Given:
Diego pays $4.50 for 3 pounds of bananas and 2 pounds of oranges.
One pound of oranges cost $0.75 more than one pound of bananas.
To find:
The equation which represents the situation, and what is the price per pound of each fruit.
Solution:
Let b represent the price per pound of bananas.
Cost of 3 pound of banana = $3b
One pound of oranges cost $0.75 more than one pound of bananas.
So, cost of one pound of oranges = $(b+0.75)
Cost of 2 pound of oranges = $2(b+0.75)
Diego pays $4.50 for 3 pounds of bananas and 2 pounds of oranges.
[tex]3b+2(b+0.75)=4.50[/tex]
Therefore, the required equation is [tex]3b+2(b+0.75)=4.50[/tex].
On solving the above equation, we get
[tex]3b+2b+1.50=4.50[/tex]
[tex]5b=4.50-1.50[/tex]
[tex]5b=3[/tex]
Divide both sides by 5.
[tex]b=\dfrac{3}{5}[/tex]
[tex]b=0.60[/tex]
Now,
[tex]b+0.75=0.60+0.75=1.35[/tex]
Therefore, the price of fruits are $0.60 per bananas, $1.35 per pound of oranges.
Hence, the correct option is C.
A new car is purchased for 24900 dollars. The value of the car depreciates at 6.75% per year. To the nearest tenth of a year, how long will it be until the value of the car is 15900 dollars?
Answer:
5.5 years
Step-by-step explanation:
24900 times 6.75% = 1,680.75
so this is how much it goes down per year, but we have to find it were the price reaches 15900. so 9000-1680.75=
7,319.25( one year)
7,319.25-1680.75 = 5,638.5 (second year)
5,638.5-1680.75= 3,957.75 (third year)
3,957.75-1680.75 = 2,277 (fourth year)
2,277-1680.75= 596.25 (fifth year)
Answer:
the correct answer would be 5.5
Step-by-step explanation:
I solved it and got it correct on the test
The question is on the screenshot
Answer:
green
Step-by-step explanation:
HIGH SCHOOL
od knowledge Matters
Spotting the opportunity Math Quiz
QUESTION 3 of 10: There are about 30.2 million small businesses in the United States and about 30,000 other larger businesses. What
percent of all businesses in the U.S. are small businesses?
a) 30%
b) 99%
c) 99.9%
d) 100%
Submit
Answer:99.9
Step-by-step explanation:
The percent of small businesses to all businesses is equal to 99.99%.
It is given that there are about 30.2 million small businesses and about 30000 large businesses.
We have to find out what percent of all businesses in the U.S. are small businesses.
What do you mean by percentage ?
A percentage is a number or say ratio that can be expressed as a fraction of 100.
As per the question ;
The approximate number of small businesses is ;
= 30.2 million
= 30200000
The number of large businesses is ;
= 30000
Total number of businesses will be ;
= 30200000 + 30000
= 30230000
The percent of small businesses to all businesses ;
= [tex]\frac{30200000}{30230000}[/tex] × 100 %
= 0.999 × 100 %
= 99.99 %
Thus , the percent of small businesses to all businesses is equal to 99.99%.
To learn more about percentage click here ;
https://brainly.com/question/18811795
#SPJ2
The mean,mode,median in
2, 5, 5, 6, 7, 3, 2, 6?
2x+y=7 solve for y. what is the answer?
Answer:
Step-by-step explanation:
There is no numeric answer, or there are many.
y = 7 - 2x is the first answer that you have to get.
Now you are away. The domain is anything.
The range (the y value) is also anything.
5.22 write the decimal as a fraction or mixed number in simplest form
Answer:
5 and 11/50
Step-by-step explanation:
5.22 = 261/50 = 5 and 11/50
Sausages come in packets of 12. Bread rolls come in packets of 9. Brian wants to buy enough packs of sausages and rolls so that there are an equal number of sausages and rolls. What is the minimum number of sausages and rolls he needs to buy?
