Answer:
The solutions are 3 and -8
Step-by-step explanation:
2x² + 10x - 48 = 0
Divide both sides by 2:
x² + 5x - 24 = 0
Factor using AM method (What two numbers add to 5 and multiply to -24?):
(x - 3)(x + 8) = 0
Set both expressions equal to 0:
x - 3 = 0 x + 8 = 0
Solve both equations for x:
x = 3 x = -8
The solutions to the quadratic equation 2x² + 10x - 48 = 0 are x = 3 and x = -8.
Explanation:To find the solutions to the quadratic equation 2x2 + 10x - 48 = 0, we can use the quadratic formula: x = (-b ± √(b2 - 4ac)) / (2a), where a, b, and c are the coefficients from the equation. In this case, a = 2, b = 10, and c = -48. Plugging these values into the formula, we have: x = (-10 ± √(102 - 4(2)(-48))) / (2(2)). Simplifying further, x = (-10 ± √(100 + 384)) / 4. Continuing to simplify, x = (-10 ± √484) / 4, which becomes x = (-10 ± 22) / 4. Finally, we have x = (-10 + 22) / 4 and x = (-10 - 22) / 4, giving us x = 3 and x = -8 as the two solutions to the quadratic equation.
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1.) Three fourths of a number is negative 12. What is the number? Represent your approach to
solving this problem in as many ways as possible.
Answer:
The number is -16.
Step-by-step explanation:
3/4x=-12
x=-12/(3/4)
x=(-12/1)(4/3)
x=-48/3
x=-16
The question attached please.
One adult ticket costs £11 and one child ticket costs £8.5
Step-by-step explanation:
Let,
Adult ticket = a
Child ticket = c
According to given statement;
3a+4c=67 Eqn 1
5a+6c=106 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(3a+4c=67)\\15a+20c=335\ \ \ Eqn\ 3[/tex]
Multiplying Eqn 2 by 3;
[tex]3(5a+6c=106)\\15a+18c=318\ \ \ Eqn\ 4[/tex]
Subtracting Eqn 4 from Eqn 3
[tex](15a+20c)-(15a+18c)=335-318\\15a+20c-15a-18c=17\\2c=17\\[/tex]
Dividing both sides by 2
[tex]\frac{2c}{2}=\frac{17}{2}\\c=8.5[/tex]
Putting c=8.5 in Eqn 1
[tex]3a+4(8.5)=67\\3a+34=67\\3a=67-34\\3a=33[/tex]
Dividing both sides by 3;
[tex]\frac{3a}{3}=\frac{33}{3}\\a=11[/tex]
One adult ticket costs £11 and one child ticket costs £8.5
Keywords: Linear equation, subtraction
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Order from least to greatest
Look at picture.
WILL MARK AS BRAINIEST IF RIGHT!
Answer:
7.5% < 7.49 < [tex]7\frac{49}{50}[/tex]
Step-by-step explanation:
To make this easier to look at, first you change them into the same form. Let us make them all into fractions and compare:
7.49 as a fraction is [tex]7\dfrac{49}{100}[/tex]
[tex]7\dfrac{49}{50}[/tex] is already a fraction so let's leave it first.
7.5% in fraction form is [tex]\dfrac{75}{1000}[/tex]
Now knowing this, we can already say that 7.5% is already the least comparing it to the others.
Now we compare the two:
[tex]7\dfrac{49}{100} < 7\dfrac{49}{50}[/tex]
If we make them into similar fractions:
[tex]7\dfrac{49}{50} = 7\dfrac{98}{100}\\\\Then\\\\7\dfrac{49}{100}<7\dfrac{98}{100}[/tex]
A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0.50, while each cylindrical container costs $0.75.
Which packaging should the company use to minimize cost? Explain.
To minimize the cost, the packaging that should be used is the rectangular prism boxes.
How to solve the cost minimizationFrom the complete information, the pencils needed is 2400. The prism can hold 60 pencils. Therefore, the number of prisms needed will be:
= 2400/60 = 40 prisms
The total cost for the prism will be:
= $0.50 × 40
= $20
The cylinder can hold 80 pencils. Therefore, the numbers needed will be:
= 2400/80
= 30
The cost of the cylinders will be:
= 30 × $0.75
= $22.50
Therefore, it implies that to minimize the cost, the packaging that should be used is the rectangular prism boxes.
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The company should use rectangular prism boxes, as they require fewer units and incur lower total cost.
