and solve x
[tex]\begin{gathered} x+7=\frac{3}{6} \\ \\ x=\frac{1}{2}-7 \\ \\ x=-\frac{13}{2}=-6.5 \end{gathered}[/tex]the number is -6.5
Want an extra challenge? This screen is **optional**: 30° If you want more practice to really level up your Right Triangle Trig skills, see if you can solve for the missing sides of the Right Triangle pictured to the left. C a You can enter your results and check your work in the table below. 7 HINT: The side that is 7 units long is OPPOSITE the 30° angle. Length of Hypotenuse (c) Length of Other Leg (a) Did I Get Them Right?!
Answer:
c = 14
a = 7√3
Explanation:
To find the value of c, we will use the sin(30) because sin(30) is equal to the opposite side over the hypothenuse. So:
[tex]\sin (30)=\frac{7}{c}[/tex]Additionally, sin(30) is also equal to 0.5, so we can replace this value and solve for c:
[tex]\begin{gathered} 0.5=\frac{7}{c} \\ 0.5c=7 \\ c=\frac{7}{0.5} \\ c=14 \end{gathered}[/tex]Therefore, the length of the hypotenuse (c) is 7.
Now, we can calculate the length of the other leg using the Pythagorean theorem, where:
[tex]a=\sqrt[]{c^2-7^2}^{}[/tex]So, replacing the value of c by 14, we get:
[tex]\begin{gathered} a=\sqrt[]{14^2-7^2} \\ a=\sqrt[]{196-49} \\ a=\sqrt[]{147} \\ a=\sqrt[]{49\cdot3} \\ a=7\sqrt[]{3} \end{gathered}[/tex]Therefore, the length of the other leg (a) is 7√3
Name
1.
Write an expression showing the sum of 8 and a number f.
How do I write this as an expression
The sum of 8 and a number of f can be written as follow:
8 + f
consider the line 4x+9y=-8find the equation of the line that is perpendicular to this line and passes through the point (-2, -2)find the equation of the line that is parallel of this line and passes through the point (-2, -2)
22. QRST is a rectangle. If RU = 3x - 6 and UT = x + 9, find x and the length of QS.RUx= 5QS =TS
We are given two lengths of the rectangle:
RU=3x-6
UT=x+9
These two lengths are shown in the following diagram:
Since this is a rectangle, the lengths of RU and UT must be equal:
[tex]RU=UT[/tex]Thus
[tex]3x-6=x+9[/tex]We need to solve this equation for x.
We start by subtracting x to both sides of the equation:
[tex]\begin{gathered} 3x-x-6=9 \\ 2x-6=9 \end{gathered}[/tex]Now, add 6 to both sides:
[tex]\begin{gathered} 2x=9+6 \\ 2x=15 \end{gathered}[/tex]Finally, divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{15}{2} \\ x=7.5 \end{gathered}[/tex]We have the value of x: x=7.5
Now we have to find the length of QS. Since QS and RT are diagonals of the same rectangle, they have to be equal:
[tex]RT=QS[/tex]This means that we can find RT by adding RU and UT, and the result will be equal to QS:
[tex]QS=RU+TU[/tex]substituting the given expressions for RU and TU:
[tex]QS=3x-6+x+9[/tex]And now, substitute x=7.5 and solve for QS:
[tex]QS=3(7.5)-6+7.5+9[/tex][tex]\begin{gathered} QS=22.5-6+7.5+9 \\ QS=33 \end{gathered}[/tex]Answer:
x=7.5 and QS=33
which equation can be used to determine the cost c
c = 8t + 12 (option C)
Explanation:
The equation will be in the form of equation of line:
y = mx + c
where y = cost
m = slope, x = change for calls, c = intercept
m = change for calls/change in lenght of call
m = slope = (28-20)/(2-1) = (36 -28)/(3-2)
m = 8/1 = 8
So we know the rate of change is 8
for t = 1, = 8 *1 = 8
for t = t , 8*t =8t
The option in the question with 8t is c = 8t + 12
To confirm if the option is correct, we use any of the value of time:
when t = 2
c = 8(2) + 12 = 16 + 12
c = $28
This is correct from the table. Hence, the equation can be used to determine the cost c is c = 8t + 12 (option C)
Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria, how many would be in the petri dish after 24 hours?
