Answer: She purchased 8 sports drinks,
Step-by-step explanation:
Let be "d" the number of sports drinks that April purchased and "p" the number of slices of pizza that April purchased.
Set up a System of equations:
[tex]\left \{ {{d=p+3} \atop {2.25p+1.25d=21.25}} \right.[/tex]
In order to solve the System of equations you can use the Substitution Method:
1. Solve for "p" from the first equation:
[tex]d=p+3\\\\p=d-3[/tex]
2. Substitute it into the second equation:
[tex]2.25(d-3)+1.25d=21.25[/tex]
3. Finally, you must solve for "d" in order to find its value. You get that this is:
[tex]2.25(d-3)+1.25d=21.25\\\\2.25d-6.75+1.25d=21.25\\\\3.5d=21.25+6.75\\\\d=\frac{28}{3.5} \\\\d=8[/tex]
Answer:
Step-by-step explanation:
8 sport drinks
For the function f(x) = 3(x - 1)2 + 2, identify the vertex, domain, and range. (2 points)
1) The vertex is (1, 2), the domain is all real numbers, and the range is y > 2.
2) The vertex is (1, 2), the domain is all real numbers, and the range is y s 2.
O3) The vertex is (-1, 2), the domain is all real numbers, and the range is y 2 2.
4) The vertex is (-1, 2), the domain is all real numbers, and the range is y s 2.
Answer:
2) The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.
Step-by-step explanation:
Look at the photo below for the graph.
:)
Help! Rewrite the expression using the LCD
Answer:
1st one is A
2nd is B
EDGE
show work please~
there are 3 1/3 red cups of paint for every 1 1/3 cups of blue paint
for every 1 cup of blue paint, ___ cups of red paint are needed
for every 1 cup of red paint, ___ cup of blue paint is needed
for every 4 cups of red paint,___ cups of blue paint are needed
For every 1 cup of blue paint, [tex]\frac{10}{4}[/tex] cups of red paint are needed
For every 1 cup of red paint, [tex]\frac{4}{10}[/tex] cup of blue paint is needed
For every 4 cups of red paint, [tex]\frac{16}{10}[/tex] cups of blue paint are needed
Solution:
Given that, there are 3 1/3 red cups of paint for every 1 1/3 cups of blue paint
Therefore, ratio is
[tex]Red : blue = 3\frac{1}{3} : 1\frac{1}{3}\\\\Red : blue = \frac{10}{3} : \frac{4}{3}[/tex]
For every 1 cup of blue paint, ___ cups of red paint are neededLet "x" be the cups of red paint needed
Then we get,
[tex]\frac{10}{3} : \frac{4}{3}\\\\x : 1[/tex]
This forms a proportion
[tex]1 \times \frac{10}{3} = \frac{4}{3} \times x\\\\x = \frac{10}{4}[/tex]
Therefore, 10/4 cups of red are needed for 1 cup of blue
For every 1 cup of red paint, ___ cup of blue paint is neededLet "x" be the cups of blue paint needed
Then, we get
[tex]\frac{10}{3} : \frac{4}{3}\\\\1 : x[/tex]
This forms a proportion
[tex]\frac{10}{3} \times x = \frac{4}{3} \times 1\\\\x = \frac{4}{10}[/tex]
Thus, 4/10 cups of blue are needed for 1 cup of red paint
For every 4 cups of red paint,___ cups of blue paint are neededLet "x" be the cups of blue paint needed
Then, we get
[tex]\frac{10}{3} : \frac{4}{3}\\\\4 : x[/tex]
This forms a proportion
[tex]\frac{10}{3} \times x = \frac{4}{3} \times 4\\\\x = \frac{16}{10}[/tex]
Thus 16/10 cups of blue paint are needed for every 4 cups of red paint
The ratio of red paint to blue paint is 5:2. Therefore, for every 1 cup of blue paint, 2.5 cups of red paint are needed, for every 1 cup of red paint, 0.4 cup of blue paint is needed and for every 4 cups of red paint, 1.6 cups of blue paint are needed.
