Answer:
x = - 27/179
Step-by-step explanation:
10x - 1 = 7x + 182x + 26
10x - 1 = 189x + 26
10x - 189x = 26 + 1
- 179x = 27
x = - 27/179
There is a rope running from the top of a flagpole to a hook in the ground. The flagpole is 21 feet high, and the hook is 20 feet from its base. How long is the rope?
Shannon invests money in a bank account which gathers
compound interest each year.
After 5 years there is $673.40 in the account.
After 8 years there is $737.99 in the account.
Work out the annual interest rate of the bank account.
Give your answer as a percentage to 1 d.p.
By using the concept of compound interest, rate of interest is 3.1 %
What is compound interest?
If the interest on a certain principal at a certain rate over a certain time increase exponentially rather than linearly, the interest earned is called Compound interest.
If the principal is P, rate is r and time is t, then amount is
[tex]A = P(1 + \frac{r}{100})^n[/tex]
Let the principal be $P and the rate be r% per annum
After 5 years there is $673.40 in the account.
[tex]673.40 = P(1 + \frac{r}{100})^5\\[/tex]............. (1)
After 8 years there is $737.99 in the account.
[tex]737.99 = P(1 + \frac{r}{100})^8[/tex] ................. (2)
Dividing (2) by (1),
[tex](1 +\frac{r}{100})^3 = 1.096\\\\1 + \frac{r}{100} = (1.096)^{\frac{1}{3}}\\\\1 + \frac{r}{100} = 1.031\\\\\frac{r}{100} = 1.031 -1\\\\\frac{r}{100} =0.031\\\\r = 0.031 \times 100\\[/tex]
r = 3.1 %
Rate is 3.1 %
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yo i need some help this determines weather i pass or fail
To make 4 dozen cookies she would need
→ 3/2 cup peanut butter
→ 3 cup of vegetable shortening
→ 1 1/2 cups of firmly packed light brown sugar
→ 6 tablespoons of milk
→ 2 3/2 tablespoons of vanilla extract
→ 2 cups of flour
→ 3/2 teaspoon of baking soda
→ 1/2 teaspoon salt
To make 4 dozen cookies
she will need double the items which are mentioned in the list
thus the required list will look like this
3/4 × 2 = 3/2 cup peanut butter
3/2 cup of vegetable shortening = 3/2 × 2 = 3 cup of vegetable shortening
1 1/4 cups of firmly packed light brown sugar = 1 1/4 × 2 = 1 1/2 cups of firmly packed light brown sugar
3 tablespoons of milk = 3 × 2 = 6 tablespoons of milk
2 3/4 tablespoons of vanilla extract = 2 3/2 tablespoons of vanilla extract
1 large egg = 1× 2 = 2 large eggs
1 1/2 cups flour = 1 1/2×2 = 1 + 1 = 2 cups of flour
3/4 teaspoon baking soda = 3/2 teaspoon of baking soda
1/4 teaspoon salt = 1/4 × 2 = 1/2 teaspoon salt
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pls help me answer these questions
Answer:
Length: 10 m
Width: 6 m
Step-by-step explanation:
The layout of the floor is l x w, which is 100 cm by 60 cm. Now, the confusing part: 1 meter (m) = 10 centimeters (cm)
To set this problem up, you'd first have to go through the logic. For every 10 centimeters of the floor layout, it is equal to 1 meter of the actualy floor plan. So you would have to scale 100 cm and 60 cm by [tex]\frac{1}{10}[/tex] (or divide by 10).
We will ignore the units, for now
Length: 100 * [tex]\frac{1}{10}[/tex] = 10 or (100/10 = 10)
Width: 60 * [tex]\frac{1}{10}[/tex] = 6 or (60/10 = 6)
Now that we've finalized the numerical value, lets move on to the units. Since the question wants us to respond in meters, the length of 10 and the width 6 6 would be in meters.
So the answer would be:
Length: 10 m
Width: 6 m
Hope this helped!
How many people did Trevor survey?
74
92
107
137
Answer:
92 I think because in my class I heard my friend tell me
A floor has 15 1/2 tiles in an area of 2 2/5 sqft how many tiles are in a square foot
Since in 2 2/5 sqft are 15 1/2 tiles, then in 1 square foot, there are:
[tex]\frac{15\frac{1}{2}}{2\frac{2}{5}}[/tex]tiles.
