O EQUATIONS AND INEQUALITIESSolving a word problem using a quadratic equation with rationa...
Answers
Answer:
[tex]\begin{gathered} length\text{ = 8 m} \\ width\text{ = 5.5 m} \end{gathered}[/tex]Explanation:
Here, we want to get the dimensions of the rectangle
Let us represent the length by l and the width by w
From the question:
The length of the rectangle is 3 m less than double the width
Mathematically:
[tex]l\text{ = 2w-3}[/tex]The product of the two represents the area
[tex]\begin{gathered} A\text{ = l }\times\text{ w} \\ lw\text{ = 44} \end{gathered}[/tex]Now, let us substitute the first equation with the second:
[tex]\begin{gathered} w(2w-3)\text{ = 44} \\ 2w^2-3w\text{ = 44} \\ 2w^2-3w-44\text{ = 0} \end{gathered}[/tex]Solving the quadratic equation, we have:
[tex]\begin{gathered} 2w^2-11w+8w-44\text{ = 0} \\ 2w^2+8w-11w-44\text{ = 0} \\ 2w(w\text{ + 4\rparen -11\lparen w+4\rparen = 0} \\ (2w-11)(w+4)\text{ = 0} \\ 2w=\text{ 11} \\ w\text{ = }\frac{11}{2} \\ \\ w\text{ = 5.5} \end{gathered}[/tex]Recall:
[tex]\begin{gathered} lw\text{ = 44} \\ 5.5l\text{ = 44} \\ l\text{ = }\frac{44}{5.5}\text{ = 8 } \end{gathered}[/tex]Related Questions
composite functions 65 points helpppppp
Answers
Answer:
[tex]4\sqrt{x+2} - 6[/tex]
Step-by-step explanation:
f(g(7)) = f(sqrt(x+2))
=4(sqrtx+2) - 6)
= [tex]4\sqrt{x+2} - 6[/tex]
Answer:
[tex](f \circ g)(7)=6[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=4x-6\\g(x)=\sqrt{x+2}\end{cases}[/tex]
(f o g)(x) is a composite function.
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function (f o g)(7) means to substitute the function g(x) when x=7 in place of the x in function f(x).
[tex]\begin{aligned}\implies (f \circ g)(7)&=f[g(7)]\\& = f(\sqrt{7+2})\\&=f(\sqrt{9})\\&=f(3)\\&=4(3)-6\\&=12-6\\&=6\end{aligned}[/tex]
write the equation of a line through ( 3, 1), parallel to y = 2/3x + 1.
Answers
Answer:
y = 2/3 x - 1
Step-by-step explanation:
Parallel slopes are equal.
y = mx + b
m = 2/3
x = 3 Use the x and y given in the point (3,1)
y = 1
Solve for b the y-intercept
y = mx + b
1 = 2/3(3) + b
1 = 2 + b Subtract 2 from both sides
-1 = b
y= mx +b
y = 2/3x -1
to be parallel, you need the same slope but to pass through the point ( 3, 1), you would need a different y- intercept.
Xavier has a bag of 20 marbles. 8 are blue, 7 are red, and 5 are green. Xavier pulls out a marble, records what color it is, and puts it back. He then selects another marble and records its color What is the probability of pulling out a blue marble and then a green marble?
Help please
Answers
Answer:
.1
We have 20 marbles.
Probability of blue marble = 8/20 = .4
Since the blue marble is put back, we still have 20 marbles.
Probability of green marble = 5/20 = .25
Multiplying these probabilities:
.4 × .25 = .1
A square has side length of 7.3 in. If the area is multiplied by 1/9, what happens to the perimeter. Please help!
Answers
Note that if the area of any figure is multiplied by a factor of a.
The perimeter will be multiplied by √a
From the problem, the are of the square is multiplied by 1/9, so we need to get the square root of that factor to get the factor for the perimeter.
[tex]\sqrt[]{\frac{1}{9}}=\frac{1}{3}[/tex]Therefore, the answer is C. multiplied by 1/3
C= 3 + ab find the variable for b
Answers
———
a
I don’t know if you understand the answer but anyways
At a simple annual interest rate of 4.5%, how many years will it take Sam to earn $135 interest on an original deposit of $1,000?
A. 3
B. 4
C. 5
D. 6
Answers
Answer: A
Step-by-step explanation:
Interest = Principal * Rate * Time
135 = 1000 * 4.5% * T
135 = 1000 * 0.045 * T
135 = 45 * T
T = 135/45
T = 3 (A)
I need some help with my math.
Answers
5√108=30√3
2√50-3√25=-14√2
√25/36=5/6
Sorry that’s all I know for right now im so sorry can I be marked as Brainlyist
Help me pleaze its hard !!