To minimize cost, we need to find out which packaging option, between the rectangular prism box and the cylindrical container, requires fewer units and hence incurs lower total cost.
Step 1 :First, let's calculate how many units of each packaging option are needed to package 2,400 pencils:
1. **Rectangular Prism Box:**
Each box holds 60 pencils.
Number of boxes needed [tex]\(= \frac{2400}{60} = 40\)[/tex]
2. **Cylindrical Container:**
Each container holds 80 pencils.
Number of containers needed [tex]\(= \frac{2400}{80} = 30\)[/tex]
Step 2 :Now, let's calculate the total cost for each option:
1. **Cost for Rectangular Prism Boxes:**
Number of boxes: 40
Cost per box: $0.50
Total cost: [tex]\(40 \times \$0.50 = \$20\)[/tex]
2. **Cost for Cylindrical Containers:**
Number of containers: 30
Cost per container: $0.75
Total cost: [tex]\(30 \times \$0.75 = \$22.50\)[/tex]
Comparing the total costs, we can see that using the rectangular prism boxes incurs a lower cost $20 compared to using the cylindrical containers $22.50.
The reason for the lower cost with rectangular prism boxes is that each box holds fewer pencils (60) compared to cylindrical containers (80). Therefore, even though the cost per unit for the cylindrical containers is lower ($0.75) compared to the rectangular prism boxes ($0.50), the higher number of units required for cylindrical containers results in a higher total cost.
Therefore, to minimize cost, the company should use the rectangular prism boxes for packaging the pencils.
Laws of sine and cosine
Law of Sines
[tex]\displaystyle \frac{sin∠C}{c} = \frac{sin∠B}{b} = \frac{sin∠A}{a} \\ \\ \frac{sin\:40°}{5} = \frac{sin∠C}{7} → \frac{7sin\:40°}{5} = sin∠C → 0,8999026535... = sin∠C → 64,14527443...° = sin^{-1}\:0,8999026535... \\ \\ 64° ≈ m∠C[/tex]
As you can see, the inverse function had to be used towards the end, or the answer would have been thrown off.
I am joyous to assist you at any time.
.
Use the Distributive Property to simplify the expression.
3 × 72
Step-by-step explanation:
(3 × 70) + (3 × 2)
210 + 6 = 216
At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43. Tori bought two pairs of gloves and two hats for $30. Find the prices of the hats and gloves.
Answer:
The price of the glove is $8.5 and the price of the hat is $6.5.
Step-by-step explanation:
2x+4y=43
2x+2y=30
---------------
2x+4y=43
x+y=15
--------------
x=15-y
2(15-y)+4y=43
30-2y+4y=43
30+2y=43
2y=43-30
2y=13
y=13/2
x+13/2=15
x=15-13/2
x=30/2-13/2=17/2
x=17/2, y=13/2.
The price of the glove is $8.5 and the price of the hat is $6.5.
Study the steps used to solve the equation. Given: c/2-5=7 Step 1: c/2-5+5=7+5 Step 2: c/2+0=12 Step 3: c/2=12 Step 4: 2 (c/2)=12(2) Step 5: c=24 Choose the property that justifies each step of the solution.
Answer:
step 1: addition property of equality
step 2: additive inverses
step 3: additive identity
step 4: multiplication property of equality
Step-by-step explanation:
edg 2020
Answer:
step 1: addition property of equality
step 2: additive inverses
step 3: additive identity
step 4: multiplication property of equality
Step-by-step explanation:
please solve with working much appreciated
Answer:
5 cm
Step-by-step explanation:
What you have there is an equilateral triangle. An equilateral triangle is a triangle that has sides with equal lengths and interior angles are equal as well. So if all angles are equal in a triangle, then that means that this is an equilateral triangle. So we can say that if one side of this triangle is 5cm
then the n would also be equal to 5cm.
A grocery store clerk put only packages of flour tortillas and packages of corn tortillas on the shelf. The ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16.
Which number could be the number of packages of flour tortillas the clerk put on the shelf?
The number of flour tortilla packages could be 9 or any number that results from subtracting 7 (corn tortilla packages) from a multiple of 16 (total packages). It's necessary to keep the ratio between corn tortillas and total packages at 7:16.
Explanation:The subject of this question refers to the mathematical concept of ratios. Given the ratio of corn tortillas to the total number of packages is 7:16, this means that out of every 16 packages, 7 are corn tortillas. Therefore, the remaining packages must be flour tortillas.