Explanation:The initial statement tells us that the ratio of red paint to blue paint needed is 3 1/3:1 1/3. Converting these mixed numbers into improper fractions, that ratio transforms to 10/3:4/3, which simplifies further to 5:2.
So, if you reduce it down:
For every 1 cup of blue paint, 5/2 or 2.5 cups of red paint are needed.For every 1 cup of red paint, 2/5 or 0.4 cup of blue paint is needed.For every 4 cups of red paint, 4*(2/5) or 1.6 cups of blue paint are needed.Learn more about Ratios here:https://brainly.com/question/32531170
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What is the solution to this polynomial equation? x3 + 2x2 - 4x - 8 = 0
Final answer:
The solution to the polynomial equation x³ + 2x² - 4x - 8 = 0 can be found by factoring, which yields the solutions x = -2 and x = 2.
Explanation:
The solution to the polynomial equation x³ + 2x² - 4x - 8 = 0 can be found by factoring, using synthetic division, or by using numerical methods such as graphing or using a calculator. Let's use factoring to find the solution.
We can begin by factoring out the greatest common factor, which is 1:
x³ + 2x² - 4x - 8 = (x + 2)(x² - 4)
We can further factor the quadratic term using the difference of squares:
(x + 2)(x + 2)(x - 2) = 0
So, the solutions to the equation are x = -2 and x = 2.
I'm solving for x, but I'm not confident with my work. I feel like x should be smaller than the other side (121) but I got a result much larger than it. Can someone help?
You have the ratios set up but you need to cross multiply everything:
(5x + 10) x 11 = 121 x 10
55x + 110 = 1210
Subtract 110 from both sides:
55x = 1100
Divide both sides by 55:
X = 1100 / 55
X = 20
what does AE equal?
Answer:
70
Step-by-step explanation:
BD is 1/2 the size of AE which is derived from the property of midpoints and the parallel lines.
Therefore if BD = 35, AE is twice as long.
AE = 70
The perimeter of the triangular park on the right is 16x-6. What is the missing length? The bottom side length is 5x+4 and the right most side is 2x-5
Answer:
[tex](9x-5)\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The perimeter of a triangle is the sum of the length of their three sides
so
[tex]P=a+b+c[/tex]
where
a,b,c are the length sides of the triangle
In this problem we have
[tex]P=(16x-6)\ units\\a=(2x-5)\ units\\b=(5x+4)\ units[/tex]
substitute and solve for the missing length
[tex](16x-6)=(2x-5)+(5x+4)+c\\c=(16x-6)-(2x-5)-(5x+4)\\c=(9x-5)\ units[/tex]
Mario says that the expression 4+3n² has four terms: 4, 3, n, and 2. Is he correct? explain.
_______________________________________________________________________________________________________________________________________
Mario says that the expression [tex]4+3n^2[/tex] has four terms: 4, 3, n, and 2. Mario is incorrect
Solution:
Given that the expression is:
[tex]4+3n^2[/tex]
Given that, Mario says that the above expression has four terms
But Mraio is incorrect
Because the given expression has two terms only
4 is one of the term
[tex]3n^2[/tex] is another term
So there are totally 2 terms only
A term can be a signed number, a variable, or a constant multiplied by a variable or variables
Here 3 is a constant multiplied by [tex]n^2[/tex]
So, [tex]3n^2[/tex] is one term
Each term in an algebraic expression is separated by a + sign or - sign
Thus there are two terms in mario expression
Does 5 go into 100 equally
There will be 25 party guests. 8
pieces of pizza dough come in a
package. How many packages do
I need to buy?
is 0.02 greater that 1/50
Answer:
No and yes.
Step-by-step explanation:
Turn both to percentages. Move the decimal point over two spots to the right, making 2%. Multiply the fraction by 2 to get 2/100. PerCENT. A dollar is 100 cents. The fraction as a percentage is 2%. They are equal.