Answers
It is to be noted that the Diagonals of a parallelogram bisect each other. Here in PQSR, it does bisect PT =ST and QT = TR). Hence, PQSR is a parallelogram.
IGHJ is a paralellogram. This is because the opposite sides of a parallelogram are congruent. Here, H = I and G = J. Hence, IGHJ is a parallelogram.
CABD is a parallelogram because of the alternative interior angles ACB = CBD and ABC = BCD.
VWYX is NOT a parallelogram. The rule states that if opposites sides are congruent then the quadrilateral is a parallelogram. In this case, clearly, line VW ≠ XY and VX ≠ WY.
What is a parallelogram?A parallelogram, rhombus, rectangle, or square is a quadrilateral with opposing sides that are congruent and parallel.
There are six crucial parallelogram qualities to understand:
Contrary sides are equivalent (AB = DC).Angles opposite each other are congruent (D = B).Consecutive angles are additive (A + D = 180°).If one angle is correct, all angles are correct.A parallelogram's diagonals cross one other.A parallelogram is divided into two congruent triangles by its diagonals.Learn more about parallelograms:
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a grocery store wonders if their sales will be better if they play ambient music or no music at all. each day for 222 months, the manager flips a coin to determine whether or not the store will play music that day. at the end of the 222 months, the manager finds that, on average, sales were significantly better on days where music was playing. what conclusion can they draw from this study?
Answers
Answer:
They should play music
Step-by-step explanation:
They should play music obviously because the sales were higher
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a
graphing utility, use it to graph the function and verify the real zeros and the given function value.
n= 3:
4 and 4 i are zeros;
f (- 1)= - 255
Answers
The polynomial is f(x) = x³ - 12x² + 64x + 128
Given,
The polynomial has 4, 4-4i, and 4+4i as its roots.
f(-1) equals -255
We have to find a polynomial of degree 3.
If x = 4 is a root, then:
(x - 4) is a factor of the polynomial.
If x = 4 - 4i is a root,
Then,
(x - 4 + 4i) is a factor of the polynomial.
If x = 4+4i is a root.
Now,
(x - 4 - 4i) is a factor of the polynomial.
All the three roots are of the same polynomial.
So,
The polynomial is the product of these factors.
f(x) = k(x - 4) (x-4+4i) (x-4-4i)
f(x) = k(x - 4) [(x-4)² - (4i)²]
f(x) = k(x- 4) [x² + 16 - 8x + 16]
f(x) = k(x - 4) [x² - 8x + 32]
f(x) = k[x³ - 8x² + 32x - 4x² + 32x - 128]
f(x) = k[x³ - 12x² + 64x + 128]
Now find "k", we know that f(-1) = -255.
f(-1) = k[(-1)³ - 12(-1)² + 64(-1) + 128]
-255 = k[-1 - 12 - 64 + 128]
-255 = k × -255
k = 1
That is, the polynomial is f(x) = x³ - 12x² + 64x + 128
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A die is rolled and the spinner is spun. Find each probability.
Answers
Hello!
First, let's write the possible options:
Dice: 6 different results.
• 1, 2, , 4, 5, 6.
Spinner: 4 different results.
• A, B, C, D.
Knowing it, let's solve each alternative of your exercise:
a. 1 and AIn the dic, we have 6 possible results and we want a specific number. SOo, we can write it as 1/6.
In the spinner, we have 4 possible results and we want a specific one too. So, we have 1/4.
Now, remember he r"and" rule: when we consider two events happening simultaneously, we must multiply their probabilities.
Solving:
[tex]\frac{1}{6}\times\frac{1}{4}=\frac{1\times1}{6\times4}=\frac{1}{24}[/tex]b. odd score and B.We'll solve it in a similar way.
We have three possible odd numbers (1, 3, 5) in a total of 6 options. So, 3/6 = 1/2.
For the spinner, the reasoning will be the same: 1/.
Let's calculate:
[tex]\frac{1}{2}\times\frac{1}{4}=\frac{1\times1}{2\times4}=\frac{1}{8}[/tex]c. number less than 5 and a consonant.In a dice, we have four numbers less than 5: 1, 2, 3,4.
In the spinner, there are 3 consonants (B, C, D).
Let's calculate:
[tex]\frac{2}{3}\times\frac{3}{4}=\frac{2\times3}{3\times4}=\frac{6}{12}=\frac{1}{2}[/tex]
Scale factor=.9 is enlarge , reduce , or preserve ?
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The scale factor K = 0.9 is smaller than 1, so this is a reduction.
What type of dilation do we have?If we have a dimension L, a change of scale of scale factor K gives the new length: K*L
Then:
if K > 1, we have an enlargement.
if K = 1, we have a preservation (nothing changes)
if 0 < K < 1, we have a reduction.
