Answer:
D.
Step-by-step explanation:
The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
The slope of y=4x+2 is 4.
Let's look at the choices:
A) The slope of y=-2x+3 is -2.
B) The slope of y=2x-3 is 2.
C) The slope of y=-4x+2 is -4.
D) The slope of y=4x-2 is 4.
So we are looking for a line that has the same slope as the given line which is 4.
The answer is D.
Answer:
D.
Y = mx + b is the equation for a straight line. "B" is called the y intercept. "M" is the value of the slope of the line. "X" is the value where the line intercepts the x axis.
so the reason the awnser is D is because the M=4 in both equations, meaning that they have the same slope
How many solutions does the following equation have? 60z+50-97z=-37z+49
[tex]\bf 60z+50-97z=-37z+49\implies 50~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+49\implies \stackrel{\textit{the what?!}}{50=49}[/tex]
well, clearly 50 ≠ 49.
but, whenever we get a result of this kind, is just a way to say no solutions.
you can look at it this way, is a system of equations, the equations are
y = -37z + 50
y = -37z + 49
now, notice, since both equations are in slope-intercept form, both equations have the same slope of -37, however, the y-intercept differs, meaning both equations are parallel and never touch each other.
since a solution for them is where they intercept and they never do, no solutions.
The given equation will have no solution.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, 60z+50-97z=-37z+49
On solving, we get,
0 = -1
Which is not possible.
Hence, There is no solution.
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Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
For this case we have the following data:
Available quantity: $ 24
Regular price: r
Sale price:[tex]r-5[/tex]
If we have that Roopesh can not pay more than $ 24, we can write the following inequality, taking into account that the item is sold in [tex]r-5[/tex]:
[tex]r-5 \leq24[/tex]
Clearing r:
[tex]r \leq24+5\\r \leq29[/tex]
Answer:
What is the unknown?[tex]r \leq29[/tex]
Which expression can represent the sale price?[tex]r-5[/tex]
Which comparison could be used?The sale price decreases $ 5 and so the regular price is obtained.
The inequality is: [tex]r-5 \leq24[/tex]Answer:
answer in pic
Write the equation of the line parallel to the
y-axis and 7 units to the left of the y-axis.
PLEASE HELP!
Answer:
x=-7
Step-by-step explanation:
If a line is parallel to the y-axis, then it is vertical because the y-axis is vertical.
A vertical line is in the form of x=a number.
Since the line we are looking for is 7 units to the left of the y-axis, then the line is x=-7. -7 is 7 units left of 0.
7 units right would have been x=7.
Answer:
x = -7Step-by-step explanation:
A line parallel to y-axis is a vertical line.
A vertical line has an equation x = a, where a is any real number.
The line is 7 units to the left of the y-axis. Therefore the equation of this line is x = -7 (look at the picture).
how many solutions does the following equation have?3(x+5)=−4x+8
Answer:
1
Step-by-step explanation:
Solve the equation for x:
3(x + 5) = -4x + 8
Distribute.
3x + 15 = -4x + 8
Combine like terms.
3x + 15 = -4x + 8
+4x +4x
7x + 15 = 8
-15 -15
7x = -7
Divide both sides by 7.
x = -1
The following equation has one solution, x = -1.
Answer:
1 solution, x = -1.
Step-by-step explanation:
3(x + 5 )= −4x + 8
3x + 15 = -4x + 8
3x + 4x = 8 - 15
7x = -7
x = -1.
What is the slope of a line passing through (3, 4) and (5,8)?
1/2
2
2/4
4/2
Answer:
2
Step-by-step explanation:
To find the slope of a line given two points [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] you could use the formula: [tex]\frac{y_2-y_1}{x_2-x_1} \text{ or even } \frac{y_1-y_2}{x_1-x_2}[/tex].
However, what I'm fixing to do is equivalent to that except I think easier to remember.
You line up the points vertically and subtract, then put 2nd difference over 1st difference.
Like this:
( 3 , 4)
- ( 5 , 8)
---------------
-2 -4
So the slope is -4/-2=4/2=2.
The slope is 2.
