches the one in the point. Let's substitute x = 2 into the equation:

y = 9 x 2

y = 18

For the point (2,10), the y-value is 10, which does not equal the calculated y-value of 18. Therefore, the point (2,10) is not a solution to the equation y = 9x.

Applying the concept of Algebra, the toll collector processed 40 cars and 5 buses during a 4-hour period. This is found by checking each option against the equations 8c + 9b = 368 and c + b = total number of vehicles (where c = cars and b = buses).

To solve this problem, we need to find the number of cars and buses that make up the total toll collected, which is $368. We can set up a system of equations to solve for the two variables: number of cars (c) and number of buses (b).

So, we have two equations: 8c + 9b = 368 and c + b = total number of vehicles. By checking each option, only 40 cars and 5 buses match these equations, because 8*40 + 9*5 = 368.

So, the toll collector processed 40 cars and 5 buses during the 4 hour period.

Learn more about Algebra here:

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Not sure if I am right but I looked online for you and it said divide the numerator and the denominator by the given rate so I guess you do 46 divided  by 5 I'm sorry if I am wrong nd let me know

The unit rate of $46 for 5 toys is calculated by dividing the total cost by the number of toys, resulting in $9.20 per toy.

This question demands complete basic understanding of mathematical concepts in general and division in particular.

To find the unit rate of $46 for 5 toys, you divide the total cost by the number of toys. This calculation will give you the cost of one toy. Here's how it's done step-by-step:

So, as per the above explaination, the unit rate is $9.20 per toy.

the key is to write [tex]n^2 + n[/tex] as [tex]n(n+1)[/tex] which can be easily seen as an area of a rectangle with one side length n and the other (n+1). That explains the rectangle made of dots - 3 x 4

Now you only have half of them because of the 1/2. So that explains the lower "triangle" of dots being greyed out - they do not count in  the area (upper triangle). So the count of the dark dots corresponds to the original expression.

For n=5 you can draw a similar rectangular matrix with 5 x 6 dots. And count only the upper triangular part.  

D) 209 with a remainder of 4

The question is about the division of 1467 by 7. The answer is '209 with a remainder of 4'.

This question is about division in mathematics. To solve this, we will divide 1467 by 7. Division is really repeated subtraction. You subtract 7 from 1467 as many times as you can until you get a number smaller than 7. That number is called the 'remainder', and the number of times you could subtract is the 'result' of the division.

After the division, the quotient is 209 and the remainder is 4. Therefore, the correct option is 'D) 209 with a remainder of 4'.

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The average is 18m/s.

The average acceleration of the roller coaster car is [tex]\( 6\, \text{m/s}^2 \)[/tex].

The average acceleration of the roller coaster car is calculated using the formula:

[tex]\[ a = \frac{{v_f - v_i}}{{\Delta t}} \][/tex]

where [tex]\( v_f \)[/tex] is the final velocity, [tex]\( v_i \)[/tex]  is the initial velocity, and [tex]\( \Delta t \)[/tex] is the time interval over which the acceleration occurs.

Given:

[tex]- Initial velocity (\( v_i \)) = 4 m/s \\- Final velocity (\( v_f \)) = 22 m/s\\ - Time interval (\( \Delta t \)) = 3 s[/tex]

Plugging in the values:

[tex]\[ a = \frac{{22\, \text{m/s} - 4\, \text{m/s}}}{{3\, \text{s}}} \] \[ a = \frac{{18\, \text{m/s}}}{{3\, \text{s}}} \] \[ a = 6\, \text{m/s}^2 \][/tex]

Answer:

9 feet will the cat cover on 24 steps.

Step-by-step explanation:

Given: A dog takes 3 steps to walk the same distance for which a cat takes 4 steps.

⇒ 3 steps of dog=4 steps of Cat

If 1 step of the dogs cover [tex]\frac{1}{2}[/tex] feet

then,

4 steps of cat=3 steps of dog

24 steps of cat=[tex]\frac{3}{4}\times(24)[/tex]=18 steps of dog

Also, 1 step of the dogs cover=[tex]\frac{1}{2}[/tex] feet

18 steps of the dogs cover=9 feet

therefore, 24 steps of cat will cover 9 feet .

[tex]6f-12=-4f+6\qquad|\text{add 12 to both sides}\\\\6f=-4f+18\qquad|\text{add 4f to both sides}\\\\10f=18\qquad|\text{divide both sides by 10}\\\\\boxed{f=1.8}[/tex]

You divide the difference in y-coordinates by the diffrence in x-coordinates. Or whatever the variables are.

Lets say the coordinates of the two points are (a,b) and (c,d). Then:

Rate of change is "rise/run" = (b - d)/(c - a) = (d - b)/(a - c)

Hey there!!

Recursive formula :

... a( n ) = a ( n - 1 ) + 7

The first term is 12

To find the second term, we will need to substitute 2 in place of ' n '

2 term :

... a( 2 ) = a ( 2 - 1 ) + 7

... a( 2 ) = a( 1 ) + 7

We know a( 1 ) = 12

... a( 2 ) = 12 + 7

... 19 is the second term and we will need to use this to find the other terms.

Hope my answer helps!

The two points on a line such that it has a slope 5/8 is:

             (0,0) and (8,5)

We know that the slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates.

Now, let us assume that the equation of a line with slope 5/8 be given by:

        [tex]y=\dfrac{5}{8}x[/tex]

Hence, the point (0,0) lie on the line.

(  since, when x=0 we have:

[tex]y=\dfrac{5}{8}\times 0\\\\y=0[/tex]  )

and also the point (8,5) lie on the line.

(  when x=8 we have:

[tex]y=\dfrac{5}{8}\times 8\\\\y=5[/tex]  )

In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. Next add the equations, and solve for y or x. Once you find out the value of either y or x you can substitute into one of the original equations to find x or y.