[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's get it solved ~
We have been given length and width of a rectangle in terms of x ~
that is :
length = x + 3width = x - 2Area of the rectangle is given ~ i.e 24 unit²
Area of rectangle in terms of x is :
[tex]\qquad \sf \dashrightarrow \:(x - 2) \sdot(x + 3) = 24[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 3x - 2x - 6= 24[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} +x - 6 - 24 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} +x -30= 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 6x - 5x - 30 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{}( x + 6) - 5(x + 6)= 0[/tex]
[tex]f(x) = \begin{cases}x = - 6 \: \textsf{ \: if \:x + 6 = 0 } \\ \\ x = 5 \: \: \: \: \: \: \textsf{if \: x - 5 = 0} \end{cases}[/tex]
but since side of a rectangle can't be negative, we have to take value of x as 5
now, Perimeter of rectangle is ~
[tex]\qquad \sf \dashrightarrow \:2(width \: + \: length)[/tex]
[tex]\qquad \sf \dashrightarrow \:2(x - 2 + x + 3)[/tex]
[tex]\qquad \sf \dashrightarrow \:2(2x + 1)[/tex]
plug In the value of x ~
[tex]\qquad \sf \dashrightarrow \:2(2(5) + 1)[/tex]
[tex]\qquad \sf \dashrightarrow \:2(10 + 1)[/tex]
[tex]\qquad \sf \dashrightarrow \:2(11)[/tex]
[tex]\qquad \sf \dashrightarrow \:22 \: \: units[/tex]
So, the correct choice is b~
Maria started the year with $235 in the bank and is saving $15 a week. Sergio started with $685 and is spending $35 a week. When will they both have the same amount of money in the bank? Write an equation(s) to represent the situation and then solve. Be sure to define your variable(s) and clearly answer the question.
Answer:
9 weeks
Step-by-step explanation:
let the time when they will both have the same amount be x
since Maria is saving then her money is bound to increase
therefore amount she will have after x weeks=235+15x
Sergio is spending so his money is reducing
therefore amount he will have after x weeks=
685-35x
so
235+15x=685-35x
685-235=15x+35x
450=50x
x= 450/50
9weeks
3ª = 69
Help pleaseeee it’s solving exponential equations with logarithms worksheet
Answer:
a = 3.8540
Step-by-step explanation:
3ª = 69
ln 3ª = ln69
a * 1n3/1n3 = ln69/ln3
a = 3.8540
please mark brainliest if i got it correct. if i didn't sorry :(
"I was told I would receive a 15% credit on the fee to activate my service but I was still charged $50.00."
Answer:
Based on the given conditions;
50÷(1-15℅)
=50/1-0.15
=50/0.85
=1000/17
Two vertices of a right triangle have coordinates (0,0) and (4.0), as plotted on the grid below. The hypotenuse of the triangle is 8 units long.
(0.6)
(4.0)
if the triangle's third vertex has coordinates (0,y), which is a possible value of y?
02
0 4√2
043
Answer:
y=2
Step-by-step explanation:
due to diagram have done the steps in the image
HELP Identify the exponential function shown in the graph
Answer:
C
Step-by-step explanation:
Points given are
(0,8) and (1, 16)
The first point given is the y-intercept, 8
The y-intercept of A is 2
The y-intercept of B is 16
The y-intercept of C is 8
the y-intercept of D is 16
The only one that works is C
HURRY I NEED TO FINSIH THIS TEST BEFORE 12:00
What graph represents the piecewise-defined function? 6 if x 3 y = 3 if 3 < x < 2 5 if x 2 >
HURRY I NEED TO FINSIH THIS TEST BEFORE 12:00
What graph represents the piecewise-defined function? 6 if x 3 y = 3 if 3 < x < 2 5 if x 2 >
Find the surface area
Answer:
the surface area is 648
Solution:
A=2(wl+hl+hw)=2·(9·9+13.5·9+13.5·9)=648
a lion gamer spent a total of 400$. the circle graph shows what percent was spent on each item. find the amount spent on a.costume b.chairs c. whips
B. chair no costume also whips
Please help on this math question!!!
