Find the length and width of a rectangle whose area is 56 units squared and whose length is 10 units less than it's width

The other root of the quadratic equation is -2, and the coefficient c is -106, found using the sum and product of roots formulas.

The other root and the coefficient c of the quadratic equation 10x²- 33x + c = 0, given that one of the roots is 5.3. Using the fact that the sum of the roots of a quadratic equation ax² + bx + c = 0 is equal to -b/a, we can find the other root. With one root known to be 5.3 and a = 10, b = -33, the sum of the roots must be 3.3. Therefore, the other root is 3.3 - 5.3 = -2. To find the coefficient c, we use the fact that the product of the roots of a quadratic equation is equal to c/a. Thus, c = 5.3 * (-2) * 10 = -106. The other root of the equation is -2, and the coefficient c is -106.

(X^3+2x^2) +(5x+10)

X^2(x+2) +5(x+2)

(X^2+5)(x+2)

Answer:

[tex](x+2)\text{ and }(x^2+5)[/tex] are the factors of given polynomial,    

Step-by-step explanation:

We are given the following information in the question:

We are given a polynomial:

[tex]x^3 + 2x^2 + 5x + 10[/tex]

We have to factor this polynomial with the help of grouping method.

Grouping can be dine with the help of taking the common factors.

Working:

[tex]\text{Taking } x^2 \text{ common from the first two terms and 5 from the other two terms, we have}\\\Rightarrow x^2(x + 2) +5(x + 2)\\\text{Aain taking the common term}\\\Rightarrow (x+2)(x^2+5)[/tex]

Hence, the two factors of the given polynomial are:

[tex](x+2)\text{ and }(x^2+5)[/tex]

Answer:

Part a) [tex]m<HIG=40\°[/tex]

Part b) IHG is a semicircle and GJI is a semicircle

Part c) HIJ is a major arc and HIJG is a major arc

Part d) [tex]arc\ GH=80\°[/tex]

Part e) [tex]arc\ GJI=180\°[/tex]

Step-by-step explanation:

Part a) Give an inscribed angle

we know that

The inscribed angle measures half that of the arc comprising

so

in this problem m<HIG is an inscribed angle

[tex]m<HIG=\frac{1}{2}(arc\ HG)[/tex]

[tex]arc\ HG=80\°[/tex] ----> by central angle

substitute

[tex]m<HIG=\frac{1}{2}(80\°)=40\°[/tex]

Part b) Give a semicircle

we know that

The diameter divide the circle into two semicircles

so

GI is a diameter

therefore

IHG is a semicircle

GJI is a semicircle

Part c) Give a major arc

we know that

The measure of a major arc is greater than 180 degrees

therefore

HIJ is a major arc

HIJG is a major arc

Part d) Measure of arc GH

we know that

[tex]arc\ GH=m<HFG[/tex] ----> by central angle

so

[tex]arc\ GH=80\°[/tex]

Part e) Measure of arc GJI

we know that

[tex]arc\ GJI=180\°[/tex] ----> the arc represent a semicircle

Answer:

75 pieces

Step-by-step explanation:

1. determine how many pieces per ounce by dividing 45 by 6 (# of pieces in a 6 oz bag)

    45/6= 7.5 pieces per ounce

2. multiply 7.5 (for one ounce) by 10

    7.5*10 = 75

Answer:

75

Step-by-step explanation:

just answer it

Answer:

Translated to the left 5 units and up 5 units and compressed horizontally by 2 units.

Step-by-step explanation:

The  parent function given is [tex]f(x)=x^2[/tex]

This function has its vertex at the origin.

If we move this function 5 units  to the left and 5 units up, then its vertex will now be at [tex](-5,5)[/tex].

If the parent function is then compressed horizontal by a factor of 2, then the transformed function will now have equation.

[tex]g(x)=2(x+5)^2+5[/tex]

Answer:

48

Step-by-step explanation:

The sample space of the experiment contains all the possible outcomes of all events.

There are 3 events that are taking place.

Rolling a die which has 6 possible outcomes.

Flipping a coin which has 2 possible outcomes.

Spinning a spinner which has 4 possible outcomes.

Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.

i.e.

Total outcomes = 6 x 2 x 4 = 48

The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48

Answer:

48

Step-by-step explanation:

In the given experiment, three events take place which include rolling a die, flipping a coin and spinning a spinner.

The possible outcomes of each of these events are as follows:

Rolling a die - 6

Flipping a coin - 2

Spinning a spinner - 4

Therefore, by multiplying their possible outcomes, we can find the number of elements in the sample space of this environment.

Number of elements = 6 × 2 × 4 = 48

Answer:

Option A.

Step-by-step explanation:

Based on the information provided on the question

the function used to model Tony's run is:

f(x) = -250*x  + 5000

This means that after x = 20 minutes, Tony will arrive to the finish line

f(20) = -250*(20)  + 5000 = -5000 + 5000 = 0

The function is always decreasing, because we are dealing with a line with negative slope.

Option A.

Answer:

  y = tan(x -π) -1

Step-by-step explanation:

It looks like a straight tangent function shifted down one unit. Since the tangent function has a period of π, ...

  tan(x -π) = tan(x)

so you're only looking for the function that has a translation downward of 1 unit. Of course that translation is accomplished by adding -1 to the original function.

The appearance of the graph is of ...

  y = tan(x) -1

The choice that is equivalent to this is ...

  y = tan(x -π) -1

Answer:

y = tan (x-pi)-1

Step-by-step explanation:

The function in the graph is a periodic function with intervals of pi and having discontinuities at regular intervals.

Hence this must be a transformation of the original trignometric funciton

tan x.   y intercept is at -1 which shows that there is a vertical shift of 1 unit down.

Hence the funciton is y = tanx-1

But tan x is not given in any of the options.

Let us check which is equivalent to tan x-1

We find that tan(x-pi) = -tan (pi-x) = -(-tanx) = tanx

Hence the option 3 is the right answer

Answer:

  C)  78 ft

Step-by-step explanation:

The side opposite the angle has the ratio to the hypotenuse:

  Sin = Opposite/Hypotenuse

Then the solution to this problem is found by substituting the given information and solving for the height.

  sin(45°) = height/(110 ft)

  (110 ft)·sin(45°) = height ≈ 77.7817 ft

Rounded to the nearest foot, the crane can raise material to a height of 78 ft.

Answer:

  a straight line: y = x -5, with a hole at (4, -1)

Step-by-step explanation:

The rational function can be simplified to ...

  [tex]f(x)=\dfrac{x^2-9x+20}{x-4}=\dfrac{(x-5)(x-4)}{(x-4)}\\\\f(x)=x-5\qquad\text{$x\ne 4$}[/tex]

The graph of this is a straight line, with a hole at x=4, where the function is not defined.

Answer:

Step-by-step explanation:

For x use the Pythagorean theorem:

[tex]x^2+6^2=10^2[/tex]

[tex]x^2+36=100[/tex]              subtract 36 from both sides

[tex]x^2=64\to x=\sqrt{64}\\\\x=8[/tex]

We know: x + y = 20. Substitute:

[tex]8+y=20[/tex]              subtract 8 from both sides

[tex]y=12[/tex]

(6•4m) + (6•5)= 24m + 30

The correct answer is 30

Here’s how you solve it!

First multiply what’s in the parentheses

6✖️4m➕6✖️5

Now calculate the produce

24m➕6✖️5

Now multiply 6 and 5 then add the number to 24m

Then you are left with your answer:

24m➕30

Hope this helps! :3

Answer:

6x-5y=-10

Step-by-step explanation:

We are given an equation in words and we are to translate it and then re-write its standard form:

'y space equals space 6 over 5 x space plus space 2 '

[tex] y = \frac { 6 } { 5 } x + 2 [/tex]

Re-arranging this given equation to get:

[tex] y - 2 = \frac { 6 } { 5 } x [/tex]

[tex]5(y-2)=6x[/tex]

[tex]5y-10=6x[/tex]

[tex]6x-5y=-10[/tex]

So the correct answer option is 6x-5y=-10.

