The value of x in the equation 3/7 = 12/x is equal to 28.
Proportion is a type of mathematical equation that is used to determine the value of the quantities that are not known by forming two equal ratios.
Ratios can be defined as an expression that is used to compare the size of two numbers in relationship to each other to determine how big is one number from the other.
The given proportion can be solved as follows:
3/7 = 12/x
3x = 12 × 7
3x = 84
If 3x is equal to 84, then x will be equal to:
x = 84/3
x= 28
Therefore, the proportion is solved as the value of x is found to be 28.
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5. The coordinates of X are (a - 5, -2a) . The coordinates of Y are (a + 1, 2a) . If the distance between X and Y is 10, find the value of a.
Applying the distance formula, the value of a is 2 or -2.
What is the Distance Formula?The distance formula is:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the following:
d = XY = 10 units
X(a - 5, -2a) = (x1, y1)
Y(a + 1, 2a) = (x2, y2)
Plug in the values into the distance formula
10 = √[((a + 1) - (a - 5))² + (2a - (-2a))²]
10 = √[(a + 1 - a + 5)² + (2a + 2a)²]
10 = √(6² + (4a)²)
10 = √(36 + 16a²)
10² = 36 + 16a²
100 = 36 + 16a²
0 = -100 + 36 + 16a²
0 = 16a² - 64
16a² - 64 = 0
Factorize
16(a² - 4) = 0
16(a - 2)(a + 2) = 0
a = 2 or a = -2
Therefore, applying the distance formula, the value of a is 2 or -2.
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Adelaide is the employee of the month at her job. Her reward is to select at random from 4 gift cards, 6 coffee mugs, 7 DVDs, 10 CDs, and 3 gift baskets. What is the probability that an employee receives a gift card, coffee mug, or CD?
According to the question, Adelaide is the employee and she has to select a reward from four gifts. And those are 6 coffee mugs, 7 DVDs, 10 CDs and 3 gift baskets.
Now, calculate the probability that the gift is either a coffee mug or CD.
Let us assume, ‘G’ represents the gift card, ‘C’ represents the coffee mug and ‘D’ represents the CD.
The total number of items are [tex]4+6+7+10+3 = 30[/tex] items
P(G or C or D) = P(G) + P(C) + P(D)
[tex]= \frac{4}{30} + \frac{6}{30} + \frac{10}{30} = \frac{20}{30} = \frac{2}{3} = 67%[/tex]
Therefore , the probability to receive either a gift card or coffee mug or CD is [tex]67[/tex] percent.
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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which term is larger log_25(1/625) or log_16(1/64)
What is the difference between −125 anThe Japan Trench is 9 km below sea level. The Peru-Chile Trench is 8 km below sea level. What is the difference of depths between them, and which trench is deeper?
−17 km, and the Japan Trench is deeper
−1 km, and the Peru-Chile Trench is deeper
1 km, and the Japan Trench is deeper
17 km, and the Peru-Chile Trench is deeperd 18?
Based on the distance below sea level of the Japan Trench and the Peru-Chile Trench, the difference and the deeper trench is 1 km, and the Japan Trench is deeper.
Which is the deeper trench?The deeper trench is the one that is further down sea level. In other words, it is the one that is a larger distance below sea level.
The Japan Trench is 9 km below sea level while the Peru-Chile trench is 8 km below sea level. This means that the Japan Trench is deeper.
The difference is:
= 9 - 8
= 1 km
In conclusion, the Japan trench is deeper by 1 km.
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a box of brownie mix calls for 2 eggs and 1/2 cups of oil how many eggs and how much oil would you need for 2 boxes of brownie mix
Answer:
1 box of brownie mix= 2 eggs and 1/2 cups of oil
ans=
2 boxes of brownie mix= (2 eggs ×2)(1/2 cups of oil × 2)
=4 eggs and 1 cup of oil
Answer:
4 eggs and 1 cup of oil.