1 A student whose eye level is 182 cm from the ground observed the top of their house at
an angle of elevation of 32 at point A She walked for 20m towards the house along a
straight road to a point B where she observed the top of the building again at an angle of
elevation of 40 Calculate corect to 2 decimal places the-
(a) Distance of A from the bouse
(3mks)
(b) The height of the house
(2mks)
2. Given that an X=5/ 12 find the value of the following without using mathematical tables or
calculator
(a) Cos x
(2mks)
(b) Sin (90-x)
2mics)
Answer:
Question 1)
[tex]\text{ Distance from A to the house is approximately 78.34 meters}\\\text{The height of the house is approximately 50.77 meters}[/tex]
Question 2)
[tex]\text{ Part A) \cos(x)=\frac{12}{13}} \\ \text{ Part B) \sin(90-x)=\frac{12}{13} }[/tex][tex]\text{ Part A) }\\\cos(x)=\frac{12}{13}\\\\\text{ Part B)}\\\sin(90-x)=\frac{12}{13}[/tex]
Step-by-step explanation:
Question 1)
Please first reference below for the image.
Also recall the basic trigonometric functions with SohCahToa.
Part 1)
In order to find the distance, we will need to find the value of [tex]x[/tex]. However, to do so, we must find the value of [tex]c[/tex] first.
First, we will need to find BM. We can use the smaller triangle. BM is opposite of the smaller triangle, and we already know that the hypotenuse is 20 meters. So, we can use sine:
[tex]\sin(A)=\frac{\text{opp}}{\text{hyp}}[/tex]
Substitute 32° for A and 20 for the hypotenuse. Our BM is our opposite, so substitute BM for opposite. This yields:
[tex]\sin(32)=\frac{BM}{20}[/tex]
Solve for BM. Multiply both sides by 20:
[tex]BM=20\sin(32)[/tex]
Don't approximate just yet. In order to make our answer to most precise, we will approximate at the very end.
So, BM is 20sin(32) meters. BM of the smaller triangle is the same as BM of the larger triangle, so BM of the larger triangle is also 20sin(32). Now, we can find the value of [tex]c[/tex]. However, we will first need to find the value of [tex]\angle MBT[/tex]. To do so, notice that [tex]\angle ABM, \angle MBT, \text{ and } 40\textdegree[/tex] form a straight angle. Therefore:
[tex]\angle ABM+\angle MBT+40^\circ=180[/tex]
Simplify:
[tex]\angle ABM+\angle MBT=140[/tex]
So, we will need to find [tex]\angle ABM[/tex], which is [tex]\angle B[/tex] of the smaller triangle. So, we can use the trig functions again. Since we now know BM, we can use cosine. So:
[tex]\cos(B)=\frac{\text{adj}}{\text{opp}}[/tex]
Substitute 20sin(32) for the adjacent and 20 for the opposite. So:
[tex]\cos(B)=\frac{20\sin(32)}{20}[/tex]
To solve for B, take the inverse cosine of both sides. Evaluate:
[tex]B=\cos^{-1}(\frac{20\sin(32)}{20})=58^\circ[/tex]
Therefore, we can substitute 58 for [tex]\angle ABM[/tex] and solve. This yields:
[tex]58+\angle MBT=140\\\Rightarrow\angle MBT=82^\circ[/tex]
So, we can now find c. We know BM and that [tex]\angle B[/tex] (of the larger triangle) is 82°. To find c, then, we will use cosine. So:
[tex]\cos(B)=\frac{\text{adj}}{\text{hyp}}[/tex]
Substitute 82 for B, 20sin(32) for the adjacent BM, and c for the hypotenuse. So:
[tex]\cos(82)=\frac{20\sin(32)}{c}[/tex]
Solve for c by cross-multiplying:
[tex]c=\frac{20\sin(32)}{\cos(82)}[/tex]
Now, finally, we can solve for [tex]x[/tex]. We know [tex]c[/tex] (the hypotenuse) and we want to find [tex]x[/tex]. We also have an angle of 40°. So, we can use cosine:
[tex]\cos(40)=\frac{x}{c}[/tex]
Multiply both sides by [tex]c[/tex]:
[tex]x=c\cos(40)[/tex]
Substitute [tex]c[/tex]:
[tex]x=\frac{20\sin(32)\cos(40)}{\cos(82)}[/tex]
Approximate:
[tex]x\approx58.34\text{ meters}[/tex]
However, this is only [tex]x[/tex]. The distance from the house is [tex]x+20[/tex]. Therefore, the distance from the house is:
[tex]d\approx58.34+20\approx78.34\text{ meters}[/tex]
Part 2)
We want to find the height h. Since we already determined [tex]c[/tex], we can use it to find [tex]h[/tex]. We will use the sine function this time:
[tex]\sin(40)=\frac{h}{c}\\\Rightarrow h=c\sin(40)\\\Rightarrow h=\frac{20\sin(32)\sin(40)}{\cos(82)}\\\Rightarrow h\approx48.95[/tex]
However, we will still need to add the eye level of 182 centimeters or 1.82 meters. So:
[tex]h\approx48.95+1.82\approx50.77\text{ meters}[/tex]
The height of the house is approximately 50.77 meters.