In this case, we have K = 0.9, this is smaller than 1, so we have a reduction.
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two cyclists, 42 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
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The speed of the faster cyclist is 14\ miles/hr.
What is speed?
It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.
Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,
[tex]2s+s=42\\3s=42\\s=14[/tex]
Now, distance coverd by the first cyclist is [tex]2s=2\times 14\\=28 \ $miles[/tex].
Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.
[tex]Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr[/tex]
Hence, the speed of the faster cyclist is 14\ miles/hr.
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PLS HELP WILL MARK BRAINLIEST
Answers
Answer:
did not understand waht should we do
The equation 9(u + 2) = -45 is solved in several steps below. For each step, choose the reason that best justifies it.
Answers
Step 1: Distributive property:
Step 2: Subtraction Property of Equality
Step 3: Simplifying
Step 4: Division property of equality
Step 5: Simplifying
Explanation:Given the expression
9(u + 2) = -45
Step 1: Expand using the Distributive property:
9u + 9(2) = -45
9u + 18 = -45
Step 2: Subtract 18 from both sides (Subtraction property of equality)
9u + 18 - 18 = -45 - 18
Step 3: Simplifying
9u = -63
Step 4: Divide both sides by 9 (Division property of equality)
9u/9 = -63/9
Step 5: Simplifying
u = -7
Which equation has no solution?
Answers
Answer:
The answer is the third one down
Step-by-step explanation:
l5-3xl = -8
Absolute value cannot equal a negative number.
Step-by-step explanation:
l5-3xl = -8
the | | is absolute value to it so it cant be negative number
A truck rental company charges $90 plus $20 per hour. Identify a function that represents the total
charge for renting a truck for a certain number of hours. What is the value of the function for an input
of 5, and what does it represent?
Of(h) = 20h + 90
$470, which is the total charge in dollars for renting a truck for 5 hours
Question 6 of t
Of(h) = 90+20h
$190, which is the total charge in dollars for renting a truck for 5 hours
Of(h) = 20 +90h
$470, which is the total charge in dollars for renting truck for 5 hours
Of(h) = 90h + 20
$190, which is the total charge in dollars for renting a truck for 5 hours / pls help lol
Answers
The function that represents the total charge for renting a truck for a certain number of hours is f(h) = 90 + 20h What is the value of the function for an input 5 represent : $190, which is the total charge in dollars for renting a truck for 5 hours.
How to find the total charges?Given data :
Charges = $90 + $20 per hour
Value = 5
Now let formulate an equation
f(h) = 90 + 20h
Where,
h = 5
So,
Total charge = 90+ 20 ×5
Total charge = 90 + 100
Total charge =190
Therefore the correct option is B.
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Subtract.
−3−6−(−1) = ?
Answers
Answer:
-8
Step-by-step explanation:
Select the correct answer.An engineering firm designs a custom hexagonal screw for a computer board. A sketch of the top of the screw is below. To the nearest tenth,what is the area of the screw head?ymm8.€4-2-x mmO-2--4--4OA15.6 mm2.OB. 93.5 mm2OC 62.4 mm2OD.1871 mm²402
Answers
We will have the following:
We can see that the shape of the head can be subdivided in smaller shapes, that is:
Now, we calculate the 5 areas, that is:
[tex]\begin{gathered} A_1=\frac{(6)(3)}{2}\Rightarrow A_1=9 \\ \\ A_2=\frac{(6)(3)}{2}\Rightarrow A_2=9 \\ \\ A_3=(6)(12)\Rightarrow A_3=72 \\ \\ A_4=\frac{(6)(3)}{2}\Rightarrow A_4=9 \\ \\ A_5=\frac{(6)(3)}{2}\Rightarrow A_5=9 \end{gathered}[/tex]Now, the total area is:
[tex]\begin{gathered} A_T=A_1+A_2+A_3+A_4+A_5\Rightarrow A_T=9+9+72+9+9 \\ \\ \Rightarrow A_T=108 \end{gathered}[/tex]So, the total area is 108 mm^2-
to
low
ing
Guess my number.
My number is a 2-digit number.
It is multiple of 5 but not a multiple
of 10.
It has an odd tens digit.
The digit total is less than 10.
What is my number?
Answers
Answer:60 and 80
Step-by-step explanation:
Use the number line shown below. What is the location of Z between X and Y such that the length of ZY is 3 times the length of XZ.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
X = -5
Y = 4
Answers
Answer:
z is -2
Step-by-step explanation:
x = -5 y = 4
<----------------------------------------->
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Z is between x and y but is 3 times the lenght of x&z
so jumb from -5 to -3 thats one, however jumb from -2 to 0 that is 1, and form 0 to 2 that is 2, and from 2 to 4 that is 3.
if u answer this can u help me with the other questions ??