Step-by-step explanation:
2x2=4 1/2x2=1
A builder is framing windows of a new with lumber each side of the window must be one piece of lumber. The windows should be three feet high and three feet wide. How many windows can be framed with three 10-foot long pieces of lumber
The number of windows which can be framed with three 10-foot long pieces of lumber given the dimensions of the windows is; two and a half.
What is the number of windows that can be made using the lumbers given the dimensions of the windows?It follows from the task content that the number of windows that can be made given the dimensions of the windows be determined.
On this note, it follows that since the windows are 3 feet high and 3 feet width, the perimeter of each window(square shaped) covered by lumber is;
P = 4s
P = 4 × 3
P = 12 feet.
Hence, each window requires 12 feet of lumber.
However, since the builder has only three 10-foot long pieces of lumber which is equivalent to; 3 × 10 = 30 feet worth.
The number of windows that can be made is;
= 30/12
= 2.5.
Ultimately, only 2 and a half windows can be framed from the three 10-foot long pieces of lumber.
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Write an equation of the line passing through the points (3,8) and (-1,-16).
Answer:
here ya go !
Step-by-step explanation:
Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) − 5?
The graph shifts 5 units up.
The graph shifts 5 units down.
The graph shifts 5 units left.
The graph shifts 5 units right.
The statement which describes the effect of replacing the graph of f(x) with the graph of f(x) - 5 is : (b) the graph shifts 5 units down.
What is Transformation?
Transformation :- The transformations of functions define how to graph a function is moving and how its shape is being changed. There are basically three types of function transformations: translation, dilation, and reflection.
f(x) = f(x) + k
This is a translation transformation that shifts the original function f(x) either k units up or k units down. If k is more than 0 then k shifts up. If k is less than 0 then k shifts down.
Here, k = -5<0
Hence, the shift is 5 units down.
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What is the difference in height between a rose bush that is 3'9” tall and Emma who is 5½ feet tall?
URGENT!!!!! ILL GIVE BRAINLIEST! AND 100 POINTS
Put the numbers in order from smallest to largest.
Answer:
(from smallest to largest)
1. 3.24 × 10^-5
2. 5.48 × 10 ^-2
3. 1.2 × 10¹
4. 4.68 × 10⁶
5. 8.34 × 10⁶
Step-by-step explanation:
We can put these in order through the exponents.
Hope this helps!
Determine whether ΔA B C ≅ ΔX Y Z . Explain. A(5,2), B(1,5), C(0,0), X(-3,3), Y(-7,6), Z(-8,1)
The given triangles are congruent its that ΔA B C ≅ ΔX Y Z.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
If ΔA B C ≅ ΔX Y Z then the corresponding sides will be the same.
Its that AB = XY , BC = YZ
The distance associated with two points (x₁, y₁) and (x₂, y₂) is given by
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
So,
(AB) = [tex]\sqrt {\left( {5 - 1 } \right)^2 + \left( {2 - 5 } \right)^2 }[/tex]
AB = 5
(XY) = [tex]\sqrt {\left( {-3 + 7 } \right)^2 + \left( {3 - 6 } \right)^2 }[/tex]
XY = 5
Similarly BC = YZ and CA = ZX.
Hence "The given triangles are congruent its that ΔA B C ≅ ΔX Y Z".
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whats is 0.5x+2=6 answer
Answer:
x=8
Step-by-step explanation:
starts with 0.5x+2=6, so move the constant to the right, 0.5x=6-2, then calculate the right side, 0.5x=4, then divide both sides, and x=8
Answer:
x = 8
Step-by-step explanation:
Get variable on left and constants on right
0.5x = 6 - 2
0.5x = 4
Divide both sides by 0.5
x = 8
28. SAND A home improvement store sells bags of sand, which are labeled as weighing . The equipment used to package the sand produces bags with a weight that is within of the labeled weight. a. Write an absolute value equation to represent the maximum and minimum weight for the bags of sand. b. Solve the equation and interpret the result.
From the situation described, we have that:
a. The absolute value equation is: |w - 35| = 8.
b. The solutions are w = 27 and w = 43, meaning that the minimum weight is of 27 pounds and the maximum weight is of 43 pounds.