Answer:D) 144

Step-by-step explanation:12*12=144

Answer:

the answer is 144

Step-by-step explanation:

Answer:

B. (0,6)

Step-by-step explanation:

To solve this question, you'll need to figure out what the final point is after reflecting each point. A quick way to figure this out is by multiplying (-1) to the x-coordinate.

When you reflect A. (2,0) over the y-axis, the point becomes (-2,0).

When you reflect C. (3,3) over the y-axis, the point becomes (-3,3).

When you reflect D. (5,5) over the y-axis, the point becomes (-5,5).

The only answer that does not change location is B. (0,6) as it stays at (0,6). If you multiply 0 by any number, it will always stay 0.

Multiplying the x-coordinate by (-1) to find the reflection point only works if you are reflecting it over the y-axis. You would multiple the y-coordinate by (-1) if you were reflecting over the x-axis.

Scholarships and grants do not need to be paid back.

Government loans and private loans do need to be paid back.

She has 2 loans. $5,000 and $6,000.

She needs to pay back $11,000

Answer: [tex]y=\frac{5}{8}x+\frac{7}{4}}[/tex]

Step-by-step explanation:

The slope-intercept form of a equation of the line is:

[tex]y=mx+b[/tex]

Where m is the slope and b the y-intercept-

If the lines are parallel then they have the same slope:

[tex]m=\frac{5}{8}[/tex]

You can find the value of b by substituting the point given and the slope into the equation and solving for b:

[tex]3=\frac{5}{8}*2+b\\b=\frac{7}{4}[[/tex]

Then the equation is:

[tex]y=\frac{5}{8}x+\frac{7}{4}}[/tex]

Answer:

[tex]y = \frac{5}{8} x+\frac{7}{4}[/tex]

Step-by-step explanation:

We are to write the slope intercept form of the equation which passes through the point (2, 3) and is parallel to the line [tex]y = \frac{5}{8} x-7[/tex].

We know that the standard (slope-intercept) form of an equation of a line is given by: [tex]y=mx+c[/tex]

where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept.

Since we are to find the equation of the line parallel to the given equation so its slope will be same as of [tex]y = \frac{5}{8} x-7[/tex].

Finding the y-intercept:

[tex]y=mx+c[/tex]

[tex]3=\frac{5}{8}(2)+c[/tex]

[tex]c=\frac{7}{4}[/tex]

Therefore, the equation will be [tex]y = \frac{5}{8} x+\frac{7}{4}[/tex].

Answer:

Athena

Step-by-step explanation:

Squares are rhombuses but rhombuses are not squares

To calculate the probability of an adult female's pulse rate being between 72 and 80 bpm, additional information like mean and standard deviation is necessary if using a normal distribution or population data for a simple probability.

To find the probability that an adult female's pulse rate is between 72 beats per minute and 80 beats per minute, we need additional information such as the mean and standard deviation if the pulse rates follow a normal distribution, or the percentage of females with pulse rates in that range if the data is available in simple probability form.

Without this information, it's not possible to provide an exact answer. However, we can reference typical heart rate data or use estimation techniques to provide a rough idea of the probability. Health organizations often provide guidelines on normal heart rates for adults that could be used as a proxy in the absence of specific data points.

Answer:

(3250/100)*80 = $ 2600 - 3250 = $650

Step-by-step explanation:

Hey there!

Let's start by adding 6 to both sides of the equation to eliminate the -6.

3y^2 = 48

Next, let's divide both sides by 3 to eliminate the 3.

y^2 = 16

Find the square root of both sides.

y = ±4

It can be both positive or negative 4 because -4 x -4 and 4 x 4 both equal 16.

The value of y is ±4.

Hope this helps!

Answer:

[tex]\large\boxed{-6y^2+12y+4}[/tex]

Step-by-step explanation:

[tex](2y^2+7y+11)-(8y^2-5y+7)\\\\=2y^2+7y+11-8y^2-(-5y)-7\\\\=2y^2+7y+11-8y^2+5y-7\qquad\text{combine like terms}\\\\=(2y^2-8y^2)+(7y+5y)+(11-7)\\\\=-6y^2+12y+4[/tex]

Answer:

$13.68

Step-by-step explanation:

3.42 x 4

Final answer:

To find the total cost of 4 baseballs, each costing $3.42, we multiply the cost of one baseball by the number of baseballs, resulting in a total cost of $13.68.