To figure out the possible number of packages of flour tortillas, you would subtract the number of corn tortilla packages (7) from the total (16). So, there could be 9 packages of flour tortillas on the shelf.
Please note that this ratio can apply to any multiple of 16. As long as the number of packages is divisible by 16, you can use the ratio to find the number of flour tortilla packets. For example, if the total number of packages was 32, you could have 18 packages of flour tortillas (since 32-14=18) and so on.
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What is the result of subtracting the second equation from the first?
2
x
+
7
y
=
−
8
2
x
−
5
y
=
−
1
2x
See in the explanation:
Explanation:Here we have the following system of linear equations in two variables:
[tex](1) \ 2x+7y=-8 \\ \\ (2) \ 2x-5y=-1[/tex]
So if you graph these two equations you will get two lines with different slopes. The question is:
What is the result of subtracting the second equation from the first?
So this can be written mathematically as:
[tex]2x+7y-(2x-5y)=-8-(-1) \\ \\ Breaking \ parentheses: \\ \\ 2x+7y-2x+5y=-8+1 \\ \\ \\ Combining 'like 'terms: \\ \\ 2x-2x+7y+5y=-7 \\ \\ 12y=-7 \\ \\ y=-\frac{7}{12}[/tex]
So the result of subtracting the second equation from the first is:
[tex]12y=-7[/tex]
and from this we can calculate y.
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Edurado started a business selling sporting goods.He spent $ 7500 to obtain hos merchandise , and it cost him $300 per week for general expenses.He earns $850 per week in sales. What is the minimum number of weeks Edurado will take to make a profit?
Answer:
C) It will take 14 weeks for Edurado to make a profit.
Step-by-step explanation:
The money spent on obtaining the merchandise = $ 7500
The general expense per week = $300
Let us assume Eduardo has to work for N weeks to break Even.
So, the general expense in N weeks = N x( Expense per week)
= N x ( $300) = 300 N
So, the total expense in N weeks = Money spent on merchandise + general expense
or, the TOTAL EXPENSE = $ 7500 + 300 N .... (1)
Now, the earning per week = $850
So, the total earning in N weeks = N x ( Earning in 1 week) = N x ( $850)
or, the TOTAL EARNING = 850 N .... (2)
Now, for N weeks ,
TOTAL EXPENSE = TOTAL EARNING
⇒ $7500 + 300 N = 850 N
or, 7500 = 850 N - 300 N = 550 N
⇒ N = 7500/550 = 13.63
So, number of weeks should at least be 13.63
Among the given options, N = 14 weeks is the most feasible answer.
Hence, it will take 14 weeks for Edurado to make a profit.
Junior's brother is 5 1/2 tall. Junior is 3/5 of his brother's height. How tall is Junior?
Answer: Junior is 3 3/10 feet tall .
Step-by-step explanation:
As given
Junior's brother is 5 1/2 feet tall
i.e
Junior's brother is 11/2 feet tall
Junior is 3/5 of his brother's height
Thus
Junior's heights = 3/5 times his brother's height
Putting all the values in the formula
Junior's Height = 3/5 X 11/2
Junior's height = 33/10
Junior's height = 3 3/10 feet
Therefore Junior is 3 3/10 feet tall .
Junior's height is calculated by taking 3/5 of his brother's height, which is 5.5 feet. Multiplying these, we find out that Junior is 3.3 feet tall.
Explanation:The student is asking to solve a problem involving fractions and proportions to find out how tall Junior is compared to his brother. Junior's brother is 5 1/2 feet tall, which is equivalent to 5.5 feet. Junior is 3/5 of his brother's height. To find out Junior's height, we multiply the brother's height by 3/5:
To find Junior's height, we need to multiply his brother's height by \( \frac{3}{5} \). If Junior's brother is 5 1/2 feet tall, we can first express this height as an improper fraction:
\[ \text{Brother's height} = 5 \frac{1}{2} = \frac{11}{2} \text{ feet} \]
Now, we can find Junior's height by multiplying his brother's height by \( \frac{3}{5} \):
\[ \text{Junior's height} = \frac{3}{5} \times \frac{11}{2} \]
Multiplying the numerators and denominators:
[tex]\[ \text{Junior's height} = \frac{33}{10} \text{ feet} \][/tex]
To express this as a mixed number:
[tex]\[ \text{Junior's height} = 3 \frac{3}{10} \text{ feet} \][/tex]
Therefore, Junior is 3 feet 3 inches tall, or 3.3 feet, which is [tex]\( \frac{3}{10} \)[/tex]than 3 feet.