What is the missing information?A home improvement store sells bags of sand, which are labeled as weighing 35 pounds. The equipment used to package the sand produces bags with a weight that is within 8 pounds of the labeled weight.
What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
For this problem, the difference between the weight w and 35 pounds is of 8 pounds, hence the equation is:
|w - 35| = 8.
From the definition, the solutions are given as follows:
w - 35 = -8 -> w = 27.w - 35 = 8 -> w = 43.The solutions are w = 27 and w = 43, meaning that the minimum weight is of 27 pounds and the maximum weight is of 43 pounds.
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Factorise 56w – 48.
Answer:8(7w+
Step-by-step explanation:
It is estimated that the annual cost of driving a certain new car is given by the formula
C = 0.39m + 2800
where m represents the number of miles driven per year and C is the cost in dollars. Jane has purchased such a car and decides to budget between $7480 and $8260 for next year's driving costs. What is the corresponding range of miles that she can drive her new car? (Enter your answer using interval notation.)
Answer:
[11000, 11600]
Step-by-step explanation:
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You and a friend are hiking in the Swiss Alps. You want to climb to a ledge that is 6 meters above you. The height of the grappling hook you throw is given by the function h(t)=-4.9t² +10t+1.5 Can you throw it high enough to reach the ledge? Why or why not? (Support your answer mathematically.)
According to the given function, we can throw it to the height of 6.6 m. So, yes we can throw it high enough to reach the ledge.
What is a Quadratic equation?The given equation is quadratic. A quadratic equation is defined as an equation of a single variable with the highest power of 2. In general, the quadratic equation can be expressed as h(x)= [tex]ax^2- bx + c[/tex], where a, b and c are arbitrary constants. The solution for a quadratic equation is given by:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
The maximum of a quadratic equation is given by:
= [tex]c-\frac{b^2}{4a}[/tex]
The length to be covered by throwing=6 meters
It is given that the height of the grappling hook you throw is a function h(t) = -4.9t² + 10t + 1.5
Here a =4.9, b = 10 and c = 1.5
The maximum of a quadratic equation is given by:
[tex]c-\frac{b^2}{4a}[/tex]
[tex]1.5-\frac{10^2}{4*(-4.9)}[/tex]
6.6
A throw can be made to reach the wall since the height of wall is less than the maximum value that is 6.6 m.
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What is the mass of gasoline (density = 0.680 g/cm3 ) in a 94.6 l gasoline tank?
A 94.6 L gasoline with a density of 0.680 g/cm^3 has a mass of 64328 g.
Density is defined as the ratio between the mass of a substance and the volume it occupies. Denoted by ρ, density is mass per unit volume and the formula is given below:
ρ = mass / volume
Converting first the volume from L to cm^3.
1 L = 1000 cm^3
94.6 L = 94.6(1000 cm^3)
94.6 L = 94,600 cm^3
Given the density of the gasoline and its volume, solve for the mass of the gasoline using the formula for the density.
ρ = mass / volume
0.680 g/cm^3 = mass / 94,600 cm^3
mass = 0.680 g/cm^3 (94,600 cm^3)
mass = 64328 g
mass = 64.328 kg
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if someone solves this there are 4 more of the same question! Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
ANSWER ASAP WILL MARK AS. BRAINLYST (Only if answer is correct)
Look at the photo and answer broth questions
Step-by-step explanation:
2 + 3 = 5
the sign of the sum is "-", because the temperature dropped (in both cases).
the total change in temperature is -5°.
the sum of 2 positive integers ... is always positive.
both numbers have a positive sign. the sum means "+", so we are adding 2 positive numbers.
nowhere in the operation are we going in the negative direction or bring a negative sign in.
so, where would a "-" sign come from ?
if I have something on the plus side, and I put something positive on top of it, the resulting pile will still be positive.
n=c-s solve for c, can anyone solve this?