Yes, 0.02 is greater than [tex]\( \frac{1}{50} \)[/tex].
Explanation:
0.02 can be represented as [tex]\( \frac{2}{100} \)[/tex], which simplifies to [tex]\( \frac{1}{50} \)[/tex].
Since [tex]\( \frac{2}{100} \)[/tex] is greater than [tex]\( \frac{1}{50} \)[/tex], it follows that 0.02 is greater than [tex]\( \frac{1}{50} \)[/tex].
Step-by-step explanation:
1. Convert 0.02 to a fraction: [tex]\( 0.02 = \frac{2}{100} \)[/tex].
2. Compare [tex]\( \frac{2}{100} \)[/tex] with [tex]\( \frac{1}{50} \)[/tex].
3. Simplify [tex]\( \frac{2}{100} \) to \( \frac{1}{50} \)[/tex].
4. Since [tex]\( \frac{1}{50} \)[/tex] is smaller than [tex]\( \frac{1}{50} \)[/tex], we conclude that 0.02 is greater than [tex]\( \frac{1}{50} \)[/tex].
What is the least common multiple of 8, 6, 9, and 5?
Answer:
LCM= 360
Steps:
8=2*2*2
6=2*3
9=3*3
5=1*5
2*2*2*3*3*5
8*9=72*5=360
Answer:
Step-by-step explanation:
The ratio of girls to boys in the 6th grade is to 6to7 how many girls are there if there are 364total students
Answer:
168 girls.
Step-by-step explanation:
There are a total of 6 + 7 = 13 'parts'.
So one part = 364 / 13 = 28.
So the number of girls = 6 * 28
= 168.
A circle with radius of 6 cm sits inside a circle with radius of 9 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
Equation for the area of a circle- π r²
The 2 radiuses are 6 and 9.
6 squared is 36 and 9 squared is 81.
The smaller one is 36π and the larger one is 81π.
The difference between them is the area of the shaded region.
81π - 36π = 45π
Use 3.14 for π.
45 x 3.14 = 141.3 u²
Hope this helps!
A circle is a curve sketched out by a point moving in a plane. The area of the shaded region is equal to 141.37 cm²
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The area of the shaded region can be found by subtracting the area of the larger circle from the area of the smaller circle. Therefore, the area of the shaded region is,
Area = π(9 cm)² - π(6 cm)²
= 141.37 cm²
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The sum of two numbers is 39. The smaller number is 11 less than the larger number. What are the numbers
Answer:
14 and 25
Step-by-step explanation:
x = smaller number
y = larger number
x + y = 39
x = y - 11
now we sub
y - 11 + y = 39
2y - 11 = 39
2y = 39 + 11
2y = 50
y = 50/2
y = 25 <=== larger number
x = y - 11
x = 25 - 11
x = 14 <==== smaller number
The problem can be solved by setting up and solving two algebraic equations. The two numbers in question are 25 and 14.
Explanation:The subject of this problem is algebra. To solve it, we can set up two equations based on the problem's statements, and then solve those equations.
First, we know that the sum of two numbers is 39, so we can write that as: x + y = 39 (Equation 1).
Second, we know that the smaller number is 11 less than the larger number. Assuming x is the larger number and y is the smaller one, we can write this as: y = x - 11 (Equation 2).
To solve these equations in parallel, insert Equation 2 into Equation 1, that results in: x + (x - 11) = 39. Solving this equation simplifies to 2x = 50, so x = 25. Substitute x = 25 in Equation 2, we get: y = 25 - 11 = 14. So, the two numbers are 25 and 14.
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In an orchard, there are 14 apple trees, 26 orange trees, and a cherry tree. What is the ratio of apple trees to cherry trees?
The ratio of apple trees to cherry tree is 14:1.
In the orchard, there are 14 apple trees and 1 cherry tree.