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $80 million after 4 years, as shown in the graph
The question revolves around understanding the concepts of fixed costs, marginal costs, and economies of scale in the context of a computer manufacturing company. The company's ability to make substantial profits over a period of four years marks an effective management of these costs and leveraging economies of scale.
Explanation:The computer company's scenario primarily involves understanding the concept of fixed costs and marginal costs in a business context. The fixed cost noted here is $250, which remains constant irrespective of the number of computers produced. The marginal cost, on the other hand, is variable depending on the volume of production.
For example, the company's marginal cost for producing computers is $700 for the first one, $250 for the second, and so on. The total cost is obtained by adding the fixed cost and the total variable (marginal) costs. Understanding these costs is critically important for the company to make decisions about pricing its products to achieve desired profit margins.
It means that if the company managed to make profits of $80 million after 4 years, they have effectively managed their fixed and variable costs and priced their computers profitably. In this example, by leveraging the economies of scale, that is, an advantage that companies gain when production becomes efficient with the increasing scale of output, the company has managed to reduce the average cost of production and increase profits.
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Find the height of a square pyramid with volume 37.3 ft3 and dimensions of base 4 ft by 4 ft. Please help!
[tex]\bf \textit{volume of a square pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ \cline{1-1} B=\stackrel{4\times 4}{16}\\ V=37.3 \end{cases}\implies 37.3=\cfrac{1}{3}(16)h\implies 111.9=16h \\\\\\ \cfrac{111.9}{16}=h\implies 6.99375=h[/tex]
Answer:
6.99
Step-by-step explanation:
To find the height use the formula 3*V/b squared
So plug the numbers you have which is the base and volume
3*37.3/4 squared
Now solve:
4 squared = 16
3*37.3 = 111.9
111.9/16 = 6.99375
6.99375 can be rounded down to 6.99
Examine the quadratic equation 9x^2+24x+16=0.
A: What is the discriminant of the quadratic equation?
B: Based on the discriminant, which statement about the roots of the quadratic equation is correct?
Select one answer choice for question A, and select one answer choice for question B.
A: 120
A: -120
A: 0
B: There is one real root with a multiplicity of 2.
B: There are two real roots.
B: There are two complex roots
Answer:
The correct answer options are,
A: 0
B: There is one real root with a multiplicity of 2.
Step-by-step explanation:
Discriminant of a quadratic equation ax² + bx + c = 0 is given by,
b² - 4ac
It is given a quadratic equation 9x² + 24x + 16 = 0
To find the discriminant
Here a = 9, b = 24 and c = 16
Discriminant = b² - 4ac
= 24² - (4 * 9 * 16)
= 576 - 576
= 0
The correct options are
A: 0
B: There is one real root with a multiplicity of 2.
The discriminant of the quadratic equation 9x^2+24x+16=0 is 0, which means there is one real root with a multiplicity of 2.
Let's examine the quadratic equation 9x^2+24x+16=0 to find the discriminant and interpret its meaning for the roots of the equation.
A: The discriminant of a quadratic equation in the form ax^2+bx+c=0 is given by the formula b^2-4ac. Substituting the coefficients from our equation (where a=9, b=24, and c=16) into this formula gives us the discriminant:
discriminant = b^2 - 4ac = 24^2 - 4(9)(16) = 576 - 576 = 0.
B: The discriminant tells us about the nature of the roots of the quadratic equation. Since the discriminant is zero, this implies that there is one real root with a multiplicity of 2. Therefore, the quadratic equation has a perfect square factor and the graph of the equation touches the x-axis at one point, indicating that both roots are the same.
At one farmer’s market, bananas cost $0.80 per pound. At another farmer’s market, bananas are sold in 5-pound bags for $4.50 per bag. Which explains how to find the better buy?
Answer with step-by-step explanation:
We are given that at one farmer’s market, bananas cost $0.80 per pound while at another market, bananas are sold in 5 pound bags for $4.50 per bag.
We are to explain how to find the better buy.
For the first market, the rate of bananas is given per pound but for the other market, the rate is given for a 5 pound bag so we will find the rate of bananas per pound to compare the rates of both markets.
