Answer:
x=3
Step-by-step explanation:
14=7(2x-4)
14/7=2x-4
2=2x-4
2x=2+4
2x=6
x=6/2
x=3
------------
14=7(2x-4)
14=14x-28
14x=14+28
14x=42
x=42/14
x=3
The equation 14 = 7(2x - 4) can be solved using two different methods: the distributive property method and the inverse operations method. Both methods yield the same solution, which is x = 3. The preference between the two methods depends on personal preference and the specific equation being solved.
Distributive Property Method:
We'll distribute the 7 to the terms inside the parentheses:
14 = 7(2x - 4)
14 = 14x - 28
Next, we'll isolate the variable term:
14x = 14 + 28
14x = 42
Finally, we'll solve for x by dividing both sides of the equation by 14:
x = 42/14
x = 3
So the solution to the equation is x = 3.
Inverse Operations Method:
We'll use inverse operations to solve the equation step by step:
14 = 7(2x - 4)
Divide both sides of the equation by 7 to isolate the term in parentheses:
14/7 = 7(2x - 4)/7
2 = 2x - 4
Add 4 to both sides of the equation to isolate the variable term:
2 + 4 = 2x - 4 + 4
6 = 2x
Divide both sides of the equation by 2 to solve for x:
6/2 = 2x/2
3 = x
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Please help me with this geometry question:((
Answer:
x = 13
RQ = 160°
Step-by-step explanation:
Inscribed angles are half the intercepted arc angle.
5x + 15 = ½ (RQ)
RQ = 10x + 30
Arc angles add up to 360°.
10x + 30 + 9x + 17 + 6x − 12 = 360
25x + 35 = 360
25x = 325
x = 13
Therefore, RQ = 160°.
Which ordered pair is a solution of the equation? 2x+4y=6x−y
Answer:
Step-by-step explanation:
"Which ordered pair" implies that there were several answer choices for this problem. It's important that you share such answer choices.
2x+4y=6x−y reduces to 5y = 8x, and so y = (8/5)x
If we choose x = 2, then y = (8/5)(2) = 16/5 is a solution of the given equation. There are an infinite number of such solutions. All lie on the line y = (8/5)x.
If a triangle has two of its shorter sides measuring 7 and 12, what is a possible length of the longest side of the triangle to make it acute?
Answer:
13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
Pls answer ASAP TY. TY. TY.
Answer:
x^ -10
Step-by-step explanation:
x^2 * x ^ -12
We know that a^b * a^c = a^ (b+c)
x^2 * x^-12
x^(2+-12)
x^ -10
Answer:
[tex]\frac{1}{x^{10}}[/tex]
Step-by-step explanation:
The two "x" terms are being multiplied, so combine the terms
Subtract the power signs:
[tex]x^2 * x^-12[/tex] = [tex]x^2/x^{12}[/tex]
[tex]x^(2 - 12)[/tex] = [tex]x^-10[/tex]
[tex]x^-10[/tex] = [tex]\frac{1}{x^{10}}[/tex]
[tex]\frac{1}{x^{10}}[/tex] is your answer.
~
The university theater uses a combination of one letter (A - Z) and two digits (0 - 9) to identify their reserved seats. How many reserved seats are
possible using a combination of one letter followed by two digits. EXPLAIN how to solve this problem in your own words.
Answer:
Hey There!! The answer to this is Correct option: 1) 2600 The letter has a total of 26 possible values (from 'a' to 'z'), and each digit has a total of 10 possible values (from 0 to 9).
So, to find the number of reserved seats possible, we just need to multiply the number of possible values of each letter and digit.