Height of Junior = 5.5 feet x 3/5
Height of Junior = 3.3 feet
Therefore, Junior is 3.3 feet tall.
Which is the endpoint of a ray r s t u
Answer:
u
Step-by-step explanation:
the endpoint will be the last one to the right
Answer all 3 with steps
Answer:
4. 24.39°
5. 27.29°
6. 38.21°
Step-by-step explanation:
Given:
Δ ABC is right angle at A
Δ PQR is right angle at Q
Δ XYZ is right angle at X
To find:
∠ C = ?
∠ P = ?
∠ Z = ?
Solution:
For 4.)
We Know the Identities,
[tex]\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse} \\[/tex]
∴ [tex]\sin C=\frac{AB}{BC} \\\sin C =\frac{19}{46} \\\sin C =0.413\\\therefore C= sin^{-1}(0.413)\\ \angle C=24.39\°[/tex]
For 5.)
[tex]\tan P = \frac{\textrm{side opposite to angle P}}{\textrm{side adjacent to angle P}}\\\tan P = \frac{QR}{QP}\\\tan P = \frac{16}{31}\\\tan P = 0.5161\\\angle P=\cos^{-1}(0.5161)\\\angle P=27.29\°[/tex]
For 6.)
[tex]\cos Z = \frac{\textrm{side adjacent to angle Z}}{Hypotenuse}\\\cos Z = \frac{XZ}{YZ}\\\cos Z = \frac{11}{14}\\\cos Z = 0.7857\\\angle Z= \cos^{-1}(0.7857)\\\angle Z= 38.21\°[/tex]
Seraphina is driving two hours to visit her family. For the first hour, she traveled at a speed of 62 miles per hour. Then, in the second hour, she traveled at a speed of 69 miles per hour. What is the percentage increase of Seraphina's speed? If necessary, round to the nearest tenth of a percent.
Answer:
11.3%
Step-by-step explanation:
[tex]\%\ increase=\frac{final-initial}{initial} \times 100\%\\\%\ increase=\frac{69-62}{62} \times 100\%\\\%\ increase=\frac{7}{62} \times 100\%\\\%\ increase=11.3\%[/tex]
Answer:
16.1%
Step-by-step explanation:
Matt has answered 20/25 questions on a test. What percentage of the test has he completed?
Answer:
80%
Step-by-step explanation:
=20/25 x 100
= 4/5 x 100
=4 x 20
= 80%
x-y=2
2x+3y=14
use the elimination method to solve the system of equations.
The asymptotes of the function f(x) = 7/(x^2 - 2x - 24) are located at x = 6 and x = -4.
Explanation:The function f(x) is a rational function, which means it's a fraction of two polynomials. The function has vertical asymptotes where the denominator (x^2 - 2x - 24) equals zero.
To find the asymptotes, set the denominator equal to zero and solve for x:
x^2 - 2x - 24 = 0
Factor the equation: (x - 6)(x + 4) = 0
Therefore, x = 6 and x = -4 are the roots of the denominator.
Since the denominator becomes zero at x = 6 and x = -4, these points represent vertical asymptotes where the function approaches positive or negative infinity.
Therefore, the function f(x) has asymptotes at x = 6 and x = -4.
Find A U B. please help much needed!
Answer:
A u B = {3,5,6,7,8,11,12}
Step-by-step explanation:
A = {3,6,7,11}
B = {3,5,7,8,12}
A u B = {3,5,6,7,8,11,12}
hey this is the question i needed help with
Answer:
should be D.
Step-by-step explanation:
hopefully that helps u out!
Answer:
This might be late but D I think
A rectangle has a length of 34 inches less than 5 times it’s width. If the area of the rectangle is 867 square inches, find the length of the rectangle.
Length of the rectangle is 51 inches
Solution:
Given that
Length of the rectangle in 34 miles less than 5 times its width
Area of rectangle = 867 square inches
Need to determine length of the rectangle.
Let assume width of the rectangle be represented by variable x.