Question 2)
We know that: [tex]\tan(x)=\frac{5}{12}[/tex]
Remember that tangent is the opposite side over the adjacent side. So, let's find the hypotenuse. We can us the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute 5 for a and 12 for b. Solve for c:
[tex]c^2=(5)^2+(12)^2\\\Rightarrow c^2=25+144\\\Rightarrow c=\sqrt{169}=13[/tex]
So, our hypotenuse is 13, our adjacent is 12, and our opposite is 5. We can now solve for the others:
A)
[tex]\cos(x)=\frac{\text{adj}}{\text{hyp}}\\\Rightarrow\cos(x)=\frac{12}{13}[/tex]
B)
[tex]\sin(90-x)=\cos(x)\\\text{Note: This is a cofunction identity}\\\Rightarrow\sin(90-x)=\frac{12}{13}[/tex]
Note: The document I found said [tex]\sin^2(90-x)[/tex]. Anyways, it will just be: [tex]\sin^2(90-x)=\frac{144}{169}[/tex]
The gardener plans to fertilize the region of grass. The
gardener can buy only full bags of fertilizer and will
use at least 1 bag per 225 square feet of grass. What is
the minimum number of bags of fertilizer the gardener
needs to buy?
Answer:4
Step-by-step explanation:
Describe what you think "domain" means
Answer:
the set of possible values of the independent variable or variables of a function.
Step-by-step explanation:
Answer:
All the x-values in the ordered pairs together make up the domain
Step-by-step explanation:
John took a 5 1/2 mile walk to his friend's house. He left at 11 a.m. and
arrived at his friend's house at 12:45 p.m. What was his average speed of
walking in miles per hour?*
Answer:
3.14 mph
Step-by-step explanation:
5.5 divided by 1.75
5.5 is the miles
1.75 is the hours
Answer: The average speed on the return trip is 2.44 miles/h
Step-by-step explanation:
Please help ASAP Cool Down: Graph the Relationship
Sketch a graph that shows the
relationship between grams of
honey and grams of salt needed
for a bakery recipe. Show on
the graph how much honey is
needed for 70 grams of salt.
Answer:
105
Step-by-step explanation:
15/10= 1.5
30/20= 1.5
70x1.5= 105
Each square below represents one whole.
What percent is represented by the shaded area?
Answer:
152%
Step-by-step explanation:
There is one whole grid shaded = 100%
The other grid has 13/25 shaded. This is the same as 52/100=52%
100+52=152%
Answer: 152%
Step-by-step explanation: To easy please like
What is a slope of A and B
A.1/3
B.1/2
C.1/4
D.3/4
Answer:
A. 1/3
Step-by-step explanation:
to find slope (rise over run), you count how many points up and how many points over it is to get from one point to another on the line graphed.
from point A to point B, it is 4 up and 12 over (4/12). then, you have to simplify it, making it 1/3.
hopefully that helped! please consider brainliest! :)
(I need one more to move up a rank lol)
What value of m makes this equation true?
m/4-3 = 9
Drag and drop the number that correctly completes the equation
Answer:
m = 9
Step-by-step explanation:
m/4-3=9
m/(4-3)=9
m/1=9
m=9
Helppp fasttt! also always contains brainliest!