Answers
Answer:
B=2, C=3, D=4, E=5
the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. what is the cutoff interest rate for the highest 15% of banks in this area?
Answers
The highest cut-off interest rate is 2.66%
Given that,
Standard deviation (sigma) = 0.37
Mean percentage (Mu) = 2.28 %
P(Z > 1.04) = 0.15
z = 1.04
Using the z-score formula,
x = (z × sigma) + mu
x = (1.04 × 0.37 )+ 2.28 = 2.66 %
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ingles TestGiven mZA = m D = 90° and AABC ADFE. If AB = 5 inches and BC = 13 inches, determine DE.POSSIBLE
Answers
We will apply the principle of similar triangles to solve this question
Given that
[tex]\begin{gathered} AB=5 \\ BC=13 \end{gathered}[/tex]Method: Find side AC
We will use the Pythagoras theorem to evaluate AC
[tex]\text{hypotenuse}^2=\text{opposite}^2+\text{adjacent}^2[/tex][tex]13^2=5^2+AC^2[/tex][tex]\begin{gathered} AC^2=13^2-5^2 \\ AC^2=169-25 \\ AC^2=144 \\ AC=\sqrt[]{144} \\ AC=12 \\ \end{gathered}[/tex]T
Please help!! Math is not my cup of tea and I’m really struggling!! ASAP
Given the function:
f(x)=x²-3x - 4
Find the following values.
a) f(2)
f(2)=
b) f(4)
ƒ(4)=
c) f(-3)
ƒ(-3) =
Answers
Answer: [tex]-6, 0, 14[/tex]
Step-by-step explanation:
[tex]f(2)=2^2 - 3(2)-4=-6\\\\f(4)=4^2 -3(4)-4=0\\\\f(-3)=(-3)^2 -3(-3)-4=14[/tex]
Answer:
5782
Step-by-step explanation:
td j envalentonado 8jdjdyzh d
Oliver estimates the weight of his cat to be 16 pounds. The actual weight of his cat is 14.25 pounds. What is the percent error of Olver's estimate? Round the percent to the nearest tenth if necessary.
Answers
ANSWER
The percent error is 10.9 %
EXPLANATION
The percent error is:
[tex]\text{ \% error}=\frac{|approx-exact|}{exact}\times100[/tex]In this problem, the approximate value is 16 and the exact value is 14.25:
[tex]\begin{gathered} \text{ \% error}=\frac{|14.25-16|}{16}\times100 \\ \text{ \% error}=\frac{1.75}{16}\times100 \\ \text{ \% error}=0.109375\times100 \\ \text{ \% error}=10.9375\approx10.9\text{ \%} \end{gathered}[/tex]Answer:
10.9%
Step-by-step explanation:
14.25/16 = 0.890625
0.890625 * 100 = 89.0625
1 - 89.0625 = 10.9375%
Find the surface area of the triangular prism Formula: SA= p * h + 2 * b
Answers
ANSWER:
139 square yards
STEP-BY-STEP EXPLANATION:
We have that the formula for the surface area of a triangular prism is the following:
[tex]A=p\cdot h+2b[/tex]Where p, is the perimeter is the base and h is the height, while b is the area of the base, we replace and calculate the area like this:
[tex]\begin{gathered} p=4+4+5=13 \\ A=13\cdot9.5+2\cdot7.75 \\ A=123.5+15.5 \\ A=139 \end{gathered}[/tex]The area is 139 square yards
simplify 20:15
simplify 35:49
simplify 81:36
simplify 27:45
simplify 21:36
pls help me i’m crying rn bro
Answers
Answer:
1. 4:3
2. 5:7
3. 9:4
4. 3:5
5. 7:12
Step-by-step explanation:
I'm sure you don't care how to get the answers, you just want them :)
Simply this equation 2(x-7)=-4
Answers
Answer:
2x - 14 = -4
that is the equation simplified
Step by step
If you only need to simplify, divide both sides by 2 and you get
x-7=-2
solve
Add 7 to both sides to solve for x
x = 5
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A (4, 5), B (12,9); 3 to 1 The coordinates of P are:
Answers
By applying line ratio, the coordinates of P are: [10, 8].
How to determine the coordinates of P?Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Given the following parameters:
Point A (4, 5)Point B (12, 9)m:n = 3:1Substituting the given parameters into the formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(3(12) + 1(4))/(3 + 1)], [(3(9) + 1(5))/(3 + 1)]
P(x, y) = [(36 + 4)/4], [(27 + 5)/4]
P(x, y) = [40/4, 32/4]
P(x, y) = [10, 8].
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