To compute the above division we transform the mixed fractions into improper fractions:
[tex]\begin{gathered} 15\text{ }\frac{1}{2}=\frac{31}{2}, \\ 2\frac{2}{5}=\frac{12}{5}. \end{gathered}[/tex]Therefore:
[tex]\frac{15\frac{1}{2}}{2\frac{2}{5}}=\frac{\frac{31}{2}}{\frac{12}{5}}=\frac{31\times5}{12\times2}=\frac{155}{24}\text{.}[/tex]Answer: 6 11/24 tiles.
There is a 40% chance that it is rainy in California. If there are 365 days in a year, how many of them would you expect to be rainy?
It is expected that 146 days will be rainy
Based on the given percentage, we want to calculate the number of rainy days
What we have to do here is to multiply the percentage by the number of days
That would be 40% of 365 days
We have this as;
[tex]\frac{40}{100}\times365\text{ = 146}[/tex]Only quadratic functions can be transformed. true or false
It is false, that only quadratic functions can be transformed.
Given that,
To justify the statement, "Only quadratic functions can be transformed."
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
It is not necessary that only quadratic functions can be transformed, all the functions can be transformed regardless of their nature such as linear functions, polynomial functions etc.
Thus, It is false, that only quadratic functions can be transformed.
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please answer this question
The value of m<2 = 107
Given:
m<SOX = 160
m<1 = x+14
m<2 = 3x - 10
x + 14 + 3x - 10 = 160
4x + 14 - 10 = 160
4x + 4 = 160
4x = 160 - 4
4x = 156
divide by 4 on both sides
4x/4 = 156/4
x = 39
m<2 = 3*39 - 10
= 117 - 10
= 107
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If you travel a 150 miles in 3 hours what was your average rate of speed
Distance (D): 150 miles
Time (t): 3 hours
[tex]Speed=\frac{D}{t}=\frac{150}{3}=50[/tex]Answer: 50 miles / hour
Multiply the two polynomials (3a² + 5a - 2)(5a² - 3a + 4)
SOLUTION
The polynomials expression given are
[tex]\mleft(3a^2+5a-2\mright)\mleft(5a^2-3a+4\mright)[/tex]Expand the expression by distributing the parentheses
[tex]3a^2\cdot\: 5a^2+3a^2\mleft(-3a\mright)+3a^2\cdot\: 4+5a\cdot\: 5a^2+5a\mleft(-3a\mright)+5a\cdot\: 4-2\cdot\: 5a^2-2\mleft(-3a\mright)-2\cdot\: 4[/tex]Simplify
[tex]\begin{gathered} 15a^4-9a^3+12a^2+25a^3-15a^2+20a-10a^2+6a-8 \\ \text{Rearranging and simplify} \\ 15a^4-9a^3+25a^3+12a^2-15a^2-10a^2+20a+6a-8 \\ 15a^4+16a^3-13a^2+26a-8 \end{gathered}[/tex]Hence, the answer is
[tex]15a^4+16a^3-13a^2+26a-8[/tex]For a certain casino slot machine, the odds in favor of a win are given as 67 to 33. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is ___
Data:
• Odds in favor of a win are given as 67 to 33.
Procedure
• We have to find the total sample (,T,), which can be calculated as follows:
[tex]T=67+33=100[/tex]Then, to calculate the probability, we have to divide the odds in favor of a win by T.
[tex]\frac{67}{100}=0.67[/tex]Answer: 0.67
Study the figures, figure 1 is similar to figure 2Part A : Describe a series of transformations and dilations that map figure 1 to figure 2Part 2: Describe a second series of transformations and dilations that map figure 1 to figure 2
In order to go from figure 1 to figure 2, there are a number of different transformations that can be selected.
First, notice that figure 2 is exactly three times as large as figure 1, therefore, there has been a dilation by a factor of three (3) that took place .
So Let's say that we do the dilation first.
Step 1: Dilation by a factor of "3" using the point (-1, -2) which is one of the vertices of the triangle, for reference. Then, the new triangle would have new coordinaes for the vertices at the points:
(-1, -2) (-1, 1) and (-6, -2)
I am making a drawing to show the change (give me a little time)
So, we see that the dilated triangle is represented by the green one in the image above.