Answer:
Im pretty sure it's F
Step-by-step explanation:
Sorry if im wrong
A recipe asks for 6 1/4cups of flour.
How many cups of flour are needed to make 1/2 of a recipe?
Express the answer in simplest form.
Enter the answer in the box.
combine like terms
5x + X =
Answer:
6x
Step-by-step explanation:
5x + x = ?
5x + x = 6x
This is because x means 1x
Answer:
Today: Monday, 12 October 2020
Hour: 09.15 WIB (in Indonesian)
_________________________
5x + x =
x = 1
5x + x = 6x
Eric sells boxes of cookies for $8 each. Yolanda sells boxes of cookies for $10. Each of them sold the same dollar amount. How many boxes did Eric sell
Answer:
If Eric sells boxes of cookies for $8 each, and Yolanda sells boxes of cookies for $10 each, and they made the same amount of money, then Eric sold 5 boxes.
Step-by-step explanation:
To solve this problem, you must find the lowest common multiple of eight and ten. That would be 40, which is how much they both made. $40 / $8 per box = 5 boxes.
...And you don't need to know this, but Yolanda sold 4.
please help MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
[tex] \frac{5(q + p)}{2} = 3 + 4p \\ [/tex]
Multiply sides by 2
[tex]5(q + p) = 2(3 + 4p)[/tex]
[tex]5q + 5p= 6 + 8p[/tex]
Subtract sides minus 5p
[tex]5q = 6 + 8p - 5p[/tex]
[tex]5q = 3p + 6[/tex]
Divided sides by 5
[tex]q = \frac{3p + 6}{5} \\ [/tex]
a = 3 , b = 6 , c = 5
They're all positive.
So we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
*DOMAIN AND RANGE HELP PLEASE
if u can tell me the answers like *A. then say the two numbers that would be helpful*
but please help me!!!!!!
Answer:
Step-by-step explanation:
A) Domain: 8 Range: 7
B) Domain: 5 Range: 6
C) Domain: 1 Range: 2
D) Domain: 3 Range: 4
NEED HELP! ASAP! 50 POINTS!
What is the slope intercept form of 4x-3y=18? Explain.
A) y = 3/4x - 6
B) y = -3/4x - 6
C) y = 4/3x - 6
D) y = -4/3x + 6
Answer:
D
You use algebra and solve it for y.
Step-by-step explanation:
4x-3y=18
3y=4x+18
y=4/3x +6
Answer:
D
Step-by-step explanation:
help please! step by step if possible
9514 1404 393
Answer:
use the formula for slope2/3Step-by-step explanation:
The formula for slope (m) of a line between two points is ...
m = (y2 -y1)/(x2 -x1)
Pick two points from the table and fill in the values. Using the last two table entries, we have ...
m = (7 -5)/(5 -2) = 2/3
The slope is 2/3.
solve for z (show your work)
Answer:
z=-3
Step-by-step explanation:
combine like terms then solve
this is the question
Answer:
v: the answer is 43/48
Step-by-step explanation:
The highway from Alton to Beasley is 250 miles long, and 3/10 of the miles are in Foster County. Of the portion of miles in Foster County, 2/5 of them are in Vista Township. How many miles of the highway are in Vista Township? (PLEASE ANSWER FAST!!)
Answer and explanation:
Find attached
(2x + 19)°
(3x + 8)°
How do I solve it?
The answer is 11° . U can see answer step by step in above picture.
Thank you ☺️☺️
Answer: X=11
(2x+19)=(3x+8)
-2x -2x
19=(x+8)
-8 -8
11=x
Which expression is equivalent to -2y+10x−2y+10x?
Answer:
-4y + 20x
Step-by-step explanation:
What number is 40% of 307
Input only whole numbers.
Answer:
123 is 40% of 307.
x2 - 10x + 21 = 0
How do you work this problem?
Answer:
x = 3, 7
Step-by-step explanation:
Step 1: Write equation
x² - 10x + 21 = 0
Step 2: Factor
(x - 7)(x - 3) = 0
Step 3: Find roots
x - 7 = 0
x = 7
x - 3 =0
x = 3