One pound of bananas at 2nd market = 4.50/5 = $0.9
Therefore, getting bananas from the first market at $0.80 per pound is a better buy.
Answer: A
Step-by-step explanation:on My quiz I got it right
for a standard normal distribution which of the following variables always equals 1
For a standard normal distribution, the standard deviation is always equals 1
What is z score?Z score is used to determine by how many standard deviations the raw score is above or below the mean.
It is given by:
z = (raw score - mean) / standard deviation
For a standard normal distribution, the standard deviation is always equals 1
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What is the height of a triangle with an area of 6.72 square meters and a base of 3.2 meters?
Answer:
4.2 meters.
Step-by-step explanation:
Area = 1/2 * base * height.
6.72 = 1/2 * 3.2 * h
h = 6.72 / 1.6
= 4.2 m.
Answer:
4.2 meters
Step-by-step explanation:
The height of a triangle with an area of 6.72 square meters and a base of 3.2 meters is 4.2 meters.
6.72 = 1/2 * 3.2 * h
URGENT 19 points!!!!! PLEASE HELP!!
Aria is playing a game at the school carnival. There is a box of marbles, and each box has a white, a green, a blue, and an orange marble. There is also a spinner separated into 3 equal sections. How many outcomes are in the sample space for pulling a marble out of the box and spinning the spinner? 7 10 12 14
Answer: 12
Step-by-step explanation: Multiply the chances of getting a marble, 4, and the chances of spinning the spinner, 3.
4 x 3 = 12
There are 12 outcomes.
Answer:12
Step-by-step explanation:
I did the test
Perimeter of 40 triangles when the sides are all 1 cm long
Answer: 120 cm.
Step-by-step explanation: Each triangle has 3 sides, and each side is 1 cm. Multiply the number of sides for one triangle by the total number of triangles. 3 x 40=120. The perimeter is 120 cm.
can someone please help me
Answer:
[tex]\large\boxed{\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot\sqrt{y^2}\cdot\sqrt{y}}\\\boxed{2\cdot2\cdot y\sqrt{2\cdot5\cdot7\cdot y}}\\\boxed{4y\sqrt{70y}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{c|c}1120&2\\560&2\\280&2\\140&2\\70&2\\35&5\\7&7\\1\end{array}\\\\1,120=2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot7=2^2\cdot2^2\cdot2^2\cdot2\cdot5\cdot7\\\\y^3=y\cdot y\cdot y=y^2\cdot y[/tex]
[tex]\sqrt{1,120y^3}=\sqrt{2^2\cdot2^2\cdot2\cdot5\cdot7\cdot y^2\cdot y}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot\sqrt{y^2}\cdot\sqrt{y}\\\\\sqrt{1,120y^3}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{y^2}\cdot\sqrt{2\cdot5\cdot7\cdot y}\qquad\text{use}\ \sqrt{a^2}=a\\\\=2\cdot2\cdot y\cdot\sqrt{2\cdot5\cdot7\cdot y}\\\\\sqrt{1,120y^3}=2\cdot2\cdot y\cdot\sqrt{2\cdot5\cdot7\cdot y}=4y\sqrt{70y}[/tex]
Given parallelogram ABCD, find the lengths and angles required
Step-by-step explanation:
let's Recall the properties of a parallelogram
1. the opposite sides of a parallelogram is congruent
AB=CD
8x-7=5x+2
8x-5x=7+2
3x=9
x=3
2. the consecutive angles are supplementary
angle A+angle D=180°
2y+50°+3y+40°=180°
5y+90°=180°
5y=90°
y=18
Javier used the expression below to represent his score in a game of mini-golf.
3x + x + 5 – 2x
If he simplifies the expression, which statements are true about the parts of the simplified expression? Check all that apply.
1-The constant is 2.
2-The coefficient is 2.
3-The constant is 5.
4-The coefficient is 5.
5-There are two variables.
6-There are two terms.
Answer: The correct options are
(2) The coefficient is 2.
(3) The constant is 5.
(6) There are two terms.
Step-by-step explanation: Given that Javier used the expression below to represent his score in a game of mini-golf :
[tex]E=3x+x+5-2x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to select the correct statements about the parts of the simplified expression if Javier simplifies the expression.