Step 2: we are now going the "reflect the green triangle around the horizontal line y = 2 represented by the blue line . When we reflect the green triangle around that line, we obtain the orange triangle.
Step 3: we are going to do another reflection, this time a reflection around the vertical line x = 1 (noted in purple in the image above). After this, we obtain the triangle in figure 2.
So we
slove the equation 4c + 7 = 23
We need to solve the expression:
[tex]4c+7=23[/tex]The first step is to subtract "7" on both sides.
[tex]\begin{gathered} 4c+7-7=23-7 \\ 4c=16 \end{gathered}[/tex]Then we need to divide both sides by 4.
[tex]\begin{gathered} \frac{4c}{4}=\frac{16}{4} \\ c=4 \end{gathered}[/tex]The result of the equation is "c=4".
Answer to the nearest tenth:
12 is 90% of what number?
Answer:
13.33 is the answer im pretty sure
Step-by-step explanation:
Answer:
13.3
Step-by-step explanation:
1. If it's possible - try cutting the number down to 10%-:
We can do that by dividing 12 by 9, which would give us 10% of that
number.
2. We get 1.33, which is 10% of the number. To get 100 percent, we just need to multiply by 10
3: 1.33*10 is 13.3, so the answer has to be 13.3
3.13 geom Which triangle congruence postulate or theorem proves that these triangles are congruent?
The AAS triangle congruence postulate proves that these triangles are congruent .
In the question,
two triangles are given that are triangle KLM and triangle XYZ .
Consider the triangle KLM and triangle XYZ .
we can see that
(i) angle L = angle Y = angle 1 .....given in the figure
(ii) angle m = angle Z = angle 2 .... given in the figure
(iii) side KM = side XZ ....given in the figure
From the above three statements we conclude that
ΔKLM ≅ ΔXYZ
both the triangles KLM and XYZ are congruent by AAS Congruence Postulate .
Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .
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Solve the quadratic equation x² + 2√2x-6=0 for x
Step-by-step explanation:
D = b²-4ac
D = (2√2)²-4×1×(-6)
D = 8+24 = 32 = 4√2
X1 =
[tex] \\ \frac{ - 2 \sqrt{2} + 4 \sqrt{2} }{ 2 } = \frac{2 \sqrt{2} }{2} = \sqrt{2} [/tex]
X2 =
[tex] \frac{ - 2 \sqrt{2 } - 4 \sqrt{2} }{2} = - 3 \sqrt{2} [/tex]
please help help me write a story to describe the graph
I'll start first by finding the slope of the line at t = 2 mins up to t = 6 mins, t = 6 mins up to t = 8 mins, and t = 14 mins up to t = 20 mins.
For the first interval (2 mins to 6 mins), we have the coordinates (2, 7) and (6, 5). The slope of the line is
[tex]m=\frac{5-7}{6-2}=-\frac{2}{4}=-\frac{1}{2}[/tex]For the second interval (6 mins up to 8 mins), we have the coordinates (6, 5) and (8,0). The slope of the line is
[tex]m=\frac{0-5}{8-6}=-\frac{5}{2}[/tex]For the last interval (14 mins up to 20 mins), we have the coordinates (14,0) and (20,9). The slope of the line is
[tex]m=\frac{9-0}{20-14}=\frac{9}{6}[/tex]The x-axis of the given graph pertains to time while its y-axis pertains to distance from home. Let's try to make a story about a person from work going home and will prepare something before going outside again.
For the first 2 mins, the person walks out of his office and will go to his car. Since he is still in the office, the distance from home does not change for the first two minutes.
For the next 4 mins (2 mins to 6 mins interval), he starts driving going home at a rate of 1/2 miles per minute. Because of traffic, he is driving slower than his usual driving speed. Upon passing away from the traffic, the person now travels at a rate of 5/2 miles per minute for 2 mins (6 to 8 mins interval). At the 8th minute mark, he is already home. He prepared something at home during the 8 min to 14 min interval time. After the preparation, he went again outside for some business trip, traveling at the speed of 9/6 miles per minute.