We have one letter and two digits, so we have:
26 * 10 * 10 = 2600 possible reserved seats
Thus, Correct option: 1)
Hope It Helped!~ ♡
ItsNobody~ ☆
The total number of combinations of one letter followed by two digits is 2600 option (1) 2600 is correct.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
The missing options are:
1.) 26002.) 2343.) 2604.) 2106We have:
The university theater uses a combination of one letter (A - Z) and two digits (0 - 9) to identify their reserved seats
As we know, in the alphabet(A to Z) there are the 26 letters and total number of digits (0 to 9) is 10
A total number of combinations of letters followed by two digits can be calculated as follows:
As we have one letter and two digits
= 26×10×10
= 2600
, so we have:
26 * 10 * 10 = 2600 possible reserved seats
Thus, the total number of combinations of one letter followed by two digits is 2600 option (1) 2600 is correct.
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can somewon help i need help
Answer:
1875 cm3
Step-by-step explanation:
20 * 20 * 5 - (5 * 5 * 5) = 1875 cm3
Answer:
1,875
Step-by-step explanation:
The polynomial function f (x) = 5 x Superscript 5 Baseline + sixteen-fifths x minus 3 is graphed below. On a coordinate plane, point P is shown on the graph of a function. Point P is at (0.6, 0). Which is a potential rational root of f(x) at point P?
Answer:
3/5
Step-by-step explanation:
What divisor is represented by the synthetic division below? x + 5. One factor of x^3+x^2+x+1. If f(-5) = 0, what are all the factors of the function mc022-... -4 and 3. The polynomial function f(x) = 5x5 + 3x - 3 is graphed below. The root at point P maybe 3/5 3.
The potential rational roots are: [tex]\pm 1, \pm \frac{1}{5}, \pm 3,\pm \frac{3}{5}[/tex]
What is the rational root theorem?The rational root theorem is used to determine the possible rational roots of a polynomial function
The equation of the function is given as:
[tex]f(x) = 5x^5 +\frac{16}{5} x -3[/tex]
Considering a polynomial function, f(x).
Such that:
[tex]f(x) = px^n + .......... +q[/tex]
The possible rational roots are:
[tex]Roots =\pm \frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
So, we have:
[tex]Roots =\pm \frac{Factors\ of\ 3}{Factors\ of\ 5}[/tex]
List the factors of 3 and 5
[tex]Roots =\pm \frac{1,3}{1,5}[/tex]
Split
[tex]Roots =\pm \frac{1}{1}, \pm \frac{1}{5}, \pm \frac{3}{1},\pm \frac{3}{5}[/tex]
Simplify
[tex]Roots =\pm 1, \pm \frac{1}{5}, \pm 3,\pm \frac{3}{5}[/tex]
Hence, the potential rational roots are:
[tex]\pm 1, \pm \frac{1}{5}, \pm 3,\pm \frac{3}{5}[/tex]
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Simplify.
sin x cot x
Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a single trigonometric function.
(please help, no idea how to solve this problem)
Answer:
cos x
Step-by-step explanation:
sin x = (sin x) / (1) and cot x = (cos x) / (sin x)
Put those fractions next to each other and multiply them out (numerator times numerator, denominator times denominator).
Cancel out the (sin x) in the numerator and denominator
You should be left with just (cos x) / (1), whoch equals just (cos x).
Hope this helps!
Someone pls help me in this plss
Im really confused in this
Answer:
Step-by-step explanation:
find LCM of the denominators= 77
so 66/77 - 63/77
3/77
hope this help you pls mark me as brainliest
working for division is on this question is
6/7 divide 9/11
so 6/7 *11/9
66/63 and then you can find its standard form and it cannot be do not
What is the area of the polygon shown below? (in the image). A. 322 mm^2 B. 364 mm^2 C. 520 mm^2 D. 584 mm^2 Show all work please!
Answer:
A. 322 mm^2
Step-by-step explanation:
First split the shape into two (a rectangle and a triangle).
Then calculate the area of those shapes.
Rectangle: 20 x 14 = 280 mm^2
Triangle: 6 x 14 / 2 = 42 mm^2
Add them together.