Answer:
It would be a lot of bavgeria
Answer:
450000
Step-by-step explanation:
125×(60×60)
=125×3600
=450000
17. Simplify the expression.1.7m² +6.5n - 4n+ 2.5m² – n1.5m² -4.2n1.5m +4.2n4.2m² + 1.5n4.2m² -1.5n
Given:
an expression is given as below
1.7m² +6.5n - 4n+ 2.5m² – n
Find:
we have to simplify the given expression.
Explanation:
we will simplify the given expression as following
1.7m² + 6.5n - 4n+ 2.5m² – n = (1.7 + 2.5)m² + (6.5 - 4 - 1)n = 4.2m² + 1.5n
Therefore, we get
1.7m² +6.5n - 4n+ 2.5m² – n = 4.2m² + 1.5n
Therefore, correct option is 4.2m² + 1.5n.
1. Lines p and q are intersected by line r, such that line p is parallel to line q. If m<1=7x - 36 and m<2 = 5x+12, what is the m<1
We are given a figure in which line r intersects two parallel lines p and q.
The angles labeled as ∠1 and ∠2 are known as same-side interior angles.
Same-side interior angles are supplementary meaning that their sum is equal to 180°.
So we can write,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ (7x-36)+(5x+12)=180\degree \end{gathered}[/tex]Now let us solve this equation for x.
[tex]\begin{gathered} 7x+5x-36+12=180 \\ 12x-24=180 \\ 12x=180+24 \\ 12x=204 \\ x=\frac{204}{12} \\ x=17\degree \end{gathered}[/tex]Now we can find the exact value of the angle ∠1
[tex]\angle1=7x-36=7(17)-36=119-36=83\degree[/tex]Therefore, angle ∠1 = 83°
drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.{{x|x\geq7}}AnswerAnswer,AnswerAnswer
In order to write this set in interval notation, first let's understand what the set represents.
This set includes all numbers that are greater than or equal to 7.
That is, the smaller number in the set is 7, and the greater value doesn't exist, so we can use positive infinity to represent that the set only grows.
Since number 7 is included in the set, we use square brackets, and since positive infinity is not included in the set (because it's not a number that is in the set), we use parenthesis, so the interval notation is:
[tex]\lbrack7,\text{inf)}[/tex]Select all that function with -4x+5=y (-4,5)(-19,6)(9,-31)(8,-27)
Answer
(9, -31) and (8, -27)
Step-by-step explanation:
Given the following function
y = -4x + 5
Testing the options
Using (9, -31)
let x = 9 and y = -31
-31 = -4(9) + 5
-31 = -36 + 5
-31 = -31
Hence, (9, -31) satisifies the function y= -4x + 5
Using (8, -27)
let x = 8 and y = -27
-27 = -4(-8) + 5
-27 = -32 + 5
-27 = -27
Hence, (8, -27) satisfy the function y = -4x + 5
ExpenseYearty costor rateGasInsurance$425.00$400,00$110.00$100.00What is the cost permile over the course ofa year for a $20,000 carthat depreciates 20%,with costs shown in thetable, and that hasbeen driven for 10,000miles?OilRegistrationDepreciation20%A $1.10 per mileB, SA. 10 per mileD. $0.50 per mileC. $0.25 per mile
First, we will find 20% of the cost of the car which is $20,000.
Thus, we have:
[tex]\begin{gathered} 20\text{\% of 20,000} \\ \Rightarrow\frac{20}{100}\times20000 \\ \Rightarrow\text{ \$4000} \end{gathered}[/tex]Adding the $4000 to the other expenses provided in the table:
[tex]4000+425+400+110+100=\text{ \$5035}[/tex]To get the cost per mile, we are going to divide the total cost of $5035 by the number of mies, 10,000.
Thus, we have:
[tex]\frac{5035}{10000}=\text{ \$0.50 per mile}[/tex]Hence, the correct option is Option D
There are 50 students in a class. Can the teacher make them sit in a rows of having six students in each row? Use divisibility test to answer
Step 1. There are 50 students and we need to answer of the teacher can make rows of 6 students in each row.
