Two people bought 48 oranges pat bought five times as many as chris. how many oranges did chris buy
Chris bought [tex]8[/tex] Oranges.
What is reasoning ?Reasoning is the process of using existing knowledge to draw conclusions, make predictions, or construct explanations.
We have,
Chris and Pat bought [tex]48[/tex] oranges.
Let,
Oranges bought by Pat [tex]= x[/tex]
Oranges bought by Chris [tex]= y[/tex]
Now,
According to the question;
As Pat bought five times as many as bought by Chris.
i.e.
[tex]x=5y[/tex] [tex]........(i)[/tex]
And,
Chris and Pat bought [tex]48[/tex] oranges.
i.e.
[tex]x+y=48[/tex] [tex]........(ii)[/tex]
Now,
Substituting value of [tex]x[/tex] from equation [tex](i)[/tex] in equation [tex](ii)[/tex];
We get,
[tex]5y+y=48[/tex]
[tex]6y=48[/tex]
[tex]y=8[/tex]
Now,
Substituting value of [tex]y[/tex] in equation [tex](i)[/tex];
[tex]x=5y[/tex]
[tex]x=5*8[/tex]
[tex]x=40[/tex]
Hence, we can say that Chris bought [tex]8[/tex] Oranges and Pat bought [tex]40[/tex] Oranges.
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Simply x squared over Y plus Y squared over X all over Y squared minus XY plus X squared
The ratio of the radii of two circles is 4:5. What is the ratio of the circumferences of the two circles?
Peter wants to put 2 coats of paint on both the inside and outside of the walls. There are 5 walls, each side having 45 ft2 of paintable surface. A gallon of paint covers x ft2. Explain how to write an expression to represent the number of gallons of paint Peter needs.
To calculate the number of gallons Peter needs, multiply the surface area of one side of the wall (225 ft2) by 2 for both sides, and then by 2 again for two coats, totaling 900 ft2. Then divide 900 ft2 by the coverage per gallon x to get the expression 900 / x.
To determine the number of gallons of paint Peter needs, we must first calculate the total paintable surface for both the inside and outside of the walls and then factor in the two coats of paint. Peter has 5 walls, with each side having 45 ft2 of paintable surface, so the total paintable surface for one side is 5 walls imes 45 ft2/wall = 225 ft2. Since he wants to paint both sides, we double this to get 450 ft2. For two coats, we need to double this again, resulting in 900 ft2. Now, if a gallon of paint covers x ft2, the number of gallons needed is total square footage divided by coverage per gallon, which is 900 ft2 / x ft2/gallon.
Therefore, the expression to represent the number of gallons Peter needs is 900 / x.
PLEASE HELP ME
The base of a triangle measures (2x + 7) units and the height measures (4x + 6) units. Part A: What is the expression that represents the area of the triangle? Show your work to receive full credit. (4 points) Hint: Area = 0.5bh Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Sparky had room for 16 rows in his garden. He planted 3 rows of tomatoes for every 5 rows of onions. How many rows of tomatoes did he plant?
Answer: 6 rows - tomatoes
Step-by-step explanation:
What number is between these 2 numbers 6,534 and 6,565
Choose the graph that matches the following system of equations 4x +2y=-2 x-3y=24
The solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.
What is system of equations?"It is a finite set of equations for which we find the solution."
For given question,
We have been given a system of equations.
4x +2y = -2 ................(i)
x - 3y = 24 ................(ii)
From equation (ii),
x = 24 + 3y .............(iii)
Substitute this value of x in equation (i)
⇒ 4(24 + 3y) +2y = -2
⇒ 96 + 12y + 2y = -2
⇒ 14y = -98
⇒ y = -7
Substitute this value of y in equation (iii)
⇒ x = 24 + 3(-7)
⇒ x = 24 - 21
⇒ x = 3
Therefore, the solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.
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Mia is three years older than twice for Sister Brooke’s age. The sum of their ages is less than 30. What is the greatest age Brooke could be? 7, 10, 8, or 9?