280 + 42 = 322 mm^2
PLEASE HELP WILL GIVE BRAINLY!!!!!!!!!!!!!!!!!!!!!Which equation, when graphed, has x-intercepts at (−1, 0) and (−5, 0) and a y-intercept at (0, −30)?
f(x) = −6(x + 1)(x + 5)
f(x) = −6(x − 1)(x − 5)
f(x) = −5(x + 1)(x + 5)
f(x) = −5(x − 1)(x − 5)
Answer:
f(x) = −6(x + 1)(x + 5)
Step-by-step explanation:
f(x) = −6(x + 1)(x + 5) & f(x) = −5(x + 1)(x + 5) are the only ones on the correct side of the y-axis, and f(x) = −6(x + 1)(x + 5) has a y-intercept of -30.
On the number line below, P represents a number. What is the value of the opposite of that number? A number line from negative 4 to positive 4 in increments of 1 over 4, with all whole numbers alone labeled is shown. Put point P at the fifth tick mark to the right of 0. negative 2 and 2 over 4 negative 1 and 1 over 4 1 and 1 over 4 2 and 2 over 4
Answer:
[tex]-1\frac{1}{4}[/tex]
option 2
Step-by-step explanation:
In this number line, each interval equals 1/4.
P represents 1 1/4
So, opposite of number P is ( [tex]-1\frac{1}{4}[/tex] )
Which of the following numbers is divisible by 24 ? (A) 13,944 (B) 15,746 (C) 15,966 (D) 16,012 (E) none of the above
Answer:
Only A is divisible by 24.
Step-by-step explanation:
A number is divisible by 24 if it's divisible by both 3 and 8.
Numbers are divisible by 3 if all their digits add to a multiple of 3, and numbers are divisible by 8 if the last 3 digits are divisible by 8.
Let's look at A, 13944. The numbers add up to [tex]1+3+9+4+4=21[/tex], which is divisible by 3.
944 is divisible by 8, and it makes 118.
So A works.
B is 15746.
[tex]1+5+7+4+6=23[/tex], so this won't work as 23 isn't divisible by 3.
C is 15966.
[tex]1+5+9+6+6=27\div3=9[/tex], so this works for 3 but let's check 8.
[tex]966\div8=120.75[/tex] so it's not divisible by 8, therefore not divisible by 24.
D is 16012.
[tex]1+6+0+1+2=10[/tex] and 10 isn't divisible by 3, so it doesn't work.
Hope this helped!
If m(2x−3)+n(x+1)=5x for all real numbers x, where m and n are constants, what is the value of m?
Answer:
m = 1
Step-by-step explanation:
From the question given,
m(2x − 3) + n(x + 1) = 5x for all real numbers x.
Since x is a real number, we can obtain the value of m as follow:
Let x = 1
m(2x − 3) + n(x + 1) = 5x
m(2×1 − 3) + n(1 + 1) = 5×1
m(2 – 3) + n(2) = 5
m(– 1) + n(2) = 5
– m + 2n = 5 ...... (1)
Let x = 2
m(2x − 3) + n(x + 1) = 5x
m(2×2 − 3) + n(2 + 1) = 5×2
m(4 – 3) + n(3) = 10
m(1) + n(3) = 10
m + 3n = 10 ...... (2)
– m + 2n = 5 ...... (1)
m + 3n = 10 ...... (2)
Solve by elimination method
Add equation 1 and 2
– m + 2n = 5
+ (m + 3n = 10)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
5n = 15
Divide both side by 5
n = 15/5
n = 3
Substitute the value of n into any of the equation to obtain the value of m. Here, we shall substitute n into equation 2.
m + 3n = 10
m + 3(3) = 10
m + 9 = 10
Collect like terms
m = 10 – 9
m = 1
Therefore, the value of m is 1
Trish entered a problem on her calculator that gave her this result on the screen: “0.1894528...”. Would this decimal be considered a repeating decimal? Why or why not?
The decimal 0.1894528 is not a repeating decimal.