To find the ratio of apple trees to cherry trees, we simply divide the number of apple trees by the number of cherry trees, yielding 14:1.
This ratio indicates that for every cherry tree in the orchard, there are 14 apple trees.
Ratios express the relationship between different quantities, providing a comparative measure.
In this case, it illustrates the abundance of apple trees in relation to the singular cherry tree, highlighting the disparity in their numbers within the orchard.
The theoretical probability of choosing a red grape from a
bag of grapes is 2/9. There are 8 red grapes in the bag. How
many grapes are in the bag?
Answer:36
Step-by-step explanation: if 2 out of 9 or red and there are 8 red that means that divide 8 by to get 4 * 9 + 36
By using the theoretical probability formula, the total number of grapes in the bag is 36
ProbabilityFrom the question, we are to determine how many grapes are in the bag
Let the total number of grapes in the bag be x
From the probability formula,
[tex]P(A) = \frac{Number\ of\ favorable \ outcomes \ to \ A }{Total\ number\ of\ possible\ outcomes}[/tex]
Let R represent red grapes,
Then,
[tex]P(R) = \frac{Number\ of\ favorable \ outcomes \ to \ R }{Total\ number\ of\ possible\ outcomes}[/tex]
From the given information,
P(R) = 2/9
Number of favorable outcomes to R = 8
Therefore,
[tex]\frac{2}{9} = \frac{8}{x}[/tex]
2x = 9 × 8
2x = 72
x = 72 / 2
x = 36
Hence, the total number of grapes in the bag is 36.
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Helpp Image attached
The area of new circle is 5625π square inches.
Step-by-step explanation:
Given,
Area of circular plate = 625π square inches
Let,
Radius = r
Area of circular plate = πr²
[tex]\pi r^2=625\pi[/tex]
Dividing both sides by π
[tex]\frac{\pi r^2}{\pi}=\frac{625\pi}{\pi}\\\\r^2=625[/tex]
Taking square root on both sides
[tex]\sqrt{r^2}=\sqrt{625}\\r=25[/tex]
The radius of plate is 25 inches.
When the radius is tripled = 25*3 = 75 inches
New area of circle = πr²
New area of circle = [tex]\pi (75)^2\\[/tex]
New area of circle = [tex]5625\pi[/tex] square inches
The area of new circle is 5625π square inches.
Keywords: circle, area
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Is d(10 + 20) equivalent to d x 10 + 20 X d?
Use a property, or properties, to explain. Please help : ‘ 0
Pleas do step by step!!! If you can’t that’s fine but if you’d like to p l e a s e
Answer:
Yes, it is.
Step-by-step explanation:
d(10 + 20) is equivalent to d * 10 + 20 * d. This can be proved with the distributive property, which states that a(b + c) = ab + ac.
Using the distributive property of multiplication over addition and the commutative property of multiplication, it is proven that d(10 + 20) is equivalent to d × 10 + 20 × d.
The question asks if the expression d(10 + 20) is equivalent to d × 10 + 20 × d, using properties of mathematics to explain.
First, let's simplify the expressions using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Applying this property, d(10 + 20) becomes d × 10 + d × 20.
Comparing d × 10 + d × 20 with d × 10 + 20 × d, we see they are indeed the same because multiplication is commutative—meaning the order of the operands does not change the result. Therefore, d(10 + 20) is equivalent to d × 10 + 20 × d.
Urgent. REALL URGENT. HHHHHHHHHHEEEEEEEEEEEEEEELLLLLLLLLLPPPPPPPPPPPPPPP MMMMMMMMMEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Subtract. 1.2 – (–7.8) 6.6 –6.6 9 –9
Option c : 9 is the answer.
Explanation:
The expression is [tex]1.2-(-7.8)[/tex]
We need to determine the subtracted value of the expression.
From the expression we can see that the expression contains two negative signs.
To simplify the expression, we know that, When we multiply two negative numbers then the product is always positive.