The simplification of expression (i) is as follows :
[tex]E\\\\=3x+x+5-2x\\\\=(3+1-2)x+5\\\\=2x+5.[/tex]
Therefore, we get
the constant term is 5,
the coefficient of x is 2
and
There are two terms.
Thus, options (2), (3) and (6) are correct.
Answer:
think its 2 3 and 6
Step-by-step explanation:
sorry if im late
sin(5x)sin(3x)
Express the given product as a sum or difference containing only sines or cosines.
[tex]\bf \textit{Product to Sum Identities} \\\\ sin(\alpha)sin(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad -\quad cos(\alpha+\beta)]\qquad \leftarrow \textit{we'll use this one} \\\\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)] \\\\\\ sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)][/tex]
[tex]\bf cos(\alpha)sin(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad -\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5x)sin(3x)\implies \cfrac{cos(5x-3x)-cos(5x+3x)}{2}\implies \cfrac{cos(2x)-cos(8x)}{2}[/tex]
Answer:[tex] \frac{1}{2}\left ( cos\left ( 2x\right )-cos\left ( 8x\right )\right )[/tex]
Step-by-step explanation:
Solution
[tex]Sin\left ( 5x\right )Sin\left ( 3x\right )[/tex]
We know
[tex] 2sin\left ( a\right )sin\left ( b\right )=cos\left ( a-b\right )-cos\left ( a+b\right ) [/tex]
Applying formula
[tex]Sin\left ( 5x\right )Sin\left ( 3x\right )=\frac{1}{2}\left ( cos\left ( 5x-3x\right )-cos\left ( 5x+3x\right )\right )[/tex]
=[tex] \frac{1}{2}\left ( cos\left ( 2x\right )-cos\left ( 8x\right )\right ) [/tex]
how do i solve this? 5×{3×[9-(4+1)]}+20÷4×2????
Answer: 70
Step-by-step explanation:
Solve the equation in the innermost parentheses first that means solving 4+1 =5
The next step would be subtracting 9 from five which gives you 4
Next multiply 3 to 4 which gives you 12
Then multiply 5 with 12 which equals 60
Now you have the equation 60+20/4*2
Solve the division and multiplication part of the equation first because of the rule pemdas which shows multiplication comes before addition
First divide 20/4 which gives you 5 then multiply with 2 which gives you ten
After dividing and multiplying you are left with the equation 60+10
The answer is 70
The image below is a triangle drawn inside a circle with center O:
8 inches
5 inches
4 inches
Which of the following expressions shows the area, in square inches, of the circle?
(TT = 3.14)
3.14.42
3.14 . 52
3.14.5
3.14 22
Answer:
area ≈ 24π
Step-by-step explanation:
We have solved this problem two ways:
Using a drawing program that writes the formula of the circumscribing circle, so gives the value of r^2.Using rarely-seen formulas for the area of a triangle and for the area of its circumscribing circle.__
Drawing
A drawing of the figure (below) can help you find the radius of circle O. It is about 4.89 inches, so the area of circle O is about ...
area = πr^2 = π(4.89 in)^2 ≈ 23.9π ≈ 24π . . . .square inches
__
Formulas
There is an interesting relationship between the area of the triangle and the radius of the circumscribing circle:
r = (abc)/(4A) . . . . . where a, b, c are the triangle side lengths, and A is the triangle area
Heron's formula can tell us the area of the triangle from the side lengths:
A = √(s(s-a)(s-b)(s-c)) . . . . where s = (a+b+c)/2
For the given triangle with side lengths 4, 5, and 8 (inches), the area can be found as ...
s = (4+5+8)/2 = 8.5
A = √(8.5·4.5·3.5·0.5) = √66.9375 ≈ 8.1815 . . . square inches
Then the radius of the circle is ...
r = (4·5·8)/(4·8.1815) = 4.889 . . . inches
The area of the circle is then ...