What is the decimal number?The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system. The numbers are first in fractions and then divided by the number to give a decimal number.
The given decimal number is “0.1894528. In the decimal number if the numbers are repeating then it is called the repeating decimal number if the numbers are not repeating then it is called a nonrepeating decimal number. Here the given decimal is nonrepeating decimal.
Therefore, the decimal 0.1894528 is not a repeating decimal.
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i dont get it plz help
Answer:
440 in²
Step-by-step explanation:
Answer:
(D) 440 in²
Step-by-step explanation:
We can find the surface area of this complex shape by breaking it down into two smaller shapes:
The base (with side lengths of 10, 10 and 2) and the top (with side lengths of 5, 5, and 8.)
Let's first find the surface area of the base.
The sides of the bass are [tex]10\cdot2 = 20[/tex] in², since there are 4 of these sides, the total side area here is [tex]20\cdot4 = 80[/tex] in².
The bottom of this prism has side lengths of 10 and 10, so [tex]10\cdot10=100[/tex].
There are two of these sides.
[tex]100\cdot2=200[/tex].
Let's add up the side lengths and the base lengths.
[tex]200+80=280[/tex]
We aren't done yet - if we see, the top part is taking away some of that surface area. To find how much it is taking away, we need to find the area of that side.
Note that the side on the base is the exact same as the top, who's side lengths are 5 and 5. So [tex]5\cdot5=25[/tex] in² are being taken away from the base, making it [tex]280-25 = 255[/tex]
Now let's find the surface area of the top.
The side, with lengths of 5 and 8, have a surface area of [tex]5\cdot8=40[/tex] in². Since there are 4 of these sides:
[tex]40\cdot4=160[/tex] in².
Now, the top of the box has side lengths of 5 and 5, so the surface area of that is [tex]5\cdot5 =25[/tex] in².
We don't want to find the area of the bottom of the top prism because that cuts into the base and technically is empty space = no surface area.
Let's add the top and the sides of the top box: [tex]160+25=185[/tex] in².
Finally, let's add the base and the top box surface areas together:
[tex]185 + 255 = 440[/tex]
So the total surface area of this design is 440 in².
Hope this helped (oh my god this took so long to write)
cqn someone answer this?
Answer:
-3Step-by-step explanation:
-11/2+27/4+(-17/4)(-22+27-17)/4(-12)/4-3Kaitlyn can build a shed in 6 days. Mark can build the same shed in 8 days. Which equation can be used to find d, the number of days it would take Kaitlyn and Mark to build the shed together? Rate (Sheds per Day) Time (Days) Fraction Completed Kaitlyn One-sixth d One-sixth dd Mark One-eighth d One-eighth dd One-sixth d minus one-eighth d = 48 One-sixth d + one-eighth d = 48 One-sixth d minus one-eighth d = 1 One-sixth d + one-eighth d = 1
Answer:
One-sixth d + one-eighth d = 1
Step-by-step explanation:
When they work together, their rates of completion add. They want to build one shed, so the number of sheds being built is ...
(Kaitlyn's sheds per day)×(days Kaitlyn works) +(Mark's sheds per day)×(days Mark works) = 1 shed
(1/6)d + (1/8)d = 1 . . . . matches the last choice
The ground temperature at sea level is 60 degrees F. For every 100-foot increase in elevation, the temperature rises 1/10 of one degree. At an altitude of 2,000 feet, what will be the likely temperature? A. 58 degrees F B. 62 degrees F C. 72 degrees F D. 80 degrees F Show ALL work please!!
====================================================
Explanation:
x = elevation in feet
y = temperature in fahrenheit
The temperature goes up 1/10 = 0.1 degrees for every 100-foot increase of elevation. So the slope is 0.1/100 = 0.001, which tells us how fast the temperature is increasing. In other words, the temperature goes up 0.001 degrees each time the elevation goes up by 1 foot.
The ground temperature is 60 degrees, which is our starting temperature. It's the value of y when x = 0. Therefore, 60 is the y intercept.