To check if this can be done, divide 50 by 6 and if the residue is 0, there can be rows of 6 and if the residue is not 0 there cannot be rows of 6 students.
Step 2. D
Diameter = 9 ftMarci purchased the rug shown. To the nearest hundredth, what area of floor space will the rug cover? (1 = 3.14)A)28.26 ft?B)58.54 ft?C) 63.59 ft2D)254.34 ft2
Given:
a.) A rug with a diameter of 9 ft.
Since the rug appears to be a circle, we will be using the following formula:
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex]Where,
D = diameter
We get,
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex][tex]\text{= }\frac{\pi(9)^2}{4}[/tex][tex]\text{= }\frac{81(3.14)}{4}[/tex][tex]\text{ Area = }63.585\text{ }\approx63.59ft.^2[/tex]Therefore, the rug will cover 63.59 ft.^2 of the floor area. The answer is letter C.
solve the problem and show your work below. I have a rectangular garden. i usually grow cucumbers in2/3 of my garden but i want to take 3/4 of the cucumber section to grow radishes. After i make the change, how much of my whole garden will be radishes?
Given data;
The area in which cucumbers usually grown are 2/3 x.
Here, x is the total area of the garden.
The area of the cucumber taken to grow raddish are,
[tex]\begin{gathered} R=\frac{3}{4}\times\frac{2}{3}x \\ =\frac{1}{2}x \end{gathered}[/tex]Thus, the area of the raddish is 50% of the total area of the garden sfter the changes.
Find the length of the segment connecting (-2, 1) and (6. - 1) Round your answer to the nearest tenth. -6 -4 - 2 6
SOLUTION
Find the length of the segment connecting (-2, 1) and (6. - 1) .
In this question, we have the formulae for length segment
D^2 = ( x 2 - x 1 ) ^2 + ( y2 - y 1 )^2
( x 1 , y 1 ) = (-2, 1) , ( x 2 , y 2 ) = ( 6 , -1 )
D^2 = ( 6 - - 2 ) ^2 + ( -1 - 1 ) ^2
D^2 = ( 8 ) ^2 + ( -2 )^2
D^2 = 64 + 4
D^2 = 68
square- root both sides, we have
D = 8.246
D = 8 . 2 ( nearest tenth)
A new video game has been released. The table shows the proportional relationship between the number of levels completed and the time it should take to complete them. Number of Levels 4 5 Time (hours) ? 2.5 How many minutes should it take to complete 4 levels? 180 minutes 120 minutes 60 minutes 50 minutes
Proportionately, the number of minutes it should take to complete 4 levels is B. 120 minutes.
What is the proportion?Proportion is the ratio between one value and another.
Proportions show the relative amount of a variable or value contained in the whole or another variable.
Proportions as fractional values are depicted using fractions, decimals, or percentages.
Number Time
of Levels (hours)
4 ?
5 2.5
The proportion of hours for level 5 = 0.5 (2.5/5) for each level.
If every level takes 0.5 hours or 30 minutes, level 4 will take 2 hours (0.5 x 4).
Or:
If level 5 takes 2.5 hours, level 4 will take 2 hours (2.5/5 x 4).
Thus, proportionately, to complete level 4 will take Option B.
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Replace * with a digit that allows you to reduce the fraction. If there are two * in thesame fraction, replace them with the same digit. Find all possible values of * in eachfraction.6*2/1*0
There are 10 possible digits that we can replace. These are from 0 - 9.
Let's start replacing with 0 first. The fraction will be 602/100 and can be reduced to 301/50.
If we replace * with 1, the fraction will be 612/110 and be reduced to 306/55.
If we replace * with 2, the fraction will be 622/120 and be reduced to 311/60.
If we replace * with 3, the fraction will be 632/130 and be reduced to 316/65.
We can use all the digits from 0 - 9 to replace * and it will allow us to reduce the fraction because the numerator and denominator ends in 2 and 0 respectively.