Explanation:

The question asks to calculate the total cost of 4 baseballs, provided that each costs $3.42. To find the total cost, we need to multiply the cost of one baseball by the number of baseballs that were purchased. Hence, the calculation of the total cost of baseball is given by $3.42 (cost of one baseball) × 4 (number of baseballs) = $13.68. Therefore, the total cost of the 4 baseballs is $13.68.

Answer:

2√5

Step-by-step explanation:

Use a factor tree to break down 20 into it's prime roots.

20 = 2 x 10

20 =  2 x 2 x 5

These are the prime factors of 20, so we can rewrite √20 as

(√2)(√2)(√5)

         (√2)(√2) = √(2x2) = √4 = 2, so we have

2√5

Answer:

The answer would be C

Final answer:

No, (-2n)⁴ is not equal to -8n⁴ because when -2 is raised to the fourth power, it results in a positive 16, making the correct evaluation of the expression 16n⁴. The correct answer is option (C).

Explanation:

The question is whether (-2n)⁴ is equal to -8n⁴. To evaluate the expression (-2n)⁴, you must raise both -2 and n to the fourth power. Since the exponent is even, the negative sign in front of 2 will become positive after being raised to the fourth power: (-2n)⁴ = (-2)⁴ × n⁴ = 16n⁴

So, the correct statement is No; for values other than 0, (–2n)⁴ = 16n⁴ not equal to  –8n⁴. When raising a negative number to an even power, the result is positive, and (-2)⁴ equates to 16, not -8. Therefore, the option C is correct.

As a result, the misconception that -2 times 4 makes -8 is incorrect when dealing with exponents, as the negative sign is squared, turning it positive.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{u^{\frac{2}{5}}}{r^{\frac{1}{2}}}\implies \cfrac{1}{u^{\frac{1}{2}}\cdot u^{-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{1}{2}-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{5-4}{10}}}\implies \cfrac{1}{u^{\frac{1}{10}}}\implies u^{-\frac{1}{10}}[/tex]

Answer:

see explanation

Step-by-step explanation:

Isolate r² by dividing both sides by πh

r² = [tex]\frac{V}{h\pi }[/tex]

Take the square root of both sides

r = ± [tex]\sqrt{\frac{V}{h\pi } }[/tex]

The negative part can be  discarded as r > 0, hence

r = [tex]\sqrt{\frac{V}{h\pi } }[/tex]

Answer:

$75000

Step-by-step explanation:

5% of $60000 is $3000 and $3000 x 5 is $15000 and $15000 + $60000 is $75000

To calculate the total salary over 5 years with an initial salary of $60,000 and a 5% annual raise, you add the salary of each year considering the raise. The salaries over 5 years will be $60,000; $63,000; $66,150; $69,457.50; $72,930.38 respectively, amounting to a total of $331,537.88, which is approximately $331,538.

The question asks how much money you would earn total after 5 years of working at a company starting with a $60,000 salary and receiving a 5% raise each year. This is a problem of geometric progression in mathematics. To calculate the total amount earned over 5 years, we have to apply the formula for the sum of a geometric series because the salary increases by a fixed percentage each year. The salary each year is as follows: Year 1 - $60,000, Year 2 - $60,000*1.05, Year 3 - $60,000*(1.05)^2, Year 4 - $60,000*(1.05)^3, and Year 5 - $60,000*(1.05)^4.

Here is the calculation step-by-step:

Now, add up the salaries for each year to find the total earnings:

Add up these amounts to get the total earnings after 5 years:

Total = $60,000 + $63,000 + $66,150 + $69,457.50 + $72,930.38 = $331,537.88, which can be rounded to approximately $331,538.

Therefore, the correct answer is: $331,538.

Answer:

  Triangles BPA and DPC are congruent.

Step-by-step explanation:

The statement above is the only one of the bunch that is true, so is the best selection.

You don't even need to worry too much about how you might make the proof. You just need to be concerned with which are plausible answers. There's only one.