Answer:
the greatest age is 8
Step-by-step explanation:
i took the test
Consider the diagram and the paragraph proof below.
Given: Right △ABC as shown where CD is an altitude of the triangle
Prove: a2 + b2 = c2
Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Which is the last sentence of the proof?
A. Because f + e = 1, a2 + b2 = c2.
B. Because f + e = c, a2 + b2 = c2.
C. Because a2 + b2 = c2, f + e = c.
D. Because a2 + b2 = c2, f + e = 1.
In the right angle triangle ABC [tex]\rm a^2+b^2=c^2[/tex] because (e + f = c) and this can be determined by using the Pythagorean theorem.
Given :
Right △ABC is shown where CD is an altitude of the triangle.
The following steps can be used in order to prove that [tex]a^2+b^2=c^2[/tex]:
Step 1 - According to the Pythagorean theorem, the sum of the square of the shorter side is equal to the square of the longer side.
Step 2 - The Pythagorean theorem is given below:
[tex]\rm H^2=B^2+P^2[/tex] --- (1)
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 3 - So, according to the given diagram:
H = e + f
B = a
P = b
Step 4 - Substitute the values of the known terms in the expression (1).
[tex]\rm a^2+b^2=(e+f)^2[/tex]
Step 5 - According to the diagram, (e + f = c). So, the above expression becomes:
[tex]\rm a^2+b^2=c^2[/tex]
Therefore, the correct option is C).
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Point H is the circumcenter of triangle DEF.
Which must be true? Check all that apply.
Point H is the center of the circle that passes through points D, E, and F.
Point H is the center of the circle that passes through points L, M, and N.
HE=HD
LH=NH
MEH NEH
DLH FNH
Answer:
the correct answers are:
a. ) Point H is the center of the circle that passes through points D, E, and F.
c. ) HE=HD
Point H, being the circumcenter, ensures it is the center of the circle through D, E, and F and that HE equals HD; other statements regarding unrelated points cannot be confirmed.
Explanation:If Point H is the circumcenter of triangle DEF, then the following must be true:
Point H is the center of the circle that passes through points D, E, and F since the circumcenter is equidistant to all vertices of the triangle, forming the circumscribed circle.HE=HD since, by the definition of a circumcenter, it is equidistant from all vertices of the triangle.The other statements regarding points L, M, N cannot be determined to be true without additional information, as they are not related to triangle DEF and its circumcenter directly.
In summary, Point H as the circumcenter ensures it is at the center of the circumscribable circle through D, E, and F, and that HE equals HD.
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What is radical 64/8 simplified
Answer:
2^(6-3) = 2^3 = 8
Step-by-step explanation:
To simplify radical 64/8
We will express 64 and 8 in powers of 2
64 = 2×2×2×2×2×2= 2^6
8 = 2×2×2=2^3
From the law of indices,
a^5 / a^3 = a^ (5-3) = a^2
Applying this law of indices to the given radical,
64/8 = 2^6/ 2^3
= 2^(6-3)
= 2^3 = 8
Also, we can try another way. since
64 = 2×2×2×2×2×2= 2^6
8 = 2×2×2=2^3
64/8 = 2×2×2×2×2×2 / 2×2×2
2×2×2 cancels out 2×2×2 and
It remains 2×2×2 = 8
So which ever way we do it,
radical 64/8 simplified is 2^3 = 8
A=12h(a+b)
Solve for h.
A. h=2Aa+b
B.h=a+b2A
C.h=A2(a+b)
D.h=2(a+b)A
Answer:
h = 2A/a+b
or 1st answer
Step-by-step explanation:
Explain how to find a general rule for the product (a+b)^3.
If k is the midpoint of hj and hk =x+6 and hj =4x-6 then What does kj equal
The value of kj is 15.
It is required to find the value of kj.
What is midpoint ?The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Given that:
k is the midpoint of hj and hk.
hk=x+6
hj=4x-6
We know that midpoint cuts the segment hj in 2 equal parts that means hk=kj and hk+kj=hj
hk+hk=hj
2hk=hj
2hk=hj
2 (x+6)=(4x-6)
2x+12=4x-6
12+6=4x-2x
18=2x
Divide 2 on both sides, we get
18/2=2x/2
9=x
hk=kj=x+6=(9)+6=15
kj=15
Therefore, the value of kj is 15.