A model of a crayon is shown. The base is a cylinder with a radius of 1 cm and a height of 6 cm. The tip is a cone with a radius of 1 cm and a height of 2 cm. What is the total volume of the crayon? 6 CN Do not enter any spaces. Round to the nearest hundredths. Use 3.14 for 7.
ANSWER:
20.93 cubic cm
STEP-BY-STEP EXPLANATION:
We can calculate the volume of the crayon by adding the volume of the cone and the volume of the cylinder.
First the volume of the cylinder would be:
[tex]\begin{gathered} V_1=\pi\cdot r^2\cdot h \\ \text{replacing:} \\ V_1=3.14\cdot1^2\cdot6 \\ V_1=18.84 \end{gathered}[/tex]Now, the volume of the cone:
[tex]\begin{gathered} V_2=\frac{1}{3}\cdot\pi\cdot r^2\cdot h \\ V_2=\frac{1}{3}\cdot3.14\cdot1^2\cdot2 \\ V_2=2.09 \end{gathered}[/tex]Now we add them and we have:
[tex]\begin{gathered} V_T=V_1+V_2 \\ V_T=18.84+2.09 \\ V_T=20.93 \end{gathered}[/tex]The volume of the crayon is 20.93 cubic cm
From the time Ryan wakes up, he spends To hour to get ready and 1 hour to travelfrom home to school..How much time does he take to get to school from the time he wakes up?
I'm working on a practice quiz I'm confused about this question
In this problem we have to use the Hero formula so first we have to find s:
[tex]s=\frac{a+b+c}{2}[/tex]and then we replace the sides of the triangle:
[tex]s=\frac{12+11+7}{2}=\frac{30}{2}=15[/tex]and with s we can use the formula of A so:
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]and replace the data so:
[tex]A=\sqrt[]{15(15-12)(15-11)(15-7)}[/tex]and we simplify it so:
[tex]\begin{gathered} A=\sqrt[]{15(3)(4)(8)} \\ A=\sqrt[]{1440} \\ A\approx37.95 \end{gathered}[/tex]Silvia manages a sub shop and needs to prepare smoked turkey sandwiches. She has 3 lb of turkey in the cooler, and each sandwich requires3lb of turkey. How many sandwiches can she make?
Silvia manages a sub shop and needs to prepare smoked turkey sandwiches. She has 3 lb of turkey in the cooler, and each sandwich requires 3 lb of turkey. How many sandwiches can she make?
we have that
each sandwich requires 3 lb of turkey
She has 3 lb of turkey in the cooler
therefore
3/3=1
Only she can make 1 sandwichTranslate the sentence into an equation.Three times the sum of a number and 9 equals 8.Use the variable y for the unknown number.
The Solution:
Given:
Let the unknown number be y.
Three times the sum of a number and 9 equals 8.
Putting the above statement in equation form, we get:
[tex]3(y+9)=8[/tex]Therefore, the correct answer is:
[tex]3(y+9)=8[/tex][tex]3(y+9)=8[/tex]Suppose that 73% of the residents in a particular community speak English as their primary language.a. What is the probability that exactly seven out of eight random residents in this community will speak English as their primary language?
Explanation
The question can be solved using the probability distribution formula, which can be seen below.
[tex]P_x=nCxp^xq^{n-r}[/tex]Part A
From the image we can see that n=8 and p=0.73 while q= 1-0.73 = 0.27
Therefore for;
[tex]\begin{gathered} P(7)=8C7(0.73)^7(0.27)^1 \\ =\frac{8!}{7!1!}\times(0.73)^7(0.27)^1 \\ =0.23862 \end{gathered}[/tex]Answer: 0.2386
Part B
[tex]\begin{gathered} Pr(x\ge7)=Pr(7)+Pr(8)=8C7(0.73)^7(0.27)^1+8C8(0.73)^8(0.27)^0 \\ =\frac{8!}{7!1!}\times(0.73)^7(0.27)^1+\frac{8!}{8!0!}\times(0.73)^8(0.27)^0 \\ =0.23862+0.08064 \\ =0.31926 \end{gathered}[/tex]Answer: 0.3193
Part C: Out of a random number of 40 people in the community, the expected number of people that speak English as a lnaguage will be;
[tex]\frac{73}{100}\times40=29.20[/tex]Answer: 29.20
In △KLM, the measure of ∠M=90°, ML = 28, LK = 53, and KM = 45. Find tan L and cos K.