EASY POINTS WILL GIVE BRAINLSIT TO BEST ASNWER HELP!!
write the slope intercept form of an equation though given points
through (3,-5) and (1,3)
Light intensity (I) is proportional (a) to the inverse square of distance (d) of a subject from a lightsource. The relationship in intensities for subjects at different distances from the same source canbe likewise seen as a ratio or proportional relationship.I x 1 1A proportional relationship can be mathematically expressed as follows for light intensity (I) inlumens when a subject is at the light source.=Lumens at origin or sourceSo, if a light intensity (I) is 569 lumens at the source, what is the light intensity (I) at 9 distancefrom the source,?Round the value to the nearest tenth if necessary. You do not need to include a label for lumens.Only the number, rounded to the tenth, will be necessary.
ANSWER
The light intensity is 7.0
STEP-BY-STEP EXPLANATION:
What to find? The value of the proportionality constant.
Given parameters
• Light intensity = 569 lumens
,• Distance = 9
According to the question, Light intensity (I) is proportional to the inverse square of the distance.
This can be expressed mathematically as
Let the intensity of light be represented as I
Let the distance be represented as d
[tex]I\text{ }\propto\text{ }\frac{1}{d^2}[/tex]The next thing is to introduce a constant k
[tex]\begin{gathered} I\text{ = }\frac{K\cdot\text{ 1}}{d^2} \\ I\text{ = }\frac{K}{d^2} \end{gathered}[/tex]Recall that,
I = 569 lumens
d = 9
The next thing is to substitute the parameters into the above formula
[tex]\begin{gathered} \frac{Lumens\text{ at current distance}}{\text{Lumens at origin or source}}\text{ = }\frac{1}{d^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{(9)^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{81} \\ \text{Cross multiply} \\ 569\cdot\text{ }1\text{ = Lumens at current distance }\cdot\text{ 81} \\ \text{Divide both sides by 81} \\ \frac{569}{81}\text{ = }\frac{Lumens\text{ at current distance }\cdot\text{ 81}}{81} \\ \text{Lumens at current distance = 7.0} \end{gathered}[/tex]In ΔOPQ, o = 9.2 cm, p = 2.4 cm and ∠Q=37°. Find the length of q, to the nearest 10th of a centimeter.
The length of q, to the nearest 10th of a centimeter is 7.6 cm.
Given in question,
In ΔOPQ,
o = 9.2 cm
p = 2.4 cm
∠Q = 37°
Cosine formula ⇒ cos θ = [tex]\frac{o^{2}+p^{2}-q^{2} }{2op}[/tex]
Putting the values in equation,
cos 37 = [tex]\frac{(9.2)^{2}+(2.4)^{2}-q^{2} }{2*9.2*2.4}[/tex]
0.799 = [tex]\frac{84.64 + 5.76-q^{2} }{44.16}[/tex]
0.799*44.16 = 90.4 - [tex]q^{2}[/tex]
32.28 = 90.4 - [tex]q^{2}[/tex]
[tex]q^{2}[/tex] = 90.4 - 32.28
[tex]q^{2}[/tex] = 58.12
[tex]q = \sqrt{58.12}[/tex]
[tex]q = 7.63[/tex]
q = 7.6 cm (to nearest 10th)
Hence, length of q is 7.6 cm.
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can you help me find BD. under the letter A the number is 25°
arc BD is 25°
Explanation:We would apply the secant-secant theorem:
[tex]\begin{gathered} \angle A\text{ =}\frac{large\text{ arc - small arc}}{2} \\ \angle A\text{ =}\frac{arc\text{ CE - arc BD}}{2} \end{gathered}[/tex]angle A = ∠A =25°
arc BD =?
arc CE = 100°
[tex]\begin{gathered} 25\text{ = }\frac{100-arc\text{ BD}}{2} \\ \text{cross multiply:} \\ 2(25)\text{ = 100 - arc BD} \end{gathered}[/tex][tex]\begin{gathered} 50\text{ = 100 - arc BD} \\ \text{subtract 100 from both sides:} \\ 50\text{ - 100 = 100 - 100 - arc BD} \\ -50\text{ = - arc BD} \end{gathered}[/tex][tex]\begin{gathered} \text{DIvide both sides by -1:} \\ \frac{-50}{-1\text{ }}=\frac{-arc\text{ BD}}{-1} \\ \text{arc BD = 50}\degree \end{gathered}[/tex]Suppose you are the manager of a firm. The accounting department has provided cost estimates, and the sales department sales estimates, on a new product. Analyze the data they give you, determine what it will take to break even, and decide whether to go ahead with production of the new product The product has a production cost function C(x)=560x + 17,080 and a revenue function R(x) = 700xThe break-even quantity is ______units.