Answer: sure ummm...
r
=
1
d
cs
Step-by-step explanation:
Answer: n+s=c
Step-by-step explanation:
n=c-s
+s +s
n+s=c
add s to both sides to get c by itself, and you end up with n+s=c
The average weight of an apple is normally distributed with a mean of 0.33 of a pound with a standard deviation of 0.07. Michael went to the store and found an apple that weighted 0.50. What percent of the apples weigh less than the one Michael found?
Step-by-step explanation:
MEAN:0.33
STANDARD DEVIATION:0.07
WEIGHTED:0.50
0.33×0.07=0.0231÷0.50=0.0462
Here are 2 polygons. Select all sequences of translations, rotations, and reflections below that would take polygon Pto polygon Q
The required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.
What is translation?Translation means the displacement of a figure or a shape from one place to another. In translation a figure can move upward, downward, vertical and horizontal.
Some of the Translation are,
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Rotation means the circular movement of an object around a centre. It is possible to rotate different shapes by an angle around the centre point.
Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system.
Thus, the required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.
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The complete question image is attached.
Four hamburgers cost 13.95. Find the unit rate
Answer:
$3.48
Step-by-step explanation:
Divide the number of hamburgers by the total cost:
13.95 / 4 =
3.4875
$3.48
solve for x. 4x-30=2x
Find the missing terms in each geometric sequence.
1. 256, ___, ___, -32, -64
2. 27, 9, ___, ___, 1/3
3. 5x^2, ___, 5x^6, 5x^8, ___, ...
Answer:
1) 256, -128, 64, -32
2) 27, 9, 3, 1, 1/3
3) 5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰,
Step-by-step explanation:
1. In this geometric series each term is obtained by multiplying the previous term by (-1/2) or dividing by (-2).
256 ÷ (-2) = - 128
-128 ÷ (-2) = 64
64 ÷ (-2) = (-32)
The geometric series is:
256, -128, 64, -32...
We can find the common ratio by dividing the second term by first term.
2) 27, 9, ___, _________, 1/3
[tex]\sf \boxed{\bf common \ ratio= \dfrac{second \ term}{first \ term}}[/tex]
[tex]\sf = \dfrac{9}{27}\\\\ = \dfrac{1}{3}[/tex]
[tex]\sf 9*\dfrac{1}{3}=3\\\\3*\dfrac{1}{3}=1[/tex]
The geometric series is:
27, 9, 3, 1, 1/3....
3) 5x², _____, 5x⁶, 5x⁸, _____, ....
Here, we can take 3rd term and 4th term to find the common ratio.
[tex]\sf common \ ratio = \dfrac{5x^8}{5x^6}\\\\[/tex]
[tex]\s = x^{8-6}\\\\=x^2[/tex]
5x² * x² = 5x⁴
8x⁸ * x² = 8x¹⁰
The geometric serious is:
5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰, ...
[tex]\sf 1.) \ 256, -128, 64, -32,..\\ \\ 2.) \ 27, 9, 3, 1, 1/3,... \\ \\3.) \ 5x^2, 5x^4, 5x^6, 5x^8,5x^{10} , ...[/tex]
[tex]\sf Geometric \ formula: ar^{n-1}[/tex]
where 'a' is first term, 'r' is common ratio.1)Find the common ratio:
next term ÷ previous term32 ÷ -64 = -1/2Equation: [tex]256(-\frac{1}{2} )^{n-1}[/tex]
2nd term: [tex]256(-\frac{1}{2} )^{2-1}=-128[/tex]
3rd term: [tex]256(-\frac{1}{2} )^{3-1}=64[/tex]
2)Find common ratio:
next term ÷ previous term9 ÷ 27 = 1/3Equation: [tex]27(\frac{1}{3} )^{n-1}[/tex]
3rd term: [tex]27(\frac{1}{3} )^{3-1}=3[/tex]
4th term: [tex]27(\frac{1}{3} )^{4-1}=1[/tex]
3)Find the common ratio:
next term ÷ previous term5x^8 ÷ 5x^6 = x^2Equation: [tex]5x^2 (x^2)^{n-1}[/tex]
2nd term: [tex]5x^2 (x^2)^{2-1} = 5x^2 (x^2) = 5x^{4}[/tex]
5ht term: [tex]5x^2 (x^2)^{5-1} = 5x^2 (x^8) = 5x^{10}[/tex]
A used car has a value of $15,250 when it is purchased in 2012. The value of the car decreases at a rate of 7.5% per year.