Equation of the line passing through (7,5) and (1, 2)
Answer:
[tex]y = \frac{1}{2}x + \frac{3}{2}[/tex]
Step-by-step explanation:
Assuming this is a linear equation in the form of [tex]y = mx + b[/tex], we can first solve for the slope using [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex], for these points, the slope would be [tex]\frac{1}{2}[/tex]. Now we plug in the points to get the equation:
plugging in (7,5), we get [tex]5 = \frac{1}{2}[/tex] ×[tex]7[/tex] + [tex]b[/tex]
and solving for b, we get b = [tex]\frac{3}{2}[/tex]
therefore, the equation of the line passing through (7,5) and (1,2) is [tex]y = \frac{1}{2}x + \frac{3}{2}[/tex].
hope this helps!
find the volume of a rectangular pyramid
Answer:
192 yd³
Step-by-step explanation:
The volume of a rectangular pyramid is given by the formula:
[tex]V=\frac{1}{3} lwh\text{ where } l \text{ is the base length, }w \text{ is the base width, and }h \text{ is the pyramid height}[/tex]
In this case: [tex]l = 9, w=8, h = 8[/tex]
[tex]\therefore V=\frac{1}{3}(9\text{ yd})(8\text{ yd})(8\text{ yd})=192\text{ yd}^3[/tex]
I really need help with this Helpppp please
square of 5=25
square of 10=100
cube of (-2) =-8
square of (-3)=9
b. Calculate the monthly payments and total payment you will be making on your loan if you do use the $5,000 to make an initial payment. Monthly Payment: Total Amount Paid:
Answer:
Read the excerpt from "Digging"The cold smell of potato mould, the squelch and slapOf soggy peat, the curt cuts of an edgeThrough living roots awaken in my head.But I’ve no spade to follow men like them.Between my finger and my thumbThe squat pen rests.I’ll dig with it.Read the haiku by Bashō. When the winter chrysanthemums go,there’s nothing to write about but radishes.What common concern do these poems share?
Step-by-step explanation:
Read the excerpt from "Digging"The cold smell of potato mould, the squelch and slapOf soggy peat, the curt cuts of an edgeThrough living roots awaken in my head.But I’ve no spade to follow men like them.Between my finger and my thumbThe squat pen rests.I’ll dig with it.Read the haiku by Bashō. When the winter chrysanthemums go,there’s nothing to write about but radishes.What common concern do these poems share?
Pls ingore all of the questions below, but help me with the attached image
What is the only number that has the same number of letters as it's meaning? ...
What number doesn't have its own Roman numeral? ...
What is the only even prime number? ...
What is the smallest perfect number? ...
What is our current numerical system based on? ...
Is Pi a rational or irrational number?
Answer:
x = 104°
Step-by-step explanation:
The 142° and <DCE form a straight line, and a straight line measures 180°, do the two angles add up to it:
180° = 142° + m<DCE
m<DCE = 38°
The red symbol in <DCE and <CDE mean they are congruent, so m<CDE is the same as m<DCE, which is 38°.
The 142° angle is an exterior angle to triangle, DCE, an exterior angles are the sum of the remote interior angles, which are <CDE and <DEC. Therefore, we can write:
142° = m<CDE + m<DEC
And we can substitute the values we have:
142° = 38° + x
x = 104°
Hannah earns $4.50 each hour walking dogs. How much money will Hannah earn after 8
hours
Answer:
36 dollars
Step-by-step explanation:
4.50 times 8 = 36 dollars
3 questions, worth a lot of points
Why were the Jews victims of genocide during World War II?
Bankers for the previous corrupt German government had been mostly from Jewish families.
Many Germans believed that Jews had masterminded the Russian communist revolution.
Many believed that the Jews were planning to take control of the German parliament.d masterminded the Russian communist revolution.