Circle O area = πr^2 = π(4.889 in)^2 = 23.9π in^2
__
The closest answer choice is 3.14×22.
y>1 and y>x on a graph
So,
[tex]y>1\wedge y>x[/tex]
1. Graph each inequality separately.
2. Choose a test point to determine which side of the line needs to be shaded.
3. The solution to the system will be the area where the shadings from each inequality overlap one another (purple area)
As for the system of inequalities we say it's unbounded.
Find the area of a triangle with legs that are: 15 mm, 10 mm, and 20 mm.
Answer:
Area = [tex]\frac{75}{4} \sqrt{15} sq mm[/tex]
Step-by-step explanation:
Here we are given with all the sides of the triangle , and we are asked to find the area of it. we will use Heron's Formula to find the area. The formula is as under
Area [tex]= \sqrt{s\times (s-a) \times (s-b) \times (s-c)}[/tex]
Where [tex]s= \frac{a+b+c}{2}[/tex]
Where a , b and c are the three sides of the triangle
a=15 , b=10 and c=20
Substituting those values in the two formula one by one we get
[tex]s=\frac{15+10+20}{2}[/tex]
[tex]s=\frac{45}{2}[/tex]
now putting this value of s in main formula we get
Area= [tex]\sqrt{s\times (s-a) \times (s-b) \times (s-c)}[/tex]
Area = [tex]\sqrt{\frac{45}{2} \times (\frac{45}{2}-15) \times (\frac{45}{2}-10) \times (\frac{45}{2}-20)}[/tex]
Area = [tex]\sqrt{\frac{45}{2} \times (\frac{45-30}{2}) \times (\frac{45-20}{2}-) \times (\frac{45-40}{2})}[/tex]
Area = [tex]\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{25}{2}) \times (\frac{5}{2})}[/tex]
Area = [tex]\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{20}{2}-) \times (\frac{5}{2})}[/tex]
Area = [tex]\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}[/tex]
Area = [tex]\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}[/tex]
Area = [tex]\frac{1}{4} \sqrt{9 \times 5 \times 5 \times 3 \times 25 \times 5}[/tex]
Area = [tex]\frac{3\times 5 \times 5}{4} \sqrt{3 \times5}[/tex]
Area = [tex]\frac{75}{4} \sqrt{15}[/tex]
The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]
Further Explanation;Area Area is a measure of how much space is occupied by a given shape. Area of a substance is determined by the type of shape in question.For example;
Area of a rectangle is given by; Length multiplied by width Area of a circle = πr². where r is the radius of a circle, Area of a square = S², Where s is the side of the square.etc.Area of a triangle The area of a triangle is given based on the type of the triangle in question.Right triangle.The area of a right triangle is given by;= 1/2 x base x height
Scalene triangleIt is a triangle that with sides and angles that are not equal.Area of a scalene triangle depends on the features of the triangle given.For example;
Sine FormulaArea of a triangle = 1/2 ab sin θ, when given two sides of the triangle and the angle between themHeron's formulaArea of a triangle = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex] when given all the sides of the triangle. where [tex]s =\frac{(a+b+c)}{2}[/tex]In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm
Therefore, we use the Heron's formula;
Area= [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s =\frac{(a+b+c)}{2}[/tex]
[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]
Therefore;
Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]22.5\sqrt{12.5(12.5-15)(22.5-10)(22.5-20)}[/tex]
=[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]
[tex]= 72.618 mm^{2}[/tex]
Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.
Learn more about: Perimeter: https://brainly.com/question/12905000 Area: https://brainly.com/question/12905000 Area of a triangle: https://brainly.com/question/4125306Heron's Formula: https://brainly.com/question/10713495Example of a question using Heron's Formula: https://brainly.com/question/10713495
Level: Middle school
Subject; Mathematics
Topic: Area
Sub-topic: Area of a triangle
x + y = 6 x - y = 8 Solve the system of equations.
Answer:
x=7
y=-1
Step-by-step explanation:
When the two equations are solved together, they form simultaneous equations.
x+y=6
x-y=8
Let us use the elimination method. if we add the two equations, we eliminate y.
2x=14
x=7
Let us substitute for the value of x obtained above.
x-y=8
7-y=8
y=7-8
y=-1
10,825.643 which digit is in the tenths place
Answer:
the number 6 is in the tenths place.
Hope this helps!