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How many solutions are there to the equation below? -46 = 3x + 7x
1. Given △PQR≅△STU, m∠R=80°, and m∠S=70°, what is the measure of ∠Q?
2. What is m∠AEB?
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A table is on sale for $403, which is 38% less than the regular price. what is the regular price
The regular price of the table is $650.
The student has asked to find the regular price of a table that is currently on sale for $403, which is 38% less than the regular price. To find the regular price, we can consider the sale price to be 62% (100% - 38%) of the regular price. Let's denote the regular price as R. Thus, we can set up the equation 0.62 * R = $403. Solving for R, we divide both sides by 0.62 to find the regular price:
R = $403 / 0.62
R = $650
Therefore, to find the regular price of a table on sale for $403 at 38% off, we determine that the sale price is 62% of the regular price. By dividing the sale price by 0.62, we discover that the regular price is $650.
M= x+n over p solve for x
For dinner, Abelita chooses the Italian salad that costs $3.99 before tax, and Franco chooses the fettuccini alfredo that costs $7.17 before tax. If the sales tax is 5 percent, explain how to find the total cost for their dinner.
Answer: The total cost of the dinner is found by adding the two prices together. Then this sum is multiplied by 1.05, which is 100% + 5%, to get a cost of $11.72.
Step-by-step explanation:
This is the sample answer.
To calculate the total cost including sales tax, convert the percent tax rate to a decimal, multiply it by the meal's cost, and add it to the original cost. In this case, a 5 percent tax on a $3.99 salad and a $7.17 fettuccini alfredo results in a final total cost of $11.72.
Explanation:Calculating Total Cost with Sales TaxFirst, to find the sales tax for Abelita's Italian salad and Franco's fettuccini alfredo, you convert the tax rate from a percent to a decimal. The tax rate is 5 percent, which as a decimal is 0.05. Next, add the cost of the Italian salad ($3.99) and fettuccini alfredo ($7.17) to get the total cost before tax, which is $11.16. Multiply this total by the tax rate to find the amount of sales tax: $11.16 × 0.05 = $0.558. Round this to the nearest cent, which gives us $0.56.
The next step is to add the sales tax to the total cost before tax to find the final total cost. Thus, $11.16 (meal cost) + $0.56 (sales tax) = $11.72. Therefore, the total cost for their dinner, including the 5 percent sales tax, is $11.72.
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a farmer has 268 cows. each cow has either one or two calves. if there are 335 calves in total, what fraction of the cows have two calves
The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2ℓ + 2w to find the length of the frame if the width is 19 inches.
The length of the picture frame is 17 inches, which is found by substituting the given width and perimeter into the perimeter formula and solving for the length.
The question asks to calculate the length of a picture frame using the perimeter formula P = 2l + 2w, where P stands for the perimeter, l is the length, and w is the width. Given that the width (w) is 19 inches and the perimeter (P) is 72 inches, we can substitute these values into the formula:
P = 2l + 2w
72 = 2l + 2(19)
72 = 2l + 38
2l = 72 - 38
2l = 34
l = 34 / 2
l = 17 inches
So, the length (l) of the frame is 17 inches.
(3p3q)^3/4
What is the expression in radical form?
Answer:
[tex]p^2\sqrt[4]{27pq^3}[/tex]
Step-by-step explanation:
[tex](3p^3q)^\frac{3}{4}[/tex]
To get radical form , remove the fractional exponent
[tex](a^m)^n=a^{mn}[/tex]
multiply the exponent 3/4 inside the parenthesis
[tex]3^\frac{3}{4} p^{3 \cdot \frac{3}{4}} q^\frac{3}{4}[/tex]
[tex]3^\frac{3}{4} p^{\frac{9}{4}} q^\frac{3}{4}[/tex]
[tex]\sqrt[4]{27} \cdot p^2\sqrt[4]{p} \cdot \sqrt[4]{q^3}[/tex]
[tex]p^2\sqrt[4]{27pq^3}[/tex]
The radical form of the expression [tex]\rm \left (3p \times 3q \right )^{\frac{3}{4}}[/tex] will be [tex]\left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex].