The German government was determined to eliminate all non-Christians from German soil.Bob's living room floor is a rectangle that measures 9 feet by 12 feet. What is the diagonal distance, in feet, across the floor? A. 13 B. 15 C. 16 D. 21
Answer:
B
Step-by-step explanation:
here, we can use the pythagorean theorem. more info here: https://en.wikipedia.org/wiki/Pythagorean_theorem
formula: a^2+b^2=c^2
so we can apply the formula by doing this:
9^2+12^2=c^2
81+144=c^2
81+144=225
c=√225
c=15
solved
How do you put x=y-1
into word form
Answer:
x equals y minus one
Step-by-step explanation:
= means equals
- is minus
x and y cannot be put into any other (word) form
hope this helps:)
Heyi please help :)
Solve for W: WXY=Z
Answer:
W = ZXY
Step-by-step explanation:
Directions: Write your answers on your paper.Show your solutions with checking.
#1. Convert the decimal number 10 to a binary digit.
#2.Give the types of Mult-meter (VOM) and differential each function.
Nonsense = Reported!!
Answer:
1010See below ~Step-by-step explanation:
Q1
Decimal number 10 written in binary terms is 1010Q2
There are different types of multimeters like Analog, Digital, and Fluke multimetersFunctions :Resistance in OhmsCapacity in FaradsThe temperature in Fahrenheit/ CelsiusAC Voltage & AmperageInductance HenrysDC Voltage & AmperageFrequency in HzConductance in SiemensDecibelsDuty Cyclehope it helps you
# 1
Conversion of decimal number 10 into binary is:
10 / 2 = 5 with remainder 0
5 / 2 = 2 with remainder 1
2 / 2 = 1 with remainder 0
1 / 2 = 0 with remainder 1
Therefore, the 10 in decimal is equal to 1010 in binary.
# 2
Analog multimeters are multifunction electrical measuring instruments with indicationby means of an arrow (analog) scale.
Modern analog multimeter
Advantages of analog multimeters:
Possibility to carry out measurements at low temperatures down to -30 ° С.Fast operation with a large amount of measurements, when high precision is not required.Do not require power consumption from the built-in power supply in the mode of voltage and current measurement.Instant display of the dynamics of the signal change.
Disadvantages and features:
Non-linear scale and setting zero before starting measurements.Absence of automatic detection of voltage polarity.A small set of functions: most models can measure only DC and AC voltage, DC current and resistance.Low input resistance and, consequently, a high error in low-voltage measurements.Sensitivity to mechanical damage, vibration.
Digital multimeters are modern, reliable measuring devices characterized by high measurement accuracy and various functional capabilities. Digital devices have replaced analogue in connection with the possibility of wide application of semiconductor technologies. Today most of the produced multimeters are digital. Specialists working with electrical equipment, if necessary, can choose among the digital multimeters a model focused on a specific task.
Advantages of digital multimeters:
Maximum possible measurement accuracy.Automatic polarity detection: If the probes are connected incorrectly, the correct values with a minus sign appear on the screen.Possibility of automatic and manual selection of measuring ranges.Multifunctionality.Does not require mandatory zero adjustment.The accuracy of the meter reading does not depend on the battery charge.Resistance to mechanical damage.The ability to record measurement results in memory and synchronize with a PC.
I need help figuring it out
Answer:
a pendulum consists of a mass hanging at the end of a string which is 18 cm long. find the vertical height through which the mass rises and falls as the pendulum swings through 30°on each side of the vertical.
Answer:
1. P = IRT
T = P/IR
2. A = 2(L + W)
L + W = A/2
W = A/2 - L
3. y = 5x - 6
x = (y +6)/5
4. 2x - 3y = 8
y = (2x - 8)/3
5. (x+y)/3 = 5
x = 5×3 - y
x = 15 - y
6. y = mx + b
b = y - mx
7. ax + by = c
by = c - ax
y = (c - ax)/b
Hope it helps!
A cube has a volume of 64 cubic inches. If you double the length of each edge what will be the volume of the new cube?
Answer:
512 cubic inches
Step-by-step explanation:
[tex] \sqrt[3]{64} = 4[/tex]
[tex] {8}^{3} = 512[/tex]
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X=3), n=8, p=0.2
Answer:
P(X = 3) = 0.14680064
Step-by-step explanation:
Formula=============================
[tex]p\left( X=k\right) =C^{k}_{n}p^{k}(1-p)^{n-k}\ \ ;\ k\in \left\{ 0,\ldots ,n\right\}[/tex]
……………………………………………………………………..