Simplify the imaginary number sqr -75
Answer:
5i[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
and [tex]\sqrt{-1}[/tex] = i
Given
[tex]\sqrt{-75}[/tex]
= [tex]\sqrt{25(3)(-1)}[/tex]
= [tex]\sqrt{25}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{-1}[/tex]
= 5 × [tex]\sqrt{3}[/tex] × i
= 5i[tex]\sqrt{3}[/tex]
Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $4,500 in interest in one year?
Answer:
The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x -----> the amount invested at 5.5%
(64,000-x) -----> the amount invested at 9%
in this problem we have
[tex]t=1\ years\\I=\$4,500\\ P=\$64,000\\r1=0.055\\P1=\$x\\P2=\$64,000-\$x\\r2=0.09[/tex]
so
[tex]I=P1(r1t)+P2(r2t)[/tex]
substitute the given values
[tex]4,500=x(0.055*1)+(64,000-x)(0.09*1)[/tex]
[tex]4,500=0.055x+5,760-0.09x[/tex]
[tex]0.09x-0.055x=5760-4,500[/tex]
[tex]0.035x=1,260[/tex]
[tex]x=\$36,000[/tex]
[tex]64,000-x=64,000-36,000=\$28,000[/tex]
therefore
The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000
Determine whether the trinomial is a
perfect square. If so, factor it. If not,
explain why.
16. 81n2 + 90n+ 100
Step-by-step explanation:
Use (a+b)²= a²+2ab+b² formula
We can see that a²=81n² (so a=9n) and b²=100 (so b=10) and 2ab = 2*9n*10=180n.
therefore only √(81n²+180n+100) would be perfect square and this - isn't.
the area of a rectangular box is 24x³-76x²-28x square units. The width of this box is (12x²+4x) units. Write and simplify an expression for the length of the rectangle. (Please show steps:) NEED ASAP
Answer:
(2x-7) units
Step-by-step explanation:
[tex]\tt length=\cfrac{area}{width}\\\\\\ length=\cfrac{24x^3-76x^2-28x}{12x^2+4x}=\cfrac{4x(6x^2-19x-7)}{4x(3x+1)}=\\\\\\=\cfrac{6x^2+2x-21x-7}{3x+1}=\cfrac{2x(3x+1)-7(3x+1)}{3x+1}=\\\\\\=\cfrac{(3x+1)(2x-7)}{3x+1}=2x-7[/tex]
The length of the rectangle can be found by dividing the area given as (24x³-76x²-28x) by the width given as (12x²+4x). This simplifies to 2x - 7 units which is the expression for the length of this rectangle.
Explanation:In mathematics, to find the length of a rectangle when given the area and the width, you have to divide the area by the width. The area A is given as 24x³-76x²-28x square units, and the width w is given as (12x²+4x) units. Following the formula A = lw, where l is length and w is width, the length can be found by rearranging this formula to l = A/w.
Applying this to the given values: l = (24x³-76x²-28x) / (12x²+4x) simplifies to l = 2x - 7 units. Therefore, the expression for the length of the rectangle is 2x - 7 units.
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9(x + 1) = 25 + x
x = 2
x = 3
x = 4
X
11
Answer:
x = 2.
Step-by-step explanation:
9(x + 1) = 25 + x
9x + 9 = 25 + x
Subtract x from both sides:
9x - x + 9 = 25
Subtract 9 from both sides:
9x - x = 25 - 9
8x = 16
x = 16/8 = 2.
Answer:
x = 2
Step-by-step explanation:
Given
9(x + 1) = 25 + x ← distribute parenthesis on left side
9x + 9 = 25 + x ( subtract x from both sides )
8x + 9 = 25 ( subtract 9 from both sides )
8x = 16 ( divide both sides by 8 )
x = 2
Can someone help me please and thank you
The shortest living man on Earth is 21 inches tall. The tallest living woman on Earth is approximately 4 times taller than the shortest man. How tall is the tallest living woman on Earth?
Answer: 84 inches, 7 feet tall.
Step-by-step explanation:
4 x 21 = 84 inches
84/12 = 7 feet ( there are 12 inches in 1 foot)