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2 years ago

Question 1: Benjamin is pricing two different

Mathematics

1 answer:

KiRa [710]2 years ago

7 0

Answer: 3 (c)

Step-by-step explanation:

2 * 3 = 6 therefore 15 * 3 = 45$

3 * 2 = 6 therefore 21 * 2 = 42$

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Y = 7x + 3 what is the X and Y intercepts

Neko [114]

To find the x intercept,plug a zero in for y and solve.
To find the y intercept,plug a zero in for x and solve.
y = 7x + 3
g = 7(0)+3
y = 3
(0,3)

y = 7x + 3
0 = 7x + 3
Subtract 3 from both sides.
-3 = 7x
Divide both sides by 7
-3/7 = x
(-3/7, 0)

3 0

3 years ago

Here's the question.

OleMash [197]

Answer:

The value of T₂₀ - T₁₅ is -20.

Step-by-step explanation:

Given :

>> If for an A.P, d = -4

To Find :

>> T₂₀ - T₁₅

Using Formula :

General term of an A.P.

$\star{\small{\underline{\boxed{\sf{\red{ T_n = a + (n - 1)d}}}}}}$

>> Tₙ = nᵗʰ term
>> a = first term
>> n = no. of terms
>> d = common difference

Solution :

Firstly finding the A.P of T₂₀ by substituting the values in the formula :

${\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}$

${\dashrightarrow{\sf{ T_{20} = a + (20 - 1) d}}}$

${\dashrightarrow{\sf{ T_{20} = a + (19)d}}}$

${\dashrightarrow{\sf{ T_{20} = a + 19 \times d}}}$

${\dashrightarrow{\sf{ T_{20} = a + 19d}}}$

${\star \: {\underline{\boxed{\sf{\pink{ T_{20} = a + 19d}}}}}}$

Hence, the value of T₂₀ is a + 19d.

$\rule{190}1$

Secondly, finding the A.P of T₁₅ by substituting the values in the formula :

${\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}$

${\dashrightarrow{\sf{ T_{15}= a + (15 - 1) d}}}$

${\dashrightarrow{\sf{ T_{15}= a + (14) d}}}$

${\dashrightarrow{\sf{ T_{15}= a + 14 \times d}}}$

${\dashrightarrow{\sf{ T_{15}= a + 14d}}}$

${\star{\underline{\boxed{\sf \pink{ T_{15}= a + 14d}}}}}$

Hence, the value of T₁₅ is a + 14d

$\rule{190}1$

Now, finding the difference between T₂₀ - T₁₅ :

${\dashrightarrow{\pmb{\sf{T_{20} - T_{15}}}}}$

${\dashrightarrow{\sf{(a + 19d) - (a + 14d)}}}$

${\dashrightarrow{\sf{a + 19d - a - 14d}}}$

${\dashrightarrow{\sf{a - a + 19d - 14d}}}$

${\dashrightarrow{\sf{0+ 19d - 14d}}}$

${\dashrightarrow{\sf{19d - 14d}}}$

${\dashrightarrow{\sf{5 \times - 4}}}$

${\dashrightarrow{\sf{ - 20}}}$

${\star \: \underline{\boxed{\sf{\pink{T_{20} - T_{15} = - 20}}}}}$

Hence, the value of T₂₀ - T₁₅ is -20.

$\underline{\rule{220pt}{3.5pt}}$

3 0

2 years ago

AB and BC form a right angle at point B. If A = (-3,-1) and B = (4,4), what is the equation of BC

m_a_m_a [10]

Answer:

$y=-1.4x+9.6$

Step-by-step explanation:

If A = (-3,-1) and B = (4,4), the slope of AB is

$\text{Slope}_{AB}=\dfrac{-1-4}{-3-4}=\dfrac{-5}{-7}=\dfrac{5}{7}$

Two perpendicular lines have slopes that have product of -1:

$\text{Slopee}_{AB}\cdot \text{Slope}_{BC}=-1\\ \\\dfrac{5}{7}\cdot \text{Slope}_{BC}=-1\\ \\\text{Slope}_{BC}=-\dfrac{7}{5}=-1.4$

The equation of the line BC with slope -1.4 and passing through the point B(4,4) is

$y-4=-1.4(x-4)\\ \\y-4=-1.4x+5.6\\ \\y=-1.4x+9.6$

7 0

3 years ago

Angela purchased a storage cube with a volume of 10 cubic feet. She wants to put it on a shelf that is 24 inches tall.

bulgar [2K]

Answer:

Step-by-step explanation:

10 cubic feets volume is equivilant o 25.85 inches.

3 0

3 years ago

The ratio of boys to girls at King Middle school is 3:2. What is the ratio of girls to all students?

Dominik [7]

The answer is: " 2 :5 " ; or, write as: " 2/5 " .
________________________________________________________
The ratio of 'girls' to 'all students' is: "2: 5 " ; or, write as: " 2/5 ".
________________________________________________________
Explanation:
________________________________________________________
Given: The ratio of boys to girls is: " 3:2 " .

Problem: Find the ratio of "girls" to "all students:
________________________________________________________
Note: This ratio of "boys to girls", which is " 3 : 2 " ;
________________________________________________________
→ can be expressed as " 3x: 2x" ;

in which the total number of students is: " 3x + 2x " = 5x " .

→ The total number of students is represented as: " 5x " .
________________________________________________________
→ The ratio of "girls to boys" is: "2x : 3x" .

→ {that is; the "inverse" of the ratio of "boys to girls"} ;
→ {that is; the "inverse" of " 3x: 2x" } ; → which is: " 2x : 3x " .
________________________________________________________

The ratio of "girls" to "all students" is: "2x : 5x " ; or " 2x/5x " ;
→ Both "x" values cancel ; {since: " x/x = 1 "} ;
_________________________________________________________
→ and we have the answer: " 2 :5 " ; or, write as: " 2/5 " .
_________________________________________________________
The ratio of 'girls' to 'all students' is: " 2 :5 " ; or, write as: " 2/5 ".
_________________________________________________________

8 0

3 years ago