Consider that the break-even quantity is the one corresponding to which the profit is zero i.e. the production cost becomes equal to the revenue earned.
Equate the functions and solve for the break-even quantity as follows,
[tex]\begin{gathered} C(x)=R(x) \\ 560x+17,080=700x \\ 700x-560x=17,080 \\ 140x=17,080 \\ x=122 \end{gathered}[/tex]Thus, the break-even quantity is 122 units.
There are two integers that
multiply to -45 and combine to -4. Find
the two integers, then the LARGER
integer is your answer for this question.
Answer:
5
Step-by-step explanation:
-9 × 5 = -45
-9 + 5 = -4
5 is greater than -9, therefore 5 is the answer
Given the lengths of the sides of a triangle, determine if it is an acute, anobtuse, or a right triangle.
Use the Pythagorean theorem to determine if the triangle is acute, obtuse or right triangle.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where} \\ c\text{ is the longest side of the triangle} \\ a\text{ and }b\text{ are the other 2 sides} \end{gathered}[/tex][tex]\begin{gathered} a^2+b^2=c^2 \\ (18)^2+(29)^2\questeq(46)^2 \\ 324+841\questeq2116 \\ 1165\questeq2116 \\ 1165<2116 \end{gathered}[/tex][tex]\begin{gathered} \text{IF} \\ a^2+b^2c^2 \\ \text{THEN, the triangle is an acute triangle} \\ \\ \text{IF} \\ a^2+b^2=c^2 \\ \text{THEN, the triangle is a right triangle} \end{gathered}[/tex]Since the sum of the square of the side of the two angles is less than the square of the longest side, then given the length of a triangle 18-29-46, the triangle is an obtuse triangle.
Given f(x)=3x^3 - 4x^2 + 2x - 1 and g(x) = x - 4, state the quotient and remainder of f(x)/g(x), in the form q(x) + r(x)/g(x)
Dividing f(x) = 3x³ - 4x² + 2x - 1 by g(x) = x - 4 will yield a quotient of q(x) = 3x² - 8x + 34 and a remainder of 135, that is (3x² - 8x + 34) + 135/(x - 4).
Calculating for the quotient and remainderApplying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.
We shall divide the dividend f(x) = 3x³ - 4x² + 2x - 1 by the divisor g(x) = x - 4 as follows;
3x³ divided by x equals 3x²
x - 4 multiplied by 3x² equals 3x³ - 12x²
subtract 3x³ - 12x² from 3x³ - 4x² + 2x - 1 will result to 8x² + 2x - 1.
8x² divided by x equals 8x
x - 4 multiplied by 8x² equals 8x² - 32x
subtract 8x² - 32x from 8x² + 2x - 1 will result to 34x - 1.
34x divided by x equals 34
x - 4 multiplied by 34 equals 34x - 136
subtract 34x - 136 from 34x - 1. will result to a remainder of 135.
Therefore by the long division method, f(x) = 3x³ - 4x² + 2x - 1 divided by g(x) = x - 4 gives a quotient q(x) = 3x² - 8x + 34 with a remainder of 135.
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6
Simplify the expression: (1318) + 24 ÷ 6
2/9x20 as a fraction
Answer:
40/9 OR 4 4/9
Step-by-step explanation:
2/9 x 20 = 2*20/9 = 40/9
Find the slope (-19,12) (-9,1)
Answer:
m= -11/10
Step-by-step explanation:
Refer to formula m= y2-y1
x2-x1
1-12 = -11 (negative bc 1 comes first but is less than 12.)
Think of it as -12+1 it would be -11 going towards 0.
-9--19 = 10
is 6(2x-7)-3=12x-21 a no solution one solution or infinitely
Step-by-step explanation:
let's do the operations :
6(2x - 7) - 3 = 12x - 21
12x - 42 - 3 = 12x - 21
-45 = -21
that is never true, no matter what values for x we come up with.
and therefore, there is no solution.