Given :
n = 8
p = 0.2
1 - p = 1 - 0.2 = 0.8
k = 3
Then
[tex]p\left( X=3\right) =C^{3}_{8}(0.2)^{3}(0.8)^{5}[/tex]
[tex]=0.14680064[/tex]
(Score for Question 1: ___ of 10 points)
1. There are 8 ounces in 1 cup and 16 cups in 1 gallon.
(a) Diane brought 4.5 gallons of water to a campout. How many ounces of water did she bring? Show your work.
(b) Diane started a hike with 24 ounces of water in her backpack. What fraction of a gallon of water did she start the hike with? Show your work.
Answer:
The total ounces of water Diane brought are 576 ounces and the fraction of a gallon of water did she start the hike with is 3/16.
What is cost price per ounce?The cost price per ounce is the amount of money required to buy one ounce of a brand or goods.
To find the cost price per ounce, divide the total amount of cost of the goods to the total number of goods.
1. There are 8 ounces in 1 cup and 16 cups in 1 gallon. Diane brought 4.5 gallons of water to a campout. Let x ounces of water, did she bring. Thus,
[tex]x=4.5\times16\times8\\x=576\rm\; ounces[/tex]
Diane started a hike with 24 ounces of water in her backpack. The fraction of gallons in 24 ounces is,
[tex]n=\dfrac{24}{8\times16}\\n=\dfrac{3}{16}[/tex]
Thus, the total ounces of water Diane brought are 576 ounces and the fraction of a gallon of water did she start the hike with is 3/16.
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) Which expression is equivalent to 5(x + 7)?
Answer:
= 5x +35
Step-by-step explanation:
Steps
5(x+7)
Apply the distributive law: ab+c) = ab + ac
5(x+7) =5x + 5: 7
=5X+5: 7
Multiply the numbers: 5 7= 35
= 5x +35
What is the measure of n?
m
n
8
4
ከ =
4V[?]
Give your answer in simplest form.
Enter
The value of n is 32 if the total; base length is 12(8+4) and n is the length of the perpendicular.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We can use the altitude rule:
8/n = n/4
n² = 32
n = √32
Thus, the value of n is 32 if the total; base length is 12(8+4) and n is the length of the perpendicular.
Learn more about the right angle triangle here:
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4. Find the length of a diagonal of a rectangle ABCD with vertices A (-3, 1), B (-1, 3), C (3, -1),
and D (1,-3).
Answer:
Step-by-step explanation:
You need to spend at least $50 in one day to receive a store discount. You have already spent $30. Let s be the amount of money (in dollars) you can now spend to qualify
for the discount. Which inequality and solution represent this situation?
s+30<50; 8 < 20
s+30 ≤ 50; s ≤ 20
s+30> 50; 8 > 20
s+ 30 ≥ 50; 8 ≥ 20
Answer: s + 30 ≥ 50; s ≥ 20
Step-by-step explanation:
let s be the amount you have yet to spend in order to reach $50 or more
you already have $30.
This means you need to spend at least $20 more ($50 - $30 = $20)
S can be greater than or equal to $20 because your total will be 50 or more, therefore qualifying for the discount.
Find the indicated measure in LMNQ. Explain your reasoning.
Answer:
In Exercises 9 − 16, Ind the indicated measure in a LMNQ. Explain your reasoning. m ∠ L M N Answer m ∠ L M N = 80 ∘ View Answer Discussion You must be signed in to discuss. AS Ahin S. February 11, 2021 Find m?LMN in parallelogram LMNQ AS Ahin S. February 11, 2021 Watch More Solved Questions in Chapter 7 Problem 1 Problem 2 Problem 3 Problem 4
Step-by-step explanation:
Write a part -to part ratio that compares the girls to boy . Write this in 3 different forms
The ratio of girls to boys is 4:5.
For every four girls that are in the camp, there are five boys.
The ratio of girls to boys is 4/5.
The ratio of boys to girls is 5:4.
The ratio of boys to girls is 5/4.
The ratio of boys to girls is 1 1/4.
What are the ratios?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign used to denote ratios is :.
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