We have a slope of m = 0.001 and a y intercept of b = 60. The equation y = mx+b becomes y = 0.1x+60
Now plug in x = 2000 to find the temperature at this elevation
y = 0.001x+60
y = 0.001*2000+60
y = 2+60
y = 62
Answer:
B.62
Step-by-step explanation:
60 + (2000/100) We find 20 is the answer to the division
60 + (20 * 1/10) We find 2 is the answer to the multiplication
60 + (2)
We can then + for elevation or - or depression or decrease.
= 62
= 62 degrees.
write the formula used to find length when the breadth height and volume are known........breadth when the length height and volume are known............ height when the breadth length and volume are known ..............Please answer this as fast as possible my homework is due tommorow
Answer: L = V/bh
b= V/Lh and h= V/Lb
Step-by-step explanation: V = Lbh or V= lwh is also used for the Basic form for the Volume of a cube or rectangular prism is
Volume = Length × breadth × height
The volume will be expressed as cubic units such as cubic meters cubic feet. Sometimes abbreviations are used like cm^3 for cubic centimeters.
When you know the Volume, and you need to find a missing dimension, just make a fraction with the V in the numerator and the dimensions you know in the denominator. This means you are dividing the Volume by the area of the dimensions you have been given to find the missing dimension.
help me plz can somewon help me
Answer:
4*10^6
Step-by-step explanation:
Answer:
4 × 10^6Step-by-step explanation:
[tex]\frac{8\times 10^2^4}{2\times 10^1^8}=\\\\\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4\\\\=\frac{10^{24}\times \:4}{10^{18}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{10^{24}}{10^{18}}=10^{24-18}\\\\=4\times \:10^{24-18}\\\\\mathrm{Subtract\:the\:numbers:}\:24-18=6\\\\=10^6\times \:4\\\\10^6=1000000\\\\=1000000\times \:4\\\\=4000000\\\\= 4\times10^6[/tex]
What property is used in the second step of solving the inequality below?
5 x minus 9 less-than 91
______Given_______
5 x less-than 100
__________________
x less-than 20
Multiplication Property
Identity Property
Addition Property
Multiplication Property
Transitive Property
Answer:
Addition property
Step-by-step explanation:
Given the inequality:
5x - 9 < 91
The step to take here to move 9 to the other side, is to perform the addition property by adding 9 to both sides.
Thus,
5x - 9 + 9 < 91 + 9
5x < 100
The final step is to perform the division property by dividing both sides by 5, in order to solve for x.
5x/5 < 100/5
x < 20.
Sally invested some money at 15 % interest. Sally also invested $172 more than 3 times that amount at
14%. How much is invested at each rate if Sally receives $1398.35 in interest after one year? (Round to
two decimal places if necessary.)
Answer:
Amount at 15%=$2,411
Amount at 14%=$7,405
Step-by-step explanation:
let
x= the amount at 15% rate.
y=amount at 14% rate
y= x times 3 plus $172
y= 3x + $172 (1)
x times 15% plus y times 14% equals a return of $1,398.35 after one year
0.15x + 0.14y= $1,398.35 (2)
Recall,
y= 3x + $172
Substitute (1) into (2)
0.15x + 0.14y= $1,398.35
0.15x + 0.14(3x+172)=1398.35
0.15x + 0.42x + 24.08=1398.35
Collect like terms
0.15x + 0.42x=1398.35 - 24.08
0.57x=1374.27
Divide both sides by 0.57
x=2,411
x=$2,411
Find y
y= 3x + $172
=3(2,411) + 172
=7,233+172
=7,405
y=$7,405
Amount at 15%=$2,411
Amount at 14%=$7,405
Check:
$2,411*0.15=$361.65
$7,405*0.14=$1036.70
Total=$361.65 + $1036.70
=$1,398.35
Given: f(x) = X2 - 3 and g(x)= x+1 The composite function g.f is
a) x² + 2x - 2
b) x² + 2x
c) x² - 2
Answer:
option (c)
Step-by-step explanation:
g.f= g(f(x))
= g(x2 -3)
= (x2 -3)+1
=x2 -2
The composite function g.f is option c) x² - 2.