So 5 times width of the rectangle =5x
34 inches less than 5 times width of the rectangle = 5x – 34
As Length of the rectangle in 34 miles less than 5 times its width
=> Length of the rectangle = 5x – 34
The formula for rectangle is given as:
[tex]\text { area of rectangle }=length \times width[/tex]
As given that Area of rectangle = 867 square inches
[tex]\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}[/tex]
On solving quadratic equation by using quadratic formula
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
In our case a = 5, b = -34 and c = -867
On substituting value of a, b and c in quadratic formula we get
[tex]\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}[/tex]
Since x represents width, it cannot be negative, so x = 17
Length of the rectangle = 5x – 34 = 5(17) – 34 = 51
Hence length of the rectangle is 51 inches
Leslie has $80 in a savings account. the interest rate is 5% per year and is not compounded.how much will she have in 1 year?n
Answer:
[tex]\$84[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ years\\ P=\$80\\ A=\$?\\r=5\%=5/100=0.05[/tex]
substitute in the formula
[tex]A=80(1+0.05*1)[/tex]
[tex]A=80(1.05)[/tex]
[tex]A=\$84[/tex]
the mean temperature for the first 7 days in January was 3c
the temperature the 8 day was 5c
what is the mean temperaturefot first 8 days in January?
Answer:
Mean = 3.25°C
Step-by-step explanation:
The mean (or average) is given by the formula:
Mean = Sum/Number of Numbers
For first 7 days, the mean was 3, so we can say:
Mean = Sum/Number of Numbers
3 = Sum/7
Sum = 3 * 7 = 21
Then on 8th day, the temperature was 5, so the new sum would be (for 8 numbers):
New Sum = 21 + 5 = 26
Now we calculate the mean for 8 numbers:
Mean = 26/8
Mean = 3.25°C
What is the symmetry in modern echinoderms called? 10 part symmetry
5 part symmetry
lateral symmetry
bilateral symmetry
Answer:
5 part symmetry
Step-by-step explanation:
I did the test
Answer:
5 part symmetry.
Step-by-step explanation:
I took the test and got it right.
The diagram below shows the construction of a line through point T perpendicular to line 1
This construction demonstrates that the set of points equidistant from the endpoints of a line segment
is the perpendicular
of the segment.
Which of the following words is the most appropriate to fill in the blank?
A. Bisector
B. Line
C. Slope
D. Transversal
Answer:
A
Step-by-step explanation:
When we read your example. we can see that we have not diagram, but we have text and we can conclude what is that tell.
This construction demonstrates that the set of points equidistant from the endpoints of a line segment
is the perpendicular
of the segment.- this text tells us that it is bisector
Answer:
a
Step-by-step explanation:
can someone please help me???
simplif (x2+16)(x2_16) =?
Answer:
[tex]x^{4}[/tex] - 256
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
x²(x² - 16) + 16(x² - 16) ← distribute both parenthesis
= [tex]x^{4}[/tex] - 16x² + 16x² - 256 ← collect like terms
= [tex]x^{4}[/tex] - 256
Answer:
Step-by-step explanation:
(x²+16)(x²-16) = (x²)² - 16² = x^4 - 256 use identity a²-b² = (a-b)(a+b)
Live Fund are selling their holding at $5,000 per share.How much would Live Fund receive it they sold half thier holding in Marks Brothers?
Live Fund receive [tex]\bold{\$2500 A}[/tex] it they sold half thier holding in Marks Brothers.
Solution:
Given: Sale price of Live Fund holding = 5000 dollar
To find: Amount that Live Fund will get if they sell half of their holding in Marks Brothers.
Assume the total number of shares held by Live Fund in Marks Brothers as A
Therfore, half the holdings (or half the number of shares) of Live Fund will be [tex]\frac{A}{2}[/tex].
Thus, if each share is valued at [tex]\$5000[/tex], then the total value of the number of shares sold will be as follows,
[tex]\Rightarrow5000\times\frac{A}{2}\text{ dollars }\rightarrow\frac{5000\times A}{2}\text{ dollars }[/tex]
[tex]\Rightarrow2500 A\text{ dollars }[/tex]
Hence, Live Fund will receive [tex]\$2500 A[/tex]
Subtract
X2 + 8x +9
- (x2 + 4x)
Answer:
4x+9
Step-by-step explanation:
x^2+8x+9-(x^2+4x)
x^2-x^2+8x+9-4x
8x-4x+9
4x+9
Please HELPPPPP!!!!
Which equation will help you solve this problem? You have 6 sheets of paper. You draw the same number of stars on each sheet. You draw 42 stars in all. How many stars are on each sheet?
The equation for this would be 6x=42
Here's an explanation.
You have 6 sheets of paper, and you draw some number of stars on each paper. The number of stars are the same. Let's put the stars one each paper as x. Now it's also given that the total number of stars are 42. Since there are x stars on each paper, then 6 times x would be the total number of stars, which is 42. So 6x=42, and x=7