This means [tex](-) *(-) = +[/tex]
Thus, the expression can be written as
[tex]1.2+7.8[/tex]
Adding the two numbers, we get,
[tex]1.2+7.8=9[/tex]
Thus, the value of the expression is 9.
Hence, Option c is the correct answer.
Solve the equation. Write solutions using integers or simplified fractions. 5−(y−3)=14−4(y+2)
of course the answer is Y=. - 2/3
Answer:
-2/3
Step-by-step explanation:
5 − (y−3)=14− 4 (y+2)
Expand
5 - y + 3 = 14 - 4y - 8
Collect like terms
-y + 4y = 14 - 8 - 5 -3
(-1 + 4)y = - 2
3y = -2
Divide both sides by 3
3y/3 = -2/3
y = -2/3
I hope this was helpful, Please mark as brainliest
What is the product of 1/2×32
Answer:
The product of 1/2*32 is taking 32/2
Half of 32 is 16
Product of 1/2*32=16
Hope this helps ;)
Answer:
16
Step-by-step explanation:
when you multiply buy a fraction you will end up with half of the one of the things you were multiplying this means that half of 32 is 16 so 16 is your answer if you need help on understanding how to multiply fractions think of it like this
1/2 x 32= 32 divided by 2
both ways will give you the same answer
hope this helps better your understanding
p² +6r - 27
factoring quadratics
Step-by-step explanation:
look at the picture shown
If you build a fence around garden that measures 10 x 15
feet; how many feet of chain link fence will you need
Answer:
We will need 50 feet of chain link fence to build a fence around the garden.
Step-by-step explanation:
Measurements of the garden = 10 * 15 feet
How many feet of chain link fence will you need to build a fence around the garden?
For answering the question, let's calculate the perimeter of the garden, this way:
Perimeter = 2 Width + 2 Length
Replacing with the values we have:
Perimeter = 2 * 10 + 2 * 15
Perimeter = 20 + 30
Perimeter = 50 feet
8 plus 4 times a number is greater than 5 times the number
Answer:
x<8
Step-by-step explanation:
4x+8>5x
8>5x-4x
8>x
A semi-truck can hold 8,500 pounds of cargo. How many tons can it hold?
Answer:4.25 tons
Step-by-step explanation:
Can someone please help first answer gets Brainlist
Answer:
0.45
Step-by-step explanation:
Find the value of the expression 21 - 2a if a = 3
Answer:
15
Step-by-step explanation:
Substitute in the values
2 X 3 = 6
21 - 6 =15
To find the value of 21 - 2a when a = 3, substitute 3 for a and simplify to get 21 - 6, which equals 15.
Explanation:The student has asked to find the value of the expression 21 - 2a given that a = 3. To solve for the expression, substitute the value of a into the expression:
21 - 2(3) = 21 - 6 = 15.
Therefore, the value of the expression when a is 3 is 15.
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Which statement describes the congruent triangles?
Triangles W Z X and Z Y X. Sides W Z and X Y are congruent, sides Z Y and W X are congruent, and sides Z X are congruent.
Triangle W X Z is congruent to triangle Y Z X
Triangle W X Z is congruent to triangle Y X Z
Triangle W X Z is congruent to triangle X Y Z
Triangle W X Z is congruent to triangle Z Y X
Answer:
Triangle W X Z is congruent to triangle Z Y X
Step-by-step explanation:
2 triangles are said to be congruent when all the corresponding sides of the angle and the interior angles are congruent .The two triangle are said to be the mirror image of each other.In the simple case above the two triangles WXZ and ZYX are congruent because every corresponding side has the same length, and every corresponding angle has the same measure.
Answer:
its acctually Triangle W X Z is congruent to triangle Y Z X
Step-by-step explanation:
what ordered pair is a solution for y-4=7(x-6)
Answer: People don't get confused by this guy the answer is basically clear its neither trust me guys.