What are composite functions?Functions which are formed by composing two or more functions in a way that one's output is another's input are called composite functions. They are also called function of functions.
Given: f(x) = x² - 3 and g(x)= x+1
The composite of the function;
g.f= g(f(x))
= g(x²-3)
= (x² -3)+1
= x² -2
Thus, The composite function g.f is option c) x² - 2.
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*PLEASE ANSWER TY* What is the density of a 50-gram pyramid with rectangular base 4 cm x 8 cm and height 10 cm?
Answer:
[tex]\frac{0.47 g}{cm^{3} }[/tex]
Step-by-step explanation:
→ First work out volume of pyramid using the formula [tex]\frac{lwh}{3}[/tex] where 'l' is the length, 'w' is the width and 'h' is the height
[tex]\frac{lwh}{3}[/tex] ⇔ [tex]\frac{4*8*10}{3}[/tex] ⇔ [tex]\frac{320}{3}[/tex] ⇔ 320 ÷ 3 = 106.666666667
→ Volume of pyramid = 106.666666667. Substitute this value into the density formula
Density = Mass ÷ Volume
Density = 50 ÷ 106.666666667
Density = 0.46875 to 1 decimal place is 0.47
PLEASE HELP!!!!Create diagrams to represent the possible cases for common tangents between two
circles. Your diagram can be created using multimedia sources or drawn by hand. They
should not be copied and pasted from a website. Explain why your diagrams satisfy the
given criteria.
One common tangent a)diagram:
b): justification
help me plx can somewon help me
Move the decimal so that there is one non-zero digit on the left of the decimal point. (The number of decimal spaces you move = exponent on 10) Since the decimal is moving to the left, we know the exponent is positive.
2 + 7 = 9
Answer: 9 * 10^16
What is the range of possible sizes for side x?
8.0
2.5
Please helpp!!
Triangle inequality theorem:
In any triangle, the length of any side must be:
less than the sum of the lengths of the other two sides.greater than the difference of the lengths of the other two sides.For the problem you have:
x must be greater than 8.0 - 2.5 and less than 8.0 + 2.5
5.5 < x < 10.5
Answer:
5.5<x<10.5
Step-by-step explanation:
A power line stretches down a 400-foot country road. A pole is to be put at each end of the road, and 1 in the midpoint of the wire. How far apart is the center pole from the left-most pole?
Answer:
200 ft
Step-by-step explanation:
Since the road is 400 ft, the midpoint of the road is 200 ft from each end of the road.
In trapezoid ABCD, AB ∥ CD , m∠A=90°, AD=8 in, DC=9 in, CB=10 in, and ∠B is acute. Find DB.
Answer:
the length of DB is 17 in
Step-by-step explanation:
Consider the sketch attached.
We will draw an imaginary line from point C to met line AB at point E.
A right-angled triangle will now be formed between points CBE.
The dimensions of the right-angled triangle will be:
CB = 10 in
CE= 8 in
EB = unknown
We will now proceed to find out the length of side EB using the Pythagoras' theorem.
[tex]EB =\sqrt{CB^2 -CE^2} \\EB =\sqrt{10^2 -8^2} \\EB = 6 in[/tex]
From the shape, we can find out that another right-angled triangle is made between points DAB.
The dimensions of the triangle are:
DA= 8in
AB = 9 in + 6 in = 15 in
DB = unknown.
We will now proceed to find out the length of side DB using the Pythagoras' theorem.
[tex]DB =\sqrt{AD^2 +AB^2} \\DB =\sqrt{8^2 +15^2} \\DB = 17 in[/tex]
Therefore, the length of DB is 17 in