How do convert the exponent into the simplest radical form?If the power of the variable "a" is b/c. Then the simplest radical form of the expression will be
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
[tex]\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}[/tex]
The expression is given below.
[tex]\rm \rightarrow \left (3p \times 3q \right )^{\frac{3}{4}}[/tex]
We know that (ab)ⁿ = aⁿ × bⁿ. Then the expression will be
[tex]\rm \rightarrow \left (3^{\frac{3}{4}} \times p^{\frac{3}{4}} \times 3^{\frac{3}{4}} \times q^{\frac{3}{4}} \right )[/tex]
Simplify the expression in the radical form. Then we have
[tex]\rm \rightarrow \left (3^{\frac{3}{2}} \times p^{\frac{3}{4}} \times q^{\frac{3}{4}} \right )\\\rightarrow \left ( \sqrt{3^3} \times \sqrt[4]{p^3} \times \sqrt[4]{q^3} \right ) \\\rightarrow \left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex]
The radical form of the expression [tex]\rm \left (3p \times 3q \right )^{\frac{3}{4}}[/tex] will be [tex]\left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex].
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Jason knows that AK←→⊥KB←→ , AK←→∥EF←→ , and AK←→∥CB←→ .
Which other facts can Jason conclude are true?
Select each correct answer.
m∠EJM=90°
KB←→⊥CB←→
m∠JFB=90°
KB←→∥DM←→−
The corresponding angles between parallel lines and their common transversal are congruent
The other facts Jason can conclude are true are:
1) [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
2) m∠JFB = 90°
The reason why the above selected options are correct are:
The relationships between the lines Jason knows are:
Segment AK is perpendicular to KB: [tex]\underset{AK}{\leftrightarrow}[/tex] ⊥ [tex]\underset{KB}{\leftrightarrow}[/tex]
Segment AK is parallel to EF: [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex]
Segment AK is parallel to CB: [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex]
m∠DKF = 90°
The required information:
The facts that Jason can conclude are true
Method:
Find the other relationships between the lines based on the relationships Jason knows
Solution:
We have;
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{EF}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex], and [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{EF}{\leftrightarrow}}[/tex] ║ [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex]
The relationship, [tex]\underset{EF}{\leftrightarrow}[/tex] ⊥ [tex]\underset{KB}{\leftrightarrow}[/tex], gives m∠JFB = 90°
Therefore;
The correct options for the facts Jason can conclude are;
1) [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
2) m∠JFB = 90°
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Which is the graph of a quadratic equation that has a positive discriminant?
Answer:
D. Last gragh
Step-by-step explanation:
Sum or difference for (6xy + 2y + 6x) + (4xy -x)
What is the value of a 3 - b 2 for a = 3 and b = ? A. 8 B. 8 3/4 26 3/4 26
Answer:
probably 26
Step-by-step explanation:
Allison practices her violin for at least 12 hours per week. She [practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her goal?
Please show the Inequality
Answer:
[tex]3+\frac{3}{4}x\geq 12[/tex]
Step-by-step explanation:
Given,
The number of hour he already practiced in this week = 3,
Also, she practices for three fourth of an hour each session,
If x be the number of remaining session,
So, the additional number of hours he practiced in this week = [tex]\frac{3x}{4}[/tex]
Thus, the total number of hours he practiced in this week = [tex]3+\frac{3x}{4}[/tex]
According to the question,
Total number of hours ≥ 12 hours
[tex]\implies 3+\frac{3x}{4}\geq 12[/tex]
Which is the required inequality.
If p(x) = 2x2 – 4x and q(x) = x – 3, what is (poq)(x)
If a cup of cereal has 12 grams of fiber, which is 40% of the recommended daily amount. What is the recommended daily amount?