Write an exponential function that models the value
of the car over
years.
To the nearest cent, what will be the value of the car after eight years?
Answer:
after 8 years the value of the car would be $8,173.42
Step-by-step explanation:
the given P=15250
r=7.5/100=0.075
t=x
y = 15250*(1 - 0.075)^x
after 8 years we would have
x = 8
y = 15250*(1 - 0.075)^8
y = $8,173.42
after 8 years the value of the car would be $8,173.42
Answer:
8173.42
Step-by-step explanation:
I just know it's correct
What is summation notation for the series?
a. -5+2+9+16+ . . . . . . . +261+268
The arithmetic series -5+2+9+16+ . . . . . . . +261+268 can be written using the summation notation as
[tex]7\sum\limits^{40}_{n=1} {n} -480[/tex]
Let
a(1) + a(2) + a(3) + ... + a(n)
be an arithmetic series.
Then, the nth term will follow the formula:
a(n) = a(1) + (n-1) . d
where d = the common difference.
The value of d is:
d = a(2) - a(1) = a(n) - a(n-1).
The series given is:
-5+2+9+16+ . . . . . . . +261+268
This is an arithmetic series with a(1) = -5 and
d = 2 - (-5) = 7
Substitute these parameters into the formula of the nth term:
a(n) = a(1) + (n-1) . d
a(n) = -5 + (n-1) . 7
a(n) = 7n - 12
Let a(n) = 268, then:
268 = 7n - 12
7n = 280
n = 40
The series can, then, be expressed as:
-5+2+9+16+ . . . . . . . +261+268
[tex]=\sum\limits^{40}_{n=1} {a(n)}[/tex]
[tex]=\sum\limits^{40}_{n=1} {(7n-12)}[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -\sum\limits^{40}_{n=1} {12}[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -40\times12[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -480[/tex]
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Let h(x) be the reflection of f(x)=3 x+3 in the x -axis. What is a function rule for h(x) ?
The function rule for h(x) = -3x -3.
In mathematics, functions can be manipulated algebraically to obtain graphs of functions through certain transformations. Such transformations are reflections of the x-axis or the y-axis. To flip a function f(x) on the x-axis, multiply the whole function by a negative value to get -f(x), and to flip a function f(x) on the y axis, f(-x ), specify the x variable with a negative value. If it is reflected around the y-axis, it will stay the same, which gives h(x) = 3x + 3. Flipping around the x-axis (assuming y = 0) has the y-axis as the axis of symmetry, but it is concave down.
The function rule around the x-axis gives a complementary sign of the value of the function, so
h(x) =-3x-3 will be reflection of f(x) =3x+3
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3. a) 27 m= .... cm.
b) 0,38 dam = .... dm.
c) 3,4 m = .... hm.
The answer is :
a) 27 m= 2700 cm.
b) 38 dam = 380 m.
c) 34 m = 0.34 hm.
Lets know about the given prefix first,
m = Meter means one hundred centimeter so,
1 m = 100 cm
cm = Centimeter means one-hundredth of a meter so,
1 cm = 0.01 m
mm = Millimeter means one-thousandth of a meter so,
1 mm = 0.001m
hm = Hectometer means one hundred meters so,
1 hm = 100 m
dam = Decameter means ten meters so,
1 dam = 10 m
So,
a) 27 m = 2700 cm
b) 38 dam = 380 m
c) 34 m = 0.34 hm.
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Find the percent of the given number. 79 % of 623
A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.
The percent of the given number 79 % of 623 is 492.17.
What is meant by percentage?A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.
Let the equation be 79 % of 623
Percentage = (value/total value) × 100 %.
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
79 % of 623 = 79/100 of 82
79/100 × 623 = 492.17
Therefore, the percent of the given number 79 % of 623 is 492.17.
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