The triangle KLM can be drawn as,
The value of tan L and cosK can be determined as,
[tex]\begin{gathered} \tan L=\frac{KM}{ML} \\ =\frac{45}{28} \\ =1.6 \\ \cos K=\frac{KM}{KL} \\ =\frac{45}{53} \\ =0.85 \end{gathered}[/tex]Thus, the required value of tanL is 1.6 and cosK is 0.85.
3. (a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down. (b) What was the equation of your linear function in slope-intercept form? (c) What was the equation of the transformed function in slope-intercept form?
The required solution,
(a) the graph has been shown,
(b) The slope-intercept equation of linear function is y = x,
(c) The slope-intercept form of transformed equation is y = x + 2 and y = x - 3
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,
Let's consider a linear function y = x,
The equation of the trasformation in slope-intercept form is given as
For 2 units up
y = x + 2
For 3 units down
y = x - 3
Thus, the required graph has been attached and the solution is determined.
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The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 432 feet long and 4 millimeters in diameter has a resistance of 1.26 ohms, find the length of a wire of the same material whose resistance is ohms and whose diameter is millimeters.
Let
R ----> resistance in ohms
L ---> the length of the wire in ft
D ---> the diameter of the wire in mm
In this problem, the equation is of the form
[tex]R=K\frac{L}{D^2}[/tex]we have
L=432 ft
D=4 mm
R=1.26 ohms
so
Find out the value of K (constant of proportionality)
substitute the given values
[tex]\begin{gathered} 1.26=K\frac{432}{4^2} \\ \\ K=\frac{1.26*16}{432} \\ \\ K=0.0467 \end{gathered}[/tex]Part 2
The formula is
[tex]R=0.0467\frac{L}{D^2}[/tex]For
R=1.41 ohms
D=5 mm
substitute in the formula above
[tex]\begin{gathered} 1.41=0.0467\frac{L}{5^2} \\ solve\text{ for L} \\ L=\frac{1.41*25}{0.0467} \\ L=754.8\text{ ft} \end{gathered}[/tex]The answer is 754.8 feetHow much would you need to deposit in an account now in order to have $2000 in the account in 5 years? Assume the account earns 5% interest compounded continuously.
The total amount of money that you can deposit in the account would be = $ 8,000
What is interest?Interest is defined as the amount of money that an individual earns from an investment made after a particular period of time.
The formula for calculating simple interest;
simple interest (SI) = Principal×time ×rate/100
The principal amount = $x
time = 5 years
Rate = 5%
simple interest = $2000
From the formula, make principal the subject of formula:
Principal= SI × 100/T ×R
Principal= 2000×100/5 × 5
principal= 200000/25
Principal=$ 8,000.
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A loan of $14,354 was repaid at the end of 16 months. What size repayment check (principal and interest) was written, if a 7.4% annual rate of interest was charged?
Principal = P = $14,354
Rate = r
if a coin was flipped 30 times, how many times would it land on tails?
It is expected that it would land on tails 15 times
Here, we want to get the number of times the coin will land on it tail
Mathematically, the probability that a coin will land on its head or on its tail is the same at 1/2
So the number of times out of 30 flips will be;
[tex]\frac{1}{2}\times30\text{ = 15 times}[/tex]Use the graph and the translation (x,y) → (x+2, y + 5) to answer parts a and b below.
A → A' (-7, 10)
B → B' (1, 5)
C → C' ( -3, 3)
Explanations:The translation rule is:
(x+2, y+5)
We are going to get the coordinates of the vertices A, B, and C.
We will also get the coordinates of the vertices A', B', and C' after translation.
A (-9, 5)
B (-1, 0)
C (-5, -2)
After the translation (x+2, y+5)
A' (-9+2, 5+5)
A' (-7, 10)
B' (-1+2, 0+5)
B' (1, 5)
C' (-5+2, -2+5)
C' (-3, 3)
Therefore:
A → A' (-7, 10)
B → B' (1, 5)
C → C' ( -3, 3)